EOMCC and most of the CI codes are part of CCMAN and CCMAN2. CCMAN is a legacy code which is being phased out. All new developments and performanceenhancing features are implemented in CCMAN2. Some options behave differently in the two modules. Below we make an effort to mark which features are available in legacy code only.
One can describe electronically excited states at a level of theory similar to that associated with coupledcluster theory for the ground state by applying either linear response theory[Koch and Jørgensen(1990)] or equationofmotion methods.[Stanton and Bartlett(1993)] A number of groups have demonstrated that excitation energies based on a coupledcluster singles and doubles ground state are generally very accurate for states that are primarily single electron promotions. The error observed in calculated excitation energies to such states is typically 0.1–0.2 eV, with 0.3 eV as a conservative estimate, including both valence and Rydberg excited states. This, of course, assumes that a basis set large and flexible enough to describe the valence and Rydberg states is employed. The accuracy of excited state coupledcluster methods is much lower for excited states that involve a substantial double excitation character, where errors may be 1 eV or even more. Such errors arise because the description of electron correlation of an excited state with substantial double excitation character requires higher truncation of the excitation operator. The description of these states can be improved by including triple excitations, as in EOM(2,3).
QChem includes coupledcluster methods for excited states based on the coupled cluster singles and doubles (CCSD) method described earlier. CCMAN also includes the optimized orbital coupledcluster doubles (OD) variant. OD excitation energies have been shown to be essentially identical in numerical performance to CCSD excited states.[Krylov et al.(2000)Krylov, Sherrill, and HeadGordon]
These methods, while far more computationally expensive than TDDFT, are nevertheless useful as proven high accuracy methods for the study of excited states of small molecules. Moreover, they are capable of describing both valence and Rydberg excited states, as well as states of a chargetransfer character. Also, when studying a series of related molecules it can be very useful to compare the performance of TDDFT and coupledcluster theory for at least a small example to understand its performance. Along similar lines, the CIS(D) method described earlier as an economical correlation energy correction to CIS excitation energies is in fact an approximation to EOMCCSD. It is useful to assess the performance of CIS(D) for a class of problems by benchmarking against the full coupledcluster treatment. Finally, QChem includes extensions of EOM methods to treat ionized or electron attachment systems, as well as di and triradicals.
EOMEE
EOMIP
EOMEA
EOMSF
QChem features the most complete set of EOMCCSD models,[Krylov(2008)] enabling accurate, robust, and efficient calculations of electronically excited states (EOMEECCSD or EOMEEOD);[Sekino and Bartlett(1984), Koch et al.(1990)Koch, Jensen, Jørgensen, and Helgaker, Stanton and Bartlett(1993), Krylov et al.(2000)Krylov, Sherrill, and HeadGordon, Levchenko and Krylov(2004)]; ground and excited states of diradicals and triradicals (EOMSFCCSD and EOMSFOD);[Krylov(2001), Levchenko and Krylov(2004)] ionization potentials and electron attachment energies, as well as problematic doublet radicals and cation or anion radicals (EOMIP/EACCSD).[Sinha et al.(1989)Sinha, Mukhopadhya, Chaudhuri, and Mukherjee, Stanton and Gauss(1994), Nooijen and Bartlett(1995)] The EOMDIPCCSD and EOM2SFCCSD methods are available as well. Conceptually, EOM is very similar to configuration interaction (CI): target EOM states are found by diagonalizing the similarity transformed Hamiltonian ,
(7.47) 
where and are general excitation operators with respect to the reference determinant . In the EOMCCSD models, and are truncated at single and double excitations, and the amplitudes satisfy the CC equations for the reference state :
(7.48)  
(7.49) 
The computational scaling of EOMCCSD and CISD methods is identical, i.e., , however EOMCCSD is numerically superior to CISD because correlation effects are “folded in” in the transformed Hamiltonian, and because EOMCCSD is rigorously sizeintensive.
By combining different types of excitation operators and references , different groups of target states can be accessed as explained in Fig. 7.1. For example, electronically excited states can be described when the reference corresponds to the ground state wave function, and operators conserve the number of electrons and a total spin.[Stanton and Bartlett(1993)] In the ionized/electron attached EOM models,[Stanton and Gauss(1994), Nooijen and Bartlett(1995)] operators are not electron conserving (i.e., include different number of creation and annihilation operators)—these models can accurately treat ground and excited states of doublet radicals and some other openshell systems. For example, singly ionized EOM methods, i.e., EOMIPCCSD and EOMEACCSD, have proven very useful for doublet radicals whose theoretical treatment is often plagued by symmetry breaking. Finally, the EOMSF method[Krylov(2001), Levchenko and Krylov(2004)] in which the excitation operators include spinflip allows one to access diradicals, triradicals, and bondbreaking.[Krylov(2017)]
QChem features EOMEE/SF/IP/EA/DIP/DSFCCSD methods for both closed and openshell references (RHF/UHF/ROHF), including frozen core/virtual options. For EE, SF, IP, and EA, a more economical flavor of EOMCCSD is available (EOMMP2 family of methods). All EOM models take full advantage of molecular point group symmetry. Analytic gradients are available for RHF and UHF references, for the full orbital space, and with frozen core/virtual orbitals.[Levchenko et al.(2005)Levchenko, Wang, and Krylov] Properties calculations (permanent and transition dipole moments, , , etc.) are also available. The current implementation of the EOMXXCCSD methods enables calculations of mediumsize molecules, e.g., up to 15–20 heavy atoms. Using RI approximation 6.8.5 or Cholesky decomposition 6.8.6 helps to reduce integral transformation time and disk usage enabling calculations on much larger systems. EOMMP2 and EOMMP2t variants are also less computationally demanding. The computational cost of EOMIP calculations can be considerably reduced (with negligible decline in accuracy) by truncating virtual orbital space using FNO scheme (see Section 7.7.8).
Legacy features available in CCMAN. The CCMAN module of QChem includes two implementations of EOMIPCCSD. The proper implementation[Pieniazek et al.(2008)Pieniazek, Bradforth, and Krylov] is used by default is more efficient and robust. The EOM_FAKE_IPEA keyword invokes is a pilot implementation in which EOMIPCCSD calculation is set up by adding a very diffuse orbital to a requested basis set, and by solving EOMEECCSD equations for the target states that include excitations of an electron to this diffuse orbital. The implementation of EOMEACCSD in CCMAN also uses this trick. Fake IP/EA calculations are only recommended for Dyson orbital calculations and debug purposes. (CCMAN2 features proper implementations of EOMIP and EOMEA (including Dyson orbitals)).
A more economical CI variant of EOMIPCCSD, IPCISD is also available in CCMAN. This is an N approximation of IPCCSD, and can be used for geometry optimizations of problematic doublet states.[Golubeva et al.(2009)Golubeva, Pieniazek, and Krylov]
The spinflip method[Krylov(2001), Krylov(2002), Krylov(2006)] addresses the bondbreaking problem associated with a singledeterminant description of the wave function. Both closed and open shell singlet states are described within a single reference as spinflipping, (e.g., excitations from the triplet reference state, for which both dynamical and nondynamical correlation effects are smaller than for the corresponding singlet state. This is because the exchange hole, which arises from the Pauli exclusion between samespin electrons, partially compensates for the poor description of the coulomb hole by the meanfield HartreeFock model. Furthermore, because two electrons cannot form a bond, no bond breaking occurs as the internuclear distance is stretched, and the triplet wave function remains essentially singlereference in character. The spinflip approach has also proved useful in the description of di and triradicals as well as some problematic doublet states.
The spinflip method is available for the CIS, CIS(D), CISD, CISDT, OD, CCSD, and EOM(2,3) levels of theory and the spin complete SFXCIS (see Section 7.2.4). An N noniterative triples corrections are also available. For the OD and CCSD models, the following nonrelaxed properties are also available: dipoles, transition dipoles, eigenvalues of the spinsquared operator (), and densities. Analytic gradients are also for SFCIS and EOMSFCCSD methods. To invoke a spinflip calculation the SF_STATES $rem should be used, along with the associated $rem settings for the chosen level of correlation by using METHOD (recommended) or using older keywords (CORRELATION, and, optionally, EOM_CORR). Note that the high multiplicity triplet or quartet reference states should be used.
Several double SF methods have also been implemented.[Casanova et al.(2009)Casanova, Slipchenko, Krylov, and HeadGordon] To invoke these methods, use DSF_STATES.
Doubleionization potential (DIP) is another nonelectronconserving variant of EOMCCSD.[Wladyslawski and Nooijen(2002), Kuś and Krylov(2011), Kuś and Krylov(2012)] In DIP, target states are reached by detaching two electrons from the reference state:
(7.50) 
and the excitation operator has the following form:
(7.51)  
(7.52)  
(7.53) 
As a reference state in the EOMDIP calculations one usually takes a wellbehaved closedshell state. EOMDIP is a useful tool for describing molecules with electronic degeneracies of the type “ electrons on degenerate orbitals”. The simplest examples of such systems are diradicals with twoelectronsontwoorbitals pattern. Moreover, DIP is a preferred method for fourelectronsonthreeorbitals wave functions.
Accuracy of the EOMDIPCCSD method is similar to accuracy of other EOMCCSD models, i.e., 0.1–0.3 eV. The scaling of EOMDIPCCSD is , analogous to that of other EOMCCSD methods. However, its computational cost is less compared to, e.g., EOMEECCSD, and it increases more slowly with the basis set size. An EOMDIP calculation is invoked by using DIP_STATES, or DIP_SINGLETS and DIP_TRIPLETS.
The corevalence separation (CVS) approximation[Cederbaum et al.(1980)Cederbaum, Domcke, and Schirmer] allows one to extend standard methods for excited and ionized states to the corelevel states. In this approach, the excitations involving core electrons are decoupled from the rest of the configurational space. This allows one to reduce computational costs and decouple the highly excited core states from the continuum. Currently, CVS is implemented within EOMEECCSD for energies and transition properties (oscillator strengths, NTOs, exciton descriptors). CVSEOMEECCSD can be used to model NEXAFS.
In QChem, a slightly different version of CVSEOMEECCSD than the original theory by Coriani and Koch[Coriani and Koch(2015)] is implemented: the reference coupledcluster amplitudes do not include core electrons[Vidal et al.()Vidal, Feng, Epifanovsky, Krylov, and Coriani]. To distinguish this method from the original[Coriani and Koch(2015)], below we refer to the QChem implementation as frozencoregroundstate/corevalenceseparated EOM (FCCVSEOM) approach.[Vidal et al.()Vidal, Feng, Epifanovsky, Krylov, and Coriani]
In the FCCVSEOM approach the groundstate parameters (amplitudes and Lagrangian multipliers) are computed within the frozencore approximation, whereas the coreexcitation energies and strengths are obtained imposing that at least one index in the EOM excitation operators refer to a core occupied orbital.
To ensure the best convergence of EOM equations, the calculation is edgespecific with respect to the highest lying edges (or deepest lying core orbitals): the frozencore and CVS spaces are selected for each edge such that the core orbitals we are addressing in the excited state calculations are explicitly frozen in the ground state calculation and specifically included in the EOM calculation. Examples 7.7.5.1 and 7.7.5.1 below illustrate this point.
To invoke the CVS approximation, use METHOD=CCSD and CVS_EE_STATES instead of EE_STATES to specify the desired target states (likewise, CVS_EE_SINGLETS and CVS_EE_TRIPLETS can be used in exactly the same way as in regular EOM calculations). CVSEOMCCSD is only available with CCMAN2.
Note: Core electrons must be frozen in CVSEOM calculations. The exact definition of the core depends on the edge.
In example 7.7.5.1, the 1 orbital on the oxygen atom is frozen in the CCSD calculation (N_FROZEN_CORE = FC). In the EOM calculation, the CVS approximation is invoked (CVS_EE_SINGLETS), so that the coreexcitation energies are obtained as the lowest excitations. The calculation of the oscillator strengths is activated by selecting CC_TRANS_PROP=1 and the libwfa analysis is invoked by STATE_ANALYSIS = TRUE (see Section 11.2.6).
Example 7.126 FCCVSEOMCCSD calculation of the first six dipole allowed core excitation energies and their intensities at the oxygen edge of water. Wavefunction analysis is also performed.
$molecule 0 1 O 0.0000 0.0000 0.1173 H 0.0000 0.7572 0.4692 H 0.0000 0.7572 0.4692 $end $rem method = eomccsd cvs_ee_singlets = [3,0,2,1] basis = augccpVDZ n_frozen_core = fc CC_TRANS_PROP = true eom_preconv_singles = true state_analysis = true !invoke libwa to compute NTOs and exciton descriptors ! libwa controls below molden_format = true nto_pairs = 3 pop_mulliken = true $end
Example 7.7.5.1 illustrates CVSEOMEECCSD calculations in a twoedge molecule (CO). In the present implementation, the calculation should be done separately for each edge. The first job computes carbonedge states. Since the carbon orbital is the highest in energy (among the core orbitals of the molecule), the input for the Cedge is similar to example 7.7.5.1. Both the oxygen’s and the carbon’s orbitals are frozen in the reference CCSD calculation. In the EOM part, the carbon coreexcited states are automatically selected. In this case, using default frozen core settings (N_FROZEN_CORE = FC) is equivalent to specifying N_FROZEN_CORE = 2. In the second input, the oxygen edge is computed. As the coreorbitals of oxygen lie deeper, the frozen core and CVS selection specifically targets the oxygen edge by using a smaller core. The 1 orbital of the oxygen atom is selected by N_FROZEN_CORE=1. If the molecule has other edges, the deepest lying core orbitals, up to and including those of the edge of interest, should be selected by an appropriate value of N_FROZEN_CORE.
Example 7.127 FCCVSEOMEECCSD calculations of the first two dipole allowed core excitation energies per irreducible representation and their intensities at the carbon and oxygen edges of carbon monoxide.
$comment CO, carbon edge $end $molecule 0 1 O 0.0000 0.0000 0.913973 C 0.0000 0.0000 1.218243 $end $rem input_bohr = true method = eomccsd cvs_ee_singlets = [2,0,2,2] basis = augccpVDZ n_frozen_core = fc eom_preconv_singles = true CC_TRANS_PROP = true $end @@@ $comment CO, oxygen edge $end $molecule read $end $rem method = eomccsd cvs_ee_singlets = [2,0,2,2] basis = augccpVDZ n_frozen_core = 1 eom_preconv_singles = true CC_TRANS_PROP = true $end
While conventional coupledcluster and equationofmotion methods allow one to tackle electronic structure ranging from wellbehaved closed shell molecules to various openshell and electronically excited species,[Krylov(2008)] metastable electronic states, socalled resonances, present a difficult case for theory. By using complex scaling and complex absorbing potential techniques, we extended these powerful methods to describe autoionizing states, such as transient anions, highly excited electronic states, and coreionized species.[Bravaya et al.(2013)Bravaya, Zuev, Epifanovsky, and Krylov, Jagau et al.(2014)Jagau, Zuev, Bravaya, Epifanovsky, and Krylov, Jagau et al.(2017)Jagau, Bravaya, and Krylov] In addition, users can employ stabilization techniques using charged sphere and scaled atomic charges options.[Kuś and Krylov(2012)] These methods are only available within CCMAN2. The complex CC/EOM code is engaged by COMPLEX_CCMAN; the specific parameters should be specified in the $complex_ccman section.
COMPLEX_CCMAN
Requests complexscaled or CAPaugmented CC/EOM calculations.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
TRUE
Engage complex CC/EOM code.
RECOMMENDATION:
Not available in CCMAN. Need to specify CAP strength or complexscaling parameter in $complex_ccman section.
The $complex_ccman section is used to specify the details of the complexscaled/CAP calculations, as illustrated below. If user specifies CS_THETA, complex scaling calculation is performed.
$complex_ccman CS_THETA 10 Complexscaling parameter theta=0.01, r>r exp(i*theta) CS_ALPHA 10 Real part of the scaling parameter alpha=0.01, ! r>alpha r exp(itheta) $end
Alternatively, for CAP calculations, the CAP parameters need to be specified.
$complex_ccman CAP_ETA 1000 CAP strength in 105 a.u. (0.01) CAP_X 2760 CAP onset along X in 10^3 bohr (2.76 bohr) CAP_Y 2760 CAP onset along Y in 10^3 bohr (2.76 bohr) CAP_Z 4880 CAP onset along Z in 10^3 bohr (4.88 bohr) CAP_TYPE 1 Use cuboid cap (CAP_TYPE=0 will use spherical CAP) $end
CS_THETA is specified in radian 10. CS_ALPHA, CAP_X/Y/Z are specified in a.u. 10, i.e., CS_THETA = 10 means =0.01; CAP_ETA is specified in a.u. 10. The CAP is calculated by numerical integration, the default grid is 000099000590. For testing the accuracy of numerical integration, the numerical overlap matrix is calculated and compared to the analytical one. If the performance of the default grid is poor, the grid type can be changed using the keyword XC_GRID (see Section 5.5 for further details). When CAP calculations are performed, CC_EOM_PROP=1 by default; this is necessary for calculating firstorder perturbative correction.
Advanced users may find the following options useful. Several ways of conducing complex calculations are possible, i.e., complex scaling/CAPs can be either engaged at all levels (HF, CCSD, EOM), or not. By default, if COMPLEX_CCMAN is specified, the EOM calculations are conducted using complex code. Other parameters are set up as follows:
$complex_ccman CS_HF=true CS_CCSD=true $end
Alternatively, the user can disable complex HF. These options are experimental and should only be used by advanced users. For CAPEOMCC, only CS_HF = TRUE and CS_CCSD = TRUE is implemented.
Noniterative triples corrections are available for all complex scaled and CAPaugmented CC/EOMCC models and requested in analogy to regular CC/EOMCC (see Section 7.7.21 for details).
Molecular properties and transition moments are requested for complex scaled or CAPaugmented CC/EOMCC calculations in analogy to regular CC/EOMCC (see Section 7.7.16 for details). Natural orbitals and natural transition orbitals can be computed and the exciton wavefunctions can be analyzed, similarly to realvalued EOMCCSD (same keywords are used to invoke the analysis). Analytic gradients are available for complex CC/EOMCC only for cuboid CAPs (CAP_TYPE = 1) introduced at the HF level (CS_HF = TRUE), as described in Ref. Benda:2017. The frozen core approximation is disabled for CAPCC/EOMCC gradient calculations. Geometry optimization can be requested in analogy to regular CC/EOMCC (see Section 7.7.16 for details).
The performance of EOMDIP deteriorates when the reference state is unstable with respect to electrondetachment,[Kuś and Krylov(2011), Kuś and Krylov(2012)] which is usually the case for dianion references employed to describe neutral diradicals by EOMDIP. Similar problems are encountered by all excitedstate methods when dealing with excited states lying above ionization or electrondetachment thresholds.
To remedy this problem, one can employ charge stabilization methods, as described in Refs. Kus:2011, Kus:2012. In this approach (which can also be used with any other electronic structure method implemented in QChem), an additional Coulomb potential is introduced to stabilize unstable wave functions. The following keywords invoke stabilization potentials: SCALE_NUCLEAR_CHARGE and ADD_CHARGED_CAGE. In the former case, the potential is generated by increasing nuclear charges by a specified amount. In the latter, the potential is generated by a cage built out of point charges comprising the molecule. There are two cages available: dodecahedral and spherical. The shape, radius, number of points, and the total charge of the cage are set by the user.
Note: A perturbative correction estimating the effect of the external Coulomb potential on EOM energy will be computed when target state densities are calculated, e.g., when CC_EOM_PROP = TRUE.
Note: Charge stabilization techniques can be used with other methods such as EOMEE, CIS, and TDDFT to improve the description of resonances. It can also be employed to describe metastable ground states.
Large computational savings are possible if the virtual space is truncated using the frozen natural orbital (FNO) approach (see Section 6.11). Extension of the FNO approach to ionized states within EOMCC formalism was recently introduced and benchmarked.[Landau et al.(2010)Landau, Khistyaev, Dolgikh, and Krylov] In addition to groundstate coupledcluster calculations, FNOs can also be used in EOMIPCCSD, EOMIPCCSD(dT/fT) and EOMIPCC(2,3). In IPCC the FNOs are computed for the reference (neutral) state and then are used to describe several target (ionized) states of interest. Different truncation scheme are described in Section 6.11.
Approximate EOMCCSD models with amplitudes obtained at the MP2 level offer reduced computational cost compared to the full EOMCCSD since the computationally demanding CCSD step is eliminated from the calculation. Two methods of this type are implemented in QChem. The first is invoked with the keyword METHOD = EOMMP2. Its formulation and implementation follow the original EOMCCSD(2) approach developed by Stanton and coworkers.[Stanton and Gauss(1995)] The second method can be requested with the METHOD = EOMMP2T keyword and is similar to EOMMP2, but it accounts for the additional terms in that appear because the MP2 amplitudes do not satisfy the CCSD equations. EOMMP2 ansatz is implemented for IP/EA/EE/SF energies, state properties, and interstate properties (EOMEOM, but not REFEOM). EOMMP2t is available for the IP/EE/EA energy calculations only.
These are very lightweight EOM methods in which the EOM problem is solved in the singles block and the effect of doubles is evaluated perturbatively. The is evaluated by using either CCSD or MP2 amplitudes, just as in the regular EOM calculations. The EOMMP2S(D) method, which is similar in level of correlation treatment to SOSCIS(D), is particularly fast. These methods are implemented for IP and EE states. For valence states, the errors for absolute ionization or excitation energies against regular EOMCCSD are about 0.4 eV and appear to be systematically blueshifted; the EOMEOM energy gaps look better. The calculations are set as in regular EOMEE/IP, but using method = EOMCCSDSD(D) or method = EOMMP2SD(D). State properties and EOMEOM transition properties can be computed using these methods (referenceEOM properties are not yet implemented). These methods are designed for treating corelevel states.[Sadybekov and Krylov(2017)]
Note: These methods are still in the experimental stage.
Vertical excitation/ionization/attachment energies can be computed for all EOMCC/MP2 methods using a nonequilibrium CPCM model. To perform a PCMEOM calculation, one has to invoke the PCM (SOLVENT_METHOD to PCM in the $rem block) and specify the solvent parameters, i.e. the dielectric constant and the squared refractive index (DIELECTRIC and DIELECTRIC_INFI in the $solvent block). If nothing is given, the parameters for water will be used by default. For EOM methods, only the simplest model, CPCM, is implemented. More sophisticated flavors of PCM are available for ADC methods (see Section 7.8.7). For a detailed description of PCM theory, see Sections 7.8.7, 12.2.2 and 12.2.3.
Note: Only energies and unrelaxed properties can be computed (no gradient).
Note: Symmetry is turned off for CCPM calculations.
An EOMCC eigenproblem is solved by an iterative diagonalization procedure that avoids full diagonalization and only looks for several eigenstates, as specified by the XX_STATES keywords.
The default procedure is based on the modified Davidson diagonalization algorithm, as explained in Ref. Levchenko:2004. In addition to several keywords that control the convergence of algorithm, memory usage, and fine details of its execution, there are several important keywords that allow user to specify how the target state selection will be performed.
By default, the diagonalization looks for several lowest eigenstates, as specified by XX_STATES. The guess vectors are generated as singly excited determinants selected by using Koopmans’ theorem; the number of guess vectors is equal to the number of target states. If necessary, the user can increase the number of singly excited guess vectors (EOM_NGUESS_SINGLES) and include doubly excited guess vectors (EOM_NGUESS_DOUBLES).
Note: In CCMAN2, if there is not enough singly excited guess vectors, the algorithm adds doubly excited guess vectors. In CCMAN, doubly excited guess vectors are generated only if EOM_NGUESS_DOUBLES is invoked.
The user can request to preconverge singles (solve the equations in singlesonly block of the Hamiltonian. This is done by using EOM_PRECONV_SINGLES.
Note: In CCMAN, the user can preconverge both singles and doubles blocks (EOM_PRECONV_SINGLES and EOM_PRECONV_DOUBLES).
If a state (or several states) of a particular character is desired (e.g., excitation or ionization), the user can specify this by using EOM_USER_GUESS keyword and $eom_user_guess section, as illustrated by an example below. The algorithm will attempt to find an eigenstate that has the maximum overlap with this guess vector. The multiplicity of the state is determined as in the regular calculations, by using the XX_SINGLETS and EE_TRIPLETS keywords. This option is useful for looking for highlying states such as coreionized or coreexcited states. It is only available with CCMAN2.
The examples below illustrate how to use userspecified guess in EOM calculations:
$eom_user_guess 4 Corresponds to 4(OCC)>5(VIRT) transition. 5 $end
or
$eom_user_guess 1 5 Ex. states corresponding to 1(OCC)>5(VIRT) and 1(OCC)>6(VIRT) 1 6 $end
In IP/EA calculations, only one set of orbitals is specified:
$eom_user_guess 4 5 6 $end
If IP_STATES is specified, this will invoke calculation of the EOMIP states corresponding to the ionization from 4th, 5th, and 6th occupied MOs. If EA_STATES is requested, then EOMEA equations will be solved for a root corresponding to electronattachment to the 4th, 5th, and 6th virtual MOs.
For these options to work correctly, user should make sure that XX_STATES requests a sufficient number of states. In case of symmetry, one can request several states in each irrep, but the algorithm will only compute those states which are consistent with the user guess orbitals.
Alternatively, the user can specify an energy shift by EOM_SHIFT. In this case, the solver looks for the XX_STATES eigenstates that are closest to this energy; the guess vectors are generated accordingly, using Koopmans’ theorem. This option is useful when highly excited states (i.e., interior eigenstates) are desired.
It is important to ensure there are sufficient resources available for the necessary integral calculations and transformations. For CCMAN/CCMAN2 algorithms, these resources are controlled using the $rem variables CC_MEMORY, MEM_STATIC and MEM_TOTAL (see Section 6.14).
The exact flavor of correlation treatment within equationofmotion methods is defined by METHOD (see Section 7.1). For EOMCCSD, once should set METHOD to EOMCCSD, for EOMMP2, METHOD = EOMCCSD, etc.. In addition, a specification of the number of target states is required through XX_STATES (XX designates the type of the target states, e.g., EE, SF, IP, EA, DIP, DSF, etc.). Users must be aware of the point group symmetry of the system being studied and also the symmetry of the initial and target states of interest, as well as symmetry of transition. It is possible to turn off the use of symmetry by CC_SYMMETRY. If set to FALSE the molecule will be treated as having symmetry and all states will be of symmetry.
Note: (1) In finitedifference calculations, the symmetry is turned off automatically, and the user must ensure that XX_STATES is adjusted accordingly.
(2) In CCMAN, mixing different EOM models in a single calculation is only allowed in Dyson orbitals calculations. In CCMAN2, different types of target states can be requested in a single calculation.
Below we describe alternative way to specify correlation treatment in EOMCC/CI calculations. These keywords will be eventually phased out. By default, the level of correlation of the EOM part of the wave function (i.e., maximum excitation level in the EOM operators ) is set to match CORRELATION, however, one can mix different correlation levels for the reference and EOM states by using EOM_CORR. To request a CI calculation, set CORRELATION = CI and select type of CI expansion by EOM_CORR. The table below shows default and allowed CORRELATION and EOM_CORR combinations.
CORRELATION 
Default 
Allowed 
Target states 
CCMAN / 
EOM_CORR 
EOM_CORR 
CCMAN2 

CI 
none 
CIS, CIS(D) 
EE, SF 
y/n 
CISD 
EE, SF, IP 
y/n 

SDT, DT 
EE, SF, DSF 
y/n 

CIS(D) 
CIS(D) 
N/A 
EE, SF 
y/n 
CCSD, OD 
CISD 
EE, SF, IP, EA, DIP 
y/y 

SD(fT) 
EE, IP, EA 
n/y 

SD(dT), SD(fT) 
EE, SF, fake IP/EA 
y/n 

SD(dT), SD(fT), SD(sT) 
IP 
y/n 

SDT, DT 
EE, SF, IP, EA, DIP, DSF 
y/n 
Table 7.1 shows the correct combinations of CORRELATION and EOM_CORR for standard EOM and CI models.
Method 
CORRELATION 
EOM_CORR 
Target states selection 
CIS 
CI 
CIS 
EE_STATES 
EE_SNGLETS, EE_TRIPLETS 

SFCIS 
CI 
CIS 
SF_STATES 
CIS(D) 
CI 
CIS(D) 
EE_STATES 
EE_SNGLETS, EE_TRIPLETS 

SFCIS(D) 
CI 
CIS(D) 
SF_STATES 
CISD 
CI 
CISD 
EE_STATES 
EE_SNGLETS, EE_TRIPLETS 

SFCISD 
CI 
CISD 
SF_STATES 
IPCISD 
CI 
CISD 
IP_STATES 
CISDT 
CI 
SDT 
EE_STATES 
EE_SNGLETS, EE_TRIPLETS 

SFCISDT 
CI 
SDT or DT 
SF_STATES 
EOMEECCSD 
CCSD 
EE_STATES 

EE_SNGLETS, EE_TRIPLETS 

EOMSFCCSD 
CCSD 
SF_STATES 

EOMIPCCSD 
CCSD 
IP_STATES 

EOMEACCSD 
CCSD 
EA_STATES 

EOMDIPCCSD 
CCSD 
DIP_STATES 

DIP_SNGLETS, DIP_TRIPLETS 

EOM2SFCCSD 
CCSD 
SDT or DT 
DSF_STATES 
EOMEE(2,3) 
CCSD 
SDT 
EE_STATES 
EE_SNGLETS, EE_TRIPLETS 

EOMSF(2,3) 
CCSD 
SDT 
SF_STATES 
EOMIP(2,3) 
CCSD 
SDT 
IP_STATES 
EOMSFCCSD(dT) 
CCSD 
SD(dT) 
SF_STATES 
EOMSFCCSD(fT) 
CCSD 
SD(fT) 
SF_STATES 
EOMIPCCSD(dT) 
CCSD 
SD(dT) 
IP_STATES 
EOMIPCCSD(fT) 
CCSD 
SD(fT) 
IP_STATES 
EOMIPCCSD(sT) 
CCSD 
SD(sT) 
IP_STATES 
The most relevant EOMCC input options follow.
EE_STATES
Sets the number of excited state roots to find. For closedshell reference, defaults into EE_SINGLETS. For openshell references, specifies all lowlying states.
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any excited states.
OPTIONS:
Find excited states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
EE_SINGLETS
Sets the number of singlet excited state roots to find. Valid only for closedshell references.
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any excited states.
OPTIONS:
Find excited states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
EE_TRIPLETS
Sets the number of triplet excited state roots to find. Valid only for closedshell references.
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any excited states.
OPTIONS:
Find excited states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
SF_STATES
Sets the number of spinflip target states roots to find.
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any excited states.
OPTIONS:
Find SF states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
DSF_STATES
Sets the number of doubly spinflipped target states roots to find.
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any DSF states.
OPTIONS:
Find doubly spinflipped states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
IP_STATES
Sets the number of ionized target states roots to find. By default, electron will be removed (see EOM_IP_BETA).
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any IP states.
OPTIONS:
Find ionized states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
EOM_IP_ALPHA
Sets the number of ionized target states derived by removing electron (M).
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any IP/ states.
OPTIONS:
Find ionized states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
EOM_IP_BETA
Sets the number of ionized target states derived by removing electron (M=, default for EOMIP).
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any IP/ states.
OPTIONS:
Find ionized states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
EA_STATES
Sets the number of attached target states roots to find. By default, electron will be attached (see EOM_EA_ALPHA).
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any EA states.
OPTIONS:
Find EA states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
EOM_EA_ALPHA
Sets the number of attached target states derived by attaching electron (M=, default in EOMEA).
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any EA states.
OPTIONS:
Find EA states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
EOM_EA_BETA
Sets the number of attached target states derived by attaching electron (M=, EASF).
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any EA states.
OPTIONS:
Find EA states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
DIP_STATES
Sets the number of DIP roots to find. For closedshell reference, defaults into DIP_SINGLETS. For openshell references, specifies all lowlying states.
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any DIP states.
OPTIONS:
Find DIP states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
DIP_SINGLETS
Sets the number of singlet DIP roots to find. Valid only for closedshell references.
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any singlet DIP states.
OPTIONS:
Find DIP singlet states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
DIP_TRIPLETS
Sets the number of triplet DIP roots to find. Valid only for closedshell references.
TYPE:
INTEGER/INTEGER ARRAY
DEFAULT:
0
Do not look for any DIP triplet states.
OPTIONS:
Find DIP triplet states in the first irrep, states in the second irrep etc.
RECOMMENDATION:
None
Note: It is a symmetry of a transition rather than that of a target state which is specified in excited state calculations. The symmetry of the target state is a product of the symmetry of the reference state and the transition. For closedshell molecules, the former is fully symmetric and the symmetry of the target state is the same as that of transition, however, for openshell references this is not so.
Note: For the XX_STATES options, QChem will increase the number of roots if it suspects degeneracy, or change it to a smaller value, if it cannot generate enough guess vectors to start the calculations.
EOM_FAKE_IPEA
If TRUE, calculates fake EOMIP or EOMEA energies and properties using the diffuse orbital trick. Default for EOMEA and Dyson orbital calculations in CCMAN.
TYPE:
LOGICAL
DEFAULT:
FALSE (use proper EOMIP code)
OPTIONS:
FALSE, TRUE
RECOMMENDATION:
None. This feature only works for CCMAN.
Note: When EOM_FAKE_IPEA is set to TRUE, it can change the convergence of HartreeFock iterations compared to the same job without EOM_FAKE_IPEA, because a very diffuse basis function is added to a center of symmetry before the HartreeFock iterations start. For the same reason, BASIS2 keyword is incompatible with EOM_FAKE_IPEA. In order to read HartreeFock guess from a previous job, you must specify EOM_FAKE_IPEA (even if you do not request for any correlation or excited states) in that previous job. Currently, the second moments of electron density and Mulliken charges and spin densities are incorrect for the EOMIP/EACCSD target states.
EOM_USER_GUESS
Specifies if userdefined guess will be used in EOM calculations.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
TRUE
Solve for a state that has maximum overlap with a transn specified in $eom_user_guess.
RECOMMENDATION:
The orbitals are ordered by energy, as printed in the beginning of the CCMAN2 output. Not available in CCMAN.
EOM_SHIFT
Specifies energy shift in EOM calculations.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
corresponds to hartree shift (i.e., 11000 = 11 hartree); solve for eigenstates around this value.
RECOMMENDATION:
Not available in CCMAN.
EOM_NGUESS_DOUBLES
Specifies number of excited state guess vectors which are double excitations.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
Include guess vectors that are double excitations
RECOMMENDATION:
This should be set to the expected number of doubly excited states, otherwise they may not be found.
EOM_NGUESS_SINGLES
Specifies number of excited state guess vectors that are single excitations.
TYPE:
INTEGER
DEFAULT:
Equal to the number of excited states requested
OPTIONS:
Include guess vectors that are single excitations
RECOMMENDATION:
Should be greater or equal than the number of excited states requested, unless .
EOM_PRECONV_SINGLES
When not zero, singly excited vectors are converged prior to a full excited states calculation. Sets the maximum number of iterations for preconverging procedure.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
0
do not preconverge
1
preconverge singles
RECOMMENDATION:
Sometimes helps with problematic convergence.
Note: In CCMAN, setting EOM_PRECONV_SINGLES = N would result in N Davidson iterations preconverging singles.
EOM_PRECONV_DOUBLES
When not zero, doubly excited vectors are converged prior to a full excited states calculation. Sets the maximum number of iterations for preconverging procedure
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
0
Do not preconverge
N
Perform N Davidson iterations preconverging doubles.
RECOMMENDATION:
Occasionally necessary to ensure a doubly excited state is found. Also used in DSF calculations instead of EOM_PRECONV_SINGLES
Note: Not available in CCMAN2.
EOM_PRECONV_SD
When not zero, EOM vectors are preconverged prior to a full excited states calculation. Sets the maximum number of iterations for preconverging procedure.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
0
do not preconverge
N
perform N Davidson iterations preconverging singles and doubles.
RECOMMENDATION:
Occasionally necessary to ensure that all lowlying states are found. Also, very useful in EOM(2,3) calculations.
None
Note: Not available in CCMAN2.
EOM_DAVIDSON_CONVERGENCE
Convergence criterion for the RMS residuals of excited state vectors.
TYPE:
INTEGER
DEFAULT:
5
Corresponding to
OPTIONS:
Corresponding to convergence criterion
RECOMMENDATION:
Use the default. Normally this value be the same as EOM_DAVIDSON_THRESHOLD.
EOM_DAVIDSON_THRESHOLD
Specifies threshold for including a new expansion vector in the iterative Davidson diagonalization. Their norm must be above this threshold.
TYPE:
INTEGER
DEFAULT:
00103
Corresponding to 0.00001
OPTIONS:
Integer code is mapped to , i.e., 02505>2.5
RECOMMENDATION:
Use the default unless converge problems are encountered. Should normally be set to the same values as EOM_DAVIDSON_CONVERGENCE, if convergence problems arise try setting to a value slightly larger than EOM_DAVIDSON_CONVERGENCE.
EOM_DAVIDSON_MAXVECTORS
Specifies maximum number of vectors in the subspace for the Davidson diagonalization.
TYPE:
INTEGER
DEFAULT:
60
OPTIONS:
Up to vectors per root before the subspace is reset
RECOMMENDATION:
Larger values increase disk storage but accelerate and stabilize convergence.
EOM_DAVIDSON_MAX_ITER
Maximum number of iteration allowed for Davidson diagonalization procedure.
TYPE:
INTEGER
DEFAULT:
30
OPTIONS:
Userdefined number of iterations
RECOMMENDATION:
Default is usually sufficient
EOM_IPEA_FILTER
If TRUE, filters the EOMIP/EA amplitudes obtained using the diffuse orbital implementation (see EOM_FAKE_IPEA). Helps with convergence.
TYPE:
LOGICAL
DEFAULT:
FALSE (EOMIP or EOMEA amplitudes will not be filtered)
OPTIONS:
FALSE, TRUE
RECOMMENDATION:
None
Note: Not available in CCMAN2.
CC_FNO_THRESH
Initialize the FNO truncation and sets the threshold to be used for both cutoffs (OCCT and POVO).
TYPE:
INTEGER
DEFAULT:
None
OPTIONS:
range
000010000
Corresponding to %
RECOMMENDATION:
None
CC_FNO_USEPOP
Selection of the truncation scheme.
TYPE:
INTEGER
DEFAULT:
1
OCCT
OPTIONS:
0
POVO
RECOMMENDATION:
None
SCALE_NUCLEAR_CHARGE
Scales charge of each nuclei by a certain value. The nuclear repulsion energy is calculated for the unscaled nuclear charges.
TYPE:
INTEGER
DEFAULT:
0
No scaling.
OPTIONS:
A total positive charge of (1+/100)e is added to the molecule.
RECOMMENDATION:
NONE
ADD_CHARGED_CAGE
Add a point charge cage of a given radius and total charge.
TYPE:
INTEGER
DEFAULT:
0
No cage.
OPTIONS:
0
No cage.
1
Dodecahedral cage.
2
Spherical cage.
RECOMMENDATION:
Spherical cage is expected to yield more accurate results, especially for small radii.
CAGE_RADIUS
Defines radius of the charged cage.
TYPE:
INTEGER
DEFAULT:
225
OPTIONS:
radius is /100 Å.
RECOMMENDATION:
None
CAGE_POINTS
Defines number of point charges for the spherical cage.
TYPE:
INTEGER
DEFAULT:
100
OPTIONS:
Number of point charges to use.
RECOMMENDATION:
None
CAGE_CHARGE
Defines the total charge of the cage.
TYPE:
INTEGER
DEFAULT:
400
Add a cage charged +4e.
OPTIONS:
Total charge of the cage is /100 a.u.
RECOMMENDATION:
None
Example 7.128 EOMEEOD and EOMEECCSD calculations of the singlet excited states of formaldehyde
$molecule 0 1 O C 1 R1 H 2 R2 1 A H 2 R2 1 A 3 180. R1 = 1.4 R2 = 1.0 A = 120. $end $rem METHOD eomod BASIS 631+g EE_STATES [2,2,2,2] $end @@@ $molecule read $end $rem METHOD eomccsd BASIS 631+g EE_SINGLETS [2,2,2,2] EE_TRIPLETS [2,2,2,2] $end
Example 7.129 EOMEECCSD calculations of the singlet excited states of PYP using Cholesky decomposition
$molecule 0 1 ...too long to enter... $end $rem METHOD eomccsd BASIS augccpVDZ PURECART 1112 N_FROZEN_CORE fc CC_T_CONV 4 CC_E_CONV 6 CHOLESKY_TOL 2 using CD/1e2 threshold EE_SINGLETS [2,2] $end
Example 7.130 EOMSFCCSD calculations for methylene from highspin B reference
$molecule 0 3 C H 1 rCH H 1 rCH 2 aHCH rCH = 1.1167 aHCH = 102.07 $end $rem METHOD eomccsd BASIS 631G* SCF_GUESS core SF_STATES [2,0,0,2] Two singlet A1 states and singlet and triplet B2 states $end
Example 7.131 EOMSFMP2 calculations for SiH from highspin B reference. Both energies and properties are computed.
$molecule 0 3 Si H 1 1.5145 H 1 1.5145 2 92.68 $end $rem BASIS = ccpVDZ UNRESTRICTED = true SCF_CONVERGENCE = 8 METHOD = eommp2 SF_STATES = [1,1,0,0] CC_EOM_PROP_TE = true ! Compute <S^2> of excited states $end
Example 7.132 EOMIPCCSD calculations for NO using closedshell anion reference
$molecule 1 1 N O 1 r1 O 1 r2 2 A2 O 1 r2 2 A2 3 180.0 r1 = 1.237 r2 = 1.237 A2 = 120.00 $end $rem METHOD eomccsd BASIS 631G* IP_STATES [1,1,2,1] ground and excited states of the radical $end
Example 7.133 EOMIPCCSD calculation using FNO with OCCT=99%.
$molecule 0 1 O H 1 1.0 H 1 1.0 2 100. $end $rem METHOD eomccsd BASIS 6311+G(2df,2pd) IP_STATES [1,0,1,1] CC_FNO_THRESH 9900 99% of the total natural population recovered $end
Example 7.134 EOMIPMP2 calculation of the three low lying ionized states of the phenolate anion
$molecule 0 1 C 0.189057 1.215927 0.000922 H 0.709319 2.157526 0.001587 C 1.194584 1.155381 0.000067 H 1.762373 2.070036 0.000230 C 1.848872 0.069673 0.000936 H 2.923593 0.111621 0.001593 C 1.103041 1.238842 0.001235 H 1.595604 2.196052 0.002078 C 0.283047 1.185547 0.000344 H 0.862269 2.095160 0.000376 C 0.929565 0.042566 0.000765 O 2.287040 0.159171 0.001759 H 2.663814 0.725029 0.001075 $end $rem THRESH 16 CC_MEMORY 30000 BASIS 631+g(d) METHOD eommp2 IP_STATES [3] $end
Example 7.135 EOMEEMP2T calculation of the excitation energies
$molecule 0 1 H 0.0000 0.0000 0.0000 H 0.0000 0.0000 0.7414 $end $rem THRESH 16 BASIS ccpvdz METHOD eommp2t EE_STATES [3,0,0,0,0,0,0,0] $end
Example 7.136 EOMEACCSD calculation of CN using userspecified guess
$molecule +1 1 C N 1 1.1718 $end $rem METHOD = eomccsd BASIS = 6311+g* EA_STATES = [1,1,1,1] CC_EOM_PROP = true EOM_USER_GUESS = true ! attach to HOMO, HOMO+1, and HOMO+3 $end $eom_user_guess 1 2 4 $end
Example 7.137 DSFCIDT calculation of methylene starting with quintet reference
$molecule 0 5 C H 1 CH H 1 CH 2 HCH CH = 1.07 HCH = 111.0 $end $rem METHOD cisdt BASIS 631G DSF_STATES [0,2,2,0] EOM_NGUESS_SINGLES 0 EOM_NGUESS_DOUBLES 2 $end
Example 7.138 EOMEACCSD job for cyano radical. We first do HartreeFock calculation for the cation in the basis set with one extremely diffuse orbital (EOM_FAKE_IPEA) and use these orbitals in the second job. We need make sure that the diffuse orbital is occupied using the OCCUPIED keyword. No SCF iterations are performed as the diffuse electron and the molecular core are uncoupled. The attached states show up as “excited” states in which electron is promoted from the diffuse orbital to the molecular ones.
$molecule +1 1 C N 1 bond bond 1.1718 $end $rem METHOD hf BASIS 6311+G* PURECART 111 SCF_CONVERGENCE 8 EOM_FAKE_IPEA true $end @@@ $molecule 0 2 C N 1 bond bond 1.1718 $end $rem BASIS 6311+G* PURECART 111 SCF_GUESS read MAX_SCF_CYCLES 0 METHOD eomccsd CC_DOV_THRESH 2501 use thresh for CC iters with convergence problems EA_STATES [2,0,0,0] EOM_FAKE_IPEA true $end $occupied 1 2 3 4 5 6 14 1 2 3 4 5 6 $end
Example 7.139 DIPEOMCCSD calculation of methylene with charged cage stabilization.
$molecule 2 1 C 0.000000 0.000000 0.106788 H 0.989216 0.000000 0.320363 H 0.989216 0.000000 0.320363 $end $rem BASIS = 6311g(d,p) SCF_ALGORITHM = diis_gdm SYMMETRY = false METHOD = eomccsd CC_SYMMETRY = false DIP_SINGLETS = [1] ! Compute one EOMDIP singlet state DIP_TRIPLETS = [1] ! Compute one EOMDIP triplet state EOM_DAVIDSON_CONVERGENCE = 5 CC_EOM_PROP = true ! Compute excited state properties ADD_CHARGED_CAGE = 2 ! Install a charged sphere around the molecule CAGE_RADIUS = 225 ! Radius = 2.25 A CAGE_CHARGE = 500 ! Charge = +5 a.u. CAGE_POINTS = 100 ! Place 100 point charges CC_MEMORY = 256 ! Use 256Mb of memory, increase for larger jobs $end
Example 7.140 EOMEECCSD calculation of excited states in NO using scaled nuclear charge stabilization method.
$molecule 1 1 N 1.08735 0.0000 0.0000 O 1.08735 0.0000 0.0000 $end $rem INPUT_BOHR = true BASIS = 631g SYMMETRY = false CC_SYMMETRY = false METHOD = eomccsd EE_SINGLETS = [2] ! Compute two EOMEE singlet excited states EE_TRIPLETS = [2] ! Compute two EOMEE triplet excited states CC_REF_PROP = true ! Compute ground state properties CC_EOM_PROP = true ! Compute excited state properties CC_MEMORY = 256 ! Use 256Mb of memory, increase for larger jobs SCALE_NUCLEAR_CHARGE = 180 ! Adds +1.80e charge to the molecule $end
Example 7.141 EOMEECCSD calculation for phenol with userspecified guess requesting the EE transition from the occupied orbital number 24 (3 A") to the virtual orbital number 2 (23 A’)
$molecule 0 1 C 0.935445 0.023376 0.000000 C 0.262495 1.197399 0.000000 C 1.130915 1.215736 0.000000 C 1.854154 0.026814 0.000000 C 1.168805 1.188579 0.000000 C 0.220600 1.220808 0.000000 O 2.298632 0.108788 0.000000 H 2.681798 0.773704 0.000000 H 0.823779 2.130309 0.000000 H 1.650336 2.170478 0.000000 H 2.939976 0.044987 0.000000 H 1.722580 2.123864 0.000000 H 0.768011 2.158602 0.000000 $end $rem METHOD EOMCCSD BASIS 631+G(d,p) CC_MEMORY 3000 ccman2 memory MEM_STATIC 250 CC_T_CONV 4 Tamplitudes convergence threshold CC_E_CONV 6 Energy convergence threshold EE_STATES [0,1] Calculate 1 A" states EOM_DAVIDSON_CONVERGENCE 5 Convergence threshold for the Davidson procedure EOM_USER_GUESS true Use user guess from $eom_user_guess section $end $eom_user_guess 24 2 $end
Example 7.142 Complexscaled EOMEE calculation for He. All roots of A symmetry are computed (full diagonalization)
$molecule 0 1 He 0 0 0.0 $end $rem COMPLEX_CCMAN 1 engage complex_ccman METHOD EOMCCSD BASIS gen use general basis PURECART 1111 EE_SINGLETS [2000,0,0,0,0,0,0,0] compute all Ag excitations EOM_DAVIDSON_CONV 5 EOM_DAVIDSON_THRESH 5 EOM_NGUESS_SINGLES 2000 Number of guess singles EOM_NGUESS_DOUBLES 2000 Number of guess doubles CC_MEMORY 2000 MEM_TOTAL 3000 $end $complex_ccman CS_HF 1 Use complex HF CS_ALPHA 1000 Set alpha equal 1 CS_THETA 300 Set theta (angle) equals 0.3 (radian) $end $basis He 0 S 4 1.000000 2.34000000E+02 2.58700000E03 3.51600000E+01 1.95330000E02 7.98900000E+00 9.09980000E02 2.21200000E+00 2.72050000E01 S 1 1.000000 6.66900000E01 1.00000000E+00 S 1 1.000000 2.08900000E01 1.00000000E+00 P 1 1.000000 3.04400000E+00 1.00000000E+00 P 1 1.000000 7.58000000E01 1.00000000E+00 D 1 1.000000 1.96500000E+00 1.00000000E+00 S 1 1.000000 5.13800000E02 1.00000000E+00 P 1 1.000000 1.99300000E01 1.00000000E+00 D 1 1.000000 4.59200000E01 1.00000000E+00 S 1 1.000000 2.44564000E02 1.00000000E+00 S 1 1.000000 1.2282000E02 1.00000000E+00 S 1 1.000000 6.1141000E03 1.00000000E+00 P 1 1.0 8.130000e02 1.0 P 1 1.0 4.065000e02 1.0 P 1 1.0 2.032500e02 1.0 D 1 1.0 2.34375e01 1.0 D 1 1.0 1.17187e01 1.0 D 1 1.0 5.85937e02 1.0 **** $end
Example 7.143 CAPaugmented EOMEACCSD calculation for N. augccpVTZ basis augmented by the 3s3p3d diffuse functions placed in the COM. Two EA states are computed for CAP strength =0.002
$molecule 0 1 N 0.0 0.0 0.54875676501 N 0.0 0.0 0.54875676501 Gh 0.0 0.0 0.0 $end $rem COMPLEX_CCMAN 1 engage complex_ccman METHOD EOMCCSD BASIS gen use general basis EA_STATES [0,0,2,0,0,0,0,0] compute electron attachment energies CC_MEMORY 5000 ccman2 memory MEM_TOTAL 2000 CC_EOM_PROP true compute excited state properties $end $complex_ccman CS_HF 1 Use complex HF CAP_ETA 200 Set strength of CAP potential 0.002 CAP_X 2760 Set length of the box along x dimension CAP_Y 2760 Set length of the box along y dimension CAP_Z 4880 Set length of the box along z dimension CAP_TYPE 1 Use cuboid CAP $end $basis N 0 augccpvtz **** Gh 0 S 1 1.000000 2.88000000E02 1.00000000E+00 S 1 1.000000 1.44000000E02 1.00000000E+00 S 1 1.000000 0.72000000E02 1.00000000E+00 P 1 1.000000 2.45000000E02 1.00000000E+00 P 1 1.000000 1.22000000E02 1.00000000E+00 P 1 1.000000 0.61000000E02 1.00000000E+00 D 1 1.000000 0.755000000E01 1.00000000E+00 D 1 1.000000 0.377500000E01 1.00000000E+00 D 1 1.000000 0.188750000E01 1.00000000E+00 **** $end
Example 7.144 CAPEOMEE calculation of water, with wavefunction analysis of state and transition properties
$molecule 0 1 O 0.00000000 0.00000000 0.13594219 H 0.00000000 1.44761450 1.07875060 H 0.00000000 1.44761450 1.07875060 $end $rem METHOD eomccsd BASIS 631G** CC_MEMORY 2000 MEM_TOTAL 2500 SCF_CONVERGENCE 12 CC_CONVERGENCE 11 EOM_DAVIDSON_CONVERGENCE 11 CC_EOM_PROP TRUE CC_FULLRESPONSE FALSE CC_TRANS_PROP TRUE COMPLEX_CCMAN 1 EE_STATES [1,0,2,0] INPUT_BOHR TRUE ! WFA KEYWORDS STATE_ANALYSIS true MOLDEN_FORMAT true NTO_PAIRS 4 POP_MULLIKEN true $end $complex_ccman CS_HF 1 CAP_TYPE 1 CAP_ETA 10000 CAP_X 2000 CAP_Y 2500 CAP_Z 2500 $end
Example 7.145 Formaldehyde, calculating EOMIPCCSDS(D) and EOMIPMP2S(D) energies of 4 valence ionized states
$molecule 0 1 C H 1 1.096135 H 1 1.096135 2 116.191164 O 1 1.207459 2 121.904418 3 180.000000 0 $end $rem METHOD eomccsds(d) BASIS 631G* IP_STATES [1,1,1,1] $end @@@ $molecule read $end $rem METHOD eommp2s(d) BASIS 631G* IP_STATES [1,1,1,1] $end
Example 7.146 Formaldehyde, calculating EOMEECCSD states with CPCM method.
$molecule 0 1 O C,1,R1 H,2,R2,1,A H,2,R2,1,A,3,180. R1 = 1.4 R2 = 1.0 A = 120. $end $rem METHOD eomccsd BASIS ccpvdz EE_STATES [4] SOLVENT_METHOD pcm $end $pcm theory cpcm $end $solvent dielectric 4.34 dielectric_infi 1.829 $end
Example 7.147 NO, calculating EOMIPCCSD states with CPCM method.
$molecule 1 1 N1 O2 N1 RNO O3 N1 RNO O2 AONO RNO = 1.305 AONO = 106.7 $end $rem METHOD eomccsd BASIS ccpvdz IP_STATES [2] SOLVENT_METHOD pcm $end $pcm theory cpcm $end $solvent dielectric 4.34 dielectric_infi 1.829 $end
In cases of problematic openshell references, e.g., strongly spincontaminated doublet, triplet or quartet states, one may choose to use DFT orbitals. This can be achieved by first doing DFT calculation and then reading the orbitals and turning HartreeFock off (by setting SCF_GUESS = READ MAX_SCF_CYCLES = 0 in the CCMAN or CCMAN2 job). In CCMAN, a more convenient way is just to specify EXCHANGE, e.g., if EXCHANGE = B3LYP, B3LYP orbitals will be computed and used.
Note: Using nonHF exchange in CCMAN2 is not possible.
The coupledcluster package in QChem can calculate properties of target EOM states including permanent dipoles, static polarizabilities, and values, nuclear gradients (and geometry optimizations). The target state of interest is selected by CC_STATE_TO_OPT $rem, which specifies the symmetry and the number of the EOM state. In addition to state properties, calculations of various interstate properties are available (transition dipoles, twophoton absorption transition moments (and crosssections), spinorbit couplings).
Analytic gradients are available for the CCSD and all EOMCCSD methods for both closed and openshell references (UHF and RHF only), including frozen core/virtual functionality[Levchenko et al.(2005)Levchenko, Wang, and Krylov] (see also Section 6.13). These calculations should be feasible whenever the corresponding singlepoint energy calculation is feasible.
Note: Gradients for ROHF and nonHF (e.g., B3LYP) orbitals are not yet available.
For the CCSD and EOMCCSD wave functions, QChem currently can calculate permanent and transition dipole moments, oscillator strengths, (as well as XX, YY and ZZ components separately, which is useful for assigning different Rydberg states, e.g., vs. , etc.), and the values. Interface of the CCSD and EOMCCSD codes with the NBO 5.0 package is also available. Furthermore, excited state analyses can be requested for EOMCCSD excited states. For EOMMP2, only state properties (dipole moments, , are available). Similar functionality is available for some EOMOD and CI models (CCMAN only).
Analysis of the real and complexvalued EOMCC wave functions can also be performed; see Sections 7.7.24 and 11.2.6. NTO analysis for EOMIP/EA/SF states is, obviously, only available for the transitions between the EOM states, so CC_STATE_TO_OPT keyword needs to be used, as in calculations of transition properties.
Users must be aware of the point group symmetry of the system being studied and also the symmetry of the excited (target) state of interest. It is possible to turn off the use of symmetry using the CC_SYMMETRY. If set to FALSE the molecule will be treated as having symmetry and all states will be of symmetry.
QChem allows flexible control of interstate properties calculations, by using CC_TRANS_PROP rem or rem section $trans_prop: the user can request the transitions between all computed EOM target states and the reference state (CC_TRANS_PROP=1) or the calculations of all transition properties between all computed EOM target states (CC_TRANS_PROP=2). By default, the reference state is the CCSD reference. To compute transition properties relative to a particular EOM state, use CC_STATE_TO_OPT.
By default, only oneelectron properties are computed. To activate calculations of twoelectron properties, such as NACs, SOCs, 2PA, additional keywords should be activated, as described below.
The $trans_prop rem section allows the user to specify precisely which properties and for which pairs of states to computed. When $trans_prop section is present in the input, it disables CC_TRANS_PROP rem.
$trans_prop state_list ! Start a list of states ee_singlets 1 1 ! state 1: EE singlet with irrep = 1 and istate = 1 ee_triplets 1 2 ! state 2: EE triplet with irrep = 1 and istate = 2 ref ! state 3: Reference state (can be CC or MP2, but the latter NYI ! in transition prop driver) end_list ! End list state_pair_list ! Start to specify pairs of states, 3 1 ! transition from state 3 to state 1 (known bug here: CC state ! needs to be 1st one) 3 2 ! transition from state 3 to state 2 (known bug here: CC state ! needs to be 1st one) end_pairs ! End list of pairs calc nac ! Compute NAC for all transition pairs listed before this keyword state_list ! Start another list of states (user is able to request multiple ! state lists for multiple tasks) ref ! reference state ee_singlets 0 0 ! zero means all requested irreps/istate in $rem end_list calc dipole soc ! Compute transition dipole and SOC calc opdm_norm ! Compute norm of transition OPDM
Notes about $trans_prop rem section:
calc computes properties for the first pair list (or state list) before it.
The pair list is optional: if there is no pair list, all possible combinations within the state list will be considered.
Options after calc include: nac, soc, dyson, 2pa, dipole, default, pcm, opdm_norm, wfa. Currently, only some of them are implemented.
$trans_prop control for CVSEOMCCSD properties is not yet implemented.
Note: $trans_prop section is a new feature and is still under development — use on your own risk. Eventually, this section will replace other controls and will become a default.
Calculation of transition moments and crosssections for twophoton absorption for EOMEECCSD wave functions is available in QChem (CCMAN2 only). Both CCSDEOM and EOMEOM transitions can be computed. The formalism is described in Ref. Nanda:2015. This feature is available both for canonical and RI/CD implementations. Relevant keywords are CC_EOM_2PA (turns on the calculation, controls NTO calculation), CC_STATE_TO_OPT (used for EOMEOM transitions); additional customization can be performed using the $2pa section.
The $2pa section is used to specify the range of frequencypairs satisfying the resonance condition. If $2pa section is absent in the input, the transition moments are computed for 2 degenerate photons with total energy matching the excitation energy of each target EOM state (for CCSDEOM) or each EOMEOM energy difference (for EOMEOM transitions):
$2pa Nondegenerate resonant 2PA N_2PA_POINTS 6 Number of frequency pairs OMEGA_1 500000 10000 Scans 500 cm$^{1}$ to 550 cm$^{1}$ in steps of 10 cm$^{1}$ $end
N_2PA_POINTS is the number of frequency pairs across the spectrum. The first value associated with OMEGA_1 is the frequency in cm at the start of the spectrum and the second value is the step size in cm. The frequency of the second photon at each step is determined within the code as the excitation energy minus OMEGA_1.
To gain insight into computed cross sections for 2PA, one can perform NTO analysis of the response oneparticle density matrices [Nanda and Krylov(2017)]. To activate NTO analysis of the 2PA response oneparticle transition density matrices, set STATE_ANALYSIS=TRUE, MOLDEN_FORMAT=TRUE (to export the orbitals as MOLDEN files), NTO_PAIRS (specifies the number of orbitals to print). The NTO analysis will be performed for the full 2PA response oneparticle transition density matrices as well as the normalized DMs (see Ref. [Nanda and Krylov(2017)] for more details).
Calculations of spinorbit couplings (SOCs) for EOMCC wave functions is available in CCMAN2.[Epifanovsky et al.(2015)Epifanovsky, Klein, Stopkowicz, Gauss, and Krylov] We employ a perturbative approach in which SOCs are computed as matrix elements of the respective part of the BreitPauli Hamiltonian using zeroorder nonrelativistic wave functions. Both the full twoelectron treatment and the meanfield approximation (a partial account of the twoelectron contributions) are available for the EOMEE/SF/IP/EA wave functions, as well as between the CCSD reference and EOMEE/SF. To enable SOC calculation, transition properties between EOM states must be enabled via CC_TRANS_PROP, and SOC requested using CALC_SOC. By default, oneelectron and meanfield twoelectron couplings will be computed. Full twoelectron coupling calculation is activated by setting CC_EOM_PROP_TE.
As with other EOM transition properties, the initial EOM state is set by CC_STATE_TO_OPT, and couplings are computed between that state and all other EOM states. In the absence of CC_STATE_TO_OPT, SOCs are computed between the reference state and all EOMEE or EOMSF states.
Note: In a spinrestricted case, such as EOMEE calculations using closedshell reference state, SOCs between the singlet and triplet EOM manifolds cannot be computed (only SOCs between the reference state and EOM triplets can be calculated). To compute SOCs between EOMEE singlets and EOMEE triplets, run the same job with UNRESTRICTED=TRUE, such that triplets and singlets appear in the same manifold.
Calculations of nonadiabatic (derivative) couplings (NACs) for EOMCC wave functions is available in CCMAN2. We employ Szalay’s approach in which couplings are computed by a modified analytic gradient code, via “summed states”:[Tajti and Szalay(2009)]
(7.54) 
where, , , and are analytic gradients for states , , and a fictitious summed state . Currently, NACs for EE/IP/EA are available.[Faraji et al.(2018)Faraji, Matsika, and Krylov]
Note: Note that the individual components of the NAC vector depend on the molecular orientation.
Calculation of the static dipole polarizability for the CCSD and EOMEE/SF wave function is available in CCMAN2. CCSD polarizabilities are calculated as second derivatives of the CCSD energy.[Nanda and Krylov(2016)] Only the response of the cluster amplitudes is taken into the account; orbital relaxation is not included. Currently, this feature is available for the canonical implementation only. Relevant keywords are CC_POL (turns on the calculation), EOM_POL (turns on the calculation for EOM states, otherwise, only the CCSD polarizability will be computed), and CC_REF_PROP/CC_FULLRESPONSE (both must be set to TRUE).
Note: EOMCCSD polarizabilities are available for EE and SF wave functions only.
CC_STATE_TO_OPT
Specifies which state to optimize (or from which state compute EOMEOM interstate properties).
TYPE:
INTEGER ARRAY
DEFAULT:
None
OPTIONS:
[,]
optimize the th state of the th irrep.
RECOMMENDATION:
None
Note: The state number should be smaller or equal to the number of excited states calculated in the corresponding irrep.
Note: If analytic gradients are not available, the finite difference calculations will be performed and the symmetry will be turned off. In this case, CC_STATE_TO_OPT should be specified assuming C symmetry, i.e., as [1,N] where N is the number of state to optimize (the states are numbered from 1).
CC_EOM_PROP
Whether or not the nonrelaxed (expectation value) oneparticle EOMCCSD target state properties will be calculated. The properties currently include permanent dipole moment, the second moments , , and of electron density, and the total (in atomic units). Incompatible with JOBTYPE=FORCE, OPT, FREQ.
TYPE:
LOGICAL
DEFAULT:
FALSE (no oneparticle properties will be calculated)
OPTIONS:
FALSE, TRUE
RECOMMENDATION:
Additional equations (EOMCCSD equations for the left eigenvectors) need to be solved for properties, approximately doubling the cost of calculation for each irrep. The cost of the oneparticle properties calculation itself is low. The oneparticle density of an EOMCCSD target state can be analyzed with NBO or libwfa packages by specifying the state with CC_STATE_TO_OPT and requesting NBO = TRUE and CC_EOM_PROP = TRUE.
CC_TRANS_PROP
Whether or not the transition dipole moment (in atomic units) and oscillator strength for the EOMCCSD target states will be calculated. By default, the transition dipole moment is calculated between the CCSD reference and the EOMCCSD target states. In order to calculate transition dipole moment between a set of EOMCCSD states and another EOMCCSD state, the CC_STATE_TO_OPT must be specified for this state.
TYPE:
INTEGER
DEFAULT:
0 (no transition properties will be calculated)
OPTIONS:
1 (calculate transition properties between all computed EOM state and the reference state)
2 (calculate transition properties between all pairs of EOM states)
RECOMMENDATION:
NONE
Additional equations (for the left EOMCCSD eigenvectors plus lambda CCSD equations in case if transition properties between the CCSD reference and EOMCCSD target states are requested) need to be solved for transition properties, approximately doubling the computational cost. The cost of the transition properties calculation itself is low.
Note: When $trans_prop section is present in the input, it disables CC_TRANS_PROP rem.
CC_EOM_2PA
Whether or not the transition moments and crosssections for twophoton absorption will be calculated. By default, the transition moments are calculated between the CCSD reference and the EOMCCSD target states. In order to calculate transition moments between a set of EOMCCSD states and another EOMCCSD state, the CC_STATE_TO_OPT must be specified for this state. If 2PA NTO analysis is requested, the CC_EOM_2PA value is redundant as long as CC_EOM_2PA .
TYPE:
INTEGER
DEFAULT:
0 (do not compute 2PA transition moments)
OPTIONS:
1
Compute 2PA using the fastest algorithm (use intermediates for canonical
and intermediates for RI/CD response calculations).
2
Use intermediates for 2PA response equation calculations.
3
Use intermediates for 2PA response equation calculations.
RECOMMENDATION:
Additional response equations (6 for each target state) will be solved, which increases the cost of calculations. The cost of 2PA moments is about 10 times that of energy calculation. Use the default algorithm. Setting CC_EOM_2PA turns on CC_TRANS_PROP.
CALC_SOC
Whether or not the spinorbit couplings between CC/EOM/ADC/CIS/TDDFT electronic states will be calculated. In the CC/EOMCC suite, by default the couplings are calculated between the CCSD reference and the EOMCCSD target states. In order to calculate couplings between EOM states, CC_STATE_TO_OPT must specify the initial EOM state.
TYPE:
LOGICAL
DEFAULT:
FALSE (no spinorbit couplings will be calculated)
OPTIONS:
FALSE, TRUE
RECOMMENDATION:
Oneelectron and meanfield twoelectron SOCs will be computed by default. To enable full twoelectron SOCs, twoparticle EOM properties must be turned on (see CC_EOM_PROP_TE).
CALC_NAC
Whether or not nonadiabatic couplings will be calculated for the EOMCC, CIS, and TDDFT wave functions.
TYPE:
INTEGER
DEFAULT:
0 (do not compute NAC)
OPTIONS:
1
NYI for EOMCC
2
Compute NACs using Szalay’s approach (this what needs to be specified for EOMCC).
RECOMMENDATION:
Additional response equations will be solved and gradients for all EOM states and for summed states will be computed, which increases the cost of calculations. Request only when needed and do not ask for too many EOM states.
CC_POL
Whether or not the static polarizability for the CCSD wave function will be calculated.
TYPE:
LOGICAL
DEFAULT:
FALSE (CCSD static polarizability will not be calculated)
OPTIONS:
FALSE, TRUE
RECOMMENDATION:
Static polarizabilities are expensive since they require solving three additional response equations. Do no request this property unless you need it.
EOM_POL
Whether or not the static polarizability for the EOMCCSD wave function will be calculated.
TYPE:
LOGICAL
DEFAULT:
FALSE (EOM polarizability will not be calculated)
OPTIONS:
FALSE, TRUE
RECOMMENDATION:
Static polarizabilities are expensive since they require solving three additional response equations. Do no request this property unless you need it.
EOM_REF_PROP_TE
Request for calculation of nonrelaxed twoparticle EOMCC properties. The twoparticle properties currently include . The oneparticle properties also will be calculated, since the additional cost of the oneparticle properties calculation is inferior compared to the cost of . The variable CC_EOM_PROP must be also set to TRUE. Alternatively, CC_CALC_SSQ can be used to request calculation.
TYPE:
LOGICAL
DEFAULT:
FALSE
(no twoparticle properties will be calculated)
OPTIONS:
FALSE, TRUE
RECOMMENDATION:
The twoparticle properties are computationally expensive since they require calculation and use of the twoparticle density matrix (the cost is approximately the same as the cost of an analytic gradient calculation). Do not request the twoparticle properties unless you really need them.
CC_FULLRESPONSE
Fully relaxed properties (including orbital relaxation terms) will be computed. The variable CC_EOM_PROP must be also set to TRUE.
TYPE:
LOGICAL
DEFAULT:
FALSE
(no orbital response will be calculated)
OPTIONS:
FALSE, TRUE
RECOMMENDATION:
Not available for nonUHF/RHF references. Only available for EOM/CI methods for which analytic gradients are available.
CC_SYMMETRY
Controls the use of symmetry in coupledcluster calculations
TYPE:
LOGICAL
DEFAULT:
TRUE
OPTIONS:
TRUE
Use the point group symmetry of the molecule
FALSE
Do not use point group symmetry (all states will be of symmetry).
RECOMMENDATION:
It is automatically turned off for any finite difference calculations, e.g. second derivatives.
STATE_ANALYSIS
Activates excited state analyses using libwfa.
TYPE:
LOGICAL
DEFAULT:
FALSE (no excited state analyses)
OPTIONS:
TRUE, FALSE
RECOMMENDATION:
Set to TRUE if excited state analysis is required, but also if plots of densities or orbitals are needed. For details see section 11.2.6.
Example 7.148 Geometry optimization for the excited openshell singlet state, , of methylene followed by the calculations of the fully relaxed oneelectron properties using EOMEECCSD
$molecule 0 1 C H 1 rCH H 1 rCH 2 aHCH rCH = 1.083 aHCH = 145. $end $rem JOBTYPE OPT METHOD EOMCCSD BASIS ccpVTZ SCF_GUESS CORE SCF_CONVERGENCE 9 EE_SINGLETS [0,0,0,1] EOM_NGUESS_SINGLES 2 CC_STATE_TO_OPT [4,1] EOM_DAVIDSON_CONVERGENCE 9 use tighter convergence for EOM amplitudes $end @@@ $molecule read $end $rem METHOD EOMCCSD BASIS ccpVTZ SCF_GUESS READ EE_SINGLETS [0,0,0,1] EOM_NGUESS_SINGLES 2 CC_EOM_PROP 1 calculate properties for EOM states CC_FULLRESPONSE 1 use fully relaxed properties $end
Example 7.149 Property and transition property calculation on the lowest singlet state of CH using EOMSFCCSD
$molecule 0 3 C H 1 rch H 1 rch 2 ahch rch = 1.1167 ahch = 102.07 $end $rem METHOD eomccsd BASIS ccpvtz SCF_GUESS core SCF_CONVERGENCE 9 SF_STATES [2,0,0,3] Get three 1^B2 and two 1^A1 SF states CC_EOM_PROP 1 CC_TRANS_PROP 1 CC_STATE_TO_OPT [4,1] First EOM state in the 4th irrep $end
Example 7.150 Geometry optimization with tight convergence for the A excited state of CHCl, followed by calculation of nonrelaxed and fully relaxed permanent dipole moment and .
$molecule 0 2 H C 1 CH CL 2 CCL 1 CCLH H 2 CH 3 CCLH 1 DIH CH = 1.096247 CCL = 2.158212 CCLH = 122.0 DIH = 180.0 $end $rem JOBTYPE OPT METHOD EOMCCSD BASIS 631G* Basis Set SCF_GUESS SAD EOM_DAVIDSON_CONVERGENCE 9 EOM amplitude convergence CC_T_CONV 9 CCSD amplitudes convergence EE_STATES [0,0,0,1] CC_STATE_TO_OPT [4,1] EOM_NGUESS_SINGLES 2 GEOM_OPT_TOL_GRADIENT 2 GEOM_OPT_TOL_DISPLACEMENT 2 GEOM_OPT_TOL_ENERGY 2 $end @@@ $molecule read $end $rem METHOD EOMCCSD BASIS 631G* Basis Set SCF_GUESS READ EE_STATES [0,0,0,1] EOM_NGUESS_SINGLES 2 CC_EOM_PROP 1 calculate oneelectron properties CC_EOM_PROP_TE 1 and twoelectron properties (S^2) $end @@@ $molecule read $end $rem METHOD EOMCCSD BASIS 631G* Basis Set SCF_GUESS READ EE_STATES [0,0,0,1] EOM_NGUESS_SINGLES 2 CC_EOM_PROP 1 calculate oneelectron properties CC_EOM_PROP_TE 1 and twoelectron properties (S^2)CC_EXSTATES_PROP 1 CC_FULLRESPONSE 1 same as above, but do fully relaxed properties $end
Example 7.151 CCSD calculation on three and one state of formaldehyde. Transition properties will be calculated between the third state and all other EOM states
$molecule 0 1 O C 1 1.4 H 2 1.0 1 120 H 2 1.0 1 120 3 180 $end $rem BASIS 631+G METHOD EOMCCSD EE_STATES [0,3,0,1] CC_STATE_TO_OPT [2,3] CC_TRANS_PROP true $end
Example 7.152 EOMIPCCSD geometry optimization of X state of .
$molecule 0 1 H 0.774767 0.000000 0.458565 O 0.000000 0.000000 0.114641 H 0.774767 0.000000 0.458565 $end $rem JOBTYPE opt METHOD eomccsd BASIS 6311G IP_STATES [0,0,0,1] CC_STATE_TO_OPT [4,1] $end
Example 7.153 CAPEOMEACCSD geometry optimization of the anionic resonance state of formaldehyde. The applied basis is augccpVDZ augmented by 3s3p diffuse functions on heavy atoms.
$molecule 0 1 C 0.0000000000 0.0000000000 0.5721328608 O 0.0000000000 0.0000000000 0.7102635035 H 0.9478180646 0.0000000000 1.1819748108 H 0.9478180646 0.0000000000 1.1819748108 $end $rem JOBTYPE opt METHOD eomccsd BASIS gen SCF_CONVERGENCE 9 CC_CONVERGENCE 9 EOM_DAVIDSON_CONVERGENCE 9 EA_STATES [0,0,0,2] CC_STATE_TO_OPT [4,1] XC_GRID 000250000974 COMPLEX_CCMAN 1 $end $complex_ccman CS_HF 1 CAP_TYPE 1 CAP_ETA 60 CAP_X 3850 CAP_Y 2950 CAP_Z 6100 $end $basis H 0 S 3 1.00 13.0100000 0.196850000E01 1.96200000 0.137977000 0.444600000 0.478148000 S 1 1.00 0.122000000 1.00000000 P 1 1.00 0.727000000 1.00000000 S 1 1.00 0.297400000E01 1.00000000 P 1 1.00 0.141000000 1.00000000 **** C 0 S 8 1.00 6665.00000 0.692000000E03 1000.00000 0.532900000E02 228.000000 0.270770000E01 64.7100000 0.101718000 21.0600000 0.274740000 7.49500000 0.448564000 2.79700000 0.285074000 0.521500000 0.152040000E01 S 8 1.00 6665.00000 0.146000000E03 1000.00000 0.115400000E02 228.000000 0.572500000E02 64.7100000 0.233120000E01 21.0600000 0.639550000E01 7.49500000 0.149981000 2.79700000 0.127262000 0.521500000 0.544529000 S 1 1.00 0.159600000 1.00000000 P 3 1.00 9.43900000 0.381090000E01 2.00200000 0.209480000 0.545600000 0.508557000 P 1 1.00 0.151700000 1.00000000 D 1 1.00 0.550000000 1.00000000 S 1 1.00 0.469000000E01 1.00000000 P 1 1.00 0.404100000E01 1.00000000 D 1 1.00 0.151000000 1.00000000 S 1 1.00 0.234500000E01 1.00000000 S 1 1.00 0.117250000E01 1.00000000 S 1 1.00 0.058625000E01 1.00000000 P 1 1.00 0.202050000E01 1.00000000 P 1 1.00 0.101025000E01 1.00000000 P 1 1.00 0.050512500E01 1.00000000 **** O 0 S 8 1.00 11720.0000 0.710000000E03 1759.00000 0.547000000E02 400.800000 0.278370000E01 113.700000 0.104800000 37.0300000 0.283062000 13.2700000 0.448719000 5.02500000 0.270952000 1.01300000 0.154580000E01 S 8 1.00 11720.0000 0.160000000E03 1759.00000 0.126300000E02 400.800000 0.626700000E02 113.700000 0.257160000E01 37.0300000 0.709240000E01 13.2700000 0.165411000 5.02500000 0.116955000 1.01300000 0.557368000 S 1 1.00 0.302300000 1.00000000 P 3 1.00 17.7000000 0.430180000E01 3.85400000 0.228913000 1.04600000 0.508728000 P 1 1.00 0.275300000 1.00000000 D 1 1.00 1.18500000 1.00000000 S 1 1.00 0.789600000E01 1.00000000 P 1 1.00 0.685600000E01 1.00000000 D 1 1.00 0.332000000 1.00000000 S 1 1.00 0.394800000E01 1.00000000 S 1 1.00 0.197400000E01 1.00000000 S 1 1.00 0.098700000E01 1.00000000 P 1 1.00 0.342800000E01 1.00000000 P 1 1.00 0.171400000E01 1.00000000 P 1 1.00 0.085700000E01 1.00000000 **** $end
Example 7.154 Calculating resonant 2PA with degenerate photons.
$molecule 0 1 O H 1 0.959 H 1 0.959 2 104.654 $end $rem METHOD eomccsd BASIS augccpvtz EE_SINGLETS [1,0,0,0] 1A_1 state CC_TRANS_PROP 1 Compute transition properties CC_EOM_2PA 1 Calculate 2PA crosssections using the fastest algorithm $end
Example 7.155 Nondegenerate, resonant 2PA scan over a range of frequency pairs.
$molecule 0 1 O H 1 0.959 H 1 0.959 2 104.654 $end $rem METHOD eomccsd BASIS augccpvtz EE_SINGLETS [2,0,0,0] Two A_1 states CC_TRANS_PROP 1 Calculate transition properties CC_EOM_2PA 1 Calculate 2PA crosssections using the fastest algorithm $end $2pa n_2pa_points 11 omega_1 500000 5000 $end
Example 7.156 Resonant 2PA with degenerate photons between two excited states.
$molecule 0 1 O H 1 0.959 H 1 0.959 2 104.654 $end $rem METHOD eomccsd BASIS augccpvtz EE_SINGLETS [2,0,0,0] Two A_1 states CC_STATE_TO_OPT [1,1] "Reference" state for transition properties is 1A_1 state CC_TRANS_PROP 1 Compute transition properties CC_EOM_2PA 1 Calculate 2PA crosssections using the fastest algorithm $end
Example 7.157 Computation of spinorbit couplings between closedshell singlet and triplet state in NH using EOMSFCCSD
$molecule 0 3 N H N 1.0450 $end $rem METHOD = eomccsd BASIS = 631g SF_STATES = [1,2,0,0] CC_TRANS_PROP = true CALC_SOC = true CC_STATE_TO_OPT = [1,1] $end
Example 7.158 Computation of nonadiabatic couplings between EOMEE states within triplet (first job) and singlet (second job) manifolds
$molecule +1 1 H 0.00000 0.00000 0.0 He 0.00000 0.00000 3.0 $end $rem JOBTYPE = FORCE BASIS = ccpVDZ METHOD = EOMCCSD INPUT_BOHR = true EE_TRIPLETS = [2] cc_eom_prop = true SYM_IGNORE = true Do not reorient molecule and turn off symmetry CALC_NAC = 2 Invoke Szalay NAC eom_davidson_convergence = 9 tight davidson convergence scf_convergence = 9 HartreeFock convergence threshold 1e9 cc_convergence = 9 $end @@@ $molecule read $end $rem JOBTYPE = FORCE BASIS = ccpVDZ METHOD = EOMCCSD INPUT_BOHR = true EE_STATES = [2] singlets SYM_IGNORE = true Do not reorient molecule and turn off symmetry CALC_NAC = 2 Invoke Szalay NAC eom_davidson_convergence = 9 tight davidson convergence scf_convergence = 9 HartreeFock convergence threshold 1e9 cc_convergence = 9 $end
Example 7.159 Calculation of the static dipole polarizability of the CCSD wave function of Helium.
$molecule 0 1 He $end $rem METHOD ccsd BASIS ccpvdz CC_REF_PROP 1 CC_POL 2 CC_DIIS_SIZE 15 CC_FULLRESPONSE 1 $end
In the EOMCC(2,3) approach,[Hirata et al.(2000)Hirata, Nooijen, and Bartlett] the transformed Hamiltonian is diagonalized in the basis of the reference, singly, doubly, and triply excited determinants, i.e., the excitation operator is truncated at triple excitations. The excitation operator , however, is truncated at double excitation level, and its amplitudes are found from the CCSD equations, just like for EOMCCSD [or EOMCC(2,2)] method.
The accuracy of the EOMCC(2,3) method closely follows that of full EOMCCSDT [which can be also called EOMCC(3,3)], whereas computational cost of the former model is less.
The inclusion of triple excitations is necessary for achieving chemical accuracy (1 kcal/mol) for ground state properties. It is even more so for excited states. In particular, triple excitations are crucial for doubly excited states,[Hirata et al.(2000)Hirata, Nooijen, and Bartlett] excited states of some radicals and SF calculations (diradicals, triradicals, bondbreaking) when a reference openshell state is heavily spincontaminated. Accuracy of EOMCCSD and EOMCC(2,3) is compared in Table 7.7.18.
System 
EOMCCSD 
EOMCC(2,3) 
Singlyexcited electronic states 
0.1–0.2 eV 
0.01 eV 
Doublyexcited electronic states 
1 eV 
0.1–0.2 eV 
Severe spincontamination of the reference 
0.5 eV 
0.1 eV 
Breaking single bond (EOMSF) 
0.1–0.2 eV 
0.01 eV 
Breaking double bond (EOM2SF) 
1 eV 
0.1–0.2 eV 
The applicability of the EOMEE/SFCC(2,3) models to larger systems can be extended by using their activespace variants, in which triple excitations are restricted to semiinternal ones.
Since the computational scaling of EOMCC(2,3) method is , these calculations can be performed only for relatively small systems. Moderate size molecules (10 heavy atoms) can be tackled by either using the active space implementation or tiny basis sets. To achieve high accuracy for these systems, energy additivity schemes can be used. For example, one can extrapolate EOMCCSDT/large basis set values by combining large basis set EOMCCSD calculations with small basis set EOMCCSDT ones.
Running the full EOMCC(2,3) calculations is straightforward, however, the calculations are expensive with the bottlenecks being storage of the data on a hard drive and the CPU time. Calculations with around 80 basis functions are possible for a molecule consisting of four first row atoms (NO dimer). The number of basis functions can be larger for smaller systems.
Note: In EE calculations, one needs to always solve for at least one lowspin root in the first symmetry irrep in order to obtain the correlated EOM energy of the reference. The triples correction to the total reference energy must be used to evaluate EOM(2,3) excitation energies.
Note: EOMCC(2,3) works for EOMEE, EOMSF, and EOMIP/EA. In EOMIP, “triples” correspond to excitations, and the computational scaling of EOMIPCC(2,3) is less.
Active space calculations are less demanding with respect to the size of a hard drive. The main bottlenecks here are the memory usage and the CPU time. Both arise due to the increased number of orbital blocks in the active space calculations. In the current implementation, each block can contain from 0 up to 16 orbitals of the same symmetry irrep, occupancy, and spinsymmetry. For example, for a typical molecule of C symmetry, in a small/moderate basis set (e.g., TMM in 631G*), the number of blocks for each index is:
occupied:
virtuals:
(usually there are more than 16 and virtual orbitals).
In EOMCCSD, the total number of blocks is . In EOMCC(2,3) the number of blocks in the EOM part is . In active space EOMCC(2,3), additional fragmentation of blocks occurs to distinguish between the restricted and active orbitals. For example, if the active space includes occupied and virtual orbitals of all symmetry irreps (this will be a very large active space), the number of occupied and virtual blocks for each index is 16 and 20, respectively, and the total number of blocks increases to . Not all of the blocks contain real information, some blocks are zero because of the spatial or spinsymmetry requirements. For the C symmetry group, the number of nonzero blocks is about 10–12 times less than the total number of blocks, i.e., . This is the number of nonzero blocks in one vector. Davidson diagonalization procedure requires (2*MAX_VECTORS + 2*NROOTS) vectors, where MAX_VECTORS is the maximum number of vectors in the subspace, and NROOTS is the number of the roots to solve for. Taking NROOTS = 2 and MAX_VECTORS = 20, we obtain 44 vectors with the total number of nonzero blocks being .
In CCMAN implementation, each block is a logical unit of information. Along with real data, which are kept on a hard drive at all the times except of their direct usage, each nonzero block contains an auxiliary information about its size, structure, relative position with respect to other blocks, location on a hard drive, and so on. The auxiliary information about blocks is always kept in memory. Currently, the approximate size of this auxiliary information is about 400 bytes per block. It means, that in order to keep information about one vector ( blocks), 1.2 Gb of memory is required! The information about 44 vectors amounts 53 Gb. Moreover, the huge number of blocks significantly slows down the code.
To make the calculations of active space EOMCC(2,3) feasible, we need to reduce the total number of blocks. One way to do this is to reduce the symmetry of the molecule to lower or C symmetry group (of course, this will result in more expensive calculation). For example, lowering the symmetry group from C to C would results in reducing the total number of blocks in active space EOMCC(2,3) calculations in about times, and the number of nonzero blocks in about 30 times (the relative portion of nonzero blocks in C symmetry group is smaller compared to that in C).
Alternatively, one may keep the MAX_VECTORS and NROOTS parameters of Davidson’s diagonalization procedure as small as possible (this mainly concerns the MAX_VECTORS parameter). For example, specifying MAX_VECTORS = 12 instead of 20 would require 30% less memory.
One more trick concerns specifying the active space. In a desperate situation of a severe lack of memory, should the two previous options fail, one can try to modify (increase) the active space in such a way that the fragmentation of active and restricted orbitals would be less. For example, if there is one restricted occupied orbital and one active occupied orbital, adding the restricted to the active space will reduce the number of blocks, by the price of increasing the number of FLOPS. In principle, adding extra orbital to the active space should increase the accuracy of calculations, however, a special care should be taken about the (near) degenerate pairs of orbitals, which should be handled in the same way, i.e., both active or both restricted.
EOMCC(2,3) is invoked by METHOD=EOMCC(2,3). The following options are available:
EOM_PRECONV_SD
Solves the EOMCCSD equations, prints energies, then uses EOMCCSD vectors as initial vectors in EOMCC(2,3). Very convenient for calculations using energy additivity schemes.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
Do SD iterations
RECOMMENDATION:
Turning this option on is recommended
CC_REST_AMPL
Forces the integrals, , and amplitudes to be determined in the full space even though the CC_REST_OCC and CC_REST_VIR keywords are used.
TYPE:
LOGICAL
DEFAULT:
TRUE
OPTIONS:
FALSE
Do apply restrictions
TRUE
Do not apply restrictions
RECOMMENDATION:
None
CC_REST_TRIPLES
Restricts amplitudes to the active space, i.e., one electron should be removed from the active occupied orbital and one electron should be added to the active virtual orbital.
TYPE:
INTEGER
DEFAULT:
1
OPTIONS:
1
Applies the restrictions
RECOMMENDATION:
None
CC_REST_OCC
Sets the number of restricted occupied orbitals including frozen occupied orbitals.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
Restrict occupied orbitals.
RECOMMENDATION:
None
CC_REST_VIR
Sets the number of restricted virtual orbitals including frozen virtual orbitals.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
Restrict virtual orbitals.
RECOMMENDATION:
None
To select the active space, orbitals can be reordered by specifying the new order in the $reorder_mosection. The section consists of two rows of numbers ( and sets), starting from , and ending with , where is the number of the last orbital specified.
Example 7.160 Example $reorder_mo section with orbitals 16 and 17 swapped for both and electrons
$reorder_mo
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 16
$end
Example 7.161 EOMSF(2,3) calculations of methylene.
$molecule 0 3 C H 1 CH H 1 CH 2 HCH CH = 1.07 HCH = 111.0 $end $rem METHOD eomcc(2,3) BASIS 631G SF_STATES [2,0,0,2] N_FROZEN_CORE 1 N_FROZEN_VIRTUAL 1 EOM_PRECONV_SD 20 Get EOMCCSD energies first (max_iter=20). $end
Example 7.162 This is activespace EOMSF(2,3) calculations for methane with an elongated CC bond. HF MOs should be reordered as specified in the $reorder_mosection such that active space for triples consists of sigma and sigma* orbitals.
$molecule 0 3 C H 1 CH H 1 CHX 2 HCH H 1 CH 2 HCH 3 A120 H 1 CH 2 HCH 4 A120 CH = 1.086 HCH = 109.4712206 A120 = 120. CHX = 1.8 $end $rem METHOD eomcc(2,3) BASIS 631G* SF_STATES [1,0] N_FROZEN_CORE 1 EOM_PRECONV_SD 20 does eomccsd first, max_iter=20 CC_REST_TRIPLES 1 triples are restricted to the active space only CC_REST_AMPL 0 ccsd and eom singles and doubles are fullspace CC_REST_OCC 4 specifies active space CC_REST_VIR 17 specifies active space PRINT_ORBITALS 10 (number of virtuals to print) $end $reorder_mo 1 2 5 4 3 1 2 3 4 5 $end
Example 7.163 EOMIPCC(2,3) calculation of three lowest electronic states of water cation.
$molecule 0 1 H 0.774767 0.000000 0.458565 O 0.000000 0.000000 0.114641 H 0.774767 0.000000 0.458565 $end $rem METHOD eomcc(2,3) BASIS 6311G IP_STATES [1,0,1,1] $end
The effect of triple excitations to EOMCCSD energies can be included via perturbation theory in an economical computational scheme. Using EOMCCSD wave functions as zeroorder wave functions, the second order triples correction to the th EOMEE or SF state is:
(7.55) 
where and denote occupied orbitals, and and are virtual orbital indices. is the EOMCCSD excitation energy of the th state. The quantities and are:
(7.56)  
(7.57) 
where, the and are left and right eigenvectors for th state. Two different choices of the denominator, , define the (dT) and (fT) variants of the correction. In (fT), is just HartreeFock orbital energy differences. A more accurate (but not fully orbital invariant) (dT) correction employs the complete three body diagonal of , , as a denominator. For the reference (e.g., a groundstate CCSD wave function), the (fT) and (dT) corrections are identical to the CCSD(2) and CRCCSD(T) corrections of Piecuch and coworkers.[Piecuch and Włoch(2005)]
The EOMSFCCSD(dT) and EOMSFCCSD(fT) methods yield a systematic improvement over EOMSFCCSD bringing the errors below 1 kcal/mol. For theoretical background and detailed benchmarks, see Ref. Manohar:2008.
Similar corrections are available for EOMIPCCSD,[Manohar et al.(2009)Manohar, Stanton, and Krylov] where triples correspond to excitations and EOMEACCSD, where triples correspond to excitations.
Note: Due to the orbital noninvariance problem, using (dT) correction is discouraged.
Note: EOMIPCCSD(fT) correction is now available both in CCMAN and CCMAN2.
Triples corrections are requested by using METHOD or EOM_CORR:
METHOD
Specifies the calculation method.
TYPE:
STRING
DEFAULT:
No default value
OPTIONS:
EOMCCSD(DT)
EOMCCSD(dT), available for EE, SF, and IP
EOMCCSD(FT)
EOMCCSD(fT), available for EE, SF, IP, and EA
EOMCCSD(ST)
EOMCCSD(sT), available for IP
RECOMMENDATION:
None
EOM_CORR
Specifies the correlation level.
TYPE:
STRING
DEFAULT:
None
No correction will be computed
OPTIONS:
SD(DT)
EOMCCSD(dT), available for EE, SF, and IP
SD(FT)
EOMCCSD(fT), available for EE, SF, IP, and EA
SD(ST)
EOMCCSD(sT), available for IP
RECOMMENDATION:
None
Note: In CCMAN2, EOMIPCCSD(fT) can be computed with or without USE_LIBPT=TRUE
Example 7.164 EOMEECCSD(fT) calculation of CH
$molecule 1 1 C H C CH CH = 2.137130 $end $rem INPUT_BOHR true METHOD eomccsd(ft) BASIS general EE_STATES [1,0,1,1] EOM_DAVIDSON_MAX_ITER 60 increase number of Davidson iterations $end $basis H 0 S 3 1.00 19.24060000 0.3282800000E01 2.899200000 0.2312080000 0.6534000000 0.8172380000 S 1 1.00 0.1776000000 1.000000000 S 1 1.00 0.0250000000 1.000000000 P 1 1.00 1.00000000 1.00000000 **** C 0 S 6 1.00 4232.610000 0.2029000000E02 634.8820000 0.1553500000E01 146.0970000 0.7541100000E01 42.49740000 0.2571210000 14.18920000 0.5965550000 1.966600000 0.2425170000 S 1 1.00 5.147700000 1.000000000 S 1 1.00 0.4962000000 1.000000000 S 1 1.00 0.1533000000 1.000000000 S 1 1.00 0.0150000000 1.000000000 P 4 1.00 18.15570000 0.1853400000E01 3.986400000 0.1154420000 1.142900000 0.3862060000 0.3594000000 0.6400890000 P 1 1.00 0.1146000000 1.000000000 P 1 1.00 0.0110000000 1.000000000 D 1 1.00 0.750000000 1.00000000 **** $end
Example 7.165 EOMSFCCSD(dT) calculations of methylene
$molecule 0 3 C H 1 CH H 1 CH 2 HCH CH = 1.07 HCH = 111.0 $end $rem METHOD eomccsd(dt) BASIS 631G SF_STATES [2,0,0,2] N_FROZEN_CORE 1 N_FROZEN_VIRTUAL 1 $end
Example 7.166 EOMIPCCSD(dT) calculations of Mg
$molecule 0 1 Mg 0.000000 0.000000 0.000000 $end $rem JOBTYPE sp METHOD eomccsd(dt) BASIS 631g IP_STATES [1,0,0,0,0,1,1,1] $end
Potential energy surface crossing optimization procedure finds energy minima on crossing seams. On the seam, the potential surfaces are degenerated in the subspace perpendicular to the plane defined by two vectors: the gradient difference
(7.58) 
and the derivative coupling
(7.59) 
At this time QChem is unable to locate crossing minima for states which have nonzero derivative coupling. Fortunately, often this is not the case. Minima on the seams of conical intersections of states of different multiplicity can be found as their derivative coupling is zero. Minima on the seams of intersections of states of different point group symmetry can be located as well.
To run a PES crossing minimization, CCSD and EOMCCSD methods must be employed for the ground and excited state calculations respectively.
Note: MECP optimization is only available for methods with analytic gradients. Finitedifference evaluation of two gradients is not possible.
XOPT_STATE_1, XOPT_STATE_2
Specify two electronic states the intersection of which will be searched.
TYPE:
[INTEGER, INTEGER, INTEGER]
DEFAULT:
No default value (the option must be specified to run this calculation)
OPTIONS:
[spin, irrep, state]
spin = 0
Addresses states with low spin,
see also EE_SINGLETS or IP_STATES,EA_STATES.
spin = 1
Addresses states with high spin,
see also EE_TRIPLETS.
irrep
Specifies the irreducible representation to which
the state belongs, for point group symmetry
irrep = 1 for , irrep = 2 for ,
irrep = 3 for , irrep = 4 for .
state
Specifies the state number within the irreducible
representation, state = 1 means the lowest excited
state, state = 2 is the second excited state, etc..
0, 0, 1
Ground state.
RECOMMENDATION:
Only intersections of states with different spin or symmetry can be calculated at this time.
Note: The spin can only be specified when using closedshell RHF references. In the case of openshell references all states are treated together, see also EE_STATES. E.g., in SF calculations use spin=0 regardless of what is the actual multiplicity of the target state.
XOPT_SEAM_ONLY
Orders an intersection seam search only, no minimization is to perform.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
TRUE
Find a point on the intersection seam and stop.
FALSE
Perform a minimization of the intersection seam.
RECOMMENDATION:
In systems with a large number of degrees of freedom it might be useful to locate the seam first setting this option to TRUE and use that geometry as a starting point for the minimization.
Example 7.167 Minimize the intersection of ÃB and A states of the N ion using EOMCCSD method
$molecule 1 1 N1 N2 N1 rnn N3 N2 rnn N1 annn rnn=1.46 annn=70.0 $end $rem JOBTYPE opt METHOD eomccsd BASIS 631g EE_SINGLETS [0,2,0,2] C2v point group symmetry XOPT_STATE_1 [0,4,1] 1B2 low spin state XOPT_STATE_2 [0,2,2] 2A2 low spin state XOPT_SEAM_ONLY true Find the seam only GEOM_OPT_TOL_GRADIENT 100 $end $opt CONSTRAINT Set constraints on the NN bond lengths stre 1 2 1.46 stre 2 3 1.46 ENDCONSTRAINT $end @@@ $molecule READ $end $rem JOBTYPE opt Optimize the intersection seam METHOD eomccsd BASIS 631g EE_SINGLETS [0,2,0,2] XOPT_STATE_1 [0,4,1] XOPT_STATE_2 [0,2,2] GEOM_OPT_TOL_GRADIENT 30 $end
Example 7.168 Minimize the intersection of ÃA and B states of the NO molecule using EOMIPCCSD method
$molecule 1 1 N1 O2 N1 rno O3 N1 rno O2 aono rno = 1.3040 aono = 106.7 $end $rem JOBTYPE opt Optimize the intersection seam UNRESTRICTED true METHOD eomccsd BASIS 631g IP_STATES [1,0,1,0] C2v point group symmetry EOM_FAKE_IPEA 1 XOPT_STATE_1 [0,1,1] 1A1 low spin state XOPT_STATE_2 [0,3,1] 1B1 low spin state GEOM_OPT_TOL_GRADIENT 30 Tighten gradient tolerance $END
Dyson orbitals can be used to compute total photodetachment/photoionization crosssections, as well as angular distribution of photoelectrons. A Dyson orbital is the overlap between the Nelectron molecular wave function and the N1/N+1 electron wave function of the corresponding cation/anion:
(7.60)  
(7.61) 
For the HartreeFock wave functions and within Koopmans’ approximation, these are just the canonical HF orbitals. For correlated wave functions, Dyson orbitals are linear combinations of the reference molecular orbitals:
(7.62)  
(7.63)  
(7.64) 
The calculation of Dyson orbitals is straightforward within the EOMIP/EACCSD methods, where cation/anion and initial molecule states are defined with respect to the same MO basis. Since the left and right CC vectors are not the same, one can define correspondingly two Dyson orbitals (left and right):
(7.65)  
(7.66) 
The norm of these orbitals is proportional to the oneelectron character of the transition.
Dyson orbitals also offer qualitative insight visualizing the difference between molecular and ionized/attached states. In ionization/photodetachment processes, these orbitals can be also interpreted as the wave function of the leaving electron. For additional details, see Refs. Oana:2007,Oana:2009. Dyson orbitals can be used for computing total and differential photoelectron crosssections using a standalone ezDyson code[Gozem and Krylov(2015)].
The calculation of Dyson orbitals is implemented for the ground (reference) and excited states ionization/electron attachment. To obtain the ground state Dyson orbitals one needs to run an EOMIP/EACCSD calculation, request transition properties calculation by setting CC_TRANS_PROP=TRUE and CC_DO_DYSON = TRUE. The Dyson orbitals decomposition in the MO basis is printed in the output, for all transitions between the reference and all IP/EA states. At the end of the file, also the coefficients of the Dyson orbitals in the AO basis are available.
Two implementations of Dyson orbitals are currently available: (i) the original implementation in CCMAN; and (ii) new implementation in CCMAN2. The CCMAN implementation is using a diffuse orbital trick (i.e., EOM_FAKE_IPEA will be automatically set to TRUE in these calculations). Note: this implementation has a bug affecting the values of norms of Dyson orbitals (the shapes are correct); thus, using this code is strongly discouraged. The CCMAN2 implementation has all types of initial states available: Dyson orbitals from ground CC, excited EOMEE, and spinflip EOMSF states; it is fully compatible with all helper features for EOM calculations, like FNO, RI, Cholesky decomposition. The CCMAN2 implementation can use a userspecified EOM guess (using EOM_USER_GUESS keyword and $eom_user_guess section), which is recommended for highly excited states (such as coreionized states). In addition, CCMAN2 can calculate Dyson orbitals involving metastable states (see Section 7.7.6).
For calculating Dyson orbitals between excited or spinflip states from the reference configuration and IP/EA states, same CC_TRANS_PROP = TRUE and CC_DO_DYSON = TRUE keywords have to be added to the combination of usual EOMIP/EACCSD and EOMEECCSD or EOMSFCCSD calculations (however, note separate keyword CC_DO_DYSON_EE = TRUE for CCMAN). The IP_STATES keyword is used to specify the target ionized states. The attached states are specified by EA_STATES. The EASF states are specified by EOM_EA_BETA. The excited (or spinflipped) states are specified by EE_STATES and SF_STATES. The Dyson orbital decomposition in MO and AO bases is printed for each EE/SFIP/EA pair of states first for reference, then for all excited states in the order: CC  IP/EA1, CC  IP/EA2,, EE/SF1  IP/EA1, EE/SF1  IP/EA2,, EE/SF2  IP/EA1, EE/SF2  IP/EA2,, and so on. CCMAN implementation keeps reference transitions separate, in accordance with separating keywords.
CC_DO_DYSON
CCMAN2: starts all types of Dyson orbitals calculations. Desired type is determined by requesting corresponding EOMXX transitions CCMAN: whether the referencestate Dyson orbitals will be calculated for EOMIP/EACCSD calculations.
TYPE:
LOGICAL
DEFAULT:
FALSE (the option must be specified to run this calculation)
OPTIONS:
TRUE/FALSE
RECOMMENDATION:
none
CC_DO_DYSON_EE
Whether excitedstate or spinflip state Dyson orbitals will be calculated for EOMIP/EACCSD calculations with CCMAN.
TYPE:
LOGICAL
DEFAULT:
FALSE (the option must be specified to run this calculation)
OPTIONS:
TRUE/FALSE
RECOMMENDATION:
none
Dyson orbitals are most easily visualized by setting GUI = 2 and reading the resulting checkpoint file into IQmol. In addition to the canonical orbitals, the Dyson orbitals will appear under the Surfaces item in the Model View. For stepbystep instructions, see ezDyson manual[Gozem and Krylov(2015)]. Alternatively Dyson orbitals can be plotted using IANLTY = 200 and the $plots utility. Only the sizes of the box need to be specified, followed by a line of zeros:
$plots comment 10 2 2 10 2 2 10 2 2 0 0 0 0 $plots
All Dyson orbitals on the Cartesian grid will be written in the resulting plot.mo file (only CCMAN). For RHF(UHF) reference, the columns order in plot.mo is:
In addition, setting the MAKE_CUBE_FILES keyword to TRUE will create cube files for Dyson orbitals which can be viewed with VMD or other programs (see Section 11.5.4 for details). This option is available for CCMAN and CCMAN2. The Dyson orbitals will be written to files mo.1.cube, mo.2.cube, in the order . For metastable states, the real and imaginary parts of the Dyson orbitals are written to separate files in the order
Visualization via the MolDen format is currently not available.
Example 7.169 Plotting grdex and exgrd state Dyson orbitals for ionization of the oxygen molecule. The target states of the cation are A and B. Works for CCMAN only.
$molecule 0 3 O 0.000 0.000 0.000 O 1.222 0.000 0.000 $end $rem BASIS 631G* METHOD eomccsd IP_STATES [1,0,0,0,0,0,1,0] Target EOMIP states CC_TRANS_PROP true request transition OPDMs to be calculated CC_DO_DYSON true calculate Dyson orbitals IANLTY 200 $end $plots plots excited states densities and trans densities 10 2 2 10 2 2 10 2 2 0 0 0 0 $plots
Example 7.170 Plotting exex state Dyson orbitals between the 1st excited state of the HO radical and the the 1st A and A excited states of HO. Works for CCMAN only.
$molecule 1 1 H 0.000 0.000 0.000 O 1.000 0.000 0.000 $end $rem METHOD eomccsd BASIS 631G* IP_STATES [1,0,0,0] states of HO radical EE_STATES [1,1,0,0] excited states of HO CC_TRANS_PROP true calculate transition properties CC_DO_DYSON_EE true calculate Dyson orbitals for ionization from ex. states IANLTY 200 $end $plots plot excited states densities and trans densities 10 2 2 10 2 2 10 2 2 0 0 0 0 $plots
Example 7.171 Dyson orbitals for ionization of CO molecule; A and B ionized states requested.
$molecule 0 1 O C O 1.131 $end $rem CORRELATION CCSD BASIS ccpVDZ PURECART 111 5d, will be required for ezDyson IP_STATES [1,0,1,0] (A1,A2,B1,B2) CCMAN2 true CC_DO_DYSON true CC_TRANS_PROP true necessary for Dyson orbitals job PRINT_GENERAL_BASIS true will be required for ezDyson $end
Example 7.172 Dyson orbitals for ionization of HO; core (A) state requested — ionization from O(1s).
$molecule 0 1 O H1 O 0.955 H2 O 0.955 H1 104.5 $end $rem CORRELATION CCSD BASIS ccpVTZ PURECART 111 5d, will be required for ezDyson IP_STATES [1,0,0,0] (A1,A2,B1,B2) EOM_USER_GUESS 1 on, further defined in $eom_user_guess CCMAN2 true CC_DO_DYSON true CC_TRANS_PROP true necessary for Dyson orbitals job PRINT_GENERAL_BASIS true will be required for ezDyson $end $eom_user_guess 1 $end
Example 7.173 Dyson orbitals for ionization of NO molecule using EOMEA and a closedshell cation reference; A and B states requested.
$molecule +1 1 N 0.00000 0.00000 0.00000 O 0.00000 0.00000 1.02286 $end $rem CORRELATION CCSD BASIS augccpVTZ PURECART 111 5d, will be required for ezDyson EA_STATES [1,0,0,1] (A1,A2,B1,B2) CCMAN2 true CC_DO_DYSON true CC_TRANS_PROP true necessary for Dyson orbitals job PRINT_GENERAL_BASIS true will be required for ezDyson $end
Example 7.174 Dyson orbitals for detachment from the metastable state of N.
$molecule 0 1 N 0.0 0.0 0.55 N 0.0 0.0 0.55 GH 0.0 0.0 0.0 $end $rem METHOD EOMCCSD EA_STATES [0,0,2,0,0,0,0,0] CC_MEMORY 5000 MEM_STATIC 1000 BASIS GEN COMPLEX_CCMAN TRUE CC_TRANS_PROP TRUE CC_DO_DYSON TRUE MAKE_CUBE_FILES TRUE IANLTY 200 $end $complex_ccman CS_HF 1 CAP_TYPE 1 CAP_X 2760 CAP_Y 2760 CAP_Z 4880 CAP_ETA 400 $end $plots plot Dyson orbitals 50 10.0 10.0 50 10.0 10.0 50 10.0 10.0 0 0 0 0 $end $basis N 0 S 8 1.000000 1.14200000E+04 5.23000000E04 1.71200000E+03 4.04500000E03 3.89300000E+02 2.07750000E02 1.10000000E+02 8.07270000E02 3.55700000E+01 2.33074000E01 1.25400000E+01 4.33501000E01 4.64400000E+00 3.47472000E01 5.11800000E01 8.50800000E03 S 8 1.000000 1.14200000E+04 1.15000000E04 1.71200000E+03 8.95000000E04 3.89300000E+02 4.62400000E03 1.10000000E+02 1.85280000E02 3.55700000E+01 5.73390000E02 1.25400000E+01 1.32076000E01 4.64400000E+00 1.72510000E01 5.11800000E01 5.99944000E01 S 1 1.000000 1.29300000E+00 1.00000000E+00 S 1 1.000000 1.78700000E01 1.00000000E+00 P 3 1.000000 2.66300000E+01 1.46700000E02 5.94800000E+00 9.17640000E02 1.74200000E+00 2.98683000E01 P 1 1.000000 5.55000000E01 1.00000000E+00 P 1 1.000000 1.72500000E01 1.00000000E+00 D 1 1.000000 1.65400000E+00 1.00000000E+00 D 1 1.000000 4.69000000E01 1.00000000E+00 F 1 1.000000 1.09300000E+00 1.00000000E+00 S 1 1.000000 5.76000000E02 1.00000000E+00 P 1 1.000000 4.91000000E02 1.00000000E+00 D 1 1.000000 1.51000000E01 1.00000000E+00 F 1 1.000000 3.64000000E01 1.00000000E+00 **** GH 0 S 1 1.000000 2.88000000E02 1.00000000E+00 S 1 1.000000 1.44000000E02 1.00000000E+00 S 1 1.000000 0.72000000E02 1.00000000E+00 S 1 1.000000 0.36000000E02 1.00000000E+00 S 1 1.000000 0.18000000E02 1.00000000E+00 S 1 1.000000 0.09000000E02 1.00000000E+00 P 1 1.000000 2.45000000E02 1.00000000E+00 P 1 1.000000 1.22000000E02 1.00000000E+00 P 1 1.000000 0.61000000E02 1.00000000E+00 P 1 1.000000 0.305000000E02 1.00000000E+00 P 1 1.000000 0.152500000E02 1.00000000E+00 P 1 1.000000 0.076250000E02 1.00000000E+00 D 1 1.000000 0.755000000E01 1.00000000E+00 D 1 1.000000 0.377500000E01 1.00000000E+00 D 1 1.000000 0.188750000E01 1.00000000E+00 D 1 1.000000 0.094375000E01 1.00000000E+00 D 1 1.000000 0.047187500E01 1.00000000E+00 D 1 1.000000 0.023593750E01 1.00000000E+00 **** $end
Example 7.175 Dyson orbitals for ionization of triplet O and O at slightly stretched (relative to the equilibrium O geometry); B states are requested.
$comment EOMIPCCSD/6311+G* and EOMEACCSD/6311+G* levels of theory, UHF reference. Start from O2: 1) detach electron  ionization of neutral (alpha IP). 2) attach electron, use EOMEA w.f. as initial state  ionization of anion (beta EA). $end $molecule 0 3 O 0.00000 0.00000 0.00000 O 0.00000 0.00000 1.30000 $end $rem CORRELATION CCSD BASIS 6311(3+)G* PURECART 2222 6d, will be required for ezDyson EOM_IP_ALPHA [0,0,0,1,0,0,0,0] (Ag,B1g,B2g,B3g,Au,B1u,B2u,B3u) EOM_EA_BETA [0,0,0,1,0,0,0,0] (Ag,B1g,B2g,B3g,Au,B1u,B2u,B3u) CCMAN2 true CC_DO_DYSON true CC_TRANS_PROP true necessary for Dyson orbitals job PRINT_GENERAL_BASIS true will be required for ezDyson $end
Example 7.176 Dyson orbitals for ionization of formaldehyde from the first excited state AND from the ground state
$molecule 0 1 O 1.535338855 0.000000000 0.438858006 C 1.535331598 0.000007025 0.767790994 H 1.535342484 0.937663512 1.362651452 H 1.535342484 0.937656488 1.362672535 $end $rem CORRELATION CCSD BASIS 631G* PURECART 2222 6d, will be required for ezDyson CCMAN2 true new Dyson code EE_STATES [1] EOM_IP_ALPHA [1] EOM_IP_BETA [1] CC_TRANS_PROP true necessary for Dyson orbitals job CC_DO_DYSON true PRINT_GENERAL_BASIS true will be required for ezDyson $end
Example 7.177 Dyson orbitals for core ionization of Li atom use Li as a reference, get neutral atom via EOMEA get 1st excitation for the cation via EOMEE totally: core ionization AND 1st ionization of Li atom
$molecule +1 1 Li 0.00000 0.00000 0.00000 $end $rem CORRELATION CCSD BASIS 6311+G* PURECART 2222 6d, will be required for ezDyson CCMAN2 true new Dyson code EE_STATES [1,0,0,0,0,0,0,0] EA_STATES [1,0,0,0,0,0,0,0] EOM_NGUESS_SINGLES 5 to converge to the lowest EA state CC_TRANS_PROP true necessary for Dyson orbitals job CC_DO_DYSON true PRINT_GENERAL_BASIS true will be required for ezDyson $end
Example 7.178 Dyson orbitals for ionization of CH2 from highspin triplet reference and from the lowest SF state
$molecule 0 3 C H 1 rCH H 1 rCH 2 aHCH rCH = 1.1167 aHCH = 102.07 $end $rem CORRELATION CCSD BASIS 631G* SCF_GUESS core CCMAN2 true new Dyson code CC_SYMMETRY false SF_STATES [1] EOM_IP_ALPHA [2] one should be careful to request EOM_EA_BETA [2] meaningful spin for EA/IP state(s) CC_TRANS_PROP true necessary for Dyson orbitals job CC_DO_DYSON true GUI 2 $end
Analysis of the leading wave function amplitudes is always necessary for determining the character of the state (e.g., excitation, openshell diradical, etc.). The CCMAN module print out leading EOM/CI amplitudes using its internal orbital numbering scheme, which is printed in the beginning. The typical CCMAN EOMCCSD output looks like:
Root 1 Convd yes Tot Ene= 113.722767530 hartree (Ex Ene 7.9548 eV), U1^2=0.858795, U2^2=0.141205 Res=4.4E07 Right U1: Value i > a 0.5358 7( B2 ) B > 17( B2 ) B 0.5358 7( B2 ) A > 17( B2 ) A 0.2278 7( B2 ) B > 18( B2 ) B 0.2278 7( B2 ) A > 18( B2 ) A
This means that this state is derived by excitation from occupied orbital #7 (which has symmetry) to virtual orbital #17 (which is also of symmetry). The two leading amplitudes correspond to and excitation (the spin part is denoted by or ). The orbital numbering for this job is defined by the following map:
The orbitals are ordered and numbered as follows: Alpha orbitals: Number Energy Type Symmetry ANLMAN number Total number: 0 20.613 AOCC A1 1A1 1 1 11.367 AOCC A1 2A1 2 2 1.324 AOCC A1 3A1 3 3 0.944 AOCC A1 4A1 4 4 0.600 AOCC A1 5A1 5 5 0.720 AOCC B1 1B1 6 6 0.473 AOCC B1 2B1 7 7 0.473 AOCC B2 1B2 8 0 0.071 AVIRT A1 6A1 9 1 0.100 AVIRT A1 7A1 10 2 0.290 AVIRT A1 8A1 11 3 0.327 AVIRT A1 9A1 12 4 0.367 AVIRT A1 10A1 13 5 0.454 AVIRT A1 11A1 14 6 0.808 AVIRT A1 12A1 15 7 1.196 AVIRT A1 13A1 16 8 1.295 AVIRT A1 14A1 17 9 1.562 AVIRT A1 15A1 18 10 2.003 AVIRT A1 16A1 19 11 0.100 AVIRT B1 3B1 20 12 0.319 AVIRT B1 4B1 21 13 0.395 AVIRT B1 5B1 22 14 0.881 AVIRT B1 6B1 23 15 1.291 AVIRT B1 7B1 24 16 1.550 AVIRT B1 8B1 25 17 0.040 AVIRT B2 2B2 26 18 0.137 AVIRT B2 3B2 27 19 0.330 AVIRT B2 4B2 28 20 0.853 AVIRT B2 5B2 29 21 1.491 AVIRT B2 6B2 30
The first column is CCMAN’s internal numbering (e.g., 7 and 17 from the example above). This is followed by the orbital energy, orbital type (frozen, restricted, active, occupied, virtual), and orbital symmetry. Note that the orbitals are blocked by symmetries and then ordered by energy within each symmetry block, (i.e., first all occupied , then all , etc.), and numbered starting from 0. The occupied and virtual orbitals are numbered separately, and frozen orbitals are excluded from CCMAN numbering. The two last columns give numbering in terms of the final ANLMAN printout (starting from 1), e.g., our occupied orbital #7 will be numbered as 1 in the final printout. The last column gives the absolute orbital number (all occupied and all virtuals together, starting from 1), which is often used by external visualization routines.
CCMAN2 numbers orbitals by their energy within each irrep keeping the same numbering for occupied and virtual orbitals. This numbering is exactly the same as in the final printout of the SCF wave function analysis. Orbital energies are printed next to the respective amplitudes. For example, a typical CCMAN2 EOMCCSD output will look like that:
EOMEECCSD transition 2/A1 Total energy = 75.87450159 a.u. Excitation energy = 11.2971 eV. R1^2 = 0.9396 R2^2 = 0.0604 Res^2 = 9.51e08 Amplitude Orbitals with energies 0.6486 1 (B2) A > 2 (B2) A 0.5101 0.1729 0.6486 1 (B2) B > 2 (B2) B 0.5101 0.1729 0.1268 3 (A1) A > 4 (A1) A 0.5863 0.0404 0.1268 3 (A1) B > 4 (A1) B 0.5863 0.0404
which means that for this state, the leading EOM amplitude corresponds to the transition from the first b orbital (orbital energy ) to the second b orbital (orbital energy 0.1729).
The most complete analysis of EOMCC calculations is afforded by deploying a general wavefunction analysis tool contained in the libwa module and described in Section 11.2.6. The EOMCC state analysis is activated by setting STATE_ANALYSIS=TRUE. In addition, keywords controlling calculations of state and interstate properties should be set up accordingly.
Note: Wave function analysis is only available for CCMAN2.
Example 7.179 Wave function analysis of the EOMIP states (He).
$molecule 0 1 He He 1 R1 He 2 R1 1 A R1 = 1.236447 A = 180.00 $end $rem METHOD = EOMCCSD BASIS = 631G IP_STATES = [1,0,0,0,0,1,0,0] CC_EOM_PROP = true Analyze state properties (state OPDM) CC_STATE_TO_OPT = [1,1] Compute transition properties wrt 1st EOM state of 1st irrep CC_TRANS_PROP = true Analyze transitions (transition OPDM) STATE_ANALYSIS = true MOLDEN_FORMAT = true NTO_PAIRS = 2 $end