Q-Chem 5.0 User’s Manual

# 6.8 Correlated Excited State Methods: The ADC() Family

## 6.8.1 The Algebraic Diagrammatic Construction (ADC) Scheme

The Algebraic Diagrammatic Construction (ADC) scheme of the polarization propagator is an excited state method originating from Green’s function theory. It has first been derived employing the diagrammatic perturbation expansion of the polarization propagator using the Møller-Plesset partition of the Hamiltonian [485]. An alternative derivation is available in terms of the intermediate state representation (ISR) [486] which will be presented in the following.

As starting point for the derivation of ADC equations via ISR serves the exact N electron ground state . From a complete set of correlated excited states is obtained by applying physical excitation operators .

 (6.64)

with

 (6.65)

Yet, the resulting excited states do not form an orthonormal basis. To construct an orthonormal basis out of the the Gram-Schmidt orthogonalization scheme is employed successively on the excited states in the various excitation classes starting from the exact ground state, the singly excited states, the doubly excited states etc.. This procedure eventually yields the basis of intermediate states in which the Hamiltonian of the system can be represented forming the Hermitian ADC matrix

 (6.66)

Here, the Hamiltonian of the system is shifted by the exact ground state energy . The solution of the secular ISR equation

 (6.67)

yields the exact excitation energies as eigenvalues. From the eigenvectors the exact excited states in terms of the intermediate states can be constructed as

 (6.68)

This also allows for the calculation of dipole transition moments via

 (6.69)

as well as excited state properties via

 (6.70)

where is the property associated with operator .

Up to now, the exact -electron ground state has been employed in the derivation of the ADC scheme, thereby resulting in exact excitation energies and exact excited state wave functions. Since the exact ground state is usually not known, a suitable approximation must be used in the derivation of the ISR equations. An obvious choice is the th order Møller-Plesset ground state yielding the th order approximation of the ADC scheme. The appropriate ADC equations have been derived in detail up to third order in Refs. Trofimov:1995,Trofimov:1999,Trofimov:2002. Due to the dependency on the Møller-Plesset ground state the th order ADC scheme should only be applied to molecular systems whose ground state is well described by the respective MP() method.

## 6.8.2 Resolution of the Identity ADC Methods

Similar to MP2 and CIS(D), the ADC equations can be reformulated using the resolution-of-the-identity (RI) approximation. This significantly reduces the cost of the integral transformation and the storage requirements. Although it does not change the overall computational scaling of for ADC(2)-s or for ADC(2)-x with the system size, employing the RI approximation will result in computational speed-up of calculations of larger systems.

The RI approximation can be used with all available ADC methods. It is invoked as soon as an auxiliary basis set is specified using AUX_BASIS.

## 6.8.3 Spin Opposite Scaling ADC(2) Models

The spin-opposite scaling (SOS) approach originates from MP2 where it was realized that the same spin contributions can be completely neglected, if the opposite spin components are scaled appropriately. In a similar way it is possible to simplify the second order ADC equations by neglecting the same spin contributions in the ADC matrix, while the opposite-spin contributions are scaled with appropriate semi-empirical parameters. [490, 491, 481]

Starting from the SOS-MP2 ground state the same scaling parameter is introduced into the ADC equations to scale the amplitudes. This alone, however, does not result in any computational savings or substantial improvements of the ADC(2) results. In addition, the opposite spin components in the ph/2p2h and 2p2h/ph coupling blocks have to be scaled using a second parameter to obtain a useful SOS-ADC(2)-s model. With this model the optimal value of the parameter has been found to be 1.17 for the calculation of singlet excited states.[491]

To extend the SOS approximation to the ADC(2)-x method yet another scaling parameter for the opposite spin components of the off-diagonal elements in the 2p2h/2p2h block has to be introduced. Here, the optimal values of the scaling parameters have been determined as and keeping unchanged.[481]

The spin-opposite scaling models can be invoked by setting METHOD to either SOSADC(2) or SOSADC(2)-x. By default, the scaling parameters are chosen as the optimal values reported above, i.e. and for ADC(2)-s and , , and for ADC(2)-x. However, it is possible to adjust any of the three parameters by setting ADC_C_T, ADC_C_C, or ADC_C_X, respectively.

Core-excited electronic states are located in the high energy X-ray region of the spectrum. Thus, to compute core-excited states using standard diagonalization procedures, which usually solve for the energetically lowest-lying excited states first, requires the calculation of a multitude of excited states. This is computationally very expensive and only feasible for calculations on very small molecules and small basis sets.

The core-valence separation (CVS) approximation solves the problem by neglecting the couplings between core and valence excited states a priori[492, 493] Thereby, the ADC matrix acquires a certain block structure which allows to solve only for core-excited states. The application of the CVS approximation is justified, since core and valence excited states are energetically well separated and the coupling between both types of states is very small. To achieve the separation of core and valence excited states the CVS approximation forces the following types of two-electron integrals to zero

 (6.71)

where capital letters refer to core orbitals while lower-case letters denote non-core occupied or virtual orbitals.

## 6.8.6 Properties and Visualization

### 6.8.7.2 Modeling Emission, Excited-State Absorption and Photochemical Reactivity

(A) Theory
To model emission/absorption of solvent-equilibrated excited states and/or to investigate their photochemical reactivity, both components of the polarization have to be relaxed with respect to the desired state. This becomes evident considering that a full solvent-field equilibration (i.e., including the nuclear component) is essentially a geometry optimization for the implicit solvent, and should thus be employed whenever the geometry of the solute is optimized for the desired excited state. The Hamiltonian for a solvent-equilibrated state simply reads

 (6.81)

Since the interaction with solvent-field is contained in the MOs, the solvent-field of the desired excited state has to be employed already in SCF step of the calculation. This means that a guess (e.g. from a previous calculation) of the solvent-field has to be used for the first SCF calculation. The resulting MOs are subjected to an ADC calculation, yielding a excited-state density, for which a new solvent field is computed and employed in the SCF of the next iteration. This is repeated until the solvent field (charges) and energies are converged, yielding the total energy and wave function of the solvent-equilibrated excited state . However, as the name already suggest, this state-specific approach yields a meaningful energy only for the solvent-equilibrated reference state . All other states have to be treated in the non-equilibrium limit and subjected to the formalism presented in the previous section to be consistent with the Franck-Condon principle. The respective generalization of the perturbative ansatz for the Hamiltonian for the out-of-equilibrium state (e.g. the ground or any other excited state) in the field of the equilibrated state reads as

 (6.82)

which can be solved using the procedure introduced in the previous section.

While most of the technical aspects concerning the application of the model will be covered in the following, we highly recommend to read at least the formalism and implementation section of Ref. Mewes:2017 before using the model.

(B) Usage
The main switch for the equilibrium solvation SS-PCM is EQSOLV in the $pcm block (SOLVENT_METHOD = PCM has to be set as well). Setting it to TRUE will cause one SCF+ADC calculation to be carried out employing the solvent-field that is found on disk, while any integer triggers the automatic solvent-field optimization and is interpreted as the maximum number of steps. We recommend to use EQSOLV = 15. Note: A SS-PCM calculation always requires a preceding converged ptSS-PCM calculation (i.e., EQSOLV = FALSE) for the desired state to provide a guess for the initial solvent-field, or it will crash. Consequently, the SS-PCM calculation is always the second (or third...) step of a multi-step job. To create the input-file for a multi step job, just add "@@@" at the end of the input for the first job and append the input for the second job. See also section 3.6. Since the reaction-field is stored in the basis of the molecular-surface elements, the geometry of the molecule as well as parameters that affect construction and discretization of the molecular cavity can not be changed between jobs. This, however, is not enforced. The state for which the solvent field should to be optimized is specified with the variable EQSTATE in the$pcm block. A value of 0 refers to the MP ground-state (for PTED calculations), 1 selects the energetically lowest excited state, 2 the second lowest, and so on. The solvent-field can in principle be optimized for any singlet, triplet or spin-flip excited state. However, only the desired class of states should be requested, i.e., either EE_SINGLETS or EE_TRIPLETS for singlet references, and either EE_STATES or SF_STATES for triplet references. To compute, e.g., the phosphorescence energy, only triplet states should be requested and EQSTATE would typically be set to the lowest excited state.

Note: Computing multiple different classes of excited states during the iterations will confuse the state-counting logic of the program.

Convergence is controlled by EQS_CONV. Criteria are the SCF energy as well as the RMSD, MAD and largest single difference of the surface-charges. The convergence should not need to be modified. It is per default derived from the SCF convergence parameter (SCF_CONVERGENCE). The default value of 4 (since SCF_CONVERGENCE is 8 for ADC calculations) corresponds to an maximum energy change of  meV and will yield converged total energies for all states. Excitation energies and in particular the total energy of the reference state converge somewhat faster than the SCF energy, and a value of 3 may save some time for the computation e.g. the emission energy of large solutes.

The self-consistent SS-PCM can also be used to compute a fully consistent solvent-field for the MP2 ground state by setting EQSTATE to 0. This is known as ptSS(PTED) approach and can improve vertical excitation energies if there are large differences between the electrostatic properties of the SCF and MP ground states (large PTD corrections). In most cases, however, the non-iterative PTD approach is a very good approximation to the PTED approach (see the sample jobs below).

The program possesses limited intelligence in detecting the type of the calculation (PTED or EQS/SS-PCM) as well as the target state of the solvent-field equilibration and will assemble and designate the ptSS corrections, total energies and transition energies accordingly. This logic can be confused if multiple classes of states (e.g. singlet and triplets) are computed simultaneously during the iterations, and/or if the ordering of the states changes. Computing singlet and triplet states together in a final job for a previously converged solvent-field should yield a correct output, but will confuse the state counting in any following steps. The output of a PTED calculation is essentially identical to that of the other ptSS-schemes.

In the “HF/MP2/MP3 Summary” section, zeroth (without ptSS) and first (with ptSS) order total energies of the respective ground-state in the solvent-field of the target state are given along with the ptSS term for a vertical transition from the equilibrated state (emission). Note that to obtain the MP3 ground state energy during an ADC(3)/EQS calculation, the ptSS term has to be added manually (it is printed in the MP2 Summary) and moreover, that the HF-dipole moment is currently incorrect (known bug). A correct HF dipole can be found at the end of the output file.

In the “Excited-State Summary” section the reference state is distinguished from the out-of-equilibrium states. Respective total and transition energies are given along with the non-equilibrium corrections, transition moments and some remarks. Note that for emission, in contrast to absorption, the ptSS term increases the transition energy as it lowers the energy of the out-of-equilibrium ground state. The so-called "self-ptSS term" is a perturbative estimate of how much the solvent field of this state is off from its equilibrium. Although the line in the output changes depending on the value (from "not converged" to "reasonably converged" to "converged") it is not used in the actual convergence check. Note that the self-ptSS term is computed with (dielectric_infi) and not , as it probably should be. The self-ptSS term may be used to judge how well a solvent-field computed with a different methodology (basis, ADC order/variant) fits. In such a case, values  eV signal a reasonable agreement.

To calculate inter-state transition moments for excited-state absorption, the variable ADC_PROP_ES2ES has to be set to TRUE. Unfortunately, transition energies have to be computed manually from the (first-order) total energies given in the excited-state summary, since the transition energies given along with the state-to-state transition moments following the excite-state summary are incorrect (missing non-equilibrium terms).

The progress of the solvent-field iteration and their convergence is reported following the “Excited-State Summary”.

(C) Tips and Tricks
To compute fluorescence and phosphorescence energies, solute geometry AND solvent-field should both be optimized for the suspected emitting state. Since hardly any programs can perform excited-state optimizations with the SS-PCM solvent models, you will probably have to use gas-phase geometries. In our experience, the errors introduced by this approximation are small to negligible (typically  eV) in non-polar solvents, but can become significant in polar solvents, in particular for polar charge-transfer states.

Concerning the predicted emission energies, we found that ADC(2)/SS-PCM typically over-stabilizes CT states, yielding emission energies that are too low. SOS-ADC(2) can improve this error, but does not eliminate it. In general, while emission energies are more accurate with (SOS-)ADC(2)/SS-PCM than with ADC(3)/SS-PCM, the latter affords better relative state energies (see Ref. Mewes:2017).

Keep in mind that the solute-solvent interaction of polar solvents with polar (e.g. charge-transfer) states can become quite large (multiple eV), and may thus affect the ordering and nature of the excited states. It should be carefully checked if the character and/or energetic ordering of the states changes during the procedure. This applies in particular to any equilibration of the solvent field for higher lying excited states (e.g. or ). In one example, however, even the solvent-field equilibration for a weakly polar in a polar solvent eventually caused a more polar state (former ) to become the lowest state during the iterations. If the excited-states swap during the procedure, find out in which step the swap occurred and do only so many iterations (i.e., set EQSOLV accordingly). In a following job, adjust the variable EQSTATE and continue the iterations. If states start to mix when they get close, it might help to use an artificially large dielectric constant in a first job to induce the change in state ordering and continue with the desired dielectric constant in the second job.

If performance is critical, the calculations may be accelerated by lowering the ADC convergence during the solvent-field iterations (set ADC_DAVIDSON_CONVERGENCE = 5). The number of iterations may be reduced by first converging the solvent-field with a smaller basis/at a lower level of ADC followed by another job with the full basis/level of ADC. However, in our experience ADC(2) and ADC(3) solvent-fields for the same state differ quite significantly and the approach probably does not help much. In contrast, the solvent-field computed with a smaller basis (e.g. SVP) is often a good approximation for that computed with a larger basis (e.g. def2-TZVP, see examples), such this may actually help. It is in general advisable to compute just as many states as is necessary during the solvent-field iterations and include higher lying excited states and triplets in the final job. In ADC(2) calculations for large systems, one should always employ the resolution-of-the-identity approximation.

To save time in PTED jobs, it is suggested to disable the computation of excited states during the solvent-field iterations of a PTED job by setting EE_SINGLETS (and/or EE_TRIPLETS/ EE_STATES) to 0 and compute the excited-states in a final job once the reaction field is converged.

For more tips and examples see the sample jobs.

## 6.8.8 Frozen-Density Embedding: FDE-ADC methods

FDE-ADC [497] represents a method to include interactions between an embedded species and its environment into an ADC() calculation based on Frozen Density Embedding Theory (FDET) [498, 499]. FDE-ADC supports ADC and CVS-ADC methods of orders 2s,2x and 3 and regular ADC job control keywords also apply.

The FDE-ADC method starts with generating an embedding potential using a MP() density for the embedded system (A) and a DFT or HF density for the environment (B). A Hartree-Fock calculation is then carried out during which the embedding potential is added to the Fock operator. The embedded Hartree-Fock orbitals act as an input for the subsequent ADC calculation which yields the embedded properties (vertical excitation energies, oscillator strengths, etc.). Further information on the FDE-ADC method and FDE-ADC job control are described in Section 11.7.1.

For an ADC calculation it is important to ensure that there are sufficient resources available for the necessary integral calculations and transformations. These resources are controlled using the $rem variables MEM_STATIC and MEM_TOTAL. The memory used by ADC is currently 95% of the difference MEM_TOTAL - MEM_STATIC. An ADC calculation is requested by setting the$rem variable METHOD to the respective ADC variant. Furthermore, the number of excited states to be calculated has to be specified using one of the $rem variables EE_STATES, EE_SINGLETS, or EE_TRIPLETS. The former variable should be used for open-shell or unrestricted closed-shell calculations, while the latter two variables are intended for restricted closed-shell calculations. Even though not recommended, it is possible to use EE_STATES in a restricted calculation which translates into EE_SINGLETS, if neither EE_SINGLETS nor EE_TRIPLETS is set. Similarly, the use EE_SINGLETS in an unrestricted calculation will translate into EE_STATES, if the latter is not set as well. All$rem variables to set the number of excited states accept either an integer number or a vector of integer numbers. A single number specifies that the same number of excited states are calculated for every irreducible representation the point group of the molecular system possesses (molecules without symmetry are treated as symmetric). In contrast, a vector of numbers determines the number of states for each irreducible representation explicitly. Thus, the length of the vector always has to match the number of irreducible representations. Hereby, the excited states are labeled according to the irreducible representation of the electronic transition which might be different from the irreducible representation of the excited state wave function. Users can choose to calculate any molecule as symmetric by setting CC_SYMMETRY = FALSE.

METHOD
 Controls the order in perturbation theory of ADC.

TYPE:
 STRING

DEFAULT:
 None

OPTIONS:

RECOMMENDATION:
 None

EE_STATES
 Controls the number of excited states to calculate.

TYPE:
 INTEGER/ARRAY

DEFAULT:
 0 Do not perform an ADC calculation

OPTIONS:
 Number of states to calculate for each irrep or Compute states for the first irrep, states for the second irrep, ...

RECOMMENDATION:
 Use this variable to define the number of excited states in case of unrestricted or open-shell calculations. In restricted calculations it can also be used, if neither EE_SINGLETS nor EE_TRIPLETS is given. Then, it has the same effect as setting EE_SINGLETS.

EE_SINGLETS
 Controls the number of singlet excited states to calculate.

TYPE:
 INTEGER/ARRAY

DEFAULT:
 0 Do not perform an ADC calculation of singlet excited states

OPTIONS:
 Number of singlet states to calculate for each irrep or Compute states for the first irrep, states for the second irrep, ...

RECOMMENDATION:
 Use this variable to define the number of excited states in case of restricted calculations of singlet states. In unrestricted calculations it can also be used, if EE_STATES not set. Then, it has the same effect as setting EE_STATES.

EE_TRIPLETS
 Controls the number of triplet excited states to calculate.

TYPE:
 INTEGER/INTEGER ARRAY

DEFAULT:
 0 Do not perform an ADC calculation of triplet excited states

OPTIONS:
 Number of triplet states to calculate for each irrep or Compute states for the first irrep, states for the second irrep, ...

RECOMMENDATION:
 Use this variable to define the number of excited states in case of restricted calculations of triplet states.

CC_SYMMETRY
 Activates point-group symmetry in the ADC calculation.

TYPE:
 LOGICAL

DEFAULT:
 TRUE If the system possesses any point-group symmetry.

OPTIONS:
 TRUE Employ point-group symmetry FALSE Do not use point-group symmetry

RECOMMENDATION:
 None

 Controls the calculation of excited state properties (currently only dipole moments).

TYPE:
 LOGICAL

DEFAULT:
 FALSE

OPTIONS:
 TRUE Calculate excited state properties. FALSE Do not compute state properties.

RECOMMENDATION:
 Set to TRUE, if properties are required.

 Controls the calculation of transition properties between excited states (currently only transition dipole moments and oscillator strengths), as well as the computation of two-photon absorption cross-sections of excited states using the sum-over-states expression.

TYPE:
 LOGICAL

DEFAULT:
 FALSE

OPTIONS:
 TRUE Calculate state-to-state transition properties. FALSE Do not compute transition properties between excited states.

RECOMMENDATION:
 Set to TRUE, if state-to-state properties or sum-over-states two-photon absorption cross-sections are required.

 Controls the calculation of two-photon absorption cross-sections of excited states using matrix inversion techniques.

TYPE:
 LOGICAL

DEFAULT:
 FALSE

OPTIONS:
 TRUE Calculate two-photon absorption cross-sections. FALSE Do not compute two-photon absorption cross-sections.

RECOMMENDATION:
 Set to TRUE, if to obtain two-photon absorption cross-sections.

STATE_ANALYSIS
 Controls the analysis and export of excited state densities and orbitals (see 10.2.7 for details).

TYPE:
 LOGICAL

DEFAULT:
 FALSE

OPTIONS:
 TRUE Perform excited state analyses. FALSE No excited state analyses or export will be performed.

RECOMMENDATION:
 Set to TRUE, if detailed analysis of the excited states is required or if density or orbital plots are needed.

 Set the spin-opposite scaling parameter for an SOS-ADC(2) calculation. The parameter value is obtained by multiplying the given integer by .

TYPE:
 INTEGER

DEFAULT:
 1300 Optimized value .

OPTIONS:
 Corresponding to

RECOMMENDATION:
 Use the default.

 Set the spin-opposite scaling parameter for the ADC(2) calculation. The parameter value is obtained by multiplying the given integer by .

TYPE:
 INTEGER

DEFAULT:

OPTIONS:
 Corresponding to

RECOMMENDATION:
 Use the default.

 Set the spin-opposite scaling parameter for the ADC(2)-x calculation. The parameter value is obtained by multiplying the given integer by .

TYPE:
 INTEGER

DEFAULT:

OPTIONS:
 Corresponding to

RECOMMENDATION:
 Use the default.

 Controls the number of excited state guess vectors which are single excitations. If the number of requested excited states exceeds the total number of guess vectors (singles and doubles), this parameter is automatically adjusted, so that the number of guess vectors matches the number of requested excited states.

TYPE:
 INTEGER

DEFAULT:
 Equals to the number of excited states requested.

OPTIONS:
 User-defined integer.

RECOMMENDATION:

 Controls the number of excited state guess vectors which are double excitations.

TYPE:
 INTEGER

DEFAULT:
 0

OPTIONS:
 User-defined integer.

RECOMMENDATION:

 Activates the use of the DIIS algorithm for the calculation of ADC(2) excited states.

TYPE:
 LOGICAL

DEFAULT:
 FALSE

OPTIONS:
 TRUE Use DIIS algorithm. FALSE Do diagonalization using Davidson algorithm.

RECOMMENDATION:
 None.

 Controls the iteration step at which DIIS is turned on.

TYPE:
 INTEGER

DEFAULT:
 1

OPTIONS:
 User-defined integer.

RECOMMENDATION:
 Set to a large number to switch off DIIS steps.

 Controls the size of the DIIS subspace.

TYPE:
 INTEGER

DEFAULT:
 7

OPTIONS:
 User-defined integer

RECOMMENDATION:
 None

 Controls the maximum number of DIIS iterations.

TYPE:
 INTEGER

DEFAULT:
 50

OPTIONS:
 User-defined integer.

RECOMMENDATION:
 Increase in case of slow convergence.

 Controls the convergence criterion for the excited state energy during DIIS.

TYPE:
 INTEGER

DEFAULT:
 6 Corresponding to

OPTIONS:
 Corresponding to

RECOMMENDATION:
 None

 Convergence criterion for the residual vector norm of the excited state during DIIS.

TYPE:
 INTEGER

DEFAULT:
 6 Corresponding to

OPTIONS:
 Corresponding to

RECOMMENDATION:
 None

 Controls the maximum subspace size for the Davidson procedure.

TYPE:
 INTEGER

DEFAULT:
 the number of excited states to be calculated.

OPTIONS:
 User-defined integer.

RECOMMENDATION:
 Should be at least the number of excited states to calculate. The larger the value the more disk space is required.

 Controls the maximum number of iterations of the Davidson procedure.

TYPE:
 INTEGER

DEFAULT:
 60

OPTIONS:
 Number of iterations

RECOMMENDATION:
 Use the default unless convergence problems are encountered.

 Controls the convergence criterion of the Davidson procedure.

TYPE:
 INTEGER

DEFAULT:
 Corresponding to

OPTIONS:
 Corresponding to .

RECOMMENDATION:
 Use the default unless higher accuracy is required or convergence problems are encountered.

 Controls the threshold for the norm of expansion vectors to be added during the Davidson procedure.

TYPE:
 INTEGER

DEFAULT:
 Twice the value of ADC_DAVIDSON_CONV, but at maximum .

OPTIONS:
 Corresponding to

RECOMMENDATION:
 Use the default unless convergence problems are encountered. The threshold value should always be smaller than the convergence criterion ADC_DAVIDSON_CONV.

 Controls the amount of printing during an ADC calculation.

TYPE:
 INTEGER

DEFAULT:
 1 Basic status information and results are printed.

OPTIONS:
 0 Quiet: almost only results are printed. 1 Normal: basic status information and results are printed. 2 Debug: more status information, extended information on timings. ...

RECOMMENDATION:
 Use the default.

 Activates the use of the CVS approximation for the calculation of CVS-ADC core-excited states.

TYPE:
 LOGICAL

DEFAULT:
 FALSE

OPTIONS:
 TRUE Activates the CVS approximation. FALSE Do not compute core-excited states using the CVS approximation.

RECOMMENDATION:
 Set to TRUE, if to obtain core-excited states for the simulation of X-ray absorption spectra. In the case of TRUE, the $rem variable CC_REST_OCC has to be defined as well. CC_REST_OCC  Sets the number of restricted occupied orbitals including active core occupied orbitals. TYPE:  INTEGER DEFAULT:  0 OPTIONS:  Restrict energetically lowest occupied orbitals to correspond to the active core space. RECOMMENDATION:  Example: cytosine with the molecular formula CHNO includes one oxygen atom. To calculate O 1s core-excited states, has to be set to 1, because the 1s orbital of oxygen is the energetically lowest. To obtain the N 1s core excitations, the integer has to be set to 4, because the 1s orbital of the oxygen atom is included as well, since it is energetically below the three 1s orbitals of the nitrogen atoms. Accordingly, to simulate the C 1s spectrum of cytosine, must be set to 8. SF_STATES  Controls the number of excited spin-flip states to calculate. TYPE:  INTEGER DEFAULT:  0 Do not perform a SF-ADC calculation OPTIONS:  Number of states to calculate for each irrep or Compute states for the first irrep, states for the second irrep, ... RECOMMENDATION:  Use this variable to define the number of excited states in the case of a spin-flip calculation. SF-ADC is available for ADC(2)-s, ADC(2)-x and ADC(3). Keywords for SS-PCM control in$pcm:

EQSOLV
 Main switch of the self-consistent SS-PCM procedure.

INPUT SECTION: $pcm TYPE:  INTEGER DEFAULT:  0 OPTIONS:  0 No self-consistent SS-PCM. 1 Single SS-PCM calculation (SCF+ADC) with the solvent-field found on disk. 1 Do a maximum of automatic solvent-field iterations. RECOMMENDATION:  We recommend to use 15 steps max. Typical convergence is 3-5 steps. In difficult cases 6-12. If the solvent-field iteration do not converge in 15 steps, something is wrong. Also make sure that a solvent-field has been stored on disk by a previous job. EQSTATE  Specifies the state for which the solvent-field is to be optimized. INPUT SECTION:$pcm
TYPE:
 INTEGER

DEFAULT:
 0

OPTIONS:
 0 MP2 ground state (for PTED approach) 1 energetically lowest excited state 2 2nd lowest excited state ...

RECOMMENDATION:
 The program will blindly select the state by its energetic position shown in the “Exited-State Summary” part in the output file. A maximum of 99 states can be stored and selected.

EQS_CONV
 Controls the convergence of the solvent-field iterations by setting the convergence criteria (a mixture of SCF energy and charge-vector). SCF energy criterion computes as  eH

INPUT SECTION: $pcm TYPE:  INTEGER DEFAULT:  SCF_CONVERGENCE OPTIONS:  3 May be sufficient for emission energies 4 Assured converged total energies (2.7 meV). 5 Really tight RECOMMENDATION:  Use the default. ## 6.8.10 Examples Example 6.178 Q-Chem input for an ADC(2)-s calculation of singlet exited states of methane with D2 symmetry. In total six excited states are requested corresponding to four (two) electronic transitions with irreducible representation (). $molecule
0 1
C
H   1 r0
H   1 r0   2  d0
H   1 r0   2  d0   3  d1
H   1 r0   2  d0   4  d1

r0 = 1.085
d0 = 109.4712206
d1 = 120.0
$end$rem
BASIS               6-31g(d,p)
MEM_TOTAL           4000
MEM_STATIC          100
EE_SINGLETS         [0,4,2,0]
$end  Example 6.179 Q-Chem input for an unrestricted RI-ADC(2)-s calculation with symmetry using DIIS. In addition, excited state properties and state-to-state properties are computed. $molecule
0 2
C    0.0    0.0   -0.630969
N    0.0    0.0    0.540831
$end$rem
BASIS            aug-cc-pVDZ
AUX_BASIS        rimp2-aug-cc-pVDZ
MEM_TOTAL        4000
MEM_STATIC       100
CC_SYMMETRY      false
EE_STATES        6
$end  Example 6.180 Q-Chem input for a restricted CVS-ADC(2)-x calculation with symmetry using 4 parallel CPU cores. In this case, the 10 lowest nitrogen K-shell singlet excitations are computed. $molecule
0 1
C    -5.17920    2.21618    0.01098
C    -3.85603    2.79078    0.05749
N    -2.74877    2.08372    0.05569
C    -5.23385    0.85443   -0.04040
C    -2.78766    0.70838    0.01226
N    -4.08565    0.13372   -0.03930
N    -3.73433    4.14564    0.16144
O    -1.81716   -0.02560    0.00909
H    -4.50497    4.74117   -0.12037
H    -2.79158    4.50980    0.04490
H    -4.10443   -0.88340   -0.07575
H    -6.08637    2.82445    0.02474
H    -6.17341    0.29221   -0.07941
$end$rem
EE_SINGLETS                 10
MEM_TOTAL                   10000
MEM_STATIC                  1000
CC_SYMMETRY                 false
BASIS                       6-31G*
SYMMETRY                    false
CC_REST_OCC                 4
$end  Example 6.181 Q-Chem input for a restricted SF-ADC(2)-s calculation of the first three spin-flip target states of cyclobutadiene without point group symmetry. $molecule
0 3
C     0.000000     0.000000     0.000000
C     1.439000     0.000000     0.000000
C     1.439000     0.000000     1.439000
C     0.000000     0.000000     1.439000
H    -0.758726     0.000000    -0.758726
H     2.197726     0.000000    -0.758726
H     2.197726     0.000000     2.197726
H    -0.758726     0.000000     2.197726
$end$rem
MEM_TOTAL       15000
MEM_STATIC      1000
CC_SYMMETRY     false
BASIS           3-21G
SF_STATES       3
$end  Example 6.182 Q-Chem input for a restricted ADC(2)-x calculation of water with symmetry. Four singlet A" excited states and two triplet A’ excited states are requested. For the first two states (1A" and 1A’) the transition densities as well as the attachment and detachment densities are exported into cube files. $molecule
0 1
O   0.000   0.000   0.000
H   0.000   0.000   0.950
H   0.896   0.000  -0.317
$end$rem
BASIS             6-31g(d,p)
MEM_TOTAL         3000
MEM_STATIC        100
EE_SINGLETS       [0,4]
EE_TRIPLETS       [2,0]
MAKE_CUBE_FILES   true
$end$plots
Plot transition and a/d densities
40 -3.0 3.0
40 -3.0 3.0
40 -3.0 3.0
0 0 2 2
1 2
1 2
$end  Example 6.183 Q-Chem input for a ADC(2)-s/ptSS-PCM calculation of the five lowest singlet-excited states of N,N-dimethylnitroaniline in diethylether. PCM settings are all default values except THEORY, which is set to IEFPCM instead of the default CPCM. $rem
BASIS                  3-21G
MEM_TOTAL              32000
MEM_STATIC             2000
EE_SINGLETS            5
PCM_PRINT              1       !increase print level
SOLVENT_METHOD         pcm     !invokes PCM solvent model
$end$pcm
ChargeSeparation        Marcus  !default
theory                  IEFPCM  !default is CPCM, IEFPCM is more accurate
method                  ISWIG
Solver                  Inversion
vdwScale                1.20
$end$solvent
dielectric              4.34  !epsilon of Et2O
dielectric_infi         1.829 !n_square of Et2O
$end$molecule
0 1
C   -4.263068      2.512843      0.025391
C   -5.030982      1.361365      0.007383
C   -4.428196      0.076338     -0.021323
C   -3.009941      0.019036     -0.030206
C   -2.243560      1.171441     -0.011984
C   -2.871710      2.416638      0.015684
H   -4.740854      3.480454      0.047090
H   -2.502361     -0.932570     -0.052168
H   -1.166655      1.104642     -0.020011
H   -6.104933      1.461766      0.015870
N   -5.178541     -1.053870     -0.039597
C   -6.632186     -0.969550     -0.034925
H   -6.998203     -0.462970      0.860349
H   -7.038179     -1.975370     -0.051945
H   -7.001616     -0.431420     -0.910237
C   -4.531894     -2.358860     -0.066222
H   -3.912683     -2.476270     -0.957890
H   -5.298508     -3.126680     -0.075403
H   -3.902757     -2.507480      0.813678
N   -2.070815      3.621238      0.033076
O   -0.842606      3.510489      0.025476
O   -2.648404      4.710370      0.054545
$end  Example 6.184 Q-Chem input for a ADC/SS-PCM EQS solvent-field equilibration for the first excited singlet state of peroxinitrite in water, which provides e.g. the fluorescence energy. After generating a starting point in the first job (using a smaller basis and lower adc convergence criteria), the solvent-field iterations are carried out until convergence in the second job. In the third job, ADC(2) excited states are computed in the converged solvent field that was left on disk by the second Job. In the fourth job, we additionally compute ADC(3) excited states. This mixed approach should in general be used with great caution. If the self-ptSS term of the reference state becomes too large (>0.01 eV) like it is the case here, the fully consistent approach should be used (i.e. also the solvent-field computed at the ADC(3) level). PCM settings are all default values except THEORY, which is set to IEFPCM instead of the default CPCM. $comment
ADC(2)/ptSS-PCM to generate starting point for the EqS
Step in the next Job
$end$rem
BASIS               3-21G !using a small basis to speed up this step
MEM_TOTAL           6000
MEM_STATIC          1000
EE_SINGLETS         1
SOLVENT_METHOD      pcm
$end$solvent !Water
dielectric       78.4
dielectric_infi   1.76
$end$molecule
-1 1
N    -0.068642000000     -0.600693000000     -0.723424000000
O     0.349666000000      0.711166000000      1.187490000000
O    -0.948593000000      0.200668000000     -0.956940000000
O     0.659040000000     -0.386002000000      0.402650000000
$end @@@$comment
for the first excited state
$end$rem
BASIS            6-31G*
MEM_TOTAL        6000
MEM_STATIC       1000
EE_SINGLETS      2 !compute 2 singlets during the equilibration
SOLVENT_METHOD   pcm !activate PCM
$end$pcm
eqsolv      15    !maximum 15 steps, converges after 5
eqstate     1     !Equilibrate 1st excited state
eqs_conv    4     !Default convergence
theory      iefpcm
$end$solvent
dielectric       78.4
dielectric_infi   1.76
$end$molecule
$end @@@$comment
Compute ADC(2) excited states in the converged solvent field
$end$rem
BASIS            6-31G*
MEM_TOTAL        6000
MEM_STATIC       1000
EE_SINGLETS      6 !compute 6 singlets
ADC_PROP_ES2ES   true !compute ES 2 ES transition moments for ESA
SOLVENT_METHOD   pcm
$end$pcm
eqsolv   true !only one calculation with converged field
eqstate  1    !Equilibrate 1st excited state
theory   iefpcm
$end$solvent
dielectric      78.4
dielectric_infi  1.76
$end$molecule
$end @@@$comment
We can also compute ADC(3) excited states in the
converged ADC(2) solvent field and use the self-
ptSS term as diagnostic.
$end$rem
BASIS            6-31G*
MEM_TOTAL        6000
MEM_STATIC       1000
EE_SINGLETS      3 !compute 3 singlets
EE_TRIPLETS      1    !and 1 triplet
SOLVENT_METHOD   pcm
$end$pcm
eqsolv   true !only one calculation with converged field
eqstate  1    !Equilibrate 1st excited state
theory   iefpcm
$end$solvent
dielectric      78.4
dielectric_infi  1.76
$end$molecule
$end  Example 6.185 Q-Chem input for a riADC(2)/ptSS-PCM(PTED) calculation for the five lowest excited states of peroxinitrite in water. After generating a starting point in the first job, which also provides the ptSS(PTE) and ptSS(PTD) results for comparison, the solvent-field is equilibrated for the MP density in the second job. During the iterations, the calculation of excited states is disabled to speed up the calculation. In the third job, five excited states are computed at the riADC(2)/ptSS(PTED) level of theory. Although the PTD corrections for this molecule are unusually large, a comparison of the PTE, PTD and PTD* results from the first job with the PTED results from the third job will reveal a reasonable agreement between the fully consistent PTED and the perturbative PTD approaches. In the fourth job, excited states are calculated with a larger basis set. The self-ptSS term of the MP ground state will be quite small, showing that the solvent-field computed with the smaller SVP basis is a good approximation. $comment
riADC(2)/ptSS-PCM to generate starting point for
the PTED iterations in the next Job and provide
PTE and PTD energies for comparing with PTED
$end$rem
BASIS            def2-SVP
AUX_BASIS        rimp2-VDZ
MEM_TOTAL        6000
MEM_STATIC       1000
EE_SINGLETS      5
SOLVENT_METHOD   pcm
$end$solvent !Water
dielectric      78.4
dielectric_infi  1.76
$end$molecule
-1 1
N    -0.068642000000     -0.600693000000     -0.723424000000
O     0.349666000000      0.711166000000      1.187490000000
O    -0.948593000000      0.200668000000     -0.956940000000
O     0.659040000000     -0.386002000000      0.402650000000
$end @@@$comment
the MP ground state. No excited states are computed
$end$rem
BASIS            def2-SVP
AUX_BASIS        rimp2-VDZ
MEM_TOTAL        6000
MEM_STATIC       1000
EE_SINGLETS      0 !dont compute ES
SOLVENT_METHOD   pcm !activate PCM
$end$pcm
eqsolv     15    !maximum 15 steps
eqstate    0     !Equilibrate MP ground state
eqs_conv   5     !higher convergence
theory     iefpcm
$end$solvent
dielectric      78.4
dielectric_infi  1.76
$end$molecule
$end @@@$comment
Compute ADC(2)/ptSS-PTED excited states in the
converged solvent field
$end$rem
BASIS            def2-SVP
AUX_BASIS        rimp2-VDZ
MEM_TOTAL        6000
MEM_STATIC       1000
EE_SINGLETS      5 !compute 5 singlets
SOLVENT_METHOD   pcm
$end$pcm
eqsolv   true !only one calculation with converged field
eqstate  0    !Equilibrate MP ground state
theory   iefpcm
$end$solvent
dielectric 78.4
dielectric_infi 1.76
$end$molecule
$end @@@$comment
We can also compute the ES in the converged field
with a larger basis and without RI in the stored
solvent-field.
$end$rem
BASIS           def2-TZVP
MEM_TOTAL       6000
MEM_STATIC      1000
EE_SINGLETS     3 !compute 3 singlets
$end$pcm
$end$solvent
$end$molecule