Many of the preceding sections of chapter 11 are concerned with properties that require the solution of underlying equations similar to those from TDDFT (see eq. eq:TDDFT), but in the presence of a (timedependent) perturbation:
(11.87) 
where and for canonical HF/DFT MOs. The functionality for solving these equations with a general choice of operators representing a perturbation is now available in QChem. Both singlet[Jørgensen et al.(1988)Jørgensen, Jensen, and Olsen] and triplet[Olsen et al.(1989)Olsen, Yeager, and Jørgensen] response are available for a variety of operators (see table 11.4).
An additional feature of the general response module is its ability to work with nonorthogonal MOs. In a formulation analogous to TDDFT(MI)[Liu and Herbert(2015)], the linear response for molecular interactions[Berquist and Lambrecht()], or LR(MI), method is available to solve the linear response equations on top of ALMOs.
The response solver can be used with any density functional available in QChem, including rangeseparated functionals (e.g. CAMB3LYP, B97X) and metaGGAs (e.g. M062X).
There are a few limitations:
No postHF/correlated methods are available yet.
Currently, only linear response is implemented.
Only calculations on top of restricted and unrestricted (not restricted openshell) references are implemented.
Density functionals including nonlocal dispersion (e.g. VV10, B97MV) are not yet available.
Only one keyword is necessary in the $rem section to activate the response module. All other options are controlled through the $response input section.
RESPONSE
Activate the general response property module.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
FALSE (or 0)
Don’t activate the general response property module.
TRUE (or 1)
Activate the general response property module.
RECOMMENDATION:
None.
ORDER
Sets the maximum order of response theory to perform.
INPUT SECTION: $response
TYPE:
STRING
DEFAULT:
LINEAR
OPTIONS:
LINEAR
Perform up through linear response.
RECOMMENDATION:
None. Currently, only linear response is implemented.
SOLVER
Sets the algorithm for solving the response equations.
INPUT SECTION: $response
TYPE:
STRING
DEFAULT:
DIIS
OPTIONS:
LINEAR
Iteratively solve the response equations without convergence acceleration.
DIIS
Iteratively solve the response equations using DIIS for convergence acceleration.
RECOMMENDATION:
DIIS
HAMILTONIAN
Sets the approximation used for the orbital Hessian.
INPUT SECTION: $response
TYPE:
STRING
DEFAULT:
RPA
OPTIONS:
RPA
No approximations.
TDA
Same as the CIS approximation.
CIS
Synonym for TDA.
RECOMMENDATION:
None.
SPIN
Does the operator access same spin (singlet) or different spin (triplet) states?
INPUT SECTION: $response
TYPE:
STRING
DEFAULT:
SINGLET
OPTIONS:
SINGLET
Operator is spinconserving.
TRIPLET
Operator is not spinconserving.
RECOMMENDATION:
None. Care must be taken as all operators in a single calculation will be forced to follow this option.
MAXITER
Maximum number of iterations.
INPUT SECTION: $response
TYPE:
INTEGER
DEFAULT:
60
OPTIONS:
Maximum number of iterations.
RECOMMENDATION:
Use the default value.
CONV
Convergence threshold. For the DIIS solver, this is the DIIS error norm. For the linear solver, this is the response vector RMSD between iterations.
INPUT SECTION: $response
TYPE:
INTEGER
DEFAULT:
8
OPTIONS:
Sets the convergence threshold to .
RECOMMENDATION:
Use the default value.
DIIS_START
Iteration number to start DIIS. Before this, linear iterations are performed.
INPUT SECTION: $response
TYPE:
INTEGER
DEFAULT:
1
OPTIONS:
Iteration number to start DIIS.
RECOMMENDATION:
Use the default value.
DIIS_VECTORS
Maximum number of DIIS vectors to keep.
INPUT SECTION: $response
TYPE:
INTEGER
DEFAULT:
7
OPTIONS:
Maximum number of DIIS vectors to keep.
RECOMMENDATION:
Use the default value.
RHF_AS_UHF
Should the response equations be solved as though an unrestricted reference is being used?
INPUT SECTION: $response
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
TRUE
Treat an RHF wavefunction as though it were UHF.
FALSE
Treat an RHF wavefunction as RHF.
RECOMMENDATION:
Use the default value. Only useful for debugging.
PRINT_LEVEL
Sets a general printing level across the response module.
INPUT SECTION: $response
TYPE:
INTEGER
DEFAULT:
2
OPTIONS:
1
Print the initial guess and the final results.
2
1 + iterations and comments.
10
Kill trees.
RECOMMENDATION:
Use the default value.
RUN_TYPE
Should a single response calculation be performed, or should all permutations of the orbital Hessian and excitation type be performed?
INPUT SECTION: $response
TYPE:
STRING
DEFAULT:
SINGLE
OPTIONS:
SINGLE
Use only the orbital Hessian and excitation type specified in their respective keywords.
ALL
Use all permutations of RPA/TDA and singlet/triplet.
RECOMMENDATION:
Use the default value, unless a comparison between approximations and excitation types is desired.
SAVE
Save any quantities to disk?
INPUT SECTION: $response
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
0
Don’t save any quantities to disk.
1
Save quantities in MO basis.
2
Save quantities in MO and AO bases.
RECOMMENDATION:
None.
READ
Read any quantities from disk?
INPUT SECTION: $response
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
0
Don’t read any quantities from disk.
1
Read quantities in MO basis.
2
Read quantities in AO basis.
RECOMMENDATION:
None.
DUMP_AO_INTEGRALS
Should AObasis property integrals be saved to disk?
INPUT SECTION: $response
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
TRUE
Save AObasis property integrals to disk.
FALSE
Don’t save AObasis property integrals to disk.
RECOMMENDATION:
None.
FORCE_NOT_NONORTHOGONAL
Should the canonical response equations be solved, ignoring the identity of the underlying orbitals?
INPUT SECTION: $response
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
TRUE
FALSE
RECOMMENDATION:
Leave as false. Using the standard (canonical) response equations with nonorthogonal MOs will give incorrect results.
FORCE_NONORTHOGONAL
Should the nonorthogonal response equations be solved, ignoring the identity of the underlying orbitals?
INPUT SECTION: $response
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
TRUE
FALSE
RECOMMENDATION:
Leave as false. When used with canonical MOs, this should give the same answer as with the standard equations, but at greater computational cost.
FREQUENCY
Strength of one or more incident fields in atomic units. A separate response calculation will be performed for every field strength. 0.0 corresponds to the static limit.
INPUT SECTION: $response
TYPE:
DOUBLE
DEFAULT:
0.0
OPTIONS:
One or more field strengths separated by spaces.
RECOMMENDATION:
None.
The specification of operators used in solving for response vectors is designed to be very flexible. The general form of the $response input section is given by
where the keywords are those found in section 11.15.1 (with the exception of RESPONSE).$response keyword_1 setting_1 keyword_2 setting_2 ... [operator_1_label, operator_1_origin] [operator_2_label, operator_2_origin] [operator_3_label, operator_3_origin] ... $end
The specification of an operator is given within a line contained by [], where the first element is a label from table 11.4, and the second element is a label from table 11.5. Operator specifications may appear in any order. Response values are calculated for all possible permutations of operators and their components.
For the Cartesian moment operator, a third field within [] may be specified for the order of the expansion, entered as . For example, the molecular response to the moment of order (2, 5, 4) with its origin at (0.2, 0.3, 0.4) a.u. can be found with the operator specification
[multipole, (0.2, 0.3, 0.4), (2, 5, 4)]
Operator Label 
Description 
Integral 
dipole or diplen 
dipole (length gauge) 

quadrupole 
second moment (length gauge) 

multipole 
arbitraryorder Cartesian moment (length gauge) 

fermi or fc 
Fermi contact 

spindip or sd 
spin dipole 

angmom or dipmag 
angular momentum 

dipvel 
dipole (velocity gauge) 

Origin Label 
Description 
zero 
Cartesian origin, same as (0.0, 0.0, 0.0) 
(x, y, z) 
arbitrary point (double precision, units are bohrs) 
Example 11.270 Input for calculating all components of the static (dipole) polarizability at the Cartesian origin for tryptophan. All of the options given are defaults.
$molecule 0 1 N 0.0699826875 0.3321987191 0.2821283177 C 1.3728035449 0.0970713322 0.0129587739 C 2.0969275417 0.0523593054 1.3682652221 O 3.1382490088 0.6563684788 1.5380162924 C 1.9529664597 1.3136139853 0.7956021969 H 1.8442727348 2.2050605044 0.1801631789 H 1.3455899915 1.4594935008 1.6885689523 C 3.4053646872 1.1270611844 1.1918075237 C 4.4845249667 1.6235038050 0.5598918002 N 5.6509089647 1.2379326369 1.2284610654 H 6.6009314349 1.4112351003 0.9028629397 C 5.2921619642 0.4356274269 2.3131617003 C 3.8942019475 0.3557998019 2.3263315791 C 3.2659168792 0.3832607567 3.3431309548 H 2.1864306677 0.4577058843 3.3815918670 C 4.0381762333 1.0087512639 4.2870993776 H 3.5696890585 1.5824763141 5.0755609734 C 5.4445159165 0.9194874753 4.2519002882 H 6.0229926396 1.4277973542 5.0130007062 C 6.0869576238 0.2024044961 3.2767702726 H 7.1656650647 0.1287762497 3.2458650647 H 4.5457621618 2.2425310766 0.3253979653 H 0.5159777859 0.7478905868 0.5487661007 H 1.5420526570 0.8143939718 0.5935463196 H 0.5302278747 0.5823989653 0.4084507634 O 1.4575846656 0.5996887308 2.4093500287 H 0.5990015339 0.8842421241 2.0047830456 $end $rem METHOD = hf BASIS = sto3g SCF_CONVERGENCE = 9 THRESH = 12 RESPONSE = true $end $response ORDER linear SOLVER diis HAMILTONIAN rpa SPIN singlet MAXITER 60 CONV 8 DIIS_START 1 DIIS_VECTORS 7 RHF_AS_UHF false PRINT_LEVEL 2 RUN_TYPE single FREQUENCY 0.0 [dipole, zero] $end
Example 11.271 Functionally identical input for calculating all components of the static (dipole) polarizability at the Cartesian origin for tryptophan.
$rem jobtype = polarizability method = hf basis = sto3g scf_convergence = 9 thresh = 12 $end $molecule 0 1 N 0.0699826875 0.3321987191 0.2821283177 C 1.3728035449 0.0970713322 0.0129587739 C 2.0969275417 0.0523593054 1.3682652221 O 3.1382490088 0.6563684788 1.5380162924 C 1.9529664597 1.3136139853 0.7956021969 H 1.8442727348 2.2050605044 0.1801631789 H 1.3455899915 1.4594935008 1.6885689523 C 3.4053646872 1.1270611844 1.1918075237 C 4.4845249667 1.6235038050 0.5598918002 N 5.6509089647 1.2379326369 1.2284610654 H 6.6009314349 1.4112351003 0.9028629397 C 5.2921619642 0.4356274269 2.3131617003 C 3.8942019475 0.3557998019 2.3263315791 C 3.2659168792 0.3832607567 3.3431309548 H 2.1864306677 0.4577058843 3.3815918670 C 4.0381762333 1.0087512639 4.2870993776 H 3.5696890585 1.5824763141 5.0755609734 C 5.4445159165 0.9194874753 4.2519002882 H 6.0229926396 1.4277973542 5.0130007062 C 6.0869576238 0.2024044961 3.2767702726 H 7.1656650647 0.1287762497 3.2458650647 H 4.5457621618 2.2425310766 0.3253979653 H 0.5159777859 0.7478905868 0.5487661007 H 1.5420526570 0.8143939718 0.5935463196 H 0.5302278747 0.5823989653 0.4084507634 O 1.4575846656 0.5996887308 2.4093500287 H 0.5990015339 0.8842421241 2.0047830456 $end