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7.3 Time-Dependent Density Functional Theory (TDDFT)

7.3.4 Job Control for TDDFT

(September 1, 2024)

7.3.4.1 Basic Settings

Input for time-dependent density functional theory calculations follows very closely the input already described for the uncorrelated excited state methods described in the previous section (in particular, see Section 7.2.4). There are several points to be aware of:

  • The exchange and correlation functionals are specified exactly as for a ground state DFT calculation, through EXCHANGE and CORRELATION. To active TDDFT, set CIS_N_ROOTS to a value 1, specifying the number of excited states to compute.

  • If RPA is set to TRUE, a “full” TDDFT calculation will be performed, however the default value is RPA = FALSE, which invokes the TDA, 542 Hirata S., Head-Gordon M.
    Chem. Phys. Lett.
    (1999), 314, pp. 291.
    Link
    in which the de-excitation amplitudes 𝐲 in Eq. (7.15) are neglected, which is usually a good approximation for excitation energies, although oscillator strengths within the TDA no longer formally satisfy the Thomas-Reiche-Kuhn sum rule. For RPA = TRUE, a TDA calculation is performed first and used as the initial guess for the full TDDFT calculation. The TDA calculation can be skipped altogether using RPA = 2. RPA is not implemented for restricted open-shell calculations, only TDA.

  • If SPIN_FLIP is set to TRUE when performing a TDDFT calculation, a SF-TDDFT calculation will also be performed. At present, SF-TDDFT is only implemented within the TDA so RPA must be set to FALSE. Remember to set the spin multiplicity to 3 for systems with an even-number of electrons (e.g., diradicals), and 4 for odd-number electron systems (e.g., triradicals).

  • If MGGA_GINV is set to 1 when performing a TDDFT calculation, gauge invariance correction will be added to meta-GGA functionals. 77 Bates J. E., Furche F.
    J. Chem. Phys.
    (2012), 137, pp. 164105.
    Link

Some basic job control variables (to be added to the $rem section) are described below. There are additional options for X-ray spectroscopy; see Section 7.13.2.

CIS_SINGLETS

CIS_SINGLETS
       Controls whether to compute singlet excited states.
TYPE:
       LOGICAL
DEFAULT:
       TRUE
OPTIONS:
       FALSE Do not compute singlet excitations. TRUE Compute singlet excitations.
RECOMMENDATION:
       This option makes sense only for a singlet ground state, since the use of an open-shell ground state does not afford spin-pure excited states.

CIS_TRIPLETS

CIS_TRIPLETS
       Controls whether to compute triplet excited states.
TYPE:
       LOGICAL
DEFAULT:
       TRUE
OPTIONS:
       FALSE Do not compute triplet excitations. TRUE Compute triplet excitations.
RECOMMENDATION:
       This option makes sense only for a singlet ground state, since the use of an open-shell ground state does not afford spin-pure excited states.

MGGA_GINV

MGGA_GINV
       Controls whether to add gauge invariance correction to meta-GGA functionals.
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 No correction. 1 Add gauge invariance correction to meta-GGA functionals.
RECOMMENDATION:
       Not recommended when TDA is used because the TDA violates gauge invariance.

SPATIAL_OVERLAP_ANAL

SPATIAL_OVERLAP_ANAL
       Controls whether to compute the Λ charge-separation metric.
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 Do not compute Λ. 1 Compute Λ for each excited state using Eq (7.16). 2 Compute Λ for each excited state using O~ia instead of Oia.
RECOMMENDATION:
       Request if desired. (There is some overhead associated with computing Λ, but it should be quite small.) The metric obtained with option 1 (using Oia not O~ia) is the one originally suggested by Peach et al.. 983 Peach M. J. G. et al.
J. Chem. Phys.
(2008), 128, pp. 044118.
Link

SPATIAL_OVERLAP_GRID

SPATIAL_OVERLAP_GRID
       Controls the grid that is used to evaluate Oia or O~ia in Eq. (7.17).
TYPE:
       INTEGER
DEFAULT:
       1
OPTIONS:
       1 Use a EML grid with Nr=300 and NΩ=302. 2 Use a EML grid with Nr=400 and NΩ=434.
RECOMMENDATION:
       None.

SPATIAL_OVERLAP_PRINT

SPATIAL_OVERLAP_PRINT
       Controls whether to print the spatial overlaps Oia or O~ia.
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 Do not print the Oia. 1 Print the frontier overlaps only (5 occupied and 5 virtual orbitals. 2 Print all of the Oia.
RECOMMENDATION:
       These may be useful for a posteriori analysis of the spatial proximity of various MOs; however, option 2 will engender significant printing for large molecules. Whether it is Oia [Eq. (7.17)] or O~ia [Eq. (7.18)] that is printed depends upon the setting of SPATIAL_OVERLAP_ANAL.

WANG_ZIEGLER_KERNEL

WANG_ZIEGLER_KERNEL
       Controls whether to use the Wang-Ziegler non-collinear exchange-correlation kernel in a SF-TDDFT calculation. Set NEW_DFT = TRUE if using a Q-Chem version older than 5.0.
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       FALSE Do not use non-collinear kernel. TRUE Use non-collinear kernel.
RECOMMENDATION:
       None

CIS_GUESS_TYPE

CIS_GUESS_TYPE
       Controls how to generate the initial guess excitation vectors in CIS/TDA/RPA calculations.
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 Generate N (no. of roots requested) occupied virtual single orbital transitions according to their orbital energy difference order (from low to high). This is the common scenario. 1 Generate N-1 occupied virtual single orbital transitions according to their orbital energy difference order (from low to high), and generate another guess excitation vector consist of all the remaining single orbital transitions in the occupied virtual transition space with equal weights. 2 Generate N occupied/virtual single orbital transitions according to their orbital energy difference order (from low to high), and generate one more guess excitation vector consist of all the remaining single orbital transitions in the occupied virtual transition space with equal weights.
RECOMMENDATION:
       The default setting should work for most of the cases. However, when the number of roots is small, in some CIS/TDA/RPA calculations, low energy excited states could be missing. The options CIS_GUESS_TYPE = 1 or 2 may remedy this root missing issue by sampling more vectors in the transition space. Setting CIS_GUESS_TYPE = 1 or 2 may take more cycles to converge in the Davidson iteration, but the results are expected to be more reliable. Currently, CIS_GUESS_TYPE = 1 or 2 are not supported in SF-XCIS calculations. Setting TRNSS = TRUE also disables the setting of CIS_GUESS_TYPE.

7.3.4.2 Options for a Truncated Subspace

The following options can be used to implement the reduced excitation space that was described in Section 7.3.2.

CISTR_PRINT

CISTR_PRINT
       Controls level of output.
TYPE:
       LOGICAL
DEFAULT:
       FALSE Minimal output.
OPTIONS:
       TRUE Increase output level.
RECOMMENDATION:
       None

CUTOCC

CUTOCC
       Specifies occupied orbital cutoff.
TYPE:
       INTEGER
DEFAULT:
       50
OPTIONS:
       0-200 Use a cutoff of CUTOCC/100
RECOMMENDATION:
       None

CUTVIR

CUTVIR
       Specifies virtual orbital cutoff.
TYPE:
       INTEGER
DEFAULT:
       0 No truncation
OPTIONS:
       0-100 CUTOFF = CUTVIR/100
RECOMMENDATION:
       None

N_SOL

N_SOL
       Specifies number of atoms or orbitals in the $solute or $alist section.
TYPE:
       INTEGER
DEFAULT:
       No default.
OPTIONS:
       User defined.
RECOMMENDATION:
       Reads from either the $solute or $alist input section.

TRNSS

TRNSS
       Controls whether reduced single excitation space is used.
TYPE:
       LOGICAL
DEFAULT:
       FALSE Use full excitation space.
OPTIONS:
       TRUE Use reduced excitation space.
RECOMMENDATION:
       None

TRTYPE

TRTYPE
       Controls how reduced subspace is specified.
TYPE:
       INTEGER
DEFAULT:
       1
OPTIONS:
       1 Select orbitals localized on a set of atoms. 2 Specify a set of orbitals. 3 Specify a set of occupied orbitals, include excitations to all virtual orbitals.
RECOMMENDATION:
       None

7.3.4.3 Job Control for EA-TDDFT

Like NOCIS/STEX/1C-NOCIS, the options for the EA-TDDFT/EA-CIS method are controlled via the $nocis section after NOCIS is set to TRUE in $rem.

NOCIS

NOCIS
       Requests a NOCIS/STEX/1C-NOCIS/EA-TDDFT calculation.
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       FALSE Do not run these methods. TRUE Run one of these methods, options controlled in $nocis.
RECOMMENDATION:
       None

The options below are set within the $nocis section.

NUM_REF
       Sets the number of reference orbitals in a NOCIS/STEX/1C-NOCIS/EA-TDDFT calculation.
INPUT SECTION: $nocis
TYPE:
       INTEGER
DEFAULT:
       NONE
OPTIONS:
       n Positive integer
RECOMMENDATION:
       Set according to the number of consecutive orbitals of interest for the calculation. For example, for the oxygen K-edge in CO2, the number of references would be 2 (two oxygen 1s orbitals), whereas for the carbon K-edge it would be 1 (one carbon 1s).

ORB_OFFSET
       Determines the starting orbital for a NOCIS/STEX/1C-NOCIS/EA-TDDFT calculation.
INPUT SECTION: $nocis
TYPE:
       INTEGER
DEFAULT:
       NONE
OPTIONS:
       n Positive integer
RECOMMENDATION:
       Set according to the first orbital of interest in the system in question. For example, this would be set to 0 for the oxygen K-edge in CO2 because the two O(1s) orbitals lie below the C(1s), so for the carbon K-edge this would be set to 2.

LOCALIZE_ORBITALS
       Choose which core orbitals to localize with the Boys objective function.
INPUT SECTION: $nocis
TYPE:
       INTEGER
DEFAULT:
       -1 for NUM_REF = 1 and equal to NUM_REF otherwise.
OPTIONS:
       n Integer, normally positive.
RECOMMENDATION:
       Set to -1 to skip Boys localization entirely, or set to a value greater than NUM_REF to include more orbitals in the preliminary localization, otherwise use the default.

SUBSYSTEM_ATOMS
       Choose which atoms to consider for an EA-TDDFT calculation.
INPUT SECTION: $nocis
TYPE:
       INTEGER
DEFAULT:
       NONE
OPTIONS:
       List of integers delimited by spaces: ijk
RECOMMENDATION:
       Use only if excitations out of a particular subset of atoms is of interest and the definition of ORB_OFFSET and NUM_REF is nontrivial. This is an expert option, and should only be used in specific situations such as isolating the oxygen K-edge of all water molecules at the air/water interface.

DSCF_ALGORITHM
       Sets the ΔSCF algorithm to be used in the optimization of the core-ionized reference determinants.
INPUT SECTION: $nocis
TYPE:
       STRING
DEFAULT:
       MOM
OPTIONS:
       MOM, IMOM, STEP, or STEP_MOM
RECOMMENDATION:
       Use MOM unless convergence issues arise. IMOM occasionally provides improved convergence, but the combination of STEP and MOM used by the STEP_MOM option is particularly robust. In rare cases, STEP may be necessary, but this is not recommended as the number of SCF cycles required is quite large. If STEP_MOM is requested, the option STEP_MOM_START must also be set.

STEP_MOM_START
       Sets the SCF cycle on which the STEP algorithm stops and the MOM algorithm starts.
INPUT SECTION: $nocis
TYPE:
       INTEGER
DEFAULT:
       5
OPTIONS:
       n Positive integer.
RECOMMENDATION:
       For best results, set such that STEP reaches a convergence threshold of at least 10-4 a.u. before switching to MOM, but if MOM continues to collapse or oscillate, then wait until tighter convergence is achieved to switch algorithms.

REF_SCF_ALGORITHM
       Sets the SCF algorithm for the core-ion reference calculations.
INPUT SECTION: $nocis
TYPE:
       STRING
DEFAULT:
       DIIS
OPTIONS:
       DIIS, GDM, GDM_LS, SGM, or SGM_LS
RECOMMENDATION:
       Use DIIS for MOM, IMOM, STEP, or STEP_MOM calculations, but if these algorithms are not providing satisfactory convergence to the desired core-ion state, this can be set to SGM or SGM_LS.

REF_SCF_CONVERGENCE
       Sets SCF convergence threshold for the core-ion reference calculations.
INPUT SECTION: $nocis
TYPE:
       INTEGER
DEFAULT:
       Same as SCF_CONVERGENCE in $rem
OPTIONS:
       n Positive integer
RECOMMENDATION:
       None

REF_SCF_GUESS
       Initial guess for core-ion reference calculations.
INPUT SECTION: $nocis
TYPE:
       STRING
DEFAULT:
       Koopman
OPTIONS:
       Read (the Koopmans guess is automatically used if no option is specified)
RECOMMENDATION:
       The default core-ion guess is generated by removing an electron from the core orbital using the ground-state MO coefficients (Koopmans guess). Alternatively, when convergence issues arise it may be useful to run an EA-TDDFT job with a different functional (i.e., LDA or GGA), then read the converged core-ion orbitals into a subsequent EA-TDDFT job with the functional of interest (i.e., a range-separated hybrid).

EA_TDA
       Invokes EA-TDDFT within the Tamm-Dancoff approximation.
INPUT SECTION: $nocis
TYPE:
       NONE
DEFAULT:
       NONE
OPTIONS:
       The presence of this keyword will activate EA_TDA.
RECOMMENDATION:
       This is the most cost-effective form of the EA-TDDFT equations and has almost no effect on results for K-edge XAS.

EA_RPA
       Solves the full EA-TDDFT equations.
INPUT SECTION: $nocis
TYPE:
       NONE
DEFAULT:
       NONE
OPTIONS:
       The presence of this keyword will activate EA_RPA.
RECOMMENDATION:
       No recommendation.

SINGLETS
       Compute only singlets.
INPUT SECTION: $nocis
TYPE:
       NONE
DEFAULT:
       NONE
OPTIONS:
       The presence of this keyword without the Triplets keyword will compute singlets without computing triplets.
RECOMMENDATION:
       No recommendation.

TRIPLETS
       Compute only triplets.
INPUT SECTION: $nocis
TYPE:
       NONE
DEFAULT:
       NONE
OPTIONS:
       The presence of this keyword without the Singlets keyword will compute triplets without computing singlets.
RECOMMENDATION:
       No recommendation.

N_ROOTS
       Sets the number of roots to print.
INPUT SECTION: $nocis
TYPE:
       INTEGER
DEFAULT:
       All
OPTIONS:
       n where n<mroots
RECOMMENDATION:
       No recommendation. Beware that unlike CIS/TDDFT jobs this keyword only prints fewer roots, but the entirety of the Hamiltonian is still diagonalized via direct diagonalization.

PRINT_NTOS
       Prints natural transition orbitals to cube files for each root that is printed via the N_ROOTS keyword.
INPUT SECTION: $nocis
TYPE:
       NONE
DEFAULT:
       NONE
OPTIONS:
       The presence of this keyword automatically generates all NTOs (default), or N_ROOTS NTOs.
RECOMMENDATION:
       No recommendation, but one should be sure to also include a $plots section with appropriate details such that the cube files can be generated.

Example 7.7  EA-TDDFT with Tamm-Dancoff approximation for the K-edge of NH3. This job truncates the number of printed (singlet) roots to 10. The core-ion SCF will use the SGM algorithm.

$rem
method          rCAM-B3LYP
rel_x2c         true
basis           aug-cc-pCVDZ
nocis           true
scf_convergence 8
thresh          14
integral_symmetry    false
point_group_symmetry false
$end

$nocis
n_roots         10
orb_offset      0
num_ref         1
singlets
ea_tda
ref_scf_algorithm sgm
$end

$molecule
0 1
N   0.0000   0.0000   0.1163
H   0.0000   0.9399  -0.2713
H   0.8140  -0.4700  -0.2713
H  -0.8140  -0.4700  -0.2713
$end

Example 7.8  Full EA-TDDFT for the K-edge of NH3. The core-ion SCF will use the default MOM algorithm.

$rem
method          rCAM-B3LYP
rel_x2c         true
scf_convergence 8
basis           aug-cc-pCVDZ
nocis           true
thresh          14
integral_symmetry    false
point_group_symmetry false
$end

$nocis
n_roots         10
orb_offset      0
num_ref         1
singlets
ea_rpa
$end

$molecule
0 1
N   0.0000   0.0000   0.1163
H   0.0000   0.9399  -0.2713
H   0.8140  -0.4700  -0.2713
H  -0.8140  -0.4700  -0.2713
$end