17.6 Time-dependent density functional theory

The time-dependent density functional linear response theory program can be used to calculate excitation energies or response properties for molecules. The program currently has the following restrictions:

- No point-group symmetry can be used in TDDFT.
- The program only works in conjunction with density-fitting of electron repulsion integrals, i.e., the user must supply an auxiliary basis set, see section 15 for details.
- Currently the exchange-correlation kernel is approximated by the adiabatic local density approximation (ALDA).
- In case of the calculation of excitation energies using hybrid-DFT functionals the reduced hessian matrix is approximated by the hermitian matrix , i.e., it is assumed that and commute. This works well for small systems/basis sets, but the excitation energies may deviate more strongly from the eigenvalues of the full hessian in case of larger systems/basis sets.

A typical input for calculating the ten lowest excitation energies is given by:

ks,<func>; save,2100.2 df-tddft,orb=2100.2,nexcit=10yielding, e.g., the following output:

n eig oscill.stren. eig (eV) 1 0.15429481 0.00000361 4.19857508 12-> 13 0.999706 0.14361479 11-> 14 0.000034 0.35333048 10-> 20 0.000027 0.58330205 10-> 16 0.000016 0.43005338 n eig oscill.stren. eig (eV) 2 0.24134275 0.10469512 6.56727008 ...As shown by the above snippet, the output will contain the excitation energies, oscillator strengths and the four most important orbital contributions to the respective transition. The latter is characterised by the orbital index pairs (

`<occ> -> <virt>`

), the
coefficient of this index pair in the eigenvector, and the orbital
energy differences contained in the last column showing the uncoupled
excitation energy for comparison.
For the calculation of frequency-dependent dipole-dipole polarisabilities use, e.g.:

ks,<func>; save,2100.2 df-tddft,orb=2100.2,pert='DMX',pert='DMY',pert='DMZ',om=[0.0,1.0]which calculates and its cartesian components at the frequencies (static response) and . Response property calculations are possible for all properties described in section 6.13.

The following list summarises the possible options to TDDFT:

`ORB`- Record for input orbitals (required).
`AUXBAS`- Auxiliary basis set (default: '
`MP2FIT`

') `FEXX`- Factor for nonlocal exchange.
`FXC`- Factor for local exchange-correlation.
`FU`- Factor for Coulomb kernel contribution (default: 1).
`MAXIT`- Maximum number of iterations in Davidson and conjugate-gradient solver.
`NEXCIT`- Number of excitation energies requested (default: 0).
`DAV`- Switches (1,2) between two different Davidson eigensolvers (default: 2).
`OM`- Real frequencies for which the linear response is
calculated, example:
`OM=[0.0,1.0,2.0]`

calculates the response at , and . `OMI`- Imaginary frequencies for which the linear response is calculated.
`PERT`- Perturbations for which the linear response is
calculated, example:
`PERT='DMX',PERT='DMY',PERT='DMZ'`

calculates the dipole-dipole polarisabilities for the three cartesian components (see section 6.13 for available properties). `TOLDAV`- Convergence tolerance used in the Davidson eigensolver.
`THRCG`- Convergence tolerance used in the conjugate-gradient solver.
`NSUBMAX`- Maximum subspace used in Davidson eigensolver
(default:
`10*NEXCIT`

) `TRIP`- Set to '1' for triplet excitation energies (default: 0).
`C6`- Set to '1' for calculating C dispersion coefficients (default: 0).
`NQUAD`- Number of quadrature points used in the calculation of dispersion coefficients.
`FXCFIT`- Set to '1' for approximating the exchange-correlation kernel matrix with density-fitting (default: 0).
`DENTHR`- Threshold for density in the calculation of the exchange-correlation kernel matrix on the auxiliary basis set (default: 1d-7).
`FULL`- Set to '1' for a full diagonalisation of the hessian matrix (experimental).
`CRITC`- Convergence threshold for the coefficients of the last added basis vector in the 2nd Davidson eigensolver (default: 1d-7).
`CRITR`- Convergence threshold for residual vector norms in the 2nd Davidson eigensolver (default: 1d-7).
`ORTHO`- The threshold over which loss of orthogonality is assumed in the 2nd Davidson eigensolver (default: 1d-8).
`NDUMP`- Number of excitation vectors (transformed to AO basis) written to file (default: 0).
`DUMP`- Record for dump of excitation vectors (default: 5000.2).

molpro@molpro.net 2019-07-16