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## 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=10

yielding, 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).
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).

Next: 17.7 Random-phase approximation Up: 17 THE DENSITY FUNCTIONAL Previous: 17.5 Empirical damped dispersion   Contents   Index

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molpro@molpro.net 2018-08-16