7.3 Time-Dependent Density Functional Theory (TDDFT)

7.3.4 TDDFT Coupled with C-PCM for Excitation Energies and Properties Calculations

As described in Section 12.2 (and especially Section 12.2.2), continuum solvent models such as C-PCM allow one to include solvent effect in the calculations. TDDFT/C-PCM allows excited-state modeling in solution. Q-Chem also features TDDFT coupled with C-PCM which extends TDDFT to calculations of properties of electronically-excited molecules in solution. In particular, TDDFT/C-PCM allows one to perform geometry optimization and vibrational analysis.581

When TDDFT/C-PCM is applied to calculate vertical excitation energies, the solvent around vertically excited solute is out of equilibrium. While the solvent electron density equilibrates fast to the density of the solute (electronic response), the relaxation of nuclear degrees of freedom (e.g., orientational polarization) takes place on a slower timescale. To describe this situation, an optical dielectric constant is employed. To distinguish between equilibrium and non-equilibrium calculations, two dielectric constants are used in these calculations: a static constant (ε0), equal to the equilibrium bulk value, and a fast constant (εfast) related to the response of the medium to high frequency perturbations. For vertical excitation energy calculations (corresponding to the unrelaxed solvent nuclear degrees of freedom), it is recommended to use the optical dielectric constant for εfast), whereas for the geometry optimization and vibrational frequency calculations, the static dielectric constant should be used.581

The example below illustrates TDDFT/C-PCM calculations of vertical excitation energies. More information concerning the C-PCM and the various PCM job control options can be found in Section 12.2.

Example 7.6  TDDFT/C-PCM low-lying vertical excitation energy

$molecule
   0 1
   C    0.0   0.0   0.0
   O    0.0   0.0   1.21
$end

$rem
   EXCHANGE         B3lyp
   CIS_N_ROOTS      10
   CIS_SINGLETS     true
   CIS_TRIPLETS     true
   RPA              TRUE
   BASIS            6-31+G*
   XC_GRID          1
   SOLVENT_METHOD   pcm
$end

$pcm
   Theory   CPCM
   Method   SWIG
   Solver   Inversion
   Radii    Bondi
$end

$solvent
   Dielectric         78.39
   OpticalDielectric  1.777849
$end