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

As described in Section 11.2 (and especially Section 11.2.2), 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.Liu:2013

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 ($\varepsilon_{0}$), equal to the equilibrium bulk value, and a fast constant ($\varepsilon_{fast}$) 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 $\varepsilon_{fast}$), whereas for the geometry optimization and vibrational frequency calculations, the static dielectric constant should be used.Liu:2013

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 11.2.

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