Formation and relaxation of excited states in solution: A new time dependent polarizable continuum model based on time dependent density functional theory

Abstract

Articles you may be interested inAnalytical second derivatives of excited-state energy within the time-dependent density functional theory coupled with a conductor-like polarizable continuum model J. Chem. Phys. 138, 024101 (2013) In this paper a novel approach to study the formation and relaxation of excited states in solution is presented within the integral equation formalism version of the polarizable continuum model. Such an approach uses the excited state relaxed density matrix to correct the time dependent density functional theory excitation energies and it introduces a state-specific solvent response, which can be further generalized within a time dependent formalism. This generalization is based on the use of a complex dielectric permittivity as a function of the frequency, ˆ͑ ͒. The approach is here presented in its theoretical formulation and applied to the various steps involved in the formation and relaxation of electronic excited states in solvated molecules. In particular, vertical excitations ͑and emissions͒, as well as time dependent Stokes shift and complete relaxation from vertical excited states back to ground state, can be obtained as different applications of the same theory. Numerical results on two molecular systems are reported to better illustrate the features of the model.

How Method-Dependent Are Calculated Differences between Vertical, Adiabatic, and 0–0 Excitation Energies?

“…Furthermore, for most of the current excited states, expanding the basis set from double-ζ to triple-ζ quality, or including diffuse basis functions, has a marginal effect on the excitation energies obtained with TD-DFT. 29 Second, excited-state geometries were optimized using analytic TD-DFT [45][46][47] and CC2 43 excited-state gradients. Then, adiabatic excitation energies were obtained as electronic energy differences between ground and excited states at their respective equilibrium geometries, to which were subsequently added ZPVE corrections derived from ground and excited-state frequency calculations at optimized ground and excitedstate structures, respectively.…”

“…Although much more expensive than ground-state geometry optimizations, such calculations are today feasible for many excited-state methods, including TD-DFT. [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] Adding a further dimension to efforts along those lines and of relevance for determining which type of transition (vertical or adiabatic) best corresponds to experimental absorption maxima, are simulations of vibrationally resolved electronic absorption spectra reported by a number of research groups. [49][50][51][52][53] Such simulations require computation of vibrational wavefunctions and their overlap (Franck-Condon factors), and may also include a dependence of the electronic dipole moment operator on nuclear coordinates (Herzberg-Teller corrections).…”

Equation of motion for the solvent polarization apparent charges in the polarizable continuum model: Application to time-dependent CI

“…[39][40][41] In particular, we need here a definition of nonequilibrium free energy, G neq , suitable for a time-dependent solvation. Such free energy has been defined by Caricato et al 11 By reformulating G neq with the quantities and nomenclature of the present work we obtain:…”

“…11, is the molecular potential that would produce the charges q(t) via the solvent static response. The dependence of charges and potentials on the coefficients of the CIS expansion is not shown explicitly in this section for the sake of clarity.…”

“…This approach was based on the definition of equations of motion (EOM) 8 for the time-dependent apparent charges that in PCM generate the time-dependent reaction field. [9][10][11] Alternative approaches to study real-time solute electron dynamics within the PCM have also been devised and applied. [12][13][14][15] In our previous work, the evolution of the electrons of the molecule was described by a real-time time-dependent density functional theory (RT-TDDFT) approach.…”