Solvent-Induced Frequency Shifts: Configuration Interaction Singles Combined with the Effective Fragment Potential Method

Abstract

The simplest variational method for treating electronic excited states, configuration interaction with single excitations (CIS), has been interfaced with the effective fragment potential (EFP) method to provide an effective and computationally efficient approach for studying the qualitative effects of solvents on the electronic spectra of molecules. Three different approaches for interfacing a non-self-consistent field (SCF) excited-state quantum mechanics (QM) method and the EFP method are discussed. The most sophisticated and complex approach (termed fully self consistent) calculates the excited-state electron density with fully self-consistent accounting for the polarization (induction) energy of effective fragments. The simplest approach (method 1) includes a strategy that indirectly adds the EFP perturbation to the CIS wave function and energy via modified Hartree−Fock molecular orbitals, so that there is no direct EFP interaction with the excited-state density. An intermediate approach (method 2) accomplishes the latter in a noniterative perturbative manner. Theoretical descriptions of the three approaches are presented, and test results of solvent-induced shifts using methods 1 and 2 are compared with fully ab initio values. These comparisons illustrate that, at least for the test cases examined here, modification of the ground-state Hartree−Fock orbitals is the largest and most important factor in the calculated solvent-induced shifts. Method 1 is then employed to study the aqueous solvation of coumarin 151 and compared with experimental measurements. PO Box 2206, Germantown, Maryland 20875 ReceiVed: February 27, 2010 ReVised Manuscript ReceiVed: May 20, 2010 The simplest variational method for treating electronic excited states, configuration interaction with single excitations (CIS), has been interfaced with the effective fragment potential (EFP) method to provide an effective and computationally efficient approach for studying the qualitative effects of solvents on the electronic spectra of molecules. Three different approaches for interfacing a non-self-consistent field (SCF) excited-state quantum mechanics (QM) method and the EFP method are discussed. The most sophisticated and complex approach (termed fully self consistent) calculates the excited-state electron density with fully self-consistent accounting for the polarization (induction) energy of effective fragments. The simplest approach (method 1) includes a strategy that indirectly adds the EFP perturbation to the CIS wave function and energy via modified Hartree-Fock molecular orbitals, so that there is no direct EFP interaction with the excited-state density. An intermediate approach (method 2) accomplishes the latter in a noniterative perturbative manner. Theoretical descriptions of the three approaches are presented, and test results of solvent-induced shifts using methods 1 and 2 are compared with fully ab initio values. These comparisons illustrate that, at least for the test cases examined here, modification of the groun...

Modeling Solvent Effects on Electronic Excited States

“…One can include this interaction perturbatively. In this case (called "method 2" in ref 35), the one-electron density of the excited state is calculated and used to repolarize the environment, that is, to obtain the EFPinduced dipoles and polarization energy corresponding to this density. This perturbative correction is called the "direct" polarization contribution to the electronic energy of the excited state.…”

Solvent-Induced Shifts in Electronic Spectra of Uracil

“…In a previous paper, 32 three approaches for interfacing the polarization interaction with a QM method were discussed. The most rigorous approach, termed "fully self-consistent," involves iterating the polarization interaction to self-consistency within the solution to the QM problem.…”

“…However, for QM methods that do not involve an explicit (iterative) orbital optimization step [e.g., CI, secondorder perturbation theory (MP2), and coupled cluster theory (CC)], implementing a fully self-consistent procedure becomes more complicated and time-consuming. An alternative, called method 1, 32 performs the fully self-consistent approach for the zeroth-order wave function (e.g., HF, DFT, MCSCF) and assumes that most of the polarization effects have been captured. Dynamic correlation (via MP2, CC, or MRMP2, for example) is then added in the field of the polarized zeroth-order solution.…”

“…32 Nonetheless, it is useful to implement the fully self-consistent method, in order to develop a detailed analysis of the change in solventÀsolute interactions. Such an analysis is developed in this section.…”

Implementation of the analytic energy gradient for the combined time-dependent density functional theory/effective fragment potential method: Application to excited-state molecular dynamics simulations

“…First, the TDDFT/EFP1 energy formulation is extended on the basis of the matrix formulation for the EFP1 polarization energy and derivative as given by Li et al 30 This is a more general approach than that presented in Ref. 28, and is closely related to the configuration interaction formulation presented by Arora et al 31 and by DeFusco et al 32 Second, the formulation of TDDFT/EFP1 analytic energy gradients is presented. The EFP1 contribution to the gas-phase TDDFT analytic gradient that was derived by Furche and Ahlrichs 8 is examined based on the new TDDFT/EFP1 excitation energy formula.…”