Polarizable continuum model excited electronic states

QM/MM approaches where the solute is QM and the solvent MM are in principle useful for computing the effect of the slow reaction field (represented by the solute point charges) but require a polarizable solvent model if electronic equilibration to the excited state is to be included (Gao 1994). With an MM solvent shell, it is no more possible to compute differential dispersion effects directly than for a continuum model. An option is to make the first solvent shell QM too, but computational costs for MC or MD simulations quickly expand with such a model. Large QM simulations with explicit solvent have appeared using the fast semiempirical INDO/S model to evaluate solvatochromic effects, and the results have been promising (Coutinho, Canute, and Zemer 1997 Coutinho and Canute 2003). Such simulations offer the potential to model solvent broadening accurately, since they can compute absorptions for an ensemble of solvent configurations. 

Abstract The computational study of excited states of molecular systems in the condensed phase implies additional complications with respect to analogous studies on isolated molecules. Some of them can be faced by a computational modeling based on a continuum (i.e., implicit) description of the solvent. Among this class of methods, the polarizable continuum model (PCM) has widely been used in its basic formulation to study ground state properties of molecular solutes. The consideration of molecular properties of excited states has led to the elaboration of numerous additional features not present in the PCM basic version. Nonequilibrium effects, state-specific versus linear response quantum mechanical description, analytical gradients, and electronic coupling between solvated chromophores are reviewed in the present contribution. The presentation of some selected computational results shows the potentialities of the approach. 

R. Cammi, B. Mennucci, Structure and properties of molecular solutes in electronic excited states A polarizable continuum model approach based on the time-dependent density functional theory, in Radiation Induced Molecular Phenomena in Nucleic Acids A Comprehensive Theoretical and Experimental Analysis, ed. by M.K. Shukla, J. Leszczynski. Series Challenges and Advances in Computational Chemistry and Physics, vol 5 (Springer, Netherlands 2008)... 

S. Comi, R. Cammi, B. Mennucci, J. Tomasi, Electronic excitation energies of molecules in solution within continuum solvation models Investigating the discrepancy between state-specific and linear-response methods, Formation and relaxation of excited states in solution A new time dependent polarizable continuum model based on time dependent density functional theory. J. Chem. Phys. 123, 134512 (2005)... 

Complementing the results obtained for the study of ground electronic states in solution, many computational studies indicate that approaches exploiting continuum solvation models are very effective tools for evaluating the solvent effect on the excited-state properties. Among continuum models, the polarizable continuum model (PCM) is probably the one most commonly used. In the following, we thus focus mainly on this method [78, 82]. 

In the present example, the electronic QM computations have been performed with the DFT/N07D model while the effect of the methanol solvent has been included by means of the polarizable continuum model, where the solvent is represented by a homogeneous dielectric polarized by the solute, placed within a cavity built as an envelope of spheres centered on the solute atoms [ 154] (see Chapter 1 for details). The solvent has been described in the nonequilibrium hmit where only its fast (electronic) degrees of freedom are equilibrated with the excited-state charge density while the slow (nuclear) degrees of freedom remain equilibrated with the ground state. This assumption is well suited to describe the broad features of the absorption spectrum in solution due to the different time scales of the electronic and nuclear response components of the solvent reaction field [89]. 

The problem of the description of the excited states within the Polarizable Continuum Model leads to two non-equivalent approaches, the approach based on the linear response (LR) approach, and the state specific (SS) approach, as already said in the Introduction. Each approach has advantages and disadvantages. The LR approach is computationally more convenient, as it gives the whole spectrum of the excited states of interest in a single calculation, but is physically biased. In fact, in the LR approach the solute-solvent interaction contains a term related to the one-particle transition densities of the solute connecting the reference state adopted in the LR calculation, which usually corresponds to the electronic groimd state, to the excited electronic state. The SS approach is computationally more expensive, as it requires a separate calculation for each of the excited states of interest, but is physically im-biased. In fact, in the SS approach the solute-solvent interaction is determined by the effective one-particle electron density of the excited state. 

We have presented a short review of very recent progresses toward the description at the coupled-cluster level of the electronic structure and properties of molecular solutes with the Polarizable Continuum Model framework (Cammi 2009). Specifically, we have presented (1) the detailed expression for the evaluation of the analytical gradients for the PCM-CC theory at the single and double excitation level, for the ground states (2) the expression of the analytical gradients for the PCM-EOM-CC theory at the single and double excitation level for the descriptions of the excited state properties of molecular solute. 

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