Nonequilibrium solvation excited states

Time-resolved fluorescence spectroscopy of polar fluorescent probes that have a dipole moment that depends upon electronic state has recently been used extensively to study microscopic solvation dynamics of a broad range of solvents. Section II of this paper deals with the subject in detail. The basic concept is outlined in Figure 1, which shows the dependence of the nonequilibrium free energies (Fg and Fe) of solvated ground state and electronically excited probes, respecitvely, as a function of a generalized solvent coordinate. Optical excitation (vertical) of an equilibrated ground state probe produces a nonequilibrium configuration of the solvent about the excited state of the probe. Subsequent relaxation is accompanied by a time-dependent fluorescence spectral shift toward lower frequencies, which can be monitored and analyzed to quantify the dynamics of solvation via the empirical solvation dynamics function C(t), which is defined by Eq. (1). 

The physicochemical stage includes the chemical processes in electron excitation states, as well as the chemical transformations of the active intermediates under nonequilibrium conditions. These are the predissociation and the ion-molecular reactions that take about 1013 s the recombination of positive ions with thermalized electrons (1CT12-10 10s) and the electron-solvation reactions (10 12-10-1° s). Thus, the physicochemical stage lasts from 1CT13 to 10-I0s. 

B. Mennucci, R. Cammi and J. Tomasi, Excited states and solvatochromic shifts within a nonequilibrium solvation approach A new formulation of the integral equation formalism method at the self-consistent field, configuration interaction, and multiconfiguration self-consistent field level, J. Chem. Phys., 109 (1998) 2798. 

In recent years many attempts have been made to extend the implicit solvent models to the description of time-dependent phenomena. One of these phenomena is nonequilibrium solvation [3] and it can be described effectively in a very simplified way, despite the fact that it actually depends on the details of the full frequency spectrum of the dielectric constant. Typical examples of nonequilibrium solvation are the absorption of light by the solute which produces an excited state which is no longer in equilibrium with the surrounding polarization of the medium [11-13], Another example is intermolecular charge transfer within the solute, also leading to a nonequilibrium polarization [14],... 

R. Cammi and J. Tomasi, Nonequilibrium solvation theory for the polarizable continuum model - a new formulation at the SCF level with application to the case of the frequency-dependent linear electric-response function, Int. J. Quantum Chem., (1995) 465-74 B. Mennucci, R. Cammi and J. Tomasi, Excited states and solvatochromic shifts within a nonequilibrium solvation approach A new formulation of the integral equation formalism method at the self-consistent field, configuration interaction, and multiconfiguration self-consistent field level, J. Chem. Phys., 109 (1998) 2798-807 R. Cammi, L. Frediani, B. Mennucci, J. Tomasi, K. Ruud and K. V. Mikkelsen, A second-order, quadratically... 

The outline of the remainder of this contribution is as follows. In Section 3.7.2, we discuss radical anion dissociation in solution, in which a conical intersection has an important impact on the ground state reaction barrier, rate constant and reaction path, all of which are also influenced by nonequilibrium solvation. The excited electronic state conical intersection problem for the cis-trans isomerization of a model protonated Schiff base in solution is discussed in Section 3.7.3, focusing on the approach to, and passage through, the conical intersection, and the influence of nonequilibrium solvation thereupon. Some concluding remarks are offered in Section 3.7.4. We make no attempt to give a complete discussion for these topics, but rather focus solely on several highlights. Similarly, the references herein are certainly incomplete. We refer the interested reader to refs [1-9] for much more extensive discussions and references. 

We have already mentioned in the Introduction (Section 3.7.1) the importance of conical intersections (CIs) in connection with excited electronic state dynamics of a photoexcited chromophore. Briefly, CIs act as photochemical funnels in the passage from the first excited S, state to the ground electronic state S0, allowing often ultrafast transition dynamics for this process. (They can also be involved in transitions between excited electronic states, not discussed here.) While most theoretical studies have focused on CIs for a chromophore in the gas phase (for a representative selection, see refs [16, 83-89], here our focus is on the influence of a condensed phase environment [4-9], In particular, as discussed below, there are important nonequilibrium solvation effects due to the lack of solvent polarization equilibration to the evolving charge distribution of the chromophore. 

In the above discussion, we have put an appropriate emphasis on the importance on the nonequilibrium solvation aspects of the excited state Cl problem. However, it has been shown in ref. [6] that an important aspect of CIs can be described solely with the aid of equilibrium solvation. In particular, a significant portion of the Cl seam in Figure 3.42 can be generated via equilibrium solvation considerations, as shown in Figure 3.44. The reasons why this can be accomplished are now discussed. 

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. 

PCM originated as a method to describe solvent effects on ground state molecules [2], but the extension to excited states was realized only after the original presentation, with a model [3], which introduced nonequilibrium effects in the solvent response for the optical processes of photon absorption and emission. The nonequilibrium solvation regime has later been applied to vibrational spectroscopies... 

Such a splitting in the medium response gives rise to the so-called nonequilibrium solvation regime. In the case of a vertical electronic transition (from the GS to an excited state for absorption, or from an excited state to the GS for emission), the arrival state feels a nonequilibrium solvation regime as the characteristic time of the electronic transition is much shorter than the response time of the inertial components of the solvent, and this component remains equilibrated with the initial electronic state. The arrival state reaches an equilibrium solvation regime only if its life time is enough to allow for a complete relaxation of the slow (inertial) polarization of the solvent. 

A third general issue regards the dynamic coupling between solute and solvent. To accurately model excited states formation and relaxation of molecules in solution, the electronic states have to be coupled with a description of the dynamics of the solvent relaxation toward an equilibrium solvation regime. The formulations of continuum models which allow to include a time dependent solvation response can be formulated as a proper extension of the time-independent solvation problem (of equilibrium or of nonequilibrium). In the most general case, such an extension is based on the formulation of the electrostatic problem in terms of Fourier components and on the use of the whole spectrum of the frequency dependent permittivity, as it contains all the informations on the dynamic of the solvent response [10-17],... 

A pump-damp-probe method (PDPM), which allows the characterization of solvation dynamics of a fluorescence probe not only in excited states but also in the ground state has been developed recently ([26] and references therein). In PDPM, a pump produces a nonequilibrium population of the probe excited, which, after media relaxation, is stimulated back to the ground state. The solvent relaxation of the nonequilibrium ground state is probed by monitoring vdth absorption technique. In the pump-dump-probe experiments, part of a series of laser output pulses was frequency doubled and softer beams were used as the probe. The delay of the probe with respect to the pump was flxed at 500 ps. 

This analysis shows that in order to account properly for solvent polarity effects, a solvation model has to be characterized by a larger flexibility with respect to the same model for ground state phenomena. In particular, it should be possible to shift easily from an equilibrium to a nonequilibrium regime according to the specific phenomenon under scrutiny. In the following section, we will show that such a flexibility can be obtained in continuum models and generalized to QM descriptions of the electronic excitations. 

R. Cammi, S. Comi, B. Mennucci, J. Tomasi, Electronic excitation energies of molecules in solution State specific and linear response methods for nonequilibrium continuum solvation models. J. Chem. Phys. 122, 104513 (2005)... 

---