Solvent dynamic effect potential energy surface

The effect of the solvent upon the breaking of the symmetry of the potential energy surface for proton transfer has a profound consequence for the reaction dynamics for proton transfer. The tunneling of the proton out of the reactant state... 

Transient absorption experiments have shown that all of the major DNA and RNA nucleosides have fluorescence lifetimes of less than one picosecond [2—4], and that covalently modified bases [5], and even individual tautomers [6], differ dramatically in their excited-state dynamics. Femtosecond fluorescence up-conversion studies have also shown that the lowest singlet excited states of monomeric bases, nucleosides, and nucleotides decay by ultrafast internal conversion [7-9]. As discussed elsewhere [2], solvent effects on the fluorescence lifetimes are quite modest, and no evidence has been found to date to support excited-state proton transfer as a decay mechanism. These observations have focused attention on the possibility of internal conversion via one or more conical intersections. Recently, computational studies have succeeded in locating conical intersections on the excited state potential energy surfaces of several isolated nucleobases [10-12]. 

By taking as a reference the calculation in vacuo, the presence of the solvent introduces several complications. In fact, besides the direct effect of the solvent on the solute electronic distribution (which implies changes in the solute properties, i.e. dipole moment, polarizability and higher order responses), it should be taken into account that indirect solvent effects exist, i.e. the solvent reaction field perturbs the molecular potential energy surface (PES). This implies that the molecular geometry of the solute (the PES minima) and vibrational frequencies (the PES curvature around minima in the harmonic approximation) are affected by the presence of a solvating environment. Also, the dynamics of the solvent molecules around the solute (the so-called nonequilibrium effect ) has to be... 

Equation (3.21) shows that the potential of the mean force is an effective potential energy surface created by the solute-solvent interaction. The PMF may be calculated by an explicit treatment of the entire solute-solvent system by molecular dynamics or Monte Carlo methods, or it may be calculated by an implicit treatment of the solvent, such as by a continuum model, which is the subject of this book. A third possibility (discussed at length in Section 3.3.3) is that some solvent molecules are explicit or discrete and others are implicit and represented as a continuous medium. Such a mixed discrete-continuum model may be considered as a special case of a continuum model in which the solute and explicit solvent molecules form a supermolecule or cluster that is embedded in a continuum. In this contribution we will emphasize continuum models (including cluster-continuum models). 

Quantum dynamics effects for hydride transfer in enzyme catalysis have been analyzed by Alhambra et. al., 2000. This process is simulated using canonically variational transition-states for overbarrier dynamics and optimized multidimensional paths for tunneling. A system is divided into a primary zone (substrate-enzyme-coenzyme), which is embedded in a secondary zone (substrate-enzyme-coenzyme-solvent). The potential energy surface of the first zone is treated by quantum mechanical electronic structure methods, and protein, coenzyme, and solvent atoms by molecular mechanical force fields. The theory allows the calculation of Schaad-Swain exponents for primary (aprim) and secondary (asec) KIE... 

In PET, the rate can be markedly affected by the solvent polarity. With the formation of each new charge-transfer intermediate, solvent dipoles undergo reorientation in response to the new charge distribution on the reactants [49]. The solvent response influences the free-energy barrier of the reaction by altering the potential energy surface of the electron transfer. We consider this facet of solvent motion in this section. In a later section, we examine dynamical solvent effects. 

An ultrafast intermolecular electron transfer (ET) from electron donating solvent to an excited dye molecule was found. A temperature-dependent non-exponential time dependence was observed in aniline, and a temperature-independent single exponential process for Nile blue (160 fs) and oxazine 1 (260 fs) was observed in N,N-Smethylaniline. The solvation times of solvent anilines were obtained by dynamic Stokes shift measurements. The rate of ET in some systems was observed to be much greater than the solvation time of anilines. The dynamic behavior was simulated by the 2-dimen ional potential energy surface for reaction, taking into account of the effects of both solvent reorientation and nuclear motion of reactants. 

The potential energy surface used in solution, G (R), is related to an effective Hamiltonian containing a solute-solvent interaction term, Vint- In the implementation of the EH-CSD model, that will be examined in Section 6, use is made of the equilibrium solute-solvent potential. There are good reasons to do so however, when the attention is shifted to a dynamical problem, we have to be careful in the definition of Vint - This operator may be formally related to a response function TZ which depends on time. For simplicity s sake, we may replace here TZ with the polarization vector P, which actually is the most important component of TZ (another important contribution is related to Gdis) For the calculation of Gei (see eq.7), we resort to a static value, while for dynamic calculations we have to use a P(t) function quantum electrodynamics offers the theoretical framework for the calculation of P as well as of TZ. The strict quantum electrodynamical approach is not practical, hence one usually resorts to simple naive models. 

The so-called Walden inversion, an SN2 reaction shown in Figure 1, has been chosen as the model, since it is a well-studied reaction, from both a static and a dynamical point of view.26-36 In the present study, we limit our analysis to the gas-phase reaction, and we do not consider solvent effects that are known to strongly modify the potential energy surface (PES).29... 

The NEQ limit is the most suitable to the treatment of the absorption process. The study of the fluorescence process is instead more complex, since in this case dynamical solvent effects cannot be rigorously decoupled from the intramolecular effects due to the motion of the wave-packet (WP) on the excited-state surface. However, it is possible to define some limit reference models, and intuitive consideration of the properties of the solvent and/or the excited potential energy surface is often sufficient to define what is the most suitable to the treat the case under study (see next sections). PCM can be used in conjunction with all the most important excited-state electronic methods. Since we selected TD-DFT as our reference electronic method, we shall treat PCM/TD-DFT in more detail in the next sections. 

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