Potential energy surfaces continuum

Figure 1. Schematic of the radial cuts of the ground- and excited-state potential energy surfaces at the linear and T-shaped orientations. Transitions of the ground-state, T-shaped complexes access the lowest lying, bound intermolecular level in the excited-state potential also with a rigid T-shaped geometry. Transitions of the linear conformer were previously believed to access the purely repulsive region of the excited-state potential and would thus give rise to a continuum signal. The results reviewed here indicate that transitions of the linear conformer can access bound excited-state levels with intermolecular vibrational excitation.

As discussed in Section 2, one key assumption of reaction field models is that the polarization field of the solvent is fully equilibrated with the solute. Such a situation is most likely to occur when the solute is a long-lived, stable molecular structure, e g., the electronic ground state for some local minimum on a Bom-Oppenheimer potential energy surface. As a result, continuum solvation models... 

Figure 2.1 Schematic representation of the ground and electronic excited potential energy surfaces (PESs) and the corresponding absorption spectra of the parent molecule, resulting from the reflection of different initial wavefunctions on a directly dissociative PES (a) absorption from a vibrationless ground state consists of a broad continuum and (b) absorption from a vibrationally excited state shows that extended regions are accessed, leading to a structured spectrum with intensities of the features being dependent on the Franck-Condon factors. Reproduced with permission from Ref. [34]. Reproduced by permission of lOP Publishing.

In order to explain the high stereocontrol occurring in the iodocyclization of 3-acylamino-2-methylenealkanoates, the conformational space of the starting molecule and the potential energy surface (PES) for the cyclization reaction was explored at the DFT level the polarized continuum formalism (PCM) for chloroform was used in order to consider the solvent effect. The observed stereoselection [(9) (10)] was (de)... 

The Sn2 reaction in solution. We saw above the application of microsolvation to Sn2 reactions ([14, 15]). Let us now look at the chloride ion-chloromethane Sn2 reaction in water, as studied by a continuum method. Figure 8.2 shows a calculated reaction profile (potential energy surface) from a continuum solvent study of the Sn2 attack of chloride ion on chloromethane (methyl chloride) in water. Calculations were by the author using B3LYP/6-31+G (plus or diffuse functions in the basis set are considered to be very important where anions are involved Section 5.3.3) with the continuum solvent method SM8 [22] as implemented in Spartan [31] some of the data for Fig. 8.2 are given in Table 8.1. Using as the reaction coordinate r the deviation from the transition state C-Cl... 

The decay of Nal can be described in an alternative way [K.B. Mpller, N.E. Henriksen, and A.H. Zewail, J. Chem. Phys. 113, 10477 (2000)]. In the bound region of the excited-state potential energy surface, one can define a discrete set of quasi-stationary states that are (weakly) coupled to the continuum states in the dissociation channel Na + I. These quasi-stationary states are also called resonance states and they have a finite lifetime due to the coupling to the continuum. Each quasi-stationary state has a time-dependent amplitude with a time evolution that can be expressed in terms of an effective (complex, non-Hermitian) Hamiltonian. 

In our discussion the usual Born-Oppenheimer (BO) approximation will be employed. This means that we assume a standard partition of the effective Hamiltonian into an electronic and a nuclear part, as well as the factorization of the solute wavefunction into an electronic and a nuclear component. As will be clear soon, the corresponding electronic problem is the main source of specificities of QM continuum models, due to the nonlinearity of the effective electronic Hamiltonian of the solute. The QM nuclear problem, whose solution gives information on solvent effects on the nuclear structure (geometry) and properties, has less specific aspects, with respect the case of the isolated molecules. In fact, once the proper potential energy surfaces are obtained from the solution of the electronic problem, such a problem can be solved using the standard methods and approximations (mechanical harmonicity, and anharmonicity of various order) used for isolated molecules. The QM nuclear problem is mainly connected with the vibrational properties of the nuclei and the corresponding spectroscopic observables, and it will be considered in more detail in the contributions in the book dedicated to the vibrational spectroscopies (IR/Raman). This contribution will be focused on the QM electronic problem. 

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). 

E. Baloitcha, G.G. BaKnt-Kurti, Theory of the photodissodation of ozone in the Hartley continuum Potential energy surfaces, conical intersections, and photodissociation dynamics, /. Chem. Phys. 123 (1) (2005), Art. No. 014306. 

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