Molecular potential diabatic states

On the potential energy surfaces thus obtained 2D wavepacket dynamics calculations have been performed in the diabatic state representation. The reduced massses are regarded as those of CH2-ethylene system. The validity was examined by using on-the-fly ab initio molecular dynamics that were supplementarily performed. The dynamics calculations performed are composed of the following steps ... 

To express the collective solvent reaction coordinate as in equation (6), it is necessary to define the specific diabatic potential surface for the reactant and product state. This, however, is not a simple task, and there is no unique way of defining such diabatic states. What is needed is a method that allows the preservation of the formal charges of the fragments of reactant and product resonance states. At the same time, solvent effects can be incorporated into electronic structure calculations in molecular dynamics and Monte Carlo simulations. Recently, we developed a block-localized wave function (BLW) method for studying resonance stabilization, hyperconjugation effects, and interaction energy decomposition of organic molecules.20-23 The BLW method can be formulated to specify the effective VB states.14... 

Running such molecular dynamic (MD) trajectories on the EVB surface of the RS can (in principle) provide the free-energy function, Eg, that is needed to calculate the activation energy, Ag. However, since trajectories on the reactant surface will reach the TS only rarely, it is usually necessary to run a series of trajectories on potential surfaces that gradually drive the system from the reactant to the product state.22 The EVB approach accomplishes this by changing the system adiabatically from one diabatic state to another. In the simple case of two diabatic states, this mapping potential, sm, can be written as a linear combination of the reactant and product potentials, 81 and 82 ... 

Diabatic states are obtained from a similar approach, except that additional term (or terms) in the Hamiltonian are disregarded in order to adopt a specific physical picture. For example, suppose we want to describe a process where an electron e is transferred between two centers of attraction, A and B, of a molecular systems. We may choose to work in a basis of vibronic states obtained for the e-A system in the absence of e-B attraction, and for the e-B system in the absence of the e-A attraction. To get these vibronic states we again use a Born-Oppenheimer procedure as described above. The potential surfaces for the nuclear motion obtained in this approximation are the corresponding diabatic potentials. By the nature of the approximation made, these potentials will correspond to electronic states that describe an electron localized on A or on B, and electron transfer between centers A and B implies that the system has crossed from one diabatic potential surface to the other. 

The electromagnetic radiation field is taken into account by adding the energy of the photons to the various molecular potential curves, Vi(R). If the photon number is initially N, when n photons are absorbed, the remaining number of photons is N — n. The resultant field-dressed diabatic state has potential energy... 

Molecular applications have thus far involved the calculation of the electronic structure and potential energy surfaces of negative ion "compound states" and of "diabatic states" in the continuous spectrum of polyelectronic diatomics and triatomics and of energies and partial widths with interchannel coupling of vibrational shape and predissociating resonances of diatomics. The same principles and methodologies can be applied to many more such cases. 

Fig. 1. Evolution of the quantum state

Divergent couplings ai e a nuisance for the computational treatment of the nuclear dynamics. In cases of exact or near degeneracy of electronic potential-energy surfaces it is therefore preferable to introduce an alternative electronic representation, the so-called diabatic (or quasi-diabatic) representation, which avoids singular coupling elements. The basic concept of diabatic states has been introduced in early descriptions of atomic collision processes and vibronic-coupling phenomena in molecular spectroscopy. ... 

In Chapter VI, Ohm and Deumens present their electron nuclear dynamics (END) time-dependent, nonadiabatic, theoretical, and computational approach to the study of molecular processes. This approach stresses the analysis of such processes in terms of dynamical, time-evolving states rather than stationary molecular states. Thus, rovibrational and scattering states are reduced to less prominent roles as is the case in most modem wavepacket treatments of molecular reaction dynamics. Unlike most theoretical methods, END also relegates electronic stationary states, potential energy surfaces, adiabatic and diabatic descriptions, and nonadiabatic coupling terms to the background in favor of a dynamic, time-evolving description of all electrons. 

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