State-specific diabatic states

The choice of so as to satisfy flo 1 is what the introduction of the concept of the Fermi-sea of orbitals is all about. (1 note that the methodology toward the satisfaction of this criterion is understood much better today than in the late 1960s and early 1970s.) It may involve either state-specific diabatic states, for example [35a, 35b], MCHF-type calculations, or in special cases as in the example (4.1) on the ethylene molecule and in example (4.2) on the computation of electron correlation in Be, NONCl calculations. The background and the syllogism that led to the Fermi-sea is discussed in the following sections. The implementation of the criterion is demonstrated in Section 10 with new calculations at the CASSCF (4>°) and MRCISD (flo F -h 4> ") level for the first 11 E+ states of Be2. 

In all calculations, standard Gaussian basis functions are used to construct the wave function for each specific diabatic state. For comparisons purposes, basis sets ranging from 3-21G to aug-cc-pVTZ have been used. Specific details on the choice and definition ofdiabatic states are given below for each individual case. 

The effect of conical intersections on the state-specific and state-to-state reactive and nonreactive scattering attributes was demonstrated with the aid of an extended two coordinate quasi Jahn-Teller (JT) model. In recent years, the photodissociation dynamics of triatomic molecules, for example O3 and H2S, have been studied by calculating the diabatic electronic states and their couplings employing an ah initio approach. The reactive scattering dynamics of insertion reactions, for example, C - - H2, ... 

It is prerequisite to define localized, diabatic state wave fimctions, representing specific Lewis resonance configurations, in a VB-like method. Although this can in principle be done using an orbital localization technique, the difficulty is that these localization methods not only include orthorgonalization tails, but also include delocalization tails, which make contribution to the electronic delocalization effect and are not appropriate to describe diabatic potential energy surfaces. We have proposed to construct the locahzed diabatic state, or Lewis resonance structure, using a strictly block-localized wave function (BLW) method, which was developed recently for the study of electronic delocalization within a molecule.(28-3 1)... 

Having defined a diabatic state as a unique VB structure, or more generally as a linear combination of a subset of VB structures leading to a specific bonding scheme, the question is now How do we calculate such a state in a meaningful way ... 

The BOVB method does not of course aim to compete with the standard ab initio methods. BOVB has its specific domain. It serves as an interface between the quantitative rigor of today s capabilities and the traditional qualitative matrix of concepts of chemistry. As such, it has been mainly devised as a tool for computing diabatic states, with applications to chemical dynamics, chemical reactivity with the VB correlation diagrams, photochemistry, resonance concepts in organic chemistry, reaction mechanisms, and more generally all cases where a valence bond reading of the wave function or the properties of one particular VB structure are desirable in order to understand better the nature of an electronic state. The method has passed its first tests of credibility and is now facing a wide field of future applications. 

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... 

This prescription maps the Hilbert space spanned by the original n diabatic states into one coinciding with a subspace of n-oscillators of unit mass and at most one quantum of excitation in a single specific oscillator. 

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. 

With respect to the above, I note that following the publication by Froese Fischer [18] and by McCullough [19] of codes for the numerical solution of HF (or MCHF) equations for atomic and for diatomic states respectively, it has been demonstrated on prototypical unstable states (neutral, negative ion, molecular diabatic) that the state-specific computation of correlated wave-functions representing the localized component of states embedded in the continuous spectrum can be done economically and accurately, for example, [9,10,17, 20-22] and references there in. 

Calculations of state-specific and of the corresponding potential energy surfaces of negative ion resonances and of diabatic states in molecules... 

It is in this spirit that a priori constructed and calculated diabatic" molecular states crossing a vibrational or an electronic continuum were obtained in Refs. [138,145]. The direct state-specific calculation avoids, in the first case the coupling towards predissociation and in the second case the coupling towards autoionization. 

We will start with a description of FDE and its ability to generate diabats and to compute Hamiltonian matrix elements—the EDE-ET method (ET stands for Electron Transfer). In the subsequent section, we will present specific examples of FDE-ET computations to provide the reader with a comprehensive view of the performance and applicability of FDE-ET. After FDE has been treated, four additional methods to generate diabatic states are presented in order of accuracy CDFT, EODFT, AOM, and Pathways. In order to output a comprehensive presentation, we also describe those methods in which wavefunctions methods can be used, in particular GMH and other adiabatic-to-diabatic diabatization methods. Finally, we provide the reader with a protocol for running FDE-ET calculations with the only available implementation of the method in the Amsterdam Density Functional software [51]. In closing, we outline our concluding remarks and our vision of what the future holds for the field of computational chemistry applyed to electron transfer. 

We particularly focused on a conically intersecting manifold of two electronic states and described the quantum flux operator formalism within a time-dependent WP approach to calculate the initial state-specific and energy resolved reaction probabilities. The flux operator is represented in the two-state diabatic as well as adiabatic representation. While the... 

In the case of Model II, neither the state-specific nor the total quantum-mechanical level densities are available. To determine the optimal value of the ZPE correction, therefore criterion (69) was applied, which yielded 7 = 0.6. The mapping results thus obtained (panels d and g) are seen to reproduce the quantum result almost quantitatively. It should be noted that this ZPE adjustment assures that the adiabatic population probabilities remain within [0,1] and at the same time also yields the best agreement with the quantum diabatic populations. 

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