Electronic states diabatization matrix

Single-valued potential, adiabatic-to-diabatic transformation matrix, non-adiabatic coupling, 49-50 topological matrix, 50-53 Skew symmetric matrix, electronic states adiabatic representation, 290-291 adiabatic-to-diabatic transformation, two-state system, 302-309 Slater determinants ... 

To describe ionization processes, the molecular Hamiltonian, given in Eq. (21), has to be extended to include ionization continua. As a specific example, we shall consider a molecular system that comprises the (uncoupled) electronic ground state o)> the diabatic excited electronic states f), 2)> which are vibronically coupled by the matrix element hu = W12, and two ionization continua which are vibronically coupled... 

To obtain potential surfaces for two electronic states that will be degenerate at these points, we write a Hamiltonian as a 2 x 2 matrix in a diabatic representation in the following form ... 

This choice of elements for the u, (qx,) matrix will diabatize the adiabatic electronic states i andj while leaving the remaining states unaltered. 

H3 (and its isotopomers) and the alkali metal triiners (denoted generally for the homonuclears by X3, where X is an atom) are typical Jahn-Teller systems where the two lowest adiabatic potential energy surfaces conically intersect. Since such manifolds of electronic states have recently been discussed [60] in some detail, we review in this section only the diabatic representation of such surfaces and their major topographical details. The relevant 2x2 diabatic potential matrix W assumes the fomi... 

The previous treatment relied on the assumption that the transition occurs on a single potential energy surface V(x) characterized by a barrier separating two wells. This potential is actually created from the terms of the initial and final electronic states. The separation of electron and nuclear coordinates in each of these states gives rise to the diabatic basis with nondiagonal Hamiltonian matrix... 

The treatment developed here is based on the density matrix of quantum mechanics and extends previous work using wavefunctions.(42 5) The density matrix approach treats all energetically accessible electronic states in the same fashion, and naturally leads to average effective potentials which have been shown to give accurate results for electronically diabatic collisions. 19) The approach is taken here for systems where the dynamics can be described by a Hamiltonian operator, as it is possible for isolated molecules or in models where environmental effects can be represented by terms in an effective Hamiltonian. 

Quantum reaction dynamics, electronic states (Continued) diabatization matrix, 295-300 electronically diabatic representation, 292-293... 

When two electronic states are degenerate at a particular point in configuration space, the elements of the diabatic potential energy matrix can be modeled as a linear function of the coordinates in the following form ... 

The electronic structure analysis given so far can be used to examine chemical reactivity features of this important subsystem. In real space, eqs. (7) and (13) can be adapted to study the change in amplitudes for the electronic states by diagonalizing the matrix equation over a finite number of diabatic states [11] ... 

Apart from the selection rules for the electronic coupling matrix element, spin-forbidden and spin-allowed nonradiative transitions are treated completely analogously. Nonradiative transitions caused by spin-orbit interaction are mostly calculated in the basis of pure spin Born-Oppenheimer states. With respect to spin-orbit coupling, this implies a diabatic behavior, meaning that curve crossings may occur in this approach. The nuclear Schrodinger equation is first solved separately for each electronic state, and the rovibronic states are spin-orbit coupled then in a second step. 

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. 

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