Everything about Diabatic totally explained
» See also adiabatic process, a concept in thermodynamics
In
quantum chemistry, the
potential energy surfaces are obtained within the
adiabatic or
Born-Oppenheimer approximation. This corresponds to a representation of the molecular
wave function where the variables corresponding to the
molecular geometry and the electronic
degrees of freedom are
separated. The
non separable terms are due to the nuclear kinetic energy terms in the
molecular Hamiltonian and are said to couple the
potential energy surfaces. In the neighbourhood of an
avoided crossing or
conical intersection, these terms can't be neglected. One therefore usually performs one
unitary transformation from the
adiabatic representation to the so-called
diabatic representation in which the nuclear kinetic energy operator is
diagonal. In this representation, the coupling is due to the
electronic energy and is a scalar quantity which is much more easy to estimate numerically.
In the diabatic representation, the potential energy surfaces are smoother so that low order
Taylor series expansions of the surface capture much of the complexity of the original system. Unfortunately, strictly diabatic states don't exist in the general case. Hence, diabatic potentials generated from transforming multiple electronic energy surfaces together are generally not exact. These can be called
pseudo-diabatic potentials, but generally the term isn't used unless it's necessary to highlight this subtletly. Hence, pseudo-diabatic potentials are synonymous with diabatic potentials.
Applicability
The motivation to calculate diabatic potentials often occurs when the
Born-Oppenheimer approximation doesn't hold, or isn't justified for the molecular system under study. For these systems, it's necessary to go
beyond the Born-Oppenheimer approximation. This is often the terminology used to refer to the study of
nonadiabatic systems.
A well-known approach involves recasting the molecular Schrödinger equation into a set of coupled eigenvalue equations. This is achieved by expansion of the exact wave function in terms of products of electronic and nuclear wave functions (adiabatic states) followed by integration over the electronic coordinates. The coupled operator equations thus obtained depend on nuclear coordinates only. Off-diagonal elements in these equations are nuclear kinetic energy terms. A diabatic transformation of the adiabatic states replaces these off-diagonal kinetic energy terms by potential energy terms. Sometimes, this is called the "adiabatic to diabatic transformation", abbreviated
ADT.
Diabatic transformation of two electronic surfaces
In order to introduce the diabatic transformation we assume now, for the sake of argument, that only two Potential Energy Surfaces (PES), 1 and 2, approach each other and that all other surfaces are well separated; the argument can be generalized to more surfaces. Let the collection of electronic coordinates be indicated by
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