Numerics.Adiabatic

Diabatic vs. adiabatic formulation

The potential energy in the above formulation of the Hamiltonian operator is in general represented by a full symmetric matrix. In particular, this matrix may have non-vanishing off-diagonal elements and the diagonal elements, viewed as a function of the coordinate(s) $R$, may intersect each other. Hence, this representation is referred to as a diabatic representation. In many cases it may be useful to apply a unitary transformation to the system of coupled Schrödinger equations to the socalled adiabatic representation where the potential energy becomes diagonal. However, this gives rise to socalled non-adiabatic coupling tensors (NACTs) arising from the kinetic energy operator. However, these may be negligible in many cases, in which case the adiabatic approximation may be invoked. Noteworthy exception are (avoided) crossings of 1-dimensional potential energy curves or conical intersections of energy (hyper-)surfaces in higher dimensionality.