Previously I discussed the importance of finding diabatic states as an alternative way to describe the electronic structure and potential energy surfaces of molecules. Here are a few key points.
In general if one knows the Born-Oppenheimer [i.e. adiabatic] eigenstates it is impossible to find perfectly diabatic states [i.e. ones which do not change with geometry] for a specific molecular system.
Hence, one must find approximately diabatic states. There are several alternative strategies.
a. Use chemically intuitive basis states such as valence bond structures [see for example].
b. Define states which constrain some physical observable, e.g., localisation of charge or bond length alternation.
c. The generalised Mulliken-Hush approach [due to Cave and Newton] is a specific case of b. One chooses the diabatic states so that the transition dipole moment between them vanishes. In different words, for a two-state system one evaluates the matrix elements of the dipole operator, with respect to the adiabatic eigenstates and then diagonalises this matrix. The basis states which diagonalise this matrix are then taken to be the diabatic states.
d. One block diagonalises the adiabatic Hamiltonian matrix according to some "minimisation" criteria. [This was pioneered by Cederbaum, Domcke, and collaborators].
See for example.
In general if one knows the Born-Oppenheimer [i.e. adiabatic] eigenstates it is impossible to find perfectly diabatic states [i.e. ones which do not change with geometry] for a specific molecular system.
Hence, one must find approximately diabatic states. There are several alternative strategies.
a. Use chemically intuitive basis states such as valence bond structures [see for example].
b. Define states which constrain some physical observable, e.g., localisation of charge or bond length alternation.
c. The generalised Mulliken-Hush approach [due to Cave and Newton] is a specific case of b. One chooses the diabatic states so that the transition dipole moment between them vanishes. In different words, for a two-state system one evaluates the matrix elements of the dipole operator, with respect to the adiabatic eigenstates and then diagonalises this matrix. The basis states which diagonalise this matrix are then taken to be the diabatic states.
d. One block diagonalises the adiabatic Hamiltonian matrix according to some "minimisation" criteria. [This was pioneered by Cederbaum, Domcke, and collaborators].
See for example.
One could argue that a) and b) are actually the same, if a charge/bond-order matrix is used to identify the bonding structure. In Coulson's scheme this is a 1-electron observable, so this would lead to a scheme based on constrained Hartree-Fock theory.
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