Appendix C Tracking the continuity of molecular orbitals along a nuclear path

10 Appendix C Tracking the continuity of molecular orbitals along a nuclear path 

In propagating an electronic wavepacket along a path, it is generally expanded with molecular orbitals as one-electron basis functions, molecular 

Chemical Theory Beyond the Born-Oppenheimer Paradigm 

One typical example, that may appeal to readers and that emphasizes the seriousness of the matter, is as follows Let us consider two degenerate 7T molecular orbitals in a diatomic molecule, whose bond direction is in the z-coordinate. At each internuclear distance, a computer program can generate a pair of tt orbitals with an arbitrary orientation in the a t/-plane. Arbitrary, of course, unless one forces them to align along, say, the x and y directions. Without this special care, the resultant CSFs including them will become useless as expansion bases in the practical propagation of an electronic wavepacket. 

A method for obtaining a set of molecular orbitals appropriate for dynamical simulation was proposed by Truhlar s group. [292, 293] It uses a variational functional to obtain a set of diabatic molecular orbitals as a function of the nuclear geometry. An advantage of this method is that such diabatization is possible without prior knowledge of the nuclear paths. 

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