Born-Huang

II. n-ELECTRONIC STATE ADIABATIC REPRESENTATION A. Born-Huang Expansion... 

Born-Huang expansion, 286—289 first-derivative coupling matrix, 290—291 nuclear motion Schrodinger equation, 289-290... 

In this equation, the gradient term U(q>)(R/jU(q>) /R) x i(R),) = W,Ik (R/J Vr x Rl) still appears and, as mentioned before, introduces numerical inefficiencies in its solution. Even though a truncated Born-Huang expansion was used to obtain Eq. (53), W VR).), although no longer zero, has no poles at conical intersection geometries [as opposed to the full W bad(R j matrix]. 

In the two-electronic-state Born-Huang expansion, the full-Hilbert space of adiabatic electronic states is approximated by the lowest two states and furnishes for the corresponding electronic wave functions the approximate closure relation... 

The familiar BO approximation is obtained by ignoring the operators A completely. This results in the picture of the nuclei moving over the PES provided by the electrons, which are moving so as to instantaneously follow the nuclear motion. Another common level of approximation is to exclude the off-diagonal elements of this operator matrix. This is known as the Born-Huang, or simply the adiabatic, approximation (see [250] for further details of the possible approximations and nomenclature associated with the nuclear Schrodinger equation). 

An explanation therefore for the crossover in terms of two competing paths is not possible in this case. However, this conclusion might need modification were it possible to incorporate the centrifugal/Born-Huang term in the original Hamiltonian. 

Born-Huang Expansion of the Total Wave Function... 

The total wave function of the dimer can be represented by the Born-Huang expansion22,... 

The approximation with (36) and (37) is called a Born-Huang (BH) approximation. In this approximation, the molecular wavefunction is written as... 

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