Nonadiabatic coupling key properties

NAC appears in the nuclear Schrodinger equation in the following manner. Let us first deal with the electronic eigenvalue problem 

The double bracket notation in equation (3) implies the integration over the electronic configuration space By definition, i) f is the ath nonadiabatic 

Nonadiabatic couplings fjj1 for all pairs of electronic eigenstates d k and Pt form a matrix F(a) with non-zero off-diagonal matrix elements = iff iff is a vector held and, therefore, according to Helmholtz theorem [45] (see also, e.g. Ref. [46] 

The former one fy 111, called the longitudinal or irrotational one, is defined by its curl, VR xfy, and is identically zero (the flow source )- It is thus represented as fj, = VR Py where P 1 is some scalar potential determined as [46] 

Similarly to equation (5), one writes the formula derived by Stokes and Helmholtz 

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