Van Vleck perturbation

Sibert, E. L. (1988), VANVLK An Algebraic Manipulation Program for Canonical Van Vleck Perturbation Theory, Comp. Phys. Comm. 51, 149. 

B. Kirtman, Simultaneous calculation of several interacting electronic states by generalized Van Vleck perturbation theory. J. Chem. Phys. 75, 798 (1981). 

With the constraints of Eq. 47 we can, in general, use perturbation theory to find the approximate eigenvalues oiT-Lp. In the coming sections we will do so by using van Vleck perturbation theory, but only after discussing Floquet energy level crossings. 

In the investigated cases the spectra are reproduced well with moments of inertia specific to the torsional state and 7a, X, V3 (V6). The fitting of the frequencies depends more on the choice of the moments of inertia than the line splittings. This limitation is a consequence of the approximation included in the Hamiltonian itself and not a consequence of the approximate numerical treatment. The usual van Vleck perturbation treatment has been checked against direct diagonalization of the... 

It would be interesting to establish the possible relationships between the Bloch formalism for constructing effective Hamiltonians and other perturbative approaches, including Van Vleck perturbation theory (161). 

Canonical Van Vleck Perturbation Theory and Its Application to Studies of Highly Vibrationally Excited States of Polyatomic Molecules... 

Figure 2 A schematic of the Van Vleck perturbation theory in a matrix representation. Each pannel represents the similarity transform TfHT = K, where T = exp(/ XS). In the upper pannel K is transformed to a diagonal representation. In lower pannel K is transformed to a block-diagonal representation. This latter transformation allows intrinsically coupled zero-order states to remain coupled in the final representation.

Canonical Van Vleck perturbation theory and variational calculation. 

The coefficients result from the Van Vleck perturbational treatment. They were tabulated [61Hay, 67Wol] and can be calculated easily [59Her, 81Van]. Their value depends on the so-called reduced barrier parameter 5 = 4F3/9F. For the -levels, the coefficients fromEq. (2.39) are zero... 

The coefficients result from the Van Vleck perturbational treatment. They were tabulated... 

---