Total angular momentum basis functions

The parity-adapted BF total angular momentum basis functions Y (R, f, r2) in... 

To illustrate the first point concerning a spectator bond for the abstraction reaction, Fig. 17 shows the total reaction probability for the abstraction reaction as a function of the translational energy for total angular momentum J = 0 on the YZCL2 PES with the H20 reactant in the ground rovibrational state [the (00)(0) state in the local mode notation], where the uncleaved bond OHb is treated in various ways. Using a limited number of one or five vibrational basis functions, VBF(OHb) = 1 or 5, means that the OHb bond is unreactive, a spectator. The abstraction reaction probability... 

Nonadiabatic Variational Energies for 15 States of the H2 Molecule with Zero Total Angular Momentum (the Ground Rotational States) Obtained with 3000 Basis Functions for Each State and Expectation Values of the Internuclear Distance and the Square of the Internuclear... 

For a total angular momentum J, the Hamiltonian of Eq. (8) is represented in a set of basis functions consisting of linear combinations of... 

The essential feature of a case (a) basis set for a 3 E molecule is that the electron spin S is strongly coupled to the rotational angular momentum N to form the total angular momentum J. The component of S along the internuclear axis, S, is therefore a conserved quantum number, but N is not and the basis functions are of the form r], A ./. S. 22 Mj). In this basis the effective Hamiltonian can be conveniently written in the form... 

Equation (54) is the basis for the semiempirical methods to be discussed below. Several approximations have been used for (rXi). In all of the methods, the matrix elements of Hso are evaluated with respect to a wave function variationally optimized in A-S coupling. The spin-orbit matrix is then diagonalized for the various values of the total angular momentum of the system. 

TB computes essentially the basis of two-dimensional functions m Pp, G0) and coupling matrix elements (p p) and the rovibrational functions v] This part is independent of the total energy E and of the total angular momentum. /. 

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