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A new translational basis set is introduced for quantum reactive scattering calculations that use the log derivative version of the Kohn variational principle. This basis set, which is similar in many respects to that used in electron–atom scattering calculations by Burke and Robb, is obtained by contracting a primitive basis of Lobatto shape functions to the box eigenfunctions of a one-dimensional reference Hamiltonian H0. In addition, a single energy-dependent scattering function is included in the variational expansion to ensure completeness at the boundary of the box. One fairly obvious choice for the reference Hamiltonian in an atom–diatom reaction is suggested, and all of the equations which are actually needed to implement the method in this context are carefully described. Example applications to the three-dimensional F+H2 reaction are then chosen to illustrate the practical potential of the approach. [ABSTRACT FROM AUTHOR]

The log derivative version of the Kohn variational principle is reviewed in the context of a general bimolecular chemical reaction. The basis of this review, namely, the Wigner and Eisenbud general formulation of rearrangement scattering, has been well known for many years. Therefore, so as to avoid any unnecessary confusion, the relationship between their equally famous R matrix theory and Kohn’s variational derivation is carefully described. The log derivative matrix is then eliminated from a basis set representation of Kohn’s principle to leave a unitary and symmetric variational expression for the scattering matrix S. This new expression is expected to find its most fruitful application in the iterative solution of very large quantum scattering problems for which transitions from only a few initial states are required. [ABSTRACT FROM AUTHOR]

We present a method for including the geometric phase in quantum reactive scattering computations based on the log derivative version of the Kohn variational principle. A new variational functional is developed which includes the influence of the geometric phase through modifications in the momentum operators. The system investigated is a two-dimensional reactive scattering model which includes the vector potential induced by the magnetic field of an infinitely long solenoid. The coordinates used in this model are analogous to Jacobi coordinates used in atom–diatom systems. Some interesting features of this study include the gauge invariance of the scattering probabilities, symmetry adaptation of the wave function, and the behavior of the probability density in the presence of the geometric phase. [ABSTRACT FROM AUTHOR]

A new approach to calculating quantum functional sensitivity maps of transition probabilities is described in this paper. This approach is based on the log-derivative version of the Kohn variational principle and is applied here to the collinear H+H2 hydrogen exchange reaction. The sensitivity maps provide detailed quantitative information about how variations in the potential energy surface affect the state-to-state transition probabilities. The key issues investigated are (i) the evolution of sensitivity structure in the 0.30–1.50 eV range of total energy; (ii) the comparison of sensitivity structure on the Porter–Karplus, the Liu–Siegbahn–Truhlar–Horowitz, and the double-many-body-expansion potential energy surfaces; and (iii) the range of linearity for first order sensitivity predictions. [ABSTRACT FROM AUTHOR]