S-Matrix Kohn method

Colbert D T and Miller W H 1992 A novel discrete variable representation for quantum mechanical reactive scattering via the S-matrix Kohn method J. Chem. Phys. 96 1982... 

D.T. Colbert and W.H. Miller, A Novel Discrete Variable Representation for Quantum Mechanical Reactive Scattering via the S-Matrix Kohn Method , J. Chem. Phys. 96, 1982 (1992). 

The three variational principles in common use in scattering theory are due to Kohn [9], Schwinger [11] and Newton [12]. Two of these variational principles, those due to Kohn and Newton, have been successfully developed and applied to reactive scattering problems in recent years there is the S-matrix Kohn method of Zhang, Chu, and Miller, the related log derivative Kohn method of Manolopoulos, D Mello, and Wyatt and the L - Amplitude Density Generalized Newton Variational Principle (L -AD GNVP) method of Schwenke, Kouri, and Truhlar. 

The final streamlined version of the S-matrix Kohn method proposed by Zhang, Chu, and Miller has been applied quite successfully in recent years. In particular, and after a preliminary calculation of J=0 reaction probabilities for F-I-H2 [106], Zhang and Miller have concentrated more or less exclusively on the calculation of high energy integral and differential cross sections for... 

Time-independent approaches to quantum dynamics can be wxriational where the wavefunction for all coordinates is expanded in some basis set and the parameters optimized. The best knowm variational implementation is perhaps the S-matrix version of Kohn s variational prineiple which was introduced by Miller and Jansen op de Haar in 1987[1]. Another time-independent approach is the so called hyperspherical coordinate method. The name is unfortunate as hyperspher-ical coordinates may also be used in other contexts, for instance in time-dependent wavepacket calculations [2]. 

Theory. Usually we do not solve the fundamental equations directly. We use a theory, for example, Har-tree-Fock theory [3], Moller-Plesset perturbation theory [4], coupled-cluster theory [5], Kohn s [6, 7], Newton s [8], or Schlessinger s [9] variational principle for scattering amplitudes, the quasiclassical trajectory method [10], the trajectory surface hopping method [11], classical S-matrix theory [12], the close-coupling approximation... 

The variational approach received a major boost also when it was realised [79] that the simplest variational method - the Kohn variational principle, which is essentially the Rayleigh-Ritz variational principle for eigenvalues modified to incorporate scattering boundary conditions - is free of anomalous (i.e., spurious, unphysical) singularities if it is formulated with S-matrix type boundary conditions rather than standing wave boundary conditions as had been typically used previously. It is useful first to state the Kohn variational approach for the general inelastic scattering. Thus the variational expression for the S-matrix is... 

S. Komorovsy, M. Repisky, O. L. Malkina, V. G. Malkin, 1. Malkin, M. Kaupp. A fully relativistic method for calculation of nudear magnetic shielding tensors with a restricted magnetically balanced basis in the framework of the matrix Dirac-Kohn-Sham equation. /. Chem. Phys., 128 (2008) 104101. 

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