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A pointwise representation of the s-matrix Kohn variational principle for quantum scattering

Andrew C. Peet, +1 more
- 19 Aug 1988 - 
- Vol. 149, Iss: 3, pp 257-264
TLDR
In this article, a method for reducing the complexity of scattering calculations carried out using the Kohn variational principle is proposed, which is based upon the use of a pointwise representation for the L 2 part of the basis set and eliminates the need to explicitly evaluate any integrals involving such functions.
About: 
This article is published in Chemical Physics Letters.The article was published on 1988-08-19 and is currently open access. It has received 17 citations till now. The article focuses on the topics: Pointwise & Variational principle.

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Citations
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Journal ArticleDOI

Quantum scattering via the log derivative version of the Kohn variational principle

David E. Manolopoulos, +1 more
- 04 Nov 1988 - 
TL;DR: In this paper, a new radial basis set is devised which is both (a) ideally suited to the log derivative boundary value problem, and (b) directly amenable to a discrete representation based on Gauss-Lobatto quadrature.
Journal ArticleDOI

Beyond transition-state theory: A rigorous quantum theory of chemical reaction rates

William H. Miller
- 01 Apr 1993 - 
TL;DR: In this article, the authors present a theoretical approach for calculating the rate constant of a chemical reaction that avoids the need to solve the complete state-to-state reactive scattering problem, with no explicit information about reactant and product states being required.
Journal ArticleDOI

Vibrational structure of hydrogen cyanide up to 18 900 cm −1

Xueming Yang, +2 more
- 01 Sep 1990 - 
TL;DR: In this article, a set of anharmonic vibrational constants was derived, unifying the SEP data reported here with previous infrared and overtone data, which is expected to be able to predict the position of normal mode states below 19 000 cm−1 with an accuracy within 3 cm −1.
Journal ArticleDOI

Iterative solution in quantum scattering theory. The log derivative Kohn approach

David E. Manolopoulos, +2 more
- 01 Jan 1990 - 
TL;DR: In this article, the log derivative version of the Kohn variational principle is reviewed in the context of a general inelastic molecular collision, and the possibility of solving the resulting linear equations iteratively for a single initial state column of the scattering matrix, S, is made.
Journal ArticleDOI

A collocation approach for quantum scattering based on the S‐matrix version of the Kohn variational principle

Weitao Yang, +2 more
- 15 Dec 1989 - 
TL;DR: In this article, a collocation approach based on the S-matrix version of the Kohn variational principle with a different linear expansion used for the two wave functions is presented, where one is a linear combination of basis functions and the other is a pointwise representation with proper asymptotic conditions imposed.
References
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Journal ArticleDOI

Coupled Equations and the Minimum Principle for Collisions of an Atom and a Diatomic Molecule, Including Rearrangements

William H. Miller
- 01 Jan 1969 - 
TL;DR: In this article, the collision of an atom with a diatomic molecule is treated by a coupled channel expansion augmented by a finite number of squareintegrable basis functions, and the coupled equations which must be solved to apply the minimum principle are obtained.
Journal ArticleDOI

Solution of the Hartree–Fock equations by a pseudospectral method: Application to diatomic molecules

Richard A. Friesner
- 01 Aug 1986 - 
TL;DR: An improved pseudospectral method was used to solve the Hartree-Fock equations for the neon atom and the diatomic molecules H2 and Li2 as discussed by the authors, which was shown to achieve accuracy comparable to conventional methods.
Journal ArticleDOI

A new basis set method for quantum scattering calculations

William H. Miller, +1 more
- 01 Jun 1987 - 
TL;DR: In this article, a new basis set approach for quantum scattering calculations is described and tested on model problems of elastic and inelastic collisions, which is essentially the Kohn variational method, but applied to the S or T matrix directly rather than to the K matrix as is normally done.
Journal ArticleDOI

Quantum scattering via the S‐matrix version of the Kohn variational principle

John Z. H. Zhang, +3 more
- 15 May 1988 - 
TL;DR: In this paper, the S-matrix version of the Kohn variational principle is used to obtain a very effective method for quantum scattering calculations, especially useful for the nonlocal (i.e., exchange) interactions that arise in chemically reactive scattering (and also in electron-atom/molecule scattering).
Journal ArticleDOI

Solution of the Hartree–Fock equations for polyatomic molecules by a pseudospectral method

Richard A. Friesner
- 15 Mar 1987 - 
TL;DR: A pseudospectral code for general polyatomic molecules has been developed using Gaussian basis functions in this paper, where the water molecule is studied using a 6−31G** basis set and the equilibrium geometry, total energy, first ionization potential, and vibrational force constants are obtained.
Related Papers (5)

A new basis set method for quantum scattering calculations

William H. Miller, +1 more
- 01 Jun 1987 - 

Quantum scattering via the S‐matrix version of the Kohn variational principle

John Z. H. Zhang, +3 more
- 15 May 1988 - 

Quantum reactive scattering via the S-matrix version of the Kohn variational principle: Integral cross sections For H+H2(ν1=j1=0)→H2(ν2=1, j2= 1, 3) + H in the energy range Etotal = 0.9–1.4 eV

John Z. H. Zhang, +1 more
- 30 Dec 1988 - 

New method for quantum reactive scattering, with applications to the 3-D H+H2 reaction

John Z. H. Zhang, +1 more
- 09 Oct 1987 - 

Variational Methods in Nuclear Collision Problems

Walter Kohn
- 15 Dec 1948 - 
Frequently Asked Questions (1)
Q1. What contributions have the authors mentioned in the paper "A pointwise representation of the s-matrix kohn variational principle for quantum scattering" ?

In this paper, a pointwise representation of the Kohn variational expression for the L2 part of the basis set is proposed.