Journal ArticleDOI
A collocation approach for quantum scattering based on the S‐matrix version of the Kohn variational principle
TLDR
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.Abstract:
A collocation approach to quantum scattering is presented. The method is based on the S‐matrix version of the Kohn variational principle with a different linear expansion used for the two wave functions—one is a linear combination of basis functions and the other is a pointwise representation with proper asymptotic conditions imposed. The resulting equations are similar in structure to the usual version of the Kohn variational principle, however, in the present approach there are no integrals between the square integrable (L2) basis functions. In addition, the method does not require the knowledge of quadrature weights associated with the collocation points as was the case in a previous pointwise method for quantum scattering. This property means that the method is readily applicable to reactive scattering problems which use different sets of coordinates for reactants and products. Appliction to a simple inelastic test problem (collinear He–H2 vibrationally inelastic scattering) shows the accuracy of the ...read more
Citations
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Journal ArticleDOI
A novel discrete variable representation for quantum mechanical reactive scattering via the S-matrix Kohn method
TL;DR: In this article, a discrete variable representation (DVR) is introduced for use as the L2 basis of the S-matrix version of the Kohn variational method for quantum reactive scattering.
Journal ArticleDOI
Beyond transition-state theory: A rigorous quantum theory of chemical reaction rates
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
Fully coupled six-dimensional calculations of the water dimer vibration-rotation-tunneling states with a split Wigner pseudo spectral approach
TL;DR: In this paper, a pseudospectral method for performing fully coupled six-dimensional bound state dynamics calculations is presented, including overall rotational effects, using a Lanczos based iterative diagonalization scheme.
Journal ArticleDOI
Intermolecular potentials, internal motions, and spectra of van der waals and hydrogen-bonded complexes.
TL;DR: Three-Body Interactions; Water Trimer Spectrum 4123 5.1.
Journal ArticleDOI
Solving the Schroedinger equation using Smolyak interpolants.
Gustavo Avila,Tucker Carrington +1 more
TL;DR: By combining Lagrange-like functions with a Smolyak interpolant, a collocation method is device that does not require solving a generalized eigenvalue problem and exploits the structure of the grid to develop an efficient algorithm for evaluating the matrix-vector products required to compute energy levels and wavefunctions.
References
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Book
The method of weighted residuals and variational principles
TL;DR: In this article, the method of Weighted Residuals is used to solve boundary-value problems in heat and mass transfer problems, and convergence and error bounds are established.
Journal ArticleDOI
Exact Quantum-Mechanical Calculation of a Collinear Collision of a Particle with a Harmonic Oscillator
Don Secrest,B. Robert Johnson +1 more
TL;DR: In this article, a semi-empirical formula for computing quantum-mechanical transition probabilities for collinear collision of an atom with a diatomic molecule is given.
Journal ArticleDOI
On distributed Gaussian bases for simple model multidimensional vibrational problems
I. P. Hamilton,John C. Light +1 more
TL;DR: The distributed Gaussian bases are defined and used to calculate eigenvalues for one and multidimensional potentials and are shown to be accurate, flexible, and efficient.
Journal ArticleDOI
Accurate localized and delocalized vibrational states of HCN/HNC
Zlatko Bačić,John C. Light +1 more
TL;DR: In this article, the first accurate quantum calculation of the delocalized, large amplitude motion vibrational (J=0) levels of HCN/HNC, lying above the isomerization barrier, is presented.
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