Ebook: Numerical Determination of the Electronic Structure of Atoms, Diatomic and Polyatomic Molecules

Quantum mechanical calculations in physics, chemistry and biology are widely recognized as useful interpretative and predictive tools. Unfortunately, they are plagued by unfavorable convergence limitations due to the use of finite linear combinations of basis functions. With the current computer technologies, there is a possible way out to the situation by solving numerically the corresponding wave equations. The present interest and need for numerical determination of electronic structure of atoms, diatomic and poly atomic molecules led us to organize a NATO-ARW devoted to these questions. The aim of the meeting was to provide a review of the state of the art about techniques and applications. The organizing committee consisted of Drs. G. Berthier, P. Claverie, M. Defranceschi, J. Delhalle, H.J. Monkhorst and P. Pyykk6. It was a great sorrow for us to be informed in January 88 of the death of Professor P. Claverie who supported so enthusiastically the idea of having such a meeting organized. The NATO Advanced Research Worshop on : " Numerical Determination of the Electronic Structure of Atoms, Diatomic and Poly atomic Molecules" was held at Versailles (France) from April 17th till April 22th, 1988.

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Content:
Front Matter....Pages i-xiii
Basic Mathematical Properties of Electronic Wave Functions in Configuration Space....Pages 1-15
Basic Mathematical Properties of Electronic Wave Functions in Momentum Space....Pages 17-48
The Analytic Structure of Atomic and Molecular Wavefunctions and its Impact on the Rate of Convergence of Variational Calculations....Pages 49-84
Stochastic Methods in Quantum Mechanics....Pages 85-105
Computational Strategies and New Applications in Green’s Function Monte Carlo....Pages 107-129
Numerical Determination of Non-Relativistic and Relativistic Pair Correlation....Pages 131-160
Fully Numerical Calculations for Diatomic Systems....Pages 161-175
Very Accurate Calculations for Diatomic, Neutral and Anionic Systems with Numerical Orbitals....Pages 177-200
The Development of an Efficient Numerical Orbital Algorithm for Polyatomic Systems: A Review of the Various Options....Pages 201-207
Electronic Structure Theory in Momentum Space....Pages 209-238
Should Numerical Orbital Calculations be done with Basis Sets?....Pages 239-244
Quantum Chemistry by Random Walk: High Accuracy for Large Molecules....Pages 245-250
Prolate Spheroidal Wavefunctions....Pages 251-256
Error Estimate in Variational Calculations of Eigenvalues and Eigenvectors....Pages 257-261
A Momentum Space Approach to Improve ab initio Hartree-Fock Results Based on the LCAO-GTF Approximation....Pages 263-268
Isotope Shift MCHF Calculations in Strontium....Pages 269-274
Finite Element Method for the Accurate Solution of Diatomic Molecules....Pages 275-282
Momentum Space Coordinate Transformations and their use in Numerical Orbital Calculations....Pages 283-288
M?ller Plesset Calculations with Explicitly Correlated Wave Functions....Pages 289-293
On the Coulomb Sturmian Basis....Pages 295-299
An Analytical L2 Method for Continuum and Autoionizing States....Pages 301-310
Application of the Two-dimensional Fully-Numerical RHF Method to Open-Shell Hydrides....Pages 311-315
Interpolation of Numerical Orbitals in Momentum Space....Pages 317-319
On the Accuracy of the Algebraic Approximation in Relativistic Electronic Structure Calculations....Pages 321-327
Numerical MCSCF in One and Two Dimensions....Pages 329-334
Numerical Methods for Calculating Multicenter Integrals for Arbitrary Orbitals....Pages 335-339
Nonlinear Sequence Transformations for the Efficient Evaluation of Auxiliary Functions for GTO Molecular Integrals....Pages 341-346
Concluding Remarks....Pages 347-348
Back Matter....Pages 349-359

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Content:
Front Matter....Pages i-xiii
Basic Mathematical Properties of Electronic Wave Functions in Configuration Space....Pages 1-15
Basic Mathematical Properties of Electronic Wave Functions in Momentum Space....Pages 17-48
The Analytic Structure of Atomic and Molecular Wavefunctions and its Impact on the Rate of Convergence of Variational Calculations....Pages 49-84
Stochastic Methods in Quantum Mechanics....Pages 85-105
Computational Strategies and New Applications in Green’s Function Monte Carlo....Pages 107-129
Numerical Determination of Non-Relativistic and Relativistic Pair Correlation....Pages 131-160
Fully Numerical Calculations for Diatomic Systems....Pages 161-175
Very Accurate Calculations for Diatomic, Neutral and Anionic Systems with Numerical Orbitals....Pages 177-200
The Development of an Efficient Numerical Orbital Algorithm for Polyatomic Systems: A Review of the Various Options....Pages 201-207
Electronic Structure Theory in Momentum Space....Pages 209-238
Should Numerical Orbital Calculations be done with Basis Sets?....Pages 239-244
Quantum Chemistry by Random Walk: High Accuracy for Large Molecules....Pages 245-250
Prolate Spheroidal Wavefunctions....Pages 251-256
Error Estimate in Variational Calculations of Eigenvalues and Eigenvectors....Pages 257-261
A Momentum Space Approach to Improve ab initio Hartree-Fock Results Based on the LCAO-GTF Approximation....Pages 263-268
Isotope Shift MCHF Calculations in Strontium....Pages 269-274
Finite Element Method for the Accurate Solution of Diatomic Molecules....Pages 275-282
Momentum Space Coordinate Transformations and their use in Numerical Orbital Calculations....Pages 283-288
M?ller Plesset Calculations with Explicitly Correlated Wave Functions....Pages 289-293
On the Coulomb Sturmian Basis....Pages 295-299
An Analytical L2 Method for Continuum and Autoionizing States....Pages 301-310
Application of the Two-dimensional Fully-Numerical RHF Method to Open-Shell Hydrides....Pages 311-315
Interpolation of Numerical Orbitals in Momentum Space....Pages 317-319
On the Accuracy of the Algebraic Approximation in Relativistic Electronic Structure Calculations....Pages 321-327
Numerical MCSCF in One and Two Dimensions....Pages 329-334
Numerical Methods for Calculating Multicenter Integrals for Arbitrary Orbitals....Pages 335-339
Nonlinear Sequence Transformations for the Efficient Evaluation of Auxiliary Functions for GTO Molecular Integrals....Pages 341-346
Concluding Remarks....Pages 347-348
Back Matter....Pages 349-359
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