Proceedings of MEST 2012: Exponential Type Orbitals for Molecular Electronic Structure Theory

1st Edition - November 19, 2013

Editor: Philip E. Hoggan

Hardback ISBN:

9 7 8 - 0 - 1 2 - 4 1 1 5 4 4 - 6

eBook ISBN:

9 7 8 - 0 - 1 2 - 4 1 1 5 5 9 - 0

Advances in Quantum Chemistry presents surveys of current topics in this rapidly developing field that has emerged at the cross section of the historically established areas of… Read more

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Advances in Quantum Chemistry presents surveys of current topics in this rapidly developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology. It features detailed reviews written by leading international researchers. This volume focuses on the theory of heavy ion physics in medicine.

Preface
- Reference
Part 1: Exponential Type Orbitals
Chapter 1. Fully Correlated Wavefunctions for Three- and Four-Body Systems
- Abstract
- 1 Introduction
- 2 Wavefunctions
- 3 Operators and matrix elements
- 4 Wavefunction optimization
- 5 Results: three-body problems
- 6 Results: four-body problems
- 7 Conclusion
- Acknowledgments
- References
Chapter 2. Electron and Electron-Pair Number and Momentum Densities for Low-Lying States of He, H^–, and Li⁺
- Abstract
- 1 Introduction
- 2 Explicitly Correlated Wave Functions
- 3 Calculations
- 4 Position-Space Densities
- 5 Momentum-Space Densities
- 6 Concluding Remarks
- Acknowledgment
- References
Chapter 3. A Basis Sets Composed of Only 1s Slater Orbitals and 1s Gaussian Orbitals to Perform Molecular Calculations, SCF-LCAO Approach
- Abstract
- 1 Introduction
- 2 The model of a free atom in this context
- 3 Examples of atomic models
- 4 Examples of molecular calculations
- 5 Concluding remarks
- Acknowledgments
- References
Chapter 4. On a Transformation for the Electrostatic Potential, Generated by the Product of Two 1s Slater Type Orbitals, Giving an Efficient Expression
- Abstract
- 1 Introduction
- 2 Method
- 3 Results
- 4 Concluding remarks
- Acknowledgments
- References
Chapter 5. d-Dimensional Kepler–Coulomb Sturmians and Hyperspherical Harmonics as Complete Orthonormal Atomic and Molecular Orbitals
- Abstract
- 1 Introduction
- 2 Sturmian basis functions in configuration space
- 3 A momentum space perspective
- 4 Applications to atomic and molecular problems
- 5 Additional and concluding remarks
- Acknowledgments
- References
Chapter 6. Fast Electron Repulsion Integrals for Molecular Coulomb Sturmians
- Abstract
- 1 Introduction
- 2 Theory
- 3 Preliminary results
- 4 Discussion
- References
Chapter 7. Three-Body Coulomb Problems with Generalized Sturmian Functions
- Abstract
- 1 Introduction
- 2 Generalized Sturmian Functions
- 3 Three-Body Problems: Bound States
- 4 Three-Body Problems: Scattering States
- 5 Three-Body Scattering States: Applications
- 6 Summary and Perspectives
- Acknowledgments
- References
Chapter 8. Further Improvements on ψ^(α*)—ETOs with Hyperbolic Cosine Functions and Their Effectiveness in Atomic Calculations
- Abstract
- 1 Introduction
- 2 General definitions and properties
- 3 Computational method
- 4 Numerical results and discussion
- 6 Conclusion
- Acknowledgment
- References
Chapter 9. Reducing and Solving Electric Multipole Moment Integrals
- Abstract
- 1 Introduction
- 2 Definitions
- 3 Calculation of EMM Integrals with the Same Screening Parameters
- 4 Summary and Conclusion
- References
Chapter 10. Recurrence Relations for Radial Parts of STOs and Evaluation of Overlap Integrals via the Fourier Transform Methods
- Abstract
- 1 Introduction
- 2 Evaluation of recurrence relations for radial part for FTSTOs
- 3 Results and discussions
- References
Chapter 11. On the β⁻-Decay in the ⁸Li and ⁹Li Atoms
- Abstract
- 1 Introduction
- 2 Evaluation of the Final State Probabilities for the Bound States
- 3 Electron Ionization During the Nuclear β-decay
- 4 Bound State Wave Functions of the Three-Electron Atoms and Ions
- 5 On the Double β Decay
- 6 Conclusion
- References
Index

Philip E. Hoggan

Born in Aberystwyth, Wales and educated at Trinity College Cambridge, Philip Hoggan has always been French and British. After a mathematical chemistry background, he has studied a number of theoretical systems, with a DSc by research obtained in 1991 at Nancy, France on the way physical interaction between molecules and solid surfaces is a precursor to catalysis. This was treated entirely on the basis of Quantum Mechanics and applied, first to cis-trans butadiene isomerization on alumina and then a number of ‘organic’ reactions. The first lectureship was at Caen, Normandy from 1992. This period led to some fundamental research of ab initio Slater electronic structure calculations for more than 3 atoms. The first related code STOP was published in February 1996 after much work by a postdoctoral fellow A. Bouferguène, now Professor at U Alberta. After continuing to study catalytic systems at Caen, from a theoretical viewpoint, Philip Hoggan was appointed to the Chair of Theoretical Chemistry in Clermont from May 1998. This is still essentially his teaching position, although research interests have switched to solid-state (surface) physics joining the Pascal Institute for physics in Clermont from 2005. This followed a visiting professor stay of 18 months at Tallahassee, Florida in Theoretical Physics. Research emphasis has shifted from the STOP era (where the problem was solved by Coulomb Resolution in 2008) to Quantum Monte Carlo (QMC). The CNRS paid leave for a couple of years for Philip Hoggan to learn about this technique from Cyrus Umrigar, Julien Toulouse, Michel Caffarel and others. Of course, it eventually led to a project to calculate catalytic reactions on metal surfaces that was initiated by G-J Kroes (Leiden, NL) and his ERC in 2014. K Doblhoff-Dier arrived in Clermont for a ground-breaking research fellowship and each of us continues to produce very accurate work e.g. on hydrogen (production and dissociation on metals), as a clean fuel for renewable energy. Now, in 2023 we enter the 400th anniversary of Blaise Pascal’s birth. He invented calculators, some of which are in the Clermont museum. It is wonderful to work in the institute that bears his name conducting QMC on catalytic hydrogen synthesis on super-calculators: the tools that trace their roots to his ‘Pascaline’. Philip Hoggan is married and has twin daughters.

Affiliations and expertise

CNRS, University Blaise Pascal, France