Electron Correlation in Molecules – ab initio Beyond Gaussian Quantum Chemistry

1st Edition, Volume 73 - January 26, 2016
Editors: Philip E. Hoggan, Telhat Ozdogan
Language: English
Hardback ISBN:
9 7 8 - 0 - 1 2 - 8 0 3 0 6 0 - 8
eBook ISBN:
9 7 8 - 0 - 1 2 - 8 0 3 0 6 1 - 5

Electron Correlation in Molecules – ab initio Beyond Gaussian Quantum Chemistry presents a series of articles concerning important topics in quantum chemistry, including survey… Read more

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Electron Correlation in Molecules – ab initio Beyond Gaussian Quantum Chemistry presents a series of articles concerning important topics in quantum chemistry, including 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.

Section I: Exponential Type Basis Quantum Chemistry

Chapter One: A Sturmian Approach to Photoionization of Molecules

Abstract
1 Introduction
2 Generalities
3 Examples Taken from the Literature
4 Survey of Theoretical Methods
5 Sturmian Approach
6 Conclusions
Acknowledgments
Appendix List of Photoionization Calculations for Different Molecules

Chapter Two: General Coalescence Conditions for the Exact Wave Functions: Higher-Order Relations for Coulombic and Non-Coulombic Systems

Abstract
1 Introduction
2 Basic Formulation
3 Primitive General Coalescence Conditions
4 General Coalescence Conditions
5 Verification of GCCs
6 Solving the SE with GCCs
7 Conclusions
Acknowledgment

Chapter Three: Exponentially Correlated Wave Functions for Four-Body Systems

Abstract
1 Introduction and History
2 Relative Coordinates
3 Four-Body Wave Functions
4 Potential and Kinetic Energy Operators
5 Matrix Elements
6 Angular Integration
7 Shape Integration
8 Applications
Acknowledgments
Appendix Boundary Integrals

Chapter Four: Analytic Formulas for Two-Center Two-Electron Integrals with Exponential Functions

Abstract
1 Introduction
2 Integral Representation for the Master Integral
3 Recurrence Relations for the General Integral with σ₀₀ ≠ 0
4 Recurrence Relations at σ₀₀ = 0
5 James-Coolidge Integrals σ₂₀ = 0
6 Conclusion
Acknowledgment
Appendix A Master Integral
Appendix B Inhomogeneous Terms

Chapter Five: Singlet and Triplet Bound State Spectra in the Four-Electron Be-Like Atomic Systems

Abstract
1 Introduction
2 Hamiltonian and Bound State Wave Functions in the CI Method
3 General Structure of the Bound State Spectra
4 Spectral Diagram of the Four-Electron Be-Like Atoms
5 Conclusion
Acknowledgments

Chapter Six: An Application of the Gaussian Transform for Approximating Some Bessel Functions and Multicenter Integrals Involving 1s Slater-Type Orbitals

Abstract
1 Introduction
2 Methodology
3 Results for the Coulomb Potential
4 Concluding Remarks
Appendix

Chapter Seven: Size-Extensivity Corrections in Single- and Multireference Configuration Interaction Calculations

Abstract
1 Introduction
2 Theoretical Background
3 Results and Discussion
4 Conclusion
Acknowledgments

Chapter Eight: Introducing a Polynomial Expression of Molecular Integrals for Algebraic the Molecular Orbital (MO) Equation

Abstract
1 Introduction
2 Method
3 Results and Discussion
4 Conclusion
Acknowledgments
Appendix Taylor Expansion of Overlap Integral of × 16 about a₀ and b₀

Chapter Nine: Analytic Calculation of Momentum Distribution and Compton Profiles of Atoms Using Hartree–Fock–Roothaan Method: Applications to Atoms 2 ≤ Z ≤ 10

Abstract
1 Introduction
2 Analytical Expression for Momentum Density and Atomic Compton Profiles
3 Auxiliary Functions B_mn^l(α, β; q)
4 Compton Profile of Atoms 2 ≤ Z ≤ 10
5 Results and Discussions
Acknowledgment

Chapter Ten: Evaluation of One-Electron Basic Integrals of Irregular Solid Harmonics and Slater-Type Orbitals Using Fourier Transforms

Abstract
1 Introduction
2 Properties of Solid Spherical Harmonics
3 One-Electron Integrals Between ISHs and STOs with Equal Screening Parameters
4 Numerical Results and Discussion

Section II: Electron Correlation in Molecules and Solids

Chapter Eleven: Excitation Energies of Molecules from Ensemble Density Functional Theory: Multiconfiguration Approaches

Abstract
1 Ensemble Variation Principle and Its Descendants
2 Multiconfiguration Wavefunction-Based Methods for Ensembles
3 State-Averaged Spin-Restricted KS Method
4 Range-Separated Approaches
5 Summary and Outlook
Acknowledgments

Chapter Twelve: Application of the Space-Pseudo-Time Method to Density Functional Theory

Abstract
1 Introduction
2 Kohn–Sham Equations
3 Radial Equations
4 Numerical Results and Conclusions
Acknowledgments

Chapter Thirteen: Potential Energy Curves of NaK Molecule from All-Electron Multireference-Coupled Cluster Calculations

Abstract
1 Introduction
2 Synopsis of the Theory
3 Results and Discussion
4 Conclusions
Acknowledgment

Chapter Fourteen: The Correlation Effects in Density Functional Theory Along the Dissociation Path

Abstract
1 Introduction
2 Theory
3 Computational Details
4 Numerical Results and Discussion
5 Final Remarks
Acknowledgments
Conflict of Interest
Appendix Analysis of the Behavior of the Investigated GGA Potentials near the Middle of the Bond

Chapter Fifteen: Introduction to the Variational and Diffusion Monte Carlo Methods

Abstract
1 Variational Monte Carlo
2 Diffusion Monte Carlo
Acknowledgments
Appendix Statistical Estimator of Nonlinear Functions of Expectation Values

Chapter Sixteen: Configuration Interaction Monte Carlo with Coupled Clusters Wave Functions

Abstract
1 Introduction
2 Method
3 Results in Homogeneous Systems
4 First Row Atoms
5 Conclusions

Chapter Seventeen: X-Ray Constrained Wave Functions: Fundamentals and Effects of the Molecular Orbitals Localization

Abstract
1 Introduction
2 Theory
3 Computational Results
4 Conclusions and Perspectives
Acknowledgments

Chapter Eighteen: Electron Impact Atomic and Ionic Ionization: Analytical, Semiempirical, and Semiclassical Methods

Abstract
1 Introduction
2 Outline of the Models
3 Experimental Data Sources
4 Discussion
5 Conclusions
Acknowledgments

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

Telhat Ozdogan

I was born in 1971 in Tatvan/Turkey, where I studied my primary and secondary education. In 1994, I graduated from the Physics Department of Faculty of Education in 19 Mayis University and in 1997, I completed my master dissertation named “Investigation of DEPT and 2D DEPT J-Resolved NMR of Some Spin Systems by Product Operator Theory”. I finished my doctoral thesis named “Combined Theory of Electric Multipole Moment Tensors and Application to Polyatomic Molecules” in 2000. I have been in Erlangen University in Germany as a researcher for 3 months and after this I was assigned to the Rize Faculty of Arts and Sciences in Black Sea Technical University as an Assist. Proffessor. In 2007, I became Assoc. Professor in Department of Physics in Atomic and Molecular Physics in Recep Tayyip Erdoğan University and worked in the same position until 2013. Same year, I became a Professor and started to work at Amasya University, Computer and Instructional Technologies Education Program of Faculty of Education and I am still working at the same university and department.

Affiliations and expertise

Amasya University, Turkey

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