Electron Correlation in Molecules – ab initio Beyond Gaussian Quantum Chemistry - 1st Edition - ISBN: 9780128030608, 9780128030615

Electron Correlation in Molecules – ab initio Beyond Gaussian Quantum Chemistry, Volume 73

1st Edition

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Serial Volume Editors: Philip Hoggan Telhat Ozdogan
Hardcover ISBN: 9780128030608
eBook ISBN: 9780128030615
Imprint: Academic Press
Published Date: 26th January 2016
Page Count: 440
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Table of Contents

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 Bmnl(αβq)
  • 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


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.

Key Features

  • 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
  • Features detailed reviews written by leading international researchers
  • The volume includes review on all the topics treated by world renown authors and cutting edge research contributions.


Researchers and post-graduates in quantum chemistry and physics from molecular to solid state applications.


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© Academic Press 2016
26th January 2016
Academic Press
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About the Serial Volume Editors

Philip Hoggan

Philip Hoggan Serial Volume Editor

Born 15.03.1961 in Aberystwyth, GB. French mother and Scottish father who were French literature specialists at the University. One sister. Schooled at Ardwyn Grammar which became Penglais Comprehensive in Aberystwyth. Admitted to Trinity College, Cambridge in 1978 to read Natural Sciences. Graduated in 1983 (MA). I had become interested in theoretical quantum chemistry. Leisure activities: Rugby, Theatre, Debate, Competitive Wine-tasting (Master of Wine). Obtained DPhil (in English) and DSc (Doctorat d’Etat-in French) doctorates by research after moving to the theoretical chemistry group in Nancy, France (1983). Began teaching in 1986. Moved to a permanent lecturer position in Caen in 1992. The stay in Nancy was devoted to methodology, including Green’s functions for electron transfer to metals from weakly interacting molecules. Caen explicitly involved catalysis. I became the first theoretician in a group, half of which worked closely with the petroleum industry and the half I was more directly associated with in Infra-red measurements to determine reaction intermediate structure. This was a very fruitful collaboration and by the time I was appointed to the chair of Theoretical Chemistry in Clermont (1998), two of my former students were able to take over the research and teaching. Presently, I am still in Clermont. In 2005, I moved to the Physics institute (Institut Pascal) to work on semi-conductor surfaces, in a set-up similar to that in Caen, with a majority of X-ray structure characterisation and some density functional theory and dynamics. The whole of 2003 and part of 2004 had been devoted to a visiting professor position in Tallahassee, Florida amid a very stimulating theoretical physics group. Since 2008, I have developed an expertise in Quantum Monte Carlo (QMC) simulations. The CNRS has supported this with a total of two full-time and one part time years of leave for research which lowed me to visit several QMC research teams, notably in Paris and Toulouse. This status includes 2017. I married a research biochemist from Clermont and we have two daughters.

Affiliations and Expertise

CNRS, University Blaise Pascal, France

Telhat Ozdogan

Telhat Ozdogan Serial Volume Editor

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