Advances in Quantum Chemistry

1st Edition, Volume 88 - September 19, 2023
Editor: Philip E. Hoggan
Language: English
Hardback ISBN:
9 7 8 - 0 - 4 4 3 - 1 8 6 6 3 - 9
eBook ISBN:
9 7 8 - 0 - 4 4 3 - 1 8 6 6 4 - 6

Advances in Quantum Chemistry, Volume 88 presents the latest ongoing research at the forefront of Electronic structure theory. Chapters in the updated release include Spin-c… Read more

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Advances in Quantum Chemistry, Volume 88 presents the latest ongoing research at the forefront of Electronic structure theory. Chapters in the updated release include Spin-constrained Hartree-Fock and the generator coordinate method for the 2-site Hubbard model, Analytical evaluation of Hylleraas-CI Coulomb and Hybrid two-center Integrals over Slater orbitals, Hartree-Fock-Roothaan Theory of Molecular Compton Profiles Via Position Space Method, Analysis of Research Trend on the Molecular Integrals Over Slater Type Orbitals, An efficient approximation for accelerating convergence of numerical power series, Results for the 1D−Schroedinger equation, The aims and objectives of algebraic molecular orbital theory, and much more.

Cover image
Title page
Table of Contents
Series Page
Copyright
Contributors
Preface
Section 1: Mathematical and general contributions
Chapter One: Fully automatic calculations of atomic energy levels with truncation energy errors
Abstract
1: Introduction
2: A posteriori truncation energy errors
3: A priori truncation energy errors
4: Summary of SCI-TEE
5: Automatic optimization of orbitals with prescribed TEE
6: Some examples favorable for SCI-TEE
7: Conclusions and perspectives of SCI-TEE
References
Chapter Two: Summation of convergent series by educated match
Abstract
1: Introduction
2: Calculation of EM approximants
3: Concluding remarks
References
Chapter Three: An efficient approximation for accelerating convergence of numerical power series: Results for the 1D-Schrödinger equation
Abstract
1: Introduction
2: Modified matrix Numerov representation for the Hamiltonian
3: A method to determine the function μ(N)
4: Example: Hydrogen-like atoms
5: Results and discussions
References
Section 2: Exponential type and related orbital contributions
Chapter Four: Analysis of research trends on the investigation of molecular integrals over Slater type orbitals
Abstract
1: Introduction
2: Why bibliometric analysis?
3: Purpose of the research
4: Methodology
5: Findings and discussion
6: Conclusion
7: Limitations
Acknowledgments
References
Chapter Five: Definition of the algebraic molecular orbital equation
Abstract
1: Introduction
2: A new molecular orbital equation under inequality constraints
3: Polynomial representation of molecular integrals
4: Application of polynomial representation of molecular integrals
5: Summary and perspectives
Appendix
References
Chapter Six: Analytical evaluation of Hylleraas-CI Coulomb and Hybrid two-center integrals over Slater-type orbitals
Abstract
1: Introduction
2: The Hy-CI wave function in the molecular orbital method
3: Auxiliary integrals
4: Method of direct integration over rij
5: Perspectives
References
Chapter Seven: Hartree–Fock calculations on atoms with coulomb Sturmian basis sets
Abstract
1: Introduction
2: Coulomb Sturmian functions
3: Space-time algorithm
4: Expansion in spherical harmonics
5: Results and conclusion
References
Chapter Eight: On the use of complex GTOs for the evaluation of radial integrals involving oscillating functions
Abstract
1: Introduction
2: Theoretical formulation
3: Numerical investigation
4: Summary
References
Chapter Nine: Hartree-Fock-Roothaan theory of molecular Compton profiles via the position space method
Abstract
1: Introduction
2: Theory
3: HFR theory for atomic and molecular Compton profiles and auto-correlation function
4: Molecular Compton profile integral calculation
5: Compton profiles of some small molecules
6: Results and discussions
Acknowledgment
References
Section 3: Contributions on highly correlated systems of electrons; excited states and applications
Chapter Ten: Spin-constrained Hartree–Fock and the generator coordinate method for the 2-site Hubbard model
Abstract
1: The generator coordinate and constrained Hartree–Fock method
2: The Hubbard model
3: Restricted, unrestricted, and constrained Hartree–Fock
4: Generator coordinate method
5: Conclusions
References
Chapter Eleven: Exploring new exchange-correlation kernels in the Bethe–Salpeter equation: A study of the asymmetric Hubbard dimer
Abstract
1: Introduction
2: Theory
3: Hubbard dimer
4: Results
5: Conclusions
References
Chapter Twelve: Potential energy curves of the LiRb+ molecular ion from ab initio calculations with all electrons correlated
Abstract
1: Introduction
2: Computational details
3: Results and discussion
4: Conclusions
References
Chapter Thirteen: Natural orbital functional theory studies of all-metal aromaticity: The Al3−anion
Abstract
1: Introduction
2: Global natural orbital functional
3: Methods
4: Results
5: Closing remarks
References
Chapter Fourteen: Convergence of Møller–Plesset perturbation theory for excited reference states
Abstract
1: Introduction
2: Theory
3: Results and discussion
4: Concluding remarks
Data availability
References
Chapter FiFteen: Quantum Monte Carlo method for metal-film catalysis: Water addition to CO adsorbed on Pt/Al(111), efficient hydrogen production
Abstract
1: Introduction
2: Theoretical method
3: The quantum Monte Carlo method: Specifications
4: Results
5: Perspectives and conclusions
References
Further reading
Chapter Sixteen: Quantum Monte Carlo method describing supported metal catalysis: Ni(111)/alumina decomposing methane as a route to hydrogen
Abstract
1: Introduction
2: Theoretical method
3: Results
4: Conclusions and perspectives
References
Chapter Seventeen: REG-MULTI: Lifting the veil on electrostatic interactions
Abstract
1: Introduction
2: Methods and background
3: Results and discussion
4: Conclusions
Acknowledgments
References
Chapter Eighteen: Electronic structure in organic dye-sensitized solar cells: Insight from density functional theory and electron dynamics
Abstract
1: Introduction
2: Methods and computational details
3: Results
4: Conclusion and outlook
References
Chapter Nineteen: Binding energies for successive addition reactions of •OH to C60: A laboratory for testing frontier molecular orbital theory
Abstract
1: Introduction
2: Computational details
3: Results
4: Concluding discussion
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