Quantum chemistry of solids: the LCAO first principles treatment of crystals

Book Details

Title	Quantum Chemistry of Solids: The LCAO First Principles Treatment of Crystals
Author(s)	Robert A. Evarestov
Publisher	Springer
Year	2007
Edition	1st Edition
Language	English
Pages	557
ISBN	9783540487487
Genre / Domain	Science, Chemistry, Physics, Materials Science
Series	Springer Series in Solid-State Sciences
Size	5.92 MB
Extension	PDF

Summary

Quantum Chemistry of Solids: The LCAO First Principles Treatment of Crystals is a comprehensive monograph that addresses the theoretical foundations and practical applications of Linear Combination of Atomic Orbitals (LCAO) methods for calculating the electronic structure of periodic systems. Authored by Robert A. Evarestov, a distinguished professor and head of the Quantum Chemistry Department at St. Petersburg State University, this work was published by Springer in 2007 as the 153rd volume in the prestigious Springer Series in Solid-State Sciences [citation:1][citation:19]. The book fills an important gap in the literature by providing a unified treatment that bridges the traditionally separate disciplines of solid-state physics and quantum chemistry, offering researchers and graduate students a rigorous yet accessible guide to first-principles calculations of crystalline materials [citation:1].

The book is structured into two principal parts that reflect its dual focus on theory and application. The first part, dedicated to theory, systematically develops the fundamental concepts underlying LCAO methods for periodic systems. It begins with an examination of space groups and crystalline structures, establishing the symmetry framework essential for understanding crystal orbitals [citation:14]. Subsequent chapters address the Hartree-Fock LCAO method for periodic systems, electron correlations in molecules and crystals, semiempirical LCAO methods, and the Kohn-Sham LCAO method based on density functional theory [citation:5][citation:10]. A crucial feature of this section is the detailed treatment of how translation and site symmetry establish connections between k-space solid-state physics and real-space quantum chemistry methods within the framework of the cyclic model of an infinite crystal [citation:1]. This approach allows readers to understand how molecular quantum chemistry concepts translate to the periodic systems encountered in solid-state research.

The second part of the book focuses on practical applications of LCAO methods for calculating properties of bulk crystals. It covers basis sets and pseudopotentials in periodic LCAO calculations, followed by detailed discussions of perfect-crystal properties, including magnetic ordering and crystal structure optimization [citation:1][citation:10]. The book presents case studies that demonstrate the efficiency of LCAO methods, including supercell calculations of point defects in non-metallic solids and the electronic structure of crystalline surfaces, particularly metal oxides [citation:14]. These applications illustrate how the theoretical framework developed in the first part translates into practical computational tools for solving real materials science problems. The inclusion of 78 figures and 126 tables throughout the text aids in understanding complex concepts and visualizing computational results [citation:1][citation:14].

The target audience for this book includes researchers and graduate students in quantum chemistry, solid-state physics, and materials science who are interested in first-principles calculations of crystalline materials. The book assumes a foundational knowledge of quantum mechanics and solid-state physics, making it most suitable for readers at the advanced graduate level or beyond. While the mathematical treatment is rigorous, the author's pedagogical approach ensures that the material remains accessible to those willing to engage with the derivations. The book's comprehensive coverage of both theory and application makes it equally valuable as a textbook for advanced courses and as a reference for practicing researchers seeking to apply LCAO methods to their own problems [citation:1].

What distinguishes this work is its thorough integration of quantum chemical and solid-state physical perspectives, an approach that reflects Evarestov's extensive experience in both disciplines. The author's development of the cyclic model of crystal, which has found wide application in scientific centers across Russia and abroad, provides a unifying framework for the book's treatment of periodic systems [citation:19]. The book has been cited over 118 times since its publication, indicating its significant impact on the field [citation:1]. A second edition was published in 2012, expanding the content to include new chapters on scalar-relativistic LCAO methods for solids containing heavy atoms and applications to inorganic nanotubes, further confirming the book's lasting value to the scientific community [citation:5].

Key Features

• The book provides a comprehensive treatment of LCAO methods for first-principles calculations of electronic structure in periodic systems, exceeding the scope of previously existing books on the subject [citation:1].
• It systematically develops the theory underlying LCAO methods applied to periodic systems, including wave-function-based (Hartree-Fock), density-based (DFT), and hybrid Hamiltonians [citation:1].
• The author establishes a crucial connection between k-space solid-state physics and real-space quantum chemistry through translation and site symmetry considerations within the cyclic model of an infinite crystal [citation:1].
• The book addresses electron correlation effects in periodic systems through localized crystalline orbitals, a topic of fundamental importance for accurate calculations [citation:1][citation:5].
• Practical applications are thoroughly explored, including calculations of bulk crystal properties, magnetic ordering, and crystal structure optimization [citation:1].
• Supercell calculations of point defects in non-metallic solids are presented, demonstrating the efficiency of LCAO methods for modeling imperfect crystals [citation:1][citation:14].
• The electronic structure of crystalline surfaces, particularly metal oxides, is examined through LCAO calculations, illustrating the method's applicability to surface science [citation:14].
• The book includes 78 figures and 126 tables that aid in understanding complex theoretical concepts and visualizing computational results [citation:1][citation:14].
• It is published as volume 153 in the Springer Series in Solid-State Sciences, a prestigious series known for high-quality monographs in condensed matter physics [citation:1][citation:11].
• The author, Robert A. Evarestov, is a leading authority who developed the cyclic model of crystal that is widely used in scientific centers internationally [citation:19].
• The work appeals not only to quantum chemists and solid-state physicists but also to materials scientists interested in computational modeling of crystalline materials [citation:1].
• The book has been influential in the field, with over 118 citations, and a second expanded edition was published in 2012 [citation:1][citation:5].

About the Author

Robert Aleksandrovich Evarestov was born in 1937 in St. Petersburg, Russia, and has dedicated his career to theoretical physics and quantum chemistry [citation:1][citation:3]. He graduated with distinction from the Department of Theoretical Physics at St. Petersburg State University in 1960, where his teachers included Professor M.I. Petrashen and Professor M.G. Veselov, both assistants of the renowned academician Vladimir A. Fock [citation:19]. He received his PhD in Theoretical Physics from the same university in 1964 and completed his postdoctoral degree in 1977 with a thesis on molecular models in the electronic structure theory of crystals [citation:4]. His academic career at St. Petersburg State University has spanned over six decades, progressing from assistant to professor, and he has held several key administrative positions including Director of the Chemistry Institute (1990–1994) and First Vice Rector of the University (1994–1999) [citation:13][citation:19].

Since 1999, Evarestov has served as Head of the Quantum Chemistry Department at St. Petersburg State University, where he has developed and taught courses on symmetry theory in chemistry, quantum chemistry of solids, and computational methods for students and graduate students [citation:13][citation:19]. His research focuses on the quantum chemistry of solid state, applying methods from solid-state physics, quantum chemistry, and molecular symmetry theory to study the electronic structure of crystals, their surfaces, and defects [citation:3][citation:19]. He is the author of over 300 scientific publications, including more than 80 in prestigious international journals, and has published six monographs [citation:4][citation:19]. His monograph Site Symmetry in Crystals: Theory and Applications, co-authored with V.P. Smirnov, was published by Springer in two editions (1993, 1997) [citation:4]. His seminal work Quantum Chemistry of Solids was published by Springer in 2007, with a second expanded edition in 2012 [citation:5].

Evarestov's contributions to science have been recognized with numerous honors and awards. He is a Full Member of the Russian Academy of Natural Sciences, a Foreign Member of the Latvian Academy of Sciences (since 2003), and a recipient of the Humboldt Foundation Award (1998) [citation:1][citation:4]. He has been awarded the title of Honored Worker of Science of the Russian Federation and has twice received the university prize for best scientific works (1982, 2005) [citation:13]. In 2024, he was awarded the Medal of the Order "For Services to the Fatherland" I degree for his contributions to scientific and pedagogical activities [citation:18]. He has supervised over 25 doctoral students and has been invited to deliver lectures at universities in Germany, France, Sweden, Spain, Japan, Canada, the United States, Switzerland, and Italy [citation:13][citation:19]. His cyclic model of crystal has found wide application in scientific centers both in Russia and abroad, cementing his reputation as a leading figure in the quantum chemistry of solids.

Related Books

• Site Symmetry in Crystals: Theory and Applications — Robert A. Evarestov and V.P. Smirnov
• Theoretical Modeling of Inorganic Nanostructures: Symmetry and ab-initio Calculations of Nanolayers, Nanotubes and Nanowires — Robert A. Evarestov
• Electronic Structure: Basic Theory and Practical Methods — Richard M. Martin
• Density Functional Theory: A Practical Introduction — David S. Sholl and Janice A. Steckel
• Quantum Chemistry — Ira N. Levine
• Solid State Physics — Neil W. Ashcroft and N. David Mermin
• Molecular Quantum Mechanics — Peter Atkins and Ronald Friedman

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FAQ

Q : What are the main differences between the first and second editions of this book?

R : The second edition, published in 2012, includes two new chapters in the application part of the book. Chapter 12 addresses recent LCAO calculations and illustrates the efficiency of the scalar-relativistic LCAO method for solids containing heavy atoms. Chapter 13 deals with the symmetry properties and recent applications of LCAO methods to inorganic nanotubes. New material was also added to chapter 9 on perfect-crystal properties, including discussions of high-frequency dielectric constants and phase transitions in solids [citation:5][citation:20].

Q : What is the cyclic model of crystal mentioned in the book?

R : The cyclic model of crystal is a theoretical framework proposed and extensively studied in the works of Robert A. Evarestov that allows the treatment of infinite periodic systems using finite computational models. It establishes a connection between k-space solid-state physics and real-space quantum chemistry methods through translation and site symmetry considerations [citation:1]. This model has found wide application in scientific centers in Russia and abroad, including France, Germany, Great Britain, and Latvia [citation:19].

Q : What types of Hamiltonians are discussed in the book?

R : The book covers three main types of Hamiltonians used in LCAO calculations for periodic systems: wave-function-based Hamiltonians (specifically the Hartree-Fock method), density-based Hamiltonians (specifically density functional theory or DFT), and hybrid Hamiltonians that combine elements of both approaches [citation:1]. Each method is developed systematically with attention to its theoretical foundations and practical implementation for crystalline systems.

Q : What are the 78 figures and 126 tables in the book used for?

R : The 78 figures and 126 tables serve to illustrate complex theoretical concepts, visualize computational results, and present data from LCAO calculations in an accessible format [citation:1][citation:14]. They aid readers in understanding the geometric and structural properties of crystals, the behavior of electron orbitals, and the outcomes of various computational experiments. These visual and tabular elements enhance the pedagogical value of the book for both students and researchers.

Q : How does this book connect quantum chemistry and solid-state physics?

R : The book establishes connections between these disciplines through its treatment of translation and site symmetry, which link k-space solid-state physics with real-space quantum chemistry methods [citation:1]. It demonstrates how molecular orbital concepts from quantum chemistry can be extended to periodic systems using LCAO methods, allowing researchers trained in either discipline to apply their knowledge to crystalline materials. This bridging approach is one of the book's most distinctive contributions.

Q : What computational methods are discussed for modeling point defects?

R : The book presents supercell calculations of point defects in non-metallic solids as a key application of LCAO methods [citation:1][citation:14]. The supercell approach involves constructing a larger periodic cell containing the defect and its surrounding lattice, allowing the defect's electronic structure to be calculated within a periodic framework. This method demonstrates the efficiency of LCAO techniques for modeling imperfect crystals, which are important for understanding real materials where defects often determine functional properties.

Q : Who should read this book?

R : The book is intended for researchers and graduate students in quantum chemistry, solid-state physics, and materials science who are interested in first-principles calculations of crystalline materials [citation:1]. It assumes foundational knowledge of quantum mechanics and solid-state physics, making it suitable for advanced graduate students and beyond. The comprehensive treatment of both theory and application makes it valuable as a textbook for specialized courses and as a reference for practicing researchers.

Q : What is the significance of the Springer Series in Solid-State Sciences volume number?

R : The book is volume 153 in the Springer Series in Solid-State Sciences, a prestigious series known for publishing high-quality monographs and advanced textbooks in condensed matter physics and related fields [citation:1][citation:11]. Being part of this series indicates the book's scholarly quality and its recognition by the academic community as an authoritative contribution to the field of solid-state sciences.