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Students starting graduate studies in quantum chemistry sometimes recognize that the gap between what they learned in junior level physical chemistry and what they are expected to know before taking a graduate quantum mechanics course is large. Shida’s book, The
Chemical Bond: A Fundamental Quantum-Mechanical Picture, fills some of these gaps. Its preface states, “this book is aimed at readers who have finished a beginning course in quantum chemistry and wish to advance a step further”. This is a fair assessment of this small, tightly packed, text.
The text opens with a quick review of the electron and electronic properties. In this context the idea of an electron trapped in a square-well potential is first presented along with the basic ideas that one would need to set up, but not necessarily solve, the Schrödinger equation. The fundamental mathematical framework for quantum mechanics is presented in chapter two. Chapter three introduces the one-electron atom and the topics (such as coulombic potentials, orbital angular momentum, and spin eigenfunctions), that one expects to be presented in relation to atomic quantum mechanics. Chapter four proceeds to multi-electron atoms and includes treatments of the Pauli exclusion principle and the concept of total angular momentum. Chapter four also introduces the Hartree–Fock self consistent field (SCF) method for solving the energetics of the multi-electron atom. Chapter five is a short chapter devoted solely to the Born–Oppenheimer approximation and its use to separate electronic and nuclear motions in solving the Schrödinger equation.
With the BO approximation established, chapter six picks up the hydrogen molecular
ion and quickly proceeds to a chapter devoted explicitly to the hydrogen molecule.
In this context the LCAO–MO theory is presented as a means to explain
the stability of the hydrogen molecular ion and the hydrogen molecule. Heitler–London
theory is also introduced. Chapter seven brings spectroscopic measurement on
small molecules into the picture as the “experiments that paved the way
to quantum theory”. Molecular orbital theory and Heitler–London
theory are further developed in this chapter. Chapter eight is the final and
capstone chapter of the text with its emphasis being polyatomic molecules and
chemical bonding. SCF–MO calculations for these systems are developed
and an example applying the HF–SCF–MO method to a ten-electron
system is presented. Within this framework, the idea of hydbridization is introduced.
The discussion of group theory is limited. The book ends with a good list of
references for further study.
As can be seen from the order of presentation, this is a classic treatment of quantum mechanics applied to chemical bonding. Shida carefully progresses from one topic to the next and, after introducing the fundamental mathematics in chapter 2, utilizes the mathematics to its fullest extent in the presentation of the material. While this translation is accessible to advanced undergraduate students, students who have had a junior-level physical chemistry class that emphasized techniques and methods for solving the Schrödinger equation will get the greatest benefit from it. The only real drawback of the text from a teaching perspective is the limited number of problems at the end of each chapter—they are sparse and solutions are not provided. I could imagine that this book, paired with Johnson and Pedersen’s Problems
and Solutions in Quantum Chemistry and Physics (1) could serve as the texts for an advanced undergraduate course in bonding theory with the goal of moving students toward graduate degrees in theoretical or computational chemistry.
Literature Cited
- Johnson, Charles S. Jr.; Pedersen, Lee G. Problems
and Solutions in Quantum Chemistry and Physics; Dover: New York, 1986.
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