Second Quantized Approach to Quantum Chemistry

1. Front Matter

   Pages I-XIII

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2. Introduction

   • Péter R. Surján

   Pages 1-5

3. The Concept of Creation and Annihilation Operators

   • Péter R. Surján

   Pages 6-17

4. Particle Number Operators

   • Péter R. Surján

   Pages 18-21

5. Second Quantized Representation of Quantum-Mechanical Operators

   • Péter R. Surján

   Pages 22-32

6. Evaluation of Matrix Elements

   • Péter R. Surján

   Pages 33-39

7. Advantages of Second Quantization—Illustrative Examples

   • Péter R. Surján

   Pages 40-45

8. Density Matrices

   • Péter R. Surján

   Pages 46-52

9. Connection to “Bra and Ket” Formalism

   • Péter R. Surján

   Pages 53-58

10. Using Spatial Orbitals

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    Pages 59-65

11. Some Model Hamiltonians in Second Quantized Form

    • Péter R. Surján

    Pages 66-86

12. The Brillouin Theorem

    • Péter R. Surján

    Pages 87-92

13. Many-Body Perturbation Theory

    • Péter R. Surján

    Pages 93-102

14. Second Quantization for Nonorthogonal Orbitals

    • Péter R. Surján

    Pages 103-113

15. Second Quantization and the Hellmann-Feynman Theorem

    • Péter R. Surján

    Pages 114-120

16. Intermolecular Interactions

    • Péter R. Surján

    Pages 121-136

17. Quasiparticle Transformations

    • Péter R. Surján

    Pages 137-152

18. Miscallenous Topics Related to Second Quantization

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    Pages 153-162

19. Problem Solutions

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    Pages 163-174

20. References

    • Péter R. Surján

    Pages 175-179

The aim of this book is to give a simple, short, and elementary introduction to the second quantized formalism as applied to a many-electron system. It is intended for those, mainly chemists, who are familiar with traditional quantum chemistry but have not yet become acquainted with second quantization. The treatment is, in part, based on a series of seminars held by the author on the subject. It has been realized that many quantum chemists either interested in theory or in applications, being educated as chemi~ts and not as physicists, have never devoted themselves to taking a course on the second quantized approach. Most available textbooks on this topic are not very easy to follow for those who are not trained in theory, or they are not detailed enough to offer a comprehensive treatment. At the same time there are several papers in quantum chemical literature which take advantage of using second quantization, and it would be worthwhile if those papers were accessible for a wider reading public. For this reason, it is intended in this survey to review the basic formalism of second quantization, and to treat some selected chapters of quantum chemistry in this language. Most derivations will be carried out in a detailed manner, so the reader need not accept gaps to understand the result.

• Second quantization
• chemistry
• electron
• perturbation theory
• quantum mechanics
• quantum theory

• Research Centre, Chinoin Pharmaceutical and Chemical Works Ltd., Budapest, Hungary

  Péter R. Surján

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