*Wai-Kee Li, Gong-Du Zhou, and Thomas Chung Wai Mak*

- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199216949
- eISBN:
- 9780191711992
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199216949.003.0005
- Subject:
- Physics, Crystallography: Physics

This chapter first discusses the difference between semi-empirical and ab initio methods, then devotes most of the remaining pages to ab initio calculations. Each ab initio calculation is defined by ...
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This chapter first discusses the difference between semi-empirical and ab initio methods, then devotes most of the remaining pages to ab initio calculations. Each ab initio calculation is defined by two ‘parameters’: the basis set employed and the level of electron correlation adopted. These two topics are discussed in some detail. Density functional theory is also discussed, which has gained popularity in recent years. After describing these computational methods, a brief assessment on the performance of various levels of theory in yielding structural parameters, vibrational frequencies, and energetic quantities is given. Finally, a few examples are selected from recent literature to show how computations complement experiments to arrive at meaningful conclusions.Less

This chapter first discusses the difference between semi-empirical and *ab initio* methods, then devotes most of the remaining pages to *ab initio* calculations. Each *ab initio* calculation is defined by two ‘parameters’: the basis set employed and the level of electron correlation adopted. These two topics are discussed in some detail. Density functional theory is also discussed, which has gained popularity in recent years. After describing these computational methods, a brief assessment on the performance of various levels of theory in yielding structural parameters, vibrational frequencies, and energetic quantities is given. Finally, a few examples are selected from recent literature to show how computations complement experiments to arrive at meaningful conclusions.

*Mary Jo Nye*

- Published in print:
- 2011
- Published Online:
- September 2013
- ISBN:
- 9780226610634
- eISBN:
- 9780226610658
- Item type:
- chapter

- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226610658.003.0005
- Subject:
- History, History of Science, Technology, and Medicine

This chapter focuses on the collaborative work between Polanyi and Eyring, which made an enduring contribution in defining and defending the use of the “semi-empirical method” in theoretical ...
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This chapter focuses on the collaborative work between Polanyi and Eyring, which made an enduring contribution in defining and defending the use of the “semi-empirical method” in theoretical chemistry, which synthesized kinetic theory and thermodynamics with quantum mechanics and the theory of the electron–valence bond. Michael Polanyi is best known and revered among chemists and physicists for his theoretical and experimental work in chemical kinetics and dynamics, especially his development of the theory of the “transition state.” Polanyi, Eyring, and Eugene Wigner together are recognized by chemists today as the founders of the field of modern chemical dynamics. The following sections discuss Polanyi and Eyring's work, its reception, and its implications in theoretical chemistry, along with Polanyi's career transition from Berlin to Manchester and his earliest philosophical paper at Manchester, on the role of the inexact in science, in 1936.Less

This chapter focuses on the collaborative work between Polanyi and Eyring, which made an enduring contribution in defining and defending the use of the “semi-empirical method” in theoretical chemistry, which synthesized kinetic theory and thermodynamics with quantum mechanics and the theory of the electron–valence bond. Michael Polanyi is best known and revered among chemists and physicists for his theoretical and experimental work in chemical kinetics and dynamics, especially his development of the theory of the “transition state.” Polanyi, Eyring, and Eugene Wigner together are recognized by chemists today as the founders of the field of modern chemical dynamics. The following sections discuss Polanyi and Eyring's work, its reception, and its implications in theoretical chemistry, along with Polanyi's career transition from Berlin to Manchester and his earliest philosophical paper at Manchester, on the role of the inexact in science, in 1936.

*Jochen Autschbach*

- Published in print:
- 2020
- Published Online:
- February 2021
- ISBN:
- 9780190920807
- eISBN:
- 9780197508350
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190920807.003.0008
- Subject:
- Chemistry, Quantum and Theoretical Chemistry

This chapter discusses the concepts underlying the Hartree-Fock (HF) electronic structure method. First, it is shown how the energy expectation value is calculated for a Slater determinant (SD) ...
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This chapter discusses the concepts underlying the Hartree-Fock (HF) electronic structure method. First, it is shown how the energy expectation value is calculated for a Slater determinant (SD) wavefunction in the case of orthonormal orbitals. This leads to the definition of the electron repulsion integrals (ERIs). Next, the energy is minimized subject to the orthonormality constraints. This leads to the HF equation for the orbitals. The HF orbital energies are Langrange multipliers representing the constraints. An unknown set of orbitals can be determined from an initial guess via a self-consistent field (SCF) cycle. The HF scheme is discussed for closed-shell versus open shell systems, leading to the distinction between spin restricted and unrestricted HF (RHF, UHF). Kohn-Sham density functional theory (DFT) is introduced and its approximate version is placed in the context of ab-initio versus semi-empirical quantum chemistry methods.Less

This chapter discusses the concepts underlying the Hartree-Fock (HF) electronic structure method. First, it is shown how the energy expectation value is calculated for a Slater determinant (SD) wavefunction in the case of orthonormal orbitals. This leads to the definition of the electron repulsion integrals (ERIs). Next, the energy is minimized subject to the orthonormality constraints. This leads to the HF equation for the orbitals. The HF orbital energies are Langrange multipliers representing the constraints. An unknown set of orbitals can be determined from an initial guess via a self-consistent field (SCF) cycle. The HF scheme is discussed for closed-shell versus open shell systems, leading to the distinction between spin restricted and unrestricted HF (RHF, UHF). Kohn-Sham density functional theory (DFT) is introduced and its approximate version is placed in the context of ab-initio versus semi-empirical quantum chemistry methods.