*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/9780199216949.003.0002
- Subject:
- Physics, Crystallography

This chapter starts off with an in-depth discussion on the angular and radial functions of the hydrogenic orbitals. Then the ground 1s 2 and the excited 1s ...
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This chapter starts off with an in-depth discussion on the angular and radial functions of the hydrogenic orbitals. Then the ground 1s 2 and the excited 1s 12s 1 configurations of the helium atom are employed to illustrate the determinantal wavefunction and the Pauli Exclusion Principle. Some simple trial wavefunctions for helium are introduced, with emphasis on the physical meaning of the adjustable parameters. For the many-electron atoms, the L-S and j-j coupling schemes are used to derive the spectroscopic terms arising from a given atomic configuration. Examples are then given to illustrate the correlation between the terms derived by these two schemes. The chapter concludes with a section on atomic properties, including ionization energy and electron affinity, electronegativity, relativistic effect on the properties of elements.Less

This chapter starts off with an in-depth discussion on the angular and radial functions of the hydrogenic orbitals. Then the ground 1*s* ^{2} and the excited 1*s* ^{1}2*s* ^{1} configurations of the helium atom are employed to illustrate the determinantal wavefunction and the Pauli Exclusion Principle. Some simple trial wavefunctions for helium are introduced, with emphasis on the physical meaning of the adjustable parameters. For the many-electron atoms, the *L-S* and *j*-*j* coupling schemes are used to derive the spectroscopic terms arising from a given atomic configuration. Examples are then given to illustrate the correlation between the terms derived by these two schemes. The chapter concludes with a section on atomic properties, including ionization energy and electron affinity, electronegativity, relativistic effect on the properties of elements.

*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/9780199216949.003.0007
- Subject:
- Physics, Crystallography

This chapter applies the group theoretic technique introduced in Chapter 6 to a number of chemically interesting problems. These problems include molecular orbital treatment of AH ...
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This chapter applies the group theoretic technique introduced in Chapter 6 to a number of chemically interesting problems. These problems include molecular orbital treatment of AH n (n = 2-6) molecules and cyclic conjugated polyenes (with and without d-orbital participation), construction of hybrid orbitals, relationship between molecular orbital and hybridization theories, molecular vibrations, etc. A large number of worked examples have been selected to illustrate that group theory can be used to simplify the physical problem and yield solutions of chemical significance. The advantage of this method becomes more obvious when the symmetry of the chemical system increases. Indeed, for highly symmetric molecules, very complex problems can have simple and elegant solutions. Even for less symmetric systems, symmetry arguments can still lead to meaningful results and conclusions that cannot be easily obtained otherwise.Less

This chapter applies the group theoretic technique introduced in Chapter 6 to a number of chemically interesting problems. These problems include molecular orbital treatment of AH_{ n } (*n* = 2-6) molecules and cyclic conjugated polyenes (with and without *d*-orbital participation), construction of hybrid orbitals, relationship between molecular orbital and hybridization theories, molecular vibrations, etc. A large number of worked examples have been selected to illustrate that group theory can be used to simplify the physical problem and yield solutions of chemical significance. The advantage of this method becomes more obvious when the symmetry of the chemical system increases. Indeed, for highly symmetric molecules, very complex problems can have simple and elegant solutions. Even for less symmetric systems, symmetry arguments can still lead to meaningful results and conclusions that cannot be easily obtained otherwise.