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1. Establish the symmetries of the resulting many-electron states. To do that, you will use the character table to determine the irrep describing a product of functions such as (1a₁) 2 (2a₁)²(1b2)²... It is pretty obvious that for this point group, any square such as (2b2)² has an A₁ symmetry, and only configurations with singly- occupied orbitals may give rise to many-electron states other than fully-symmetric ones A₁. Ground state 0 O A1 A2 O B₁ O B2 Excited state 1 O A1 A2 O B₁ O B2 Excited state 2 О А1 О А2 ОB1 B2 Excited state 3 O A1 A2 O B₁ O B2

1. Establish the symmetries of the resulting many-electron states. To do that, you will use the character table to determine the irrep describing a product of functions such as (1a₁) 2 (2a₁)²(1b2)²... It is pretty obvious that for this point group, any square such as (2b2)² has an A₁ symmetry, and only configurations with singly- occupied orbitals may give rise to many-electron states other than fully-symmetric ones A₁. Ground state 0 O A1 A2 O B₁ O B2 Excited state 1 O A1 A2 O B₁ O B2 Excited state 2 О А1 О А2 ОB1 B2 Excited state 3 O A1 A2 O B₁ O B2

Physical Chemistry
Physical Chemistry
2nd Edition
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Ball, David W. (david Warren), BAER, Tomas
Chapter12: Atoms And Molecules
Section: Chapter Questions
Problem 12.22E: Write a Slater determinant for the lithide ion, Li.
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1. Establish the symmetries of the resulting many-electron states. To do that, you will use the character table to determine the irrep describing a product of functions such as (1a₁) 2 (2a₁)²(1b2)²... It is pretty obvious that for this point group, any square such as (2b2)² has an A₁ symmetry, and only configurations with singly- occupied orbitals may give rise to many-electron states other than fully-symmetric ones A₁. Ground state 0 O A1 A2 O B₁ O B2 Excited state 1 O A1 A2 O B₁ O B2 Excited state 2 О А1 О А2 ОB1 B2 Excited state 3 O A1 A2 O B₁ O B2
Transcribed Image Text:1. Establish the symmetries of the resulting many-electron states. To do that, you will use the character table to determine the irrep describing a product of functions such as (1a₁) 2 (2a₁)²(1b2)²... It is pretty obvious that for this point group, any square such as (2b2)² has an A₁ symmetry, and only configurations with singly- occupied orbitals may give rise to many-electron states other than fully-symmetric ones A₁. Ground state 0 O A1 A2 O B₁ O B2 Excited state 1 O A1 A2 O B₁ O B2 Excited state 2 О А1 О А2 ОB1 B2 Excited state 3 O A1 A2 O B₁ O B2
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ISBN:
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