Some properties of symmetrized transition density matrices based on configuration interaction wavefunctions
✍ Scribed by Annette Guldberg
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 337 KB
- Volume
- 154
- Category
- Article
- ISSN
- 0009-2614
No coin nor oath required. For personal study only.
✦ Synopsis
The discrete, spinless first-order transition density matrix, rQn, associated with two electronic wavefunctions, !+'Q and 'f'a, is normally not Hermitian (or symmetric).
In the real case a symmetric transition density matrix, AQs, is defined by A%" = 3 (r? +f 2"). In the present work some properties of this symmetric matrix are discussed. It is proven that in some cases the eigenvalues of AQR occur in pairs such that if I ( # 0) is an eigenvalue than -1 is also an eigenvalue. When IrQ and '&belong to different irreducible representations (IRS) of an Abelian point group the relation is proven to be exact. If the functions belong to the same IR it is demonstrated by numerical computations that the correspondence is only approximately fulfilled.