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Spin Eigenstates and Spin-Independent Alternant Systems

Tomislav P. Živković ; Rugjer Bošković Institute, P.O.B. 1016, 41001 Zagreb, Croatia, Yugoslavia

Sažetak

The configuration interaction space Xn, built upon n electrons
moving over n spin-o orbitals Xi = Wi a and n spin-p orbitals Xi = Wi p, Wi being othonormalized atomic orbitals, is considered. Spin-independent alternant systems are defined in terms of the corresponding Hamiltonians. Each Hamiltonian H describing such a system is a linear combination of a spin-independent alternant operator Oalo and operator Z vanishing over Xn• The space of all spin-independent alternant operators is a linear space and it is spanned by »reduced« spin-independent alternant operators, which are explicitly obtained. Similarly, the space of all operators vanishing over X" is spanned by some basis operators, which are also explicitly given. Hence, each Hamiltonian describing a spin-independent alternant system can easily be constructed and identified. All such Hamiltonians have a complete set of semi-alternantlike (SAL) eigenstates. These states have many properties which generalize the well known properties of n-electron eigenstates of neutral alternant hydrocarbons. In particular, each SAL state rp E X; has a uniform total charge density distribution over all vertices (i), vanishing total bond orders between vertices of the same parity, etc. The complete
set of spin-independent properties common to all SAL states is
obtained. Standard representations {82, 8,} are also considered.
These representations are defined by basis vectors rp",m,T E X«,
common eigenstates to operators 82 and 8, with eigenvalues
s (s + 1) and m, respectively. It is shown that among all such
representations there are some with a special property that each
space E"T spanned by (2s + 1) vectors rp",m,T (variable m) contains
only SAL states. In particular, all basis vectors rp",m,T are SAL
states. Such representations are called »alternatlike« (AL). A
similar result is obtained for the standard representations {82, 8,},
and the connection between AL representations {82, 8,} and {82, 8x} is established. It is shown that common eigenstates to the Hamiltonian H describing a spin-independent alternant system and operators 82 and 8, (or 8,) can be chosen to be SAL states. In addition, if beside spin multipli city there is no other degeneracy, all eigenstates common to operators H, 82 and 8, (or 8x) are SAL states.

Ključne riječi

Hrčak ID:

177266

URI

https://hrcak.srce.hr/177266

Datum izdavanja:

5.11.1986.

Posjeta: 572 *