Creation operators nonorthogonal spin orbitals

The creation operators aj, for nonorthogonal spin orbitals are defined in the same way as for orthonormal spin orbitals (1.2.5). As for orthonormal spin orbitals, the anticommutation relations of the creation operators and the properties of their Hermitian adjoints (the annihilation operators) may be deduced from the definition of the creation operators and from the inner product (1.9.2). However, it is easier to proceed in the following manner. We introduce an auxiliary set of symmetrically orthonormalized spin orbitals... 

The treatment of orbital overlap in conjunction with the use of nonorthogonal basis sets deserves particular attention in treatments in terms of electron field operators. The definition of creation and annihilation operators and their anticommutation rules are basic for this development. Let s( ) be a set of atomic spin orbitals used to define the creation operators... 

It is noteworthy that the corresponding ex ession for a nonorthogonal creation operator working on an ON vector is identical to the expression for orthonormal spin orbitals (1.2.5)... 

Here and are the creation operators for electrons of spin a in 1 a and Isb, respectively. The 15a and 15b orbitals are nonorthogonal, but we recall from Section 1.9 that nonorthogonality affects only the anticommutation relations between creation and annihilation operators (1.9.12) - not the anticommutations between two creation operators and between two annihilation operators. 

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See also in sourсe #XX -- [ ]

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