Antisymmetry constraint

Our task is to find approximate solutions to the time-independent Schrodinger equation (Eq. (2)) subject to the Pauli antisymmetry constraints of many-electron wave functions. Once such an approximate solution has been obtained, we may extract from it information about the electronic system and go on to compute different molecular properties related to experimental observations. Usually, we must explore a range of nuclear configurations in our calculations to determine critical points of the potential energy surface, or to include the effects of vibrational and rotational motions on the calculated properties. For properties related to time-dependent perturbations (e.g., all interactions with radiation), we must determine the time development of the... 

Since in those forms of the UHF wave functions, one drops a constraint (either the need of a pure spin state in the first case or the Pauli antisymmetry rule in the second case), it is expected that the resulting wave function will give a lower energy than in the RHF case and thus introduce a part of the correlation energy. As shown in the table above, there is... 

As was mentioned previously, simple orbital products (electron configurations) must be converted into antisymmetrized orbital products (Slater determinants) in order to satisfy the Pauli principle. Thus, proper many-electron wavefunctions satisfy constraints of exchange antisymmetry that have no counterpart in pre-quantum theories. 

The antisymmetry of many-electron spin-orbital products places constraints on any acceptable model wavefunction, which give rise to important physical consequences. For example, it is antisymmetry that makes a function of the form I Isa Isa I vanish (thereby enforcing the Pauli exclusion principle) while I lsa2sa I does not vanish, except at points ri and 1 2 where ls(ri) = 2s(r2), and hence is acceptable. The Pauli principle is embodied in the fact that if any two or more columns (or rows) of a determinant are identical, the determinant vanishes. Antisymmetry also enforces indistinguishability of the electrons in that Ilsals(32sa2sp I =... 

As we have just implied, solutions to the many-electron scattering problem, like solutions to the many-electron bound-state problems of quantum chemistry, are obtained in terms of products of one-electron functions, subject to constraints of spin, exchange antisymmetry (the Pauli principle), and possibly spatial (point... 

Note that, in spite of the symmetrical form in which the constraints have been presented here, antisymmetry is a requirement, while spin eigenfunctions are not required and will emerge from the calculation (or not) when it is performed. 

If we insist on using tensor operators as well as on separating real and imaginary rotations, the antisymmetry of k imposes the following constraints [Pg.92]

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