Wave function single-determinantal

ORTHOGONALITY CONSTRAINTS FOR SINGLE DETERMINANTAL WAVE FUNCTIONS... 

We shall be concerned with ground and excited electronic states which can be adequately described by a single determinantal wave function, i.e. doublet states, triplet states, etc. with spin 5/0). Let 0 be the Slater determinant constructed from a set of spin-orbitals consisting of spatial part ( = 1,2,. ..,n") associated with a spin functions and orbitals... 

Another way that additional configurations can be added to the the ground-state wave function is by the use of Moller-Plesset perturbation theory (MPPT). As it happens, a Hamiltonian operator constructed from a sum of Fock operators has as its set of solutions the HF single determinantal wave function and all other determinantal wave... 

Although in principle an exact solution to the Schrodinger equation can be expressed in the form of equation (A.13), the wave functions and coefficients da cannot to determined for an infinitely large set. In the Hartree-Fock approximation, it is assumed that the summation in equation (A.13) may be approximated by a single term, that is, that the correct wave function may be approximated by a single determinantal wave function , the first term of equation (A.13). The method of variations is used to determine the... 

Notice that the energy of the HF determinantal wave function, equation (A.68), and for that matter for any single determinantal wave function, can be written by inspection Each spatial orbital contributes ha or 2h according to its occupancy, and each orbital contributes 2J — in its interaction with every other molecular orbital. Thus, the energy of the determinant for the molecular ion, M+, obtained by removing an electron from orbital of the RHF determinant, is given as... 

Earlier it was argued that the many-electron wave function (the true solution to the electronic Schrodinger equation) could be expanded in terms of an infinite series of single determinantal wave functions [Equation (A. 13)] ... 

Hartree-Fock theory makes the fundamental approximation that each electron moves in the static electric field created by all of the other electrons, and then proceeds to optimize orbitals for all of the electrons in a self-consistent fashion subject to a variational constraint. The resulting wave function, when operated upon by the Hamiltonian, delivers as its expectation value the lowest possible energy for a single-determinantal wave function formed from the chosen basis set. 

For a single determinantal wave function k = 1 holds true (no reduction). 

The problem to be solved is expressed by Parr [10] in the following way. For an electronic system containing an even number of electrons, how can we find the best single determinantal wave function of the form (6.36) We calculate the energy using... 

In (6.106) we gave a single-determinantal wave function for a system of n electrons if there are N functions Vv, we can define 2N so-called spin-orbital basis functions of the type linearly combined into 2N spin-orbitals... 

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