What is the Hartree-Fock method all about

Ihe Hartree-Fock method is a variational one (p. 196) and uses the variational wave function in the form of a single Slater determinant. 

In other words we seek (among the Hsiater set of trial functions) the determinant ( Ahf ) which results in the lowest mean value of the Hamiltonian. 

In this case the mathematical form of the spinorbitals undergoes variation -change n r) as well as tpi2 r) in eq. (8.1) (however you want) to try to lower the mean value of the Hamiltonian as much as possible. The output determinant which provides the minimum mean value of the Hamiltonian is called the Hartree-Fock function. The Hartree-Fock function is an approximation of the true wave function (which satisfies the Schrodinger equation = E ), because the former is indeed the optimal solution, but only among single Slater determinants. The Slater determinant is an antisymmetric function, but an antisymmetric function does not necessarily need to take the shape of a Slater determinant. 

Ikking the variational wave function in the form of one determinant means an automatic limitation to the subset Osiater for searching for the optimum wave function. In fact, we should search the optimum wave function in the set H — Hsiater- Thus it is an approximation for the solution of the Schrodinger equation, with no chance of representing the exact result. 

The true solution of the Schrodinger equation is never a single determinant. Why are Slater determinants used so willingly There are two reasons for this  

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Within the Hartree method, the electronic spin does not appear explicitly except for the fact that no more than two electrons may go into a single orbital. The existence of the Pauli exclusion principle, however, needs to be accounted for in order to go beyond the Hartree method, and that is what the Hartree-Fock method [120] is all about. We first formulate an arbitrary three-dimensional orbital for electron i by writing it as the product of a purely space-dependent part and a spin function (spinor), a or characterizing spin-up or spin-down electron, for example (pi Xi) = i(ri)iXi here we use x to indicate a variable which includes both space (r) and spin (a). A Hartree-like product wave function between two one-electron wave functions and 2 could then be written as... 

A highly readable account of early efforts to apply the independent-particle approximation to problems of organic chemistry. Although more accurate computational methods have since been developed for treating all of the problems discussed in the text, its discussion of approximate Hartree-Fock (semiempirical) methods and their accuracy is still useful. Moreover, the view supplied about what was understood and what was not understood in physical organic chemistry three decades ago is... 

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