The linear variation method is the most commonly used method to find approximate molecular wave functions, and matrix algebra gives the most computationally efficient method to solve the equations of the linear variation method. If the functions /i, in the linear variation function

Configuration Interaction A variational method with the trial wave function in the form of a linear combination of the given set of the Slater determinants. [Pg.1014]

Historically, the most common technique used has been the linear variation method. In this procedure, the wave functions are expressed as linear combinations of harmonic-oscillator basis functions [Pg.17]

We will describe first the classical MC SCF approach. This is a variational method. As was mentioned, the wave function in this method has the form of a finite linear combination of Slater determinants [Pg.535]

We wish to prove that the approximate wave functions obtained in the linear variation method are orthogonal and that the approximate energies obtained are upper bounds to the energies of the n lowest states. Let the approximate function have the value W for the variational integral and the coefficients cj in (8.40). (We add a to distinguish the n different s.) We rewrite (8.53) as [Pg.227]

The Hylleraas variation method has the advantage that we can calculate the wave-function corrections from variations in a nonlinear set of parameters that define the electronic state. We are thus not restricted to a linear variational space. As a bonus, the error in <2 ) jg quadratic in the error in the nth-order wave function. The lower-order corrections (C with k < n) must, however, be accurately calculated. [Pg.214]

CAS SCF Complete Active Space Self-Consistent Field An iterative and variational method of solving the Schrddinger equation with the variational wave function in the form of a linear combination of all the Slater determinants (coefficients and spinorbitals are determined variationally) that can be built from a limited set of the spinorbitals (forming the active space). [Pg.1013]

Among the classes of the trial wave functions, those employing the form of the linear combination of the functions taken from some predefined basis set lead to the most powerful technique known as the linear variational method. It is constructed as follows. First a set of M normalized functions dy, each satisfying the boundary conditions of the problem, is selected. The functions dy are called the basis functions of the problem. They must be chosen to be linearly independent. However we do not assume that the set of fdy is complete so that any T can be exactly represented as an expansion over it (in contrast with exact expansion eq. (1.36)) neither is it assumed that the functions of the basis set are orthogonal. A priori they do not have any relation to the Hamiltonian under study - only boundary conditions must be fulfilled. Then the trial wave function (D is taken as a linear combination of the basis functions dyy [Pg.17]

Thus, the linear variation method provides upper bounds to the energies of the lowest n bound states of the system. We use the roots W], W2,..., W as approximations to the energies of the lowest states. If approximations to the energies of more states are wanted, we add more functions / to the trial function

The most direct way to represent the electronic structure is to refer to the electronic wave function dependent on the coordinates and spin projections of N electrons. To apply the linear variational method in this context one has to introduce the complete set of basis functions k for this problem. The complication is to guarantee the necessary symmetry properties (antisymmetry under transpositions of the sets of coordinates referring to any two electrons). This is done as follows. [Pg.39]

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