Orbital optimization, trial wavefunction

The most straightforward way to introduce the concept of optimal molecular orbitals is to consider a trial wavefunction of the form which was introduced earlier in Chapter 9.II. The expectation value of the Hamiltonian for a wavefunction of the multiconfigurational fomn... 

Variational intra-orbit optimization of trial wavefunctions... 

One of the main advantages of the Monte Carlo method of integration is that one can use any computable trial function, including those going beyond the traditional sum of one-body orbital products (i.e., linear combination of Slater determinants). Even the exponential ansatz of the coupled cluster (CC) method [27, 28], which includes an infinite number of terms, is not very efficient because its convergence in the basis set remains very slow. In this section we review recent progress in construction and optimization of the trial wavefunctions. 

The lower value for E is the lowest energy attainable with the trial basis set. The corresponding coefficients give the character of the most bonding orbital. It should be noted that a secular determinant must be solved whenever a linear combination of wavefunctions is optimized. 

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