Jastrow functions, trial wavefunctions

The typical trial wavefunction for QMC calculations on molecular systems consists of the product of a Slater determinant multiplied by a second function, which accounts to some extent for electron correlation with use of interelectron distances. The trial wavefunctions are most often taken from relatively simple analytic variational calculations, in most cases from calculations at the SCF level. Thus, for the 10-electron system methane," the trial function may be the product of the SCF function, which is a 10 x 10 determinant made up of two 5x5 determinants, and a Jastrow function for each pair of electrons. 

Now let us look at the paper. Eqn. (1) gives the form of the transcorrelated wave function C0, where C = li >jfiri,rj) is a Jastrow factor, and is a determinant. This compact wave function includes the effects of electron correlation through the introduction of r in C. The form C0 is taken as the trial wave function in quantum Monte Carlo (QMC) molecular computations today. Indeed the explicit form for/(r r,j is most often used by the QMC community. The transcorrelated wave function was obtained by solving (C //C - W) = 0, which Boys called the transcorrelation wave equation. Because C //C is a non-Hermitian operator, it was important to devise independent assessments of the accuracy of the wavefunction C0. 

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