Boys-Handy transcorrelated method

Table 6 Selected Results from the Boys-Handy Transcorrelated Method ...

The assessment of the accuracy of fully correlated wavefunctions by means of variance methods requires computation which only varies as N, a lower power of N, the number of electrons, than had been expected. This seems to be dependent on an indirect approach first constructed for a trans correlated method. This means that various different variance tests could be used for the assessment of the accuracy of wavefunctions calculated by the transcorrelated method developed by Handy and Boys. These would require much less equipment in programmes and computer facilities, th the original calculations of such wavefunctions. Supplementary investigations on correlated wave-functions at this level might make possible a whole variety of informative experiments on very exact wavefunctions and energies. 

The idea of generating density functionals from correlated wave functions continues to attract attention [199]. Imamura and Scuseria [200] recently derived a correlation functional starting from a Colle-Salvetti type correlated wave function and using the transcorrelated method of Boys and Handy [201,202]. Colle-Salvetti-type correlation functionals that treat parallel-spin and opposite-spin contributions to the correlation energy separately have been also developed by Tsuneda and Hirao [203], Tsuneda et al. [204]. 

Ellis has recently shown how this procedure can be applied effectively for evaluating the matrix components needed in unrestricted Hartree-Fock and configuration interaction calculations, while Boys and Handy- have employed a similar method in the application of the transcorrelated method to lithium hydride. 

After optimization of the Jastrow correlation factor the orbitals which have been taken from HF or KS-DFT calculations may no longer be optimal. Forty years ago. Boys and Handy developed the transcorrelated method, a SCF method that determines variationally optimal orbitals like HF-SCF, but with a simple correlation factor present. Umezawa and Tsuneyuki have adapted the transcorrelated method to VMC to obtain variationally optimal orbitals in the presence of a Jastrow factor." This method was applied to first row atoms in a series of papers. VMC energies were greatly improved when using the transcorrelated orbitals instead of HF or B3LYP orbitals, but, unfortunately, the DMC energies could not be improved." ... 

In about 1969 the transcorrelated method of Boys and Handy appeared to be an interesting alternative to the standard methods of numerical quantum chemistry employing explicitly correlated functions, As mentioned before, the inclusion of explicitly correlated functions into variational calculations not only gives rise to difficult three-electron integrals, but also to four-electron integrals (or more if more complicated R-electron functions are used). In order to avoid the four-electron integrals. Boys and Handy proposed to consider the non-Hermitian Hamiltonian... 

According to the transcorrelated function method of Boys and Handy [45], we can take advantage of the fact that CC-1 = 1, to rewrite Eq. (52) as ... 

One of the major advances in recent years in attempts to calculate more exact wavefunctions, including electron correlation, has been the implementation by Boys and Handy,46 47 of a computational scheme based on the method of moments, called the transcorrelated wavefunction method. In this method, a correlation factor is built into the wavefunction, which is written in the form (1), where 0 is a Slater... 

---