Computational studies Hartree-Fock calculations

As it is now very well known, accurate studies of the water-water interaction by means of ab-initio techniques require the use of larger and flexible basis sets and methods which consider correlation effects [85,94-96], Since high level ab-initio post-Hartree-Fock calculations are unfeasible because of their high computational cost for systems with many degrees of freedom, Density Functional Theory, more economical from the computational point of view, is being more and more considered as a viable alternative. Recently, we have presented [97] results of structural parameters and vibrational frequencies for the water clusters (H20) , n=2 to 8, using the DFT method with gradient corrected density functionals. 

A pitch is made for a renewed, rigorous and systematic implementation of the GW method of Hedin and Lundquist for extended, periodic systems. Building on previous accurate Hartree-Fock calculations with Slater orbital basis set expansions, in which extensive use was made of Fourier transform methods, it is advocated to use a mixed Slater-orbital/plane-wave basis. Earher studies showed the amehoration of approximate linear dependence problems, while such a basis set also holds various physical and anal3ftical advantages. The basic formahsm and its realization with Fourier transform expressions is explained. Modem needs of materials by precise design, assisted by the enormous advances in computational capabilities, should make such a program viable, attractive and necessary. 

It has been demonstrated that for the excited states of the atoms He, Li and Be considered in the present work, a simple optimization of the a and [3 parameters for each size of basis set leads to a sequence of even-tempered basis sets capable of supporting high accuracy in Hartree-Fock calculations for excited state energies of atoms. Furthermore, optimization of the a and f3 parameters for the smallest basis set in a sequence, M = 6 in the present study, followed by application of the recursion formulae (40) and (41) represents a good compromise which undoubtedly proved useful in case where full optimization of these parameters for each size of basis set is computationally demanding. 

Because of the latter contradiction an ab initio Hartree-Fock calculation has been performed (61). To reduce the computer time only a linear Ni—CO molecule has been studied. Such a calculation cannot be assumed to give accurate ionisation potentials of a chemisorbed system, but if the surface molecule picture is valid, it may supply us with some relevant information. The calculation predicts similar to the CNDO calculation that the first CO peak is due to the 1 n and 5a orbitals and the second peak due to the 4a orbital of CO. The ordering of the In and 55 orbitals of chemisorbed CO is, however, different from the ordering... 

Although the dependence of the hyperfine properties, such as the isotropic hfcc, on computational method and/or basis sets has been extensively studied in the literature [12], it is in the present connection instructive to examine specifically the performance of different types of hydrogen atom basis sets. This will also give us some insight in the possible errors of the reported calculations. Hj has the advantage that the effect of electron correlation is not present in this system and hence the error of the Hartree-Fock calculation is identical with the error due to the AO basis set. 

Assuming that an ab initio or semiempirical technique has been used to obtain p(r), we address the important question of how the calculated electrostatic potential depends on the nature of the wavefunction used for computing p(r). Historically, and today as well, most ab initio calculations of V(r) for reasonably sized molecules have been based on self-consistent-field (SCF) or near Hartree-Fock wavefunctions and therefore do not reflect electron correlation. Whereas the availability of supercomputers has made post-Hartree-Fock calculations of V(r) (which include electron correlation) a realistic possibility even for molecules with 5 to 10 first-row atoms, there is reason to believe that such computational levels are usually not necessary and not warranted. The M0l er-Plesset theorem states that properties computed from Hartree-Fock wavefunctions using one-electron operators, as is V(r), are correct through first order " any errors are no more than second-order effects. Whereas second-order corrections may not always be insignificant, several studies have shown that near-Hartree-Fock electron densities are affected to only a minor extent by the inclusion of correlation.The limited evidence available suggests that the same is true of V(r), ° ° as is indicated also by the following example. 

Let us first discuss preliminary computations we conducted for carbon monoxide in the gas phase. The experimental vc-o frequency is 2143 cm , while our calculations deliver 2102cm , i.e. a deviation of 2% from the experimental value. This good agreement thus asseses the quality of what we may expect for computed stretching frequencies in the absence of any chemisorption nor electric field effect. One may note that (i) onr compnted valne is in better agreement than the one obtained previously on the basis of Hartree-Fock calculations (2270 cm ) [45] and (ii) this value is lower than the experimental valne, which we attribute to the partial account of anharmonic effects undertaken in the present study (one indeed expects theoretical frequencies to be higher than experimental valnes on the basis of the harmonic approximation, see e.g. [45]). 

Gas phase studies of flexible systems owe their success to the high sensitivity of the observables to the structure, but, in return, this approach is very demanding for theoretical methods. As an illustration, an H-bond distance mispredicted by 1 pm may lead to an error of 2 cm on the calculated vibrational frequency. The main issue of this step is then to get a theoretical structure accurate enough to predict observables quantitatively at a reasonable computational cost. In this quest, it has been rapidly realised how important it was to take dispersive interactions into account in these systems. Early Hartree-Fock calculations or DPT calculations dominated by the popular B3LYP functional with post-Hartree-Fock methods rapidly reached their limits because of the underestimation of dispersion interactions. In contrast, the Moller-Plesset approach treated as a second-order perturbation (MP2) overestimated dispersion at an additional computational cost, making its... 

---