Explicitly correlated methods

If affordable, there is a range of very accurate coupled-cluster and symmetry-adapted perturbation theories available which can approach spectroscopic accuracy [57, 200, 201]. However, these are only applicable to the smallest alcohol cluster systems using currently available computational resources. Near-linear scaling algorithms [192] and explicit correlation methods [57] promise to extend the applicability range considerably. Furthermore, benchmark results for small systems can guide both experimentalists and theoreticians in the characterization of larger molecular assemblies. 

Unfortunately, extending Hylleraas s approach to systems containing three or more electrons leads to very cumbersome mathematics. More practical approaches, known as explicitly correlated methods, are classified into two categories. The first group of approaches uses Boys Gaussian-type geminal (GTG) functions with the explicit dependence on the interelectronic coordinate built into the exponent [95]... 

Truly spectroscopic accuracy for total energies is still difficult to obtain from either explicitly correlated methods or extrapolation approaches for all but the simplest... 

The slow X 3 convergence cannot easily be avoided. To improve on it, one can try to describe electron correlation not only by means of virtual orbital excitations but also by means of spatial two-electron basis functions that depend explicitly on the electron-electron distances. This is the idea behind the explicitly correlated methods [69]. Indeed, in this manner, it is possible to accelerate the convergence from X 3 to X 7, greatly reducing the basis set requirements for high accuracy. Nevertheless, such calculations are complex and cannot yet be used routinely on large molecules. 

Explicitly correlated methods Density functional theory Ab initio... 

N. O. J. Malcolm and D. L. Yeager, Purely theoretical electron-impact ionization cross-sections of silicon hydrides and silicon fluorides obtained from explicitly correlated methods, The Journal of Chemical Physics, vol. 113, no. 1, pp. 8—17, 2000. 

Weak molecular interactions are another traditional area of application for explicitly correlated methods. The most taunting aspect about the calculation of interaction energies is the basis set superposition error (BSSE), i.e. the spurious extra interaction energy that is actually only the increase of pure intra-fragment correlation energy due to the overlap with basis functions from the other fragment. The BSSE vanishes for a sufficiently complete basis, which can be most efficiently achieved by explicit electron correlation, e.g. F12 methods. 

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