QMC meets DFT and Quantum Information
Density Functional Theory is undoubtedly the most successful approach to simulate many-electron systems. In principle the theory is exact, in practice it is extremely empirical, at least for systems of interest to modern technology.
The empiricism of DFT lies in the determination of the universal energy functional of Hohenberg and Kohn; we know that such a functional exists but we do not know its explicit form. In the practical approach developed by Kohn and Sham the universal functional is reduced to the exchange and correlation part; there exists an enormous industry which continuously produces new exchange and correlation functionals, none of which has the minimal hope of being "universal". This project attempts instead to explore a different path, that is merge DFT with other, numerically more rigorous but computationally more expensive, many-electron approaches such as Quantum Monte Carlo. The guiding principle is that the computational efficiency of QMC is enhanced by DFT and at the same time the numerical accuracy of DFT is enhanced by QMC and the empiricism is minimized. The resulting approach is a hybrid between DFT and QMC (but not a parametrization of DFT based on QMC). The key of this nested scheme is the Levy-Lieb principle which lies at the basis of DFT. This principle formalizes the implicit meaning (merit) of DFT: "Given a ground state density its corresponding ground state wavefunction can be determined in an exact way". Moreover, numerical similarities between the QMC correlation energies and the Shannon Information expression even suggest that DFT may be a specific expression of a wider Quantum Information principle.
In such a case the Levy-Lieb principle would represent a decoding key of a 3-dimensional set of data in a 3N-dimensional set of data, its practical consequences may be rather appealing. The principle of decoding is already implicitly used in chemistry, for example in problems of "Inverse Chemistry". In this context the Levy-Lieb principle may play a major role. This research proceeds through thorns and brambles of skepticism of applied/computational scientists (i.e. no funding) but at the same time seems to stimulate the best theoreticians. If to such a research can be given the possibility of exploring its computational advantages/limitations, perhaps we may get pleasant surprises....hard to convince those who uses PRL publications and engineering-based crunched numbers as evaluation criteria for the quality of a theory....
Collaboration with Luca M.Ghiringhelli, Ian P.Hamilton and David M.Ceperley
Selected References:
L.Delle Site, L.M.Ghiringhelli and D.Ceperley:
Int.J.Quant.Chem., DOI:10.1002/qua.24321 (2012).
L.Delle Site:
Int.J.Quant.Chem. 115, 1396-1404 (2015)
L.Delle Site:
Chem.Phys.Lett.doi:10.1016/j.cplett.2014.11.060. (2015)
Volker Bach and Luigi Delle Site Eds.:
"Many-Electron Approaches in Physics, Chemistry and Mathematics: A Multidisciplinary View"
Springer Verlag 2014, Book Series: Studies in Mathematical Physics