International Workshop on 'New challenges in Reduced Density Matrix Functional Theory: Symmetries, time-evolution and entanglement'

September 26, 2017 to September 29, 2017
Location : CECAM-HQ-EPFL, Lausanne, Switzerland
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Novel approaches towards constructing reduced density matrix functionals within random phase approximation framework

Kasia Pernal
Technical University of Lodz, Poland


Over years there has been a constant progress in development density matrix functionals (or natural orbital functionals) [1]. The accuracy and general usefulness of the most successful functionals still lag behind widely used density functionals. Recently Random Phase Approximation (RPA) electron correlation methods have re- emerged in the Kohn-Sham DFT framework leading to a new class of correlation orbital-dependent functionals (for a review of RPA methods see Ref.[2]). Foundations of most RPA approaches trace back to an exact expression for two-electron reduced density matrix written in terms of one-electron density matrix and dynamic one-electron response functions presented i.g. in the seminal paper of MacLachlan and Ball [3]. Interestingly, the MacLachlan and Ball expression lead to formulations of the density matrix functional if combined with the extended random phase approximation. In other words, two-electron reduced density matrix can be reconstructed from one-electron functions. Another way of exploiting the MacLachlan and Ball expression leading to novel density matrix functionals employs the adiabatic connection construction. The latter is only viable if one can define a 0th-order Hamiltonian (or a reference state). Both ways have been explored recently [4,5].

In my presentation first I will give a short introduction to the derivation of the MacLachlan and Ball expression and RPA functionals in DFT. Then two routes leading to density matrix depending correlation energy expression, which exploit random phase approximations will be presented. It will be shown that the “direct” approach resulting in reconstructing a full two-electron density matrix from approximate one-electron functions leads to strong overcorrelation when applied to molecules. The adiabatic connection route is much more promising and yields excellent results if one employs a Hamiltonian for a group product function as a reference.


[1] K. Pernal and K. J. H. Giesbertz, vol. 368 of Topics in Current Chemistry 2016, p. 125.
[2] H. Eshuis, J. Bates, and F. Furche, Theor. Chem. Acc. 131 1084 (2012).
[3] A. D. McLachlan and M. A. Ball, Rev. Mod. Phys. 36 844 (1964).
[4] K. Pernal. Int. J. Quant. Chem. 2017,
[5]. K. Pernal, submitted (2017).