Recent Publications

Takeshita, T. Y. ; de Jong, W. A. ; Neuhauser, D. ; Baer, R. ; Rabani, E. Stochastic Formulation of the Resolution of Identity: Application to Second Order Møller–Plesset Perturbation Theory. J. Chem. Theory Comput. 2017, 13, 4605. Publisher's VersionAbstract

A stochastic orbital approach to the resolution of identity (RI) approximation for 4 index electron repulsion integrals (ERIs) is presented. The stochastic RI-ERIs are then applied to second order Møller-Plesset perturbation theory (MP2) utilizing a multiple stochastic orbital approach. The introduction of multiple stochastic orbitals results in an O(N_AO^3 ) scaling for both the stochastic RI-ERIs and stochastic RI-MP2, NAO being the number of basis functions. For a range of water clusters we demonstrate that this method exhibits a small prefactor and observed scalings of O(Ne^2.4) for total energies and O(Ne^3.1) for forces (Ne being the number of correlated electrons), outperforming MP2 for clusters with as few as 21 water molecules.

Vlček, V. ; Baer, R. ; Rabani, E. ; Neuhauser, D. Self-consistent band-gap renormalization GW. arXiv preprint arXiv:1701.02023 2017.Abstract

Partially-self-consistent gap-renormalization GW (grGW) is introduced to calculate quasiparticle (QP) energies within the many-body perturbation theory of Hedin. Self-consistency of the Green's function is obtained by renormalization of the band gap, removing the most significant approximation of the single-shot G0W0 approach. The formalism is performed as a post-processing step and thus, can be implemented within any GW algorithm which calculates the full frequency-dependent self-energies. Here, the grGW approach is combined with the stochastic GW (sGW) formalism developed in [Phys. Rev. Lett. 113, 076402 (2014)]. The computational cost and scaling are similar to that of the single-shot sGW. We illustrate the approach for two confined semiconducting systems with open boundary conditions: Silicon nanocrystal (NC) quantum dots (QDs) and 2D planar and bent phosphorene nanoribbons (PNRs).

Vlcek, V. ; Rabani, E. ; Neuhauser, D. ; Baer, R. Stochastic GW calculations for molecules. J. Chem. Theory Comput. 2017, 13, 4997–5003.Abstract

Quasiparticle (QP) excitations are extremely important for understanding and predicting charge transfer and transport in molecules, nanostructures and extended systems. Since density functional theory (DFT) within Kohn-Sham (KS) formulation does not provide reliable QP energies, a many-body perturbation technique within the GW approximation are essential. The steep computational scaling of GW prohibits its use in extended, open boundary, systems with thousands of electrons and more. Recently, a stochastic formulation of GW has been proposed [Phys. Rev. Lett. 113, 076402 (2014)] which scales nearly linearly with the system size, as illustrated for a series of silicon nanocrystals exceeding 3000 electrons. Here, we implement the stochastic GW (sGW) approach to study the ionization potential (IP) of a subset of molecules taken from the "GW 100" benchmark. We show that sGW provides a reliable results in comparison to GW WEST code and to experimental results, numerically establishing its validity. For completeness, we also provide a detailed review of sGW and a summary of the numerical algorithm.

Neuhauser, D. ; Baer, R. ; Zgid, D. Stochastic self-consistent second-order Green’s function method for correlation energies of large electronic systems. J. Chem. Theory Comput. 2017, 13, 5396−5403.Abstract

The second-order Matsubara Green’s function method (GF2) is a robust temperature dependent quantum chemistry approach, extending beyond the random-phase approximation. However, till now the scope of GF2 applications was quite limited as they require computer resources which rise steeply with system size. In each step of the self-consistent GF2 calculation there are two parts: the estimation of the self-energy from the previous step’s Green’s function, and updating the Green’s function from the self-energy. The first part formally scales as the fifth power of the system size while the second has a much gentler cubic scaling. Here, we develop a stochastic approach to GF2 (sGF2) which reduces the fifth power scaling of the first step to merely quadratic, leaving the overall sGF2 scaling as cubic. We apply the method to linear hydrogen chains containing up to 1000 electrons, showing that the approach is numerically stable, efficient and accurate. The stochastic errors are very small, of the order of 0.1% or less of the correlation energy for large systems, with only a moderate computational effort. The first iteration of GF2 is an MP2 calculation that is done in linear scaling, hence we obtain an extremely fast stochastic MP2 (sMP2) method as a by-product. While here we consider finite systems with large band gaps where at low temperatures effects are negligible, the sGF2 formalism is temperature dependent and general and can be applied to finite or periodic systems with small gaps at finite temperatures.

Hadad, R. E. ; Baer, R. Minimally corrected partial atomic charges for non-covalent electrostatic interactions. Mol. Phys. 2017, 115, 3155-3163. Publisher's VersionAbstract

We develop a new scheme for determining molecular partial atomic charges (PACs) with external electrostatic potential (ESP) closely mimicking that of the molecule. The PACs are the ‘minimal corrections’ to a reference set of PACs necessaryfor reproducing exactly the tensor components of the Cartesian zero-, first- and second- molecular electrostatic multipoles. We evaluate the quality of ESP reproduction when ‘minimally correcting’(MC) Mulliken, Hirshfeld or iterative-Hirshfeld reference PACs. In all these cases, the MC-PACs significantly improve the ESP while preserving the reference PACs’invariance under the molecular symmetry operations. When iterative-Hirshfeld PACs are used as reference, the MC-PACs yield ESPs of comparable quality to those of the ChElPG charge fitting method.

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