6 Search Results

We develop a range-separated stochastic resolution of identity (RS-SRI) approach for the four-index electron repulsion integrals, where the larger terms (above a predefined threshold) are treated using a deterministic RI and the remaining terms are treated using a SRI. The approach is implemented within a second-order Green’s function formalism with an improved O(N³) scaling with the size of the basis set, N. Moreover, the RS approach greatly reduces the statistical error compared to the full stochastic version [T. Y. Takeshita et al., J. Chem. Phys. 151, 044114 (2019)], resulting in computational speedups of ground and excited state energies of nearlymore » two orders of magnitude, as demonstrated for hydrogen dimer chains and water clusters.« less

Here, we develop a stochastic resolution of identity approach to the real-time second-order Green's function (real-time sRI-GF2) theory, extending our recent work for imaginary-time Matsubara Green's function [ Takeshita et al. J. Chem. Phys. 2019 , 151 , 044114 ]. The approach provides a framework to obtain the quasi-particle spectra across a wide range of frequencies and predicts ionization potentials and electron affinities. To assess the accuracy of the real-time sRI-GF2, we study a series of molecules and compare our results to experiments as well as to a many-body perturbation approach based on the GW approximation, where we find thatmore » the real-time sRI-GF2 is as accurate as self-consistent GW. The stochastic formulation reduces the formal computatinal scaling from O(N_e⁵) down to O(N_e³) where N_e is the number of electrons. Finally, this is illustrated for a chain of hydrogen dimers, where we observe a slightly lower than cubic scaling for systems containing up to N_e ≈ 1000 electrons.« less

We create a stochastic resolution of identity representation to the second-order Matsubara Green’s function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/ contractions, which reduces the computational cost from O(N⁵) to O(N³) (with N being the number of atomic orbitals). Currently, the method can be viewed as an extension to our previous work on stochastic resolution of identity second order Møller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulationsmore » [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 10³ electrons and more.« less

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_AO³) 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(N_e^2.4) for total energies and O(N_e^3.1) for forces (N_e being the number of correlated electrons), outperforming MP2more » for clusters with as few as 21 water molecules.« less

Development of exponentially scaling methods has seen great progress in tackling larger systems than previously thought possible. One such approach, full configuration interaction quantum Monte Carlo, is a useful algorithm that allows exact diagonalization through stochastically sampling determinants. The method derives its utility from the information in the matrix elements of the Hamiltonian, along with a stochastic projected wave function, to find the important parts of Hilbert space. Yet, the stochastic representation of the wave function is not required to search Hilbert space efficiently, and here we describe a highly efficient deterministic method that can achieve chemical accuracy for amore » wide range of systems, including the difficult Cr₂ molecule. We demonstrate for systems like Cr₂ that such calculations can be performed in just a few cpu hours which makes it one of the most efficient and accurate methods that can attain chemical accuracy for strongly correlated systems. Furthermore, our method also allows efficient calculation of excited state energies, which we illustrate with benchmark results for the excited states of C₂.« less

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