Related papers: Range-Separated Stochastic Resolution of Identity:…
A stochastic orbital approach to the resolution of identity (RI) approximation for 4-index 2-electron electron repulsion integrals (ERIs) is presented. The stochastic RI-ERIs are then applied to M\o ller-Plesset perturbation theory (MP2)…
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 {\em J. Chem. Phys.} {\bf 151},…
Stochastic orbital techniques offer reduced computational scaling and memory requirements to describe ground and excited states at the cost of introducing controlled statistical errors. Such techniques often rely on two basic operations,…
An implementation of stochastic resolution of identity (sRI) approximation to CC2 oscillator strengths as well as ground state analytical gradients is presented. The essential 4-index electron repulsion integrals (ERIs) are contracted with…
A stochastic resolution of identity approach (sRI) is applied to the second-order coupled cluster singles and doubles (CC2) model to calculate the ground-state energy. Utilizing a set of stochastic orbitals to optimize the expensive tensor…
We apply a stochastic resolution of identity approximation (sRI) to the CC2 method for excitation energy calculations. A set of stochastic orbitals are employed to decouple the crucial 4-index electron repulsion integrals and optimize the…
We present a real-time second-order Green's function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of $O(N_{\rm e}^3$), where $N_{\rm e}$ is the number of electrons. The cubic scaling…
The recently developed Doubles Connected Moments (DCM) expansion offers a tractable approach for computing correlation energy, exhibiting an noniterative O(N^6) scaling with system size N. Benchmark calculations on a set of molecules…
We develop and implement a formalism which enables calculating the analytical gradients of particle-hole random-phase approximation (RPA) ground-state energy with respect to the atomic positions within the atomic orbital basis set…
The second-order Green's function method (GF2) was shown recently to be an accurate self-consistent approach for electronic structure of correlated systems since the self-energy accounts for both the weak and some of the strong correlation.…
We explore a separable resolution-of-the-identity formalism built on quadratures over limited sets of real-space points designed for all-electron calculations. Our implementation preserves in particular the use of common atomic orbitals and…
When the available information is noisy zeroth-order (ZO) oracle, stochastic approximation methods are popular for estimating the root of the multivariate gradient equation. Inspired by the Stein's identity, this work establishes a novel…
The stochastic resolution of identity (sRI) approximation significantly reduces the computational scaling of CC2 from O(N^5) to O(N^3), where N is a measure of system size. However, the inherent stochastic noise, while controllable, can…
The numerical evaluation of statistics plays a crucial role in statistical physics and its applied fields. It is possible to evaluate the statistics for a stochastic differential equation with Gaussian white noise via the corresponding…
The Green's function method which has been originally proposed for linear systems has several extensions to the case of nonlinear equations. A recent extension has been proposed to deal with certain applications in quantum field theory. The…
We extend Green's function method developed by Stewart and Gong to calculate the power spectrum of density perturbation in the case with a time-dependent sound speed, and explicitly give the power spectrum and spectral index up to…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
In this work, the required algebra to employ the resolution of the identity approximation within Piris Natural Orbital Functional (PNOF) is developed, leading to an implementation named DoNOF-RI. The arithmetic scaling is reduced from…
Efficient implementations of electronic structure methods are essential for first-principles modeling of molecules and solids. We here present a particularly efficient common framework for methods beyond semilocal density-functional theory,…
Calculations of excited states in Green's function formalism often invoke the diagonal approximation, in which the quasiparticle states are taken from a mean-field calculation. Here, we extend the stochastic approaches applied in the…