TITLE

Quartic scaling second-order approximate coupled cluster singles and doubles via tensor hypercontraction: THC-CC2

AUTHOR(S)
Hohenstein, Edward G.; Kokkila, Sara I. L.; Parrish, Robert M.; Martínez, Todd J.
PUB. DATE
March 2013
SOURCE
Journal of Chemical Physics;Mar2013, Vol. 138 Issue 12, p124111
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The second-order approximate coupled cluster singles and doubles method (CC2) is a valuable tool in electronic structure theory. Although the density fitting approximation has been successful in extending CC2 to larger molecules, it cannot address the steep O(N5) scaling with the number of basis functions, N. Here, we introduce the tensor hypercontraction (THC) approximation to CC2 (THC-CC2), which reduces the scaling to O(N4) and the storage requirements to O(N2). We present an algorithm to efficiently evaluate the THC-CC2 correlation energy and demonstrate its quartic scaling. This implementation of THC-CC2 uses a grid-based least-squares THC (LS-THC) approximation to the density-fitted electron repulsion integrals. The accuracy of the CC2 correlation energy under these approximations is shown to be suitable for most practical applications.
ACCESSION #
86446756

 

Related Articles

  • Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctions. Hohenstein, Edward G.; Parrish, Robert M.; Sherrill, C. David; Martínez, Todd J. // Journal of Chemical Physics;12/14/2012, Vol. 137 Issue 22, p221101 

    The manipulation of the rank-four tensor of double excitation amplitudes represents a challenge to the efficient implementation of many electronic structure methods. We present a proof of concept for the approximation of doubles amplitudes in the tensor hypercontraction (THC) representation. In...

  • Tensor hypercontracted ppRPA: Reducing the cost of the particle-particle random phase approximation from O(r6) to O(r4). Shenvi, Neil; van Aggelen, Helen; Yang Yang; Weitao Yang // Journal of Chemical Physics;7/14/2014, Vol. 141 Issue 2, p024119-1 

    In recent years, interest in the random-phase approximation (RPA) has grown rapidly. At the same time, tensor hypercontraction has emerged as an intriguing method to reduce the computational cost of electronic structure algorithms. In this paper, we combine the particle-particle random phase...

  • Tensor hypercontraction. II. Least-squares renormalization. Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David // Journal of Chemical Physics;12/14/2012, Vol. 137 Issue 22, p224106 

    The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G....

  • RECONSTRUCTION OF SOLENOIDAL 2-TENSOR FIELDS, GIVEN IN A UNIT DISK, IN THEIR LONGITUDINAL RAY TRANSFORMS. SVETOV, I. E. // Sibirskie Elektronnye Matematicheskie Izvestiia;2010, Vol. 7, pC.139 

    The numerical method for solving a tensor tomography problem of reconstructing symmetric solenoidal 2-tensor fields, given in a unit disk, is offered. Desired field with fixed properties on the boundary are found from longitudinal ray transforms, calculated along the straight lines crossing the...

  • Discrete variable representation in electronic structure theory: Quadrature grids for least-squares tensor hypercontraction. Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David // Journal of Chemical Physics;May2013, Vol. 138 Issue 19, p194107 

    We investigate the application of molecular quadratures obtained from either standard Becke-type grids or discrete variable representation (DVR) techniques to the recently developed least-squares tensor hypercontraction (LS-THC) representation of the electron repulsion integral (ERI) tensor....

  • A proximal ANLS algorithm for nonnegative tensor factorization with a periodic enhanced line search. Bunker, Douglas; Han, Lixing; Zhang, Shuhua // Applications of Mathematics;Oct2013, Vol. 58 Issue 5, p493 

    The Alternating Nonnegative Least Squares (ANLS) method is commonly used for solving nonnegative tensor factorization problems. In this paper, we focus on algorithmic improvement of this method. We present a Proximal ANLS (PANLS) algorithm to enforce convergence. To speed up the PANLS method, we...

  • Tensor Distance Based Least Square Twin Support Tensor Machine. Haifa Shi; Xinbin Zhao; Ling Jing // Applied Mechanics & Materials;2014, Issue 667-679, p1170 

    Nowadays, there have been many data which are represented by tensor, that how to deal with these tensor data directly remains a significant challenge. In this paper, we propose a new tensor distance (TD) based least square twin support tensor machine (called TDLS-TSTM). Unlike the traditional...

  • Identification for a Nonlinear Periodic Wave Equation. Moroşanu, C.; Trenchea, C. // Applied Mathematics & Optimization;2001, Vol. 44 Issue 2, p87 

    This work is concerned with an approximation process for the identification of nonlinearities in the nonlinear periodic wave equation. It is based on the least-squares approach and on a splitting method. A numerical algorithm of gradient type and the numerical implementation are given.

  • Weighted Average Errors in Set-Membership Estimation. Kacewicz, Boleslaw // Mathematics of Control, Signals & Systems;Sep2003, Vol. 16 Issue 2/3, p238 

    Average-case analysis provides knowledge about the quality of estimation algorithms in the case when the influence of outliers (exceptionally difficult elements) is to be neglected. This is in contrast with the worst-case analysis, where exceptionally difficult elements are of particular...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics