Wavefunction quality and error estimation of single- and multi-reference coupled-cluster and CI methods: The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si21.gif" display="inline" overflow="scroll"><mml:mrow><mml:msub><mml:mrow><mml:mtext>H</mml:mtext></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> model system

Hanrath, Michael

doi:10.1016/j.cplett.2008.10.046

Cited by 10 publications

(2 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A combined study of both the discretization and algorithmic errors was published in 9 (see also 10 ). We also refer to [11][12][13][14][15][16][17][18][19][20] and references therein for other works on error analysis for electronic structure calculation.…”

Section: Introductionmentioning

confidence: 99%

Discretization error cancellation in electronic structure calculation: toward a quantitative study

Cancès

Dusson

2017

ESAIM: M2AN

View full text Add to dashboard Cite

It is often claimed that error cancellation plays an essential role in quantum chemistry and firstprinciple simulation for condensed matter physics and materials science. Indeed, while the energy of a large, or even medium-size, molecular system cannot be estimated numerically within chemical accuracy (typically 1 kcal/mol or 1 mHa), it is considered that the energy difference between two configurations of the same system can be computed in practice within the desired accuracy.The purpose of this paper is to provide a quantitative study of discretization error cancellation. The latter is the error component due to the fact that the model used in the calculation (e.g. Kohn-Sham LDA) must be discretized in a finite basis set to be solved by a computer. We first report comprehensive numerical simulations performed with Abinit 1,2 on two simple chemical systems, the hydrogen molecule on the one hand, and a system consisting of two oxygen atoms and four hydrogen atoms on the other hand. We observe that errors on energy differences are indeed significantly smaller than errors on energies, but that these two quantities asymptotically converge at the same rate when the energy cut-off goes to infinity. We then analyze a simple one-dimensional periodic Schrödinger equation with Dirac potentials, for which analytic solutions are available. This allows us to explain the discretization error cancellation phenomenon on this test case with quantitative mathematical arguments. a cances@cermics.enpc.fr b dusson@ljll.math.upmc.fr arXiv:1701.04643v1 [cond-mat.mtrl-sci]

show abstract

Section: Introductionmentioning

confidence: 99%

Discretization error cancellation in electronic structure calculation: toward a quantitative study

Cancès

Dusson

2017

ESAIM: M2AN

View full text Add to dashboard Cite

show abstract

“…Hanrath has shown the MRexpT Ansatz to be size-consistent [166] and core-extensive [168,170,171], which indicates that the method has a potential to be accurate for large molecules. Presently, only results for small model systems are available [167,169,172], probably due to the higher complexity of the working equations resulting from the determinantal indexing. See Chapter 7 for more detail.…”

Section: Hanrath's Mr Exponential Ansatzmentioning

confidence: 96%

Multireference Coupled-Cluster Methods: Recent Developments

Paldus

Pittner

Čárský

2010

Challenges and Advances in Computational Chemistry and Physics

View full text Add to dashboard Cite

Abstract:The objective of this paper is to provide an overview of various multi-reference (MR) coupled-cluster (CC) approaches, particularly those relating to our own research. Although MR CC methods have been around for almost three decades and much work has been expended on their development and implementation, no general purpose codes are presently available. In view of the complexity, inherent difficulties, and computational demands of both genuine valence and state universal (VU and SU) MR CC methods, attention has been directed towards the state selective or state specific (SS) approaches that focus on one state at a time. These methods are based on either the genuine MR CC formalism or on a singlereference (SR) CC Ansatz, in which higher-than-pair clusters are accounted for by relying on basic ideas of general MR approaches. This is achieved either internally by relying on CC or MBPT formalism or by exploiting some external source providing approximate values of these clusters and accomplished by either correcting equations yielding the cluster amplitudes or directly by evaluating the corrections to the CCSD energy. Nowadays there exists a whole plethora of such various approaches for handling of quasi-degenerate states with a various degree of MR character and our goal is to outline their basic features and comment on their pro's and con's, their usefulness and weaknesses, as well as point out their mutual relationship.

show abstract

Portably parallel construction of a configuration‐interaction wave function from a matrix–product state using the Charm++ framework

Wang

Zhao

et al. 2020

J Comput Chem

View full text Add to dashboard Cite

The construction of configuration-interaction (CI) expansions from a matrix product state (MPS) involves numerous matrix operations and the skillful sampling of important configurations in a large Hilbert space. In this work, we present an efficient procedure for constructing CI expansions from MPS employing the parallel objectoriented CHARM++ programming framework, upon which automatic load-balancing and object migrating facilities can be employed. This procedure was employed in the MPS-to-CI utility (Moritz et al.,

show abstract

Wavefunction quality and error estimation of single- and multi-reference coupled-cluster and CI methods: The H4 model system

Cited by 10 publications

References 47 publications

Discretization error cancellation in electronic structure calculation: toward a quantitative study

Discretization error cancellation in electronic structure calculation: toward a quantitative study

Multireference Coupled-Cluster Methods: Recent Developments

Portably parallel construction of a configuration‐interaction wave function from a matrix–product state using the Charm++ framework

Contact Info

Product

Resources

About