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Communication: A flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states

Sharma, Sandeep and Chan, Garnet Kin-Lic (2014) Communication: A flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states. Journal of Chemical Physics, 141 (11). Art. No. 111101. ISSN 0021-9606. http://resolver.caltech.edu/CaltechAUTHORS:20170106-123434796

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Abstract

We describe a formulation of multi-reference perturbation theory that obtains a rigorous upper bound to the second order energy by minimizing the Hylleraas functional in the space of matrix product states (MPS). The first order wavefunctions so obtained can also be used to compute the third order energy with little overhead. Our formulation has several advantages including (i) flexibility with respect to the choice of zeroth order Hamiltonian, (ii) recovery of the exact uncontracted multi-reference perturbation theory energies in the limit of large MPS bond dimension, (iii) no requirement to compute high body density matrices, (iv) an embarrassingly parallel algorithm (scaling up to the number of virtual orbitals, squared, processors). Preliminary numerical examples show that the MPS bond dimension required for accurate first order wavefunctions scales sub-linearly with the size of the basis.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.4895977DOIArticle
http://aip.scitation.org/doi/abs/10.1063/1.4895977PublisherArticle
ORCID:
AuthorORCID
Sharma, Sandeep0000-0002-6598-8887
Chan, Garnet Kin-Lic0000-0001-8009-6038
Additional Information:© 2014 AIP Publishing LLC. Received 7 August 2014; accepted 8 September 2014; published online 19 September 2014. This work was supported by the US National Science Foundation (NSF) through Grant No. NSF-CHE-1265277. Additional support for software development was provided through Grant No. NSF-OCI-1265278. S.S. would also like to thank Brecht Verstichel for many helpful discussions.
Funders:
Funding AgencyGrant Number
NSFCHE-1265277
NSFOCI-1265278
Subject Keywords:Wave functions; Tensor methods; Perturbation theory; Electron correlation calculations; Linear equations
Record Number:CaltechAUTHORS:20170106-123434796
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170106-123434796
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73300
Collection:CaltechAUTHORS
Deposited By: Donna Wrublewski
Deposited On:06 Jan 2017 21:13
Last Modified:22 Mar 2019 21:01

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