Center for Molecular Modeling - G. K.-L. Chan

A practical guide to density matrix embedding theory in quantum chemistry

seba — Thu, 19 May 2016 07:04:09 +0000

S. Wouters, C. A. Jiménez-Hoyos, Q. Sun, G. K.-L. Chan

Journal of Chemical Theory and Computation

Publication Date (Web): May 09, 2016

2016

Published while none of the authors were employed at the CMM

Abstract

Density matrix embedding theory (DMET) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In this work, we give a practically oriented and explicit description of the numerical and theoretical formulation of DMET. We also describe in detail how to perform self-consistent DMET optimizations. We explore different embedding strategies with and without a self-consistency condition in hydrogen rings, beryllium rings, and a sample SN2 reaction. The source code for the calculations in this work can be obtained from https://github.com/sebwouters/qc-dmet.

DOI

http://dx.doi.org/10.1021/acs.jctc.6b00316

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acs%2Ejctc%2E6b00316.pdf

A practical guide to density matrix embedding theory in quantum chemistry

wim — Tue, 17 May 2016 06:29:14 +0000

S. Wouters, C.A. Jiménez-Hoyos, Q. Sun, G. K.-L. Chan, A. Bruder

Journal of Chemical Theory and Computation

2016

Published while none of the authors were employed at the CMM

Abstract

DOI

http://dx.doi.org/

Private attachment

1603.08443v2.pdf

Projector quantum Monte Carlo with matrix product states

seba — Tue, 24 Jun 2014 09:01:00 +0000

S. Wouters, B. Verstichel, D. Van Neck, G. K.-L. Chan

Physical Review B

90, 045104

2014

Abstract

We marry tensor network states (TNS) and projector quantum Monte Carlo (PMC) to overcome the high computational scaling of TNS and the sign problem of PMC. Using TNS as trial wavefunctions provides a route to systematically improve the sign structure and to eliminate the bias in fixed-node and constrained-path PMC. As a specific example, we describe phaseless auxiliary-field quantum Monte Carlo with matrix product states (MPS-AFQMC). MPS-AFQMC improves significantly on the DMRG ground-state energy. For the J1-J2 model on two-dimensional square lattices, we observe with MPS-AFQMC an order of magnitude reduction in the error for all couplings, compared to DMRG. The improvement is independent of walker bond dimension, and we therefore use bond dimension one for the walkers. The computational cost of MPS-AFQMC is then quadratic in the bond dimension of the trial wavefunction, which is lower than the cubic scaling of DMRG. The error due to the constrained-path bias is proportional to the variational error of the trial wavefunction. We show that for the J1-J2 model on two-dimensional square lattices, a linear extrapolation of the MPS-AFQMC energy with the discarded weight from the DMRG calculation allows to remove the constrained-path bias. Extensions to other tensor networks are briefly discussed.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1103/PhysRevB.90.045104

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paper8.pdf

Linear response theory for the density matrix renormalization group: Efficient algorithms for strongly correlated excited states

seba — Fri, 08 Nov 2013 07:58:29 +0000

N. Nakatani, S. Wouters, D. Van Neck, G. K.-L. Chan

Journal of Chemical Physics

140 (2), 024108

2014

Abstract

Linear response theory for the density matrix renormalization group (DMRG-LRT) was first presented in terms of the DMRG renormalization projectors [J. J. Dorando, J. Hachmann, and G. K.-L. Chan, J. Chem. Phys.130, 184111 (2009)]. Later, with an understanding of the manifold structure of the matrix product state (MPS) ansatz, which lies at the basis of the DMRG algorithm, a way was found to construct the linear response space for general choices of the MPS gauge in terms of the tangent space vectors [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett.107, 070601 (2011)]. These two developments led to the formulation of the Tamm-Dancoff and random phase approximations (TDA and RPA) for MPS. This work describes how these LRTs may be efficiently implemented through minor modifications of the DMRG sweep algorithm, at a computational cost which scales the same as the ground-state DMRG algorithm. In fact, the mixed canonical MPS form implicit to the DMRG sweep is essential for efficient implementation of the RPA, due to the structure of the second-order tangent space. We present ab initio DMRG-TDA results for excited states of polyenes, the water molecule, and a [2Fe-2S] iron-sulfur cluster.

DOI

http://dx.doi.org/10.1063/1.4860375

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paper4.pdf

Thouless theorem for matrix product states and subsequent post density matrix renormalization group methods

seba — Fri, 14 Jun 2013 08:38:32 +0000

S. Wouters, N. Nakatani, D. Van Neck, G. K.-L. Chan

Physical Review B

88, 075122

2013

Abstract

The similarities between Hartree-Fock (HF) theory and the density matrix renormalization group (DMRG) are explored. Both methods can be formulated as the variational optimization of a wave-function Ansatz. Linearization of the time-dependent variational principle near a variational minimum allows to derive the random phase approximation (RPA). We show that the nonredundant parameterization of the matrix product state (MPS) tangent space [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde and F. Verstraete, Phys. Rev. Lett. 107, 070601 (2011)] leads to the Thouless theorem for MPS, i.e., an explicit nonredundant parameterization of the entire MPS manifold, starting from a specific MPS reference. Excitation operators are identified, which extends the analogy between HF and DMRG to the Tamm-Dancoff approximation (TDA), the configuration interaction (CI) expansion, and coupled cluster theory. For a small one-dimensional Hubbard chain, we use a CI-MPS Ansatz with single and double excitations to improve on the ground state and to calculate low-lying excitation energies. For a symmetry-broken ground state of this model, we show that RPA-MPS allows to retrieve the Goldstone mode. We also discuss calculations of the RPA-MPS correlation energy. With the long-range quantum chemical Pariser-Parr-Pople Hamiltonian, low-lying TDA-MPS and RPA-MPS excitation energies for polyenes are obtained.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1103/PhysRevB.88.075122

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PhysRevB.88.075122.pdf

Five years of density matrix embedding theory

seba — Thu, 19 May 2016 07:18:47 +0000

S. Wouters, C. A. Jiménez-Hoyos, G. K.-L. Chan

Wiley

2017

ISBN

978-111912924-0

Short content

Density matrix embedding theory (DMET) describes finite fragments in the presence of a surrounding environment. In contrast to most embedding methods, DMET explicitly allows for quantum entanglement between both. In this chapter, we discuss both the ground-state and response theory formulations of DMET, and review several applications. In addition, a proof is given that the local density of states can be obtained by working with a Fock space of bath orbitals.

http://arxiv.org/abs/1605.05547

1605.05547v1.pdf

Density matrix embedding theory: accurate reaction paths and a second-quantized formulation for the local density of states

wim — Tue, 29 Mar 2016 07:53:31 +0000

S. Wouters, G. K.-L. Chan

ISBN/ISSN:

Invited talk

Conference / event / venue

ACS - Division of Computers in Chemistry

San Diego, USA

Sunday, 13 March, 2016 to Thursday, 17 March, 2016

Abstract

ACS-SWouters-032016.pdf

Conference reference

ACS - Division of Computers in Chemistry

Projector quantum Monte Carlo with matrix product states

seba — Fri, 04 Jul 2014 12:50:05 +0000

B. Verstichel, S. Wouters, D. Van Neck, G. K.-L. Chan

ISBN/ISSN:

Poster

Conference / event / venue

Low-scaling and Unconventional Electronic Structure Techniques Conference

Telluride, CO, USA

Sunday, 1 June, 2014 to Thursday, 5 June, 2014