Center for Molecular Modeling - C. Lanssens

Method for making 2-electron response reduced density matrices approximately N-representable

caitlin — Thu, 01 Mar 2018 08:49:44 +0000

C. Lanssens, Paul W. Ayers, D. Van Neck, S. De Baerdemacker, K. Gunst, P. Bultinck

Journal of Chemical Physics

148, 8, 084104

2018

Abstract

In methods like geminal-based approaches or coupled cluster that are solved using the projected Schrödinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not $N$-representable. That is, the response 2-RDM does not correspond to an actual physical $N$-electron wave function. We present a new algorithm for making these non-$N$-representable 2-RDMs approximately $N$-representable, i.e., it has the right symmetry and normalization and it fulfills the $P$-, $Q$-, and $G$-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties which is the closest (in the sense of the Frobenius norm) to the non-$N$-representable 2-RDM by minimizing the square norm of the difference between this initial response 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, $Q$-matrix, and $G$-matrix are positive semidefinite, i.e., their eigenvalues are non-negative. Our method is suitable for fixing non-$N$-representable 2-RDMs which are close to being $N$-representable. Through the $N$-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important $N$-representability conditions.

DOI

https://doi.org/10.1063/1.4994618

An Explicit Approach to Conceptual Density Functional Theory Descriptors of Arbitrary Order

toon — Thu, 30 Jun 2016 08:16:28 +0000

F. Heidar-Zadeh, M. Richer, S. Fias, R.A. Miranda-Quintana, M. Chan, M. Franco-Perez, C. Gonzalez-Espinoza, T.D. Kim, C. Lanssens, A.H.G. Patel, X.D. Yang, E. Vohringer-Martinez, C. Cárdenas, T. Verstraelen, P.W. Ayers

Chemical Physics Letters

660, 307–312

2016

Abstract

We present explicit formulas for arbitrary-order derivatives of the energy, grand potential, electron density, and higher-order response functions with respect to the number of electrons, and the chemical potential for any smooth and differentiable model of the energy versus the number of electrons. The resulting expressions for global reactivity descriptors (hyperhardnesses and hypersoftnesses), local reactivity descriptors (hyperFukui functions and local hypersoftnesses), and nonlocal response functions are easy to evaluate computationally. Specifically, the explicit formulas for global/local/nonlocal hypersoftnesses of arbitrary order are derived using Bell polynomials. Explicit expressions for global and local hypersoftness indicators up to fifth order are presented.

DOI

http://dx.doi.org/10.1016/j.cplett.2016.07.039

Private attachment

1-s2.0-S0009261416305280-main.pdf

Integrable quantum many-body systems

wim — Fri, 02 Mar 2018 09:32:22 +0000

Making 2-electron response reduced density matrices N-representable

caitlin — Wed, 26 Jul 2017 13:29:17 +0000

C. Lanssens, P.W. Ayers, D. Van Neck, S. De Baerdemacker, K. Gunst, P. Bultinck

ISBN/ISSN:

Poster

Conference / event / venue

International Summer School in Electronic Structure Theory: Electron Correlation in Physics and Chemistry

Aussois, France

Sunday, 18 June, 2017 to Saturday, 1 July, 2017

Abstract (private)

AussoisPoster.pdf

ISTPC 2017

wim — Tue, 25 Apr 2017 06:46:58 +0000

Aussois, France

Sunday, 18 June, 2017 to Saturday, 1 July, 2017

Participant(s)

C. Lanssens

Project ref.

None

Conference reference

ISTPC 2017

Mini-school on mathematics in electronic structure theory

wim — Wed, 12 Apr 2017 11:01:56 +0000

Paris, France

Monday, 9 January, 2017 to Wednesday, 11 January, 2017

Participant(s)

C. Lanssens

Project ref.

None

Conference reference

Mini-school on mathematics in electronic structure theory

Alternative algorithm for variational 2-RDM theory

wim — Tue, 07 Mar 2017 13:36:48 +0000

Pairing phenomena in quantum many-body systems

wim — Wed, 22 Feb 2017 10:47:06 +0000

Making 2-electron response reduced density matrices N-representable

caitlin — Wed, 19 Oct 2016 12:57:28 +0000

C. Lanssens, P.W. Ayers, P. Bultinck, D. Van Neck

ISBN/ISSN:

Poster

Conference / event / venue

Summer School Modern Wavefunction Methods in Electronic Structure Theory

Gelsenkirchen, Germany

Monday, 3 October, 2016 to Saturday, 8 October, 2016

Abstract (private)

CaitlinLanssens_MWM.pdf

Modern Wavefunction Methods in Electronic Structure Theory

wim — Tue, 04 Oct 2016 06:41:49 +0000

Mainz, Germany

Monday, 3 October, 2016 to Saturday, 8 October, 2016

Participant(s)

K. Gunst, C. Lanssens

Project ref.

FWO K. Gunst FWO3F02016002701

Conference reference

Modern Wavefunction Methods in Electronic Structure Theory