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Analysis of Electron Correlation Effects in Strongly Correlated Systems

Christian Stemmle

Published Jan 1, 2019• 0 citations
Publisher

Abstract

To explore new approaches for wave function based correlation methods in chemistry, the electron correlation effects of different model systems are analyzed by means of Quantum Information Theory (QIT) and the Method of Increments (MoI). Data for the QIT is obtained based on calculations employing the Density Matrix Renormalization Group (DMRG) and Full Configuration Interaction Quantum Monte Carlo (FCIQMC) methods. The investigation covers standard model systems for strong correlation, such as the dissociation of N2 and N2+, as well as polyacetylene, Be6 rings and the cobalt fluorides CoF2, CoF3 and CoF4. The latter represent challenging open-shell, transition metal containing compounds that may be systematically extended to linear chains. The observations stimulate a novel approach to select the configuration space in multi-reference calculations, promising reduced computational scaling for strongly correlated systems with large active spaces. Furthermore, a correspondence between entropies (QIT) and increments (MoI) is demonstrated, which suggests the related methods may be combined to exploit their different advantages. Finally, the correlation analysis of the cobalt fluorides yields valuable insights to extent the study to longer, linear chains.

DOI
10.17169/refubium-25604

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To explore new approaches for wave function based correlation methods in chemistry, the electron correlation effects of different model systems are analyzed by means of Quantum Information Theory (QIT) and the Method of Increments (MoI). Data for the QIT is obtained based on calculations employing the Density Matrix Renormalization Group (DMRG) and Full Configuration Interaction Quantum Monte Carlo (FCIQMC) methods. The investigation covers standard model systems for strong correlation, such as the dissociation of N2 and N2+, as well as polyacetylene, Be6 rings and the cobalt fluorides CoF2, CoF3 and CoF4. The latter represent challenging open-shell, transition metal containing compounds that may be systematically extended to linear chains. The observations stimulate a novel approach to select the configuration space in multi-reference calculations, promising reduced computational scaling for strongly correlated systems with large active spaces. Furthermore, a correspondence between entropies (QIT) and increments (MoI) is demonstrated, which suggests the related methods may be combined to exploit their different advantages. Finally, the correlation analysis of the cobalt fluorides yields valuable insights to extent the study to longer, linear chains.
Abstract Understanding electron correlation is crucial for developing new concepts in electronic structure theory, especially for strongly correlated electrons. We compare and apply two different approaches to quantify correlation contributions of orbitals: Quantum Information Theory (QIT) based on a Density Matrix Renormalization Group (DMRG) calculation and the Method of Increments (MoI). Although both approaches define very different correlation measures, we show that they exhibit very similar patterns when being applied to a polyacetelene model system. These results suggest one may deduce from one to the other, allowing the MoI to leverage from QIT results by screening correlation contributions with a cheap (“sloppy”) DMRG with a reduced number of block states. Or the other way around, one may select the active space in DMRG from cheap one‐body MoI calculations.
Abstract The accurate electronic structure calculation for strongly correlated chemical systems requires an adequate description for both static and dynamic electron correlation, and is a persistent challenge for quantum chemistry. In order to account for static and dynamic electron correlations accurately and efficiently, in this work we propose a new method by integrating the density matrix renormalization group (DMRG) method and multi-reference second-order Epstein–Nesbet perturbation theory (ENPT2) with a selected configuration interaction (SCI) approximation. Compared with previous DMRG-based dynamic correlation methods, the DMRG-ENPT2 method extends the range of applicability, allowing us to efficiently calculate systems with very large active space beyond 30 orbitals. We demonstrate this by performing calculations on H 2 S with an active space of (16e, 15o), hexacene with an active space of (26e, 26o) and 2D H 64 square lattice with an active space of (42e, 42o).
A major challenge in molecular electronic structure theory arises from chemical systems where the mean-field picture based upon a single electronic configuration fails to properly describe mechanics of many electrons. Such complex electronic states should be accounted for using a correlated superposition of multiple determinants and are referred to as multireference in quantum chemistry. Application domain of traditional multireference methods is severely limited to systems containing a small number of correlated electrons because of their exponential complexity. In recent years, much attention has been drawn to the density matrix renormalization group (DMRG) theory as a promising alternative. It has been introduced in ab initio quantum chemistry calculations and shown to be a highly-scalable multireference method that can handle full quantum degrees of freedom for the strongly-correlated wavefunction with unprecedented large configuration space. In this article, we provide an explicative introduction to the underlying theory and formalism built into the DMRG method and give a brief overview of our methodological extensions that combine DMRG and active-space correlation models.
Accurately predicting the effects of correlations caused by strong interactions between electrons represents one of the key unsolved challenges in quantum chemistry. This thesis details theoretical developments addressing two aspects of this challenge. First, advances in Canonical Transformation (CT) theory address the task of describing weak interactions between the chemically active valence electrons and the chemically inert core electrons when the valence electrons are strongly correlated. Second, new methodologies for Jastrow factor wavefunctions are explored in an attempt to describe strong interactions amongst the valence electrons. In its original form, CT theory suffered from poorly understood numerical instabilities in strongly interacting systems and poor accuracy relative to coupled cluster theory in weakly interacting systems. Here the numeric issues are identified as consequences of CT theory's central approximation and shown to be similar to the intruder states of many-body perturbation theory. It is demonstrated that these instabilities can be avoided by placing particular restrictions on the theory's degrees of freedom. In weakly interacting systems, we show that using a quadratic, rather than linear, commutator approximation improves accuracy, and that the accuracy in any system can be improved by making use of the system's 3-body reduced density matrix. These improvements are demonstrated in a variety of systems, including N2 , H2 O, NiO, and free base porphin. Jastrow factor wavefunctions have traditionally been handled using quan- tum Monte Carlo techniques such as variational Monte Carlo (VMC). Here we explore how VMC can be made to accommodate the unconventionally large numbers of variational parameters present in many-body Jastrow factors and show that the stochastic reconfiguration algorithm can be thus improved by employing the method of conjugate gradients to solve its central linear equation. In addition to extending the reach of VMC, we have also developed nonstochastic methods for working with Jastrow factor wavefunctions that do not rely on random sampling. These methods, similar in design to those used with the coupled cluster wavefunction, produce energies very close to those of VMC in applications to the Heisenberg, spinless Hubbard, and full Hubbard model Hamiltonians.
The quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as one of the methods of choice for calculations of strongly correlated molecular systems. Despite its great ability to capture strong electronic correlation in large active spaces, it is not suitable for computations of dynamical electron correlation. In this work, we present a new approach to the electronic structure problem of strongly correlated molecules, in which DMRG is responsible for a proper description of the strong correlation, whereas dynamical correlation is computed via the recently developed adiabatic connection (AC) technique which requires only up to two-body active space reduced density matrices. We report the encouraging results of this approach on typical candidates for DMRG computations, namely, n -acenes ( n = 2 → 7), Fe(II)–porphyrin, and the Fe 3 S 4 cluster.