We propose a simple DFT-based diagnostic for nondynamical correlation effects, namely A
 λ = (1 − TAE[X
 λ
 C]/TAE[XC])/λ where TAE stands for the molecular total atomization energy, XC is a pure-DFT exchange-correlation functional, and X
 λ
 C represents the corresponding hybrid with 100λ % Hartree–Fock-type exchange. The diagnostic is a good predictor for sensitivity of energetics to the level of theory, unlike most wavefunction-based diagnostics. For GGA functionals, A
 λ values approaching unity indicate severe nondynamical correlation, while values between 0 and about 0.1 indicate systems where correlation is predominantly dynamical in character (or entirely absent). The diagnostic is only weakly sensitive to the basis set (beyond polarized valence double zeta) and can easily be applied to problems beyond the practical reach of wavefunction ab initio methods required for other diagnostics. We also propose a simple measure for the importance of dynamic correlation.

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A simple DFT-based diagnostic for nondynamical correlation

The accurate calculation of the (differential) correlation energy is central to the quantum chemical description of bond-formation and bond-dissociation processes. In order to estimate the quality of single- and multireference approaches for this purpose, various diagnostic tools have been developed. In this work, we elaborate on our previous observation [J. Phys. Chem. Lett.2012, 3, 3129] that one- and two-orbital-based entanglement measures provide quantitative means for the assessment and classification of electron correlation effects among molecular orbitals. The dissociation behavior of some prototypical diatomic molecules features all types of correlation effects relevant for chemical bonding. We demonstrate that our entanglement analysis is convenient to dissect these electron correlation effects and to provide a conceptual understanding of bond-forming and bond-breaking processes from the point of view of quantum information theory.

Orbital Entanglement in Bond-Formation Processes

Shannon information entropy in position space for two-electron atomic systems

Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA~Received 7 March 2003; published 30 June 2003!We study a set of localized spins coupled through exchange interaction and subject to an external magneticﬁeld. We demonstrate, for such a class of one-dimensional magnetic systems, that entanglement can be con-trolled and tuned by varying the anisotropy parameter in the Hamiltonian and by introducing impurities into thesystems. In particular, for certain parameters, the entanglement is zero up to a critical point l

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Tuning the entanglement for a two-dimensional magnetic system with anisotropic coupling and impurities

Theoretic-information measures of the Shan- non type are employed to describe the course of the sim- plest hydrogen abstraction and the identity SN2 exchange chemical reactions. For these elementary chemical pro- cesses, the transition state is detected and the bond breaking/forming regions are revealed. A plausibility argument of the former is provided and verified numeri- cally. It is shown that the information entropy profiles posses much more chemically meaningful structure than the profile of the total energy for these chemical reactions. Our results support the concept of a continuum of transient of Zewail and Polanyi for the transition state rather than a single state, which is also in agreement with reaction force analyses. This is performed by following the intrinsic reaction coordinate (IRC) path calculated at the MP2 level of theory from which Shannon entropies in position and momentum spaces at the QCISD(T)/6-311??G(3df,2p) level are determined. Several selected descriptors of the density are utilized to support the observations, such as the molecular electrostatic potential, the hardness, the dipole moment along with geometrical parameters.

Phenomenological description of the transition state, and the bond breaking and bond forming processes of selected elementary chemical reactions: an information-theoretic study

Electron–electron correlation in quantum chemistry calculations can be analysed in terms of entanglement between electrons. Two exactly solvable models: two fixed spin-1/2 particles and two-electron two-site Hubbard model are used to define and discuss the entanglement as a function of the system parameters. Ab initio configuration interaction calculation for entanglement is presented for the H2 molecule. Qualitatively, entanglement and electron–electron correlation have similar behaviour. Thus, entanglement might be used as an alternative measure of electron correlation in quantum chemistry calculations.

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H. Wang

Papers

Entanglement and electron correlation in quantum chemistry calculations