skip to main content

Attention:

The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Friday, May 17 until 8:00 AM ET on Saturday, May 18 due to maintenance. We apologize for the inconvenience.


Title: Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory
Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.  more » « less
Award ID(s):
2054723
NSF-PAR ID:
10339918
Author(s) / Creator(s):
; ; ; ; ; ; ; ; ; ;
Date Published:
Journal Name:
Chemical Science
Volume:
13
Issue:
26
ISSN:
2041-6520
Page Range / eLocation ID:
7685 to 7706
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Kohn-Sham density functional theory with the available exchange–correlation functionals is less accurate for strongly correlated systems, which require a multiconfigurational description as a zero-order function, than for weakly correlated systems, and available functionals of the spin densities do not accurately predict energies for many strongly correlated systems when one uses multiconfigurational wave functions with spin symmetry. Furthermore, adding a correlation functional to a multiconfigurational reference energy can lead to double counting of electron correlation. Multiconfiguration pair-density functional theory (MC-PDFT) overcomes both obstacles, the second by calculating the quantum mechanical part of the electronic energy entirely by a functional, and the first by using a functional of the total density and the on-top pair density rather than the spin densities. This allows one to calculate the energy of strongly correlated systems efficiently with a pair-density functional and a suitable multiconfigurational reference function. This article reviews MC-PDFT and related background information. 
    more » « less
  2. The strong couplings between electronic states in conical intersection regions are among the most challenging problems in quantum chemistry. XMS-CASPT2, a second-order multireference quasidegenerate perturbation theory, has been successful in describing potential energy surfaces near the conical intersections. We have recently proposed a less expensive method for this problem, namely state-interaction pair-density functional theory (SI-PDFT), which considers the coupling between electronic states described by multiconfiguration pair-density functional theory (MC-PDFT). Here we test the accuracy of SI-PDFT for closely coupled potential energy surfaces of methylamine along five different reaction paths for N–H bond fission. We choose paths that pass close to a conical intersection of the ground and first excited states. We find that SI-PDFT predicts potential energy curves and energy splittings near the locally avoided crossing in close proximity to those obtained by XMS-CASPT2. This validates the method for application to photochemical simulations. 
    more » « less
  3. Standard approximations for the exchange–correlation functional in Kohn–Sham density functional theory (KS-DFT) typically lead to unacceptably large errors when applied to strongly correlated electronic systems. Partition-DFT (PDFT) is a formally exact reformulation of KS-DFT in which the ground-state density and energy of a system are obtained through self-consistent calculations on isolated fragments, with a partition energy representing inter-fragment interactions. Here, we show how typical errors of the local density approximation (LDA) in KS-DFT can be largely suppressed through a simple approximation, the multi-fragment overlap approximation (MFOA), for the partition energy in PDFT. Our method is illustrated on simple models of one-dimensional strongly correlated linear hydrogen chains. The MFOA, when used in combination with the LDA for the fragments, improves LDA dissociation curves of hydrogen chains and produces results that are comparable to those of spin-unrestricted LDA, but without breaking the spin symmetry. MFOA also induces a correction to the LDA electron density that partially captures the correct density dimerization in strongly correlated hydrogen chains. Moreover, with an additional correction to the partition energy that is specific to the one-dimensional LDA, the approximation is shown to produce dissociation energies in quantitative agreement with calculations based on the density matrix renormalization group method.

     
    more » « less
  4. The molecules 1,4-cyclohexadiene (unconjugated 1,4-CHD) and 1,3-cyclohexadiene (conjugated 1,3-CHD) both have two double bonds, but these bonds interact in different ways. These molecules have long served as examples of through-bond and through-space interactions, respectively, and their electronic structures have been studied in detail both experimentally and theoretically, with the experimental assignments being especially complete. The existence of Rydberg states interspersed with the valence states makes the quantum mechanical calculation of their spectra a challenging task. In this work, we explore the electronic excitation energies of 1,4-CHD and 1,3-CHD for both valence and Rydberg states by means of complete active space second-order perturbation theory (CASPT2), extended multi-state CASPT2 (XMS-CASPT2), and multiconfiguration pair-density functional theory (MC-PDFT); it is shown by comparison to experiment that MC-PDFT yields the most accurate results. We found that the inclusion of Rydberg orbitals in the active space not only enables the calculation of Rydberg excitation energies but also improves the accuracy of the valence ones. A special characteristic of the present analysis is the calculation of the second moments of the excited-state orbitals. Because we find that the CASPT2 densities agree well with the CASSCF ones and since the MC-PDFT methods gets accurate excitation energies based on the CASSCF densities, we believe that we can trust these moments as far as giving a more accurate picture of the diffuseness of the excited-state orbitals in these prototype molecules than has previously been available. 
    more » « less
  5. Methane‐to‐methanol conversion (MMC) can be facilitated with high methanol selectivities by copper‐exchanged zeolites. There are however two open questions regarding the use of these zeolites to facilitate the MMC process. The first concerns the possibility of operating the three cycles in the stepwise MMC process by these zeolites in an isothermal fashion. The second concerns the possibility of improving the methanol yields by systematic substitution of some copper centers in these active sites with other earth‐abundant transition metals. Quantum‐mechanical computations can be used to compare methane activation by copper oxide species and analogous mixed‐metal systems. To carry out such screening, it is important that we use theoretical methods that are accurate and computationally affordable for describing the properties of the hetero‐metallic catalytic species. We have examined the performance of 47 exchange‐correlation density functionals for predicting the relative spin‐state energies and chemical reactivities of six hetero‐metallic [M‐O‐Cu]2+and [M‐O2‐Cu]2+, (where MCo, Fe, and Ni), species by comparison with coupled cluster theory including iterative single, double excitations as well as perturbative treatment of triple excitations, CCSD(T). We also performed multireference calculations on some of these systems. We considered two types of reactions (hydrogen addition and oxygen addition) that are relevant to MMC. We recommend the use of τ‐HCTH and OLYP to determine the spin‐state energy splittings in the hetero‐metallic motifs. ωB97, ωB97X, ωB97X‐D3, and MN15 performed best for predicting the energies of the hydrogen and oxygen addition reactions. In contrast, local, and semilocal functionals do poorly for chemical reactivity. Using [Fe‐O‐Cu]2+as a test, we see that the nonlocal functionals perform well for the methane CH activation barrier. In contrast, the semilocal functionals perform rather poorly. © 2018 Wiley Periodicals, Inc.

     
    more » « less