Search

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.

We analyzed static and dynamic electron correlation by decomposing the total electronic energy of calculations by restricted Hartree-Fock theory, complete active-space self-consistent field (CASSCF) theory, and multireference configuration interaction (MRCI). We used three different schemes to break down the relative energy contributions to the potential energy curves for the dissociation of H2, F2, and N2. The first decomposition scheme involves the classical and nonclassical components of the energy. The second and third recognize the part of the energy that is not expressible in terms of the one-body reduced density matrix; this is called the connected energy. The unconnected component is further decomposed into a part calculable from the density and the part calculable from the density coherence. The first decomposition scheme shows that the sum of the one-electron energy and the classical two-electron energy contains a negligible portion of the static correlation. This quantity has a relatively small variance between the three levels, especially for CASSCF and MRCI. This provides an explanation of why multiconfiguration pair-density functional theory and multiconfiguration density-coherence functional theory are able to improve the CASSCF energy. The latter two decompositions show that the connected energy contains a significant portion of static correlation. The energy representable by either the density or the density coherence is significantly different at the three levels. Mixing the density and density coherence between different methods may lead to a systematic error in the bond dissociation energy and the equilibrium bond distance, indicating that the density energy component and the density coherence energy component both include a significant amount of both static and dynamic correlation. These wave function decompositions can be useful for developing new functionals for density functional theory, density-coherence functional theory, density matrix functional theory, and pair-density functional theory and for guiding expectations for these theories.

This paper presents a new theory called multiconfiguration density coherence functional theory (MC-DCFT). This theory provides a new route to define density functionals for multiconfiguration wave functions, in particular by using the one-particle density matrix in the coordinate representation. The theory is illustrated by calculating the dissociation curve of four heteronuclear and homonuclear diatomic molecules, namely, H2, F2, N2, and HF, using density coherence functionals converted from PBE, BLYP, and PW91. By introducing two parameters in the converted density functionals, we are able to calculate bond dissociation energies of comparable accuracy as those calculated by multiconfiguration pair-density functional theory (MC-PDFT) and complete active space second-order perturbation theory (CASPT2). This demonstrates that it would be possible to build a successful multiconfiguration density functional theory based on density coherence.

This paper is a study of density coherences in multiconfiguration self-consistent field theory and Kohn-Sham (KS) density functional theory. We visualize and compare the nondiagonal elements of the first-order reduced density matrix in the electronic coordinate representation. This is the electronic density coherence, and it also appears in Hartree-Fock (HF) theory in the integrand of the exchange integral. The density coherence is calculated as a function of the internuclear distance for three diatomic molecules (H2, F2, and HF) using both restricted and unrestricted KS and HF theory, as well as the complete active space self-consistent field method. We identify a group of closely associated peaks corresponding to the coherence of electrons on opposite sides of the center of the molecule, and we call this the exchange massif. We find that Slater-determinant methods with a higher percentage of HF exchange tend to underestimate the density coherence at the exchange massif. We explain the trends in terms of a multireference diagnostic and the number of unpaired electrons.

Phase change memory (PCM) is considered as a leading candidate for next generation data storage as well as emerging computing device, but the advancement has been hampered by high switching energy due to the melting process and amorphous relaxation induced large resistance drift. Polymorphic crystal-crystal transition without amorphization in metal dichalcogenides (TMDs) could be employed to solve these issues. Yet, the mechanism is still controversy. A melting-free PCM made of two dimensional (2D) MoTe2, which exhibits unipolar resistive switching (RS) and multi-level states with substantially reduced resistance drift via joule heating, is reported in this work. The device is first prepared based on the temperature dependence of Raman spectrum and electrical transport investigations on MoTe2 films. Significantly improved device performances on energy efficiency, switching speed, and memory window are further achieved by electrode size scaling down, indicating the key role of localized heating. Then, device scale transmission electron microscopy images reveal that the resistive switching stems from the transition between semiconducting 2H phase and metallic 1T′ phase. An entropy induced Te vacancies model is proposed to explain the reversible phase change mechanism in the MoTe2 based device. This study paves the way for further development of PCM based on atomically thin 2D TMDs, aiming for high density storage-class memory and high-precision neuromorphic computing.

To uncover the way Hartree-Fock exchange brings static correlation error into hybrid Kohn-Sham density functional theory, we compare the potential energy curves of four diatomic molecules, namely, H2, F2, HF, and NaF, using both restricted and unrestricted Kohn-Sham theory. We find that increasing the percentage of Hartree-Fock exchange significantly increases the static correlation error because Hartree-Fock exchange replaces the ability of local exchange in density functionals to account for the localization effects associated with static correlation.

Accurately predicting the spin splitting energy of chemical species is important for understanding their reactivity and magnetic properties, but it is very challenging, especially for molecules containing transition metals. One impediment to progress is the scarcity of accurate benchmark data. Here we report a set of calculations designed to yield reliable benchmarks for simple transition-metal complexes that can be used to test density functional methods that are affordable for large systems of more practical interest. Various wave function methods are tested against experiment for Fe2+, Fe3+, and Co3+, including CASSCF, CASPT2, CASPT3, MRCISD, MRCISD+Q, ACPF, AQCC, CCSD­(T), and CASPT2/CCSD­(T) and also a new method called CASPT2.5, which is performed by taking the average of the CASPT2 and CASPT3 energies. We find that MRCISD+Q, ACPF, and AQCC require smaller active spaces for good accuracy than are required by CASPT2 and CASPT3, and this aspect may be important for calculations on larger molecules; here we find that CASPT2.5 extrapolated to a complete basis set is the most suitable methodin terms of computational cost and in terms of accuracy on monatomic systemsand therefore we chose this method for molecular benchmarks. Then Kohn–Sham density functional calculations with 60 exchange-correlation functionals are tested for FeF2, FeCl2, and CoF2. We find that MN15-L, M06-SX, and revM06 have very good agreement with CASPT2.5 benchmarks in terms of both the spin splitting energy and the optimized geometry for each spin state. In addition, we recommend def2-TZVP as the most suitable basis set to perform density functional calculations for molecular spin splitting energies; extra polarization functions in the basis set do not help to increase the accuracy of the spin splitting energy in KS calculations.

A self-assembly technology allows metal-organic framework materials to constitute a honeycomb internal structure while being shaped into millimeter-scale spheres. The ZIF-8 load is up to 83 wt% through solidification of chitosan (CS). This approach can be expanded to other morphologies (fibers) or crystals and is transformative for industrial manufacturing of nanomaterials.