Application of Multiconfiguration Pair-Density Functional Theory to the Diels-Alder Reaction.

Transition states for Diels-Alder reactions are strongly correlated, as evidenced by high-to-very-high M diagnostics, and therefore they require treatment by multireference methods. Multiconfiguration pair-density functional theory (MC-PDFT) combines a multiconfiguration wave function with a functional of the electron density and the on-top pair density to calculate the electronic energy for strongly correlated systems at a much lower cost than wave function methods that do not employ density functionals. Here we apply MC-PDFT to the Diels-Alder cycloaddition reaction of 1,3-butadiene with ethylene, where two kinds of reaction paths have been widely studied: concerted synchronous paths and diradical stepwise paths. The lowest-energy reaction path is now known to be a concerted synchronous one, and a method's ability to predict this is an important test. By comparison to the best available theoretical results in the literature, we test the accuracy of MC-PDFT with several choices of on-top functional for geometries and enthalpies of stable structures along both paths and for the transition state geometries. We also calculate the Arrhenius activation energies for both paths and compare these to experiment. We also compare to Kohn-Sham density functional theory (KS-DFT) with selected exchange-correlation functionals. CAS-PDFT gives consistently good energies and geometries for both the concerted and stepwise mechanisms, but none of the KS-DFT functionals gives accurate activation energies for both. The stepwise transition state is very strongly correlated, and MC-PDFT can treat it, but KS-DFT (which involves a single-configuration treatment) has larger errors. The results confirm that using a multiconfigurational reference function for strongly correlated transition states can significantly improve the reliability and that MC-PDFT can provide good accuracy at a much lower computational cost than competing multireference methods.

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.

One-electron bonds in copper-aluminum and copper-gallium complexes.

Odd-electron bonds have unique electronic structures and are often encountered as transiently stable, homonuclear species. In this study, a pair of copper complexes supported by Group 13 metalloligands, M[N((o-C6H4)NCH2PiPr2)3] (M = Al or Ga), featuring two-center/one-electron (2c/1e) σ-bonds were synthesized by one-electron reduction of the corresponding Cu(i) ⇢ M(III) counterparts. The copper bimetallic complexes were investigated by X-ray diffraction, cyclic voltammetry, electron paramagnetic spectroscopy, and density functional theory calculations. The combined experimental and theoretical data corroborate that the unpaired spin is delocalized across Cu, M, and ancillary atoms, and the singly occupied molecular orbital (SOMO) corresponds to a σ-(Cu-M) bond involving the Cu 4pz and M ns/npz atomic orbitals. Collectively, the data suggest the covalent nature of these interactions, which represent the first examples of odd-electron σ-bonds for the heavier Group 13 elements Al and Ga.

Electron transitions in a Ce(III)-catecholate metal-organic framework.

A rare three-dimensional catecholate-based Ce(III) metal-organic framework (MOF), denoted as NU-1701, has been synthesized and crystallographically characterized. Density functional theory calculations highlight various possible electronic transitions that may present in NU-1701. These transitions are competitive and indicate increased lanthanide character of Ce(III).

Analytic gradients for multiconfiguration pair-density functional theory with density fitting: Development and application to geometry optimization in the ground and excited states.

Density fitting reduces the computational cost of both energy and gradient calculations by avoiding the computation and manipulation of four-index electron repulsion integrals. With this algorithm, one can efficiently optimize the geometries of large systems with an accurate multireference treatment. Here, we present the derivation of multiconfiguration pair-density functional theory for energies and analytic gradients with density fitting. Six systems are studied, and the results are compared to those obtained with no approximation to the electron repulsion integrals and to the results obtained by complete active space second-order perturbation theory. With the new approach, there is an increase in the speed of computation with a negligible loss in accuracy. Smaller grid sizes have also been used to reduce the computational cost of multiconfiguration pair-density functional theory with little effect on the optimized geometries and gradient values.

Intrastrand Photolesion Formation in Thio-Substituted DNA: A Case Study Including Single-Reference and Multireference Methods.

The substitution of canonical nucleobases by thiated analogues in natural DNA has been exploited in pharmacology, photochemotherapy, and structural biology. Thionucleobases react with adjacent thymines leading to 6-4 pyrimidine-pyrimidone photoproducts (6-4PPs), which are a major source of DNA photodamage, in particular intrastrand cross-linked photolesions. Here, we study the mechanism responsible for the formation of 6-4PPs in thionucleobases by employing quantum-mechanical calculations. We use multiconfiguration pair-density functional theory, complete active space second-order perturbation theory, and Kohn-Sham density functional theory. Scrutinizing the photochemistry of thionucleobases can elucidate the reaction mechanism of these prodrugs and identify the role that triplet excited states play in the generation of photolesions in the natural biopolymer. Three different possible mechanisms to generate the 6-4PPs are presented, and we conclude that the use of multireference approaches is indispensable to capture important features of the potential energy surface.

Analytic gradients for state-averaged multiconfiguration pair-density functional theory.

Analytic gradients are important for efficient calculations of stationary points on potential energy surfaces, for interpreting spectroscopic observations, and for efficient direct dynamics simulations. For excited electronic states, as are involved in UV-Vis spectroscopy and photochemistry, analytic gradients are readily available and often affordable for calculations using a state-averaged complete active space self-consistent-field (SA-CASSCF) wave function. However, in most cases, a post-SA-CASSCF step is necessary for quantitative accuracy, and such calculations are often too expensive if carried out by perturbation theory or configuration interaction. In this work, we present the analytic gradients for multiconfiguration pair-density functional theory based on SA-CASSCF wave functions, which is a more affordable alternative. A test set of molecules has been studied with this method, and the stationary geometries and energetics are compared to values in the literature as obtained by other methods. Excited-state geometries computed with state-averaged pair-density functional theory have similar accuracy to those from complete active space perturbation theory at the second-order.

A Multireference Ab Initio Study of the Diradical Isomers of Pyrazine.

Three diradical pyrazine isomers were characterized using highly correlated, multireference methods. The lowest lying singlet and triplet state geometries of 2,3-didehydropyrazine ( ortho), 2,5-didehydropyrazine ( para), and 2,6-didehydropyrazine ( meta) were determined. Two active reference spaces were utilized. The complete active space (CAS) (8,8) includes the σ and σ* orbitals on the dehydrocarbon atoms as well as the valence π and π* orbitals. The CAS (12,10) reference space includes two additional orbitals corresponding to the in-phase and out-of-phase nitrogen lone pair orbitals. Adiabatic and vertical gaps between the lowest lying singlet and triplet states, optimized geometries, canonicalized orbital energies, unpaired electron densities, and spin polarization effects were compared. We find that the singlet states of each diradical isomer contain two significantly weighted configurations, and the larger active space is necessary for the proper physical characterization of both the singlet and triplet states. The singlet-triplet splitting is very small for the 2,3-didehydropyrazine ( ortho) and 2,6-didehydropyrazine ( meta) isomers (+1.8 and -1.4 kcal/mol, respectively) and significant for the 2,5-didehydropyrazine ( para) isomer (+28.2 kcal/mol). Singlet geometries show through-space interactions between the dehydocarbon atoms in the 2,3-didehydropyrazine ( ortho) and 2,6-didehydropyrazine ( meta) isomers. An analysis of the effectively unpaired electrons suggests that the 2,5-didehydropyrazine ( para) isomer also displays through-bond coupling between the diradical electrons.

An Extended Multireference Study of the Singlet and Triplet States of the 9,10-didehydroanthracene Diradical.

The 9,10-didehydroanthracene is an aromatic diradical produced by the Bergman cyclization of a benzannulated 10-membered enediyne. It is a 1,4 diradical, similar to p-benzyne. Here we study the spin state occupancy of the ground state of 9,10-didehydroanthracene by employing multireference methods (MR-CISD and MR-AQCC) with different basis sets (cc-pVDZ and cc-pVTZ) and active space sizes (CAS (2,2) through CAS (8,8)). At the CAS (8,8) MR-AQCC/cc-pVDZ level of theory, we find a two-configurational singlet ground state with an adiabatic Δ EST of 6.13 kcal/mol. Unpaired electron density populations and dominant electronic configuration interactions were used to analyze the features of the 9,10-didehydroanthracene diradical.