Divergent Bimetallic Mechanisms in Copper(II)-Mediated C-C, N-N, and O-O Oxidative Coupling Reactions.

Copper-catalyzed aerobic oxidative coupling of diaryl imines provides a route for conversion of ammonia to hydrazine. The present study uses experimental and density functional theory computational methods to investigate the mechanism of N-N bond formation, and the data support a mechanism involving bimolecular coupling of Cu-coordinated iminyl radicals. Computational analysis is extended to CuII-mediated C-C, N-N, and O-O coupling reactions involved in the formation of cyanogen (NC-CN) from HCN, 1,3-butadiyne from ethyne (i.e., Glaser coupling), hydrazine from ammonia, and hydrogen peroxide from water. The results reveal two different mechanistic pathways. Heteroatom ligands with an uncoordinated lone pair (iminyl, NH2, OH) undergo charge transfer to CuII, generating ligand-centered radicals that undergo facile bimolecular radical-radical coupling. Ligands lacking a lone pair (CN and CCH) form bridged binuclear diamond-core structures that undergo C-C coupling. This mechanistic bifurcation is rationalized by analysis of spin densities in key intermediates and transition states, as well as multiconfigurational calculations. Radical-radical coupling is especially favorable for N-N coupling owing to energetically favorable charge transfer in the intermediate and thermodynamically favorable product formation.

Incorporation of [Cp*Rh] and [Cp*Ir] Species into Heterobimetallic Complexes via Protonolysis Reactivity and Dioximato Chelation.

The synthesis of multimetallic compounds can enable the placement of two or more metals in close proximity, but efforts in this area are often hindered by reagent incompatibilities and a lack of selectivity. Here, we show that organometallic half-sandwich [Cp*M] (M = Rh, Ir) fragments (where Cp* is η5-pentamethylcyclopentadienyl) can be cleanly installed into metallomacrocyclic structures based on the workhorse diimine-monooxime-monooximato ligand system. Six new heterobimetallic compounds have been prepared to explore this synthetic chemistry, which relies on in situ protonolysis reactivity with precursor Ni(II) or Co(III) monometallic complexes in the presence of suitable [Cp*M] species. Solid-state X-ray diffraction studies confirm installation of the [Cp*M] fragments into the metallomacrocycles via effective chelation of the Rh(III) and Ir(III) centers by the nascent dioximato site. Contrasting with square-planar Ni(II) centers, the Co(III) centers prefer octahedral geometry in the heterobimetallic compounds, promoting bridging ligation of acetate across the two metals. Spectroscopic and electrochemical studies reveal subtle influences of the metals on each other's properties, consistent with the moderate M'···M distances of ca. 3.6-3.7 Å in the modular compounds. Taken together, our results show that heterobimetallic complexes can be assembled with organometallic [Cp*M] fragments on the diimine-dioximato platform.

Automatic State Interaction with Large Localized Active Spaces for Multimetallic Systems.

The localized active space self-consistent field method factorizes a complete active space wave function into an antisymmetrized product of localized active space wave function fragments. Correlation between fragments is then reintroduced through localized active space state interaction (LASSI), in which the Hamiltonian is diagonalized in a model space of LAS states. However, the optimal procedure for defining the LAS fragments and LASSI model space is unknown. We here present an automated framework to explore systematically convergent sets of model spaces, which we call LASSI[r, q]. This method requires the user to select only r, the number of electron hops from one fragment to another, and q, the number of fragment basis functions per Hilbert space, which converges to CASCI in the limit of r, q → ∞. Numerical tests of this method on the trimetal oxo-centered complexes [Fe(III)Al(III)Fe(II)(µ3-O)(HCOO)6] and [Fe(III)2Fe(II)(µ3-O)(HCOO)6] show efficient convergence to the CASCI limit with 4-10 orders of magnitude fewer states than CASCI.

Organic Reactivity Made Easy and Accurate with Automated Multireference Calculations.

In organic reactivity studies, quantum chemical calculations play a pivotal role as the foundation of understanding and machine learning model development. While prevalent black-box methods like density functional theory (DFT) and coupled-cluster theory (e.g., CCSD(T)) have significantly advanced our understanding of chemical reactivity, they frequently fall short in describing multiconfigurational transition states and intermediates. Achieving a more accurate description necessitates the use of multireference methods. However, these methods have not been used at scale due to their often-faulty predictions without expert input. Here, we overcome this deficiency with automated multiconfigurational pair-density functional theory (MC-PDFT) calculations. We apply this method to 908 automatically generated organic reactions. We find 68% of these reactions present significant multiconfigurational character in which the automated multiconfigurational approach often provides a more accurate and/or efficient description than DFT and CCSD(T). This work presents the first high-throughput application of automated multiconfigurational methods to reactivity, enabled by automated active space selection algorithms and the computation of electronic correlation with MC-PDFT on-top functionals. This approach can be used in a black-box fashion, avoiding significant active space inconsistency error in both single- and multireference cases and providing accurate multiconfigurational descriptions when needed.

Linearized Pair-Density Functional Theory for Vertical Excitation Energies.

Multiconfiguration pair-density functional theory (MC-PDFT) is a computationally efficient method that computes the energies of electronic states in a state specific or state average framework via an on-top functional. However, MC-PDFT does not include state interaction among these states since the final energies do not come from the diagonalization of an effective model-space Hamiltonian. Recently, multistate extensions such as linearized PDFT (L-PDFT) have been developed to accurately model the potentials near conical intersections and avoided crossings. However, there has not been any systematic study evaluating their performance for predicting vertical excitations at the equilibrium geometry of a molecule, when the excited states are generally well separated. In this paper, we report the performance of L-PDFT on the extensive QUESTDB data set of vertical excitations using a database of automatically selected active spaces. We show that L-PDFT performs well on all these excitations and successfully reproduces the performance of MC-PDFT. These results further demonstrate the potential of L-PDFT, as its scaling is constant with the number of states included in the state-average manifold, whereas MC-PDFT scales linearly in this regard.

Variational Active Space Selection with Multiconfiguration Pair-Density Functional Theory.

The selection of an adequate set of active orbitals for modeling strongly correlated electronic states is difficult to automate because it is highly dependent on the states and molecule of interest. Although many approaches have shown some success, no single approach has worked well in all cases. In light of this, we present the "discrete variational selection" (DVS) approach to active space selection, in which one generates multiple trial wave functions from a diverse set of systematically constructed active spaces and then selects between these wave functions variationally. We apply this DVS approach to 207 vertical excitations of small-to-medium-sized organic and inorganic molecules (with 3 to 18 atoms) in the QUESTDB database by (i) constructing various sets of active space orbitals through diagonalization of parametrized operators and (ii) choosing the result with the lowest average energy among the states of interest. This approach proves ineffective when variationally selecting between wave functions using the density matrix renormalization group (DMRG) or complete active space self-consistent field (CASSCF) energy but is able to provide good results when variationally selecting between wave functions using the energy of the translated PBE (tPBE) functional from multiconfiguration pair-density functional theory (MC-PDFT). Applying this DVS-tPBE approach to selection among state-averaged DMRG wave functions, we obtain a mean unsigned error of only 0.17 eV using hybrid MC-PDFT. This result matches that of our previous benchmark without the need to filter out poor active spaces and with no further orbital optimization following active space selection of the SA-DMRG wave functions. Furthermore, we find that DVS-tPBE is able to robustly and effectively select between the new SA-DMRG wave functions and our previous SA-CASSCF results.

High-Throughput Experimentation, Theoretical Modeling, and Human Intuition: Lessons Learned in Metal-Organic-Framework-Supported Catalyst Design.

We have screened an array of 23 metals deposited onto the metal-organic framework (MOF) NU-1000 for propyne dimerization to hexadienes. By a first-of-its-kind study utilizing data-driven algorithms and high-throughput experimentation (HTE) in MOF catalysis, yields on Cu-deposited NU-1000 were improved from 0.4 to 24.4%. Characterization of the best-performing catalysts reveal conversion to hexadiene to be due to the formation of large Cu nanoparticles, which is further supported by reaction mechanisms calculated with density functional theory (DFT). Our results demonstrate both the strengths and weaknesses of the HTE approach. As a strength, HTE excels at being able to find interesting and novel catalytic activity; any a priori theoretical approach would be hard-pressed to find success, as high-performing catalysts required highly specific operating conditions difficult to model theoretically, and initial simple single-atom models of the active site did not prove representative of the nanoparticle catalysts responsible for conversion to hexadiene. As a weakness, our results show how the HTE approach must be designed and monitored carefully to find success; in our initial campaign, only minor catalytic performances (up to 4.2% yield) were achieved, which were only improved following a complete overhaul of our HTE approach and questioning our initial assumptions.

The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry.

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

Large-Scale Benchmarking of Multireference Vertical-Excitation Calculations via Automated Active-Space Selection.

We have calculated state-averaged complete-active-space self-consistent-field (SA-CASSCF), multiconfiguration pair-density functional theory (MC-PDFT), hybrid MC-PDFT (HMC-PDFT), and n-electron valence state second-order perturbation theory (NEVPT2) excitation energies with the approximate pair coefficient (APC) automated active-space selection scheme for the QUESTDB benchmark database of 542 vertical excitation energies. We eliminated poor active spaces (20-40% of calculations) by applying a threshold to the SA-CASSCF absolute error. With the remaining calculations, we find that NEVPT2 performance is significantly impacted by the size of the basis set the wave functions are converged in, regardless of the quality of their description, which is a problem absent in MC-PDFT. Additionally, we find that HMC-PDFT is a significant improvement over MC-PDFT with the translated PBE (tPBE) density functional and that it performs about as well as NEVPT2 and second-order coupled cluster on a set of 373 excitations in the QUESTDB database. We optimized the percentage of SA-CASSCF energy to include in HMC-PDFT when using the tPBE on-top functional, and we find the 25% value used in tPBE0 to be optimal. This work is by far the largest benchmarking of MC-PDFT and HMC-PDFT to date, and the data produced in this work are useful as a validation of HMC-PDFT and of the APC active-space selection scheme. We have made all the wave functions produced in this work (orbitals and CI vectors) available to the public and encourage the community to utilize this data as a tool in the development of further multireference model chemistries.

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.

A Ranked-Orbital Approach to Select Active Spaces for High-Throughput Multireference Computation.

The past decade has seen a great increase in the application of high-throughput computation to a variety of important problems in chemistry. However, one area which has been resistant to the high-throughput approach is multireference wave function methods, in large part due to the technicalities of setting up these calculations and in particular the not always intuitive challenge of active space selection. As we look toward a future of applying high-throughput computation to all areas of chemistry, it is important to prepare these methods for large-scale automation. Here, we propose a ranked-orbital approach to select active spaces with the goal of standardizing multireference methods for high-throughput computation. This method allows for the meaningful comparison of different active space selection schemes and orbital localizations, and we demonstrate the utility of this approach across 1120 multireference calculations for the excitation energies of small molecules. Our results reveal that it is helpful to distinguish the method used to generate orbitals from the method of ranking orbitals in terms of importance for the active space. Additionally, we propose our own orbital ranking scheme that estimates the importance of an orbital for the active space through a pair-interaction framework from orbital energies and features of the Hartree-Fock exchange matrix. We call this new scheme the "approximate pair coefficient" (APC) method and we show that it performs quite well for the test systems presented.

Machine-Learned Energy Functionals for Multiconfigurational Wave Functions.

We introduce multiconfiguration data-driven functional methods (MC-DDFMs), a group of methods which aim to correct the total or classical energy of a qualitatively accurate multiconfigurational wave function using a machine-learned functional of some featurization of the wave function such as its density, on-top density, or both. On a data set of carbene singlet-triplet energy splittings, we show that MC-DDFMs are able to achieve near-benchmark performance on systems not used for training with a robust degree of active-space independence. Beyond demonstrating that the density and on-top density hold the information necessary to correct the singlet-triplet energy splittings of multiconfigurational wave functions, this approach shows great promise for the development of functionals for MC-PDFT because corrections to the classical energy appear to be more transferable to types of molecules not included in the training data than corrections to total energies such as those yielded by CASSCF or NEVPT2.