Mechanistic Study of the Production of NOx Gases from the Reaction of Copper with Nitric Acid.

Copper dissolution in nitric acid is a historic reaction playing a central role in many industrial processes, particularly for metal recovery from the electronics to nuclear industries. The mechanism through which this process occurs is debated. In order to better understand this process, quantum chemical calculations were performed to elucidate the key steps in the mechanism of copper dissolution in nitric acid. We combine both Kohn-Sham density functional theory and ab initio molecular dynamics simulations to understand the mechanism of the formation of the key products: NO2, HNO2, and NO. Our calculations suggest that the mechanisms of formation of NO2, HNO2, and NO are interconnected.

On-Top Ratio for Atoms and Molecules.

The on-top ratio, R, is the ratio of the on-top pair density to the square of half the total density. Here, we explore the on-top ratio as a tool to understand different types of bonds, including covalent, polar covalent, ionic, and dispersion-dominated weak interactions. We show for several diatomic molecules and for ethylene that the partial derivative of R is a useful indicator of covalent-bond breaking. R also presents a local maximum for each electron shell when all electrons are correlated.

Multiconfiguration Pair-Density Functional Theory: A New Way To Treat Strongly Correlated Systems.

The electronic energy of a system provides the Born-Oppenheimer potential energy for internuclear motion and thus determines molecular structure and spectra, bond energies, conformational energies, reaction barrier heights, and vibrational frequencies. The development of more efficient and more accurate ways to calculate the electronic energy of systems with inherently multiconfigurational electronic structure is essential for many applications, including transition metal and actinide chemistry, systems with partially broken bonds, many transition states, and most electronically excited states. Inherently multiconfigurational systems are called strongly correlated systems or multireference systems, where the latter name refers to the need for using more than one ("multiple") configuration state function to provide a good zero-order reference wave function. This Account describes multiconfiguration pair-density functional theory (MC-PDFT), which was developed as a way to combine the advantages of wave function theory (WFT) and density functional theory (DFT) to provide a better treatment of strongly correlated systems. First we review background material: the widely used Kohn-Sham DFT (which uses only a single Slater determinant as reference wave function), multiconfiguration WFT methods that treat inherently multiconfigurational systems based on an active space, and previous attempts to combine multiconfiguration WFT with DFT. Then we review the formulation of MC-PDFT. It is a generalization of Kohn-Sham DFT in that the electron kinetic energy and classical electrostatic energy are calculated from a reference wave function, while the rest of the energy is obtained from a density functional. However, there are two main differences with respent to Kohn-Sham DFT: (i) The reference wave function is multiconfigurational rather than being a single Slater determinant. (ii) The density functional is a function of the total density and the on-top pair density rather than being a function of the spin-up and spin-down densities. In work carried out so far, the multiconfigurational wave function is a multiconfiguration self-consistent-field wave function. The new formulation has the advantage that the reference wave function has the correct spatial and spin symmetry and can describe bond dissociation (of both single and multiple bonds) and electronic excitations in a formally and physically correct way. We then review the formulation of density functionals in terms of the on-top pair density. Finally we review successful applications of the theory to bond energies and bond dissociation potential energy curves of main-group and transition metal bonds, to barrier heights (including pericyclic reactions), to proton affinities, to the hydrogen bond energy of water dimer, to ground- and excited-state charge transfer, to valence and Rydberg excitations of molecules, and to singlet-triplet splittings of radicals. We find that that MC-PDFT can give accurate results not only with complete-active-space multiconfiguration wave functions but also with generalized-active-space multiconfiguration wave functions, which are practical for larger numbers of active electrons and active orbitals than are complete-active-space wave functions. The separated-pair approximation, which is a special case of generalized active space self-consistent-field theory, is especially promising. MC-PDFT, because it requires much less computer time and storage than pure WFT methods, has the potential to open larger and more complex strongly correlated systems to accurate simulation.

On-Top Pair Density as a Measure of Left-Right Correlation in Bond Breaking.

To better understand left-right electron correlation and the effect of bond breaking on the on-top pair density, analytic expressions for the total density, the on-top pair density, and the ratio of the on-top pair density to the square of the total density were derived for H2 for both a restricted Hartree-Fock wave function and a complete active space self-consistent-field wave function with two electrons in two active orbitals. These quantities are compared for the two wave functions for various points in space around the molecule as functions of internuclear distance. At some points in space, in the CASSCF(2,2) wave function, electron correlation, perhaps counterintuitively, increases the probability that two electrons are at the same point in space. At the Coulson-Fischer point, the on-top pair density for the complete active space wave function starts to rapidly approach zero, and this can be taken as an indicator of bond breaking.

Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table.

In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas-Kroll-Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC-PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large-scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added, two surface hopping algorithms are included to enable nonadiabatic calculations, and the DQ method for diabatization is added. Finally, we report on the subject of improvements with respects to alternative file options and parallelization.

Bimetallic cobalt-dinitrogen complexes: impact of the supporting metal on N2 activation.

Expanding a family of cobalt bimetallic complexes, we report the synthesis of the Ti(III) metalloligand, Ti[N(o-(NCH2P((i)Pr)2)C6H4)3] (abbreviated as TiL), and three heterobimetallics that pair cobalt with an early transition metal ion: CoTiL (1), K(crypt-222)[(N2)CoVL] (2), and K(crypt-222)[(N2)CoCrL] (3). The latter two complexes, along with previously reported K(crypt-222)[(N2)CoAlL] and K(crypt-222)[(N2)Co2L], constitute an isostructural series of cobalt bimetallics that bind dinitrogen in an end-on fashion, i.e. [(N2)CoML](-). The characterization of 1-3 includes cyclic voltammetry, X-ray crystallography, and infrared spectroscopy. The [CoTiL](0/-) reduction potential is extremely negative at -3.20 V versus Fc(+)/Fc. In the CoML series where M is a transition metal, the reduction potentials shift anodically as M is varied across the first-row period. Among the [(N2)CoML](-) compounds, the dinitrogen ligand is weakly activated, as evidenced by N-N bond lengths between 1.110(8) and 1.135(4) Å and by N-N stretching frequencies between 1971 and 1995 cm(-1). Though changes in νN2 are subtle, the extent of N2 activation decreases across the first-row period. A correlation is found between the [CoML](0/-) reduction potentials and N2 activation, where the more cathodic potentials correspond to lower N-N frequencies. Theoretical calculations of the [(N2)CoML](-) complexes reveal important variations in the electronic structure and Co-M interactions, which depend on the exact nature of the supporting metal ion, M.

Heterobimetallic Complexes That Bond Vanadium to Iron, Cobalt, and Nickel.

Zero-valent iron, cobalt, and nickel were installed into the metalloligand V[N(o-(NCH2P((i)Pr)2)C6H4)3] (1, VL), generating the heterobimetallic trio FeVL (2), CoVL (3), and NiVL (4), respectively. In addition, the one-electron-oxidized analogues [FeVL]X ([2(ox)]X, where X(-) = BPh4 or PF6) and [CoVL]BPh4 ([3(ox)]BPh4) were prepared. The complexes were characterized by a host of physical methods, including cyclic voltammetry, X-ray crystallography, magnetic susceptibility, electronic absorption, NMR, electron paramagnetic resonance (EPR), and Mössbauer spectroscopies. The CoV and FeV heterobimetallic compounds have short M-V bond lengths that are consistent with M-M multiple bonding. As revealed by theoretical calculations, the M-V bond is triple in 2, 2(ox), and 3(ox), double in 3, and dative (Ni → V) in 4. The (d-d)(10) species, 2 and 3(ox), are diamagnetic and exhibit large diamagnetic anisotropies of -4700 × 10(-36) m(3)/molecule. Complexes 2 and 3(ox) are also characterized by intense visible bands at 760 and 610 nm (ε > 1000 M(-1) cm(-1)), respectively, which correspond to an intermetal (M → V) charge-transfer transition. Magnetic susceptibility measurements and EPR characterization establish S = (1)/2 ground states for (d-d)(9) 2(ox) and (d-d)(11) 3, while (d-d)(12) 4 is S = 1 based on Evans' method.

Influence of Copper Oxidation State on the Bonding and Electronic Structure of Cobalt-Copper Complexes.

Heterobimetallic complexes that pair cobalt and copper were synthesized and characterized by a suite of physical methods, including X-ray diffraction, X-ray anomalous scattering, cyclic voltammetry, magnetometry, electronic absorption spectroscopy, electron paramagnetic resonance, and quantum chemical methods. Both Cu(II) and Cu(I) reagents were independently added to a Co(II) metalloligand to provide (py3tren)CoCuCl (1-Cl) and (py3tren)CoCu(CH3CN) (2-CH3CN), respectively, where py3tren is the triply deprotonated form of N,N,N-tris(2-(2-pyridylamino)ethyl)amine. Complex 2-CH3CN can lose the acetonitrile ligand to generate a coordination polymer consistent with the formula "(py3tren)CoCu" (2). One-electron chemical oxidation of 2-CH3CN with AgOTf generated (py3tren)CoCuOTf (1-OTf). The Cu(II)/Cu(I) redox couple for 1-OTf and 2-CH3CN is reversible at -0.56 and -0.33 V vs Fc(+)/Fc, respectively. The copper oxidation state impacts the electronic structure of the heterobimetallic core, as well as the nature of the Co-Cu interaction. Quantum chemical calculations showed modest electron delocalization in the (CoCu)(+4) state via a Co-Cu σ bond that is weakened by partial population of the Co-Cu σ antibonding orbital. By contrast, no covalent Co-Cu bonding is predicted for the (CoCu)(+3) analogue, and the d-electrons are fully localized at individual metals.

Pushing the Limits of Delta Bonding in Metal-Chromium Complexes with Redox Changes and Metal Swapping.

Into the metalloligand Cr[N(o-(NCH2P((i)Pr)2)C6H4)3] (1, CrL) was inserted a second chromium atom to generate the dichromium complex Cr2L (2), which is a homobimetallic analogue of the known MCrL complexes, where M is manganese (3) or iron (4). The cationic and anionic counterparts, [MCrL](+) and [MCrL](-), respectively, were targeted, and each MCr pair was isolated in at least one other redox state. The solid-state structures of the [MCrL](+,0,-) redox members are essentially the same, with ultrashort metal-metal bonds between 1.96 and 1.74 Å. The formal shortness ratios (r) of these interactions are between 0.84 and 0.74 and are interpreted as triple to quintuple metal-metal bonds with the aid of theory. The trio of (d-d)(10) species [Cr2L](-) (2(red)), MnCrL (3), and [FeCrL](+) (4(ox)) are S = 0 diamagnets. On the basis of M-Cr bond distances and theoretical calculations, the strength of the metal-metal bond across the (d-d)(10) series increases in the order Fe < Mn < Cr. The methylene protons in the ligand are shifted downfield in the (1)H NMR spectra, and the diamagnetic anisotropy of the metal-metal bond was calculated as -3500 × 10(-36), -3900 × 10(-36), and -5800 × 10(-36) m(3) molecule(-1) for 2(red), 3, and 4(ox) respectively. The magnitude of diamagnetic anisotropy is, thus, affected more by bond polarity than by bond order. A comparative vis-NIR study of quintuply bonded 2(red) and 3 revealed a large red shift in the δ(4) → δ(3)δ* transition energy upon swapping from the (Cr2)(2+) to the (MnCr)(3+) core. Complex 2(red) was further investigated by resonance Raman spectroscopy, and a band at 434 cm(-1) was assigned as the Cr-Cr bond vibration. Finally, 4(ox) exhibited a Mössbauer doublet with an isomer shift of 0.18 mm/s that suggests a primarily Fe-based oxidation to Fe(I).

Role of the metal in the bonding and properties of bimetallic complexes involving manganese, iron, and cobalt.

A multidentate ligand platform is introduced that enables the isolation of both homo- and heterobimetallic complexes of divalent first-row transition metal ions such as Mn(II), Fe(II), and Co(II). By means of a two-step metalation strategy, five bimetallic coordination complexes were synthesized with the general formula M1M2Cl(py3tren), where py3tren is the triply deprotonated form of N,N,N-tris(2-(2-pyridylamino)ethyl)amine. The metal-metal pairings include dicobalt (1), cobalt-iron (2), cobalt-manganese (3), diiron (4), and iron-manganese (5). The bimetallic complexes have been investigated by X-ray diffraction and X-ray anomalous scattering studies, cyclic voltammetry, magnetometry, Mössbauer spectroscopy, UV-vis-NIR spectroscopy, NMR spectroscopy, combustion analyses, inductively coupled plasma optical emission spectrometry, and ab initio quantum chemical methods. Only the diiron chloride complex in this series contains a metal-metal single bond (2.29 Å). The others show weak metal-metal interactions (2.49 to 2.53 Å). The diiron complex is also distinct with a septet ground state, while the other bimetallic species have much lower spin states from S = 0 to S = 1. We propose that the diiron system has delocalized metal-metal bonding electrons, which seems to correlate with a short metal-metal bond and a higher spin state. Multiconfigurational wave function calculations revealed that, indeed, the metal-metal bonding orbitals in the diiron complex are much more delocalized than those of the dicobalt analogue.

Predicting paramagnetic 1H NMR chemical shifts and state-energy separations in spin-crossover host-guest systems.

The behaviour of metal-organic cages upon guest encapsulation can be difficult to elucidate in solution. Paramagnetic metal centres introduce additional dispersion of signals that is useful for characterisation of host-guest complexes in solution using nuclear magnetic resonance (NMR). However, paramagnetic centres also complicate spectral assignment due to line broadening, signal integration error, and large changes in chemical shifts, which can be difficult to assign even for known compounds. Quantum chemical predictions can provide information that greatly facilitates the assignment of NMR signals and identification of species present. Here we explore how the prediction of paramagnetic NMR spectra may be used to gain insight into the spin crossover (SCO) properties of iron(II)-based metal organic coordination cages, specifically examining how the structure of the local metal coordination environment affects SCO. To represent the tetrahedral metal-organic cage, a model system is generated by considering an isolated metal-ion vertex: fac-ML3(2+) (M = Fe(II), Co(II); L = N-phenyl-2-pyridinaldimine). The sensitivity of the (1)H paramagnetic chemical shifts to local coordination environments is assessed and utilised to shed light on spin crossover behaviour in iron complexes. Our data indicate that expansion of the metal coordination sphere must precede any thermal SCO. An attempt to correlate experimental enthalpies of SCO with static properties of bound guests shows that no simple relationship exists, and that effects are likely due to nuanced dynamic response to encapsulation.

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.

Spectroscopic and electrochemical characterization of a Pr4+ imidophosphorane complex and the redox chemistry of Nd3+ and Dy3+ complexes.

The molecular tetravalent oxidation state for praseodymium is observed in solution via oxidation of the anionic trivalent precursor [K][Pr3+(NP(1,2-bis-tBu-diamidoethane)(NEt2))4] (1-Pr(NP*)) with AgI at -35 °C. The Pr4+ complex is characterized in solution via cyclic voltammetry, UV-vis-NIR electronic absorption spectroscopy, and EPR spectroscopy. Electrochemical analyses of [K][Ln3+(NP(1,2-bis-tBu-diamidoethane)(NEt2))4] (Ln = Nd and Dy) by cyclic voltammetry are reported and, in conjunction with theoretical modeling of electronic structure and oxidation potential, are indicative of principal ligand oxidations in contrast to the metal-centered oxidation observed for 1-Pr(NP*). The identification of a tetravalent praseodymium complex in in situ UV-vis and EPR experiments is further validated by theoretical modeling of the redox chemistry and the UV-vis spectrum. The latter study was performed by extended multistate pair-density functional theory (XMS-PDFT) and implicates a multiconfigurational ground state for the tetravalent praseodymium complex.

Tight-Binding Modeling of Uranium in an Aqueous Environment.

The first density functional tight-binding (DFTB) parameters for uranium, oxygen, and hydrogen chemistry are reported, which enable quantum molecular dynamics simulations that will be instrumental in understanding actinide speciation, reaction mechanisms, and kinetics. These parameters were fitted to atomization energies and forces obtained from density functional theory with a training set of small molecules that includes various oxidation states. The energetic results with these DFTB parameters for various reactions of hydration, hydrolysis, dimerization, and isomerization demonstrate that the DFTB method can qualitatively capture the correct chemistry with a small systematic deviation from the density functional theory reference values. Structural results on the molecules not in the training set, including dimers, show generally good agreement with the reference and demonstrate the transferability of these first DFTB parameters for uranium chemistry.

OpenMolcas: From Source Code to Insight.

In this Article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform. This is followed by brief presentations of many new methods, implementations, and features of the OpenMolcas program suite. These developments include novel wave function methods such as stochastic complete active space self-consistent field, density matrix renormalization group (DMRG) methods, and hybrid multiconfigurational wave function and density functional theory models. Some of these implementations include an array of additional options and functionalities. The paper proceeds and describes developments related to explorations of potential energy surfaces. Here we present methods for the optimization of conical intersections, the simulation of adiabatic and nonadiabatic molecular dynamics, and interfaces to tools for semiclassical and quantum mechanical nuclear dynamics. Furthermore, the Article describes features unique to simulations of spectroscopic and magnetic phenomena such as the exact semiclassical description of the interaction between light and matter, various X-ray processes, magnetic circular dichroism, and properties. Finally, the paper describes a number of built-in and add-on features to support the OpenMolcas platform with postcalculation analysis and visualization, a multiscale simulation option using frozen-density embedding theory, and new electronic and muonic basis sets.

Structure and bonding of group 4-nickel heterobimetallics supported by 2-(diphenylphosphino)pyrrolide ligands.

The synthesis of a full series of group 4/nickel complexes supported by a 2-(diphenylphosphino)pyrrolide (NP) ligand is reported. Treatment of the homoleptic, 8-coordinate M(NP)4 monometallic precursors with Ni(COD)2 (COD = 1,5-cyclooctadiene) yielded the heterobimetallic complexes (κ(2)-NP)M(µ2-NP)3Ni (M = Ti, Zr, Hf). Although X-ray crystallographic analysis reveals similarly short metal-metal distances in all three complexes, quantum chemical calculations indicate that ZrNi () and HfNi () contain only single Ni → M dative bonds while TiNi () has an additional Ti-Ni π-bond. All three complexes have quasireversible reductions by cyclic voltammetry, and 1-electron chemical reduction of by Na(Hg) yields the anion, [Na][(κ(2)-NP)Ti(µ2-NP)3Ni] (). X-ray and computational analysis indicate that the 1-electron reduction of completely breaks the metal-metal bond, yielding a formally Ti(III)-Ni(0) complex. Ti-Ni bonding can also be disrupted by coordination of CO, wherein Ni → CO backbonding effectively outcompetes Ni → Ti dative bonding.

Separated-pair approximation and separated-pair pair-density functional theory.

Multi-configuration pair-density functional theory (MC-PDFT) has proved to be a powerful way to combine the capabilities of multi-configuration self-consistent-field theory to represent the an electronic wave function with a highly efficient way to include dynamic correlation energy by density functional theory. All applications reported previously involved complete active space self-consistent-field (CASSCF) theory for the reference wave function. For treating large systems efficiently, it is necessary to ask whether good accuracy is retained when using less complete configuration interaction spaces. To answer this question, we present here calculations employing MC-PDFT with the separated pair (SP) approximation, which is a special case (defined in this article) of generalized active space self-consistent-field (GASSCF) theory in which no more than two orbitals are included in any GAS subspace and in which inter-subspace excitations are excluded. This special case of MC-PDFT will be called SP-PDFT. In SP-PDFT, the electronic kinetic energy and the classical Coulomb energy, the electronic density and its gradient, and the on-top pair density and its gradient are obtained from an SP approximation wave function; the electronic energy is then calculated from the first two of these quantities and an on-top density functional of the last four. The accuracy of the SP-PDFT method for predicting the structural properties and bond dissociation energies of twelve diatomic molecules and two triatomic molecules is compared to the SP approximation itself and to CASSCF, MC-PDFT based on CASSCF, CASSCF followed by second order perturbation theory (CASPT2), and Kohn-Sham density functional theory with the PBE exchange-correlation potential. We show that SP-PDFT reproduces the accuracy of MC-PDFT based on the corresponding CASSCF wave function for predicting C-H bond dissociation energies, the reaction barriers of pericyclic reactions and the properties of open-shell singlet systems, all at only a small fraction of the computational cost.

Multiconfiguration Pair-Density Functional Theory: A Fully Translated Gradient Approximation and Its Performance for Transition Metal Dimers and the Spectroscopy of Re2Cl8(2-).

We extend the on-top density functional of multiconfiguration pair-density functional theory (MC-PDFT) to include the gradient of the on-top density as well as the gradient of the density. We find that the theory is reasonably stable to this extension; furthermore, it provides improved accuracy for molecules containing transition metals. We illustrate the extended on-top density functionals by applying them to Cr2, Cu2, Ag2, Os2, and Re2Cl8(2-) as well as to our previous database of 56 data for bond dissociation energies, barrier heights, reaction energies, proton affinities, and the water dimer. The performance of MC-PDFT is comparable to or better than that of CASPT2.

Can Multiconfigurational Self-Consistent Field Theory and Density Functional Theory Correctly Predict the Ground State of Metal-Metal-Bonded Complexes?

The electronic structure of a diiron (FeFe) complex with strong metal-metal interaction and those of analogous complexes (CoCo, CoMn, CoFe, and FeMn) with much weaker metal-metal bonding are investigated with wave function-based methods and density functional theory. The delocalization and bonding between the metal centers in the diiron complex is only fully captured after inclusion of the complete set of 3d and 4d orbitals in the active space, a situation best suited for restricted active space (RAS) approaches. Truncation of the included set of 4d orbitals results in inappropriate localization of some 3d orbitals, incorrect description of the ground spin state as well as wrong spin state energetics, as compared to experiment. Using density functional theory, some local functionals are able to predict the correct ground spin states, and describe the chemical bonding and structural properties of all the metal-metal complexes considered in this work. In contrast, the introduction of some exact exchange results in increased localization of 3d orbitals and wrong spin state energetics, a situation that is particularly troublesome for the diiron complex.

Multiconfiguration pair-density functional theory: barrier heights and main group and transition metal energetics.

Kohn-Sham density functional theory, resting on the representation of the electronic density and kinetic energy by a single Slater determinant, has revolutionized chemistry, but for open-shell systems, the Kohn-Sham Slater determinant has the wrong symmetry properties as compared to an accurate wave function. We have recently proposed a theory, called multiconfiguration pair-density functional theory (MC-PDFT), in which the electronic kinetic energy and classical Coulomb energy are calculated from a multiconfiguration wave function with the correct symmetry properties, and the rest of the energy is calculated from a density functional, called the on-top density functional, that depends on the density and the on-top pair density calculated from this wave function. We also proposed a simple way to approximate the on-top density functional by translation of Kohn-Sham exchange-correlation functionals. The method is much less expensive than other post-SCF methods for calculating the dynamical correlation energy starting with a multiconfiguration self-consistent-field wave function as the reference wave function, and initial tests of the theory were quite encouraging. Here, we provide a broader test of the theory by applying it to bond energies of main-group molecules and transition metal complexes, barrier heights and reaction energies for diverse chemical reactions, proton affinities, and the water dimerization energy. Averaged over 56 data points, the mean unsigned error is 3.2 kcal/mol for MC-PDFT, as compared to 6.9 kcal/mol for Kohn-Sham theory with a comparable density functional. MC-PDFT is more accurate on average than complete active space second-order perturbation theory (CASPT2) for main-group small-molecule bond energies, alkyl bond dissociation energies, transition-metal-ligand bond energies, proton affinities, and the water dimerization energy.