Main Group Molecules Research Articles

Potential energy surfaces and dynamic properties via ab initio composite and density functional approaches.

Vibrational spectroscopy enables critical insight into the structural and dynamic properties of molecules. Presently, the majority of theoretical approaches to spectroscopy employ wavefunction-based ab initio or density functional methods that rely on the harmonic approximation. This approximation breaks down for large molecules with strongly anharmonic bonds or for molecules with large internuclear separations. An alternative to these methods involves generating molecular anharmonic potential energy surfaces (potentials) and using them to extrapolate the vibrational frequencies. This study examines the efficacy of density functional theory (DFT) and the correlation consistent Composite Approach (ccCA) in generating anharmonic frequencies from potentials of small main group molecules. Vibrational self-consistent field Theory (VSCF) and post-VSCF methods were used to calculate the fundamental frequencies of these molecules from their potentials. Functional choice, basis set selection, and mode-coupling are also examined as factors in influencing accuracy. The absolute deviations for the calculated frequencies using potentials at the ccCA level of theory were lower than the potentials at the DFT level. With DFT resulting in bending modes that are better described than those of ccCA, a multilevel DFT:ccCA approach where DFT potentials are used for single vibrational mode potentials and ccCA is used for vibrational mode-mode couplings can be utilized for larger polyatomic systems. The frequencies obtained with this multilevel approach using VCIPSI-PT2 were closer to experimental frequencies than the scaled harmonic frequencies, indicating the success of utilizing post-VSCF methods to generate more accurate representations of computed infrared spectra.

Dearomatization of C6 Aromatic Hydrocarbons by Main Group Complexes.

The dearomatization reaction is a powerful method for transformation of simple aromatic compounds to unique chemical architectures rapidly in synthetic chemistry. Over the past decades, the chemistry in this field has evolved significantly and various important organic compounds such as crucial bioactive molecules have been synthesized through dearomatization. In general, photochemical conditions or assistance by transition metals are required for dearomatization of rigid arenes. Recently, main-group elements, especially naturally abundant elements in the Earth's crust, have attracted attention as they have low toxicity and are cost-effective compared to the late transition metals. In recent decades, a variety of low-valent main-group molecules, which enable the activation of stable aromatic compounds under mild conditions, have been developed. This minireview highlights the developments in the chemistry of dearomatization of C6 aromatic hydrocarbons by main-group compounds leading to the formation of seven-membered EC6 (E = main-group elements) ring or cycloaddition products.

Population analysis and the effects of Gaussian basis set quality and quantum mechanical approach: main group through heavy element species.

Atomic charge and its distribution across molecules provide important insight into chemical behavior. Though there are many studies on various routes for the determination of atomic charge, there are few studies that examine the broader impact of basis set and quantum method used over many types of population analysis methods across the periodic table. Largely, such a study of population analysis has focused on main-group species. In this work, atomic charges were calculated using several population analysis methods including orbital-based methods (Mulliken, Löwdin, and Natural Population Analysis), volume-based methods (Atoms-in-Molecules (AIM) and Hirshfeld), and potential derived charges (CHELP, CHELPG, and Merz-Kollman). The impact of basis set and quantum mechanical method choices upon population analysis has been considered. The basis sets utilized include Pople (6-21G**, 6-31G**, 6-311G**) and Dunning (cc-pVnZ, aug-cc-pVnZ; n = D, T, Q, 5) basis sets for main group molecules. For the transition metal and heavy element species examined, relativistic forms of the correlation consistent basis sets were used. This is the first time the cc-pVnZ-DK3 and cc-pwCVnZ-DK3 basis sets have been examined with respect to their behavior across all levels of basis sets for atomic charges for an actinide. The quantum methods chosen include two density functional (PBE0 and B3LYP), Hartree-Fock, and second-order Møller-Plesset perturbation theory (MP2) approaches.

Unique Phosphorus-Based Avenues for the Tuning of Functional Materials.

ConspectusRecent ground-breaking advances in synthetic chemistry have transformed main-group molecules from simple laboratory curiosities into powerful materials for a range of applications in all realms of life. Electron-accepting or -deficient materials, in particular, have been the focus of development since their generally limited availability and stability have been major hurdles in establishing new practical applications. In addition to the general requirements for the design of these materials, a deeper understanding of their inherent electronics and molecular interactions is a requirement for the successful expansion of their utility. Previously, the incorporation of electron-deficient main-group elements, such as boron, into a conjugated organic framework was considered to be an effective route toward the synthesis of high-performing electron-accepting materials. However, challenging conditions such as the need for bulky substituents for kinetic stabilization, air-free and moisture-sensitive synthesis, and restricted storage abilities have led to the investigation of other elements across the periodic table to be used in a similar vein. Lately, heavier main-group elements such as Si, Ge, P, As, Sb, Bi, S, Se, and Te have also proven to be advantageous for electron-accepting materials as they exhibit polarizable molecular orbitals that are easily accessible to electrons or nucleophiles. This has laid the foundation for materials chemistry research on a variety of applications, including optoelectronic devices such as OLEDs, organic photovoltaics, energy storage such as in batteries and capacitors, fluorescent sensors with both biological and physiological applications, organocatalysis and synthesis, and many more. Among the main-group-element-based materials, organophosphorus species are privileged as their frontier orbitals are easily altered by chemical modification or/and structural and geometrical manipulations at the phosphorus center itself, without the need for kinetic stabilization, or through electronic modification of the conjugated system. The five-membered phosphorus-based heterocycle, phosphole, is a particularly interesting motif in this context, and extensive studies on the corresponding materials have uncovered the rich fundamentals of the σ*-π* interaction that imparts intriguing accepting properties while sustaining morphological and physiological stability for utilization in real-life scenarios. Moreover, beyond the σ*-π* interaction in phospholes that is key to many of their acceptor properties as a material, the use of phosphorus also gives rise to easily accessible, low-lying antibonding orbitals. They pave the way for Lewis acid phosphorus species that, despite being considered to be electron-rich species in general, open up several possibilities for intriguing chemical reactivity through hypervalency. Herein, we representatively discuss some recent advancements through the various approaches that leverage the unique structures and electronics of organophosphorus species toward the design of materials with outstanding electronic, chemical, and structural properties and reactivities for the functional material world.

Geometries and vibrational frequencies with Kohn-Sham methods using σ-functionals for the correlation energy.

Recently, Kohn-Sham (KS) methods with new correlation functionals, called σ-functionals, have been introduced. Technically, σ-functionals are closely related to the well-known random phase approximation (RPA); formally, σ-functionals are rooted in perturbation theory along the adiabatic connection. If employed in a post-self-consistent field manner in a Gaussian basis set framework, then, σ-functional methods are computationally very efficient. Moreover, for main group chemistry, σ-functionals are highly accurate and can compete with high-level wave-function methods. For reaction and transition state energies, e.g., chemical accuracy of 1 kcal/mol is reached. Here, we show how to calculate first derivatives of the total energy with respect to nuclear coordinates for methods using σ-functionals and then carry out geometry optimizations for test sets of main group molecules, transition metal compounds, and non-covalently bonded systems. For main group molecules, we additionally calculate vibrational frequencies. σ-Functional methods are found to yield very accurate geometries and vibrational frequencies for main group molecules superior not only to those from conventional KS methods but also to those from RPA methods. For geometries of transition metal compounds, not surprisingly, best geometries are found for RPA methods, while σ-functional methods yield somewhat less good results. This is attributed to the fact that in the optimization of σ-functionals, transition metal compounds could not be represented well due to the lack of reliable reference data. For non-covalently bonded systems, σ-functionals yield geometries of the same quality as the RPA or as conventional KS schemes combined with dispersion corrections.

Reactions of main group compounds with azides forming organic nitrogen-containing species.

Since the seminal discovery of phenyl azide by Grieß in 1864, a variety of organic azides (R-N3) have been developed and extensively studied. The amenability of azides to a number of reactions has expanded their utility as building blocks not only in organic synthesis but also in bioorthogonal chemistry and materials science. Over the decades, it has been demonstrated that the reactions of main group compounds with azides lead to diverse N-containing main group molecules. In view of the pronounced progress in this area, this review summarizes the reactions of main group compounds with azides, emphatically introducing their reaction patterns and mechanisms. The reactions of forming inorganic nitrogen species are not included in this review.

Ab Initio Calculation of Ground- and Low-Excited-State Spectroscopic Data and Transition Properties of SBr.

In this paper, potential energy curves of Λ-S and Ω states of SBr+ are reported for the first time, and the spectrum data of some low excited bound states are obtained. The differences in the spectrum properties of main-group molecules and SBr+ were compared and analyzed, providing a sufficient theoretical basis for the subsequent study of main-group molecules. The avoided crossing that occurs in the Ω state is analyzed, and finally it is concluded that this phenomenon mainly occurs in the energy region between 20,000 and 40,000 cm-1 that is relative to the minimum energy value. Potential transitions in the Ω state capable of achieving laser cooling of SBr+ are explored. The Franck-Condon factor, radiation lifetime, and Einstein coefficient between X3Σ0+- and b1Σ0++ are calculated. From the calculation results, we concluded that direct laser cooling of SBr+ is not feasible. What we have studied in this paper provides a theoretical basis for subsequent computational exploration of the spectrum properties of SBr+.

Importance of imposing gauge invariance in time-dependent density functional theory calculations with meta-generalized gradient approximations.

It has been known for more than a decade that the gauge variance of the kinetic energy density τ leads to additional terms in the magnetic orbital rotation Hessian used in linear-response time-dependent density functional theory (TDDFT), affecting excitation energies obtained with τ-dependent exchange-correlation functionals. While previous investigations found that a correction scheme based on the paramagnetic current density has a small effect on benchmark results, we report more pronounced effects here, in particular, for the popular M06-2X functional and for some other meta-generalized gradient approximations (mGGAs). In the first part of this communication, this is shown by a reassessment of a set of five Ni(II) complexes for which a previous benchmark study that did not impose gauge invariance has found surprisingly large errors for excitation energies obtained with M06-2X. These errors are more than halved by restoring gauge invariance. The variable importance of imposing gauge invariance for different mGGA-based functionals can be rationalized by the derivative of the mGGA exchange energy integrand with respect to τ. In the second part, a large set of valence excitations in small main-group molecules is analyzed. For M06-2X, several selected n → π* and π→π⊥ * excitations are heavily gauge-dependent with average changes of -0.17 and -0.28eV, respectively, while π→π‖ * excitations are marginally affected (-0.04eV). Similar patterns, but of the opposite signs, are found for SCAN0. The results suggest that reevaluation of previous gauge variant TDDFT results based on M06-2X and other mGGA functionals is warranted.

CIDER: An Expressive, Nonlocal Feature Set for Machine Learning Density Functionals with Exact Constraints.

Machine learning (ML) has recently gained attention as a means to develop more accurate exchange-correlation (XC) functionals for density functional theory, but functionals developed thus far need to be improved on several metrics, including accuracy, numerical stability, and transferability across chemical space. In this work, we introduce a set of nonlocal features of the density called the CIDER formalism, which we use to train a Gaussian process model for the exchange energy that obeys the critical uniform scaling rule for exchange. The resulting CIDER exchange functional is significantly more accurate than any semilocal functional tested here, and it has good transferability across main-group molecules. This work therefore serves as an initial step toward more accurate exchange functionals, and it also introduces useful techniques for developing robust, physics-informed XC models via ML.

Pushing the frontiers of density functionals by solving the fractional electron problem

Improving DFT with deep learning In the past 30 years, density functional theory (DFT) has emerged as the most widely used electronic structure method to predict the properties of various systems in chemistry, biology, and materials science. Despite a long history of successes, state-of-the-art DFT functionals have crucial limitations. In particular, significant systematic errors are observed for charge densities involving mobile charges and spins. Kirkpatrick et al . developed a framework to train a deep neural network on accurate chemical data and fractional electron constraints (see the Perspective by Perdew). The resulting functional outperforms traditional functionals on thorough benchmarks for main-group atoms and molecules. The present work offers a solution to a long-standing critical problem in DFT and demonstrates the success of combining DFT with the modern machine-learning methodology. —YS

NMR Indirect Spin–Spin Coupling Constants in a Modern Quasi-Relativistic Density Functional Framework

A quasi-relativistic implementation of NMR indirect spin-spin coupling constants is presented. The exact two-component (X2C) Hamiltonian and its diagonal local approximation to the unitary decoupling transformation (DLU) are utilized together with the (modified) screened nuclear spin-orbit approach. In a restricted kinetic balance, the finite nucleus model is available for both the scalar and vector potentials. The implementation supports density functionals up to the fourth rung of Jacob's ladder, i.e., (range-separated) hybrid and local hybrid functionals based on a seminumerical ansatz. We assess the quality of our quasi-relativistic X2C approach by comparison with "fully" relativistic four-component results for small main-group molecules and alkynyl compounds. The mean absolute error introduced by the DLU scheme is less than 0.05 × 1019 T J-2 of the reduced coupling constant for the small main-group molecules and 0.5 Hz for the alkynyl compounds. Thus, the error is significantly smaller than finite nucleus size effects for heavy elements. The basis set convergence and the impact of different density functional approximations are further studied. We propose a simple scheme to develop segmented-contracted relativistic all-electron basis sets for NMR spin-spin couplings. Our implementation allows us to perform calculations of extended molecules with reasonable computational effort, which is illustrated for the 1J(119Sn, 31P) coupling constant of a low-valent tin phosphinidenide complex. The corresponding results are in good agreement with the experimental findings.

R2SCAN-D4: Dispersion corrected meta-generalized gradient approximation for general chemical applications.

We combine a regularized variant of the strongly constrained and appropriately normed semilocal density functional [J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)] with the latest generation semi-classical London dispersion correction. The resulting density functional approximation r2SCAN-D4 has the speed of generalized gradient approximations while approaching the accuracy of hybrid functionals for general chemical applications. We demonstrate its numerical robustness in real-life settings and benchmark molecular geometries, general main group and organo-metallic thermochemistry, and non-covalent interactions in supramolecular complexes and molecular crystals. Main group and transition metal bond lengths have errors of just 0.8%, which is competitive with hybrid functionals for main group molecules and outperforms them for transition metal complexes. The weighted mean absolute deviation (WTMAD2) on the large GMTKN55 database of chemical properties is exceptionally small at 7.5 kcal/mol. This also holds for metal organic reactions with an MAD of 3.3 kcal/mol. The versatile applicability to organic and metal-organic systems transfers to condensed systems, where lattice energies of molecular crystals are within the chemical accuracy (errors <1 kcal/mol).

Nuclear Spin–Spin Couplings: Efficient Evaluation of Exact Exchange and Extension to Local Hybrid Functionals

We present an efficient implementation for the computation of nuclear spin-spin coupling tensors within density functional theory into the TURBOMOLE software suite. Emphasis is put on methods to efficiently evaluate the Hartree-Fock exchange needed for hybrid functionals: resolution of the identity and seminumerical evaluation on a grid. Our algorithm allows for the selection of specific nuclei for the reduction of calculation times. Further, the accuracy of locally dense basis sets in the density functional theory framework is investigated. These features allow for the routine computation of coupling constants in systems comprising about 100 carbon atoms within less than one day on a single CPU and within a few hours when using the OpenMP variant. Based on seminumerical integration, the first implementation of local hybrid functionals for spin-spin couplings is reported. This has allowed a preliminary evaluation of position-dependent exact-exchange admixture in three local hybrid functionals for a set of 80 isotropic spin-spin couplings in 23 small main-group molecules against CC3 and MCSCF reference data. Two of the local hybrids (LH14t-calPBE and LH07t-SVWN) are the top performers in the overall statistical evaluation compared to several standard functionals (TPSS, TPSSh, B3LYP, PBE0, and BHLYP), in particular, as they do not exhibit notable outliers for specific coupling types.

The Atomic Partial Charges Arboretum: Trying to See the Forest for the Trees.

Atomic partial charges are among the most commonly used interpretive tools in quantum chemistry. Dozens of different ‘population analyses’ are in use, which are best seen as proxies (indirect gauges) rather than measurements of a ‘general ionicity’. For the GMTKN55 benchmark of nearly 2,500 main‐group molecules, which span a broad swathe of chemical space, some two dozen different charge distributions were evaluated at the PBE0 level near the 1‐particle basis set limit. The correlation matrix between the different charge distributions exhibits a block structure; blocking is, broadly speaking, by charge distribution class. A principal component analysis on the entire dataset suggests that nearly all variation can be accounted for by just two ‘principal components of ionicity’: one has all the distributions going in sync, while the second corresponds mainly to Bader QTAIM vs. all others. A weaker third component corresponds to electrostatic charge models in opposition to the orbital‐based ones. The single charge distributions that have the greatest statistical similarity to the first principal component are iterated Hirshfeld (Hirshfeld‐I) and a minimal‐basis projected modification of Bickelhaupt charges. If three individual variables, rather than three principal components, are to be identified that contain most of the information in the whole dataset, one representative for each of the three classes of Corminboeuf et al. is needed: one based on partitioning of the density (such as QTAIM), a second based on orbital partitioning (such as NPA), and a third based on the molecular electrostatic potential (such as HLY or CHELPG).

An Efficient Coupled-Perturbed Kohn-Sham Implementation of NMR Chemical Shift Computations with Local Hybrid Functionals and Gauge-Including Atomic Orbitals.

Nuclear shielding calculations for local hybrid (LH) functionals with position-dependent exact-exchange admixtures within a coupled-perturbed Kohn-Sham (CPKS) framework have been implemented into the Turbomole code using efficient seminumerical integration techniques to deal with two-electron integrals. When using gauge-including atomic orbitals, LHs generate additional terms within the "pre-loop" section of the CPKS scheme compared to global hybrid (GH) functionals, related to perturbed electron-repulsion integrals. These terms have been implemented and tested in detail, together with dependencies on grid sizes and integral screening procedures. Even with relatively small grids, a seminumerical treatment of GHs reproduces analytical GH results with high accuracy while improving scaling with system and basis-set sizes significantly. The extra terms generated by LHs in the pre-loop part increase the scaling of that contribution slightly, but the advantages compared to the analytical scheme are largely retained, in particular for the typically large basis sets used in NMR shift calculations, allowing for a very efficient computational scheme. An initial comparison of four first-generation LHs based on LDA exchange for a shielding test set of 15 small main-group molecules against high-level CCSD(T) benchmark data indicates a substantial reduction of the systematically underestimated shieldings compared to semilocal functionals or GHs for non-hydrogen nuclei when a so-called t-LMF is used to control the position dependence of the exact-exchange admixture. In contrast, proton shieldings are underestimated with this LMF, while an LH with a so-called s-LMF performs much better. These results are discussed in the context of experience for other properties, and they suggest directions for further improvements of LHs regarding nuclear shieldings.

Metallomimetic Chemistry of Boron.

The study of main-group molecules that behave and react similarly to transition-metal (TM) complexes has attracted significant interest in recent decades. Most notably, the attractive idea of replacing the all-too-often rare and costly metals from catalysis has motivated efforts to develop main-group-element-mediated reactions. Main-group elements, however, lack the electronic flexibility of TM complexes that arises from combinations of empty and filled d orbitals and that seem ideally suited to bind and activate many substrates. In this review, we look at boron, an element that despite its nonmetal nature, low atomic weight, and relative redox staticity has achieved great milestones in terms of TM-like reactivity. We show how in interelement cooperative systems, diboron molecules, and hypovalent complexes the fifth element can acquire a truly metallomimetic character. As we discuss, this character is powerfully demonstrated by the reactivity of boron-based molecules with H2, CO, alkynes, alkenes and even with N2.

Reactivity of bulky Ln(ii) amidinates towards P4, As4, and As4S4.

The reduction of P4, As4 and As4S4 (realgar) with the sterically encumbered reductants [(DippForm)2Ln(thf)2] (Ln = Sm, Yb; DippForm = {(2,6-iPr2C6H3)NC(H) = N(2,6-iPr2C6H3)}-) is reported. For the first time, purely f-element containing inverse inorganic sandwich complexes [{(DippForm)2Sm}2(μ2-η4:η4-E4)] (E = P, As), featuring a π-aromatic cyclo [E4]2- middle deck, were obtained upon reaction with P4 and As4. The reaction with realgar leads to a cage disruption and the formation of the unusual species [{(DippForm)(DippForm-AsS2)}Ln(thf)]. The reactivity of divalent Ln amidinates towards main group molecules is in comparison to metallocenes faster, more efficient and thus significantly influenced by the ligand environment. Experimental results are supported by DFT calculations.

The Main Group Elements, Fragments, Compounds and Clusters Obey the 4n Rule and Form 4n Series: They are Close relatives to Transition Metal Counterparts via the 14n Linkage

&lt;p&gt;The paper presents numbers which were derived from 4n-based series in a matrix table. The numbers agree precisely with the total number of valence electrons surrounding the respective skeletal elements. The series approach focuses mainly on the number of skeletal elements and their respective number of valence electron content regardless of the origin of the electrons and the type of skeletal elements. For instance, any 6 skeletal elements of transition metal carbonyls surrounded by 86 valence electrons coded as (6,86), series S = 14n+2 normally adopt an octahedral geometry whereas (6,26) series S = 4n+2 for main group elements also tend to adopt an octahedral shape. The transition metal carbonyl cluster series were extensively covered in our previous articles. This paper demonstrates that the main group fragments, clusters and molecules which we normally explain by terms such as valency, valence electrons and octet rule also obey the 4n-based series. The fragments, molecules and clusters of the main group elements correspond well to those of respective transition metal clusters especially the carbonyls if the masking electrons are removed from them. Hence, the series approach is a qualitative method that acts as a unifier of some transition metal clusters with some main group elements clusters.&lt;/p&gt;

Components of the Bond Energy in Polar Diatomic Molecules, Radicals, and Ions Formed by Group-1 and Group-2 Metal Atoms.

Although many transition metal complexes are known to have high multireference character, the multireference character of main-group closed-shell singlet diatomic molecules like BeF, CaO, and MgO has been less studied. However, many group-1 and group-2 diatomic molecules do have multireference character, and they provide informative systems for studying multireference character because they are simpler than transition metal compounds. The goal of the present work is to understand these multireference systems better so that, ultimately, we can apply what we learn to more complicated multireference systems and to the design of new exchange-correlation functionals for treating multireference systems more adequately. Fourteen main-group diatomic molecules and one triatomic molecule (including radicals, cations, and anions, as well as neutral closed-shell species) have been studied for this article. Eight of these molecules contain a group-1 element, and six contain a group-2 element. Seven of these molecules are multireference systems, and eight of them are single-reference systems. Fifty-three exchange-correlation functionals of 11 types [local spin-density approximation (LSDA), generalized gradient approximation (GGA), nonseparable gradient approximation (NGA), global-hybrid GGA, meta-GGA, meta-NGA, global-hybrid meta GGA, range-separated hybrid GGA, range-separated hybrid meta-GGA, range-separated hybrid meta-NGA, and DFT augmented with molecular mechanics damped dispersion (DFT-D)] and the Hartree-Fock method have been applied to calculate the bond distance, bond dissociation energy (BDE), and dipole moment of these molecules. All of the calculations are converged to a stable solution by allowing the symmetry of the Slater determinant to be broken. A reliable functional should not only predict an accurate BDE but also predict accurate components of the BDE, so each bond dissociation energy has been decomposed into ionization potential (IP) of the electropositive element, electron affinity of the electronegative bonding partner (EA), atomic excitation energy (EE) to prepare the valence states of the interacting partners, and interaction energy (IE) of the valence-prepared states. Adding Hartree-Fock exchange helps to obtain better results for atomic excitation energy, and this leads to improvements in getting the right answer for the right reason. The following functionals are singled out for reasonably good performance on all three of bond distance, BDE, and dipole moment: B97-1, B97-3, MPW1B95, M05, M06, M06-2X, M08-SO, N12-SX, O3LYP, TPSS, τ-HCTHhyb, and GAM; all but two (TPSS and GAM) of these functionals are hybrid functionals.

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.