The Energetic Origins of Pi-Pi Contacts in Proteins.

Accurate potential energy models of proteins must describe the many different types of noncovalent interactions that contribute to a protein's stability and structure. Pi-pi contacts are ubiquitous structural motifs in all proteins, occurring between aromatic and nonaromatic residues and play a nontrivial role in protein folding and in the formation of biomolecular condensates. Guided by a geometric criterion for isolating pi-pi contacts from classical molecular dynamics simulations of proteins, we use quantum mechanical energy decomposition analysis to determine the molecular interactions that stabilize different pi-pi contact motifs. We find that neutral pi-pi interactions in proteins are dominated by Pauli repulsion and London dispersion rather than repulsive quadrupole electrostatics, which is central to the textbook Hunter-Sanders model. This results in a notable lack of variability in the interaction profiles of neutral pi-pi contacts even with extreme changes in the dielectric medium, explaining the prevalence of pi-stacked arrangements in and between proteins. We also find interactions involving pi-containing anions and cations to be extremely malleable, interacting like neutral pi-pi contacts in polar media and like typical ion-pi interactions in nonpolar environments. Like-charged pairs such as arginine-arginine contacts are particularly sensitive to the polarity of their immediate surroundings and exhibit canonical pi-pi stacking behavior only if the interaction is mediated by environmental effects, such as aqueous solvation.

Templating Bicarbonate in the Second Coordination Sphere Enhances Electrochemical CO2 Reduction Catalyzed by Iron Porphyrins.

Bicarbonate-based electrolytes are ubiquitous in aqueous electrochemical CO2 reduction, particularly in heterogenous catalysis, where they demonstrate improved catalytic performance relative to other buffers. In contrast, the presence of bicarbonate in organic electrolytes and its roles in homogeneous electrocatalysis remain underexplored. Here, we investigate the influence of bicarbonate on iron porphyrin-catalyzed electrochemical CO2 reduction. We show that bicarbonate is a viable proton donor in organic electrolyte (pKa = 20.8 in dimethyl sulfoxide) and that urea pendants in the second coordination sphere can be used to template bicarbonate in the vicinity of a molecular iron porphyrin catalyst. The templated binding of bicarbonate increases its acidity, resulting in a 1500-fold enhancement in catalytic rates relative to unmodified parent iron porphyrin. This work emphasizes the importance of bicarbonate speciation in wet organic electrolytes and establishes second-sphere bicarbonate templating as a design strategy to harness this adventitious acid and enhance CO2 reduction catalysis.

From Intermolecular Interaction Energies and Observable Shifts to Component Contributions and Back Again: A Tale of Variational Energy Decomposition Analysis.

Quantum chemistry in the form of density functional theory (DFT) calculations is a powerful numerical experiment for predicting intermolecular interaction energies. However, no chemical insight is gained in this way beyond predictions of observables. Energy decomposition analysis (EDA) can quantitatively bridge this gap by providing values for the chemical drivers of the interactions, such as permanent electrostatics, Pauli repulsion, dispersion, and charge transfer. These energetic contributions are identified by performing DFT calculations with constraints that disable components of the interaction. This review describes the second-generation version of the absolutely localized molecular orbital EDA (ALMO-EDA-II). The effects of different physical contributions on changes in observables such as structure and vibrational frequencies upon complex formation are characterized via the adiabatic EDA. Example applications include red- versus blue-shifting hydrogen bonds; the bonding and frequency shifts of CO, N2, and BF bound to a [Ru(II)(NH3)5]2 + moiety; and the nature of the strongly bound complexes between pyridine and the benzene and naphthalene radical cations. Additionally, the use of ALMO-EDA-II to benchmark and guide the development of advanced force fields for molecular simulation is illustrated with the recent, very promising, MB-UCB potential.

Deciphering Distinct Overpotential-Dependent Pathways for Electrochemical CO2 Reduction Catalyzed by an Iron-Terpyridine Complex.

[Fe(tpyPY2Me)]2+ ([Fe]2+) is a homogeneous electrocatalyst for converting CO2 into CO featuring low overpotentials of <100 mV, near-unity selectivity, and high activity with turnover frequencies faster than 100 000 s-1. To identify the origins of its exceptional performance and inform future catalyst design, we report a combined computational and experimental study that establishes two distinct mechanistic pathways for electrochemical CO2 reduction catalyzed by [Fe]2+ as a function of applied overpotential. Electrochemical data shows the formation of two catalytic regimes at low (ηTOF/2 of 160 mV) and high (ηTOF/2 of 590 mV) overpotential plateaus. We propose that at low overpotentials [Fe]2+ undergoes a two-electron reduction, two-proton-transfer mechanism (electrochemical-electrochemical-chemical-chemical, EECC), where turnover occurs through the dicationic iron complex, [Fe]2+. Computational analysis supports the importance of the singlet ground-state electronic structure for CO2 binding and that the rate-limiting step is the second protonation in this low-overpotential regime. When more negative potentials are applied, an additional electron-transfer event occurs through either a stepwise or proton-coupled electron-transfer (PCET) pathway, enabling catalytic turnover from the monocationic iron complex ([Fe]+) via an electrochemical-chemical-electrochemical-chemical (ECEC) mechanism. Comparison of experimental kinetic data obtained from variable controlled potential electrolysis (CPE) experiments with direct product detection with calculated rates obtained from the energetic span model supports the PCET pathway as the most likely mechanism. Moreover, we build upon this mechanistic understanding to propose the design of an improved ligand framework that is predicted to stabilize the key transition states identified in our study and explore their electronic structures using an energy decomposition analysis. Taken together, this work highlights the value of synergistic computational/experimental approaches to decipher mechanisms of new electrocatalysts and direct the rational design of improved platforms.

Revisiting the Bonding Model for Gold(I) Species: The Importance of Pauli Repulsion Revealed in a Gold(I)-Cyclobutadiene Complex.

Understanding the bonding of gold(I) species has been central to the development of gold(I) catalysis. Herein, we present the synthesis and characterization of the first gold(I)-cyclobutadiene complex, accompanied with bonding analysis by state-of-the-art energy decomposition analysis methods. Analysis of possible coordination modes for the new species not only confirms established characteristics of gold(I) bonding, but also suggests that Pauli repulsion is a key yet hitherto overlooked element. Additionally, we obtain a new perspective on gold(I)-bonding by comparison of the gold(I)-cyclobutadiene to congeners stabilized by p-, d-, and f-block metals. Consequently, we refine the gold(I) bonding model, with a delicate interplay of Pauli repulsion and charge transfer as the key driving force for various coordination motifs. Pauli repulsion is similarly determined as a significant interaction in AuI -alkyne species, corroborating this revised understanding of AuI bonding.

Mechanistic Insights into Co and Fe Quaterpyridine-Based CO2 Reduction Catalysts: Metal-Ligand Orbital Interaction as the Key Driving Force for Distinct Pathways.

Both [CoII(qpy)(H2O)2]2+ and [FeII(qpy)(H2O)2]2+ (with qpy = 2,2':6',2″:6'',2‴-quaterpyridine) are efficient homogeneous electrocatalysts and photoelectrocatalysts for the reduction of CO2 to CO. The Co catalyst is more efficient in the electrochemical reduction, while the Fe catalyst is an excellent photoelectrocatalyst ( ACS Catal. 2018, 8, 3411-3417). This work uses density functional theory to shed light on the contrasting catalytic pathways. While both catalysts experience primarily ligand-based reductions, the second reduction in the Co catalyst is delocalized onto the metal via a metal-ligand bonding interaction, causing a spin transition and a distorted ligand framework. This orbital interaction explains the experimentally observed mild reduction potential and slow kinetics of the second reduction. The decreased hardness and doubly occupied dz2-orbital facilitate a σ-bond with the CO2-π* in an η1-κC binding mode. CO2 binding is only possible after two reductions resulting in an EEC mechanism (E = electron transfer, C = chemical reaction), and the second protonation is rate-limiting. In contrast, the Fe catalyst maintains a Lewis acidic metal center throughout the reduction process because the metal orbitals do not strongly mix with the qpy-π* orbitals. This allows binding of the activated CO2 in an η2-binding mode. This interaction stabilizes the activated CO2 via a π-type interaction of a Fe-t2g orbital and the CO2-π* and a dative bond of the oxygen lone pair. This facilitates CO2 binding to a singly reduced catalyst resulting in an ECE mechanism. The barrier for CO2 addition and the second protonation are higher than those for the Co catalyst and rate-limiting.

Controlled Single-Electron Transfer via Metal-Ligand Cooperativity Drives Divergent Nickel-Electrocatalyzed Radical Pathways.

Electrocatalysis enables the construction of C-C bonds under mild conditions via controlled formation of carbon-centered radicals. For sequences initiated by alkyl halide reduction, coordinatively unsaturated Ni complexes commonly serve as single-electron transfer agents, giving rise to the foundational question of whether outer- or inner-sphere electron transfer oxidative addition prevails in redox mediation. Indeed, rational design of electrochemical processes requires the discrimination of these two electron transfer pathways, as they can have outsized effects on the rate of substrate bond activation and thus impact radical generation rates and downstream product selectivities. We present results from combined synthetic, electroanalytical, and computational studies that examine the mechanistic differences of single electron transfer to alkyl halides imparted by Ni metal-ligand cooperativity. Electrogenerated reduced Ni species, stabilized by delocalized spin density onto a redox-active tpyPY2Me polypyridyl ligand, activates alkyl iodides via outer-sphere electron transfer, allowing for the selective activation of alkyl iodide substrates over halogen atom donors and the controlled generation and sequestration of electrogenerated radicals. In contrast, the Ni complex possessing a redox-innocent pentapyridine congener activates the substrates in an inner-sphere fashion owning to a purely metal-localized spin, thereby activating both substrates and halogen atom donors in an indiscriminate fashion, generating a high concentration of radicals and leading to unproductive dimerization. Our data establish that controlled electron transfer via Ni-ligand cooperativity can be used to limit undesired radical recombination products and promote selective radical processes in electrochemical environments, providing a generalizable framework for designing redox mediators with distinct rate and potential requirements.

Revealing the nature of electron correlation in transition metal complexes with symmetry breaking and chemical intuition.

In this work, we provide a nuanced view of electron correlation in the context of transition metal complexes, reconciling computational characterization via spin and spatial symmetry breaking in single-reference methods with qualitative concepts from ligand-field and molecular orbital theories. These insights provide the tools to reliably diagnose the multi-reference character, and our analysis reveals that while strong (i.e., static) correlation can be found in linear molecules (e.g., diatomics) and weakly bound and antiferromagnetically coupled (monometal-noninnocent ligand or multi-metal) complexes, it is rarely found in the ground-states of mono-transition-metal complexes. This leads to a picture of static correlation that is no more complex for transition metals than it is, e.g., for organic biradicaloids. In contrast, the ability of organometallic species to form more complex interactions, involving both ligand-to-metal σ-donation and metal-to-ligand π-backdonation, places a larger burden on a theory's treatment of dynamic correlation. We hypothesize that chemical bonds in which inter-electron pair correlation is non-negligible cannot be adequately described by theories using MP2 correlation energies and indeed find large errors vs experiment for carbonyl-dissociation energies from double-hybrid density functionals. A theory's description of dynamic correlation (and to a less important extent, delocalization error), which affects relative spin-state energetics and thus spin symmetry breaking, is found to govern the efficacy of its use to diagnose static correlation.

Metal-Ligand Cooperativity via Exchange Coupling Promotes Iron- Catalyzed Electrochemical CO2 Reduction at Low Overpotentials.

Biological and heterogeneous catalysts for the electrochemical CO2 reduction reaction (CO2RR) often exhibit a high degree of electronic delocalization that serves to minimize overpotential and maximize selectivity over the hydrogen evolution reaction (HER). Here, we report a molecular iron(II) system that captures this design concept in a homogeneous setting through the use of a redox non-innocent terpyridine-based pentapyridine ligand (tpyPY2Me). As a result of strong metal-ligand exchange coupling between the Fe(II) center and ligand, [Fe(tpyPY2Me)]2+ exhibits redox behavior at potentials 640 mV more positive than the isostructural [Zn(tpyPY2Me)]2+ analog containing the redox-inactive Zn(II) ion. This shift in redox potential is attributed to the requirement for both an open-shell metal ion and a redox non-innocent ligand. The metal-ligand cooperativity in [Fe(tpyPY2Me)]2+ drives the electrochemical reduction of CO2 to CO at low overpotentials with high selectivity for CO2RR (>90%) and turnover frequencies of 100 000 s-1 with no degradation over 20 h. The decrease in the thermodynamic barrier engendered by this coupling also enables homogeneous CO2 reduction catalysis in water without compromising selectivity or rates. Synthesis of the two-electron reduction product, [Fe(tpyPY2Me)]0, and characterization by X-ray crystallography, Mössbauer spectroscopy, X-ray absorption spectroscopy (XAS), variable temperature NMR, and density functional theory (DFT) calculations, support assignment of an open-shell singlet electronic structure that maintains a formal Fe(II) oxidation state with a doubly reduced ligand system. This work provides a starting point for the design of systems that exploit metal-ligand cooperativity for electrocatalysis where the electrochemical potential of redox non-innocent ligands can be tuned through secondary metal-dependent interactions.

Computational Study of an Iron(II) Polypyridine Electrocatalyst for CO2 Reduction: Key Roles for Intramolecular Interactions in CO2 Binding and Proton Transfer.

A solar-driven conversion of CO2 into fuels by artificial photosynthesis would not only mitigate the greenhouse effect but also provide an alternative to obtain fuels in a renewable fashion. To this end, the new iron polypyridine catalyst [Fe(bpyNHEtPY2Me)L2]2+ (L = H2O, CH3CN) was recently developed for the electrochemical reduction of CO2 to CO. In this study, we performed density functional theory (DFT) electronic structure calculations to shed light on a possible pathway for CO2 reduction and the origin of the selectivity between CO2 reduction versus the hydrogen evolution reaction. The metal center remains Lewis acidic throughout the reduction process due to ligand loss and mainly ligand-based reduction stabilized by antiferromagnetic coupling to a high-spin Fe(II) center. This results in a high barrier for hydride formation but a facile addition and activation of CO2 via an η2 coordination and stabilizing hydrogen bonding by the amine group. The second unoccupied equatorial coordination site opens up the possibility for an intramolecular protonation with a coordinated water ligand. This facilitates protonation because not only CO2 but also the proton source H2O is activated and properly aligned for a proton transfer due to the Fe-OH2 bond; consequently, both protonation steps are facile. The moderate ligand field allows a rapid ligand exchange for a second intramolecular protonation step and facilitates an exergonic CO release. The lower selectivity of the related [Fe(bpyOHPY2Me)L2]2+ complex can be related to its more acidic second coordination sphere, which enables an intramolecular proton transfer that is kinetically competitive with CO2 addition.

Probing radical-molecule interactions with a second generation energy decomposition analysis of DFT calculations using absolutely localized molecular orbitals.

Intermolecular interactions between radicals and closed-shell molecules are ubiquitous in chemical processes, ranging from the benchtop to the atmosphere and extraterrestrial space. While energy decomposition analysis (EDA) schemes for closed-shell molecules can be generalized for studying radical-molecule interactions, they face challenges arising from the unique characteristics of the electronic structure of open-shell species. In this work, we introduce additional steps that are necessary for the proper treatment of radical-molecule interactions to our previously developed unrestricted Absolutely Localized Molecular Orbital (uALMO)-EDA based on density functional theory calculations. A "polarize-then-depolarize" (PtD) scheme is used to remove arbitrariness in the definition of the frozen wavefunction, rendering the ALMO-EDA results independent of the orientation of the unpaired electron obtained from isolated fragment calculations. The contribution of radical rehybridization to polarization energies is evaluated. It is also valuable to monitor the wavefunction stability of each intermediate state, as well as their associated spin density profiles, to ensure the EDA results correspond to a desired electronic state. These radical extensions are incorporated into the "vertical" and "adiabatic" variants of uALMO-EDA for studies of energy changes and property shifts upon complexation. The EDA is validated on two model complexes, H2O˙F and FH˙OH. It is then applied to several chemically interesting radical-molecule complexes, including the sandwiched and T-shaped benzene dimer radical cation, complexes of pyridine with benzene and naphthalene radical cations, binary and ternary complexes of the hydroxyl radical with water (˙OH(H2O) and ˙OH(H2O)2), and the pre-reactive complexes and transition states in the ˙OH + HCHO and ˙OH + CH3CHO reactions. These examples suggest that this second generation uALMO-EDA is a useful tool for furthering one's understanding of both energetic and property changes associated with radical-molecule interactions.

Energy Decomposition Analysis for Interactions of Radicals: Theory and Implementation at the MP2 Level with Application to Hydration of Halogenated Benzene Cations and Complexes between CO2-· and Pyridine and Imidazole.

To study intermolecular interactions involving radicals at the correlated level, the energy decomposition analysis scheme for second-order MoÌ·ller-Plesset perturbation theory based on absolutely localized molecular orbitals (ALMO-MP2-EDA) is generalized to unrestricted and restricted open-shell MP2. The benefit of restricted open-shell MP2 is that it can provide accurate binding energies for radical complexes where density functional theory can be error-prone due to delocalization errors. As a model application, the open-shell ALMO-MP2-EDA is applied to study the first solvation step of halogenated benzene radical cations, where both halogen- and hydrogen-bonded isomers are possible. We determine that the lighter halogens favor the hydrogen-bonded form, while the iodine-substituted species prefers halogen bonding due to larger polarizability and charge transfer at the halogen. As a second application, relevant to the activation of CO2 in photoelectrocatalysis, complexes of CO2-· interacting with both pyridine and imidazole are analyzed with ALMO-MP2-EDA. The results reveal the importance of charge transfer into the π* orbital of the heterocycle in controlling the stability of the carbamate binding mode, which is favored for pyridine but not for imidazole.

Precursor Chemistry of Lead Bromide Perovskite Nanocrystals.

We investigate the early stages of cesium lead bromide perovskite formation through absorption spectroscopy of stopped-flow reactions, high-throughput mapping, and direct synthesis and titration of potential precursor species. Calorimetric and spectroscopic measurements of lead bromide complex titrations combined with theoretical calculations suggest that bromide complexes with higher coordination numbers than previously considered for nonpolar systems can better explain observed behaviors. Synthesis mapping of binary lead halides reveals multiple lead bromide species with absorption peaks higher than 300 nm, including a previously observed species with a peak at 313 nm and two species with peaks at 345 and 370 nm that also appear as reaction intermediates during the formation of lead bromide perovskites. Based on theoretical calculations of excitonic energies that match within 50 meV, we give a preliminary assignment of these species as two-dimensional magic-sized clusters with side lengths of 2, 3, and 4 unit cells. Kinetic measurements of the conversion of benzoyl bromide precursor are connected to stopped-flow measurements of product formation and demonstrate that the formation of complexes and magic-sized clusters (i.e., nucleation) is controlled by precursor decomposition, whereas the growth rate of 2D and 3D perovskites is significantly slower.

Estimation of Electrostatic Interaction Energies on a Trapped-Ion Quantum Computer.

We present the first hardware implementation of electrostatic interaction energies by using a trapped-ion quantum computer. As test system for our computation, we focus on the reduction of NO to N2O catalyzed by a nitric oxide reductase (NOR). The quantum computer is used to generate an approximate ground state within the NOR active space. To efficiently measure the necessary one-particle density matrices, we incorporate fermionic basis rotations into the quantum circuit without extending the circuit length, laying the groundwork for further efficient measurement routines using factorizations. Measurements in the computational basis are then used as inputs for computing the electrostatic interaction energies on a classical computer. Our experimental results strongly agree with classical noise-less simulations of the same circuits, finding electrostatic interaction energies within chemical accuracy despite hardware noise. This work shows that algorithms tailored to specific observables of interest, such as interaction energies, may require significantly fewer quantum resources than individual ground state energies would require in the straightforward supermolecular approach.

Accurate non-covalent interaction energies on noisy intermediate-scale quantum computers via second-order symmetry-adapted perturbation theory.

The calculation of non-covalent interaction energies on noisy intermediate-scale quantum (NISQ) computers appears to be challenging with straightforward application of existing quantum algorithms. For example, the use of the standard supermolecular method with the variational quantum eigensolver (VQE) would require extremely precise resolution of the total energies of the fragments to provide for accurate subtraction to the interaction energy. Here we present a symmetry-adapted perturbation theory (SAPT) method that may provide interaction energies with high quantum resource efficiency. Of particular note, we present a quantum extended random-phase approximation (ERPA) treatment of the SAPT second-order induction and dispersion terms, including exchange counterparts. Together with previous work on first-order terms (Chem. Sci., 2022, 13, 3094), this provides a recipe for complete SAPT(VQE) interaction energies up to second order, which is a well established truncation. The SAPT interaction energy terms are computed as first-level observables with no subtraction of monomer energies invoked, and the only quantum observations needed are the VQE one- and two-particle density matrices. We find empirically that SAPT(VQE) can provide accurate interaction energies even with coarsely optimized, low circuit depth wavefunctions from a quantum computer, simulated through ideal statevectors. The errors of the total interaction energy are orders of magnitude lower than the corresponding VQE total energy errors of the monomer wavefunctions. In addition, we present heme-nitrosyl model complexes as a system class for near term quantum computing simulations. They are strongly correlated, biologically relevant and difficult to simulate with classical quantum chemical methods. This is illustrated with density functional theory (DFT) as the predicted interaction energies exhibit a strong sensitivity with respect to the choice of functional. Thus, this work paves the way to obtain accurate interaction energies on a NISQ-era quantum computer with few quantum resources. It is the first step in alleviating one of the major challenges in quantum chemistry, where in-depth knowledge of both the method and system is required a priori to reliably generate accurate interaction energies.

Exploring the Limits of Second- and Third-Order Møller-Plesset Perturbation Theories for Noncovalent Interactions: Revisiting MP2.5 and Assessing the Importance of Regularization and Reference Orbitals.

This work systematically assesses the influence of reference orbitals, regularization, and scaling on the performance of second- and third-order Møller-Plesset perturbation theory wave function methods for noncovalent interactions (NCIs). Testing on 19 data sets (A24, DS14, HB15, HSG, S22, X40, HW30, NC15, S66, AlkBind12, CO2Nitrogen16, HB49, Ionic43, TA13, XB18, Bauza30, CT20, XB51, and Orel26rad) covers a wide range of different NCIs including hydrogen bonding, dispersion, and halogen bonding. Inclusion of potential energy surfaces from different hydrogen bonds and dispersion-bound complexes gauges accuracy for nonequilibrium geometries. Fifteen methods are tested. In notation where nonstandard choices of orbitals are denoted as methods:orbitals, these are MP2, κ-MP2, SCS-MP2, OOMP2, κ-OOMP2, MP3, MP2.5, MP3:OOMP2, MP2.5:OOMP2, MP3:κ-OOMP2, MP2.5:κ-OOMP2, κ-MP3:κ-OOMP2, κ-MP2.5:κ-OOMP2, MP3:ωB97X-V, and MP2.5:ωB97X-V. Furthermore, we compare these methods to the ωB97M-V and B3LYP-D3 density functionals, as well as CCSD. We find that the κ-regularization (κ = 1.45 au was used throughout) improves the energetics in almost all data sets for both MP2 (in 17 out of 19 data sets) and OOMP2 (16 out of 19). The improvement is significant (e.g., the root-mean-square deviation (RMSD) for the S66 data set is 0.29 kcal/mol for κ-OOMP2 versus 0.67 kcal/mol for MP2) and for interactions between stable closed-shell molecules, not strongly dependent on the reference orbitals. Scaled MP3 (with a factor of 0.5) using κ-OOMP2 reference orbitals (MP2.5:κ-OOMP2) provides significantly more accurate results for NCIs across all data sets with noniterative O(N6) scaling (S66 data set RMSD: 0.10 kcal/mol). Across the entire data set of 356 points, the improvement over standard MP2.5 is approximately a factor of 2: RMSD for MP3:κ-OOMP2 is 0.25 vs 0.50 kcal/mol for MP2.5. The use of high-quality density functional reference orbitals (ωB97X-V) also significantly improves the results of MP2.5 for NCI over a Hartree-Fock orbital reference. All our assessments and conclusions are based on the use of the medium-sized aug-cc-pVTZ basis to yield results that are directly compared against complete basis set limit reference values.

Regularized Second-Order Møller-Plesset Theory: A More Accurate Alternative to Conventional MP2 for Noncovalent Interactions and Transition Metal Thermochemistry for the Same Computational Cost.

Second-order Møller-Plesset theory (MP2) notoriously breaks down for π-driven dispersion interactions and dative bonds in transition metal complexes. Herein, we investigate three physically justified forms of single-parameter, energy-gap dependent regularization which can yield high and transferable accuracy for a variety of noncovalent interactions (including S22, S66, and L7 test sets) and (mostly closed shell) transition metal thermochemistry. Regularization serves to damp overestimated pairwise additive contributions, renormalizing first-order amplitudes such that the effects of higher-order correlations are incorporated. The optimal parameter values for the noncovalent and transition metal sets are 1.1, 0.7, and 0.4 for κ, σ, and σ2 regularizers, respectively. However, such regularization slightly degrades the accuracy of conventional MP2 for some small-molecule test sets, most of which have relatively large average frontier energy gaps. Our results suggest that appropriately regularized MP2 models may improve double hybrid density functionals, at no additional cost over conventional MP2.

Variational Forward-Backward Charge Transfer Analysis Based on Absolutely Localized Molecular Orbitals: Energetics and Molecular Properties.

To facilitate the understanding of charge-transfer (CT) effects in dative complexes, we propose a variational forward-backward (VFB) approach to decompose the overall CT stabilization energy into contributions from forward and backward donation in the framework of energy decomposition analysis based on absolutely localized molecular orbitals (ALMO-EDA). Such a decomposition is achieved by introducing two additional constrained intermediate states in which only one direction of CT is permitted. These two "one-way" CT states are variationally relaxed such that the associated nuclear forces can be readily obtained. This allows for a facile integration into the previously developed adiabatic EDA scheme, so that the molecular property changes arising from forward and back donation can be separately assigned. Using ALMO-EDA augmented by this VFB model, we investigate the energetic, geometric, and vibrational features of complexes composed of CO and main group Lewis acids (BH3, BeO/BeCO3) and complexes of the N2, CO, and BF isoelectronic series with [Ru(II)(NH3)5]2+. We identify that the shift in the stretching frequency of a diatomic π-acidic ligand (XY), such as CO, results from a superposition of the shifts induced by permanent electrostatics and backward CT: permanent electrostatics can cause an either red or blue shift depending on the alignment of the XY dipole in the dative complex, and this effect becomes more pronounced with a more polar XY ligand; the back-donation to the antibonding π orbital of XY always lowers the X-Y bond order and thus red-shifts its stretching frequency, and the strength of this interaction decays rapidly with the intermolecular distance. We also reveal that while σ forward donation contributes significantly to energetic stabilization, it affects the vibrational feature of XY mainly by shortening the intermolecular distance, which enhances both the electrostatic interaction and backward CT but in different rates. The synergistic effect of the forward and backward donations appears to be more significant in the transition-metal complexes, where the forward CT plays an essential role in overcoming the strong Pauli repulsion. These findings highlight that the shift in the XY stretching frequency is not a reliable metric for the strength of π back-donation. Overall, the VFB-augmented EDA scheme that we propose and apply in this work provides a useful tool to characterize the role played by each physical component that all together lead to the frequency shift observed.

Consistent inclusion of continuum solvation in energy decomposition analysis: theory and application to molecular CO2 reduction catalysts.

To facilitate computational investigation of intermolecular interactions in the solution phase, we report the development of ALMO-EDA(solv), a scheme that allows the application of continuum solvent models within the framework of energy decomposition analysis (EDA) based on absolutely localized molecular orbitals (ALMOs). In this scheme, all the quantum mechanical states involved in the variational EDA procedure are computed with the presence of solvent environment so that solvation effects are incorporated in the evaluation of all its energy components. After validation on several model complexes, we employ ALMO-EDA(solv) to investigate substituent effects on two classes of complexes that are related to molecular CO2 reduction catalysis. For [FeTPP(CO2-κC)]2- (TPP = tetraphenylporphyrin), we reveal that two ortho substituents which yield most favorable CO2 binding, -N(CH3)3 + (TMA) and -OH, stabilize the complex via through-structure and through-space mechanisms, respectively. The coulombic interaction between the positively charged TMA group and activated CO2 is found to be largely attenuated by the polar solvent. Furthermore, we also provide computational support for the design strategy of utilizing bulky, flexible ligands to stabilize activated CO2 via long-range Coulomb interactions, which creates biomimetic solvent-inaccessible "pockets" in that electrostatics is unscreened. For the reactant and product complexes associated with the electron transfer from the p-terphenyl radical anion to CO2, we demonstrate that the double terminal substitution of p-terphenyl by electron-withdrawing groups considerably strengthens the binding in the product state while moderately weakens that in the reactant state, which are both dominated by the substituent tuning of the electrostatics component. These applications illustrate that this new extension of ALMO-EDA provides a valuable means to unravel the nature of intermolecular interactions and quantify their impacts on chemical reactivity in solution.

Development of an Advanced Force Field for Water Using Variational Energy Decomposition Analysis.

Given the piecewise approach to modeling intermolecular interactions for force fields, they can be difficult to parametrize since they are fit to data like total energies that only indirectly connect to their separable functional forms. Furthermore, by neglecting certain types of molecular interactions such as charge penetration and charge transfer, most classical force fields must rely on, but do not always demonstrate, how cancellation of errors occurs among the remaining molecular interactions accounted for such as exchange repulsion, electrostatics, and polarization. In this work we present the first generation of the (many-body) MB-UCB force field that explicitly accounts for the decomposed molecular interactions commensurate with a variational energy decomposition analysis, including charge transfer, with force field design choices that reduce the computational expense of the MB-UCB potential while remaining accurate. We optimize parameters using only a single water molecule and water cluster data up through pentamers, with no fitting to condensed phase data, and we demonstrate that high accuracy is maintained when the force field is subsequently validated against conformational energies of larger water cluster data sets, radial distribution functions of the liquid phase, and the temperature dependence of thermodynamic and transport water properties. We conclude that MB-UCB is comparable in performance to MB-Pol but is less expensive and more transferable by eliminating the need to represent short-ranged interactions through large parameter fits to high order polynomials.