A Projector-Embedding Approach for Multiscale Coupled-Cluster Calculations Applied to Citrate Synthase

Development of analytic gradients for the Huzinaga quantum embedding method and its applications to large-scale hybrid and double hybrid DFT forces

The theory of analytic gradients is presented for the projector-based density functional theory (DFT) embedding approach utilizing the Huzinaga-equation. The advantages of the Huzinaga-equation-based formulation are demonstrated. In particular, it is shown that the projector employed does not appear in the Lagrangian, and the potential risk of numerical problems is avoided at the evaluation of the gradients. The efficient implementation of the analytic gradient theory is presented for approaches where hybrid DFT, second-order Møller-Plesset perturbation theory, or double hybrid DFT are embedded in lower-level DFT environments. To demonstrate the applicability of the method and to gain insight into its accuracy, it is applied to equilibrium geometry optimizations, transition state searches, and potential energy surface scans. Our results show that bond lengths and angles converge rapidly with the size of the embedded system. While providing structural parameters close to high-level quality for the embedded atoms, the embedding approach has the potential to relax the coordinates of the environment as well. Our demonstrations on a 171-atom zeolite and a 570-atom protein system show that the Huzinaga-equation-based embedding can accelerate (double) hybrid gradient computations by an order of magnitude with sufficient active regions and enables affordable force evaluations or geometry optimizations for molecules of hundreds of atoms.

Interactive molecular dynamics in virtual reality for modelling materials and catalysts

Interactive molecular dynamics simulation in virtual reality (iMD-VR) is emerging as a promising technique in molecular science. Here, we demonstrate its use in a range of fifteen applications in materials science and heterogeneous catalysis. In this work, the iMD-VR package Narupa is used with the MD package, DL_POLY [1]. We show how iMD-VR can be used to: (i) investigate the mechanism of lithium fast ion conduction by directing the formation of defects showing that vacancy transport is favoured over interstitialcy mechanisms, and (ii) guide a molecule through a zeolite pore to explore diffusion within zeolites, examining in detail the motion of methyl n-hexanoate in H-ZSM-5 zeolite and identifying bottlenecks restricting diffusion. iMD-VR allows users to manipulate these systems intuitively, to drive changes in them and observe the resulting changes in structure and dynamics. We make these simulations available, as a resource for both teaching and research. All simulation files, with videos, can be found online (https://doi.org/10.5281/zenodo.8252314) and are provided as open-source material.

Static embedding with pair coupled cluster doubles based methods

Quantum embedding methods have recently been significantly developed to model large molecular structures. This work proposes a novel wave function theory in a density functional theory (WTF-in-DFT) embedding scheme based on pair-coupled cluster doubles (pCCD)-type methods. While pCCD can reliably describe strongly-correlated systems with mean-field-like computational cost, the large extent of the dynamic correlation can be accounted for by (linearized) coupled-cluster corrections on top of the pCCD wave function. Here we focus on the linearized coupled-cluster singles and doubles (LCCSD) ansatz for electronic ground states and its extension to excited states within the equation of motion (EOM) formalism. We test our EOM-pCCD-LCCSD-in-DFT approach for the vertical excitation energies of the hydrogen-bonded water-ammonia complex, micro-solvated thymine, and uranyl tetrahalides (UO2X42-, X = F, Cl, Br). Furthermore, we assess the quality of the embedding potential using an orbital entanglement and correlation analysis. The approximate embedding models successfully capture changes in the excitation energies going from bare fragments to supramolecular structures and represent a promising computational method for excited states in large molecular systems.

Challenges in modelling dynamic processes in realistic nanostructured materials at operating conditions

The question is addressed in how far current modelling strategies are capable of modelling dynamic phenomena in realistic nanostructured materials at operating conditions. Nanostructured materials used in applications are far from perfect; they possess a broad range of heterogeneities in space and time extending over several orders of magnitude. Spatial heterogeneities from the subnanometre to the micrometre scale in crystal particles with a finite size and specific morphology, impact the material's dynamics. Furthermore, the material's functional behaviour is largely determined by the operating conditions. Currently, there exists a huge length-time scale gap between attainable theoretical length-time scales and experimentally relevant scales. Within this perspective, three key challenges are highlighted within the molecular modelling chain to bridge this length-time scale gap. Methods are needed that enable (i) building structural models for realistic crystal particles having mesoscale dimensions with isolated defects, correlated nanoregions, mesoporosity, internal and external surfaces; (ii) the evaluation of interatomic forces with quantum mechanical accuracy albeit at much lower computational cost than the currently used density functional theory methods and (iii) derivation of the kinetics of phenomena taking place in a multi-length-time scale window to obtain an overall view of the dynamics of the process. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Integrated Multiscale Multilevel Approach to Open Shell Molecular Systems

We present a novel multiscale approach to study the electronic structure of open shell molecular systems embedded in an external environment. The method is based on the coupling of multilevel Hartree-Fock (MLHF) and Density Functional Theory (MLDFT), suitably extended to the unrestricted formalism, to Molecular Mechanics (MM) force fields (FF). Within the ML region, the system is divided into active and inactive parts, thus describing the most relevant interactions (electrostatic, polarization, and Pauli repulsion) at the quantum level. The surrounding MM part, which is formulated in terms of nonpolarizable or polarizable FFs, permits a physically consistent treatment of long-range electrostatics and polarization effects. The approach is extended to the calculation of hyperfine coupling constants and applied to selected nitroxyl radicals in an aqueous solution.

On the accuracy of orbital based multi-level approaches for closed-shell transition metal chemistry

In this work, we investigate the accuracy of the local molecular orbital molecular orbital (LMOMO) scheme and projection-based wave function-in-density functional theory (WF-in-DFT) embedding for the prediction of reaction energies and barriers of typical reactions involving transition metals. To analyze the dependence of the accuracy on the system partitioning, we apply a manual orbital selection for LMOMO as well as the so-called direct orbital selection (DOS) for both approaches. We benchmark these methods on 30 closed shell reactions involving 16 different transition metals. This allows us to devise guidelines for the manual selection as well as settings for the DOS that provide accurate results within an error of 2 kcal mol^-1 compared to local coupled cluster. To reach this accuracy, on average 55% of the occupied orbitals have to be correlated with coupled cluster for the current test set. Furthermore, we find that LMOMO gives more reliable relative energies for small embedded regions than WF-in-DFT embedding.

Modeling the Ligand Effect on the Structure of CYP 450 Within the Density Functional Theory

An improved understanding of the P450 structure is relevant to the development of biomimetic catalysts and inhibitors for controlled CH-bond activation, an outstanding challenge of synthetic chemistry. Motivated by the experimental findings of an unusually short Fe-S bond of 2.18 Å for the wild-type (WT) OleT P450 decarboxylase relative to a cysteine pocket mutant form (A369P), a computational model that captures the effect of the thiolate axial ligand on the iron-sulfur distance is presented. With the computational efficiency and streamlined analysis in mind, this model combines a cluster representation of the enzyme─40-110 atoms, depending on the heme and ligand truncation level─with a density functional theory (DFT) description of the electronic structure (ES) and is calibrated against the experimental data. The optimized Fe-S distances show a difference of 0.25 Å between the low and high spin states, in agreement with the crystallographic structures of the OleT WT and mutant forms. We speculate that this difference is attributable to the packing of the ligand; the mutant is bulkier due to an alanine-to-proline replacement, meaning that it is excluded from the energetically favored low-spin minimum because of steric constraints. The presence of pure spin-state pairs and the intersection of the low/high spin states for the enzyme model is indicative of the limitations of single-reference ES methods in such systems and emphasizes the significance of using the proper state when modeling the hydrogen atom transfer (HAT) reaction catalyzed by OleT. At the same time, the correct characterization of both the short and long Fe-S bonds within a small DFT-based model of 42 atoms paves the way for quantum dynamics modeling of the HAT step, which initiates the OleT decarboxylation reaction.

Direct orbital selection within the domain-based local pair natural orbital coupled-cluster method

Domain-based local pair natural orbital coupled cluster (DLPNO-CC) has become increasingly popular to calculate relative energies (e.g., reaction energies and reaction barriers). It can be applied within a multi-level DLPNO-CC-in-DLPNO-CC ansatz to reduce the computational cost and focus the available computational resources on a specific subset of the occupied orbitals. We demonstrate how this multi-level DLPNO-CC ansatz can be combined with our direct orbital selection (DOS) approach [M. Bensberg and J. Neugebauer, J. Chem. Phys. 150, 214106 (2019)] to automatically select orbital sets for any multi-level calculation. We find that the parameters for the DOS procedure can be chosen conservatively such that they are transferable between reactions. The resulting automatic multi-level DLPNO-CC method requires no user input and is extremely robust and accurate. The computational cost is easily reduced by a factor of 3 without sacrificing accuracy. We demonstrate the accuracy of the method for a total of 61 reactions containing up to 174 atoms and use it to predict the relative stability of conformers of a Ru-based catalyst.

Three-Layer Multiscale Approach Based on Extremely Localized Molecular Orbitals to Investigate Enzyme Reactions

Quantum mechanics/molecular mechanics (QM/MM) calculations are widely used embedding techniques to computationally investigate enzyme reactions. In most QM/MM computations, the quantum mechanical region is treated through density functional theory (DFT), which offers the best compromise between chemical accuracy and computational cost. Nevertheless, to obtain more accurate results, one should resort to wave function-based methods, which however lead to a much larger computational cost already for relatively small QM subsystems. To overcome this drawback, we propose the coupling of our QM/ELMO (quantum mechanics/extremely localized molecular orbital) approach with molecular mechanics, thus introducing the three-layer QM/ELMO/MM technique. The QM/ELMO strategy is an embedding method in which the chemically relevant part of the system is treated at the quantum mechanical level, while the rest is described through frozen ELMOs. Since the QM/ELMO method reproduces results of fully QM computations within chemical accuracy and with a much lower computational effort, it can be considered a suitable strategy to extend the range of applicability and accuracy of the QM/MM scheme. In this paper, other than briefly presenting the theoretical bases of the QM/ELMO/MM technique, we will also discuss its validation on the well-tested deprotonation of acetyl coenzyme A by aspartate in citrate synthase.

Catalytic mechanism of the colistin resistance protein MCR-1

The mcr-1 gene encodes a membrane-bound Zn2+-metalloenzyme, MCR-1, which catalyses phosphoethanolamine transfer onto bacterial lipid A, making bacteria resistant to colistin, a last-resort antibiotic. Mechanistic understanding of this process remains incomplete. Here, we investigate possible catalytic pathways using DFT and ab initio calculations on cluster models and identify a complete two-step reaction mechanism. The first step, formation of a covalent phosphointermediate via transfer of phosphoethanolamine from a membrane phospholipid donor to the acceptor Thr285, is rate-limiting and proceeds with a single Zn2+ ion. The second step, transfer of the phosphoethanolamine group to lipid A, requires an additional Zn2+. The calculations suggest the involvement of the Zn2+ orbitals directly in the reaction is limited, with the second Zn2+ acting to bind incoming lipid A and direct phosphoethanolamine addition. The new level of mechanistic detail obtained here, which distinguishes these enzymes from other phosphotransferases, will aid in the development of inhibitors specific to MCR-1 and related bacterial phosphoethanolamine transferases.

Estimates of electron correlation based on density expansions

Two methods for estimating the correlation energy of molecules and other electronic systems are discussed based on the assumption that the correlation energy can be partitioned between atomic regions. In the first method, the electron density is expanded in terms of atomic contributions using rigorous electron repulsion bounds, and in the second method, correlation contributions are associated with basis function pairs. These methods do not consider the detailed nature of localized excitations but instead define a correlation energy per electron factor that is unique to a specific atom. The correlation factors are basis function dependent and are determined by configuration interaction (CI) calculations on diatomic and hydride molecules. The correlation energy estimates are compared with the results of high-level CI calculations for a test set of 27 molecules representing a wide range of bonding environments (average error of 2.6%). An extension based on truncated CI calculations in which d-type and hydrogen p-type functions are eliminated from the virtual space combined with estimates of dynamical correlation contributions using atomic correlation factors is discussed and applied to the dissociation of several molecules.

Electronic structure benchmark calculations of CO2 fixing elementary chemical steps in RuBisCO using the projector-based embedding approach

Ribulose 1,5-bisphosphate carboxylase-oxygenase (RuBisCO) is the main enzyme involved in atmospheric carbon dioxide (CO₂ ) fixation in the biosphere. This enzyme catalyzes a set of five chemical steps that take place in the same active-site within magnesium (II) coordination sphere. Here, a set of electronic structure benchmark calculations have been carried out on a reaction path proposed by Gready et al. by means of the projector-based embedding approach. Activation and reaction energies for all main steps catalyzed by RuBisCO have been calculated at the MP2, SCS-MP2, CCSD, and CCSD(T)/aug-cc-pVDZ and cc-pVDZ levels of theory. The treatment of the magnesium cation with post-HF methods is explored to determine the nature of its involvement in the mechanism. With the high-level ab initio values as a reference, we tested the performance of a set of density functional theory (DFT) exchange-correlation (xc) functionals in reproducing the reaction energetics of RuBisCO carboxylase activity on a set of model fragments. Different DFT xc-functionals show large variation in activation and reaction energies. Activation and reaction energies computed at the B3LYP level are close to the reference SCS-MP2 results for carboxylation, hydration and protonation reactions. However, for the carbon-carbon bond dissociation reaction, B3LYP and other functionals give results that differ significantly from the ab initio reference values. The results show the applicability of the projector-based embedding approach to metalloenzymes. This technique removes the uncertainty associated with the selection of different DFT xc-functionals and so can overcome some of inherent limitations of DFT calculations, complementing, and potentially adding to modeling of enzyme reaction mechanisms with DFT methods.

Embedded Mean-Field Theory for Solution-Phase Transition-Metal Polyolefin Catalysis

Decreasing the wall-clock time of quantum mechanics/molecular mechanics (QM/MM) calculations without sacrificing accuracy is a crucial prerequisite for widespread simulation of solution-phase dynamical processes. In this work, we demonstrate the use of embedded mean-field theory (EMFT) as the QM engine in QM/MM molecular dynamics (MD) simulations to examine polyolefin catalysts in solution. We show that employing EMFT in this mode preserves the accuracy of hybrid-functional DFT in the QM region, while providing up to 20-fold reductions in the cost per SCF cycle, thereby increasing the accessible simulation time-scales. We find that EMFT reproduces DFT-computed binding energies and optimized bond lengths to within chemical accuracy, as well as consistently ranking conformer stability. Furthermore, solution-phase EMFT/MM simulations provide insight into the interaction strength of strongly coordinating and bulky counterions.

Benchmarking quantum mechanical methods for calculating reaction energies of reactions catalyzed by enzymes

To assess the accuracy of different quantum mechanical methods for biochemical modeling, the reaction energies of 20 small model reactions (chosen to represent chemical steps catalyzed by commonly studied enzymes) were calculated. The methods tested included several popular Density Functional Theory (DFT) functionals, second-order Møller Plesset perturbation theory (MP2) and its spin-component scaled variant (SCS-MP2), and coupled cluster singles and doubles and perturbative triples (CCSD(T)). Different basis sets were tested. CCSD(T)/aug-cc-pVTZ results for all 20 reactions were used to benchmark the other methods. It was found that MP2 and SCS-MP2 reaction energy calculation results are similar in quality to CCSD(T) (mean absolute error (MAE) of 1.2 and 1.3 kcal mol−1, respectively). MP2 calculations gave a large error in one case, and are more subject to basis set effects, so in general SCS-MP2 calculations are a good choice when CCSD(T) calculations are not feasible. Results with different DFT functionals were of reasonably good quality (MAEs of 2.5–5.1 kcal mol−1), whereas popular semi-empirical methods (AM1, PM3, SCC-DFTB) gave much larger errors (MAEs of 11.6–14.6 kcal mol−1). These results should be useful in guiding methodological choices and assessing the accuracy of QM/MM calculations on enzyme-catalyzed reactions.

The Molpro quantum chemistry package

Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.

Ab Initio Calculations for Molecule-Surface Interactions with Chemical Accuracy

Atomistic understanding of complex surface phenomena such as heterogeneous catalysis or storage and separation of energy-relevant gases in nanoporous materials (zeolites; metal-organic frameworks, MOFs) requires knowledge about reaction energies and energy barriers for elementary steps. This is difficult to obtain from experiment since the number of possible chemical, adsorption/desorption, and diffusion steps coupled to complex reaction networks is large, and so is the number of possible surface sites. Here is an important role of quantum chemistry which can provide rate and equilibrium constants for elementary steps "ab initio." To be useful, the predictions have to reach chemical accuracy (4 kJ/mol) which is difficult to achieve because realistic models of the surface systems may comprise of the order of a thousand atoms. While density functional theory (DFT) as a rule cannot be trusted to yield results within chemical accuracy limits, methods that are accurate enough (Coupled Cluster with Single, Double, and perturbative Triple Substitution, CCSD(T)) cannot be applied because of their exponential scaling with system size. This Account presents a hybrid high-level-low-level quantum method that combines DFT with dispersion for the full periodic system with second order Møller-Plesset perturbation theory (MP2) for the reaction site within a mechanical embedding scheme. In addition, to check if MP2 is accurate enough, we calculate Coupled Cluster (CC) corrections with Single, Double, and perturbatively treated Triple substitutions (CCSD(T)) for sufficiently small models of the reaction site. This multilevel hybrid MP2:DFT-D+ΔCC method is shown to yield chemical accuracy for a set of 12 molecule-surface interaction systems for which reliable experimental data are available. For CO/MgO(001), the history of the experiment-theory comparison illustrates two problems: (i) Do experiment and theory look at the same surface site? (ii) Does theory calculate the same quantity as derived from experiment? The hybrid MP2:DFT-D+ΔCC data set generated includes the MgO(001) surface, the Mg₂(dobdc) metal-organic framework, and the proton forms of the CHA and MFI zeolites interacting with the H₂, N₂, CO, CO₂, CH₄, and C₂H₆ molecules. It serves two purposes. First, it will be useful for testing density functionals with respect to their performance for molecule-surface interactions. Second, it establishes the hybrid MP2:DFT-D+ΔCC method as a reliable and powerful tool for ab initio predictions of adsorption and reaction energies as well as energy barriers when testing reaction mechanisms. For adsorption of small molecules in MOFs, isotherm predictions have reached a level of accuracy that deviations between theoretical predictions and experiments indicate sample imperfections. For elementary steps of the industrially important methanol-to-olefin process, our hybrid MP2:PBE+D+ΔCC calculations yield rate constants in agreement with experiment within chemical accuracy limits, finally achieving for molecule-surface reactions which was possible so hitherto only for gas phase reactions involving not more than 10 atoms.

Limitations of Ligand-Only Approaches for Predicting the Reactivity of Covalent Inhibitors

Covalent inhibition has undergone a resurgence and is an important modern-day drug design and chemical biology approach. To avoid off-target interactions and to fine-tune reactivity, the ability to accurately predict reactivity is vitally important for the design and development of safer and more effective covalent drugs. Several ligand-only metrics have been proposed that promise quick and simple ways of determining covalent reactivity. In particular, we examine proton affinity and reaction energies calculated with the density functional B3LYP-D3/6-311+G**//B3LYP-D3/6-31G* method to assess the reactivity of a series of α,β-unsaturated carbonyl compounds that form covalent adducts with cysteine. We demonstrate that while these metrics correlate well with experiment for a diverse range of small reactive molecules these approaches fail for predicting the reactivity of drug-like compounds. We conclude that ligand-only metrics such as proton affinity and reaction energies do not capture determinants of reactivity in situ and fail to account for important factors such as conformation, solvation, and intermolecular interactions.

The reaction mechanism of Zika virus NS2B/NS3 serine protease inhibition by dipeptidyl aldehyde: a QM/MM study

Zika virus (ZIKV) infection has become a global public health problem, associated with microcephaly in newborns and Guillain-Barré syndrome in adults. Currently, there are no commercially available anti-ZIKV drugs. The viral protease NS2B/NS3, which is involved in viral replication and maturation, is a potential drug target. Peptidomimetic aldehyde inhibitors bind covalently to the catalytic S135 of the NS3 protease. Here, we apply hybrid quantum mechanics/molecular mechanics (QM/MM) free-energy simulations at the PDDG-PM3/ff14SB level to investigate the inhibition mechanism of the ZIKV protease by a dipeptidyl aldehyde inhibitor (acyl-KR-aldehyde). The results show that proton transfer from the catalytic S135 to H51 occurs in concert with nucleophilic addition on the aldehyde warhead by S135. The anionic covalent complex between the dipeptidyl aldehyde and the ZIKV protease is analogous to the tetrahedral intermediate for substrate hydrolysis. Spontaneous protonation by H51 forms the hemiacetal. In addition, we use correlated ab initio QM/MM potential energy path calculations at levels up to LCCSD(T)/(aug)-cc-pVTZ to obtain accurate potential energy profiles of the reaction, which also support a concerted mechanism. These results provide detailed insight into the mechanism of ZIKV protease inhibition by a peptidyl aldehyde inhibitor, which will guide in the design of inhibitors.

Projector-Based Embedding Eliminates Density Functional Dependence for QM/MM Calculations of Reactions in Enzymes and Solution

Combined quantum mechanics/molecular mechanics (QM/MM) methods are increasingly widely utilized in studies of reactions in enzymes and other large systems. Here, we apply a range of QM/MM methods to investigate the Claisen rearrangement of chorismate to prephenate, in solution, and in the enzyme chorismate mutase. Using projector-based embedding in a QM/MM framework, we apply treatments up to the CCSD(T) level. We test a range of density functional QM/MM methods and QM region sizes. The results show that the calculated reaction energetics are significantly more sensitive to the choice of density functional than they are to the size of the QM region in these systems. Projector-based embedding of a wave function method in DFT reduced the 13 kcal/mol spread in barrier heights calculated at the DFT/MM level to a spread of just 0.3 kcal/mol, essentially eliminating dependence on the functional. Projector-based embedding of correlated ab initio methods provides a practical method for achieving high accuracy for energy profiles derived from DFT and DFT/MM calculations for reactions in condensed phases.

Projection-Based Wavefunction-in-DFT Embedding

Complex chemical systems present challenges to electronic structure theory stemming from large system sizes, subtle interactions, coupled dynamical time scales, and electronically nonadiabatic effects. New methods are needed to perform reliable, rigorous, and affordable electronic structure calculations for simulating the properties and dynamics of such systems. This Account reviews projection-based quantum embedding for electronic structure, which provides a formally exact method for density functional theory (DFT) embedding. The method also provides a rigorous and accurate approach for describing a small part of a chemical system at the level of a correlated wavefunction (WF) method while the remainder of the system is described at the level of DFT. A key advantage of projection-based embedding is that it can be formulated in terms of an extremely simple level-shift projection operator, which eliminates the need for any optimized effective potential calculation or kinetic energy functional approximation while simultaneously ensuring that no extra programming is needed to perform WF-in-DFT embedding with an arbitrary WF method. The current work presents the theoretical underpinnings of projection-based embedding, describes use of the method for combining wavefunction and density functional theories, and discusses technical refinements that have improved the applicability and robustness of the method. Applications of projection-based WF-in-DFT embedding are also reviewed, with particular focus on recent work on transition-metal catalysis, enzyme reactivity, and battery electrolyte decomposition. In particular, we review the application of projection-based embedding for the prediction of electrochemical potentials and reaction pathways in a Co-centered hydrogen evolution catalyst. Projection-based WF-in-DFT calculations are shown to provide quantitative accuracy while greatly reducing the computational cost compared with a reference coupled cluster calculation on the full system. Additionally, projection-based WF-in-DFT embedding is used to study the mechanism of citrate synthase; it is shown that projection-based WF-in-DFT largely eliminates the sensitivity of the potential energy landscape to the employed DFT exchange-correlation functional. Finally, we demonstrate the use of projection-based WF-in-DFT to study electron transfer reactions associated with battery electrolyte decomposition. Projection-based WF-in-DFT embedding is used to calculate the oxidation potentials of neat ethylene carbonate (EC), neat dimethyl carbonate (DMC), and 1:1 mixtures of EC and DMC in order to overcome qualitative inaccuracies in the electron densities and ionization energies obtained from conventional DFT methods. By further embedding the WF-in-DFT description in a molecular mechanics point-charge environment, this work enables an explicit description of the solvent and ensemble averaging of the solvent configurations. Looking forward, we anticipate continued refinement of the projection-based embedding methodology as well as its increasingly widespread application in diverse areas of chemistry, biology, and materials science.

Acetyl Coenzyme A Analogues as Rationally Designed Inhibitors of Citrate Synthase

In this study, we probed the inhibition of pig heart citrate synthase (E.C. 4.1.3.7) by synthesising seven analogues either designed to mimic the proposed enolate intermediate in this enzyme reaction or developed from historical inhibitors. The most potent inhibitor was fluorovinyl thioether 9 (K_i =4.3 μm), in which a fluorine replaces the oxygen atom of the enolate. A comparison of the potency of 9 with that of its non-fluorinated vinyl thioether analogue 10 (K_i =68.3 μm) revealed a clear "fluorine effect" favouring 9 by an order of magnitude. The dethia analogues of 9 and 10 proved to be poor inhibitors. A methyl sulfoxide analogue was a moderate inhibitor (K_i =11.1 μm), thus suggesting hydrogen bonding interactions in the enolate site. Finally, E and Z propenoate thioether isomers were explored as conformationally constrained carboxylates, but these were not inhibitors. All compounds were prepared by the synthesis of the appropriate pantetheinyl diol and then assembly of the coenzyme A structure according to a three-enzyme biotransformation protocol. A quantum mechanical study, modelling both inhibitors 9 and 10 into the active site indicated short CF⋅⋅⋅H contacts of ≈2.0 Å, consistent with fluorine making two stabilising hydrogen bonds, and mimicking an enolate rather than an enol intermediate. Computation also indicated that binding of 9 to citrate synthase increases the basicity of a key aspartic acid carboxylate, which becomes protonated.

Analysis of Phosphoryl-Transfer Enzymes with QM/MM Free Energy Simulations

We discuss the application of quantum mechanics/molecular mechanics (QM/MM) free energy simulations to the analysis of phosphoryl transfers catalyzed by two enzymes: alkaline phosphatase and myosin. We focus on the nature of the transition state and the issue of mechanochemical coupling, respectively, in the two enzymes. The results illustrate unique insights that emerged from the QM/MM simulations, especially concerning the interpretation of experimental data regarding the nature of enzymatic transition states and coupling between global structural transition and catalysis in the active site. We also highlight a number of technical issues worthy of attention when applying QM/MM free energy simulations, and comment on a number of technical and mechanistic issues that require further studies.

QM/MM Simulations with the Gaussian Electrostatic Model: A Density-based Polarizable Potential

The use of advanced polarizable potentials in quantum mechanical/molecular mechanical (QM/MM) simulations has been shown to improve the overall accuracy of the calculation. We have developed a density-based potential called the Gaussian electrostatic model (GEM), which has been shown to provide very accurate environments for QM wave functions in QM/MM. In this contribution we present a new implementation of QM/GEM that extends our implementation to include all components (Coulomb, exchange-repulsion, polarization, and dispersion) for the total intermolecular interaction energy in QM/MM calculations, except for the charge-transfer term. The accuracy of the method is tested using a subset of water dimers from the water dimer potential energy surface reported by Babin et al. ( J. Chem. Theory Comput. 2013 9, 5395-5403). Additionally, results of the new implementation are contrasted with results obtained with the classical AMOEBA potential. Our results indicate that GEM provides an accurate MM environment with average root-mean-square error <0.15 kcal/mol for every intermolecular interaction energy component compared with SAPT2+3/aug-cc-pVTZ reference calculations.

Multiscale Methods in Drug Design Bridge Chemical and Biological Complexity in the Search for Cures

Drug action is inherently multiscale: it connects molecular interactions to emergent properties at cellular and larger scales. Simulation techniques at each of these different scales are already central to drug design and development, but methods capable of connecting across these scales will extend understanding of complex mechanisms and the ability to predict biological effects. Improved algorithms, ever-more-powerful computing architectures and the accelerating growth of rich datasets are driving advances in multiscale modeling methods capable of bridging chemical and biological complexity from the atom to the cell. Particularly exciting is the development of highly detailed, structure-based, physical simulations of biochemical systems, which are now able to access experimentally relevant timescales for large systems and, at the same time, achieve unprecedented accuracy. In this Perspective, we discuss how emerging data-rich, physics-based multiscale approaches are of the cusp of realizing long-promised impact in the discovery, design and development of novel therapeutics. We highlight emerging methods and applications in this growing field, and outline how different scales can be combined in practical modelling and simulation strategies.

Multiscale analysis of enantioselectivity in enzyme-catalysed 'lethal synthesis' using projector-based embedding

The action of fluoroacetate as a broad-spectrum mammalian pesticide depends on the 'lethal synthesis' of fluorocitrate by citrate synthase, through a subtle enantioselective enolization of fluoroacetyl-coenzyme A. In this work, we demonstrate how a projection-based embedding method can be applied to calculate coupled cluster (CCSD(T)) reaction profiles from quantum mechanics/molecular mechanics optimized pathways for this enzyme reaction. Comparison of pro-R and pro-S proton abstraction in citrate synthase at the CCSD(T)-in-DFT//MM level yields the correct enantioselectivity. We thus demonstrate the potential of projection-based embedding for determining stereoselectivity in enzymatic systems. We further show that the method is simple to apply, eliminates variability due to the choice of density functional theory functional and allows the efficient calculation of CCSD(T) quality enzyme reaction barriers.

Combined Quantum Mechanics and Molecular Mechanics Studies of Enzymatic Reaction Mechanisms

The combined quantum mechanics/molecular mechanics (QM/MM) methods have become a valuable tool in computational biochemistry and received versatile applications for studying the reaction mechanisms of enzymes. The approach combines the calculations of the electronic structure of the active site by QM, with modeling of the protein environment using MM force field, which allows the long-range electrostatics and steric effects on the enzyme reactivity to be accounted for. In this review, we review some key theoretical and computational aspects of the method and we also present some applications to particular enzymatic reactions such as tryptophan-7-halogenase, cyclooxygenase-1, and the epidermal growth factor receptor.

Mechanistic Insights into the Reaction of Chlorination of Tryptophan Catalyzed by Tryptophan 7-Halogenase

Tryptophan 7-halogenase catalyzes chlorination of free tryptophan to 7-chlorotryptophan, which is the first step in the antibiotic pyrrolnitrin biosynthesis. Many biologically and pharmaceutically active natural products contain chlorine and thus, an understanding of the mechanism of its introduction into organic molecules is important. Whilst enzyme-catalyzed chlorination is accomplished with ease, it remains a difficult task for the chemists. Therefore, utilizing enzymes in the synthesis of chlorinated organic compounds is important, and providing atomistic mechanistic insights about the reaction mechanism of tryptophan 7-halogenase is vital and timely. In this work, we examined a mechanism for the reaction of tryptophan chlorination, performed by tryptophan 7-halogenase, by calculating potential energy and free energy surfaces using two different Combined Quantum Mechanical/Molecular Mechanical (QM/MM) methods both employing Density Functional Theory (DFT) for the QM region. Both computational strategies agree on the nature of the rate-limiting step and provided close results for the reaction barriers of the two reaction steps. The calculations for both the potential energy and the free energy profiles showed very similar geometric features and hydrogen bonding interactions for the characterized stationary points.

Pushing the Limits of EOM-CCSD with Projector-Based Embedding for Excitation Energies

The calculation of accurate excitation energies using ab initio electronic structure methods such as standard equation of motion coupled cluster singles and doubles (EOM-CCSD) has been cost prohibitive for large systems. In this work, we use a simple projector-based embedding scheme to calculate the EOM-CCSD excitation energies of acrolein solvated in water molecules modeled using density functional theory (DFT). We demonstrate the accuracy of this approach gives excitation energies within 0.01 eV of full EOM-CCSD, but with significantly reduced computational cost. This approach is also shown to be relatively invariant to the choice of functional used in the environment and allows for the description of systems with large numbers of basis functions (>1000) to be treated using state-of-the-art wave function methods. The flexibility of embedding to select orbitals to add to the excited-state method provides insights into the origins of the excitations and can reduce artifacts that could arise in traditional linear response time-dependent DFT (LR-TDDFT).

Ab Initio QM/MM Modeling of the Rate-Limiting Proton Transfer Step in the Deamination of Tryptamine by Aromatic Amine Dehydrogenase

Aromatic amine dehydrogenase (AADH) and related enzymes are at the heart of debates on the roles of quantum tunneling and protein dynamics in catalysis. The reaction of tryptamine in AADH involves significant quantum tunneling in the rate-limiting proton transfer step, shown by large H/D primary kinetic isotope effects (KIEs), with unusual temperature dependence. We apply correlated ab initio combined quantum mechanics/molecular mechanics (QM/MM) methods, at levels up to local coupled cluster theory (LCCSD(T)/(aug)-cc-pVTZ), to calculate accurate potential energy surfaces for this reaction, which are necessary for quantitative analysis of tunneling contributions and reaction dynamics. Different levels of QM/MM treatment are tested. Multiple pathways are calculated with fully flexible transition state optimization by the climbing-image nudged elastic band method at the density functional QM/MM level. The average LCCSD(T) potential energy barriers to proton transfer are 16.7 and 14.0 kcal/mol for proton transfer to the two carboxylate atoms of the catalytic base, Asp128β. The results show that two similar, but distinct pathways are energetically accessible. These two pathways have different barriers, exothermicity and curvature, and should be considered in analyses of the temperature dependence of reaction and KIEs in AADH and other enzymes. These results provide a benchmark for this prototypical enzyme reaction and will be useful for developing empirical models, and analyzing experimental data, to distinguish between different conceptual models of enzyme catalysis.

Metal Fluorides: Tools for Structural and Computational Analysis of Phosphoryl Transfer Enzymes

The phosphoryl group, PO₃^-, is the dynamic structural unit in the biological chemistry of phosphorus. Its transfer from a donor to an acceptor atom, with oxygen much more prevalent than nitrogen, carbon, or sulfur, is at the core of a great majority of enzyme-catalyzed reactions involving phosphate esters, anhydrides, amidates, and phosphorothioates. The serendipitous discovery that the phosphoryl group could be labeled by "nuclear mutation," by substitution of PO₃^- by MgF₃^- or AlF₄^-, has underpinned the application of metal fluoride (MF _x ) complexes to mimic transition states for enzymatic phosphoryl transfer reactions, with sufficient stability for experimental analysis. Protein crystallography in the solid state and ¹⁹F NMR in solution have enabled direct observation of ternary and quaternary protein complexes embracing MF _x transition state models with precision. These studies have underpinned a radically new mechanistic approach to enzyme catalysis for a huge range of phosphoryl transfer processes, as varied as kinases, phosphatases, phosphomutases, and phosphohydrolases. The results, without exception, have endorsed trigonal bipyramidal geometry (tbp) for concerted, "in-line" stereochemistry of phosphoryl transfer. QM computations have established the validity of tbp MF _x complexes as reliable models for true transition states, delivering similar bond lengths, coordination to essential metal ions, and virtually identical hydrogen bond networks. The emergence of protein control of reactant orbital overlap between bond-forming species within enzyme transition states is a new challenging theme for wider exploration.

Correcting density-driven errors in projection-based embedding

Projection-based embedding provides a simple and numerically robust framework for multiscale wavefunction-in-density-functional-theory (WF-in-DFT) calculations. The approach works well when the approximate DFT is sufficiently accurate to describe the energetics of the low-level subsystem and the coupling between subsystems. It is also necessary that the low-level DFT produces a qualitatively reasonable description of the total density, and in this work, we study model systems where delocalization error prevents this from being the case. We find substantial errors in embedding calculations on open-shell doublet systems in which self-interaction errors cause spurious delocalization of the singly occupied orbital. We propose a solution to this error by evaluating the DFT energy using a more accurate self-consistent density, such as that of Hartree-Fock (HF) theory. These so-called WF-in-(HF-DFT) calculations show excellent convergence towards full-system wavefunction calculations.

Electron correlation by polarization of interacting densities

Coulomb interactions that occur in electronic structure calculations are correlated by allowing basis function components of the interacting densities to polarize dynamically, thereby reducing the magnitude of the interaction. Exchange integrals of molecular orbitals are not correlated. The modified Coulomb interactions are used in single-determinant or configuration interaction calculations. The objective is to account for dynamical correlation effects without explicitly introducing higher spherical harmonic functions into the molecular orbital basis. Molecular orbital densities are decomposed into a distribution of spherical components that conserve the charge and each of the interacting components is considered as a two-electron wavefunction embedded in the system acted on by an average field Hamiltonian plus r₁₂^-1. A method of avoiding redundancy is described. Applications to atoms, negative ions, and molecules representing different types of bonding and spin states are discussed.