On the question of steric repulsion versus noncovalent attractive interactions in chiral phosphoric acid catalyzed asymmetric reactions.

The origin of enantioselectivity in asymmetric catalysis is often built around the differential steric interaction in the enantiocontrolling transition states (TSs). A closer perusal of enantiocontrolling TSs in an increasingly diverse range of reactions has revealed that the cumulative effect of weak noncovalent interactions could even outweigh the steric effects. While enunciating this balance is conspicuously important, quantification of such intramolecular forces within a TS continues to remain scarce and challenging. Herein, we demonstrate the utility of the fragment molecular orbital method in establishing the relative contributions of various attractive and repulsive contributions in the total interaction energy between the suitably chosen fragments in enantiocontrolling TSs. Three types of reactions of high contemporary importance, namely, axially chiral phosphoric acid (CPA) catalyzed kinetic resolution of rac-α-methyl-γ-hydroxy ester (reaction I), asymmetric dearomative amination of ß-naphthols by dimethyl azodicarboxylate (IIa and IIb), and intramolecular desymmetrization of ß,ß-disubstituted methyl oxetanes (IIIa) and hydroxyl oxetane (IIIb), bearing a tethered alcohol (-OCH2CH2OH or -(CH2)2CH2OH), are considered. In all the five reactions, the differences in the stabilizing contributions arising due to electrostatic, charge-transfer, and dispersion interactions between the catalyst and the reacting partners in the enantiocontrolling transition states are weighed against the destabilizing exchange interaction. The balancing interactions are found to be between dispersion and exchange repulsion in reaction I, a combination of charge transfer and dispersion energies offsets the repulsive energy in reaction IIb involving the electron rich anthryl groups in the catalyst, whereas the -(CF3)2C6H4 3,3'-substituent in the catalyst (reaction IIa) leads to a trade-off between dispersion and exchange energies. In reactions IIIa and IIIb, however, electrostatic and dispersion energies help compensate the repulsive interactions. These quantitative insights on the intramolecular interactions in the stereocontrolling TSs could help in the rational design of asymmetric catalysis.

Pair Interaction Energy Decomposition Analysis for Density Functional Theory and Density-Functional Tight-Binding with an Evaluation of Energy Fluctuations in Molecular Dynamics.

Pair interaction energy decomposition analysis in the fragment molecular orbital (FMO) method is extended to treat density functional theory (DFT) and density-functional tight-binding (DFTB). Fluctuations of energy contributions are obtained from molecular dynamics simulations. Interactions at the DFT and DFTB levels are compared to the values obtained with Hartree-Fock, second-order Møller-Plesset (MP2), and coupled cluster methods. Hydrogen bonding in water clusters is analyzed. 200 ps NVT molecular dynamics simulations are performed with FMO for two ligands bound to the Trp-cage miniprotein (PDB 1L2Y ); the fluctuations of fragment energies and interactions are analyzed.

Many-body expansion of the Fock matrix in the fragment molecular orbital method.

A many-body expansion of the Fock matrix in the fragment molecular orbital method is derived up to three-body terms for restricted Hartree-Fock and density functional theory in the atomic orbital basis and compared to the expansion in the basis of fragment molecular orbitals (MOs). The physical nature of many-body corrections is revealed in terms of charge transfer terms. An improvement of the fragment MO expansion is proposed by adding exchange to the embedding. The accuracy of all developed methods is demonstrated in comparison to unfragmented results for polyalanines, a water cluster, Trp-cage (PDB: 1L2Y) and crambin (PDB: 1CRN) proteins, a zeolite cluster, a Si nano-wire, and a boron nitride ribbon. The physical nature of metallicity is discussed, and it is shown what kinds of metallic systems can be treated by fragment-based methods. The density of states is calculated for a fully closed and a partially open nano-ring of boron nitride with a diameter of 105 nm.

The reaction mechanism of sarcosine oxidase elucidated using FMO and QM/MM methods.

Monomeric sarcosine oxidase (MSOX) is a flavoprotein that oxidizes sarcosine to the corresponding imine product and is widely used in clinical diagnostics to test renal function. In the past decade, several experimental studies have been performed to elucidate the underlying mechanism of this oxidation reaction. However, the details of the molecular mechanism remain unknown. In this study, we theoretically examined three possible reaction mechanisms, namely, the single-electron transfer, hydride-transfer, and polar mechanisms, using the fragment molecular orbital (FMO) and mixed quantum mechanics/molecular mechanics (QM/MM) methods. We found that, of the three possible reaction pathways, hydride-transfer is the most energetically favorable mechanism. Significantly, hydrogen is not transferred in the hydride state (H-) but in a hydrogen atom state (H˙). Furthermore, a single electron is simultaneously transferred from sarcosine to flavin through their overlapping orbitals. Therefore, based on a detailed theoretical analysis of the calculated reaction pathway, the reaction mechanism of MSOX can be labeled the "hydrogen-atom-coupled electron-transfer" (HACET) mechanism instead of being categorized as the classical hydride-transfer mechanism. QM/MM and FMO calculations revealed that sarcosine is moved close to the flavin ring because of a small charge transfer (about 0.2 electrons in state 1 (MSOX-sarcosine complex)) and that the positively charged residues (Arg49, Arg52, and Lys348) near the active site play a prominent role in stabilizing the sarcosine-flavin complex. These results indicate that strong Coulombic interactions primarily control amine oxidation in the case of MSOX. The new reaction mechanism, HACET, will be important for all the flavoprotein-catalyzed oxidation reactions.

Group molecular orbital approach to solve the Huzinaga subsystem self-consistent-field equations.

An algorithm to solve the Huzinaga subsystem self-consistent field equations is proposed using two approximations: a local expansion of subsystem molecular orbitals and a truncation of the projection operator. Test calculations are performed on water and ammonia clusters, and n-alkane and poly-glycine. The errors were 2.2 and -0.6 kcal/mol for (H2O)40 and C40H82, respectively, at the Hartree-Fock level with the 6-31G basis set.

Subsystem Analysis for the Fragment Molecular Orbital Method and Its Application to Protein-Ligand Binding in Solution.

A subsystem analysis is derived incorporating interfragment interactions into the fragment properties, such as energies or charges. The relative stabilities of three alanine isomers, the α-helix, the ß-turn, and the extended form are studied and the differences in fragment properties are elucidated. The analysis is further elaborated for studies of binding energies. The binding of the Trp-cage protein (PDB: 1L2Y ) to two ligands is studied in detail. Binding energies defined for each fragment can be used as a convenient descriptor for analyzing contributions to binding in solution.

Importance of Three-Body Interactions in Molecular Dynamics Simulations of Water Demonstrated with the Fragment Molecular Orbital Method.

The analytic first derivative with respect to nuclear coordinates is formulated and implemented in the framework of the three-body fragment molecular orbital (FMO) method. The gradient has been derived and implemented for restricted second-order Møller-Plesset perturbation theory, as well as for both restricted and unrestricted Hartree-Fock and density functional theory. The importance of the three-body fully analytic gradient is illustrated through the failure of the two-body FMO method during molecular dynamics simulations of a small water cluster. The parallel implementation of the fragment molecular orbital method, its parallel efficiency, and its scalability on the Blue Gene/Q architecture up to 262,144 CPU cores are also discussed.

Simulations of Chemical Reactions with the Frozen Domain Formulation of the Fragment Molecular Orbital Method.

The fully analytic first and second derivatives of the energy in the frozen domain formulation of the fragment molecular orbital (FMO) were developed and applied to locate transition states and determine vibrational contributions to free energies. The development is focused on the frozen domain with dimers (FDD) model. The intrinsic reaction coordinate method was interfaced with FMO. Simulations of IR and Raman spectra were enabled using FMO/FDD by developing the calculation of intensities. The accuracy is evaluated for S(N)2 reactions in explicit solvent, and for the free binding energies of a protein-ligand complex of the Trp cage protein (PDB: 1L2Y ). FMO/FDD is applied to study the keto-enol tautomeric reaction of phosphoglycolohydroxamic acid and the triosephosphate isomerase (PDB: 7TIM ), and the role of amino acid residue fragments in the reaction is discussed.

Identification of protein kinase CK2 inhibitors using solvent dipole ordering virtual screening.

Novel protein kinase CK2 inhibitors were identified using the solvent dipole ordering virtual screening method. A total of 26 compounds categorized in 15 distinct scaffold classes inhibited greater than 50% of enzyme activity at 50 µM, and eight exhibited IC50 values less than 10 µM. Most of the identified compounds are lead-like and dissimilar to known inhibitors. The crystal structures of two of the CK2 complexes revealed the high accuracy of the predicted binding modes.

Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method.

Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted Hartree-Fock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluated for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in SN2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented.

Efficient molecular dynamics simulations of multiple radical center systems based on the fragment molecular orbital method.

The fully analytic energy gradient has been developed and implemented for the restricted open-shell Hartree-Fock (ROHF) method based on the fragment molecular orbital (FMO) theory for systems that have multiple open-shell molecules. The accuracy of the analytic ROHF energy gradient is compared with the corresponding numerical gradient, illustrating the accuracy of the analytic gradient. The ROHF analytic gradient is used to perform molecular dynamics simulations of an unusual open-shell system, liquid oxygen, and mixtures of oxygen and nitrogen. These molecular dynamics simulations provide some insight about how triplet oxygen molecules interact with each other. Timings reveal that the method can calculate the energy gradient for a system containing 4000 atoms in only 6 h. Therefore, it is concluded that the FMO-ROHF method will be useful for investigating systems with multiple open shells.

The use of many-body expansions and geometry optimizations in fragment-based methods.

Conspectus Chemists routinely work with complex molecular systems: solutions, biochemical molecules, and amorphous and composite materials provide some typical examples. The questions one often asks are what are the driving forces for a chemical phenomenon? How reasonable are our views of chemical systems in terms of subunits, such as functional groups and individual molecules? How can one quantify the difference in physicochemical properties of functional units found in a different chemical environment? Are various effects on functional units in molecular systems additive? Can they be represented by pairwise potentials? Are there effects that cannot be represented in a simple picture of pairwise interactions? How can we obtain quantitative values for these effects? Many of these questions can be formulated in the language of many-body effects. They quantify the properties of subunits (fragments), referred to as one-body properties, pairwise interactions (two-body properties), couplings of two-body interactions described by three-body properties, and so on. By introducing the notion of fragments in the framework of quantum chemistry, one obtains two immense benefits: (a) chemists can finally relate to quantum chemistry, which now speaks their language, by discussing chemically interesting subunits and their interactions and (b) calculations become much faster due to a reduced computational scaling. For instance, the somewhat academic sounding question of the importance of three-body effects in water clusters is actually another way of asking how two hydrogen bonds affect each other, when they involve three water molecules. One aspect of this is the many-body charge transfer (CT), because the charge transfers in the two hydrogen bonds are coupled to each other (not independent). In this work, we provide a generalized view on the use of many-body expansions in fragment-based methods, focusing on the general aspects of the property expansion and a contraction of a many-body expansion in a formally two-body series, as exemplified in the development of the fragment molecular orbital (FMO) method. Fragment-based methods have been very successful in delivering the properties of fragments, as well as the fragment interactions, providing insights into complex chemical processes in large molecular systems. We briefly review geometry optimizations performed with fragment-based methods and present an efficient geometry optimization method based on the combination of FMO with molecular mechanics (MM), applied to the complex of a subunit of protein kinase 2 (CK2) with a ligand. FMO results are discussed in comparison with experimental and MM-optimized structures.

Unrestricted density functional theory based on the fragment molecular orbital method for the ground and excited state calculations of large systems.

We extended the fragment molecular orbital (FMO) method interfaced with density functional theory (DFT) into spin unrestricted formalism (UDFT) and developed energy gradients for the ground state and single point excited state energies based on time-dependent DFT. The accuracy of FMO is evaluated in comparison to the full calculations without fragmentation. Electronic excitations in solvated organic radicals and in the blue copper protein, plastocyanin (PDB code: 1BXV), are reported. The contributions of solvent molecules to the electronic excitations are analyzed in terms of the fragment polarization and quantum effects such as interfragment charge transfer.

Simulations of Raman Spectra Using the Fragment Molecular Orbital Method.

We developed an approach to calculate normal Raman activities based on the fragment molecular orbital method. For this purpose, we derived the FMO gradient and coupled-perturbed Hartree-Fock equations in the presence of the static electric field. The accuracy is evaluated in comparison with full ab initio calculations for a set of closed-shell and radical systems. We applied the method to calculate Raman and IR spectra of a polystyrene oligomer and crambin (PDB: 1CRN ) and performed an assignment of peaks based on localized normal modes. The computational timings demonstrate the efficiency of the method.

Analytic second derivatives of the energy in the fragment molecular orbital method.

We developed the analytic second derivatives of the energy for the fragment molecular orbital (FMO) method. First we derived the analytic expressions and then introduced some approximations related to the first and second order coupled perturbed Hartree-Fock equations. We developed a parallel program for the FMO Hessian with approximations in GAMESS and used it to calculate infrared (IR) spectra and Gibbs free energies and to locate the transition states in SN2 reactions. The accuracy of the Hessian is demonstrated in comparison to ab initio results for polypeptides and a water cluster. By using the two residues per fragment division, we achieved the accuracy of 3 cm(-1) in the reduced mean square deviation of vibrational frequencies from ab initio for all three polyalanine isomers, while the zero point energy had the error not exceeding 0.3 kcal/mol. The role of the secondary structure on IR spectra, zero point energies, and Gibbs free energies is discussed.

Open-shell pair interaction energy decomposition analysis (PIEDA): formulation and application to the hydrogen abstraction in tripeptides.

An open-shell extension of the pair interaction energy decomposition analysis (PIEDA) within the framework of the fragment molecular orbital (FMO) method is developed. The open-shell PIEDA method allows the analysis of inter- and intramolecular interactions in terms of electrostatic, exchange-repulsion, charge-transfer, dispersion, and optional polarization energies for molecular systems with a radical or high-spin fragment. Taking into account the low computational cost and scalability of the FMO and PIEDA methods, the new scheme provides a means to characterize the stabilization of radical and open-shell sites in biologically relevant species. The open-shell PIEDA is applied to the characterization of intramolecular interactions in capped trialanine upon hydrogen abstraction (HA) at various sites on the peptide. Hydrogen abstraction reaction is the first step in the oxidative pathway initiated by reactive oxygen or nitrogen species, associated with oxidative stress. It is found that HA results in significant geometrical reorganization of the trialanine peptide. Depending on the HA site, terminal interactions in the radical fold conformers may become weaker or stronger compared to the parent molecule, and often change the character of the non-covalent bonding from amide stacking to hydrogen bonding.

An Efficient Method to Evaluate Intermolecular Interaction Energies in Large Systems Using Overlapping Multicenter ONIOM and the Fragment Molecular Orbital Method.

We propose an approach based on the overlapping multicenter ONIOM to evaluate intermolecular interaction energies in large systems and demonstrate its accuracy on several representative systems in the complete basis set limit at the MP2 and CCSD(T) level of theory. In the application to the intermolecular interaction energy between insulin dimer and 4'-hydroxyacetanilide at the MP2/CBS level, we use the fragment molecular orbital method for the calculation of the entire complex assigned to the lowest layer in three-layer ONIOM. The developed method is shown to be efficient and accurate in the evaluation of the protein-ligand interaction energies.

Unrestricted Hartree-Fock based on the fragment molecular orbital method: energy and its analytic gradient.

A consideration of the surrounding environment is necessary for a meaningful analysis of the reaction activity in large molecular systems. We propose an approach to perform unrestricted Hartree-Fock (UHF) calculations within the framework of the fragment molecular orbital (FMO) method (FMO-UHF) to study large systems with unpaired electrons. Prior to an energy analysis one has to optimize geometry, which requires an accurate analytic energy gradient. We derive the FMO-UHF energy and its analytic gradient and implement them into GAMESS. The performance of FMO-UHF is evaluated for a solvated organic molecule and a solvated metal complex, as well as for the active part of a protein, in terms of energy, gradient, and geometry optimization.

Analysis of solute-solvent interactions in the fragment molecular orbital method interfaced with effective fragment potentials: theory and application to a solvated griffithsin-carbohydrate complex.

Based on the proposed new expression of the polarization energy for the fragment molecular orbital (FMO) method interfaced with effective fragment potentials (EFPs), we develop an analysis of the solute(FMO)-solvent(EFP) interactions by defining individual fragment contributions for both solute and solvent. The obtained components are compared to all-electron calculations where water is treated as FMO fragments in the pair interaction energy decomposition analysis. The new energy expression is shown to be accurate, and the developed energy analysis is applied to the solvated griffithsin-carbohydrate complex. The details of the ligand recognition are revealed in the context with their interplay with the solvent effects. Tyr residue fragments are shown to reduce the desolvation penalty for Asp, which strongly binds the ligand.

Analytic gradient for second order Møller-Plesset perturbation theory with the polarizable continuum model based on the fragment molecular orbital method.

A new energy expression is proposed for the fragment molecular orbital method interfaced with the polarizable continuum model (FMO/PCM). The solvation free energy is shown to be more accurate on a set of representative polypeptides with neutral and charged residues, in comparison to the original formulation at the same level of the many-body expansion of the electrostatic potential determining the apparent surface charges. The analytic first derivative of the energy with respect to nuclear coordinates is formulated at the second-order Møller-Plesset (MP2) perturbation theory level combined with PCM, for which we derived coupled perturbed Hartree-Fock equations. The accuracy of the analytic gradient is demonstrated on test calculations in comparison to numeric gradient. Geometry optimization of the small Trp-cage protein (PDB: 1L2Y) is performed with FMO/PCM/6-31(+)G(d) at the MP2 and restricted Hartree-Fock with empirical dispersion (RHF/D). The root mean square deviations between the FMO optimized and NMR experimental structure are found to be 0.414 and 0.426 Å for RHF/D and MP2, respectively. The details of the hydrogen bond network in the Trp-cage protein are revealed.