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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 β-naphthols by dimethyl azodicarboxylate (IIa and IIb), and intramolecular desymmetrization of β,β-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.

The charge transport rate constant is calculated using the Marcus theory for a pair of fragments in two different ways: neglecting and accounting for the effect of the environment. The latter is accomplished with the fragment molecular orbital (FMO) method. In order to apply FMO to charge transport materials (CTMs), it is first validated by comparing the accuracy and timings to full calculations without fragmentation, for several types of fragmentation models applied to dispersive and cross-linked CTMs. Secondly, the Marcus theory combined with FMO is applied to simulate charge transport phenomena using Einstein's diffusion model or kinetic Monte Carlo (KMC) method. The result of charge mobility simulation shows qualitative agreement with experiment, and KMC is found to give better results than the diffusion theory because it takes into account the directionality and the charge transport path.

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 β-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.

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 Moller-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.

The analytic energy gradient is developed for open-shell fragment molecular orbital methods (FMO) interfaced with the polarizable continuum model. A pair interaction energy decomposition analysis, spin density and atomic spin populations are also developed. The accuracy is tested on a polypeptide oxidation reaction in solution, comparing three isomers. FMO is applied to study the spin density distribution and radical stabilization of the doublet state of the ribonucleotide reductase in solution, containing 11 536 atoms.

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.

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.

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.

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.

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.

We developed the analytic second derivative of the energy for unrestricted Hartree–Fock based on the fragment molecular orbital (FMO) method. We formulated the second order derivative for the separated dimer approximation in both restricted and unrestricted methods, which accelerated the calculations by the factor of 9 for a radical system containing 704 atoms. The accuracy was evaluated for organic radicals in explicit solvent, in comparison to full ab initio results. The method was applied to study the change of IR absorption spectra in the tyrosine oxidation reaction for a polypeptide representing the active part of the photosynthetic reaction center.

We developed a dual basis approach within the fragment molecular orbital formalism enabling efficient and accurate use of large basis sets. The method was tested on water clusters and polypeptides and applied to perform geometry optimization of chignolin (PDB: 1UAO ) in solution at the level of DFT/6-31++G ∗∗ , obtaining a structure in agreement with experiment (RMSD of 0.4526 A). The polarization in polypeptides is discussed with a comparison of the α-helix and β-strand.

To obtain chemical shifts in large molecular systems accurately with a low computational cost, we developed an octahedral point-charge model that mimics the electrostatic potential due to charge distributions. The point-charges in this model are defined to reproduce the multipole moments calculated using the revised distributed multipole analysis. The accuracy of charge representations was tested on formamide. The octahedral point-charge model was used in the fragment molecular orbital method and applied to NMR calculation of a β-sheet polypeptide. The maximum errors relative to conventional ab initio NMR calculation were 0.13, 0.73, and 0.09 ppm for 13 C, 15 N, and 1 H, respectively.

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 Moller-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.

The first analytic derivative with respect to nuclear coordinates is derived for the fragment molecular orbital method used with electrostatic approximations. It is shown how response contributions due to the coupling between the electronic state of fragments and the embedding potential can be accurately and efficiently calculated. The accuracy of the analytic gradient is shown in comparison to the numerical gradient for a polypeptide and water clusters. For the largest system the overall speedup of about 4.9 is observed when approximations are used in FMO.

Protein kinase CK2 (CK2) is a ubiquitous serine/threonine protein kinase for hundreds of endogenous substrates. CK2 has been considered to be involved in many diseases, including cancers. Herein we report the discovery of a novel ATP-competitive CK2 inhibitor. Virtual screening of a compound library led to the identification of a hit 2-phenyl-1,3,4-thiadiazole compound. Subsequent structural optimization resulted in the identification of a promising 4-(thiazol-5-yl)benzoic acid derivative.

We develop the pair interaction energy decomposition analysis (PIEDA) in solution by combining the fragment molecular orbital (FMO) method with the polarizable continuum model (PCM). The solvent screening of the electrostatic interaction and the desolvation penalty in complex formation are described by this approach from ab initio calculations of fragments and their pairs. The applications to the complex of solvated sodium and chlorine ions, as well as to lysine and aspartic acid, show how the analysis helps reveal the physical picture. The PIEDA/PCM method is also applied to a small protein chignolin (PDB: 1UAO), and the solvent screening of the pair interactions is discussed.

We examined CH/π hydrogen bonds in protein/ligand complexes involving at least one proline residue using the ab initio fragment molecular orbital (FMO) method and the program CHPI. FMO calculations were carried out at the Hartree–Fock (HF)/6-31G*, HF/6-31G**, second-order Moller–Plesset perturbation (MP2)/6-31G*, and MP2/6-31G** levels for three Src homology 3 (SH3) domains and five proline-recognition domains (PRDs) complexed with their corresponding ligand peptides. PRDs use a conserved set of aromatic residues to recognize proline-rich sequences of specific ligands. Many CH/π hydrogen bonds were identified in these complexes. CH/π hydrogen bonds occurred, in particular, in the central part of the proline-rich motifs. Our results suggest that CH/π hydrogen bonds are important in the recognition of SH3 and PRDs by their ligand peptides and play a vital role in the signal transduction system. Combined use of the FMO method and CHPI analysis is a valuable tool for the study of protein/protein and protein/ligand interactions and may be useful in rational drug design. © 2011 Wiley Periodicals, Inc. J Comput Chem 2011

The kinesin spindle protein (KSP) is a mitotic kinesin involved in the establishment of a functional bipolar mitotic spindle during cell division. It is considered to be an attractive target for cancer chemotherapy with reduced side effects. Based on natural product scaffold-derived fused indole-based inhibitors and known biphenyl-type KSP inhibitors, various carboline and carbazole derivatives were synthesized and biologically evaluated. β-Carboline and lactam-fused carbazole derivatives exhibited remarkably potent KSP inhibitory activity and mitotic arrest in prometaphase with formation of an irregular monopolar spindle. The planar tri- and tetracyclic analogs inhibited KSP ATPase in an ATP-competitive manner just like biphenyl-type inhibitors.

An efficient formulation of the fragment molecular orbital method is introduced based on dividing the system into frozen and polarizable domains. The former is computed once taking into account the many-body polarization of the whole system, while the latter is recalculated for each step of a geometry optimization. We performed ligand docking and calibrated the method on the complexes of the Trp−cage miniprotein construct (PDB: 1L2Y) with neutral and charged ligands and applied it to optimize a partially solvated structure of prostaglandin H(2) synthase-1 in complex with the reversible competitive inhibitor ibuprofen (PDB: 1EQG) containing 19471 atoms at the B3LYP-D/6-31G* and RHF/STO-3G levels of theory for the polarizable and frozen domains, respectively. The optimization took 32 h on six dual CPU quad-core 2.83 GHz Xeon nodes. Our method requires no fitted parameters and allows optimizations of large systems based solely on quantum mechanics.

The selective binding between avian and human influenza A viral hemagglutinins (HA) subtype H3 and Neu5Acα2-3 and α2-6Gal (avian α2-3, human α2-6) is qualitatively rationalized by the fragment molecular orbital (FMO) method. We suggest a general model of analyzing protein-ligand interactions based on the electrostatic, polarization, dispersion, and desolvation components obtained from quantum-mechanical calculations at the MP2/6-31G(d) level with the polarizable continuum model of solvation. The favorable avian H3 (A/duck/Ukraine/1963)-avian α2-3 binding arises from the hydrophilic interaction between Gal-4 OH and side-chain NH(2)CO on Gln226, which is supported by the intermolecular hydrogen-bond network to the 1-COO group on Neu5Ac moiety. A substitution of Gln226Leu in the avian H3 HA1 domain increases the binding affinity to human α2-6 due to the Leu226···human α2-6 dispersion with a small entropic penalty during the complex formation. The remarkable human H3 (A/Aichi/2/1968)-human α2-6 binding is not governed by the Ser228-OH···OH-9 Neu5Ac hydrogen bond. These fragment-based chemical aspects can help design monovalent inhibitors of the influenza viral HA-sialoside binding and the simulation studies on the viral HAs-human α2-6 binding.

We analyzed the accuracy of the fragment molecular orbital method using various representations of the embedding potential and extended its applicability to large basis sets by proposing to use potential-derived point charges with screening combined with the adaptive frozen orbital treatment of the detached bonds. A comprehensive set of basis sets: STO-3G, 6-31G*, 6-311G*, 6-31++G**, 6-311++G**, cc-pVDZ, cc-pVTZ, aug-cc-pVDZ, and aug-cc-pVTZ was employed; for tests systems we used water clusters with 16 and 32 molecules, the alpha-helices and beta-strands of alanine containing 10 and 20 residues, as well as chignolin (PDB: 1UAO ) and Trp-cage miniprotein (PDB: 1L2Y ).

An ab initio computational method, based on the fragment molecular orbital (FMO) method, for calculating nuclear magnetic resonance (NMR) chemical shifts has been developed by introducing the concept of a merged fragment with a cutoff distance. Using point charges or density based on electrostatic potential obtained from FMO calculations, the NMR calculations (GIAO and CSGT) with the 6-31G(d) and 6-311G(d,p) basis sets were performed on α-helix and β-sheet polypeptides. The cutoff distance defines the optimal merged fragment size for NMR calculations. This method accurately reproduces electrostatic effects and magnetic susceptibilities. The chemical shifts determined with a cutoff distance not shorter than 8 A for both α-helix and β-sheet polypeptides agree well with those calculated by conventional ab initio NMR calculations.

Performing accurate calculations on large molecular systems is desirable for closed- and open-shell systems. In this work, the fragment molecular orbital method is extended to open-shell systems and implemented in the GAMESS (General Atomic and Molecular Electronic Structure System) program package. The accuracy of the method is tested, and the ability to reproduce reaction enthalpies is demonstrated. These tests also demonstrate its utility in providing an efficient means to model large open-shell systems.

A geometry analysis of Cl–π interactions in protein–ligand complex crystal structures, showed two distinct geometries: “edge-on” approach of a Cl atom to a ring atom or CC bond and “face-on” approach towards the ring centroid, with an average interatomic distance of 3.6 A. The interaction energies were estimated as a sum of the CCSD(T) correlation contribution and the Hartree–Fock energy at the complete basis set limit, for the geometries of the benzene–chlorohydrocarbon model structures at the energy minimum obtained by potential energy surface scans using RMP2(FC)/cc-pVTZ. The calculated Cl–π interaction energy was −2.01 kcal/mol, and the dispersion force was found to be the major source of attraction. We also discuss the geometry flexibility in Cl–π interactions.

We have developed and implemented the analytic energy gradient for the bond detachment scheme in the fragment molecular orbital method (FMO) suitable to describe solids, and applied it to the geometry optimization of a silicon nanowire at several levels of theory. In addition, we have examined in detail the effects of the particular choice of the fragmentation upon the accuracy and introduced a number of numerical criteria to characterize the errors. The established route is expected to provide guidance for future applications of FMO to surfaces, solids and nanosystems.

The electrostatic potential in the Fragment Molecular Orbital (FMO) method describes the effect of the environment upon fragments, but approximations are necessary to achieve linear scaling. We have developed the derivative of the point charge approximation in this study to enable accurate and fast gradient calculations for geometry optimizations and molecular dynamics of large systems. The accuracy is tested in comparison with the numeric gradient for solvated sodium cation, water cluster, α-helix of polyalanine, and hydrated chignolin. The errors are found to be reduced by approximately one order of magnitude.

The energy gradient method is introduced to the fragment molecular orbital based time-dependent density functional theory (FMO-TDDFT), which we have recently developed to calculate excitation energies of large systems by dividing them into fragments. By using the energy gradient of FMO-TDDFT, excited state geometry optimizations of a polypeptide and solvated formaldehyde are carried out using the LC-BOP functional and the 6-31G∗ basis set. The accuracy of the optimized structures and the excitation energies in comparison to conventional TDDFT is discussed.

The fragment molecular orbital method (FMO) was applied to the geometry optimization of several heparin oligosaccharides at the RHF/6-31(+)G(d) level combined with the polarizable continuum model (PCM). For comparison, GLYCAM force field optimization in explicit solvent was also conducted. Good accuracy of FMO was demonstrated in comparison to ab initio at the MP2/PCM level. The interaction analysis was conducted using the pair interaction energy decomposition analysis (PIEDA), and the role of hydrogen bonding and solvent was elucidated in the helix formation of heparin in solution. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

To improve the accuracy of the fragment molecular orbital method (FMO), we introduce a new fragmentation scheme based on using frozen orbitals to describe fractioned bonds. By applying this scheme to a set of polyalanine systems of up to 40 residues for the alpha-helix and beta-strand isomers, we established its accuracy, which is considerably improved compared to the original hybrid orbital projection method used for detaching bonds in FMO. For instance, at the two-body FMO expansion with the 6-311G* basis set, the error was typically reduced 2-4 times, and for 6-31G* the accuracy increase was even larger (10 times in terms of the maximum error). For the Trp-cage protein (PDB file 1L2Y) with many charged residues, a fairly large error was observed, which was shown to become small with a larger fragment size or at the three-body level. Consequently, we applied the new scheme to the adsorption of toluene and phenol on a faujasite zeolite, and we demonstrated that good accuracy can be achieved in reproducing ab initio results.

We applied the fragment molecular orbital (FMO) method, which enables total electronic calculations of large molecules at ab initio level, to the evaluation of binding affinities between the human progesterone receptor ligand-binding domain (PR LBD) and various steroidal ligands. The FMO calculations were performed on the entire structure of the PR LBD, which is composed of approximately 4,100 atoms. Our computational binding energies of PR LBD/ligand complexes agreed well with experimental binding affinities (r=0.909). Interaction energies between each ligand and specific amino acid residues were also obtained from the FMO calculations. The principal residues involved in the interactions with these ligands were Arg766 and Asn719, with some additional contribution by Gln725. The main factor determining differences in binding affinity of the various ligands was not interactions with particular residues, but with the binding-site residues closest to the ligand. The interfragment interaction energy analysis is proving to be a useful method for gaining detailed information on ligand binding.

An efficient computational method to calculate NMR chemical shifts of large biomolecular systems is proposed. The method is based on the fragment molecular orbital (FMO) method combined with the gauge-including atomic orbital (GIAO) and continuous set of gauge transformations (CSGT) methods. It accurately reproduced the conventional ab initio NMR values for a 10-residues peptide. The method was also applied to ubiquitin (76 amino-acid residues), and the calculated chemical shifts agree well with experimentally measured shifts. The proposed method requires a much lower computational cost than the conventional ab initio methods to calculate chemical shifts of large systems.

Time-dependent density functional theory (TDDFT) is combined with the multilayer fragment molecular orbital (FMO) method. The excitation energies of the system are estimated from those of its small active part, whereas the remaining part is described by its electron density distribution and the corresponding Coulomb field. The efficiency of this approach is illustrated on the lowest excitations of several solvated systems and phenylalanine–(alanine) n . The full TDDFT excitation energies calculated are reproduced within 0.01 eV with LC-BLYP and the 6-31G ∗ basis set.

Following the brief review of the modern fragment-based methods and other approaches to perform quantum-mechanical calculations of large systems, the theoretical development of the fragment molecular orbital method (FMO) is covered in detail, with the emphasis on the physical properties, which can be computed with FMO. The FMO-based polarizable continuum model (PCM) for treating the solvent effects in large systems and the pair interaction energy decomposition analysis (PIEDA) are described in some detail, and a range of applications of FMO to biological studies is introduced. The factors determining the relative stability of polypeptide conformers (alpha-helix, beta-turn, and extended form) are elucidated using FMO/PCM and PIEDA, and the interactions in the Trp-cage miniprotein construct (PDB: 1L2Y) are analyzed using PIEDA.

The three-body energy expansion in the fragment molecular orbital method (FMO) was applied to the 2nd order Moller–Plesset theory (MP2). The accuracy of both the two and three-body expansions was determined for water clusters, alanine n-mers (α-helices and β-strands) and one synthetic protein, using the 6-31G* and 6-311G* basis sets. At the best level of theory (three-body, two molecules/residues per fragment), the absolute errors in energy relative to ab initio MP2 were at most 1.2 and 5.0 mhartree, for the 6-31G* and 6-311G* basis sets, respectively. The relative accuracy was at worst 99.996% and 99.96%, for 6-31G* and 6-311G*, respectively. A three-body approximation was introduced and the optimum threshold value was determined. The protein calculation (6-31G*) at the production level (FMO2/2) took 3 h on 36 3.2-GHz Pentium 4 nodes and had the absolute error in the MP2 correlation energy of only 2 kcal/mol. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007

Comparative binding energy (COMBINE) analysis method is one of the QSAR techniques for the prediction of biological activities of inhibitors based on interaction energies between ligands and proteins decomposed into each amino acid residue. We supposed that the predictive ability of the COMBINE method does not depend essentially on the molecular frameworks of ligands. To verify this idea, we performed the COMBINE analysis of non-peptide inhibitors of HIV-1 protease (HIVp), where the prediction model was constructed using inhibitors with a peptide scaffold as a training set. The predictive performance of the AMBER and CHARMm force fields was very high and at the same level ( q 2 = 0.75, 0.67, SDEP cv = 0.76, 0.89, and SDEP ex = 0.92, 0.66, respectively). The high predictive ability of the COMBINE method for the distinct scaffold compounds is due to the informative description of the interaction energies for compounds that are located at the binding site. This result suggests that COMBINE analysis may be applied not only to the lead optimization stage but also to the lead evolution stages.

The approximations used in the context of the fragment molecular orbital method were critically revised, the origin of the approximation error determined and an improvement proposed. The three-body method which has been so far very expensive, was reformulated to be used with the approximations, and its efficacy both in terms of accuracy and computational timings carefully established on a set of representative systems. Timings and accuracy are reported for the two and three-body methods, including their application to two proteins 1L2Y and 1IO5 (PDB codes) and (H2O)1024 (at the RHF/6-31G∗ level).

The ab initio fragment molecular orbital calculations were performed for molecular interactions of the whole estrogen receptor (ER) ligand-binding domain with a natural ligand, 17beta-estradiol (EST). The interaction energies of the ligand at the residue level were calculated using HF and MP2 methods with several basis sets. The charge-transfer (CT) interactions were also analyzed based on configuration analysis for fragment interaction. Strong electrostatic interactions were observed between the EST and surrounding charged/polarized residues, Glu353, Arg394, His524, and Thr347. Weak electrostatic and significant van der Waals dispersion interactions were observed between the EST and the many surrounding hydrophobic residues. Together with the experimental interpretations, both interactions equally contributed to the total binding energies, and it was found that the inclusion of electron correlation was essential to obtain an appropriate picture of the interaction. The strongest interaction energy was observed between Glu353 and the EST, and the CT interactions from the lone-pair orbital of the carbonyl oxygen of Glu353 to the sigma(OmicronEta) orbital of the hydroxyl group of EST were found to be important. The CT interactions from the lone-pair orbital of EST to the sigma(NuEta) of Arg394 and from the lone-pair orbital of EST to the sigma(NuEta) of His524 were also observed. These CT interactions occurred through the hydrogen-bond networks between the ER and EST. Therefore, electron donations from the ER to the EST and electron back-donations from EST to the ER were characteristic of ER-ligand binding. Our approach provides a powerful tool to understanding detailed molecular interactions at the quantum mechanical level.

Organocopper-mediated anti-SN2' reactions of gamma-phosphoryloxy-alpha,beta-unsaturated-delta-lactams were used to prepare highly functionalized diketopiperazine mimetics. The substrate phosphates 24, 32, and 47 were prepared from alpha-amino acid-derived allylic alcohols 10 by a sequence of reactions that included ring-closing metathesis. In the reactions of phosphates with organocopper reagents, the addition of LiCl dramatically improved anti-SN2' selectivity, indicating that an organocopper cluster containing lithium chloride plays an important role in the determination of regioselectivity. This reaction system was applied to the preparation of novel low molecular weight CXCR4-chemokine receptor antagonists.

The polarizable continuum model (PCM) for the description of solvent effects is combined with the fragment molecular orbital (FMO) method at several levels of theory, using a many-body expansion of the electron density and the corresponding electrostatic potential, thereby determining solute (FMO)-solvent (PCM) interactions. The resulting method, denoted FMO/PCM, is applied to a set of model systems, including alpha-helices and beta-strands of alanine consisting of 10, 20, and 40 residues and their mutants to charged arginine and glutamate residues. The FMO/PCM error in reproducing the PCM solvation energy for a full system is found to be below 1 kcal/mol in all cases if a two-body expansion of the electron density is used in the PCM potential calculation and two residues are assigned to each fragment. The scaling of the FMO/PCM method is demonstrated to be nearly linear at all levels for polyalanine systems. A study of the relative stabilities of alpha-helices and beta-strands is performed, and the magnitude of the contributing factors is determined. The method is applied to three proteins consisting of 20, 129, and 245 residues, and the solvation energy and computational efficiency are discussed.

To elucidate the catalytic power of enzymes, we analyzed the reaction profile of Claisen rearrangement of Bacillus subtilis chorismate mutase (BsCM) by all electron quantum chemical calculations using the fragment molecular orbital (FMO) method. To the best of our knowledge, this is the first report of ab initio-based quantum chemical calculations of the entire enzyme system, where we provide a detailed analysis of the catalytic factors that accomplish transition-state stabilization (TSS). FMO calculations deliver an ab initio-level estimate of the intermolecular interaction between the substrate and the amino acid residues of the enzyme. To clarify the catalytic role of Arg90, we calculated the reaction profile of the wild-type BsCM as well as Lys90 and Cit90 mutant BsCMs. Structural refinement and the reaction path determination were performed at the ab initio QM/MM level, and FMO calculations were applied to the QM/MM refined structures. Comparison between three types of reactions established two collective catalytic factors in the BsCM reaction: (1) the hydrogen bonds connecting the Glu78-Arg90-substrate cooperatively control the stability of TS relative to the ES complex and (2) the positive charge on Arg90 polarizes the substrate in the TS region to gain more electrostatic stabilization.

We propose a modified version of configuration analysis (CA) for the fragment interaction in conjunction with Kitaura’s fragment molecular orbital (FMO) scheme. The proposal is abbreviated as CAFI. The MO sets of fragments are merged and then orthonormalized by the use of a weighted Lowdin orthonormalization. The energy calculation is performed with the concurrent electron relaxation functional (CERF). The relaxation energy is obtained in an orbital-wise fashion and is distinguished as the charge-transfer and the polarization. The utility of CAFI is demonstrated through test calculations on hydrogen-bonding systems.

We have developed a parallelized integral-direct solver for configuration interaction singles (CIS) in the A binit-mp program, by accepting the recently proposed multilayer fragment molecular orbital (MLFMO) method. In the MLFMO–CIS scheme, the region of interest in photoactive issues can be treated with the environmental potential at the Hartree–Fock (HF) level. The parallel efficiency is observed to be reasonable for the formaldehyde hydration system. A realistic applicability of the method is demonstrated for the photoactive yellow protein (PYP) including 125 amino acid residues.

We propose a parallelized integral-direct algorithm of the second-order Moller–Plesset perturbation theory (MP2) as a size-consistent correlated method. The algorithm is a modification of the recipe by Mochizuki et al. [(1996) Theor Chim Acta 93:211]. There is no need to communicate the bulky data of integrals across worker processes, keeping the formal fifth-power dependence on the number of basis functions. A multiple integral screening procedure is incorporated to reduce the operation costs effectively. An approximate MP2 density matrix can also be directly calculated through the integral contraction with orbital energies. We implement the MP2 code by accepting Kitaura’s fragment molecular orbital (FMO) scheme as in the program ABINIT-MP developed by Nakano et al. [(2002) Chem Phys Lett 351:475]. The error in the FMO–MP2 energies is found to be within the order of the chemical accuracy. Timing and parallel acceleration results are shown for test molecules.

We have recently developed a parallelized integral-direct algorithm for the second-order Moller–Plesset perturbation theory (MP2) and implemented it into the ABINIT-MP program of the fragment molecular orbital (FMO) scheme. A flexible parallelization is possible by combining the fragment indices (upper level) and the two-electron integral indices (lower level) on distributed computational resources, leading to an enhancement of in-core processings. In this Letter, we carry out a series of benchmark FMO–MP2 calculations of realistic proteins consisting of the tens of thousands of basis functions. The performance is shown to be high, indicating that the ABINIT-MP program is easily applicable to the realistic systems.