Fragment Molecular Orbital Research Articles

Efficient and accurate fragmentation methods.

Conspectus Three novel fragmentation methods that are available in the electronic structure program GAMESS (general atomic and molecular electronic structure system) are discussed in this Account. The fragment molecular orbital (FMO) method can be combined with any electronic structure method to perform accurate calculations on large molecular species with no reliance on capping atoms or empirical parameters. The FMO method is highly scalable and can take advantage of massively parallel computer systems. For example, the method has been shown to scale nearly linearly on up to 131 000 processor cores for calculations on large water clusters. There have been many applications of the FMO method to large molecular clusters, to biomolecules (e.g., proteins), and to materials that are used as heterogeneous catalysts. The effective fragment potential (EFP) method is a model potential approach that is fully derived from first principles and has no empirically fitted parameters. Consequently, an EFP can be generated for any molecule by a simple preparatory GAMESS calculation. The EFP method provides accurate descriptions of all types of intermolecular interactions, including Coulombic interactions, polarization/induction, exchange repulsion, dispersion, and charge transfer. The EFP method has been applied successfully to the study of liquid water, π-stacking in substituted benzenes and in DNA base pairs, solvent effects on positive and negative ions, electronic spectra and dynamics, non-adiabatic phenomena in electronic excited states, and nonlinear excited state properties. The effective fragment molecular orbital (EFMO) method is a merger of the FMO and EFP methods, in which interfragment interactions are described by the EFP potential, rather than the less accurate electrostatic potential. The use of EFP in this manner facilitates the use of a smaller value for the distance cut-off (Rcut). Rcut determines the distance at which EFP interactions replace fully quantum mechanical calculations on fragment-fragment (dimer) interactions. The EFMO method is both more accurate and more computationally efficient than the most commonly used FMO implementation (FMO2), in which all dimers are explicitly included in the calculation. While the FMO2 method itself does not incorporate three-body interactions, such interactions are included in the EFMO method via the EFP self-consistent induction term. Several applications (ranging from clusters to proteins) of the three methods are discussed to demonstrate their efficacy. The EFMO method will be especially exciting once the analytic gradients have been completed, because this will allow geometry optimizations, the prediction of vibrational spectra, reaction path following, and molecular dynamics simulations using the method.

Molecular tailoring approach: a route for ab initio treatment of large clusters.

Conspectus Chemistry on the scale of molecular clusters may be dramatically different from that in the macroscopic bulk. Greater understanding of chemistry in this size regime could greatly influence fields such as materials science and atmospheric and environmental chemistry. Recent advances in experimental techniques and computational resources have led to accurate investigations of the energies and spectral properties of weakly bonded molecular clusters. These have enabled researchers to learn how the physicochemical properties evolve from individual molecules to bulk materials and to understand the growth patterns of clusters. Experimental techniques such as infrared, microwave, and photoelectron spectroscopy are the most popular and powerful tools for probing molecular clusters. In general, these experimental techniques do not directly reveal the atomistic details of the clusters but provide data from which the structural details need to be unearthed. Furthermore, the resolution of the spectral properties of energetically close cluster conformers can be prohibitively difficult. Thus, these investigations of molecular aggregates require a combination of experiments and theory. On the theoretical front, researchers have been actively engaged in quantum chemical ab initio calculations as well as simulation-based studies for the last few decades. To obtain reliable results, there is a need to use correlated methods such as Møller-Plesset second order method, coupled cluster theory, or dispersion corrected density functional theory. However, due to nonlinear scaling of these methods, optimizing the geometry of large clusters still remains a formidable quantum chemistry challenge. Fragment-based methods, such as divide-and-conquer, molecular tailoring approach (MTA), fragment molecular orbitals, and generalized energy-based fragmentation approach, provide alternatives for overcoming the scaling problem for spatially extended molecular systems. Within MTA, a large system is broken down into two or more subsystems that can be readily treated computationally. Finally, the properties of the large system are obtained by patching the corresponding properties of all the subsystems. Due to these approximations, the resulting MTA-based energies carry some error in comparison with calculations based on the full system. An approach for correcting these errors has been attempted by grafting the error at a lower basis set onto a higher basis set. Furthermore, investigating the growth patterns and nucleation processes in clusters is necessary for understanding the structural transitions and the phenomena of magic numbers in cluster chemistry. Therefore, systematic building-up or the introduction of stochastics for generating molecular assemblies is the most crucial step for studying large clusters. In this Account, we discuss the working principle of MTA for probing molecular clusters at ab initio level followed by a brief summary of an automated and electrostatics-guided algorithm for building molecular assemblies. The molecular aggregates presented here as test cases are generated based on either an electrostatic criterion or the basin hopping method. At MP2 level computation, the errors in MTA-based grafted energies are typically reduced to a submillihartree level, reflecting the potential of finding accurate energies of molecular clusters much more quickly. In summary, MTA provides a platform for effectively studying large molecular clusters at ab initio level of theory using minimal computer hardware.

The DFT+Umol method and its application to the adsorption of CO on platinum model clusters

Semi-local DFT approximations are well-known for their difficulty with describing the correct site preference for the adsorption of CO molecules on (111) surfaces of several late transition metals. To address this problem originating from a residual self-interaction in the CO LUMO, we present the DFT+Umol approach which generalizes the empirical DFT+U correction to fragment molecular orbitals. This correction is applied to examine CO adsorption energies at various sites on the (111) facets of cuboctahedral clusters Ptm(CO)8 (m = 79, 140, 225). The DFT+Umol correction leaves the electronic ground state of metal clusters, in particular their d-band structure, essentially unchanged, affecting almost exclusively the energy of the CO LUMO. As a result, that correction is significantly stronger for complexes at hollow sites, hence increases the propensity for adsorption at top sites. We also analyze competing edge effects on the (111) facets of the cluster models.

Efficient vibrational analysis for unrestricted Hartree–Fock based on the fragment molecular orbital method

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.

Effect of D23N mutation on the dimer conformation of amyloid β-proteins: Ab initio molecular simulations in water

The molecular pathogenesis of Alzheimer's disease (AD) is deeply involved in aggregations of amyloid β-proteins (Aβ) in a diseased brain. The recent experimental studies indicated that the mutation of Asp23 by Asn (D23N) within the coding sequence of Aβ increases the risk for the pathogeny of cerebral amyloid angiopathy and early-onset familial ADs. Fibrils of the D23N mutated Aβs can form both parallel and antiparallel structures, and the parallel one is considered to be associated with the pathogeny. However, the structure and the aggregation mechanism of the mutated Aβ fibrils are not elucidated at atomic and electronic levels. We here investigated solvated structures of the two types of Aβ dimers, each of which is composed of the wild-type or the D23N mutated Aβ, using classical molecular mechanics and ab initio fragment molecular orbital (FMO) methods, in order to reveal the effect of the D23N mutation on the structure of Aβ dimer as well as the specific interactions between the Aβ monomers. The results elucidate that the effect of the D23N mutation is significant for the parallel structure of Aβ dimer and that the solvating water molecules around the Aβ dimer have significant contribution to the stability of Aβ dimer.

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.

Binding affinity between AhR and exogenous/endogenous ligands: molecular simulations and biological experiment

Aryl hydrocarbon receptor (AhR) plays critical roles in cell differentiation, and its mechanism is controlled by exogenous and endogenous ligands. However, structures of AhR and its complex with ligand have not been determined by experimental structural biology. We here obtain stable structures of the complexes with rat AhR (rAhR) and some ligands in water by molecular simulations based on homology modelling, protein–ligand docking, classical molecular mechanics optimisation and ab initio fragment molecular orbital (FMO) calculations. In addition, the binding affinities and the specific interactions between rAhR and the ligands are investigated by ab initio FMO calculations and biological experiments. The experiments reveal the dependence of the rAhR-mediated transcriptional activation on the ligand binding. On the other hand, the results of FMO calculations elucidate that the exogenous ligands interact with many residues of rAhR, while the endogenous ligands interact specifically with a few residues, and that the side chain of Gln381 of rAhR interacts strongly with the oxygen atom located at the centre of the ligand. Furthermore, we evaluate the binding energies between rAhR and the ligands by the FMO method and compare them with the transcriptional activation obtained by the experiment.

Accuracy of the fragment molecular orbital (FMO) calculations for DNA: Total energy, molecular orbital, and inter-fragment interaction energy

The fragment molecular orbital (FMO) method can calculate the electronic structure of macromolecules such as DNA by dividing them into several fragments and introducing suitable approximations. To establish guiding principles for FMO calculation of DNA, benchmark tests were performed for several small DNA models consisting of one or two bases or two base pairs. The effects of several factors on the accuracy of FMO calculations were investigated, including the methods used to fragment the nucleotide units, approximations for the electrostatic potential, charge neutralization, and electron correlation. It was found that charge neutralization is indispensable for the reliable calculation of energies and spatial distribution of molecular orbitals, but not necessarily so for inter-fragment interaction energy analyses, such as calculation of the base–base interaction. The electrostatic approximations were shown to have only an insignificant effect on the qualitative nature of the calculations. It was also confirmed that the base–base stacking energy can be reproduced semi-quantitatively by the Møller–Plesset second-order perturbation (MP2) method though with some overestimation, and that the overestimation can be alleviated by the spin-component-scaled MP2 method.

Affinity of HIV-1 antibody 2G12 with monosaccharides: A theoretical study based on explicit and implicit water models

In order to develop potential ligands to HIV-1 antibody 2G12 toward HIV-1 vaccine, binding mechanisms of the antibody 2G12 with the glycan ligand of d-mannose and d-fructose were theoretically examined. d-Fructose, whose molecular structure is slightly different from d-mannose, has experimentally shown to have stronger binding affinity to the antibody than that of d-mannose. To clarify the nature of d-fructose's higher binding affinity over d-mannose, we studied interaction between the monosaccharides and the antibody using ab initio fragment molecular orbital (FMO) method considering solvation effect as implicit model (FMO-PCM) as well as explicit water model. The calculated binding free energies of the glycans were qualitatively well consistent with the experimentally reported order of their affinities with the antibody 2G12. In addition, the FMO-PCM calculation elucidated the advantages of d-fructose over d-mannose in the solvation energy as well as the entropic contribution term obtained by MD simulations. The effects of explicit water molecules observed in the X-ray crystal structure were also scrutinized by means of FMO methods. Significant pair interaction energies among d-fructose, amino acids, and water molecules were uncovered, which indicated contributions from the water molecules to the strong binding ability of d-fructose to the antibody 2G12. These FMO calculation results of explicit water model as well as implicit water model indicated that the strong binding of d-fructose over d-mannose was due to the solvation effects on the d-fructose interaction energy.

FMO法を用いた核内受容体–リガンド間の相互作用解析

FMO法を用いた核内受容体–リガンド間の相互作用解析

CHEMICAL DESCRIPTION OF THE INTERACTION BETWEEN GLYCAN LIGAND AND SIGLEC-7 USINGAB INITIOFMO METHOD AND CLASSICAL MD SIMULATION

We clarified in detail the theoretical features of the interaction between the glycan ligand containing α(2,8)-disialyl residue and a lectin called Siglec (sialic acid Ig-like binding lectin)-7 by ab initio fragment molecular orbital (FMO) calculations and classical molecular dynamics (MD) simulations. By comparing the ligand–Siglec-7 interaction of the wild-type Siglec-7 and those of mutant-Siglec-7s, we herein describe protein–glycan interactions thoroughly, and provide fundamentals to elucidate ligand-recognition mechanism. The experimentally observed decrease in ligand binding produced by mutagenesis at residues in non-active site was explained with MD simulations; both Trp85 and Trp74 residues are fundamental in structural stability of the Siglec-7, which is involved in the binding of the glycan ligand. The interaction energies obtained by the FMO method were consistent with the experimental ligand-binding results. The glycan ligand preferentially interacted with Siglec-7 via sialic acid residues. The stabilization by the dispersion interaction between the neutral parts of the ligand was also considerable in the binding.

Trimer effects in fragment molecular orbital-linear combination of molecular orbitals calculation of one-electron orbitals for biomolecules

The fragment molecular orbital (FMO)-linear combination of molecular orbitals (LCMO) method incorporates as an efficient post-process calculation of one-electron orbitals of the whole system after the FMO total energy calculation. A straightforward way to increase the accuracy is inclusion of the trimer effect. Here, we derive a comprehensive formulation called the FMO3-LCMO method. To keep the computational costs of the trimer term low enough, we use a matrix-size reduction technique. We evaluated the accuracy and efficiency of the FMO3-LCMO scheme in model biological systems (alanine oligomer and chignolin). The results show that delocalized electronic orbitals with covalent and hydrogen bonds are better described at the trimer level, and the FMO3-LCMO method is applicable to quantitative evaluations of a wide range of frontier orbitals in large biosystems.

Ab Initio Study of Molecular Interactions in Cellulose Iα

Biomass recalcitrance, the resistance of cellulosic biomass to degradation, is due in part to the stability of the hydrogen bond network and stacking forces between the polysaccharide chains in cellulose microfibers. The fragment molecular orbital (FMO) method at the correlated Møller-Plesset second order perturbation level of theory was used on a model of the crystalline cellulose Iα core with a total of 144 glucose units. These computations show that the intersheet chain interactions are stronger than the intrasheet chain interactions for the crystalline structure, while they are more similar to each other for a relaxed structure. An FMO chain pair interaction energy decomposition analysis for both the crystal and relaxed structures reveals an intricate interplay between electrostatic, dispersion, charge transfer, and exchange repulsion effects. The role of the primary alcohol groups in stabilizing the interchain hydrogen bond network in the inner sheet of the crystal and relaxed structures of cellulose Iα, where edge effects are absent, was analyzed. The maximum attractive intrasheet interaction is observed for the GT-TG residue pair with one intrasheet hydrogen bond, suggesting that the relative orientation of the residues is as important as the hydrogen bond network in strengthening the interaction between the residues.

Theoretical interpretations of electronic and fluorescence spectra of new 2(1H)-pyridone derivatives in solution and solid state

A combined experimental and computational study was performed for the spectroscopic properties of novel 2(1H)-pyridones. The compounds were found to be virtually non-fluorescence in solution while modestly fluorescent in solid state. The solvent effects on the UV–vis and fluorescence maxima were estimated by means of a series of ab-initio quantum chemical calculations in conjunction with Polarizable Continuum Model (PCM) method. Influence of structural displacements and intermolecular interactions in crystalline state were examined in details on the spectra of two representative compounds by using Fragment Molecular Orbital (FMO) scheme. The FMO pair interaction analysis of the spectra indicate that (1) intermolecular hydrogen bonds provoke bathochromic shifts (2) electrostatic interactions induce hypsochromic shifts (3) crystal packing effects induce hypsochromic shifts in total from the maxima in vacuo.

Interaction analysis of HIV-1 antibody 2G12 and Man9GlcNAc2 ligand: Theoretical calculations by fragment molecular orbital and MD methods

In HIV-1 infection, human antibody 2G12 is capable of recognizing the high-mannose glycans on the HIV-1 surface glycoprotein, gp120. To investigate the ligand binding mechanisms of antibody 2G12 with glycans aiming for the contribution to the medications, we carried out classical molecular dynamics (MD) simulations and ab initio fragment molecular orbital (FMO) calculations on the antibody 2G12 complex with its high-mannose ligand. We found that Mannose D1 of the ligand had the largest binding affinity with the antibody, which was well consistent with experimental reports. Furthermore, significant roles of Mannose 4 and 4′ in the ligand binding were theoretically indicated.

Geometry Optimization and Stability of Hydrated Trialanine: FMO/EFP Study

The fragment molecular orbital (FMO) method interfaced with effective fragment potentials (EFP), denoted by FMO/EFP, was developed and applied to polypeptides solvated in water. The structures of neutral and zwitterionic trialanine immersed in water layers of 3.0, 3.5, 4.0, 4.5 and 5.0 A were investigated by performing FMO/EFP geometry optimizations at the RHF/cc-pVDZ level of theory. Using the optimized geometries, the relative stability of the hydrated zwitterionic and neutral structures is discussed structurally and in terms of energetics at the second-order Moller-Plesset theory (MP2)/cc-pVDZ level.

Stable conformation of full-length amyloid-β (1–42) monomer in water: Replica exchange molecular dynamics and ab initio molecular orbital simulations

Aggregation of amyloid β-proteins (Aβ) plays a key role in the mechanism of molecular pathogenesis of Alzheimer’s disease (AD). It is known that full-length Aβ(1–42) is more prone to aggregation than Aβ(1–40). We here search stable conformations of solvated Aβ(1–42) monomer by replica exchange molecular dynamics simulations based on classical force fields, and the most stable conformation is determined from the total energies evaluated by the ab initio fragment molecular orbital (FMO) calculations. In addition, based on the FMO results, the amino acid residues of Aβ(1–42) contributing to the stabilization of the monomer are highlighted.

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.

Fully Integrated Effective Fragment Molecular Orbital Method.

In this work, the effective fragment potential (EFP) method is fully integrated (FI) into the fragment molecular orbital (FMO) method to produce an effective fragment molecular orbital (EFMO) method that is able to account for all of the fundamental types of both bonded and intermolecular interactions, including many-body effects, in an accurate and efficient manner. The accuracy of the method is tested and compared to both the standard FMO method as well as to fully ab initio methods. It is shown that the FIEFMO method provides significant reductions in error while at the same time reducing the computational cost associated with standard FMO calculations by up to 96%.

Diffusion energy profiles in silica mesoporous molecular sieves modelled with the fragment molecular orbital method

The fragment molecular orbital (FMO) method is used to model truncated portions of mesoporous silica nanoparticle (MSN) pores. The application of the FMO/RHF (restricted Hartree–Fock) method to MCM-41 type MSNs is discussed and an error analysis is given. The FMO/RHF method is shown to reliably approximate the RHF energy (error ∼0.2 kcal/mol), dipole moment (error ∼0.2 debye) and energy gradient (root mean square [RMS] error ∼0.2 × 10−3 a.u./bohr). Several FMO fragmentation schemes are employed to provide guidance for future applications to MSN models. An MSN pore model is functionalised with (phenyl)propyl substituents and the diffusion barrier for benzene passing through the pore is computed by the FMO/RHF-D method with the Grimme dispersion correction (RHF-D). For the reaction coordinates examined here, the maximum FMO/RHF-D interaction energies range from −0.3 to −5.8 kcal/mol.