Application of a semi-empirical dispersion correction for modeling water clusters

The Grimme-D3 semi-empirical dispersion energy correction has been implemented for the original effective fragment potential for water (EFP1), and for systems that contain water molecules described by both correlated ab initio quantum mechanical (QM) molecules and EFP1. Binding energies obtained with these EFP1-D and QM/EFP1-D methods were tested using 27 benchmark species, including neutral, protonated, deprotonated, and auto-ionized water clusters and nine solute–water binary complexes. The EFP1-D and QM/EFP1-D binding energies are compared with those obtained using fully QM methods: second-order perturbation theory, and coupled cluster theory, CCSD(T), at the complete basis set (CBS) limit. The results show that the EFP1-D and QM/EFP1-D binding energies are in good agreement with CCSD(T)/CBS binding energies with a mean absolute error of 5.9 kcal/mol for water clusters and 0.8 kcal/mol for solute–water binary complexes. © 2018 Wiley Periodicals, Inc.     

Solvent effects on the S(N)2 reaction: Application of the density functional theory-based effective fragment potential method

The performance of the density functional theory (DFT)-based effective fragment potential (EFP) method is assessed using the S(N)2 reaction: Cl- + nH2O + CH3Br = CH3Cl + Br- + nH2O. The effect of the systematic addition of water molecules on the structures and relative energies of all species involved in the reaction has been studied. The EFP1 method is compared with second-order perturbation theory (MP2) and DFT results for n = 1, 2, and 3, and EFP1 results are also presented for four water molecules. The incremental hydration effects on the barrier height are the same for all methods. However, only full MP2 or MP2 with EFP1 solvent molecules are able to provide an accurate treatment of the transition state (TS) and hence the central barriers. Full DFT and DFT with EFP1 solvent molecules both predict central barriers that are too small. The results illustrate that the EFP1-based DFT method gives reliable results when combined with an accurate quantum mechanical (QM) method, so it may be used as an efficient alternative to fully QM methods in the treatment of larger microsolvated systems.     

Analytic energy gradient in combined second-order Møller-Plesset perturbation theory and polarizable force field calculation

Second-order M?ller-Plesset perturbation theory (MP2) is used to describe electronic correlation on the basis of Hartree-Fock (HF) variational calculations that incorporate induced dipole polarizable force fields (i.e., QM/MMpol style HF and MP2). The Z-vector equations for regular closed shell and open shell MP2 methods (RMP2, ZAPT2, and UMP2) are extended to include induced dipole contributions to determine the MP2 response density so that nuclear gradient and other properties can be efficiently evaluated. A better estimation of the induced dipole polarization energy can be obtained using the MP2 relaxed density. QM/MMpol style MP2 molecular dynamics simulations are performed for the ground state and first triplet state of acetone solvated by 1024 polarizable water molecules. A switching function is used to ensure energy conservation in QM/MM simulation under periodic boundary condition.     

The effective fragment potential: small clusters and radial distribution functions

The effective fragment potential (EFP) method for treating solvent effects provides relative energies and structures that are in excellent agreement with the analogous fully quantum [i.e., Hartree-Fock (HF), density functional theory (DFT), and second order perturbation theory (MP2)] results for small water clusters. The ability of the method to predict bulk water properties with a comparable accuracy is assessed by performing EFP molecular dynamics simulations. The resulting radial distribution functions (RDF) suggest that as the underlying quantum method is improved from HF to DFT to MP2, the agreement with the experimental RDF also improves. The MP2-based EFP method yields a RDF that is in excellent agreement with experiment.     

Higher order alchemical derivatives from coupled perturbed self-consistent field theory

We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the "surrounding" molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals.     

Analytic gradient and molecular dynamics simulations using the fragment molecular orbital method combined with effective potentials

The completely analytic energy gradients are derived and implemented for the two-body fragment molecular orbital (FMO2) method combined with the model core potentials (MCP) and effective fragment potentials (EFP). The many-body terms in EFP require solving coupled-perturbed Hartree-Fock equations, which are derived and implemented. The molecular dynamics (MD) simulations are performed using the FMO2/MCP method for the capped alanine decamer and with the FMO2/EFP method for the zwitterionic conformer of glycine tetramer immersed in the water layer of 6.0 Å (135 water molecules). The results of the MD simulations using the FMO2/EFP and FMO2/MCP gradients show that the total energy is conserved at the time steps less than 1 fs.     

Fast fragments: the development of a parallel effective fragment potential method

The Effective Fragment Potential (EFP) method for solvation decreases the cost of a fully quantum mechanical calculation by dividing a chemical system into an ab initio region that contains the solute plus some number of solvent molecules, if desired, and an "effective fragment" region that contains the remaining solvent molecules. Interactions introduced with this fragment region (for example, Coulomb and polarization interactions) are added as one-electron terms to the total system Hamiltonian. As larger systems and dynamics are just starting to be studied with the EFP method, more needs to be done to decrease the calculation time of the method. This article considers parallelization of both the EFP fragment-fragment and mixed quantum mechanics (QM)-EFP interaction energy and gradient computation within the GAMESS suite of programs. The iteratively self-consistent polarization term is treated with a new algorithm that makes use of nonblocking communication to obtain better scalability. Results show that reasonable speedup is achieved with a variety of sizes of water clusters and number of processors.     

Gradients of the polarization energy in the effective fragment potential method

The effective fragment potential (EFP) method is an ab initio based polarizable classical method in which the intermolecular interaction parameters are obtained from preparative ab initio calculations on isolated molecules. The polarization energy in the EFP method is modeled with asymmetric anisotropic dipole polarizability tensors located at the centroids of localized bond and lone pair orbitals of the molecules. Analytic expressions for the translational and rotational gradients (forces and torques) of the EFP polarization energy have been derived and implemented. Periodic boundary conditions (the minimum image convention) and switching functions have also been implemented for the polarization energy, as well as for other EFP interaction terms. With these improvements, molecular dynamics simulations can be performed with the EFP method for various chemical systems.     

Interactions between phosphate and water in solution: a natural bond orbital based analysis in a QM/MM framework

The natural bond orbital (NBO) and natural energy decomposition analysis (NEDA) calculations are used to analyze the interaction between mono-methyl phosphate-ester (MMP) and its solvation environment in a combined quantum mechanical/molecular mechanical (QM/MM) framework. The solute-solvent configurations are generated using a specific parametrization of the self-consistent-charge density functional tight-binding (SCC-DFTB) model for the MMP and TIP3P for water. The NBO and NEDA calculations are done with several QM/MM partitioning schemes with HF/6-31+G** as the QM level. Regardless of the size of the QM region, a notable amount of charge transfer is observed between MMP and the neighboring water molecules and the charge-transfer interactions are, in the NEDA framework, as important as the electric (electrostatic and polarization) components. This work illustrates that NBO based analyses are effective tools for probing intermolecular interactions in condensed phase systems.     

Benzene-pyridine interactions predicted by the effective fragment potential method

The accurate representation of nitrogen-containing heterocycles is essential for modeling biological systems. In this study, the general effective fragment potential (EFP2) method is used to model dimers of benzene and pyridine, complexes for which high-level theoretical data -including large basis spin-component-scaled second-order perturbation theory (SCS-MP2), symmetry-adapted perturbation theory (SAPT), and coupled cluster with singles, doubles, and perturbative triples (CCSD(T))-are available. An extensive comparison of potential energy curves and components of the interaction energy is presented for sandwich, T-shaped, parallel displaced, and hydrogen-bonded structures of these dimers. EFP2 and CCSD(T) potential energy curves for the sandwich, T-shaped, and hydrogen-bonded dimers have an average root-mean-square deviation (RMSD) of 0.49 kcal/mol; EFP2 and SCS-MP2 curves for the parallel displaced dimers have an average RMSD of 0.52 kcal/mol. Additionally, results are presented from an EFP2 Monte Carlo/simulated annealing (MC/SA) computation to sample the potential energy surface of the benzene-pyridine and pyridine dimers.     

(BN)n团簇的结构和稳定性

用HF方法、密度泛函理论的B3LYP以及微扰理论的MP2方法，在6—31G(d)基组 水平上，对(BN)n(n=1-16)团簇的各种可能结构进行了优化．讨论了环状与笼状稳 定团簇的几何构型、自然键轨道(NBO）、振动频率、结合能、核独立化学位移 (NICS)和能量二次差分，得到了(BN)n(n＝1-16)团簇结构的稳定性信息．比较了 HF，B3LYP以及MP2三种理论方法对(BN)n团簇的适应性所表现出的差异．     

Binding free energies in the SAMPL6 octa-acid host–guest challenge calculated with MM and QM methods

We have estimated free energies for the binding of eight carboxylate ligands to two variants of the octa-acid deep-cavity host in the SAMPL6 blind-test challenge (with or without endo methyl groups on the four upper-rim benzoate groups, OAM and OAH, respectively). We employed free-energy perturbation (FEP) for relative binding energies at the molecular mechanics (MM) and the combined quantum mechanical (QM) and MM (QM/MM) levels, the latter obtained with the reference-potential approach with QM/MM sampling for the MM → QM/MM FEP. The semiempirical QM method PM6-DH+ was employed for the ligand in the latter calculations. Moreover, binding free energies were also estimated from QM/MM optimised structures, combined with COSMO-RS estimates of the solvation energy and thermostatistical corrections from MM frequencies. They were performed at the PM6-DH+ level of theory with the full host and guest molecule in the QM system (and also four water molecules in the geometry optimisations) for 10–20 snapshots from molecular dynamics simulations of the complex. Finally, the structure with the lowest free energy was recalculated using the dispersion-corrected density-functional theory method TPSS-D3, for both the structure and the energy. The two FEP approaches gave similar results (PM6-DH+/MM slightly better for OAM), which were among the five submissions with the best performance in the challenge and gave the best results without any fit to data from the SAMPL5 challenge, with mean absolute deviations (MAD) of 2.4–5.2 kJ/mol and a correlation coefficient (R²) of 0.77–0.93. This is the first time QM/MM approaches give binding free energies that are competitive to those obtained with MM for the octa-acid host. The QM/MM-optimised structures gave somewhat worse performance (MAD?=?3–8 kJ/mol and R²?=?0.1–0.9), but the results were improved compared to previous studies of this system with similar methods.     

Energy analysis of weak electron-donor-acceptor complexes and water clusters with the perturbation theory based on the locally projected molecular orbitals: charge-transfer and dispersion terms

The third order single excitation perturbation theory corrected with the dispersion energy based on the locally projected molecular orbital was applied to study the weak electron-donor-acceptor (charge-transfer) complexes and the hydrogen bonds in the water clusters. In the weak electron-donor-acceptor complexes, the dispersion energy is larger than the charge-transfer energy in absolute value. The dispersion energy is as large as the charge-transfer energy in the hydrogen bond. The cage form of (H(2)O)(6) is the most stable among eight isomers examined, because the dispersion energy is the largest among them.     

Electrostatic energy in the effective fragment potential method: theory and application to benzene dimer

Evaluation of the electrostatic energy within the effective fragment potential (EFP) method is presented. The performance of two variants of the distributed multipole analysis (DMA) together with two different models for estimating the charge penetration energies was studied using six homonuclear dimers. The importance of damping the higher order multipole terms, i.e. charge dipole, was also investigated. Damping corrections recover more than 70% of the charge penetration energy in all dimers, whereas higher order damping introduces only minor improvement. Electrostatic energies calculated by the numerical DMA are less accurate than those calculated by the analytic DMA. Analysis of bonding in the benzene dimer shows that EFP with inclusion of the electrostatic damping term performs very well compared to the high-level coupled cluster singles, doubles, and perturbative triples method. The largest error of 0.4 kcal/mol occurs for the sandwich dimer configuration. This error is about half the size of the corresponding error in second order perturbation theory. Thus, EFP in the current implementation is an accurate and computationally inexpensive method for calculating interaction energies in weakly bonded molecular complexes.     

Binding affinities by alchemical perturbation using QM/MM with a large QM system and polarizable MM model

The most general way to improve the accuracy of binding‐affinity calculations for protein–ligand systems is to use quantum‐mechanical (QM) methods together with rigorous alchemical‐perturbation (AP) methods. We explore this approach by calculating the relative binding free energy of two synthetic disaccharides binding to galectin‐3 at a reasonably high QM level (dispersion‐corrected density functional theory with a triple‐zeta basis set) and with a sufficiently large QM system to include all short‐range interactions with the ligand (744–748 atoms). The rest of the protein is treated as a collection of atomic multipoles (up to quadrupoles) and polarizabilities. Several methods for evaluating the binding free energy from the 3600 QM calculations are investigated in terms of stability and accuracy. In particular, methods using QM calculations only at the endpoints of the transformation are compared with the recently proposed non‐Boltzmann Bennett acceptance ratio (NBB) method that uses QM calculations at several stages of the transformation. Unfortunately, none of the rigorous approaches give sufficient statistical precision. However, a novel approximate method, involving the direct use of QM energies in the Bennett acceptance ratio method, gives similar results as NBB but with better precision, ～3 kJ/mol. The statistical error can be further reduced by performing a greater number of QM calculations. © 2015 Wiley Periodicals, Inc.     

Theoretical study of vitamin properties from combined QM-MM methods: Comparison of chemical shifts and energy

The combination of quantum mechanics (QM) and molecular mechanics (MM) methods has become an alternative tool for many applications for which pure QM and MM are not suitable. The QM-MM method has been used for different types of problems, for example, structural biology, surface phenomena, and the liquid phase. In this paper, we have implemented these methods for vitamins, an important kind of biological molecule, and then compared results. The calculations were done by the full ab initio method (HF/3–21 g and HF/6–31 g) and QM-MM (ONIOM) method with HF(3–21 g)/AM1/UFF; then, we found that the geometry obtained by the QM-MM method is very accurate and this rapid method can be used in place of time consuming ab initio methods for large molecules. A comparison of energy values in the QM-MM and QM methods is given. We compare chemical shifts and conclude that the QM-MM method is a perturbed full QM method. The text was submitted by the authors in English.     

BeH2与HX(X=F,Cl, Br,I)形成的二氢键复合物的结构特征与本质

对BeH2与HX(X=F, Cl, Br, I)形成的二氢键复合物的结构特征及本质进行了探讨. 在MP2/6-311++G(3d,3p)水平优化、频率验证, 得到复合物的分子结构, 用分子间距离及电子密度拓扑理论确认BeH2与卤化氢已形成了二氢键型复合物. 在MP2/6-311++G(3d, 3p)水平下进行基函数重叠误差(BSSE)校正后的结合能在-14.468 kJ·mol-1到-5.464 kJ·mol-1之间.用对称匹配微扰理论(SAPT)对复合物的结合能进行分解, 结果表明, BeH2…HX二氢键复合物中静电能对总吸引能的贡献都是最主要的, 但交换排斥能、诱导能、色散能对总结合能的贡献也很重要. 从BeH2…HF到BeH2…HI, 诱导能对总吸引能的贡献从37.8%逐渐减小到24.0%. 而色散能对总吸引能的贡献从BeH2…HF体系中的16.0%逐渐增加到BeH2…HI体系中的33.8%.     

Accurate assessment of the strain energy in a protein-bound drug using QM/MM X-ray refinement and converged quantum chemistry

An ongoing question regarding the energetics of protein‐ligand binding has been; what is the strain energy that a ligand pays (if any) when binding to its protein target? The traditional method to estimate strain energy uses force fields to calculate the energy difference between the ligand bound conformation and its nearest local minimum/global minimum on the gas‐phase or aqueous phase potential energy surface. This makes the implicit assumption that the underlying force field as well as the reference crystal structure is accurate. Herein, we use ibuprofen as a test case and compare MMFF and ab initio QM methods to identify the local and global minimum conformations. Nine low energy conformations were identified with HF/6‐31G* geometry optimization in vacuo. We also obtained highly accurate relative energies for ibuprofen's conformational energy surface based on M06/aug‐cc‐pVXZ (X = D and T), MP2/aug‐cc‐pVXZ (X = D and T) and the MP2/CBS method (with and without solvent corrections). Moreover, we curate and re‐refine the ibuprofen‐protein complex (PDB 2BXG) using QM/MM X‐ray refinement approaches (HF/6‐31G* was the QM method and the MM model was the AMBER force field ff99sb), which were compared with the low energy conformers to calculate the strain energy. The result indicates that there was an 88% reduction in ibuprofen conformation strain using the QM/MM refined structure versus the original PDB ibuprofen conformations. Furthermore, our results indicate that, due to its inherent limitations in estimating electrostatic interactions, force fields are not suitable to gauge strain energy for charged drug molecules like ibuprofen. The present work offers a carefully validated conformational potential energy surface for a drug molecule as well as a reliable QM/MM re‐refined X‐ray structure that can be used to test current structure‐based drug design approaches. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Quantum chemical calculations of reduction potentials of AnO2(2+)/AnO2+ (An = U, Np, Pu, Am) and Fe3+/Fe2+ couples

The reduction potentials of the AnO(2)(H(2)O)(5)(2+)/AnO(2)(H(2)O)(5)(+) couple (An = U, Np, Pu, and Am) and Fe(H(2)O)(6)(3+) to Fe(H(2)O)(6)(2+) in aqueous solution were calculated at MP2, CASPT2, and CCSD(T) levels of theory. Spin-orbit effects for all species were estimated at the CASSCF level. Solvation of the hydrated metal cations was modeled both by polarizable conductor model (PCM) calculation and by solvating the solutes with over one thousand TIP3P water molecules in the QM/MM framework. The redox reaction energy calculated by QM/MM method agreed well with the PCM method after corrections using the classical Born formula for the contribution from the rest of the solvation sphere and correction for dynamic response of solvent polarization in the MM region. Calculated reduction potentials inclusive of spin-orbit effect, zero-point energy, thermal corrections, entropy effect, and PCM solvation energy were found to be comparable with experimental data. The difference between CASPT2 calculated and experimental reduction energies were less than 35 kJ/mol in all cases, which ensures that CASPT2 (and CCSD(T)) calculations provide reasonable estimates of the thermochemistry of these reactions.