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.     

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.     

The dispersion interaction between quantum mechanics and effective fragment potential molecules

A method for calculating the dispersion energy between molecules modeled with the general effective fragment potential (EFP2) method and those modeled using a full quantum mechanics (QM) method, e.g., Hartree-Fock (HF) or second-order perturbation theory, is presented. C(6) dispersion coefficients are calculated for pairs of orbitals using dynamic polarizabilities from the EFP2 portion, and dipole integrals and orbital energies from the QM portion of the system. Dividing by the sixth power of the distance between localized molecular orbital centroids yields the first term in the commonly employed London series expansion. A C(8) term is estimated from the C(6) term to achieve closer agreement with symmetry adapted perturbation theory values. Two damping functions for the dispersion energy are evaluated. By using terms that are already computed during an ordinary HF or EFP2 calculation, the new method enables accurate and extremely rapid evaluation of the dispersion interaction between EFP2 and QM molecules.     

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.     

Gradients of the Exchange-repulsion Energy in the General Effective Fragment Potential Method

Formulae for calculating the analytic gradients of the exchange-repulsion energy in the general effective fragment potential (EFP2) method are derived and implemented using a direct differentiation approach. The timings for the exchange repulsion gradient evaluations are approximately three times longer than the energy evaluations, orders of magnitude faster than a previous implementation. Since the direct differentiation approach is not approximate, the gradients can be used with confidence in molecular dynamics and Monte Carlo simulations with the EFP2 method.     

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.     

Implementation of the analytic energy gradient for the combined time-dependent density functional theory/effective fragment potential method: application to excited-state molecular dynamics simulations

Excited-state quantum mechanics/molecular mechanics molecular dynamics simulations are performed, to examine the solvent effects on the fluorescence spectra of aqueous formaldehyde. For that purpose, the analytical energy gradient has been derived and implemented for the linear-response time-dependent density functional theory (TDDFT) combined with the effective fragment potential (EFP) method. The EFP method is an efficient ab initio based polarizable model that describes the explicit solvent effects on electronic excitations, in the present work within a hybrid TDDFT/EFP scheme. The new method is applied to the excited-state MD of aqueous formaldehyde in the n-π* state. The calculated π*→n transition energy and solvatochromic shift are in good agreement with other theoretical results.     

Optimizing conical intersections of solvated molecules: the combined spin-flip density functional theory/effective fragment potential method

Solvent effects on a potential energy surface crossing are investigated by optimizing a conical intersection (CI) in solution. To this end, the analytic energy gradient has been derived and implemented for the collinear spin-flip density functional theory (SFDFT) combined with the effective fragment potential (EFP) solvent model. The new method is applied to the azomethane-water cluster and the chromophore of green fluorescent protein in aqueous solution. These applications illustrate not only dramatic changes in the CI geometries but also strong stabilization of the CI in a polar solvent. Furthermore, the CI geometries obtained by the hybrid SFDFT/EFP scheme reproduce those by the full SFDFT, indicating that the SFDFT/EFP method is an efficient and promising approach for understanding nonadiabatic processes in solution.     

Charge transfer interaction in the effective fragment potential method

An approximate formula is derived and implemented in the general effective fragment potential (EFP2) method to model the intermolecular charge transfer interaction. This formula is based on second order intermolecular perturbation theory and utilizes canonical molecular orbitals and Fock matrices obtained with preparative self-consistent field calculations. It predicts charge transfer energies that are in reasonable agreement with the reduced variational space energy decomposition analysis. The formulas for the charge transfer gradients with respect to EFP translational and rotational displacements are also derived and implemented.     

Noncovalent interactions in extended systems described by the effective fragment potential method: theory and application to nucleobase oligomers

The implementation of the effective fragment potential (EFP) method within the Q-CHEM electronic structure package is presented. The EFP method is used to study noncovalent π-π and hydrogen-bonding interactions in DNA strands. Since EFP is a computationally inexpensive alternative to high-level ab initio calculations, it is possible to go beyond the dimers of nucleic acid bases and to investigate the asymptotic behavior of different components of the total interaction energy. The calculations demonstrated that the dispersion energy is a leading component in π-stacked oligomers of all sizes. Exchange-repulsion energy also plays an important role. The contribution of polarization is small in these systems, whereas the magnitude of electrostatics varies. Pairwise fragment interactions (i.e., the sum of dimer binding energies) were found to be a good approximation for the oligomer energy.     

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.     

Solvent effects on the electronic transitions of p-nitroaniline: a QM/EFP study

Solvatochromic shifts of the electronic states of a chromophore can be used as a measure of solute-solvent interactions. The shifts of the electronic states of a model organic chromophore, p-nitroaniline (pNA), embedded in solvents with different polarities (water, 1,4-dioxane, and cyclohexane) are studied using a hybrid quantum mechanics/molecular-mechanics-type technique in which the chromophore is described by the configuration interaction singles with perturbative doubles (CIS(D)) method while the solvent is treated by the effective fragment potential (EFP) method. This newly developed CIS(D)/EFP scheme includes the quantum-mechanical coupling of the Coulomb and polarization terms; however, short-range dispersion and exchange-repulsion terms of EFP are not included in the quantum Hamiltonian. The CIS(D)/EFP model is benchmarked against the more accurate equation of motion coupled cluster with singles and doubles (EOM-CCSD)/EFP method on a set of small pNA-water clusters. CIS(D)/EFP accurately predicts the red solvatochromic shift of the charge-transfer π → π* state of pNA in polar water. The shift is underestimated in less polar dioxane and cyclohexane probably because of the omission of the explicit quantum-mechanical treatment of the short-range terms. Different solvation of singlet and triplet states of pNA results in different probabilities of intersystem crossing (ISC) and internal conversion (IC) pathways of energy relaxation in solvents of different polarity. Computed singlet-triplet splittings in water and dioxane qualitatively explain the active ISC channel in dioxane and predict almost no conversion to the triplet manifold in water, in agreement with experimental findings.     

C-H bond activation of methane in aqueous solution: a hybrid quantum mechanical/effective fragment potential study

In this study, we investigated the C? H bond activation of methane catalyzed by the complex [PtCl₄]^2?, using the hybrid quantum mechanical/effective fragment potential (EFP) approach. We analyzed the structures, energetic properties, and reaction mechanism involved in the elementary steps that compose the catalytic cycle of the Shilov reaction. Our B3LYP/SBKJC/cc‐pVDZ/EFP results show that the methane activation may proceed through two pathways: (i) electrophilic addition or (ii) direct oxidative addition of the C? H bond of the alkane. The electrophilic addition pathway proceeds in two steps with formation of a σ‐methane complex, with a Gibbs free energy barrier of 24.6 kcal mol^?1, followed by the cleavage of the C? H bond, with an energy barrier of 4.3 kcal mol^?1. The activation Gibbs free energy, calculated for the methane uptake step was 24.6 kcal mol^?1, which is in good agreement with experimental value of 23.1 kcal mol^?1 obtained for a related system. The results shows that the activation of the C? H bond promoted by the [PtCl₄]^2? catalyst in aqueous solution occurs through a direct oxidative addition of the C? H bond, in a single step, with an activation free energy of 25.2 kcal mol^?1, as the electrophilic addition pathway leads to the formation of a σ‐methane intermediate that rapidly undergoes decomposition. The inclusion of long‐range solvent effects with polarizable continuum model does not change the activation energies computed at the B3LYP/SBKJC/cc‐pVDZ/EFP level of theory significantly, indicating that the large EFP water cluster used, obtained from Monte Carlo simulations and analysis of the center‐of‐mass radial pair distribution function, captures the most important solvent effects. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Modeling pi-pi interactions with the effective fragment potential method: the benzene dimer and substituents

This study compares the results of the general effective fragment potential (EFP2) method to the results of a previous combined coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] and symmetry-adapted perturbation theory (SAPT) study [Sinnokrot and Sherrill, J. Am. Chem. Soc., 2004, 126, 7690] on substituent effects in pi-pi interactions. EFP2 is found to accurately model the binding energies of the benzene-benzene, benzene-phenol, benzene-toluene, benzene-fluorobenzene, and benzene-benzonitrile dimers, as compared with high-level methods [Sinnokrot and Sherrill, J. Am. Chem. Soc., 2004, 126, 7690], but at a fraction of the computational cost of CCSD(T). In addition, an EFP-based Monte Carlo/simulated annealing study was undertaken to examine the potential energy surface of the substituted dimers.     

Theoretical study of the solvation of fluorine and chlorine anions by water

The solvation of fluoride and chloride anions (F(-) and Cl(-), respectively) by water has been studied using effective fragment potentials (EFPs) for the water molecules and ab initio quantum mechanics for the anions. In particular, the number of water molecules required to fully surround each anion has been investigated. Monte Carlo calculations have been used in an attempt to find the solvated system X(-)(H(2)O)(n) (X = F, Cl) with the lowest energy for each value of n. It is predicted that 18 water molecules are required to form a complete solvation shell around a Cl(-) anion, where "complete solvation" is interpreted as an ion that is completely surrounded by solvent molecules. Although fewer water molecules may fully solvate the Cl(-) anion, such structures are higher in energy than partially solvated molecules, up to n > or = 18. Calculations on the F(-) anion suggest that 15 water molecules are required for a complete solvation shell. The EFP predictions are in good agreement with the relative energies predicted by ab initio energy calculations at the EFP geometries.     

Solvent-induced shift of the lowest singlet π → π* charge-transfer excited state of p-nitroaniline in water: an application of the TDDFT/EFP1 method

The combined time-dependent density functional theory effective fragment potential method (TDDFT/EFP1) is applied to a study of the solvent-induced shift of the lowest singlet π → π* charge-transfer excited state of p-nitroaniline (pNA) from the gas to the condensed phase in water. Molecular dynamics simulations of pNA with 150 EFP1 water molecules are used to model the condensed-phase and generate a simulated spectrum of the lowest singlet charge-transfer excitation. The TDDFT/EFP1 method successfully reproduces the experimental condensed-phase π → π* vertical excitation energy and solvent-induced red shift of pNA in water. The largest contribution to the red shift comes from Coulomb interactions, between pNA and water, and solute relaxation. The solvent shift contributions reflect the increase in zwitterionic character of pNA upon solvation.     

Comparison of overlap-based models for approximating the exchange-repulsion energy

Different ways of approximating the exchange-repulsion energy with a classical potential function have been investigated by fitting various expressions to the exact exchange-repulsion energy for a large set of molecular dimers. The expressions involve either the orbital overlap or the electron-density overlap. For comparison, the parameter-free exchange-repulsion model of the effective fragment potential (EFP) is also evaluated. The results show that exchange-repulsion energy is nearly proportional to both the orbital overlap and the density overlap. For accurate results, a distance-dependent correction is needed in both cases. If few parameters are desired, orbital overlap is superior to density overlap, but the fit to density overlap can be significantly improved by introducing more parameters. The EFP performs well, except for delocalized pi systems. However, an overlap expression with a few parameters seems to be slightly more accurate and considerably easier to approximate.     

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.     

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.     

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.