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.     

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.     

Solvent-induced shifts in electronic spectra of uracil

Highly accurate excitation spectra are predicted for the low-lying n-π* and π-π* states of uracil for both the gas phase and in water employing the complete active space self-consistent field (CASSCF) and multiconfigurational quasidegenerate perturbation theory (MCQDPT) methods. Implementation of the effective fragment potential (EFP) solvent method with CASSCF and MCQDPT enables the prediction of highly accurate solvated spectra, along with a direct interpretation of solvent shifts in terms of intermolecular interactions between solvent and solute. Solvent shifts of the n-π* and π-π* excited states arise mainly from a change in the electrostatic interaction between solvent and solute upon photoexcitation. Polarization (induction) interactions contribute about 0.1 eV to the solvent-shifted excitation. The blue shift of the n-π* state is found to be 0.43 eV and the red shift of the π-π* state is found to be -0.26 eV. Furthermore, the spectra show that in solution the π-π* state is 0.4 eV lower in energy than the n-π* state.     

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.     

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.     

pyEFP: Automatic decomposition of the complex molecular systems into rigid polarizable fragments

We present an open source tool able to describe intermolecular electrostatic interactions within the framework of the effective fragment potential (EFP) method. Complex molecular structure is subdivided into compact rigid fragments and parameters of their interactions are obtained from ab initio calculations. Automatic procedure allows for searching of these parameters into the existing database and merge new fragments into it. A set of standard fragments useful for the studies of organic semiconductors is also provided. Input files both for purely EFP and hybrid QM/MM calculations can be generated. The program is written in python and freely available on GitHub: https://github.com/ale-odinokov/pyEFP © 2017 Wiley Periodicals, Inc.     

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.     

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.     

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.     

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.     

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 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.     

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.     

Effective fragment potential study of the interaction of DNA bases

Hydrogen-bonded and stacked structures of adenine-thymine and guanine-cytosine nucleotide base pairs, along with their methylated analogues, are examined with the ab inito based general effective fragment potential (EFP2) method. A comparison of coupled cluster with single, double, and perturbative triple (CCSD(T)) energies is presented, along with an EFP2 energy decomposition to illustrate the components of the interaction energy.     

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.     

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.     

Modeling styrene-styrene interactions

This study is the first step in the systematic investigation of substituted (carboxyl) polystyrene nanoparticles. Understanding the fundamental interactions between the p-carboxyl styrene monomers, where an ethyl group is used instead of a vinyl group (referenced, for convenience, as "p-carboxyl styrene"), provides the basic information needed to construct potentials for nanoparticles composed of these monomers. In this work, low-energy isomers of p-carboxyl styrene dimer were studied. The dimer structures and their relative and binding energies were determined using both M?ller-Plesset second-order perturbation theory (MP2) and the general effective fragment potential (EFP2) method. Sections of the intermolecular potential energy surface (PES) of the p-carboxylated styrene dimer in its global minimum orientation were also determined. As expected, double hydrogen bonding between the two carboxylic groups provides the strongest interaction in this system, followed by isomers with a single H-bond and strong benzene ring-benzene ring (pi-pi) type interactions. Generally, the EFP2 method reproduces the MP2 geometries and relative energies with good accuracy, so it appears to be an efficient alternative to the correlated ab initio methods, which are too computationally demanding to be routinely used in the study of the more-complex polymeric systems of interest.     

Amino acid analogues bind to carbon nanotube via π-π interactions: comparison of molecular mechanical and quantum mechanical calculations

Understanding the interaction between carbon nanotubes (CNTs) and biomolecules is essential to the CNT-based nanotechnology and biotechnology. Some recent experiments have suggested that the π-π stacking interactions between protein's aromatic residues and CNTs might play a key role in their binding, which raises interest in large scale modeling of protein-CNT complexes and associated π-π interactions at atomic detail. However, there is concern on the accuracy of classical fixed-charge molecular force fields due to their classical treatments and lack of polarizability. Here, we study the binding of three aromatic residue analogues (mimicking phenylalanine, tyrosine, and tryptophan) and benzene to a single-walled CNT, and compare the molecular mechanical (MM) calculations using three popular fixed-charge force fields (OPLSAA, AMBER, and CHARMM), with quantum mechanical (QM) calculations using the density-functional tight-binding method with the inclusion of dispersion correction (DFTB-D). Two typical configurations commonly found in π-π interactions are used, one with the aromatic rings parallel to the CNT surface (flat), and the other perpendicular (edge). Our calculations reveal that compared to the QM results the MM approaches can appropriately reproduce the strength of π-π interactions for both configurations, and more importantly, the energy difference between them, indicating that the various contributions to π-π interactions have been implicitly included in the van der Waals parameters of the standard MM force fields. Meanwhile, these MM models are less accurate in predicting the exact structural binding patterns (matching surface), meaning there are still rooms to be improved. In addition, we have provided a comprehensive and reliable QM picture for the π-π interactions of aromatic molecules with CNTs in gas phase, which might be used as a benchmark for future force field developments.     

An interface between the universal force field and the effective fragment potential method

In order to properly describe reactions in heterogeneous catalyst systems, the reactants, solvent, and bulk effects of the surface must be taken into account. Embedded-cluster QM (quantum mechanics)/MM (molecular mechanics) methods can treat reactions on surfaces (the gas-surface interface), and the effective fragment potential method (EFP) can accurately treat the solvent effects on reactions (the gas-liquid interface). In order to create a QM/MM/EFP hybrid method for treatment of heterogeneous catalytic systems in the presence of a solvent (the liquid-surface interface), an EFP-MM interaction potential has been developed. Example calculations on small clusters of silica and water have been carried out.