Polarization energy gradients in combined quantum mechanics, effective fragment potential, and polarizable continuum model calculations

A method that combines quantum mechanics (QM), typically a solute, the effective fragment potential (EFP) discrete solvent model, and the polarizable continuum model is described. The EFP induced dipoles and polarizable continuum model (PCM) induced surface charges are determined in a self-consistent fashion. The gradients of these two energies with respect to molecular coordinate changes are derived and implemented. In general, the gradients can be formulated as simple electrostatic forces and torques among the QM nuclei, electrons, EFP static multipoles, induced dipoles, and PCM induced charges. Molecular geometry optimizations can be performed efficiently with these gradients. The formulas derived for EFPPCM can be generally applied to other combined molecular mechanics and continuum methods that employ induced dipoles and charges.     

Conformational analysis,tautomeric preference,intramolecular hydrogen bonding,and solvent effect on dinitrosamine: A quantum chemical study

HF, B3LYP, and MP2 methods with the standard basis set, 6‐311++G(d,p), were used to study various aspects of dinitrosamine. These results were compared with the outcomes of G2 and CBS‐QB3 methods. First, the conformational analysis and characterization of equilibrium conformations, especially global minima, were performed. On the basis of relative energies, we found that the dinitroso tautomers are more stable than the nitroso‐hydroxy (NH) ones. This preference is well‐interpreted in terms of tautomerization process and nitrosamine resonance. Furthermore, the nature of O? H···O intramolecular hydrogen bond (IMHB), in chelated forms of NH (NH‐11 and NH‐13) was comprehensively studied to evaluate the effect of hetero atoms (N) on the characteristic of IMHB systems. According to the results of isodesmic reaction method, the hydrogen bond energy of NH‐11 is greater than the malonaldehyde (MA) and NH‐13, whereas the electron density analysis and energy‐geometry correlation methods clearly predict that the hydrogen bond of NH‐11 is weaker than the MA. Additionally, the geometrical, atoms in molecules (AIM) and natural bond orbital's (NBO) parameters also emphasize on the MA as a chelated form with the strongest hydrogen bond. Finally, the solvent effects on the relative stability of selected dinitrosamine conformers are evaluated by different continuum (polarizable‐continuum model, isodensity polarizable continuum model, and self‐consistent isodensity polarizable continuum model), discrete and mixed solvent models. Theoretical results readily show that the potential energy surface of dinitrosamine, especially global minima, is strongly affected by the solvent. © 2012 Wiley Periodicals, Inc.     

Hybrid supermolecule-polarizable continuum approach to solvation: Application to the mechanism of the Stevens rearrangement

Semiempirical molecular orbital theory has been used to study the effects of solvation by acetonitrile on the Stevens rearrangement of methylammonium formylmethylide to 2-aminopropanal. Three methods of solvation have been used to investigate both the electrostatic and specific solvent–solute effects of solvation: a supermolecule calculation involving the complete geometry optimization of up to six solvent molecules about the solute, the conductor-like screening model (COSMO) polarizable continuum method which allows for geometry optimization of the solute in a solvent defined by its dielectric constant, and a hybrid method in which up to five solvent molecules are incorporated inside the solute cavity and complete geometry optimization of the complex is carried out within the polarizable continuum. A comparison of the calculated geometries, rearrangement activation energies, and enthalpies of solvation from these approaches is presented, and the explicit versus bulk solvation effects are discussed. The overall effect of all methods for incorporating solvation effects is that the radical pair pathway is perferred over the concerted mechanism. © 1996 by John Wiley & Sons, Inc.     

QuanPol: A full spectrum and seamless QM/MM program

The quantum chemistry polarizable force field program (QuanPol) is implemented to perform combined quantum mechanical and molecular mechanical (QM/MM) calculations with induced dipole polarizable force fields and induced surface charge continuum solvation models. The QM methods include Hartree–Fock method, density functional theory method (DFT), generalized valence bond theory method, multiconfiguration self‐consistent field method, Møller–Plesset perturbation theory method, and time‐dependent DFT method. The induced dipoles of the MM atoms and the induced surface charges of the continuum solvation model are self‐consistently and variationally determined together with the QM wavefunction. The MM force field methods can be user specified, or a standard force field such as MMFF94, Chemistry at Harvard Molecular Mechanics (CHARMM), Assisted Model Building with Energy Refinement (AMBER), and Optimized Potentials for Liquid Simulations‐All Atom (OPLS‐AA). Analytic gradients for all of these methods are implemented so geometry optimization and molecular dynamics (MD) simulation can be performed. MD free energy perturbation and umbrella sampling methods are also implemented. © 2013 Wiley Periodicals, Inc.     

Continuum polarizable force field within the Poisson-Boltzmann framework

We have developed and tested a complete set of nonbonded parameters for a continuum polarizable force field. Our analysis shows that the new continuum polarizable model is consistent with B3LYP/cc-pVTZ in modeling electronic response upon variation of dielectric environment. Comparison with experiment also shows that the new continuum polarizable model is reasonable, with accuracy similar to that of B3LYP/cc-pVTZ in reproduction of dipole moments of selected organic molecules in the gas phase. We have further tested the validity to interchange the Amber van der Waals parameters between the explicit and continuum polarizable force fields with a series of dimers. It can be found that the continuum polarizable model agrees well with MP2/cc-pVTZ, with deviations in dimer binding energies less than 0.9 kcal/mol in the aqueous dielectric environment. Finally, we have optimized atomic cavity radii with respect to experimental solvation free energies of 177 training molecules. To validate the optimized cavity radii, we have tested these parameters against 176 test molecules. It is found that the optimized Poisson-Boltzmann atomic cavity radii transfer well from the training set to the test set, with an overall root-mean-square deviation of 1.30 kcal/mol, an unsigned average error of 1.07 kcal/mol, and a correlation coefficient of 92% for all 353 molecules in both the training and test sets. Given the development documented here, the next natural step is the construction of a full protein/nucleic acid force field within the new continuum polarization framework.     

Free energy of solvation from molecular dynamics simulation applying Voronoi-Delaunay triangulation to the cavity creation

The free energy of solvation for a large number of representative solutes in various solvents has been calculated from the polarizable continuum model coupled to molecular dynamics computer simulation. A new algorithm based on the Voronoi-Delaunay triangulation of atom-atom contact points between the solute and the solvent molecules is presented for the estimation of the solvent-accessible surface surrounding the solute. The volume of the inscribed cavity is used to rescale the cavitational contribution to the solvation free energy for each atom of the solute atom within scaled particle theory. The computation of the electrostatic free energy of solvation is performed using the Voronoi-Delaunay surface around the solute as the boundary for the polarizable continuum model. Additional short-range contributions to the solvation free energy are included directly from the solute-solvent force field for the van der Waals-type interactions. Calculated solvation free energies for neutral molecules dissolved in benzene, water, CCl4, and octanol are compared with experimental data. We found an excellent correlation between the experimental and computed free energies of solvation for all the solvents. In addition, the employed algorithm for the cavity creation by Voronoi-Delaunay triangulation is compared with the GEPOL algorithm and is shown to predict more accurate free energies of solvation, especially in solvents composed by molecules with nonspherical molecular shapes.     

Parallelization of the integral equation formulation of the polarizable continuum model for higher-order response functions

We present a parallel implementation of the integral equation formalism of the polarizable continuum model for Hartree-Fock and density functional theory calculations of energies and linear, quadratic, and cubic response functions. The contributions to the free energy of the solute due to the polarizable continuum have been implemented using a master-slave approach with load balancing to ensure good scalability also on parallel machines with a slow interconnect. We demonstrate the good scaling behavior of the code through calculations of Hartree-Fock energies and linear, quadratic, and cubic response function for a modest-sized sample molecule. We also explore the behavior of the parallelization of the integral equation formulation of the polarizable continuum model code when used in conjunction with a recent scheme for the storage of two-electron integrals in the memory of the different slaves in order to achieve superlinear scaling in the parallel calculations.     

A molecule on the surface or inside a spherical nanoparticle: the computation of the interaction energy in terms of the dielectric continuum model

The electrostatic interaction energy between a charged or polar molecule and a spherical polarizable nanoparticle is studied within the advanced dielectric continuum model proposed previously. The molecule can be located either inside or outside the nanoparticle or in the vicinity of its boundary surface. The nanoparticle and its environment are considered as a polarizable medium and described in terms of a nonuniform dielectric continuum approximation with a position-dependent dielectric permittivity function e(r) \varepsilon (r) , where r is the position vector. A special construction of this function accounts for the proper treatment of sophisticated boundary effects. Test computations are performed for a number of sample molecules.     

Combining a polarizable force-field and a coarse-grained polarizable solvent model. II. Accounting for hydrophobic effects

A revised and improved version of our efficient polarizable force-field/coarse grained solvent combined approach (Masella, Borgis, and Cuniasse, J. Comput. Chem. 2008, 29, 1707) is described. The polarizable pseudo-particle solvent model represents the macroscopic solvent polarization by induced dipoles placed on mobile pseudo-particles. In this study, we propose a new formulation of the energy term handling the nonelectrostatic interactions among the pseudo-particles. This term is now able to reproduce the energetic and structural response of liquid water due to the presence of a hydrophobic spherical cavity. Accordingly, the parameters of the energy term handling the nonpolar solute/solvent interactions have been refined to reproduce the free-solvation energy of small solutes, based on a standard thermodynamic integration scheme. The reliability of this new approach has been checked for the properties of solvated methane and of the solvated methane dimer, as well as by performing 10 × 20 ns molecular dynamics (MD) trajectories for three solvated proteins. A long-time stability of the protein structures along the trajectories is observed. Moreover, our method still provides a measure of the protein solvation thermodynamic at the same accuracy as standard Poisson-Boltzman continuum methods. These results show the relevance of our approach and its applicability to massively coupled MD schemes to accurately and intensively explore solvated macromolecule potential energy surfaces.     

Quantum Chemical Study of the Mechanism of Action of Vitamin K Carboxylase in Solvent

We investigate the post-translational generation of Gla (γ-carboxy glutamic acid) from Glu (glutamic acid) by vitamin K carboxylase (VKC) in solvent. VKC is thought to convert vitamin K, in the vitamin K cycle, to an alkoxide-epoxide form, which then reacts with CO(2) to generate an essential ingredient in blood coagulation, γ-carboxyglutamic acid (Gla). The generation of Gla from Glu is found to be exergenic (-15 kcal/mol) in aqueous solution with the SM6 method. We also produced the free energy profile for this model biochemical process with other solvent methods (polarizable continuum model, dielectric polarizable continuum model) and different dielectric constants. The biological implications are discussed.     

Vibrational spectra and structures of the anions of urazole and 4-methylurazole: DFT calculations of the normal modes and the influence of hydrogen bonding

Solid state IR and Raman as well as aqueous solution state Raman spectra are reported for the anions of urazole and 4-methylurazole, and their N-deuterated derivatives. DFT calculations, at the B3-LYP/cc-pVTZ level, established that the structures and vibrational spectra of both anions can be interpreted using a model that incorporates hydrogen-bonded water molecules, in conjunction with the polarizable continuum solvation method. In the case of the urazole anion it is shown that deprotonation occurs primarily at N1 rather than N4, but there is also evidence for the second tautomer both in the solid state and in aqueous solution. The vibrational spectra were computed at the optimised molecular geometry in each case, enabling normal coordinate analysis, which yielded satisfactory agreement with the experimental IR and Raman data. Computed potential energy distributions of the normal modes provided detailed vibrational assignments.     

Energy gradients in combined fragment molecular orbital and polarizable continuum model (FMO/PCM) calculation

The analytic energy gradients for the combined fragment molecular orbital and polarizable continuum model (FMO/PCM) method are derived and implemented. Applications of FMO/PCM geometry optimization to polyalanine show that the structures obtained with the FMO/PCM method are very close to those obtained with the corresponding full ab initio PCM methods. FMO/PCM (RHF/6‐31G* level) is used to optimize the solution structure of the 304‐atom Trp‐cage miniprotein and the result is in agreement with NMR experiments. The key factors determining the relative stability of the α‐helix, β‐turn and the extended form in solution are elucidated for polyalanine. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

On the calculations of interaction energies and induced electric properties within the polarizable continuum model

In this work we investigate the influence of a polarizable environment on the interaction energies and the interaction-induced (excess) static electric dipole properties for the selected model hydrogen-bonded complexes. The excess properties were estimated for water and hydrogen fluoride dimers using the supermolecular approach and assuming the polarizable continuum model (PCM) as a representation of the polarizable environment. We analyze in this context the performance of the counterpoise correction and the consequences of various possible monomer cavity choices. The polarizable environment reduces the absolute magnitudes of interaction energies and interaction-induced dipole moments, whereas an increase is observed for the absolute magnitudes of induced polarizabilities and first hyperpolarizabilities. Our results indicate that the use of either monomeric (MC) or dimeric (DC) cavities in calculations of monomer properties does not change qualitatively the resultant excess properties. We conclude that the DC scheme is more consistent with the definition of the interaction energy and consequently also the interaction-induced property, whereas the MC scheme corresponds to the definition of stabilization energy. Our results indicate also a good performance of the counterpoise correction scheme for the self-consistent methods in the case of all studied properties.     

Molecular structure, vibrational spectra and HOMO, LUMO analysis of yohimbine hydrochloride by density functional theory and ab initio Hartree-Fock calculations

Yohimbine hydrochloride (YHCl) is an aphrodisiac and promoted for erectile dysfunction, weight loss and depression. The optimized geometry, total energy, potential energy surface and vibrational wavenumbers of yohimbine hydrochloride have been determined using ab initio, Hartree–Fock (HF) and density functional theory (DFT/B3LYP) method with 6-311++G(d,p) basis set. A complete vibrational assignment is provided for the observed Raman and IR spectra of YHCl. The UV absorption spectrum was examined in ethanol solvent and compared with the calculated one in gas phase as well as in solvent environment (polarizable continuum model, PCM) using TD-DFT/6-31G basis set. These methods are proposed as a tool to be applied in the structural characterization of YHCl. The calculated highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) with frontier orbital gap are presented.     

A simple polarizable continuum solvation model for electrolyte solutions

We propose a Debye-Hu?ckel-like screening model (DESMO) that generalizes the familiar conductor-like screening model (COSMO) to solvents with non-zero ionic strength and furthermore provides a numerical generalization of the Debye-Hu?ckel model that is applicable to non-spherical solute cavities. The numerical implementation of DESMO is based upon the switching/Gaussian (SWIG) method for smooth cavity discretization, which we have recently introduced in the context of polarizable continuum models (PCMs). This approach guarantees that the potential energy is a smooth function of the solute geometry and analytic gradients for DESMO are reported here. The SWIG formalism also facilitates analytic implementation of two other PCMs that are based on a screened Coulomb potential: the "integral equation formalism" (IEF-PCM) and the "surface and simulation of volume polarization for electrostatics" [SS(V)PE] method. Fully analytic implementations of these screened PCMs are reported here for the first time. Numerical results, for model systems where an exact solution of the linearized Poisson-Boltzmann equation is available, demonstrate that these screened PCMs are highly accurate. In realistic test cases, they are as accurate as the best available three-dimensional finite-difference methods. In polar solvents, DESMO is nearly as accurate as more sophisticated screened PCMs, but is significantly simpler and more efficient.     

The effect of the position of methyl substituents on photophysical and photochemical properties of [Ru(x,x'-dmb)(CN)4]2- complexes: experimental confirmation of the theoretical predictions

The molecular geometry, electronic structure and electronic spectra and the energy levels of the molecular orbitals responsible for the photophysical characteristics of a series of solvent tunable [Ru(x,x'-dmb)(CN)(4)](2-) complexes (where x,x'-dmb = x,x'-dimethyl-2,2'-bipyridine) were calculated by density-functional theory-based quantum chemical methods, with the purpose of proposing for experimental study the best candidate for sensitizing electron- and energy transfer processes or for light induced structural changes in the molecule. The methods applied include geometry optimization using the B3LYP functional combination and various basis sets, time-dependent density functional theory with the B3LYP and PBE0 functionals, with and without explicit inclusion of coordinated solvent H(2)O molecules and the conductor-like polarizable continuum model for solvation. The accuracy of the theoretical predictions was tested by experiments: the model compounds have been synthesized and characterized by various spectroscopic methods, such as (1)H-NMR, UV-Vis absorption and emission spectroscopy and by cyclic voltammetry. Excellent correlation was found between the theoretically calculated and the experimentally determined photophysical and photochemical characteristics. The electronic transition energies measured in water are superbly reproduced by TD-PBE0 and well by TD-B3LYP, but the performance of both functionals is worse if the solvent is acetonitrile.     

Solvent dependence of the 2-naphthyl(carbomethoxy)carbene singlet-triplet energy gap

The solvent dependence of the 2-naphthyl(carbomethoxy)carbene (2) singlet-triplet energy gap has been examined by time-resolved infrared (TRIR) and computational methods. The ground state of 2 changes from the triplet state in hexane to the singlet state in acetonitrile. Preferential stabilization of the singlet carbene is the result of its increased dipole moment in polar solvents. Variable-temperature TRIR experiments provide measurements of the enthalpic and entropic differences between (1)2 and (3)2 and suggest that solvent and geometry effects on the entropy of singlet and triplet carbenes can offset differences arising from spin multiplicity. B3LYP calculations using the polarizable continuum solvation model (PCM) reproduce the general trends in enthalpic differences seen experimentally.     

Brueckner doubles coupled cluster method with the polarizable continuum model of solvation

We present the theory and implementation for computing the (free) energy and its analytical gradients with the Brueckner doubles (BD) coupled cluster method in solution, in combination with the polarizable continuum model of solvation (PCM). The complete model, called PTED, and an efficient approximation, called PTE, are introduced and tested with numerical examples. Implementation details are also discussed. A comparison with the coupled-cluster singles and doubles CCSD-PCM-PTED and CCSD-PCM-PTE schemes, which use Hartree-Fock (HF) orbitals, is presented. The results show that the two PTED approaches are mostly equivalent, while BD-PCM-PTE is shown to be superior to the corresponding CCSD scheme when the HF reference wave function is unstable. The BD-PCM-PTE scheme, whose computational cost is equivalent to gas phase BD, is therefore a promising approach to study molecular systems with complicated electronic structure in solution.