Comparing polarizable force fields to ab initio calculations reveals nonclassical effects in condensed phases

In a recent work [Giese and York J. Chem. Phys. 120, 9903 (2004)] showed that many-body force field models based solely on pairwise Coulomb screening cannot simultaneously reproduce both gas-phase and condensed-phase polarizability limits. In particular, polarizable force fields applied to bifurcated water chains have been demonstrated to be overpolarized with respect to ab initio methods. This behavior was ascribed to the neglect of coupling between many-body exchange and polarization. In the present article we reproduce those results using different ab initio levels of theory and a polarizable model based on the chemical-potential equalization principle. Moreover we show that, when hydrogen-bond (H-bond) forming systems are considered, an additional nonclassical effect, i.e., intermolecular charge transfer, must be taken into account. Such effect, contrarily to that of coupling between many-body exchange and polarization, makes classical polarizable force fields underpolarized. In the case of water at standard conditions, being H-bonded geometries much more probable than the bifurcated ones, intermolecular charge transfer is the dominant effect.     

Toward accurate solvation dynamics of lanthanides and actinides in water using polarizable force fields: from gas-phase energetics to hydration free energies

In this contribution, we focused on the use of polarizable force fields to model the structural, energetic, and thermodynamical properties of lanthanides and actinides in water. In a first part, we chose the particular case of the Th(IV) cation to demonstrate the capabilities of the AMOEBA polarizable force field to reproduce both reference ab initio gas-phase energetics and experimental data including coordination numbers and radial distribution functions. Using such model, we predicted the first polarizable force field estimate of Th(IV) solvation free energy, which accounts for −1,638 kcal/mol. In addition, we proposed in a second part of this work a full extension of the SIBFA (Sum of Interaction Between Fragments Ab initio computed) polarizable potential to lanthanides (La(III) and Lu(III)) and to actinides (Th(IV)) in water. We demonstrate its capabilities to reproduce all ab initio contributions as extracted from energy decomposition analysis computations, including many-body charge transfer and discussed its applicability to extended molecular dynamics and its parametrization on high-level post-Hartree–Fock data.     

Simulation of Ca2+ and Mg2+ solvation using polarizable atomic multipole potential

The alkaline earth metals calcium and magnesium are critically involved in many biomolecular processes. To understand the hydration thermodynamics of these ions, we have performed molecular dynamics simulations using a polarizable potential. Particle-mesh Ewald for point multipoles has been applied to the calculation of electrostatic interactions. The parameters in this model have been determined from an ab initio quantum mechanical calculation of dimer interactions between ions and water. Two methods for ion solvation free energy calculation, free energy perturbation, and the Bennett acceptance ratio have been compared. Both predict results consistent with other theoretical estimations while the Bennett approach leads to a much smaller statistical error. Based on the Born theory and the ion-oxygen radial distribution functions, we estimate the effective size of the ions in solution, concluding that K(+) > Na(+) congruent with Ca(2+) > Mg(2+). There appears to be much stronger perturbation in water structure, dynamics, and dipole moment around the divalent cations than the monovalent K(+) and Na(+). The average water coordination numbers for Ca(2+) and Mg(2+) are 7.3 and 6, respectively. The lifetime of water molecules in the first solvation shell of Mg(2+) is on the order of hundreds of picoseconds, in contrast to only few picoseconds for Ca(2+), K(+), or Na(+).     

Many-body force field models based solely on pairwise Coulomb screening do not simultaneously reproduce correct gas-phase and condensed-phase polarizability limits

It is demonstrated that many-body force field models based solely on pairwise Coulomb screening cannot simultaneously reproduce both gas-phase and condensed-phase polarizability limits. Several many-body force field model forms are tested and compared with basis set-corrected ab initio results for a series of bifurcated water chains. Models are parameterized to reproduce the ab initio polarizability of an isolated water molecule, and pairwise damping functions are set to reproduce the polarizability of a water dimer as a function of dimer separation. When these models are applied to extended water chains, the polarization is over-predicted, and this over-polarization increased as a function of the overlap of molecular orbitals as the chains are compressed. This suggests that polarizable models based solely on pairwise Coulomb screening have some limitations, and that coupling with non-classical many-body effects, in particular exchange terms, may be important.     

Pair interaction potentials with explicit polarization for molecular dynamics simulations of La(3+) in bulk water

Pair interaction potentials (IPs) were defined to describe the La(3+)-OH(2) interaction for simulating the La(3+) hydration in aqueous solution. La(3+)-OH(2) IPs are taken from the literature or parametrized essentially to reproduce ab initio calculations at the second-order Moller-Plesset level of theory on La(H(2)O)(8) (3+). The IPs are compared and used with molecular dynamics (MD) including explicit polarization, periodic boundary conditions of La(H(2)O)(216) (3+) boxes, and TIP3P water model modified to include explicit polarization. As expected, explicit polarization is crucial for obtaining both correct La-O distances (r(La-O)) and La(3+) coordination number (CN). Including polarization also modifies hydration structure up to the second hydration shell and decreases the number of water exchanges between the La(3+) first and second hydration shells. r(La-O) ((1))=2.52 A and CN((1))=9.02 are obtained here for our best potential. These values are in good agreement with experimental data. The tested La-O IPs appear to essentially account for the La-O short distance repulsion. As a consequence, we propose that most of the multibody effects are correctly described by the explicit polarization contributions even in the first La(3+) hydration shell. The MD simulation results are slightly improved by adding a-typically negative 1r(6)-slightly attractive contribution to the-typically exponential-repulsive term of the La-O IP. Mean residence times are obtained from MD simulations for a water molecule in the first (1082 ps) and second (7.6 ps) hydration shells of La(3+). The corresponding water exchange is a concerted mechanism: a water molecule leaving La(H(2)O)(9) (3+) in the opposite direction to the incoming water molecule. La(H(2)O)(9) (3+) has a slightly distorded "6+3" tricapped trigonal prism D(3h) structure, and the weakest bonding is in the medium triangle, where water exchanges take place.     

Zn protein simulations including charge transfer and local polarization effects

Nearly half of all proteins contain metal ions, which perform a wide variety of specific functions associated with life processes. However, insights into the local/global, structural and dynamical fluctuations in metalloproteins from molecular dynamics simulations have been hampered by the "conventional" potential energy function (PEF) used in nonmetalloprotein simulations, which does not take into the nonnegligible charge transfer and polarization effects in many metal complexes. Here, we have carried out molecular dynamics simulations of Zn(2+) bound to Cys(-) and/or His(0) in proteins using both the conventional PEF and a novel PEF that accounts for the significant charge transfer and polarization effects in these Zn complexes. Simulations with the conventional PEF yield a nontetrahedral Cys(2)His(2) Zn-binding site and significantly overestimate the experimental Zn-S(Cys(-)) distance. In contrast, simulations with the new PEF accurately reproduce the experimentally observed tetrahedral structures of Cys(2)His(2) and Cys(4) Zn-binding sites in proteins, even when the simulation started from a nontetrahedral Zn(2+) configuration. This suggests that simulations with the new PEF could account for coordinational changes at Zn, which occurs during the folding/unfolding of Zn-finger proteins and certain enzymatic reactions The strategy introduced here can easily be applied to investigate Zn(2+) interacting with protein ligands other than Cys(-) and His(0). It can also be extended to study the interaction of other metals that have significant charge transfer and polarization effects.     

Effect of polarization on the opsin shift in rhodopsins. 2. Empirical polarization models for proteins

The explicit treatment of polarization as a many-body interaction in condensed-phase systems represents a current problem in empirical force-field development. Although a variety of efficient models for molecular polarization have been suggested, polarizable force fields are still far from common use nowadays. In this work, we consider interactive polarization models employing Thole's short-range damping scheme and assess them for application on polypeptides. Despite the simplicity of the model, we find mean polarizabilities and anisotropies of amino acid side chains in excellent agreement with MP2/cc-pVQZ benchmark calculations. Combined with restrained electrostatic potential (RESP) derived atomic charges, the models are applied in a quantum-mechanical/molecular-mechanical (QM/MM) approach. An iterative scheme is used to establish a self-consistent mutual polarization between the QM and MM moieties. This ansatz is employed to study the influence of the protein polarizability on calculated optical properties of the protonated Schiff base of retinal in rhodopsin (Rh), bacterio-rhodopsin (bR), and pharaonis sensory rhodopsin II (psRII). The shifts of the excitation energy due to the instantaneous polarization response of the protein to the charge transfer on the retinal chromophore are quantified using the high level ab initio multireference spectroscopy-oriented configuration interaction (SORCI) method. The results are compared with those of previously published QM1/QM2/MM models for bR and psRII.     

Polarizable Atomistic Calculation of Site Energy Disorder in Amorphous Alq3

A polarizable molecular dynamics simulation and calculation scheme for site energy disorder is presented in amorphous tris(8‐hydroxyquinolinato)aluminum (Alq₃) by means of the charge response kernel (CRK) method. The CRK fit to the electrostatic potential and the tight‐binding approximation are introduced, which enables modeling of the polarizable electrostatic interaction for a large molecule systematically from an ab initio calculation. The site energy disorder for electron and hole transfers is calculated in amorphous Alq₃ and the effect of the polarization on the site energy disorder is discussed.     

Ab initio study of the hydration of carbon dioxide: Additional comments based on refined calculations

Ab initio calculations on the formation of carbonic acid from the hydration of carbon dioxide with water dimer are re-examined. Fully optimized geometries of the three stationary points (minima and transition state) with the 3-21G basis set are reported. They possess non-planar structures. The inclusion of polarization (with the 6-31G* basis) and electron correlation (via Møller-Plesset perturbation theory to second through to fourth-order using the 6-31G basis) tends to enlarge the energy barrier (35–40 kcal mol⁻¹) for the double hydrogen transfer. This suggests that the neutral hydrolysis of CO₂ could require more water molecules (an oligomer) in an autocatalytic process rather than a dimer.     

Behavior of polarizable models in presence of strong electric fields. I. Origin of nonlinear effects in water point-charge systems

In the current opinion, the inclusion of polarization response in classical computer simulations is considered as one of the most important and urgent improvements to be implemented in modern empirical potential models. In this work we focus on the capability of polarizable models, based on the pairwise Coulomb interactions, to model systems where strong electric fields enter into play. As shown by Masia, Probst, and Rey (MPR) [in J. Chem. Phys. 121, 7362 (2004)], when a molecule interacts with point charges, polarizable models show underpolarization with respect to ab initio methods. We prove that this underpolarization, clearly related to nonlinear polarization effects, cannot be simply ascribed to the lack of hyperpolarization in the polarizable models, as suggested by MPR. Analysis of the electron-density rearrangement induced on a water molecule by a point charge reveals a twofold level of polarization response. One level involves intramolecular charge transfer on the whole molecular volume, with the related polarization exhibiting a seemingly linear behavior with the external electric field. The other nonlinear polarization level occurs only at strong electric fields and is found to be strictly correlated to the quantum-mechanical nature of the water molecule. The latter type of polarization has a local character, being limited to the space region of the water lone pairs.     

Key role of the polarization anisotropy of water in modeling classical polarizable force fields

We have evaluated the extent to which classical polarizable force fields, based either on the chemical potential equalization principle or on distributed polarizabilities in the framework of the Sum of Interactions Between Fragments Ab initio computed (SIBFA), can reproduce the ab initio polarization energy and the dipole moment of three distinct water oligomers: bifurcated chains, transverse hydrogen-bonded chains, and longitudinal hydrogen-bonded chains of helical shape. To analyze the many-body polarization effect, chains of different size, i.e., from 2 to 12 water monomers, have been considered. Although the dipole moment is a well-defined quantity in both classical polarizable models and quantum mechanical methods, polarization energy can be defined unequivocally only in the former type of approaches. In this study we have used the Kitaura-Morokuma (KM) procedure. Although the KM approach is on the one hand known to overestimate the polarization energy for strongly interacting molecules, on the other hand it can account for the many-body polarization effectively, whereas some other procedures do not. Our data show that, if off-centered lone pair polarizabilities are explicitly represented, classical polarizable force fields can afford a close agreement with the ab initio results, both in terms of polarization energy and in terms of dipole moment.     

A theoretical study of aqueous solvation of K comparing ab initio, polarizable, and fixed-charge models

The hydration of K(+) is studied using a hierarchy of theoretical approaches, including ab initio Born-Oppenheimer molecular dynamics and Car-Parrinello molecular dynamics, a polarizable force field model based on classical Drude oscillators, and a nonpolarizable fixed-charge potential based on the TIP3P water model. While models based more directly on quantum mechanics offer the possibility to account for complex electronic effects, polarizable and fixed-charges force fields allow for simulations of large systems and the calculation of thermodynamic observables with relatively modest computational costs. A particular emphasis is placed on investigating the sensitivity of the polarizable model to reproduce key aspects of aqueous K(+), such as the coordination structure, the bulk hydration free energy, and the self diffusion of K(+). It is generally found that, while the simple functional form of the polarizable Drude model imposes some restrictions on the range of properties that can simultaneously be fitted, the resulting hydration structure for aqueous K(+) agrees well with experiment and with more sophisticated computational models. A counterintuitive result, seen in Car-Parrinello molecular dynamics and in simulations with the Drude polarizable force field, is that the average induced molecular dipole of the water molecules within the first hydration shell around K(+) is slightly smaller than the corresponding value in the bulk. In final analysis, the perspective of K(+) hydration emerging from the various computational models is broadly consistent with experimental data, though at a finer level there remain a number of issues that should be resolved to further our ability in modeling ion hydration accurately.     

Structure and electronic properties of a benzene-water solution

Electronic properties of benzene in water were investigated by a sequential quantum mechanical/molecular dynamics approach. Emphasis was placed on the analysis of the structure, polarization effects, and ionization spectrum. By adopting a polarizable model for both benzene and water the structure of the benzene-water solution is in good agreement with data from first principles molecular dynamics. Further, strong evidence that water molecules acquire enhanced orientational order near the benzene molecule is found. Upon hydration, the quadrupole moment of benzene is not significantly changed in comparison with the gas-phase value. We are also reporting results for the dynamic polarizability of benzene in water. Our results indicate that the low energy behaviour of the dynamic polarizability of gas-phase and hydrated benzene is quite similar. Outer valence Green's function calculations for benzene in liquid water show a splitting of the gas-phase energy levels associated with the 1e(1g)(π), 2e(2g), and 2e(1u) orbitals upon hydration. Lifting of the orbitals degeneracy and redshift of the outer valence bands is related to symmetry breaking of the benzene structure in solution and polarization effects from the surrounding water molecules.     

Hydroxide ion hydration in aqueous solutions

Hydroxide ion hydration was studied in aqueous solutions of selected alkali metal hydroxides by means of Fourier transform infrared (FTIR) spectroscopy of HDO isotopically diluted in H2O. The quantitative difference spectra procedure was applied for the first time to investigate such systems. It allowed removal of bulk water contribution and separation of the spectra of solute-affected HDO. The obtained spectral data were confronted with ab initio calculated structures of small gas-phase and polarizable continuum solvation model (PCM) solvated aqueous clusters, OH-(H2O)n, n = 1-7, to establish the structural and energetic states of hydration spheres of the hydrated hydroxide anion. This was achieved by comparison of the calculated optimal geometries with the interatomic distances derived from HDO band positions. The energetic state of water in OH- hydration shells, as revealed by solute-affected HDO spectra, is similar to that of an isoelectronic F- anion. No evidence was found for the existence of stable hydroxide dimer, H3O2-, in an aqueous solution. Spectral data do confirm, however, existence of a weak interaction with a single water molecule at the hydrogen site of OH-.     

Predicting the coordination geometry for Mg2+ in the p53 DNA-binding domain: insights from computational studies

Zn(2+) in the tumor-suppressor protein p53 DNA-binding domain (DBD) is essential for its structural stability and DNA-binding specificity. Mg(2+) has also been recently reported to bind to the p53DBD and influence its DNA-binding activity. In this contribution, the binding geometry of Mg(2+) in the p53DBD and the mechanism of how Mg(2+) affects its DNA-binding activity were investigated using density functional theory (DFT) calculations and molecular dynamics (MD) simulations. Various possible coordination geometries of Mg(2+) binding to histidines (His), cysteines (Cys), and water molecules were studied at the B3LYP/6-311+g** level of theory. The protonation state of Cys and the environment were taken into account to explore the factors governing the coordination geometry. The free energy of the reaction to form the Mg(2+) complexes was estimated, suggesting that the favorable binding mode changes from a four- to six-coordinated geometry as the number of the protonated Cys increases. Furthermore, MD simulations were employed to explore the binding modes of Mg(2+) in the active site of the p53DBD. The simulation results of the Mg(2+) system and the native Zn(2+) system show that the binding affinity of Mg(2+)to the p53DBD is weaker than that of Zn(2+), in agreement with the DFT calculation results and experiments. In addition, the two metal ions are found to make a significant contribution to maintain a favorable orientation for Arg248 to interact with putative DNA, which is critically important to the sequence-specific DNA-binding activity of the p53DBD. However, the effect of Mg(2+) is less marked. Additionally, analysis of the natural bond orbital (NBO) charge transfer reveals that Mg(2+) has a higher net positive charge than Zn(2+), leading to a stronger electrostatic attractive interaction between Mg(2+) and putative DNA. This may partly explain the higher sequence-independent DNA-binding affinity of p53DBD-Mg(2+) compared to p53DBD-Zn(2+) observed in experiment.     

Estimating and modeling charge transfer from the SAPT induction energy

Recent studies using quantum mechanics energy decomposition methods, for example, SAPT and ALMO, have revealed that the charge transfer energy may play an important role in short ranged inter‐molecular interactions, and have a different distance dependence comparing with the polarization energy. However, the charge transfer energy component has been ignored in most current polarizable or non‐polarizable force fields. In this work, first, we proposed an empirical decomposition of SAPT induction energy into charge transfer and polarization energy that mimics the regularized SAPT method (ED‐SAPT). This empirical decomposition is free of the divergence issue, hence providing a good reference for force field development. Then, we further extended this concept in the context of AMOEBA polarizable force field, proposed a consistent approach to treat the charge transfer phenomenon. Current results show a promising application of this charge transfer model in future force field development. © 2017 Wiley Periodicals, Inc.     

The significance of the alkene size and the nature of the metal ion in metal-alkene complexes: a theoretical study

Cation interactions with π-systems are a problem of outstanding contemporary interest and the nature of these interactions seems to be quite different for transition and main group metal ions. In this paper, we have systematically analyzed the contrast in the bonding of Cu(+) and main group metal ions. The molecular structures and energetics of the complexes formed by various alkenes (A = C(n)H(2n), n = 2-6; C(n)H(2n- 2), n = 3-8 and C(n)H(2n + 2), n = 5-10) and metal ions (M = Li(+), Na(+), K(+), Ca(2+), Mg(2+), Cu(+) and Zn(2+)) are investigated by employing ab initio post Hartree-Fock (MP2/6-311++G**) calculations and are reported in the current study. The study, which also aims to evaluate the effect of the size of the alkyl portion attached to the π-system on the complexation energy, indicates a linear relationship between the two. The decreasing order of complexation energy with various metal ion-alkene complexes follows the order Zn(2+)-A > Mg(2+)-A > Ca(2+)-A > Cu(+)-A > Li(+)-A > Na(+)-A > K(+)-A. The increased charge transfer and the electron density at (3,-1) intermolecular bond critical point corroborates well with the size of the π-system and the complexation energy. The observed deviation from the linear dependency of the Cu(+)-A complexes is attributed to the dπ→π* back bonding interaction. An energy decomposition analysis via the reduced variational space (RVS) procedure was also carried out to analyze which component among polarization, charge transfer, coulomb and exchange repulsion contributes to the increase in the complexation energy. The RVS results suggest that the polarization component significantly contributes to the increase in the complexation energy when the alkene size increases.     

Force fields including charge transfer and local polarization effects: Application to proteins containing multi/heavy metal ions

The question whether molecular dynamics (MD) simulations can yield reliable structural and dynamical properties of metalloproteins depend on the accuracy of the force field, i.e., the potential energy function (PEF) and associated parameters modeling the interactions of the metal ion of interest with water and protein ligands. Previously, we had developed a CTPOL PEF for protein simulations of Zn(2+) bound to Cys(-) and/or His(0) that includes charge transfer and local polarization effects as well as metal van der Waals parameters that reproduce the structural and thermodynamical properties of 22 dications. Here, we evaluate if the CTPOL PEF and the new metal parameters (referred to as the CTPOLa force field) can be applied to proteins containing polynuclear metal-binding sites and heavy toxic metal ions, using the CdZn(2)-Cys(9) beta-domain of rat liver metallothionein-2 and the Hg(2+)-bound 18-residue peptide from MerP as test systems. Using the CTPOLa force field, simulations of the beta-domain of rat liver metallothionein-2 totaling 19 ns could preserve the experimentally observed CdZn(2)-Cys(9) complex geometry and overall protein structure, whereas simulations neglecting charge transfer and local polarization effects could not. However, the CTPOLa force field cannot reproduce the experimentally observed linear bicoordination of Hg(2+) in the MerP peptide without adding an angular restraint to the CTPOL PEF to correct the angle distribution about Hg(2+). Thus, the force fields presented herein for the group IIB metal ions can be applied to simulation studies of proteins containing polynuclear metal-binding sites and heavy metal ions in aqueous solution. PEF neglecting charge transfer and local polarization effects in conjunction with vdW parameters adjusted to reproduce the structural and thermodynamical properties of only the metal ion in question could not yield an accurate representation of the metal-binding site and overall protein structure.