Polarizable atomic multipole solutes in a Poisson-Boltzmann continuum

Modeling the change in the electrostatics of organic molecules upon moving from vacuum into solvent, due to polarization, has long been an interesting problem. In vacuum, experimental values for the dipole moments and polarizabilities of small, rigid molecules are known to high accuracy; however, it has generally been difficult to determine these quantities for a polar molecule in water. A theoretical approach introduced by Onsager [J. Am. Chem. Soc. 58, 1486 (1936)] used vacuum properties of small molecules, including polarizability, dipole moment, and size, to predict experimentally known permittivities of neat liquids via the Poisson equation. Since this important advance in understanding the condensed phase, a large number of computational methods have been developed to study solutes embedded in a continuum via numerical solutions to the Poisson-Boltzmann equation. Only recently have the classical force fields used for studying biomolecules begun to include explicit polarization in their functional forms. Here the authors describe the theory underlying a newly developed polarizable multipole Poisson-Boltzmann (PMPB) continuum electrostatics model, which builds on the atomic multipole optimized energetics for biomolecular applications (AMOEBA) force field. As an application of the PMPB methodology, results are presented for several small folded proteins studied by molecular dynamics in explicit water as well as embedded in the PMPB continuum. The dipole moment of each protein increased on average by a factor of 1.27 in explicit AMOEBA water and 1.26 in continuum solvent. The essentially identical electrostatic response in both models suggests that PMPB electrostatics offers an efficient alternative to sampling explicit solvent molecules for a variety of interesting applications, including binding energies, conformational analysis, and pK(a) prediction. Introduction of 150 mM salt lowered the electrostatic solvation energy between 2 and 13 kcalmole, depending on the formal charge of the protein, but had only a small influence on dipole moments.     

Unusually Strong Dipole–Dipole and Dipole–Quadrupole Interactions in a Nanoporous Solid. Crystal Structure and Related Properties of (VO)3[M(CN)6]2·nH2O (M = Fe,Co)

In porous Prussian blue (PB) analogues, the partially naked central metal atoms found at the cavities surface are responsible for many of their physical properties, among them the adsorption potentials. In the as‐synthesized PB analogues, such metal sites stabilize water molecules inside the cavity through coordination bond formation. The filling of the cavity volume is completed with water molecules linked to the coordinated ones through hydrogen bonds formation. Vanadyl‐based PB analogue shows quite different features. The metal(V) at the cavities surface has saturated its coordination sphere with the O atom of the vanadyl ion (V=O). In this material, the V=O group preserves enough strong dipole moment to stabilize adsorbed species at the cavity through dipole–dipole and dipole–quadrupole interactions. This contribution reports the preparation, crystal structure and properties for (VO)₃[M(CN)₆]₂ · nH₂O (M = Fe, Co). According to the refined crystal structure, IR spectra and TG data, six water molecules remain stabilized inside the cavities through a strong dipole–dipole coupling with the vanadyl group. The cavity contains additional water molecules interacting through hydrogen bond bridges with the water molecules coupled to the V=O group. The vanadyl ion is free of hydrogen bonding interactions with the water molecules. The recorded adsorption isotherms for N₂, CO₂ and H₂, three molecules with only quadrupole moment, reveal presence of relative strong adsorption forces due to dipole‐quadrupole interactions.     

Dipole moments of water molecules confined in Na–LSX zeolites – Molecular dynamics simulations including polarization of water

Molecular dynamics simulations of hydrated Na–LSX zeolite at 300 K were performed with the explicit inclusion of the polarization of water. The Si/Al ratio of LSX is 1 and the number of water molecules per unit cell ranged from 0 to 224 to represent a range of hydration. The calculation results show that the dipole moments of water molecules increase with increasing hydration. By using the SPC–FQ water model instead of the SPC/E water model, the differential heat of adsorption showed similar trends in both models, whereas the differential potential energies between water–water and between water–zeolite are more sensitive to hydration.     

Simulation studies of dipole correlation in the isotropic liquid phase

The Kirkwood correlation factor g₁ determines the preference for local parallel or antiparallel dipole association in the isotropic phase. Calamitic mesogens with longitudinal dipole moments and Kirkwood factors greater than 1 have an enhanced effective dipole moment along the molecular long axis. This leads to higher values of Δ? in the nematic phase. This paper describes state-of-the-art molecular dynamics simulations of two calamitic mesogens 4-(trans-4-n-pentylcyclohexyl)benzonitrile (PCH5) and 4-(trans-4-n-pentylcyclohexyl)chlorobenzene (PCH5-Cl) in the isotropic liquid phase using an all-atom force field and taking long range electrostatics into account using an Ewald summation. Using this methodology, PCH5 is seen to prefer antiparallel dipole alignment with a negative g₁ and PCH5-Cl is seen to prefer parallel dipole alignment with a positive g₁; this is in accordance with experimental dielectric measurements. Analysis of the molecular dynamics trajectories allows an assessment of why these molecules behave differently.     

Difficulties with multiple time stepping and fast multipole algorithm in molecular dynamics

Numerical experiments are performed on a 36,000-atom protein–DNA–water simulation to ascertain the effectiveness of two devices for reducing the time spent computing long-range electrostatics interactions. It is shown for Verlet-I/r-RESPA multiple time stepping, which is based on approximating long-range forces as widely separated impulses, that a long time step of 5 fs results in a dramatic energy drift and that this is reduced by using an even larger long time step. It is also shown that the use of as many as six terms in a fast multipole algorithm approximation to long-range electrostatics still fails to prevent significant energy drift even though four digits of accuracy is obtained. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1785–1791, 1997     

Potential energy function for cation–peptide interactions: An ab initio study

A potential energy function is developed to represent the interaction of small monovalent cations, Li⁺, Na⁺, and K⁺, with the backbone of polypeptides. The results are based on ab initio calculations up to the 6-31G* level of the interactions of the ions with acetamide and N-methylacetamide. Basis set superposition errors are corrected with the counterpoise method. A systematic overestimate of the bond polarities is taken into account by an empirical scaling procedure that uses the ratio of the experimental to ab initio dipole moment. The calculated binding energies obtained with this procedure show consistent convergence with different basis sets and are in good agreement with experimental data on cation–water and cation–dimethylformamide systems. Investigations of the calculated ab initio potential energy surface indicate that the cation–peptide interaction is dominated by electrostatics and includes a nonnegligible contribution from polarization of the peptide group by the ion. The induced polarization results in a steeper-than-Coulombic interaction and cannot be described by fixed ion–peptide partial charges electrostatics. Atomic polarizabilities located on the atoms of the ligand molecule are introduced to account for the induced polarization in the empirical energy function. A ～1/r⁴ attractive interaction appears in the potential function. The resulting radial and angular dependence of the potential energy surface is well reproduced. © 1995 by John Wiley & Sons, Inc.     

How ions affect the structure of water

We model ion solvation in water. We use the MB model of water, a simple two-dimensional statistical mechanical model in which waters are represented as Lennard-Jones disks having Gaussian hydrogen-bonding arms. We introduce a charge dipole into MB waters. We perform (NPT) Monte Carlo simulations to explore how water molecules are organized around ions and around nonpolar solutes in salt solutions. The model gives good qualitative agreement with experiments, including Jones-Dole viscosity B coefficients, Samoilov and Hirata ion hydration activation energies, ion solvation thermodynamics, and Setschenow coefficients for Hofmeister series ions, which describe the salt concentration dependence of the solubilities of hydrophobic solutes. The two main ideas captured here are (1) that charge densities govern the interactions of ions with water, and (2) that a balance of forces determines water structure: electrostatics (water's dipole interacting with ions) and hydrogen bonding (water interacting with neighboring waters). Small ions (kosmotropes) have high charge densities so they cause strong electrostatic ordering of nearby waters, breaking hydrogen bonds. In contrast, large ions (chaotropes) have low charge densities, and surrounding water molecules are largely hydrogen bonded.     

Monte Carlo simulation of salt effect on water structure through 3D mechanistic potentials

Highly concentrated electrolyte solutions were studied through a Monte Carlo-based simulator, developed to consider the water molecules not a homogeneous dielectric as usual, but as dipoles that can move and rotate within a 3D lattice. This approach allowed fast calculations of detailed interactions between the particles, which were described from mechanistic potentials including dipole–dipole, ion–dipole, ion–ion, and hydrogen bonding (HB) interactions. A good agreement was found between experimental data and simulated results. The study also provides new insights about the balance of the different interactions in systems with or without electrolytes, and the effects of the electrolytes addition on the original water structure. The proposed model was also compared with previous explicit models.     

DFT Study of Solvent Effects for Some Organic Molecules Using a Polarizable Continuum Model

Forty ionic molecules are studied by DFT (B3LYP, B3P86), MP4 with different basis sets using the PCM/UAHF model within the self-consistent reaction-field method to assess solvent effects. For these molecules, the solvation free energies (ΔG _sol) in water and the dipole moments in vacuoas well as in water are obtained. By comparing the calculated values of ΔG _sol with experimental values and molecular simulation results, it is found that the ΔG _sol values generated by the DFT method are in better agreement with experimental values. Moreover, especially for the B3LYP/6-31+G_∗ level, the results of both ΔG _sol and dipole moments are more accurate considering the lower computational cost. It can be noted that the dipole moments of solutes in water show some increase relative to those in vacuo.     

Collisional reorientation of symmetric‐top molecules in stark fields

Calculated cross sections for collisional defocusing of a beam of symmetric‐top molecules in a hexapole field are compared with new and recent experimental values. The calculations show that collision processes involving changes in K have much smaller cross sections than those for changing M, and cross sections for changing J are smaller still. The beam defocusing produced by collisions with a background gas that is not the same species as the molecules in the beam occurs mainly as a consequence of ΔM transitions induced by a time‐varying field which comprises the dipole‐induced dipole potential and the anisotropic part of the London potential between the symmetric top and its collision partner. Because the dipole–dipole potential depends on 1/r³, its time variation is much slower, and so it is much less effective than the potentials which vary as 1/r⁶ at inducing transitions by this mechanism during long‐range (∼1 nm) collisions at moderate relative velocity (∼500 m/s). ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 75–82, 1999     

Solution Properties of NaHSO4 and Na2SO4: A New Sight from the Water–Ion and Water–Dipole Cooperative Interactions Using Dielectric Relaxation Spectroscopy

The aqueous NaHSO₄ and Na₂SO₄ solutions at concentrations of 0.1–1.0 mol/l in a limited frequency range 0.2–20 GHz are studied by dielectric relaxation spectroscopy with a newly developed fractal concept spectral function. The fractal analysis with α(lnτ) diagrams from dielectric relaxation spectroscopy as functions proposed a new strategy to shed light on the dual nature of ion–water and dipole–water cooperative interactions. A distinct cooperative interaction of ion–water and dipole–water is observed and water molecules perturbed by ions contributing to dielectric constant beyond the first hydration shell is obtained.     

Density functional study of ion hydration for the alkali metal ions (Li+, Na+, K+) and the halide ions (F-, Br-, Cl-)

We performed first principles density functional calculations to study the effect of monovalent ions M+ (M = Li,Na,K) and A- (A = F,Cl,Br) in water with the aim of characterizing the local molecular properties of hydration. For this reason, several ion-water clusters, up to five or six water molecules were considered; such structures were optimized, and the Wannier analysis was then applied to determine the average molecular dipole moment of water. We found that with an increasing number of water molecules, the molecular polarization is determined by the water-water interaction rather than the water-ion interaction, as one would intuitively expect. These results are consistent with those obtained in previous density functional calculations and with other results obtained by employing classical polarizable water models. The main message of this work is that as one increases the number of molecules the average dipole moment of all water molecules and the ones in the first shell tends to the same value as the average of a similar sized cluster of pure water. This supports the use of nonpolarizable classical models of water in classical atomistic simulations.