Study of multipole contributions to the structure of water around ions in solution using the soft sticky dipole-quadrupole-octupole (SSDQO) model of water

The solvation of ions in the soft sticky dipole-quadrupole-octupole (SSDQO) model for liquid water is presented here. This new potential energy function for liquid water describes water-water interactions by a Lennard-Jones term plus a sticky potential consisting of an approximate moment expansion with point dipole, quadrupole, and octupole moments. The SSDQO potential energy function using the moments from extended simple point charge (SPC/E), TIP3P, or TIP5P reproduces the pair potential energy functions and radial distribution functions of the respective multipoint model but it is much faster than even the three-point models. Here, the solvation of ions in SSDQO water is studied using ion-water potential energy functions consisting of moment expansions up to the charge-quadrupole term, up to the charge-octupole term, and up to an approximate charge-hexadecapole term using the moments of SPC/E water. The radial distributions from Monte Carlo simulations show the best agreement with the results for ions in SPC/E water for the expansion up to the charge-hexadecapole term. Thus, the best results are obtained when the water-water and ion-water potentials are exact up to the 1r(4) term and also contain an approximate 1r(5) term. Overall, the simplicity, efficiency, and accuracy of the SSDQO potential make it potentially very useful for computer simulations of aqueous solvation.     

Dynamical properties of the soft sticky dipole-quadrupole-octupole water model: a molecular dynamics study

The dynamical properties of the soft sticky dipole-quadrupole-octupole (SSDQO) water model using SPC/E moments are calculated utilizing molecular dynamics simulations. This new potential for liquid water describes the water-water interactions by a Lennard-Jones term and a sticky potential, which is an approximate moment expansion with point dipole, quadrupole, and octupole moments, and reproduces radial distribution functions of pure liquid water using the moments of SPC/E [Ichiye and Tan, J. Chem. Phys. 124, 134504 (2006)]. The forces and torques of SSDQO water for the dipole-quadrupole, quadrupole-quadrupole, and dipole-octupole interactions are derived here. The simulations are carried out at 298 K in the microcanonical ensemble employing the Ewald method for the long-range dipole-dipole interactions. Here, various dynamical properties associated with translational and rotational motions of SSDQO water using the moments of SPC/E (SSDQO:SPC/E) water are compared with the results from SPC/E and also experiment. The self-diffusion coefficient of SSDQO:SPC/E water is found to be in excellent agreement with both SPC/E and experiment whereas the single particle orientational relaxation time for dipole vector is better than SPC/E water but it is somewhat smaller than experiment. The dielectric constant of SSDQO:SPC/E is essentially identical to SPC/E, and both are slightly lower than experiment. Also, molecular dynamics simulations of the SSDQO water model are found to be about twice as fast as three-site models such as SPC/E.     

UNDERSTANDING STRUCTURAL EFFECTS OF MULTIPOLE MOMENTS ON AQUEOUS SOLVATION OF IONS USING THE SOFT-STICKY DIPOLE-QUADRUPOLE-OCTUPOLE WATER MODEL

The effects of water multipole moments on the aqueous solvation of ions were determined in Monte Carlo simulations using soft-sticky dipole-quadrupole-octupole (SSDQO) water. Water molecules formed linear hydrogen bonds to Cl(-) using the new SSDQO1 parameters, similar to multi-site models. However, the dipole vector was tilted rather than parallel to the oxygen-Na(+) internuclear vector as in most multi-site model, while experiment and ab initio molecular dynamics simulations generally indicate a range of values between tilted and parallel. By varying the multipoles in SSDQO, the octupole was found to determine the orientation around Na(+). Moreover, analysis of the multipoles of more conventional models is predictive of their performance as solvents.     

Solvation of Glucose, Trehalose, and Sucrose by the Soft Sticky Dipole-Quadrupole-Octupole Water Model

Water structure around sugars modeled by partial charges is compared for soft-sticky dipole-quadrupole-octupole (SSDQO), a fast single-site multipole model, and commonly used multi-site models in Monte Carlo simulations. Radial distribution functions and coordination numbers of all the models indicate similar hydration by hydrogen-bond donor and acceptor waters. However, the new optimized SSDQO1 parameters as well as TIP4P-Ew and TIP5P predict a "lone-pair" orientation for the water accepting the sugar hydroxyl hydrogen bond that is more consistent with the limited experimental data than the "dipole" orientation in SPC/E, which has important implications for studies of the cryoprotectant properties of sugars.     

Nonconformal interaction models and thermodynamics of polar fluids

In this work, we develop a simple potential model for polar molecules which represents effectively and accurately the thermodynamics of dilute gases. This potential models dipolar interactions whose nonpolar part is either spherical, as in Stockmayer (SM) molecules, or diatomic, as for 2-center Lennard-Jones molecules (2CLJ). Predictions of the second virial coefficient for SM and polar 2CLJ fluids for various dipole moments and elongations agree very well with results of recent numerical calculations by C. Vega and co-workers (Phys. Chem. Chem Phys. 2002, 4, 3000). The model is used to predict the critical temperature of Stockmayer fluids for variable dipole moment and is applied to HCl as an example of a real polar molecule.     

Monte Carlo configuration interaction applied to multipole moments,ionization energies,and electron affinities

The method of Monte Carlo configuration interaction (MCCI) (Greer, J. Chem. Phys. 1995a, 103, 1821; Tong, Nolan, Cheng, and Greer, Comp. Phys. Comm. 2000, 142, 132) is applied to the calculation of multipole moments. We look at the ground and excited state dipole moments in carbon monoxide. We then consider the dipole of NO, the quadrupole of N₂ and of BH. An octupole of methane is also calculated. We consider experimental geometries and also stretched bonds. We show that these nonvariational quantities may be found to relatively good accuracy when compared with full configuration interaction results, yet using only a small fraction of the full configuration interaction space. MCCI results in the aug‐cc‐pVDZ basis are seen to generally have reasonably good agreement with experiment. We also investigate the performance of MCCI when applied to ionisation energies and electron affinities of atoms in an aug‐cc‐pVQZ basis. We compare the MCCI results with full configuration interaction quantum Monte Carlo (Booth and Alavi, J. Chem. Phys. 2010, 132, 174104; Cleland, Booth, and Alavi, J. Chem. Phys. 2011, 134, 024112) and “exact” nonrelativistic results (Booth and Alavi, J. Chem. Phys. 2010, 132, 174104; Cleland, Booth, and Alavi, J. Chem. Phys. 2011, 134, 024112). We show that MCCI could be a useful alternative for the calculation of atomic ionisation energies however electron affinities appear much more challenging for MCCI. Due to the small magnitude of the electron affinities their percentage errors can be high, but with regards to absolute errors MCCI performs similarly for ionisation energies and electron affinities. © 2013 Wiley Periodicals, Inc.     

Classical interaction model for the water molecule

The authors propose a new classical model for the water molecule. The geometry of the molecule is built on the rigid TIP5P model and has the experimental gas phase dipole moment of water created by four equal point charges. The model preserves its rigidity but the size of the charges increases or decreases following the electric field created by the rest of the molecules. The polarization is expressed by an electric field dependent nonlinear polarization function. The increasing dipole of the molecule slightly increases the size of the water molecule expressed by the oxygen-centered sigma parameter of the Lennard-Jones interaction. After refining the adjustable parameters, the authors performed Monte Carlo simulations to check the ability of the new model in the ice, liquid, and gas phases. They determined the density and internal energy of several ice polymorphs, liquid water, and gaseous water and calculated the heat capacity, the isothermal compressibility, the isobar heat expansion coefficients, and the dielectric constant of ambient water. They also determined the pair-correlation functions of ambient water and calculated the energy of the water dimer. The accuracy of theirs results was satisfactory.     

Computation of dipole, quadrupole, and octupole surfaces from the variational two-electron reduced density matrix method

Recent advances in the direct determination of the two-electron reduced density matrix (2-RDM) by imposing known N-representability conditions have mostly focused on the accuracy of molecular potential energy surfaces where multireference effects are significant. While the norm of the 2-RDM's deviation from full configuration interaction has been computed, few properties have been carefully investigated as a function of molecular geometry. Here the dipole, quadrupole, and octupole moments are computed for a range of molecular geometries. The addition of Erdahl's T2 condition [Int. J. Quantum Chem. 13, 697 (1978)] to the D, Q, and G conditions produces dipole and multipole moments that agree with full configuration interaction in a double-zeta basis set at all internuclear distances.     

Monte Carlo simulations of critical cluster sizes and nucleation rates of water

We have calculated the critical cluster sizes and homogeneous nucleation rates of water at temperatures and vapor densities corresponding to experiments by Wolk and Strey [J. Phys. Chem B 105, 11683 (2001)]. The calculations have been done with an expanded version of a Monte Carlo method originally developed by Vehkamaki and Ford [J. Chem. Phys. 112, 4193 (2000)]. Their method calculates the statistical growth and decay probabilities of molecular clusters. We have derived a connection between these probabilities and kinetic condensation and evaporation rates, and introduce a new way for the calculation of the work of formation of clusters. Three different interaction potential models of water have been used in the simulations. These include the unpolarizable SPC/E [J. Phys. Chem. 91, 6269 (1987)] and TIP4P [J. Chem. Phys. 79, 926 (1983)] models and a polarizable model by Guillot and Guissani [J. Chem. Phys. 114, 6720 (2001)]. We show that TIP4P produces critical cluster sizes and a temperature and vapor density dependence for the nucleation rate that agree well with the experimental data, although the magnitude of nucleation rate is constantly overestimated by a factor of 2 x 10(4). Guissani and Guillot's model is somewhat less successful, but both the TIP4P and Guillot and Guissani models are able to reproduce a much better experimental temperature dependency of the nucleation rate than the classical nucleation theory. Using SPC/E results in dramatically too small critical clusters and high nucleation rates. The water models give different average binding energies for clusters. We show that stronger binding between cluster molecules suppresses the decay probability of a cluster, while the growth probability is not affected. This explains the differences in results from different water models.     

The flexible, polarizable, thole-type interaction potential for water (TTM2-F) revisited

We present a revision of the flexible, polarizable, Thole-type interaction potential for water [J. Chem. Phys.2002, 116, 5115], which allows for condensed-phase simulations. The revised version (TTM2.1-F) of the potential correctly describes the individual water molecular dipole moment and alleviates problems arising at short intermolecular separations that can be sampled in the course of molecular dynamics and Monte Carlo simulations of condensed environments. Furthermore, its parallel implementation under periodic boundary conditions enables the efficient calculation of the macroscopic structural and thermodynamic properties of liquid water, as its performance scales superlinearly with up to a number of 64 processors for a simulation box of 512 molecules. We report the radial distribution functions, average energy, internal geometry, and dipole moment in the liquid as well as the density, dielectric constant, and self-diffusion coefficient at T = 300 K from (NVT) and (NPT) classical molecular dynamics simulations by using the revised version of the potential.     

Atomic dipole moments calculated using analytical molecular second-moment gradients

We have implemented analytical second-moment gradients for Hartree-Fock and multiconfigurational self-consistent-field wave functions. The code is used to calculate atomic dipole moments based on the generalized atomic polar tensor (GAPT) formalism [Phys. Rev. Lett. 62, 1469 (1989)], and the proposal of Dinur and Hagler (DH) for the calculation of atomic multipoles [J. Chem. Phys. 91, 2949 (1989)]. Both approaches display smooth basis-set convergence toward a well-defined basis-set limit and give reasonable electron correlation effects on the calculated atomic properties. However, the atomic charges and atomic dipole moments obtained from the GAPT partitioning scheme are unable to provide even qualitatively meaningful molecular quadrupole moments for some molecules, and thus the atomic multipole moments calculated in this scheme cannot be considered well suited for analyzing the electron density in molecules and for calculating intermolecular interaction energies. In contrast, the DH approach gives atomic charges and dipole moments that by definition exactly reproduce the molecular quadrupole moments. The approach of DH is, however, restricted to planar molecules and thus suffers from not being applicable to molecules of arbitrary shape. Both the GAPT and DH approaches give rather poor results for octupole and hexadecapole moments, indicating that at least atomic quadrupole moments are required for an accurate representation of the molecular charge distribution in terms of atomic electric moments.     

Ab initio potential energy surfaces, bound states, and electronic spectrum of the Ar-SH complex

New ab initio potential energy surfaces for the (2)Pi ground electronic state of the Ar-SH complex are presented, calculated at the RCCSD(T)/aug-cc-pV5Z level. Weakly bound rotation-vibration levels are calculated using coupled-channel methods that properly account for the coupling between the two electronic states. The resulting wave functions are analyzed and a new adiabatic approximation including spin-orbit coupling is proposed. The ground-state wave functions are combined with those obtained for the excited (2)Sigma(+) state [D. M. Hirst, R. J. Doyle, and S. R. Mackenzie, Phys. Chem. Chem. Phys. 6, 5463 (2004)] to produce transition dipole moments. Modeling the transition intensities as a combination of these dipole moments and calculated lifetime values [A. B. McCoy, J. Chem. Phys. 109, 170 (1998)] leads to a good representation of the experimental fluorescence excitation spectrum [M.-C. Yang, A. P. Salzberg, B.-C. Chang, C. C. Carter, and T. A. Miller, J. Chem. Phys. 98, 4301 (1993)].     

Quantum effects in liquid water and ice: model dependence

This paper explores the influence of choice of potential model on the quantum effects observed in liquid water and ice. This study utilizes standard rigid models and a more formal context for the rigid-body centroid molecular dynamics methodology used to perform the quantum simulations is provided. Quantum and classical molecular dynamics simulations are carried out for liquid water and ice Ih at 298 and 220 K, respectively, with the simple point charge/extended and TIP4P-Ew water models. The results obtained for equilibrium and dynamical properties are compared with those recently reported on TIP4P [L. Hernandez de la Pena and P. G. Kusalik, J. Chem. Phys. 121, 5992 (2004); L. Hernandez de la Pena et al., J. Chem. Phys 123, 144506 (2005)]. For the liquid, an energy shift of about 8% and an average molecular uncertainty of about 11 degrees were found independently of the water model. The self-diffusion coefficient consistently increases by more than 50% when going from the classical to the quantum system and quantum dynamics are found to reproduce the experimental isotopic shifts with the models examined. The ice results compare remarkably well with those previously reported for the TIP4P water model; they confirm that quantum effects are considerable and that the quantum mechanical uncertainty and the energy shifts due to quantization are smaller in ice than in liquid water. The relevance of these findings in the context of the construction of water models is briefly discussed.     

Radiative transition probabilities, lifetimes and dipole moments for the vibrational levels of the X1Sigma+ ground state of 39K85Rb

Using a potential energy curve (based primarily on the RKR potential of Amiot and Verges [J. Chem. Phys. 112, 7068 (2000)]) and a dipole moment function (based primarily on ab initio calculations of Park et al. [Chem. Phys. 257, 135 (2000)]), we have calculated radiative transition probabilities (Einstein A coefficients), radiative lifetimes, and dipole moment expectation values involving all vibrational levels (for several rotational quantum numbers) of the X1Sigma+ ground state of 39K85Rb. We observe that the radiative lifetimes of vibrationally excited levels, in particular, are approximately 10(3)-10(6) seconds, far too long to be significant in most ultracold experiments involving 39K85Rb or its isotopomers. Comparison with other molecules (LiH and HF) suggests that simple scaling (A approximately mu2nu3 approximately tau(-1)) will predict similarly long lifetimes for many other heteronuclear molecules, e.g., RbCs.     

A molecular dynamics study of water nucleation using the TIP4P/2005 model

Extensive molecular dynamics simulations were conducted using the TIP4P/2005 water model of Abascal and Vega [J. Chem. Phys. 123, 234505 (2005)] to investigate its condensation from supersaturated vapor to liquid at 330 K. The mean first passage time method [J. Wedekind, R. Strey, and D. Reguera, J. Chem. Phys. 126, 134103 (2007); L. S. Bartell and D. T. Wu, 125, 194503 (2006)] was used to analyze the influence of finite size effects, thermostats, and charged species on the nucleation dynamics. We find that the Nose?-Hoover thermostat and the one proposed by Bussi et al. [J. Chem. Phys. 126, 014101 (2007)] give essentially the same averages. We identify the maximum thermostat coupling time to guarantee proper thermostating for these simulations. The presence of charged species has a dramatic impact on the dynamics, inducing a marked change towards a pure growth regime, which highlights the importance of ions in the formation of liquid droplets in the atmosphere. It was found a small but noticeable sign preference at intermediate cluster sizes (between 5 and 30 water molecules) corresponding mostly to the formation of the second solvation shell around the ion. The TIP4P/2005 water model predicts that anions induce faster formation of water clusters than cations of the same magnitude of charge.     

Molecular dynamics simulation of the dielectric constant of water: the effect of bond flexibility

The role of bond flexibility on the dielectric constant of water is investigated via molecular dynamics simulations using a flexible intermolecular potential SPC/Fw [Y. Wu, H. L. Tepper, and G. A. Voth, J. Chem. Phys. 128, 024503 (2006)]. Dielectric constants and densities are reported for the liquid phase at temperatures of 298.15 K and 473.15 K and the supercritical phase at 673.15 K for pressures between 0.1 MPa and 200 MPa. Comparison with both experimental data and other rigid bond intermolecular potentials indicates that introducing bond flexibility significantly improves the prediction of both dielectric constants and pressure-temperature-density behavior. In some cases, the predicted densities and dielectric constants almost exactly coincide with experimental data. The results are analyzed in terms of dipole moments, quadrupole moments, and equilibrium bond angles and lengths. It appears that bond flexibility allows the molecular dipole and quadrupole moment to change with the thermodynamic state point, and thereby mimic the change of the intermolecular interactions in response to the local environment.     

Molecular properties from variational reduced-density-matrix theory with three-particle N-representability conditions

Molecular ground-state energies and two-electron reduced density matrices (2-RDMs) have recently been computed without the many-electron wave function by constraining the 2-RDM to satisfy a complete set of three-positivity conditions for N representability [D. A. Mazziotti, Phys. Rev. A 74, 032501 (2006)]. Energies at both equilibrium and nonequilibrium geometries are obtained within 0.3% of the correlation energy. In this paper the authors extend this work to examine the accuracy of molecular properties, including multipole moments and components of the ground-state energy, relative to full configuration interaction (FCI). Comparisons are also made with 2-RDM methods with two-positivity conditions and two-positivity plus the generalized T1T2 conditions as well as several approximate wave function methods. Using the 2-RDM method with three-positivity conditions, the authors obtain dipole, quadrupole, and octupole moments for BeH2, BH, H2O, CO, and NH3 at equilibrium geometries that are within 0.04% of their FCI values. In addition, for the potential energy surface of N2, the 2-RDM method with three-positivity yields not only accurate total ground-state energies but also accurate expectation values of the kinetic energy operator, the electron-nuclei potential, and electron-electron repulsion.     

CHARMM fluctuating charge force field for proteins: I parameterization and application to bulk organic liquid simulations

A first-generation fluctuating charge (FQ) force field to be ultimately applied for protein simulations is presented. The electrostatic model parameters, the atomic hardnesses, and electronegativities, are parameterized by fitting to DFT-based charge responses of small molecules perturbed by a dipolar probe mimicking a water dipole. The nonbonded parameters for atoms based on the CHARMM atom-typing scheme are determined via simultaneously optimizing vacuum water-solute geometries and energies (for a set of small organic molecules) and condensed phase properties (densities and vaporization enthalpies) for pure bulk liquids. Vacuum solute-water geometries, specifically hydrogen bond distances, are fit to 0.19 A r.m.s. error, while dimerization energies are fit to 0.98 kcal/mol r.m.s. error. Properties of the liquids studied include bulk liquid structure and polarization. The FQ model does indeed show a condensed phase effect in the shifting of molecular dipole moments to higher values relative to the gas phase. The FQ liquids also appear to be more strongly associated, in the case of hydrogen bonding liquids, due to the enhanced dipolar interactions as evidenced by shifts toward lower energies in pair energy distributions. We present results from a short simulation of NMA in bulk TIP4P-FQ water as a step towards simulating solvated peptide/protein systems. As expected, there is a nontrivial dipole moment enhancement of the NMA (although the quantitative accuracy is difficult to assess). Furthermore, the distribution of dipole moments of water molecules in the vicinity of the solutes is shifted towards larger values by 0.1-0.2 Debye in keeping with previously reported work.     

The impact of the multipolar distribution on chiral discrimination in racemates

This article explores the impact of the multipolar distribution on chiral discrimination in a series of racemic fluids. Discrimination is measured via the difference between the like-like (LL) and the like-unlike (LU) radial distributions in the liquid. We have found previously that the magnitude and orientation of the molecular dipole have a decisive impact on the short-ranged enantiomeric imbalance in racemates. Although quadrupolar and octupolar interactions decrease more rapidly with intermolecular separation, they can be significant at small separations, where enantiomeric imbalances occur. We have carefully selected a number of models in which we isolate the effects of the molecular quadrupole and octupole. We find that discrimination can be greatly enhanced by changes in the quadrupole moments. However, for octupole moments, changes in discrimination are small and some octupoles inhibit discrimination. We identify the quadrupole moment closest to the plane perpendicular to the direction of the molecular dipole as the moment that has the greatest favorable effect on chiral discrimination in racemates. In racemates where this moment is large, we have found differences of up to 40% between the LL and the LU radial distributions.