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We build on previous work [S. Y. Liem and P. L. A. Popelier, J. Chem. Theory Comput. 4, 353 (2008)], where for the first time, a high-rank multipolar electrostatic potential was used in molecular dynamics simulations of liquid water at a wide range of pressures and temperatures, and using a multipolar Ewald summation. Water is represented as a rigid body, with atomic multipole moments defined by quantum chemical topology partitioning its gas phase electron density. The effect of the level of theory on the local structure of liquid water is systematically addressed. Values for Lennard-Jones (LJ) parameters are optimized, for both oxygen and hydrogen atoms, against bulk properties. The best LJ parameters were then used in a set of simulations at 30 different temperatures (1 atm) and another set at 11 different pressures (at 298 K). Inclusion of the hydrogen LJ parameters significantly increases the self-diffusion coefficient. The behavior of bulk properties was studied and the local water structure analyzed by both radial and spatial distribution functions. Comparisons with familiar point-charge potentials, such as TIP3P, TIP4P, TIP5P, and simple point charge, show the benefits of multipole moments.

Rigid body molecular dynamics simulations were carried out on pure liquid imidazole at four different temperatures and at 1 atm. Imidazole, which is important both in life science and materials science, is one of the simplest molecules to possess both a lone pair and a π system. These two features are known to benefit from multipolar electrostatics. Here the electrostatic interaction is governed by atomic multipole moments obtained from topologically partitioned ab initio electron densities. The non-electrostatic terms are modeled with Lennard-Jones parameters adjusted to fit the experimental liquid density. All σ values are incrementally increased by one single scaling factor. We report on how the presence of multipolar electrostatics influences the local structure, dynamics and thermodynamics of the liquid compared to electrostatics by atomic point charges. The point charge force field exaggerates the number of π-stacked dimers in the liquid, and underestimates the number of hydrogen-bonded dimers. The effect of the temperature on the local structure of liquid imidazole was analysed using radial and spatial distribution functions. © the Owner Societies 2010.

To model liquid water correctly and to reproduce its structural, dynamic and thermodynamic properties warrants models that account accurately for electronic polarisation. We have previously demonstrated that polarisation can be represented by fluctuating multipole moments (derived by quantum chemical topology) predicted by multilayer perceptrons (MLPs) in response to the local structure of the cluster. Here we further develop this methodology of modeling polarisation enabling control of the balance between accuracy, in terms of errors in Coulomb energy and computing time. First, the predictive ability and speed of two additional machine learning methods, radial basis function neural networks (RBFNN) and Kriging, are assessed with respect to our previous MLP based polarisable water models, for water dimer, trimer, tetramer, pentamer and hexamer clusters. Compared to MLPs, we find that RBFNNs achieve a 14-26% decrease in median Coulomb energy error, with a factor 2.5-3 slowdown in speed, whilst Kriging achieves a 40-67% decrease in median energy error with a 6.5-8.5 factor slowdown in speed. Then, these compromises between accuracy and speed are improved upon through a simple multi-objective optimisation to identify Pareto-optimal combinations. Compared to the Kriging results, combinations are found that are no less accurate (at the 90th energy error percentile), yet are 58% faster for the dimer, and 26% faster for the pentamer.

We have performed classical molecular dynamics to study the properties of a water-miscible and a water-immiscible room-temperature ionic liquid when mixed with small quantities of water. The two ionic liquids consist of the same 1-ethyl-3-methylimidazolium ([EMIM]) cation combined with either the boron tetrafluoride ([BF(4)]) or bis(trifluoromethylsulfonyl)imide ([NTf(2)]) anion. It is found that, in both ionic liquids, water clusters of varying sizes are typically hydrogen bonded to two anions with the cation playing a minor role. We also highlight the difficulties of obtaining dynamic quantities such as self-diffusion coefficients from simulations of such viscous systems.

Traditionally force fields express 1,3 and 1,4 interactions as bonded terms via potentials that involve valence and torsion angles, respectively. These interactions are not modeled by point charge terms, which are confined to electrostatic interactions between more distant atoms (1,n where n>4). Here we show that both 1,3 and 1,4 interactions can be described on the same footing as 1,n (n>4) interactions by a convergent multipole expansion of the Coulomb energy of the participating atom pairs. The atomic multipole moments are generated by the theory of quantum chemical topology. The procedure to make the multipole expansion convergent is based on a “shift procedure” described in earlier work [L. Joubert and P. L. A. Popelier, Molec. Phys. 100, 3357 (2002)].

The recently developed program ORIENT 3 is applied to several complexes including acetonitrile dimer, benzene–water, benzene–ammonia and chlorine dimer. We employ distributed multipole analysis in conjunction with the eigenvector-following optimization technique to calculate minima, saddle points and rearrangement pathways. The potential-energy surface of the chlorine dimer is investigated as an example of anisotropic repulsion.

Li(C 4 H 3 O 4 )•2H 2 O cristallise dans P2 1 /n avec a=5,858, b=6,051 et c=18,800 A, β=91,47 o , Z=4; affinement jusqu'a 0,042. Le cristal se presente en feuillets d'ions (HM) lies par des liaisons hydrogene a partir de deux molecules d'eau sur la meme couche. Les couches sont interconnectees par interactions Li…O. Li est coordonne dans un tetraedre deforme. Deux molecules cristallographiquement independantes apparaissent et agissent en tant que donneurs et non en tant qu'accepteurs de liaisons hydrogene et ont des environnements differents. O(W1) est coordonne selon les orbitales du doublet electronique Sp 3 a deux ions Li, par contre O(W2) est coordonne a un seul ion Li le long de la bissectrice de HO-H

A model of the solid state is constructed by optimizing a central molecule in an electrostatic field of the proper symmetry, produced by Mulliken point charges. Attention is paid to ensure convergence, with respect to the number of contributing neighboring molecules as well as to self-consistency of the field. Despite the neglect of orbital overlap between neighboring molecules, the simple crystal field adaptation of standard ab initio methods is capable of reproducing all significant differences observed between the gas-phase and the solid-state geometry of acetamide. Specifically we note (i) the rotation of the methyl group from a form in which a CH eclipses the C=O to a form in which a CH is perpendicular to C=O, (ii) the increase of C=O and NH bond lengths, the decrease of the CN bond, the stability of the CH bonds, and the variation in valence angles, and (iii) the pyramidization of the amide group. Since the method does not increase the number of two-electron integrals, the crystal simulations do not seriously increase the demands on computer facilities.

We exploit the transferability of quantum topological atoms in the construction of a multipolar polarizable protein force field QCTFF. A helical oligopeptide of 10 alanine residues (103 atoms) has its total electrostatic energy predicted using the kriging machine learning method with a mean error of 6.4 kJ mol−1. This error is similar to that found in smaller molecules presented in past QCTFF publications. Kriging relates the molecular geometry to atomic multipole moments that describe the ab initio electron density. Atom types are constructed from similar atoms within the helix. As the atoms within a given atom type share a local chemical environment, they can share a kriging model with a reduced number of input descriptors (i.e. features). The feature reduction decreases the kriging training times by more than 23 times but increases the prediction error by only 1.3 %. In transferability tests, transferable models give a 5.7 % error when predicting moments of an atom outside the training set, compared to the 3.9 % error when tested against data belonging to atoms included in the training data. The transferable kriging models successfully predict atomic multipole moments with useful accuracy, opening an avenue to QCTFF modelling of a whole protein.

The construction of a novel protein force field called FFLUX, which uses topological atoms, is founded on high-rank and fully polarizable multipolar electrostatics. The machine learning method kriging successfully predicts multipole moments of a given atom with as only input the nuclear coordinates of the atoms surrounding this given atom. Thus, trained kriging models accurately capture the polarizable multipolar electrostatics of amino acids. Here we show that successful kriging models can also be constructed for non-electrostatic energy contributions. As a result, the full potential energy surface of the (molecular) system trained for can be predicted by the corresponding set of atomic kriging models. In particular, we report on the performance of kriging models for each atom’s (A) (1) total atomic energy (E IQA ), (2) intra-atomic energy (E intra ) (both kinetic and potential energy), (3) exchange energy ( $$V_{XC}^{{AA^{\prime } }}$$ ) and (4) electrostatic energy ( $$V_{\text{cl}}^{{AA^{{\prime }} }}$$ ) of atom A with the rest of the system (A′), and (5) interatomic energy ( $$V_{\text{inter}}^{{AA^{{\prime }} }}$$ ). The total molecular energy can be reconstructed from the kriging predictions of these atomic energies. For the three case studies investigated (i.e. methanol, N-methylacetamide and peptide-capped glycine), the molecular energies were produced with mean absolute errors under 0.4, 0.8 and 1.1 kJ mol−1, respectively.