NCIPLOT: a program for plotting non-covalent interaction regions

Non-covalent interactions hold the key to understanding many chemical, biological, and technological problems. Describing these non-covalent interactions accurately, including their positions in real space, constitutes a first step in the process of decoupling the complex balance of forces that define non-covalent interactions. Because of the size of macromolecules, the most common approach has been to assign van der Waals interactions (vdW), steric clashes (SC), and hydrogen bonds (HBs) based on pairwise distances between atoms according to their van der Waals radii. We recently developed an alternative perspective, derived from the electronic density: the Non-Covalent Interactions (NCI) index [J. Am. Chem. Soc. 2010, 132, 6498]. This index has the dual advantages of being generally transferable to diverse chemical applications and being very fast to compute, since it can be calculated from promolecular densities. Thus, NCI analysis is applicable to large systems, including proteins and DNA, where analysis of non-covalent interactions is of great potential value. Here, we describe the NCI computational algorithms and their implementation for the analysis and visualization of weak interactions, using both self-consistent fully quantum-mechanical, as well as promolecular, densities. A wide range of options for tuning the range of interactions to be plotted is also presented. To demonstrate the capabilities of our approach, several examples are given from organic, inorganic, solid state, and macromolecular chemistry, including cases where NCI analysis gives insight into unconventional chemical bonding. The NCI code and its manual are available for download at http://www.chem.duke.edu/~yang/software.htm.     

Investigating the Double Beta Decay of <Superscript>58</Superscript>Ni

Double beta decay (β + EC, EC/EC) of ⁵⁸Ni is investigated at France’s Modane Underground Laboratory (4800 m water equivalent) using the OBELIX ultralow-background HPGe detector with a sensitive volume of 600 cm³ and a natural nickel sample of ~68% 58Ni with a mass of ~21.7 kg. After preliminary analysis of the experimental data accumulated over ~144 days, new experimental limits are obtained for the 2νβ⁺EC decay of ⁵⁸Ni to the 0⁺ ground state and the 2 ₁ ⁺ , 811 keV excited state of ⁵⁸Fe, and for the 2νEC/EC decay of ⁵⁸Ni to the 2 ₁ ⁺ , 811 keV and 2 ₂ ⁺ , 1675 keV excited states of ⁵⁸Fe. The limits are T_1/2(β⁺EC,0→0⁺) > 1.7 × 10²² yr, T_1/2(β⁺EC,0→2 ₁ ⁺ ) > 2.3 × 10²² yr, T_1/2(EC/EC,0→2 ₁ ⁺ ) > 3.3 × 10²² yr, and T_1/2(EC/EC,0→2 ₂ ⁺ ) > 3.4 × 10²² yr. Experimental limit T_1/2(0νEC/EC–res, 1918 keV > 4.1 × 10²² yr is obtained for resonant neutrinoless radiative EC/EC decay with an energy of 1918.3 keV. All limits are at 90% CL.     

Numerical fitting of molecular properties to Hermite Gaussians

A procedure is presented to fit gridded molecular properties to auxiliary basis sets (ABSs) of Hermite Gaussians, analogous to the density fitting (DF) method (Dunlap; et al. J. Chem. Phys. 1979, 71, 4993). In this procedure, the ab initio calculated properties (density, electrostatic potential, and/or electric field) are fitted via a linear- or nonlinear-least-squares procedure to auxiliary basis sets (ABS). The calculated fitting coefficients from the numerical grids are shown to be more robust than analytic density fitting due to the neglect of the core contributions. The fitting coefficients are tested by calculating intermolecular Coulomb and exchange interactions for a set of dimers. It is shown that the numerical instabilities observed in DF are caused by the attempt of the ABS to fit the core contributions. In addition, this new approach allows us to reduce the number of functions required to obtain an accurate fit. This results in decreased computational cost, which is shown by calculating the Coulomb energy of a 4096 water box in periodic boundary conditions. Using atom centered Hermite Gaussians, this calculation is only 1 order of magnitude slower than conventional atom-centered point charges.     

Towards a force field based on density fitting

Total intermolecular interaction energies are determined with a first version of the Gaussian electrostatic model (GEM-0), a force field based on a density fitting approach using s-type Gaussian functions. The total interaction energy is computed in the spirit of the sum of interacting fragment ab initio (SIBFA) force field by separately evaluating each one of its components: electrostatic (Coulomb), exchange repulsion, polarization, and charge transfer intermolecular interaction energies, in order to reproduce reference constrained space orbital variation (CSOV) energy decomposition calculations at the B3LYP/aug-cc-pVTZ level. The use of an auxiliary basis set restricted to spherical Gaussian functions facilitates the rotation of the fitted densities of rigid fragments and enables a fast and accurate density fitting evaluation of Coulomb and exchange-repulsion energy, the latter using the overlap model introduced by Wheatley and Price [Mol. Phys. 69, 50718 (1990)]. The SIBFA energy scheme for polarization and charge transfer has been implemented using the electric fields and electrostatic potentials generated by the fitted densities. GEM-0 has been tested on ten stationary points of the water dimer potential energy surface and on three water clusters (n = 16,20,64). The results show very good agreement with density functional theory calculations, reproducing the individual CSOV energy contributions for a given interaction as well as the B3LYP total interaction energies with errors below kBT at room temperature. Preliminary results for Coulomb and exchange-repulsion energies of metal cation complexes and coupled cluster singles doubles electron densities are discussed.     

Polarizable molecular dynamics simulation of Zn(II) in water using the AMOEBA force field

The hydration free energy, structure, and dynamics of the zinc divalent cation are studied using a polarizable force field in molecular dynamics simulations. Parameters for the Zn(2+) are derived from gas-phase ab initio calculation of Zn(2+)-water dimer. The Thole-based dipole polarization is adjusted based on the Constrained Space Orbital Variations (CSOV) calculation while the Symmetry Adapted Perturbation Theory (SAPT) approach is also discussed. The vdW parameters of Zn(2+) have been obtained by comparing the AMOEBA Zn(2+)-water dimerization energy with results from several theory levels and basis sets over a range of distances. Molecular dynamics simulations of Zn(2+) solvation in bulk water are subsequently performed with the polarizable force field. The calculated first-shell water coordination number, water residence time and free energy of hydration are consistent with experimental and previous theoretical values. The study is supplemented with extensive Reduced Variational Space (RVS) and Electron Localization Function (ELF) computations in order to unravel the nature of the bonding in Zn(2+)(H(2)O)(n) (n=1,6) complexes and to analyze the charge transfer contribution to the complexes. Results show that the importance of charge transfer decreases as the size of Zn-water cluster grows due to anticooperativity and to changes in the nature of the metal-ligand bonds. Induction could be dominated by polarization when the system approaches condensed-phase and the covelant effects are eliminated from the Zn(II)-water interaction. To construct an "effective" classical polarizable potential for Zn(2+) in bulk water, one should therefore avoid over-fitting to the ab initio charge transfer energy of Zn(2+)-water dimer. Indeed, in order to avoid overestimation of condensed-phase many-body effects, which is crucial to the transferability of polarizable molecular dynamics, charge transfer should not be included within the classical polarization contribution and should preferably be either incorporated in to the pairwise van der Waals contribution or treated explicitly.     

Advancing beyond charge analysis using the electronic localization function: Chemically intuitive distribution of electrostatic moments

We propose here an evaluation of chemically intuitive distributed electrostatic moments using the topological analysis of the electron localization function (ELF). As this partition of the total charge density provides an accurate representation of the molecular dipole, the distributed electrostatic moments based on the ELF partition (DEMEP) allows computing of local moments located at non atomic centers such as lone pairs, sigma bonds and pi systems. As the local dipole contribution can be decomposed in polarization and charge transfer components, our results indicate that local dipolar polarization of the lone pairs and chemical reactivity are closely related whereas the charge transfer contribution is the key factor driving the local bond dipole. Results on relevant molecules show that local dipole contributions can be used to rationalize inductive polarization effects in alcohols derivatives and typical hydrogen bond interactions. Moreover, bond quadrupole polarization moments being related to a pi character enable to discuss bond multiplicities, and to sort families of molecules according to their bond order. That way, the nature of the C-O bond has been revisited for several typical systems by means of the DEMEP analysis which appears also helpful to discuss aromaticity. Special attention has been given to the carbon monoxide molecule, to the CuCO complex and to a weak intramolecular N|-CO interaction involved in several biological systems. In this latter case, it is confirmed that the bond formation is mainly linked to the CO bond polarization. Transferability tests show that the approach is suitable for the design of advanced force fields.     

Double-beta decay with the NEMO experiment: Status of the NEMO 3 detector

The NEMO 3 detector, devoted to search for the neutrinoless double-beta decay, will be able to reach the sensitivity to 〈m _ν〉 of the order of 0.1 eV. The expected performance of the detector for signal detection and both internal and external background rejection is presented. A specific study of the neutron-induced background is given. The NEMO Collaboration is now mounting the detector in the Fréjus underground laboratory.     

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.     

Scalable improvement of SPME multipolar electrostatics in anisotropic polarizable molecular mechanics using a general short‐range penetration correction up to quadrupoles

We propose a general coupling of the Smooth Particle Mesh Ewald SPME approach for distributed multipoles to a short‐range charge penetration correction modifying the charge‐charge, charge‐dipole and charge‐quadrupole energies. Such an approach significantly improves electrostatics when compared to ab initio values and has been calibrated on Symmetry‐Adapted Perturbation Theory reference data. Various neutral molecular dimers have been tested and results on the complexes of mono‐ and divalent cations with a water ligand are also provided. Transferability of the correction is adressed in the context of the implementation of the AMOEBA and SIBFA polarizable force fields in the TINKER‐HP software. As the choices of the multipolar distribution are discussed, conclusions are drawn for the future penetration‐corrected polarizable force fields highlighting the mandatory need of non‐spurious procedures for the obtention of well balanced and physically meaningful distributed moments. Finally, scalability and parallelism of the short‐range corrected SPME approach are addressed, demonstrating that the damping function is computationally affordable and accurate for molecular dynamics simulations of complex bio‐ or bioinorganic systems in periodic boundary conditions. © 2016 Wiley Periodicals, Inc.