Search

In this study, we analyze various Iterative Stockholder Analysis (ISA) methods for molecular density partitioning, focusing on the numerical performance of the recently proposed Linear approximation of Iterative Stockholder Analysis model (LISA) [J. Chem. Phys. 156, 164107 (2022)]. We first provide a systematic derivation of various iterative solvers to find the unique LISA solution. In a subsequent systematic numerical study, we evaluate their performance on 48 organic and inorganic, neutral and charged molecules and also compare LISA to two other well-known ISA variants: the Gaussian Iterative Stockholder Analysis (GISA) and Minimum Basis Iterative Stockholder analysis (MBIS). The study reveals that LISA-family methods can offer a numerically more efficient approach with better accuracy compared to the two comparative methods. Moreover, the well-known issue with the MBIS method, where atomic charges obtained for negatively charged molecules are anomalously negative, is not observed in LISA-family methods. Despite the fact that LISA occasionally exhibits elevated entropy as a consequence of the absence of more diffuse basis functions, this issue can be readily mitigated by incorporating additional or integrating supplementary basis functions within the LISA framework. This research provides the foundation for future studies on the efficiency and chemical accuracy of molecular density partitioning schemes.

The many-body polarization energy is the major source of non-additivity in strongly polar systems such as water. This non-additivity is often considerable and must be included, if only in an average manner, to correctly describe the physical properties of the system. Models for the polarization energy are usually parameterized using experimental data, or theoretical estimates of the many-body effects. Here we show how many-body polarization models can be developed for water complexes using data for the monomer and dimer only using ideas recently developed in the field of intermolecular perturbation theory and state-of-the-art approaches for calculating distributed molecular properties based on the iterated stockholder atoms (ISA) algorithm. We show how these models can be calculated, and validate their accuracy in describing the many-body non-additive energies of a range of water clusters. We further investigate their sensitivity to the details of the polarization damping models used. We show how our very best polarization models yield many-body energies that agree with those computed with coupled-cluster methods, but at a fraction of the computational cost., Comment: 21 pages, 19 figures, SI

Nearly all standard force fields employ the 'sum-of-spheres' approximation, which models intermolecular interactions purely in terms of interatomic distances. Nonetheless, atoms in molecules can have significantly non-spherical shapes, leading to interatomic interaction energies with strong orientation dependencies. Neglecting this 'atomic-level anisotropy' can lead to significant errors in predicting interaction energies. Herein we propose a simple, transferable, and computationally-efficient model (MASTIFF) whereby atomic-level orientation dependence can be incorporated into ab initio intermolecular force fields. MASTIFF includes anisotropic exchange-repulsion, charge penetration, and dispersion effects, in conjunction with a standard treatment of anisotropic long-range (multipolar) electrostatics. To validate our approach, we benchmark MASTIFF against various sum-of-spheres models over a large library of intermolecular interactions between small organic molecules. MASTIFF achieves quantitative accuracy with respect to both high-level electronic structure theory and experiment, thus showing promise as a basis for 'next-generation' force field development.

Recently we have developed a robust, basis-space implementation of the iterated stockholder atoms (BS-ISA) approach for defining atoms in a molecule. This approach has been shown to yield rapidly convergent distributed multipole expansions with a well-defined basis-set limit. Here we use this method as the basis of a new approach, termed ISA-Pol, for obtaining non-local distributed frequency-dependent polarizabilities. We demonstrate how ISA-Pol can be combined with localization methods to obtain distributed dispersion models that share the many unique properties of the ISA: These models have a well-defined basis-set limit, lead to very accurate dispersion energies, and, remarkably, satisfy commonly used combination rules to a good accuracy. As these models are based on the ISA, they can be expected to respond to chemical and physical changes naturally, and thus they may serve as the basis for the next generation of polarization and dispersion models for ab initio force-field development., Comment: 18 pages, 9 figures

Four kinds of magic-size CdS clusters and two different regular CdS quantum dots have been studied by x-ray total scattering technique and pair distribution function method. Results for the regular CdS quantum dots could be modelled as a mixed phase of atomic structures based on the two bulk crystalline phases, which is interpreted as representing the effects of stacking disorder. However, the results for the magic-size clusters were significantly different. On one hand, the short-range features in the pair distribution function reflect the bulk, indicating that these structures are based on the same tetrahedral coordination found in the bulk phases (and therefore excluding new types of structures such as cage-like arrangements of atoms). But on the other hand, the longer- range atomic structure clearly does not reflect the layer structures found in the bulk and the regular quantum dots. We compare the effects of two ligands, phenylacetic acid and oleic acid, showing that in two cases the ligand has little effect on the atomic structure of the magic-size nanocluster and in another it has a significant effect., Comment: 8 pages in the main paper, 6 figures in the main paper, 7 pages in the electronic supporting information, 4 figures in the electronic supporting information

Short-range repulsion within inter-molecular force fields is conventionally described by either Lennard-Jones (${A}/{r^{12}}$) or Born-Mayer ($A\exp(-Br)$) forms. Despite their widespread use, these simple functional forms are often unable to describe the interaction energy accurately over a broad range of inter-molecular distances, thus creating challenges in the development of ab initio force fields and potentially leading to decreased accuracy and transferability. Herein, we derive a novel short-range functional form based on a simple Slater-like model of overlapping atomic densities and an iterated stockholder atom (ISA) partitioning of the molecular electron density. We demonstrate that this Slater-ISA methodology yields a more accurate, transferable, and robust description of the short-range interactions at minimal additional computational cost compared to standard Lennard-Jones or Born-Mayer approaches. Finally, we show how this methodology can be adapted to yield the standard Born-Mayer functional form while still retaining many of the advantages of the Slater-ISA approach., Comment: 52 pages, 11 figures

In Part I of this two-part investigation we described a methodology for the development of robust, analytic, many-body atom-atom potentials for small organic molecules from first principles and demonstrated how the CamCASP program can be used to derive the damped, distributed multipole models for pyridine. Here we demonstrate how the theoretical ideas for the short-range models described in Part I, which are implemented in the CamCASP suite of programs, can be used to develop a series of many-body potentials for the pyridine system. Even the simplest of these potentials exhibit r.m.s. errors of only about 0.6kJ mol-1 for the low-energy pyridine dimers, significantly surpassing the best empirical potentials. Our best model is shown to support eight stable minima, four of which have not been reported in the literature before. Further, the functional form can be made systematically more elaborate so as to improve the accuracy without a significant increase in the human-time spent in their generation. We investigate the effects of anisotropy, rank of multipoles, and choice of polarizability and dispersion models., Comment: 15 pages, 12 figures, part 2 of a two part work

Creating accurate, analytic atom--atom potentials for small organic molecules from first principles can be a time-consuming and computationally intensive task, particularly if we also require them to include explicit polarization terms, which are essential in many systems. In this first part of a two-part investigation, we describe how the {\sc CamCASP} suite of programs can be used to generate such potentials using some of the most accurate electronic structure methods currently applicable. In particular, we derive the long-range terms from monomer properties, and determine the short-range anisotropy parameters by a novel and robust method based on the iterated stockholder atom approach. We use the techniques described here to develop distributed multipole models for the electrostatic, polarization and dispersion interactions in the pyridine dimer. In the second part of this work we will apply these methods to develop a series of many-body potentials for the pyridine system., Comment: 17 pages, 5 figures, part I of a two part paper

The recently developed iterated stockholder atoms (ISA) approach of Lillestolen and Wheatley (Chem. Commun. {\bf 2008}, 5909 (2008)) offers a powerful method for defining atoms in a molecule. However, the real-space algorithm is known to converge very slowly, if at all. Here we present a robust, basis-space algorithm of the ISA method and demonstrate its applicability on a variety of systems. We show that this algorithm exhibits rapid convergence (taking around 10--80 iterations) with the number of iterations needed being unrelated to the system size or basis set used. Further, we show that the multipole moments calculated using this basis-space ISA method are as good as, or better than those obtained from Stone's distributed multipole analysis (J. Chem. Theory Comput. {\bf 1}, 1128 (2005) ), exhibiting better convergence properties and resulting in better behaved penetration energies. This can have significant consequences in the development of intermolecular interaction models., Comment: 16 pages, 7 figures

The non-additive dispersion contribution to the binding energy of three one-dimensional (1D) wires is investigated using wires modelled by (i) chains of hydrogen atoms and (ii) homogeneous electron gases. We demonstrate that the non-additive dispersion contribution to the binding energy is significantly enhanced compared with that expected from Axilrod-Teller-Muto-type triple-dipole summations and follows a different power-law decay with separation. The triwire non-additive dispersion for 1D electron gases scales according to the power law $d^{-\beta}$, where $d$ is the wire separation, with exponents $\beta(r_s)$ smaller than 3 and slightly increasing with $r_s$ from 2.4 at $r_s = 1$ to 2.9 at $r_s=10$, where $r_s$ is the density parameter of the 1D electron gas. This is in good agreement with the exponent $\beta=3$ suggested by the leading-order charge-flow contribution to the triwire non-additivity, and is a significantly slower decay than the $\sim d^{-7}$ behaviour that would be expected from triple-dipole summations., Comment: 10 pages, 8 figures, 1 table

The charge-transfer (CT) together with the polarization energy appears at second and higher orders in symmetry-adapted perturbation theory (SAPT). At present there is no theoretically compelling way of isolating the charge-transfer energy that is simultaneously basis-set independent and applicable for arbitrary intermolecular separation. We argue that the charge-transfer can be interpreted as a tunneling phenomenon, and can therefore be defined via regularized SAPT. This leads to a physically convincing, basis-independent definition of the charge-transfer energy that captures subtleties of the process, such as the asymmetry in the forward and backward charge transfer, as well as secondary transfer effects. With this definition of the charge-transfer the damping needed for polarization models can be determined with a level of confidence hitherto not possible., Comment: 16 pages, 16 figures

Pressure and temperature dependence of the negative thermal expansion in Zn(CN)$_2$ is fully investigated using molecular dynamics simulations with a built potential model. The advantage of this study allows us to reproduce all the exotic behaviours of the material, including the negative thermal expansion (NTE), the reduction of NTE with elevated temperature, the pressure enhancement of NTE and the pressure-induced softening. Results of the study provide us detailed data to link the properties in the energy space and the real space, giving us insights to understand the properties and the connections between them., Comment: 12 pages, 16 figures

A combination of first-principles density functional theory calculations and a search over structures predicts the stability of a proton-transfer modification of ammonia monohydrate with space group P4/nmm. The phase diagram is calculated with the PBE density functional, and the effects of a semi-empirical dispersion correction, zero point motion, and finite temperature are investigated. Comparison with MP2 and coupled cluster calculations shows that the PBE functional over-stabilizes proton transfer phases because too much electronic charge moves with the proton. This over-binding is partially corrected by using the PBE0 hybrid exchange-correlation functional, which increases the enthalpy of P4/nmm by about 0.6 eV per formula unit relative to phase I of ammonia monohydrate (AMH-I) and shifts the transition to the proton transfer phase from the PBE pressure of 2.8 GPa to about 10 GPa. This is consistent with experiment as proton transfer phases have not been observed at pressures up to ~9 GPa, while higher pressures have not yet been explored experimentally., Comment: 10 pages, 9 figures

The dispersion energy between extended molecular chains (or equivalently infinite wires) with non-zero band gaps is generally assumed to be expressible as a pair-wise sum of atom-atom terms which decay as $R^{-6}$. Using a model system of two parallel wires with a variable band gap, we show that this is not the case. The dispersion interaction scales as $z^{-5}$ for large interwire separations $z$, as expected for an insulator, but as the band gap decreases the interaction is greatly enhanced; while at shorter (but non-overlapping) separations it approaches a power-law scaling given by $z^{-2}$, \emph{i.e.} the dispersion interaction expected between \emph{metallic} wires. We demonstrate that these effects can be understood from the increasing length scale of the plasmon modes (charge fluctuations), and their increasing contribution to the molecular dipole polarizability and the dispersion interaction, as the band gaps are reduced. This result calls into question methods which invoke locality assumptions in deriving dispersion interactions between extended small-gap systems., Comment: 8 pages, 5 figures