A finite field method for calculating molecular polarizability tensors for arbitrary multipole rank

A building-block database of distributed polarizabilities and dipole moments to estimate optical properties of biomacromolecules in isolation or in an explicitly solvated medium

Since atomic or functional-group properties in the bulk are generally not available from experimental methods, computational approaches based on partitioning schemes have emerged as a rapid yet accurate pathway to estimate the materials behavior from chemically meaningful building blocks. Among several applications, a comprehensive and systematically built database of atomic or group polarizabilities and related opto-electronic quantities would be very useful not only to envisage linear or non-linear optical properties of biomacromolecules but also to improve the accuracy of classical force fields devoted to simulate biochemical processes. In this work, we propose the first entries of such database that contains distributed polarizabilities and dipole moments extracted from fragments of peptides. Twenty three prototypical conformers of the dipeptides alanine-alanine and glycine-glycine were used to extract functional groups such as CH₂ , CHCH₃ , NH₂ , COOH, CONH, thus allowing construction of a diversity of chemically relevant environments. To evaluate the accuracy of our database, reconstructed properties of larger peptides containing up to six residues of alanine and glycine were tested against density functional theory calculations at the M06-HF/aug-cc-pVDZ level of theory. The procedure is particularly accurate for the diagonal components of the polarizability tensor with errors up to 15%. In order to include solvent effects explicitly, the peptides were also surrounded by a box of water molecules whose distribution was optimized using the CHARMM force field. Solvent effects introduced by a classical dipole-dipole interaction model were compared to those obtained from polarizable-continuum model calculations.

Polarizabilities, dispersion coefficients, and retardation functions at the complete basis set CCSD limit: From Be to Ba plus Yb

Static and dynamic polarizabilities of alkaline earth metal atoms Be-Ba and of the Yb atom, as well as dispersion coefficients and retardation functions for their long-range interactions, are used as a benchmark for the restricted coupled cluster method with singles and doubles (CCSD) and noniterative triples added [CCSD(T)] and related polarization propagator CCSD(3) methods at the complete basis set limit. The latter is attained through the sequence of the augmented correlation-consistent polarized weighted core valence n-zeta basis sets with the exact 2-component approximation for the scalar relativistic effects and with the small-core effective core potentials (for Ca, Sr, and Ba). At the converged level of core correlation treatment, the finite-field CCSD(T) method reproduces the best available data for the static dipole and quadrupole polarizabilities better than 1% and 4%, respectively. Systematic cancelation of the triple contribution in the CCSD(3) calculations of the dynamic polarizabilities of alkaline earth metal atoms makes their dispersion coefficients accurate within 3%. The retardation functions are computed and used for the analysis of the long-range interactions in the homonuclear dimers. Implications to accurate ab initio calculations of the global interaction potentials are discussed.

On the geometric dependence of the molecular dipole polarizability in water: A benchmark study of higher-order electron correlation, basis set incompleteness error, core electron effects, and zero-point vibrational contributions

In this work, we investigate how geometric changes influence the static dipole polarizability (α) of a water molecule by explicitly computing the corresponding dipole polarizability surface (DPS) across 3125 total (1625 symmetry-unique) geometries using linear response coupled cluster theory including single, double, and triple excitations (LR-CCSDT) and the doubly augmented triple-ζ basis set (d-aug-cc-pVTZ). Analytical formulae based on power series expansions of this ab initio surface are generated using linear least-squares analysis and provide highly accurate estimates of this quantity as a function of molecular geometry (i.e., bond and angle variations) in a computationally tractable manner. An additional database, which consists of 25 representative molecular geometries and incorporates a more thorough treatment of both basis sets and core electron effects, is provided as a current benchmark for this quantity and the corresponding leading-order C ₆ dispersion coefficient. This database has been utilized to assess the importance of these effects as well as the relative accuracy that can be obtained using several quantum chemical methods and a library of density functional approximations. In addition to high-level electron correlation methods (like CCSD) and our analytical least-squares formulae, we find that the SCAN0, PBE0, MN15, and B97-2 hybrid functionals yield the most accurate descriptions of the molecular polarizability tensor in H₂O. Using first-order perturbation theory, we compute the zero-point vibrational correction to α at the CCSDT/d-aug-cc-pVTZ level and find that this correction contributes approximately 3% to the isotropic (α _iso) and nearly 50% to the anisotropic (α _aniso) polarizability values. In doing so, we find that α _iso = 9.8307 bohr³, which is in excellent agreement with the experimental value of 9.83 ± 0.02 bohr³ provided by Russell and Spackman. The DPS reported herein provides a benchmark-quality quantum mechanical estimate of this fundamental quantity of interest and should find extensive use in the development (and assessment) of next-generation force fields and machine-learning based approaches for modeling water in complex condensed-phase environments.

Torque and atomic forces for Cartesian tensor atomic multipoles with an application to crystal unit cell optimization

New equations for torque and atomic force are derived for use in flexible molecule force fields with atomic multipoles. The expressions are based on Cartesian tensors with arbitrary multipole rank. The standard method for rotating Cartesian tensor multipoles and calculating torque is to first represent the tensor with n indexes and 3(n) redundant components. In this work, new expressions for directly rotating the unique (n + 1)(n + 2)/2 Cartesian tensor multipole components Θpqr are given by introducing Cartesian tensor rotation matrix elements X(R). A polynomial expression and a recursion relation for X(R) are derived. For comparison, the analogous rotation matrix for spherical tensor multipoles are the Wigner functions D(R). The expressions for X(R) are used to derive simple equations for torque and atomic force. The torque and atomic force equations are applied to the geometry optimization of small molecule crystal unit cells. In addition, a discussion of computational efficiency as a function of increasing multipole rank is given for Cartesian tensors. © 2016 Wiley Periodicals, Inc.

Crystal structure prediction of rigid molecules

A non-polarizable force field based on atomic multipoles fit to reproduce experimental crystal properties andab initiogas-phase dimers is described. The Ewald method is used to calculate both long-range electrostatic and 1/r6dispersion energies of crystals. The dispersion energy of a crystal calculated by a cutoff method is shown to converge slowly to the exact Ewald result. A method for constraining space-group symmetry during unit-cell optimization is derived. Results for locally optimizing 4427 unit cells including volume, cell parameters, unit-cell r.m.s.d. and CPU timings are given for both flexible and rigid molecule optimization. An algorithm for randomly generating rigid molecule crystals is described. Using the correct experimentally determined space group, the average and maximum number of random crystals needed to find the correct experimental structure is given for 2440 rigid single component crystals. The force field energy rank of the correct experimental structure is presented for the same set of 2440 rigid single component crystals assuming the correct space group. A complete crystal prediction is performed for two rigid molecules by searching over the 32 most probable space groups.

Pair-potential approach to accurate dispersion energies between group 12 (Zn, Cd, Hg) clusters

Dispersion interactions between group 12 (Zn, Cd, Hg) metal clusters are studied at the CCSD(T) level with triple-ζ basis sets. We use atomic orientation dependent C6 dispersion coefficients derived from simple model systems to calculate the intermolecular dispersion energy between larger metal clusters. By using an atomic pair-potential model, we are able to obtain highly accurate results comparable to the CCSD(T) level of theory. For all the systems studied, our method results in a robust description of the dispersion energy at long distances, and it is able to outperform the examined dispersion corrected DFT calculations.

Limiting assumptions in molecular modeling: electrostatics

Molecular mechanics attempts to represent intermolecular interactions in terms of classical physics. Initial efforts assumed a point charge located at the atom center and coulombic interactions. It is been recognized over multiple decades that simply representing electrostatics with a charge on each atom failed to reproduce the electrostatic potential surrounding a molecule as estimated by quantum mechanics. Molecular orbitals are not spherically symmetrical, an implicit assumption of monopole electrostatics. This perspective reviews recent evidence that requires use of multipole electrostatics and polarizability in molecular modeling.

Can lattice models predict the density of states of amorphous organic semiconductors?

We extend existing lattice models of small-molecule amorphous semiconductors by accounting for changes in molecular polarizability upon charging or excitation. A compact expression of this contribution to the density of states is provided. Although the lattice model and the description based on a microscopic morphology both qualitatively predict an additional broadening, shift, and an exponential tail (traps) of the density of states, a quantitative agreement between the two cannot be achieved.

HPAM: Hirshfeld Partitioned Atomic Multipoles

An implementation of the Hirshfeld (HD) and Hirshfeld-Iterated (HD-I) atomic charge density partitioning schemes is described. Atomic charges and atomic multipoles are calculated from the HD and HD-I atomic charge densities for arbitrary atomic multipole rank l(max) on molecules of arbitrary shape and size. The HD and HD-I atomic charges/multipoles are tested by comparing molecular multipole moments and the electrostatic potential (ESP) surrounding a molecule with their reference ab initio values. In general, the HD-I atomic charges/multipoles are found to better reproduce ab initio electrostatic properties over HD atomic charges/multipoles. A systematic increase in precision for reproducing ab initio electrostatic properties is demonstrated by increasing the atomic multipole rank from l(max) = 0 (atomic charges) to l(max) = 4 (atomic hexadecapoles). Both HD and HD-I atomic multipoles up to rank l(max) are shown to exactly reproduce ab initio molecular multipole moments of rank L for L ≤ l(max). In addition, molecular dipole moments calculated by HD, HD-I, and ChelpG atomic charges only (l(max) = 0) are compared with reference ab initio values. Significant errors in reproducing ab initio molecular dipole moments are found if only HD or HD-I atomic charges used.