81 research outputs found
Interatomic Methods for the Dispersion Energy Derived from the Adiabatic Connection Fluctuation-Dissipation Theorem
Interatomic pairwise methods are currently among the most popular and
accurate ways to include dispersion energy in density functional theory (DFT)
calculations. However, when applied to more than two atoms, these methods are
still frequently perceived to be based on \textit{ad hoc} assumptions, rather
than a rigorous derivation from quantum mechanics. Starting from the adiabatic
connection fluctuation-dissipation (ACFD) theorem, an exact expression for the
electronic exchange-correlation energy, we demonstrate that the pairwise
interatomic dispersion energy for an arbitrary collection of isotropic
polarizable dipoles emerges from the second-order expansion of the ACFD
formula. Moreover, for a system of quantum harmonic oscillators coupled through
a dipole--dipole potential, we prove the equivalence between the full
interaction energy obtained from the Hamiltonian diagonalization and the ACFD
correlation energy in the random-phase approximation. This property makes the
Hamiltonian diagonalization an efficient method for the calculation of the
many-body dispersion energy. In addition, we show that the switching function
used to damp the dispersion interaction at short distances arises from a
short-range screened Coulomb potential, whose role is to account for the
spatial spread of the individual atomic dipole moments. By using the ACFD
formula we gain a deeper understanding of the approximations made in the
interatomic pairwise approaches, providing a powerful formalism for further
development of accurate and efficient methods for the calculation of the
dispersion energy
Long-range correlation energy calculated from coupled atomic response functions
An accurate determination of the electron correlation energy is essential for
describing the structure, stability, and function in a wide variety of systems,
ranging from gas-phase molecular assemblies to condensed matter and
organic/inorganic interfaces. Even small errors in the correlation energy can
have a large impact on the description of chemical and physical properties in
the systems of interest. In this context, the development of efficient
approaches for the accurate calculation of the long-range correlation energy
(and hence dispersion) is the main challenge. In the last years a number of
methods have been developed to augment density functional approximations via
dispersion energy corrections, but most of these approaches ignore the
intrinsic many-body nature of correlation effects, leading to inconsistent and
sometimes even qualitatively incorrect predictions. Here we build upon the
recent many-body dispersion (MBD) framework, which is intimately linked to the
random-phase approximation for the correlation energy. We separate the
correlation energy into short-range contributions that are modeled by
semi-local functionals and long-range contributions that are calculated by
mapping the complex all-electron problem onto a set of atomic response
functions coupled in the dipole approximation. We propose an effective
range-separation of the coupling between the atomic response functions that
extends the already broad applicability of the MBD method to non-metallic
materials with highly anisotropic responses, such as layered nanostructures.
Application to a variety of high-quality benchmark datasets illustrates the
accuracy and applicability of the improved MBD approach, which offers the
prospect of first-principles modeling of large structurally complex systems
with an accurate description of the long-range correlation energy.Comment: 15 pages, 3 figure
Inverse design of disordered stealthy hyperuniform spin chains
Positioned between crystalline solids and liquids, disordered many-particle
systems which are stealthy and hyperuniform represent new states of matter that
are endowed with novel physical and thermodynamic properties. Such stealthy and
hyperuniform states are unique in that they are transparent to radiation for a
range of wavenumbers around the origin. In this work, we employ recently
developed inverse statistical-mechanical methods, which seek to obtain the
optimal set of interactions that will spontaneously produce a targeted
structure or configuration as a unique ground state, to investigate the
spin-spin interaction potentials required to stabilize disordered stealthy
hyperuniform one-dimensional (1D) Ising-like spin chains. By performing an
exhaustive search over the spin configurations that can be enumerated on
periodic 1D integer lattices containing sites, we were able
to identify and structurally characterize \textit{all} stealthy hyperuniform
spin chains in this range of system sizes. Within this pool of stealthy
hyperuniform spin configurations, we then utilized such inverse optimization
techniques to demonstrate that stealthy hyperuniform spin chains can be
realized as either unique or degenerate disordered ground states of radial
long-ranged (relative to the spin chain length) spin-spin interactions. Such
exotic ground states are distinctly different from spin glasses in both their
inherent structural properties and the nature of the spin-spin interactions
required to stabilize them. As such, the implications and significance of the
existence of such disordered stealthy hyperuniform ground state spin systems
warrants further study, including whether their bulk physical properties and
excited states, like their many-particle system counterparts, are singularly
remarkable, and can be experimentally realized.Comment: 11 pages, 9 figure
Electronic Properties of Molecules and Surfaces with a Self\uad-Consistent Interatomic van der Waals Density Functional.
How strong is the effect of van der Waals (vdW) interactions on the electronic properties of molecules
and extended systems? To answer this question, we derived a fully self-consistent implementation of the
density-dependent interatomic vdW functional of Tkatchenko and Scheffler [Phys. Rev. Lett. 102, 073005
(2009)]. Not surprisingly, vdW self-consistency leads to tiny modifications of the structure, stability, and
electronic properties of molecular dimers and crystals. However, unexpectedly large effects were found in
the binding energies, distances, and electrostatic moments of highly polarizable alkali-metal dimers. Most
importantly, vdW interactions induced complex and sizable electronic charge redistribution in the vicinity
of metallic surfaces and at organic-metal interfaces. As a result, a substantial influence on the computed
work functions was found, revealing a nontrivial connection between electrostatics and long-range electron
correlation effects
The Individual and Collective Effects of Exact Exchange and Dispersion Interactions on the Ab Initio Structure of Liquid Water
In this work, we report the results of a series of density functional theory
(DFT) based ab initio molecular dynamics (AIMD) simulations of ambient liquid
water using a hierarchy of exchange-correlation (XC) functionals to investigate
the individual and collective effects of exact exchange (Exx), via the PBE0
hybrid functional, non-local vdW/dispersion interactions, via a fully
self-consistent density-dependent dispersion correction, and approximate
nuclear quantum effects (aNQE), via a 30 K increase in the simulation
temperature, on the microscopic structure of liquid water. Based on these AIMD
simulations, we found that the collective inclusion of Exx, vdW, and aNQE as
resulting from a large-scale AIMD simulation of (HO) at the
PBE0+vdW level of theory, significantly softens the structure of ambient liquid
water and yields an oxygen-oxygen structure factor, , and
corresponding oxygen-oxygen radial distribution function, , that
are now in quantitative agreement with the best available experimental data.
This level of agreement between simulation and experiment as demonstrated
herein originates from an increase in the relative population of water
molecules in the interstitial region between the first and second coordination
shells, a collective reorganization in the liquid phase which is facilitated by
a weakening of the hydrogen bond strength by the use of the PBE0 hybrid XC
functional, coupled with a relative stabilization of the resultant disordered
liquid water configurations by the inclusion of non-local vdW/dispersion
interactions
Accurate molecular polarizabilities with coupled-cluster theory and machine learning
The molecular polarizability describes the tendency of a molecule to deform
or polarize in response to an applied electric field. As such, this quantity
governs key intra- and inter-molecular interactions such as induction and
dispersion, plays a key role in determining the spectroscopic signatures of
molecules, and is an essential ingredient in polarizable force fields and other
empirical models for collective interactions. Compared to other ground-state
properties, an accurate and reliable prediction of the molecular polarizability
is considerably more difficult as this response quantity is quite sensitive to
the description of the underlying molecular electronic structure. In this work,
we present state-of-the-art quantum mechanical calculations of the static
dipole polarizability tensors of 7,211 small organic molecules computed using
linear-response coupled-cluster singles and doubles theory (LR-CCSD). Using a
symmetry-adapted machine-learning based approach, we demonstrate that it is
possible to predict the molecular polarizability with LR-CCSD accuracy at a
negligible computational cost. The employed model is quite robust and
transferable, yielding molecular polarizabilities for a diverse set of 52
larger molecules (which includes challenging conjugated systems, carbohydrates,
small drugs, amino acids, nucleobases, and hydrocarbon isomers) at an accuracy
that exceeds that of hybrid density functional theory (DFT). The atom-centered
decomposition implicit in our machine-learning approach offers some insight
into the shortcomings of DFT in the prediction of this fundamental quantity of
interest
Non-covalent interactions across organic and biological subsets of chemical space: Physics-based potentials parametrized from machine learning
Classical intermolecular potentials typically require an extensive
parametrization procedure for any new compound considered. To do away with
prior parametrization, we propose a combination of physics-based potentials
with machine learning (ML), coined IPML, which is transferable across small
neutral organic and biologically-relevant molecules. ML models provide
on-the-fly predictions for environment-dependent local atomic properties:
electrostatic multipole coefficients (significant error reduction compared to
previously reported), the population and decay rate of valence atomic
densities, and polarizabilities across conformations and chemical compositions
of H, C, N, and O atoms. These parameters enable accurate calculations of
intermolecular contributions---electrostatics, charge penetration, repulsion,
induction/polarization, and many-body dispersion. Unlike other potentials, this
model is transferable in its ability to handle new molecules and conformations
without explicit prior parametrization: All local atomic properties are
predicted from ML, leaving only eight global parameters---optimized once and
for all across compounds. We validate IPML on various gas-phase dimers at and
away from equilibrium separation, where we obtain mean absolute errors between
0.4 and 0.7 kcal/mol for several chemically and conformationally diverse
datasets representative of non-covalent interactions in biologically-relevant
molecules. We further focus on hydrogen-bonded complexes---essential but
challenging due to their directional nature---where datasets of DNA base pairs
and amino acids yield an extremely encouraging 1.4 kcal/mol error. Finally, and
as a first look, we consider IPML in denser systems: water clusters,
supramolecular host-guest complexes, and the benzene crystal.Comment: 15 pages, 9 figure
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