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Direct determination of amorphous number density from the reduced pair distribution function.

ABSTRACT: The inference of amorphous bulk density, while straightforward for nonporous, soluble materials, may present a formidable challenge in some of the most important classes of industrial applications, involving melts, porous solids, and non-soluble organic pharmaceuticals, with varied implications depending on the material's level of technological interest. Within nanotechnology and the life sciences in particular, accurate determination of amorphous true density is a frequent requirement and a regular puzzle, when, e.g., neither the Archimedean principle nor gas pycnometry may be applied, the former being only applicable to insoluble compounds, while the latter yielding skeletal density - an overestimate of true density to the extent of blind pores - and its efficiency is affected by the choice of the gas medium. In these cases, it is feasible to infer amorphous density from diffraction experiments through the use of the reduced Pair Distribution Function (PDF). Although an estimate of crystalline density has been known to be possible via the PDF shape, here we outline a new method extending this facility to include the estimation of amorphous density. •Amorphous density may be inferred from the position of a local minimum of the reduced PDF profile, the latter extracted via a Fourier transformation of collected diffraction intensity.•The PDF minimum is located within the PDF range bounded by r_min?=?2?/Q_max and the position of the first coordination peak, where Q_max is the maximum length of the scattering vector achieved in the diffraction experiment.•Amorphous density is calculated as the ratio of the value of the reduced PDF at the local minimum, divided by the term 4?r, where r is the real space coordinate of the local minimum.

SUBMITTER: Antipas GSE

PROVIDER: S-EPMC6446046 | biostudies-literature | 2019

REPOSITORIES: biostudies-literature

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Direct determination of amorphous number density from the reduced pair distribution function.

Antipas Georgios S E GSE Karalis Konstantinos T KT

MethodsX 20190321

The inference of amorphous bulk density, while straightforward for nonporous, soluble materials, may present a formidable challenge in some of the most important classes of industrial applications, involving melts, porous solids, and non-soluble organic pharmaceuticals, with varied implications depending on the material's level of technological interest. Within nanotechnology and the life sciences in particular, accurate determination of amorphous true density is a frequent requirement and a reg ...[more]

PMID: 30984568

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Project description:Multi-configuration pair-density functional theory (MC-PDFT) has proved to be a powerful way to combine the capabilities of multi-configuration self-consistent-field theory to represent the an electronic wave function with a highly efficient way to include dynamic correlation energy by density functional theory. All applications reported previously involved complete active space self-consistent-field (CASSCF) theory for the reference wave function. For treating large systems efficiently, it is necessary to ask whether good accuracy is retained when using less complete configuration interaction spaces. To answer this question, we present here calculations employing MC-PDFT with the separated pair (SP) approximation, which is a special case (defined in this article) of generalized active space self-consistent-field (GASSCF) theory in which no more than two orbitals are included in any GAS subspace and in which inter-subspace excitations are excluded. This special case of MC-PDFT will be called SP-PDFT. In SP-PDFT, the electronic kinetic energy and the classical Coulomb energy, the electronic density and its gradient, and the on-top pair density and its gradient are obtained from an SP approximation wave function; the electronic energy is then calculated from the first two of these quantities and an on-top density functional of the last four. The accuracy of the SP-PDFT method for predicting the structural properties and bond dissociation energies of twelve diatomic molecules and two triatomic molecules is compared to the SP approximation itself and to CASSCF, MC-PDFT based on CASSCF, CASSCF followed by second order perturbation theory (CASPT2), and Kohn-Sham density functional theory with the PBE exchange-correlation potential. We show that SP-PDFT reproduces the accuracy of MC-PDFT based on the corresponding CASSCF wave function for predicting C-H bond dissociation energies, the reaction barriers of pericyclic reactions and the properties of open-shell singlet systems, all at only a small fraction of the computational cost.

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Direct determination of amorphous number density from the reduced pair distribution function.

Publications

Direct determination of amorphous number density from the reduced pair distribution function.

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