Modeling nuclear volume isotope effects in crystals

Abstract

Mass-independent isotope fractionations driven by differences in volumes and shapes of nuclei (the field shift effect) are known in several elements and are likely to be found in more. All-electron relativistic electronic structure calculations can predict this effect but at present are computationally intensive and limited to modeling small gas phase molecules and clusters. Density functional theory, using the projector augmented wave method (DFT-PAW), has advantages in greater speed and compatibility with a three-dimensional periodic boundary condition while preserving information about the effects of chemistry on electron densities within nuclei. These electron density variations determine the volume component of the field shift effect. In this study, DFT-PAW calculations are calibrated against all-electron, relativistic DiracHartree-Fock, and coupled-cluster with single, double (triple) excitation methods for estimating nuclear volume isotope effects. DFT-PAW calculations accurately reproduce changes in electron densities within nuclei in typical molecules, when PAW datasets constructed with finite nuclei are used. Nuclear volume contributions to vapor-crystal isotope fractionation are calculated for elemental cadmium and mercury, showing good agreement with experiments. The nuclear-volume component of mercury and cadmium isotope fractionations between atomic vapor and montroydite (HgO), cinnabar (HgS), calomel (Hg 2 Cl 2 ), monteponite (CdO), and the CdS polymorphs hawleyite and greenockite are calculated, indicating preferential incorporation of neutron-rich isotopes in more oxidized, ionically bonded phases. Finally, field shift energies are related to Mössbauer isomer shifts, and equilibrium massindependent fractionations for several tin-bearing crystals are calculated from 119 Sn spectra. Isomer shift data should simplify calculations of mass-independent isotope fractionations in other elements with Mössbauer isotopes, such as platinum and uranium.Mössbauer spectroscopy | nuclear field shift | mass independent fractionation A mong the various causes of mass-independent isotope fractionation discovered over the past 40 years, the nuclear field shift effect (1) is unique in that it is an equilibrium thermodynamic phenomenon (and may also impart an identifiable and distinct signature in disequilibrium conditions) (2, 3). It has also proven amenable to prediction by electronic structure methods, at least in simple molecular systems (e.g., refs. 4-7). The goal of the present study is to extend the scope of systems that can be modeled to include condensed phases and crystals, and to speed up calculations for complex materials while retaining enough accuracy to be useful.Nuclear field shift effects result from the finite volume and sometimes nonspherical shapes of atomic nuclei, which are slightly different from one isotope to another. These differences in size and shape affect the coulomb potential felt by bound electrons, and thus the electronic structures of atoms and molecules. Nuclear field shifts have lo...

Nuclear field shift effects on stable isotope fractionation: a review

“…Therefore, Schauble (2013) chose not to use Eq. (19) but to figure out a way that can indirectly obtain the energy shift (dT).…”

“…To date, there is only one paper that reports the nuclear field shift effects in crystalline solids. Schauble (2013) estimated that the all-electron four-component Dirac-Hartree-Fock (DHF) method can be affordable only for systems with less than 20 atoms due to its computation intensity. Therefore, a density functional theory (DFT) based method is developed by Schauble (2013) to model the nuclear field shift effects in crystals.…”

“…Schauble (2013) estimated that the all-electron four-component Dirac-Hartree-Fock (DHF) method can be affordable only for systems with less than 20 atoms due to its computation intensity. Therefore, a density functional theory (DFT) based method is developed by Schauble (2013) to model the nuclear field shift effects in crystals. This new method uses the projector augmented wave method (DFT-PAW) with the three-dimensional periodic boundary condition for greater speed and compatibility (Schauble 2013).…”

“…Therefore, a density functional theory (DFT) based method is developed by Schauble (2013) to model the nuclear field shift effects in crystals. This new method uses the projector augmented wave method (DFT-PAW) with the three-dimensional periodic boundary condition for greater speed and compatibility (Schauble 2013). Schauble (2013) compared the contact densities of a few species by the four-component relativistic Dirac-HartreeFock (DHF) method and by the DFT-PAW method (with the Perdew-Wang functional in the local density approximation and the Perdew, Burke, and Ernzerhof functional in the generalized gradient approximation methods), which are implemented in DIRAC and ABINIT software packages, respectively (Fig.…”

Introduction to Chemistry and Applications in Nature of Mass Independent Isotope Effects Special Feature

“…In ref. 75, the basic chemical physics of the nuclear volume effect, specifically for crystals, has been treated using density functional theory and applying a projector augmented wave method (DFT-PAW). This technique has the advantage in its computational ability, and the results are contrasted against other techniques that estimate nuclear volume.…”