797 publications from this institution
The SPB of SCI patients is at a moderate level and is correlated with caregiver reactions. Rehabilitation professionals should actively guide caregivers, enhance their emotional regulation abilities, and reduce the SPB of patients.
The classical turning radius Rt of an atom can be defined as the radius where the KS potential is equal to the negative ionisation potential of the atom, i.e. where v_s(R_t)=\epsilon_h. It was recently shown [P.N.A.S. 115, E11578 (2018)] to yield chemically relevant bonding distances, in line with known empirical values. In this work we show that extension of the concept to non-integer electron number yields additional information about atomic systems, and can be used to detect the difficulty of adding or subtracting electrons. Notably, it reflects the ease of bonding in open p-shells, and its greater difficulty in open s-shells. The latter manifests in significant discontinuities in the turning radius as the electron number changes the principal quantum number of the outermost electronic shell (e.g. going from Na to Na^{2+}). We then show that a non-integer picture is required to correctly interpret bonding and dissociation in H_2^+. Results are consistent when properties are calculated exactly, or via an appropriate approximation. They can be interpreted in the context of conceptual density functional theory.
Correlation of a quantum many-body state makes the one-particle density matrix nonidempotent. Therefore, the Shannon entropy of the natural occupation numbers measures the correlation strength on the one-particle level. Here, it is shown how this general idea of a correlation entropy must be adapted for two-electron systems in view of conservation laws which mix Slater determinants even in the noninteracting limit. Results are presented for the correlation entropy s of H2 as a function of the nucleus-nucleus separation R. In the ground state, the entropy of the spatial factor of the wave function maximizes 1.7 bohr beyond the Coulson-Fischer separation. The role of the correlation entropy in density functional theory is also discussed. © 1997 John Wiley & Sons, Inc.
While first-principles density functional theory (DFT)-based models have been effective in capturing the physics of ferroelectric phase transitions in ${\mathrm{BaTiO}}_{3}, {\mathrm{PbTiO}}_{3}$, and ${\mathrm{KNbO}}_{3}$, quantitative estimates of the transition temperatures (${T}_{C}$) suffer from errors that are believed to originate from the errors in estimating lattice constants obtained within the local density approximation (LDA) and generalized gradient approximation (GGA) of DFT. The recently developed strongly constrained and appropriately normed (SCAN) meta-GGA functional has been shown to be quite accurate in the estimation of lattice constants. Here, we present a quantitative analysis of the estimates of ferroelectric ground-state properties of eight perovskite oxides and transition temperatures of ${\mathrm{BaTiO}}_{3}, {\mathrm{PbTiO}}_{3}$, and ${\mathrm{KNbO}}_{3}$ obtained with molecular dynamics simulations using an effective Hamiltonian derived from the SCAN meta-GGA-based DFT. Relative to LDA, we find an improvement in the estimates of ${T}_{C}$, which arises from the changes in the calculated strain-phonon, anharmonic coupling constants, and strength of ferroelectric instabilities, i.e., frequencies of the soft modes. We also assess the errors in ${T}_{C}$ originating from approximately integrating out the high-energy phonons during construction of the model Hamiltonian through estimates of the effects of fourth-order couplings between the soft mode and higher-energy modes of ${\mathrm{BaTiO}}_{3}, {\mathrm{PbTiO}}_{3}$, and ${\mathrm{KNbO}}_{3}$. We find that inclusion of these anharmonic couplings results in deeper double-well energy functions of ferroelectric distortions and further improvement in the estimates of transition temperatures. Consistently improved estimates of lattice constants and transition temperatures with the SCAN meta-GGA calculations augur well for their use in simulations of superlattices or heterostructures of perovskite oxides, in which the effects of lattice matching are critical.
2-Aminoethoxydiphenylborate (2-APB) is a broad-spectrum modulator of various membrane proteins. Specifically, it exhibits concentration dependent modulation of calcium signaling through store-operated calcium (SOC) channels: low micromolar concentration of 2-APB stimulates SOC entry while a higher concentration induces complete inhibition. Ab initio quantum chemical calculations show that the relative stability of the two major isomers of 2-APB (cyclic and extended) is about 8 kcal/mol. The dual functionality of 2-APB for SOC channels is thus likely associated with its ability to switch among isomeric forms, suited to different binding sites in the SOC channels with distinct binding affinities. Importantly, the moderate relative stability of different isomers results from a delicate balance between the intramolecular boron-nitrogen coordinate bond with strength about -45 kcal/mol and ring strain engendered by cyclic oligomerization. The synergistic effect of these two factors likely makes 2-APB an ideal dual effect drug.
Lieb and Oxford (1981) derived rigorous lower bounds, in the form of local functionals of the electron density, on the indirect part of the Coulomb repulsion energy. The greatest lower bound for a given electron number $N$ depends monotonically upon $N$, and the $N\to\infty$ limit is a bound for all $N$. These bounds have been shown to apply to the exact density functionals for the exchange- and exchange-correlation energies that must be approximated for an accurate and computationally efficient description of atoms, molecules, and solids. A tight bound on the exact exchange energy has been derived therefrom for two-electron ground states, and is conjectured to apply to all spin-unpolarized electronic ground states. Some of these and other exact constraints have been used to construct two generations of non-empirical density functionals beyond the local density approximation: the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA), and the strongly constrained and appropriately normed (SCAN) meta-GGA.
We approximate the exchange-correlation energy of density functional theory as a controlled extrapolation from the slowly varying limit. While generalized gradient approximations (GGA's) require only the local density and its first gradient as input, our meta-GGA also requires the orbital kinetic energy density. Its exchange energy component recovers the fourth-order gradient expansion, while its correlation energy is free of self-interaction error. Molecular atomization energies and metal surface energies are significantly improved over GGA, while lattice constants are little changed.
We construct analytic formulas that represent the coupling-constant-averaged pair distribution function ${g}_{\mathrm{xc}}{(r}_{s},\ensuremath{\zeta}{,k}_{F}u)$ of a three-dimensional nonrelativistic ground-state electron gas constrained to a uniform density with density parameter ${r}_{s}=(9\ensuremath{\pi}{/4)}^{1/3}{/k}_{F}$ and relative spin polarization $\ensuremath{\zeta}$ over the whole range $0<{r}_{s}<\ensuremath{\infty}$ and $\ensuremath{-}1<\ensuremath{\zeta}<1,$ with energetically unimportant long range $(\stackrel{\ensuremath{\rightarrow}}{u}\ensuremath{\infty})$ oscillations averaged out. The pair distribution function ${g}_{\mathrm{xc}}$ at the physical coupling constant is then given by differentiation with respect to ${r}_{s}.$ Our formulas are constructed using only known theoretical constraints plus the correlation energy ${\ensuremath{\epsilon}}_{c}{(r}_{s},\ensuremath{\zeta}),$ and accurately reproduce the ${g}_{\mathrm{xc}}$ of the quantum Monte Carlo method and of the fluctuation-dissipation theorem with the Richardson-Ashcroft dynamical local-field factor. Our ${g}_{\mathrm{xc}}$ is correct even in the high-density ${(r}_{s}\ensuremath{\rightarrow}0)$ and low-density ${(r}_{s}\ensuremath{\rightarrow}\ensuremath{\infty})$ limits. When the spin resolution of ${\ensuremath{\epsilon}}_{c}$ into $\ensuremath{\uparrow}\ensuremath{\uparrow},$ $\ensuremath{\downarrow}\ensuremath{\downarrow},$ and $\ensuremath{\uparrow}\ensuremath{\downarrow}$ contributions is known, as it is in the high- and low-density limits, our formulas also yield the spin resolution of ${g}_{\mathrm{xc}}.$ Because of these features, our formulas may be useful for the construction of density functionals for nonuniform systems. We also analyze the kinetic energy of correlation into contributions from density fluctuations of various wave vectors. The exchange and long-range correlation parts of our ${g}_{\mathrm{xc}}{(r}_{s},\ensuremath{\zeta}{,k}_{F}u)\ensuremath{-}1$ are analytically Fourier transformable, so that the static structure factor ${S}_{\mathrm{xc}}{(r}_{s},\ensuremath{\zeta}{,k/k}_{F})$ is easily evaluated.
From a global perspective, the density of an atom is strongly inhomogeneous and not at all like the density of a uniform or nearly-uniform electron gas. But, from the semi-local or myopic perspective of standard density functional approximations to the exchange-correlation energy,it is not so easy to tell an atom from an electron gas. We address the following problem: Given the ground-state electron density n and orbital kinetic energy density in the neighborhood of a point r, can we construct an "inhomogeneity index" w(r) which approaches zero for weakly-inhomogeneous densities and unity for strongly-inhomogeneous ones? The solution requires not only the usual local ingredients of a meta-generalized gradient approximation (n,rn,r2n, ),but also r and r2 . The inhomogeneity index is displayed for atoms, and for model densities of metal surfaces and bulk metals. Scaling behavior and a possible application to functional interpolation are discussed.
A comprehensive study of the lattice dynamics, elastic moduli, and liquid metal resistivities for 16 simple metals in the bcc and fcc crystal structures is made using a density-based local pseudopotential. The phonon frequencies exhibit excellent agreement with both experiment and nonlocal pseudopotential theory. The bulk modulus is evaluated by the long wave and homogeneous deformation methods, which agree after a correction is applied to the former. Calculated bulk and Voigt shear moduli are insensitive to crystal structure, and long-wavelength soft modes are found in certain cases. Resistivity calculations confirm that electrons scatter off the whole Kohn-Sham potential, including its exchange-correlation part as well as its Hartree part. All of these results are found in second-order pseudopotential perturbation theory. However, the effect of a nonperturbative treatment on the calculated lattice constant is not negligible, showing that higher-order contributions have been subsumed into the pseudopotential by construction. For bcc sodium, the band structures of local and nonlocal pseudopotentials are found to be almost identical.
The void formation energy is the work needed to create the curved surface of a void. For a spherical hole in a homogeneous metal (jellium or stabilized jellium), the void formation energy is calculated for large radii from the liquid-drop model (surface plus curvature terms), and for small radii from perturbation theory. A Pad\'e approximation is proposed to link these limits. For radii greater than or equal to that of a single atom or monovacancy, the liquid-drop model is found to be usefully accurate. Moreover, the predicted monovacancy formation energies for stabilized jellium agree reasonably well with those measured for simple metals. These results suggest a generalized liquid-drop model of possible high accuracy and explanatory value for the energetics of stable metal surfaces curved on the atomic scale (crystal faces, edges, corners, etc.). The bending energy per unit length for an edge at angle \ensuremath{\theta} is estimated to be \ensuremath{\gamma}(\ensuremath{\pi}-\ensuremath{\theta})/4, where \ensuremath{\gamma} is the intrinsic curvature energy. The step energy is estimated as (n-2+\ensuremath{\pi}/2)\ensuremath{\sigma}d, where \ensuremath{\sigma} is the intrinsic surface energy, n\ensuremath{\ge}1 is the number of atomic layers at the step, and d is the layer height.
