Exchange energy density and exchange potential via a hartree–fock plus mp2 study of the electron liquid in the ground-state conformer of glycine

Very recent criticisms of existing exchange-correlation functionals by Wanko et al. applied to systems of biological interest have led us to reopen the question of the ground-state conformer of glycine: the simplest amino acid. We immediately show that the global minimum of the Hartree–Fock (HF) ground-state leads to a planar structure of the five non-hydrogenic nuclei, in the non-ionized form NH₂–CH₂–COOH. This is shown to lie lower in energy than the zwitterion structure NHB₃ ⁺–CH₂–COO^?, as required by experiment. Refinement of the nuclear geometry using second-order Møller–Plesset perturbation theory (MP2) is also carried out, and bond lengths are found to accord satisfactorily with experimentally determined values. The ground-state electron density for the MP2 geometry is then redetermined by HF theory and equidensity contours are displayed. The HF first-order density matrix γ( r , r ′) is then used to obtain similar exchange-energy density (ε _x ( r )) contours for the lowest conformer of glycine. At first sight, their shape looks almost the same as for the density ρ( r ), which seems to vindicate the LDA proportional to ρ( r )^3/4. However, by way of an analytically soluble model for an atomic ion, it is shown that this has to be corrected to obtain an accurate HF exchange energy E_x as the volume integral of ε _x ( r ). Finally, recognizing that for larger amino acids, the use of HF plus MP2 perturbation corrections will become prohibitive, we have used the HF information for ε _x ( r ) and ρ( r ) to plot the truly non-local exchange potential proposed by Slater, from the density matrix γ( r , r ′). This latter calculation should be practicable for large amino acids, but there adopting Becke's one-parameter form of ε _x ( r ) correcting LDA exchange. Some future directions are suggested.     

DFT studies and AIM analysis of AlN-polycycles

The structure and properties of AlN-polycycles were studied by DFT (density functional theory) method. The results of calculations were obtained at B3LYP/6-311G(d, p) level on model species. Topological parameters such as electron density, its Laplacian, kinetic electron energy density, potential electron energy density, and total electron energy density at the ring critical points (RCP) from Bader’s ‘Atoms in molecules’ (AIM) theory were analyzed in detail. These results indicate a good correlation between ρ(3, +1), G(r), H(r), and V(r) averaged values and hardness of AlN-polycycles. The aromaticity of all molecules has been studied by nucleus-independent chemical shift. There is a linear correlation between ΣNICS(0.0)_molecule values and polarizability.     

Fourier-transform rheology of unvulcanized styrene butadiene rubber filled with increasingly silanized silica

ABSTRACT

Silica as one the most important fillers for rubber material is routinely modified by silane to improve its compatibility with the rubber matrix. Silanization of the silica particle affects both the linear and nonlinear rheological behaviors of the compounds. Their rheological nonlinearity, however, is mostly analyzed in an indirect way from linear rheological parameters, e.g. G′(ω₁, γ₀) and G″(ω₁, γ₀), which lose their physical meaning in the nonlinear viscoelastic regime. In the present work, the nonlinearity is directly quantified by the Fourier-transform rheology (FT-Rheology) technique in terms of I_3/1(ω₁, γ₀), the third relative higher harmonic, for unvulcanized styrene butadiene rubber compounds filled with a fixed amount of silica, but varying dosages of silane. With the proposed model for I_3/1(γ₀), the contributions toward nonlinearity from the filler networks at a low strain amplitude and the one from the polymer networks at high strain amplitude can be successfully separated for filled systems. The utmost nonlinearity contribution from the filler networks decreases with the silane content, which is assigned to the weakening interparticle interaction of the filler. With increasing silanization of silica, the utmost nonlinearity contribution from the polymer networks is found to increase. This nonlinear mechanical response is attributed to the enhanced interfacial interaction between the filler and polymer.     

Dynamics of the photoinduced desorption of nitric oxide molecules from the surface of pure and modified platinum

The distribution of NO molecules desorbed from a Pt(111) surface due to valence electron excitation over rotational energy levels N(J) is analyzed using a simple impulse-induced model. A linear dependence is found between lnN(J) and (E_r)^1/2, where E_r is the rotational energy of the desorbed molecules. The lifetime of the excited state and the critical time of residence in the excited state estimated using this dependence are found to be close to one another (~10^?15 s). The frequency and amplitude of the tilting vibrations of the adsorbed molecules in the excited state are estimated.     

Quantum mechanics and quasiclassical study of the H/D+FO → OH/OD+F,HF/DF+O reactions: Chemical stereodynamics

The time‐dependent quantum wave packet and the quasi‐classical trajectory (QCT) calculations for the title reactions are carried out using three recent‐developed accurate potential energy surfaces of the 1¹A′, 1³A′, and 1³A″ states. The two commonly used polarization‐dependent differential cross sections, dσ₀₀/dω_t, dσ₂₀/dω_t, with ω_t being the polar coordinates of the product velocity ω′, and the three angular distributions, P(θ_r), P(Φ_r), and P(θ_r,Φ_r), with θ_r, Φ_r being the polar angles of the product angular momentum, are generated in the center‐of‐mass frame using the QCT method to gain insight into the alignment and the orientation of the product molecules. Influences of the potential energy surface, the collision energy, and the isotope mass on the stereodynamics are shown and discussed. Validity of the QCT calculation has been examined and proved in the comparison with the quantum wave packet calculation. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Chemical bond breaking/forming as a Franck–Condon electronic process

We describe chemical bond changes as Franck–Condon electronic processes within a new theoretical ansatz that we call ‘rigged’ Born–Oppenheimer (R-BO) approach. The notion of the separability of nuclear and electron states implied in the standard Born–Oppenheimer (BO) scheme is retained. However, in the present scheme the electronic wave functions do not depend upon the nuclear coordinate (R-space). The new functions are obtained from an auxiliary Hamiltonian corresponding to the electronic system (r-coordinates) submitted to a Coulomb potential generated by external sources of charges in real space (α-coordinates) instead of massive nuclear objects. A stationary arrangement characterized by the coordinates α_0A, is determined by a particular electronic wave function, ψ(r;α_0A); it is only at this stationary point, where an electronic Schrödinger equation: H_e(r,α_0A)|Ψ(r;α_0A)=E(α_0A)|Ψ(r;α_0A) must hold. This equation permits us to use modern electronic methods based upon analytic first and second derivatives to construct model electronic wave functions and stationary geometry for external sources. If the set of wave functions {Ψ(r;α_0A)} is made orthogonal, the energy functional in α-space, E(α;α_0A)=Ψ(r;α_0A)|H_e(r,α_0A)|Ψ(r;α_0A) is isomorphic to a potential energy function in R-space: E(R;α_0A)=Ψ(r;α_0A)|H_e(r,R)|Ψ(r;α_0A). This functional defines, by hypothesis, a trapping convex potential in R-space and the nuclear quantum states are determined by a particular Schrödinger equation. The total wave function for the chemical species A reads as a product of our electronic wave function with the nuclear wave function (Ξ_ik(R;α_0A)): Φ_ik(r,R)=Ψ_i(r,α_0A)Ξ_ik(R;α_0A). This approach facilitates the introduction of molecular frame without restrictions in the R-space. Two molecules (characterized with different electronic spectra) that are decomposable into the same number of particles (isomers) have the same Coulomb Hamiltonian and they are then characterized by different electronic wave functions for which no R-coordinate ‘deformation’ can possibly change its electronic structure. A bond breaking/forming process must be formally described as a spectroscopic-like electronic process. The theory provides an alternative to the adiabatic as well as the diabatic scheme for understanding molecular processes. As an illustration of the present ideas, the reaction of H₂+CO leading to formaldehyde is examined in some detail.     

Structural properties of some liquid transition metals

This article addresses the computation of structural properties of liquid transition metals, namely, 3d (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn), 4d (Zr, Pd, Ag and Cd) and 5d (Pt, Au and Hg). We have calculated the structure factor S(q), pair distribution function g(r), interatomic distance r ₁, coordination number n ₁, long wavelength limit of structure factor S(0) and isothermal compressibility χ_T for liquid transition metals. To describe electron–ion interaction, we have used our own model potential along with one component plasma reference system. To see the influence of exchange and correlation effect, Sarkar et al.'s [Mod. Phys. Lett. B12, 639 (1998)] local field correlation function is used. Thus, our newly constructed model potential has successfully generated the structural properties (structure factor S(q), pair distribution function g(r), interatomic distance r ₁, coordination number n ₁, long wavelength limit of structure factor S(0) and isothermal compressibility χ_T ) for liquid transition metals.     

On the inner and outer radial density functions

Starting from the two-electron radial density D ₂(r ₁,r ₂), a generalized partitioning of the one-electron radial density function D(r) into two component densities D _a (r) and D _b (r) is discussed for many-electron systems. The literature partitioning (Koga and Matsuyama Theor Chem Acc 115:59, 2006) of D(r) into the inner D _<(r) and outer D _>(r) radial densities is shown to minimize the average variance of the two component density functions D _a (r) and D _b (r). It is also found that the average radial separation halved, , constitutes a lower bound to the standard deviation σ of D(r).     

Rotational viscosity γ1 of nematic liquid crystals as a function of temperature,pressure and density

Abstract

Measurements of the rotational viscosity γ₁ and the density are presented for a mixture of 4′-methoxybenzylidenebutylaniline (MBBA) and its ethoxy homologue EBBA and a mixture of cyclohexylphenylnitriles (ZLI 2413 from Merck AG) as a function of temperature and pressure. A new set-up for the measurement of densities under pressures of up to 3kbar is described. It is shown that the pressure dependence of the kinematic rotational viscosity γ₁/ρ and the temperature dependence of γ₁ under isobaric and isochoric conditions have common features with that of the shear viscosity of isotropic liquids. Furthermore, it is found that the curves γ₁ = f(1/T) for constant p and γ₁ = g(ρ) for constant T can be shifted one onto another by an appropriate shift of the scale of the independent variable.     

Discrepancy in the near-solute electric dipole moment calculated from the electric field

The electric dipole moment p ( r ) was computed as the integral of the permanent dipole moment of the solvent molecule μ( r ) weighted by the orientational probability distribution Ω( r ; O ) over all orientations, where O is the orientation of the solvent molecule at r . The relationship between Ω( r ; O ) and the potential of the mean torque was derived; p ( r ) is proportional to the electric field E ( r ) under the following assumptions: (1) the van der Waals (vdW) interaction is independent of the orientation of the solvent molecule at r ; (2) the solvent molecule and its electrical effect are modeled as a point dipole moment; (3) the solvent molecule at r is in a region far from the solute; and (4) μE( r ) ? k_BT, where k_B is Boltzmann's constant and T is absolute temperature. The errors caused by calculating near‐solute Ω( r ) and p ( r ) from E ( r ) are unclear. The results show that Ω( r ) is inconsistent with the value calculated from E ( r ) for water molecules in the first and second shells of solute with charge state Q = ±1 e, and a large variation in solvent molecular polarizability γ_mol(r), which appeared in the first valley of 4πr²E(r) for |Q| < 1 e. Nonetheless, p (r) is consistent with the values calculated from E (r) for |Q| ≤ 1 e. The implication is that the assumptions for calculating p ( r ) can be ignored in the calculation of the solvation free energy of biomolecules, as they pertain to protein folding and protein–protein/ligand interactions. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Exact electronic properties in the classically forbidden region of a metal surface

We derive exact properties of the inhomogeneous electron gas in the asymptotic classically forbidden region at a metal–vacuum interface within the framework of local effective potential energy theory. We derive a new expression for the asymptotic structure of the Kohn–Sham density functional theory (KS‐DFT) exchange‐correlation potential energy v_xc(r) in terms of the irreducible electron self‐energy. We also derive the exact asymptotic structure of the orbitals, density, the Dirac density matrix, the kinetic energy density, and KS exchange energy density. We further obtain the exact expression for the Fermi hole and demonstrate its structure in this asymptotic limit. The exchange‐correlation potential energy is derived to be v_xc(z → ∞) = ?α_KS,xc/z, and its exchange and correlation components to be v_x(z → ∞) = ?α_KS,x/z and v_c(z → ∞) = ?α_KS,c/z, respectively. The analytical expressions for the coefficients α_KS,xc and α_KS,x show them to be dependent on the bulk‐metal Wigner–Seitz radius and the barrier height at the surface. The coefficient α_KS,c = 1/4 is determined in the plasmon‐pole approximation and is independent of these metal parameters. Thus, the asymptotic structure of v_xc(z) in the vacuum region is image‐potential‐like but not the commonly accepted one of ?1/4z. Furthermore, this structure depends on the properties of the metal. Additionally, an analysis of these results via quantal density functional theory (Q‐DFT) shows that both the Pauli W_x(z → ∞) and lowest‐order correlation‐kinetic W(z → ∞) components of the exchange potential energy v_x(z → ∞), and the Coulomb W_c(z → ∞) and higher‐order correlation‐kinetic components of the correlation potential energy v_c(z → ∞), all contribute terms of O(1/z) to the structure. Hence correlations attributable to the Pauli exclusion principle, Coulomb repulsion, and correlation‐kinetic effects all contribute to the asymptotic structure of the effective potential energy at a metal surface. The relevance of the results derived to the theory of image states and to KS‐DFT is also discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Inner and outer radial density functions in many-electron atoms

When any two electrons are considered simultaneously, the radial density function D(r) in many-electron atoms is shown to be rigorously separated into inner D _<(r) and outer D _>(r) radial densities. Accordingly, radial properties such as the electron–nucleus attraction energy V _en and the diamagnetic susceptibility χ _d are the sum of the inner and outer contributions. The electron–electron repulsion energy V _ee has an approximate relation with the minus first moment of the outer density D _>(r). For the 102 atoms He through Lr in their ground states, different characteristics of local maxima in the radial densities D _<(r), D _>(r), and D(r) are reported based on the numerical Hartree-Fock wave functions. Relative contributions of the inner and outer components to V _en and are also discussed for these atoms.     

Electron density and its derivatives at the nucleus for spherically confined hydrogen atom

It is shown that the energy of a hydrogen‐like atom confined inside a spherical cavity of radius, R, and potential barrier, V₀, is quantitatively defined by the ratio . Here, the conventional spherical density (r) is scaled as η_l(r) = and the ratio of the second derivative η(r) to η_l(r) is evaluated at the nucleus. Numerical results of the ratios are presented for 1s, 2s, 2p, and 3d states at several values of V₀. For such states, the characteristic radii of confinement leading to the well‐defined values of energy are identified. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Spatial correlation of atomic electrons: He

For any two-electron wavefunction whose angular dependence is given in terms of the spherical harmonics of the individual electrons and/or o₁₂, where o₁₂ is the interelectronic angle. a transformation is generated which reduces |ψ(r₁, r₂, o₂, o₁, o₁₂ )|² to |ψ(r₁, r₂, o₁₂)|². Geometric aspects of electron correlation are analyzed in terms of this resulting three-coordinate function, with specific application to a number of wave functions for doubly-excited helium. Angular correlation has been studied by integrating |ψ(r₁, r₂, o₁₂)|² over its radial dependence to yield p(o₁₂), the probability density function for the interelectronic angle. Trends of p(o₁₂) for doubly-excited states of the helium atom are related to a number of quantities including energies and autoionization widths. These trends can be rationalized in terms of a simple classical model. The full spatial correlation involving |ψ(r₁, r₂, o₁₂)|² is explored by the use of three-dimensional graphs for some of these states.     

Experimental electron density overlapping in hydrogen bonds: topology vs. energetics

We have investigated the relationship between the energetic properties of the hydrogen bond (HB) interaction and the topological overlapping of the electronic clouds at the HO critical point r_CP. This study involves a total of 83 X–HO (X=C, N, O) HBs, which have been described in terms of the topological properties of the electron density ρ(r) at r_CP for a large set of compounds. Kinetic G(r_CP) and potential V(r_CP) contributions to the local energy density of electrons exhibit linear functionalities against, respectively, the positive and negative curvatures of ρ(r) at the critical point, showing an effective deconvolution in the local form of the Virial theorem. The topological variation of the curvatures at r_CP, and therefore changes in the HO overlapping, are related to the onset of the repulsion between the electronic clouds of the basic and acid atoms.