Simple theories for simple metals: Face-dependent surface energies and work functions

The stabilized jellium model, which preserves the simplicity of ordinary jellium while accounting for discrete-ion effects in an average way, provides an “intrinsic” surface energy and work function for each metal, determined by the mean valence electron density of the bulk. The liquid drop model asserts a dependence of the surface energy and work function on the atomic corrugation of the exposed crystal face. Together, these models are shown to make simple, quantitative predictions in good agreement with the results of all-electron calculations by Skriver and Rosengaard. Also discussed are the surface stress and the location of the image plane for stabilized jellium.     

Theoretical studies on the topographical features and energetics of diacetylene-hydrogen fluoride complexes

Ab initio supermolecular SCF calculations have been carried out on diacetylene-HF complexes at the STO-4-31G level. The reverse σ (Rσ) complex has been found to have the lowest energy. Of the two π complexes. T and L, the symmetrical one T is found to be energetically less stable than the asymmetrical one L. Theoretical vibrational analysis tends to support this stability order. Electrostatic interaction energy calculations also lead to an almost identical sequence. Hydrogen bond energies corrected for basis set superposition error indicate that ΔE_H (Rσ) > ΔE_H (Tπ) ≈ ΔE_H (Lπ).     

Solidification of metallic tin in dispersed phase

Differential scanning calorimetry (DSC) and particle size measurements were carried out on disproportionation products of pure SnO to investigate the fusion and solidification behaviour of Sn droplets and their catalytic nucleation on Sn oxides. If disproportionation reaction takes place at T ≥ 798 K, the products are metallic Sn and SnO₂; but for 523 < T < 798 K, SnO₂ is replaced by an intermediate oxide (IO) Sn_xO_(1+x). On melting, samples with IO show a drop of melting point of metallic tin due to Gibbs–Thomson effect; no lowering of melting point was observed in samples with SnO₂. On the other hand, if solidification occurs in the presence of IO, Tin droplets always displayed three distinct exothermic solidification peaks, but if it takes place in the presence of SnO₂, only one exothermic peak is observed. Undercooling values and contact angles were determined for each of the heterogeneous nucleation processes. The different behaviour of metallic Tin droplets was related to the different lattice symmetry of SnO₂ and IO, which act as nucleation catalysts.     

Solute alignment in liquid crystal solvents The Saupe ordering matrix for anthracene dissolved in uniaxial liquid crystals

We have described a theory for U, the potential of mean torque of rigid solutes at infinite dilution in a uniaxial liquid crystal phase; this may be used to calculate (S_xx - S_yy) and S_zz, the principal elements of the Saupe ordering matrix. In its simplest form U(ω) contains only second-rank terms and the dependence of the biaxiality (S_xx - S_yy) is determined by ω, a parameter which describes the departure of the potential of mean torque from cylindrical symmetry, and is predicted to be temperature independent. If dispersion forces are responsible for the magnitude of the orientational order parameter then ω should be independent of the solvent and depend only on the anisotropy in the electric polarizability of the solute. Indeed, this independence should result for any pair potential which can be factorized into a product of solute and solvent properties. These predictions are tested here by determining values of S_zz and (S_xx - S_yy) for anthracene-d₁₀ as a solute in several liquid crystal solvents, from the quadrupolar splittings obtained from the deuteron N.M.R. spectra. It is found that ω has a strong dependence on the nature of the solvent, which demonstrates that the solute ordering cannot be determined primarily by dispersion forces, or by a factorizable potential. There is also a weaker temperature dependence of λ observed for each binary mixture, and we show how this might be caused by a dependence of ω on solvent ordering, or by the inclusion of a fourth-rank term in U(ω).     

Calculation of the surface charge and potential and of the structural component of disjoining pressure in an interlayer in KCl solutions between glass samples

The dependence of the Stern potential, ψ₁, of glass samples on the distance between these, H, has been theoretically calculated, while taking into account the Stern isotherm and the electroneutrality equation. Comparison of the theoretical dependences ψ₁(C)_H→∞ with those previously experimentally obtained enables one to calculate the energy of adsorption of OH ions on glass and, further, the dependence ψ₁(H). It has been shown that for pH 4–6 and C_KCl = 10^-2-10^-5 mol/L, the value of ψ₁ practically does not depend on H. The result obtained was used to calculate theoretically the ionic-electrostatic forces and to compute (from the experimental values of the interaction forces) structural forces U_s(H). The dependence thus obtained, U_s(H), is of exponential character.     

Dimensional changes as a function of charge injection in single-walled carbon nanotubes

Motivated by the central importance of charge-induced dimensional changes for carbon nanotube electromechanical actuators, we here predict changes in nanotube length and diameter as a function of charge injection for armchair and zigzag nanotubes having different diameters. Density functional theory with periodic boundary conditions is used, which we show provides results consistent with experimental observations for intercalated graphites. Strain-versus-charge relationships are predicted from dimensional changes calculated with a uniform background charge ("jellium") for representing the counterions. These jellium calculations are consistent with presented calculations that include specific counterions for intercalated graphite, showing that hybridization between the ions and the graphite sheets is unimportant. The charge-strain relationships calculated with the jellium approximation for graphite and isolated single-walled nanotubes are asymmetric with respect to the sign of charge transfer. The dependence of nanotube strain on charge approaches that for a graphite sheet for intermediate-sized metallic nanotubes and for larger diameter semiconducting nanotubes. However, the strain-charge curves strongly depend on nanotube type when the nanotube diameter is small. This reflects both the dependence of the frontier orbitals for the semiconducting nanotubes on the nanotube type and the pi-sigma mixing when the nanotube diameter is small.     

The potential energy surfaces and the radiationless dynamics of excited states of benzene and pyrazine

The potential energy surfaces of the lowest excited states of benzene and pyrazine are investigated as a function of some of the symmetry-adapted internal coordinates by means of the INDO/S method. A large stabilization of the T₂ (ππ*) state of pyrazine (≈ 0.5 eV) along the S_8b vibrational coordinate is found. The calculated potential energy in some excited states (T₁ in benzene, T₂ and S₂ in pyrazine) is a very flat function of the S_16b vibrational coordinate, leading to a crossing with the potential energy of the ground state at relatively small excess of vibrational energy (≈ 1 eV). Thus the ν_16b vibrational mode is postulated to play an important role in the radiationless relaxation to the ground states of these systems. No such crossing has been found near the “channel three” threshold of benzene.     

A simple model for polysoaps' thread-like aggregates

The equilibrium polymerization, a model for one-dimensional reversible aggregates is used under conditions of theta and bad solvent to describe thread-like aggregates of polysoaps. In two dimensions, the aggregate size distribution decreases always more slowly than an exponential distribution and the dependence of the mean aggregate size L on the density φ and end-cap energy E of the polysoap cylindrical micelle is of the form L[φexp(E/KT)]^δ with δ<1/2. On the other hand, in three dimensions in the bad solvent regime, the dependence of L on φ becomes exponential explaining the high φ dependence of the viscosity in experimental results.     

Study of near resonant energy transfer from laser excited CO2 to SO2

Collisional energy transfer from CO₂ to SO₂ was studied subsequent to pumping of CO₂ (ν₃) by a Q-switched laser. The measurements were made in the temperature range 300–800 K and in the pressure range 1–30 Torr. The fluorescence from the ν₃ level of CO₂ was monitored with the help of a Ge:Au detector at 77 K with an estimated response time of ≈2 μs. The probability of the energy transfer was found to be increasing with increasing temperature. The probable kinetic models for the V---V relaxation pathways were discussed and the experimentally measured energy transfer rate is related to the cross-over transfer processes. Theoretical calculations using both a simple SSH-breathing sphere model and the Sharma-Brau theory were carried out to evaluate the probabilities of the involved cross-over energy transfer processes and the results were compared with the experimental rates.     

H NMR relaxation in urea

Proton NMR spin–lattice relaxation times T₁ were measured for urea as a function of temperature. An activation energy of 46.3 ± 4.7 kJ/mol was extracted and compared with the range of 38–65 kJ/mol previously reported in the literature as measured by different magnetic resonance techniques. In addition, proton NMR spin–lattice relaxation times in the rotating frame T_1ρ were measured as a function of temperature. These measurements provide acquisition conditions for the ¹³C and ¹⁵N CP/MAS spectra of pure urea in the crystalline phase.     

Microdynamics of solid anilinium chloride

Intraionic C₃ reorientation of the anilinium NH⁺₃ group was evidenced by measurements of the temperature dependence of the proton spin—lattice relaxation time, by rotating frame experiments and cw NMR data. Analysis of the results yielded a rotor hindering potential E = 33.6 kJ/mole and τ_o = 4 × 10⁻¹³ s.     

On the origin of the splittings of the ν3(SO4) modes in the specular reflectance IR spectra of gypsum

The IR polarized spectra of gypsum CaSO₄·2H₂O were recorded at incidence angles of approximately 10 and 16 degrees. Band singlet or doublet was observed for the higher frequency ν₃(SO₄²⁻) mode of B_u symmetry type, depending on polarization (n or p). A doublet was observed for the lower frequency ν₃(SO₄²⁻) mode of B_u symmetry type too, irrespectively of the type of polarization. In order to give an explanation for the doublets origin, a model permittivity function was constructed. Quite good agreement exists between the reflectance based on the model permittivity function and the experimentally measured one for the high-frequency doublet. The origin of the lower frequency doublet could not be explained in this way, but may be speculated to result from an Evans type interaction between a combination of a water libration and ν₂(SO₄²⁻), with the lower frequency ν₃(SO₄²⁻) mode.     

The cis—trans isomerization of nitrostilbenes XV: mixed singlet and triplet mechanism for trans → cis photoisomerization of 4-nitro-4′-dialkylaminostilbenes in non-polar solvents

The quantum yields of direct cis trans photoisomerization (φ_c → _t and φ_{t → c}) and of fluorescence of the trans isomers (φ_f) of three 4-nitro-4′-R-stilbenes (R amino (1), dimethylamino (2) and diethylamino (3)) were measured in several saturated hydrocarbons. Formation and decay of the lowest triplet state was observed by nanosecond laser flash photolysis. The triplet yield (φ_T), the triplet lifetime (τ_T), φ_{t → c} and φ_f were measured as a function of temperature and of the concentration of the quenchers ferrocene, azulene (Q) and oxygen. Twisting in the triplet, involving a ³t* ³p* equilibrium, analogous to that in other 4-nitrostilbenes, is suggested on the basis of the effects of temperature and quenchers on φ_T and τ_T. The trans → cis photoisomerization of 1 follows the triplet route almost completely. The existence of a singlet pathway (20% – 30% contribution) for 2 and 3 in non-polar solvents at room temperature is concluded from the non-linear dependence of the φ⁰_{t → c}/φ_{t → c} ratio on the concentration of Q. For these two nitrostilbenes a mixed singlet—triplet mechanism for the trans → cis photoisomerization is suggested.     

The electrostatic potential at atomic sites as a reactivity index in the hydrogen bond formation

The paper reviews results from computational studies by molecular orbital and density functional theories on several series of hydrogen bonded complexes. These studies aim at quantifying the reactivity of molecules for the complexation process. Excellent linear relationships are found between the electrostatic potential values at the sites of the electron donor and electron accepting atoms and the energy of hydrogen bond formation (ΔE). The series studied are: (a) complexes of R–CHO and R–CN molecules with hydrogen fluoride; (b) complexes of mono-substituted acetylene derivatives with ammonia; (c) (HCN)_n hydrogen bonded cluster for n=2–7. All 22 studied complexes of carbonyl and nitrile compounds with hydrogen fluoride fall in the same dependence between the energy of hydrogen bond formation and the electrostatic potential at the atomic site of the carbonyl oxygen and nitrile nitrogen atoms, with linear regression correlation coefficient r=0.979. In the case of complexes of mono-substituted acetylene and diacetylene derivatives with NH₃, the correlation coefficient for the dependence between the electrostatic potential at the acidic hydrogen atom and ΔE equals 0.996. For the series of hydrogen bonded (HCN)_n clusters, the correlation coefficient for the relationship between the electrostatic potential at the end nitrogen atom and ΔE is r=0.9996. Similarly, the analogous relationship with the electrostatic potential at the end hydrogen atom has a regression coefficient equal to 0.9994. The dependencies found are theoretically substantiated by applying the Morokuma energy decomposition scheme. The results show that the molecular electrostatic potential at atomic sites can be successfully used to predict the ability of molecules to form hydrogen bonds.     

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

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.     

Comparative study of isotope and chemical effects on the exciton states in LiH crystals

Scientific interest, technological promise and increased availability of highly enriched isotope have led to a sharp rise in the number of experimental and theoretical studies with isotopically controlled crystals. Isotope pure compounds are really the material of future mankind. LiH has a giant isotope effect. Therefore, this review in the first step is devoted to some peculiarities of exciton states in isotope pure and mixed crystals of LiH. Excitons are the energetically lowest excitations of the electronic system in an ideal, crystallized insulator (semiconductor) at zero temperature. It is a collective excitation which has the full translational symmetry of the crystal lattice. For the first time a systematic analysis of experimental results is presented of isotopic and chemical effects on the exciton states observed in LiH_xD_1−x crystals of various isotopic (and chemical) composition (0≤x≤1) using low temperature optical and luminescence spectroscopy. LiH (LiD) is an direct band-gap material with an energy gap 4.992 (5.095) eV at low temperature. Substituting a light isotope with a heavy one (or H→F) increases the interband transition energy (E_g) and the binding energy (E_b) of the Wannier–Mott exciton as well as the magnitude of the longitudinal–transverse splitting. The nonlinear variation of E_g, E_b with the isotope (or F) concentration is due to the compositional disordering of the crystal lattice and is consist with the concentration dependence of line half-width in exciton reflection and luminescence spectra. The free exciton luminescence spectrum of the LiH (LiH_xD_1−x, LiH_xF_1−x; 0≤x≤1) crystals under optical (X-ray) excitations consists of a narrow zero-phonon line and its more wider 5LO replicas. At 100 % substitution of hydrogen by deuterium the energy shift of the maximum of zero-phonon line is the following: ΔE=E_n=1s(LiD)−E_n=1s(LiH)=95 meV. The shift of the emission line maximum of 2LO replica overlaps the energetical interval of ≤200meV. The nonlinear dependence of the free exciton luminescence (especially LiH_xF_1−x (LiD_xF_1−x)) intensity on the excitation density allows to consider these crystals as potential solid state lasers in the UV part of spectrum. It is shown that potential fluctuation due to compositional disorder of alloy have a strong effect on both the exciton broadening and the band-gap energy shift. The review closes with a brief discussion of the present and future applications of these crystals.     

Atomic and electronic structure of microclusters

The atomic and electronic structure of alkali metal, noble metal and Si_N (N=6,10) clusters examined theoretically are reviewed. On metal clusters, validity of the spherical jellium model is discussed by examining stabilization by multiplets formation and crystalline fields. In connection with the fragmentation of metal clusters, the shell correction of a largely deformed metal clusters is discussed by referring to Strutinsky's theory of nuclear fission. On the Si₆ and Si₁₀ clusters a large reconstruction theoretically found is discussed in terms of the interaction among dangling bonds. Finally, recent work on dynamical properties of clusters are briefly reviewed.     

The effect of molecular biaxiality on the bulk properties of some nematic liquid crystals

The nematic substance 5CB is known from N.M.R. studies to be slightly biaxial, not in the sense that any bulk property measured in a direction at right angles to the director is liable to vary with rotation about the director, but in the sense that there are biaxial terms in the ordering matrix that describes the alignment of individual molecules; (S_xx - S_yy) is non-zero as well as S_zz. We show that the biaxial terms should make a significant contribution to the magnetic anisotropy Δχ^(m) of 5CB, and that the magnitude and temperature dependence of this bulk property, which we have measured, can be understood if, and only if, they are taken into account. The contribution which they make to the optical birefringence term ∑ should, however, be relatively trivial. Although ∑ may in principle be affected by local field corrections of a complicated nature, which do not affect Δχ^(m), a new theory presented in an Appendix to the paper suggests that these too are likely to be relatively trivial. Hence we believe that ∑ is more nearly proportional than is Δχ^(m) to the principal order parameter S_zz.

The paper includes unpublished data for the magnetic anisotropy and/or the principal refractive indices, n_e and n_o, in a number of other nematics (6CB, 7CB, 8CB, 9CB, 5OCB, 6OCB, 7OCB, 8OCB, 7CCH, MBBA and PAA). Comparison between the temperature dependence of Δχ^(m) and of ∑ suggests that biaxiality is present in all cyanobiphenyls, on much the same scale as in 5CB, and is not affected by the presence of an oxygen atom between the phenyl core of the molecule and its alkyl tail.     

One-electron wavefunctions. Accurate expectation values

Accurate expectation values for the total energy, the kinetic energy, the potential energy and the quadrupole moment integrals <X²> and <Z²> are calculated using the exact wavefunctions for the Isσ and 2pσ_u states of H⁺₂. A method has been developed to determine which regions of the wavefunction contribute most to a given expectation value.