The density of states for interacting systems with inelastic transitions and its relation to the collision lifetime

The quantum mechanical excess density of states ρ(E) is shown to be given in terms of the S matrix by (i/2π) Tr{SdS⁺/dE}, giving the relationship ρ(E) = h⁻¹ Tr{Q}, where Q is the collision lifetime matrix of Smith.     

Alignment and orientation effects in resonant charge exchange from laser excited Na*(3p)

A collisional alignment and orientation study with planar symmetry is described, determining the complete density matrix for resonant charge transfer from laser excited atoms. Results are reported for the Na⁺+Na*(3p) system over the collision energy rangeE _c.m.=50?100 eV. We communicate the optimal alignment angle γ and linear polarisationP _l ⁺ of the charge cloud as well as its relative height ρ₀₀ and the angular momentumL _⊥ ⁺ transferred in the collision as a function of the scattering angle. For preparation of the sodium 3p orbital in the scattering plane (positive reflection symmetry) we observe that at small reduced scattering angles (<20 eV°) the preparation of apσ at large internuclear distances contributes most to the scattering intensity whereas at larger reduced scattering angles (>60 eV°) apπ⁺ preparation is more important. In contrast, preparation of thepπ^? orbital (perpendicular to the scattering plane) is large at small and vanishes at larger scattering angles. We conclude that orbital following cannot be assumed in this resonant charge transfer process. The angular momentum transfer is observed to be small, indicating only little coherence in the process, but shows nevertheless an interesting behaviour as a function of scattering angle.     

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.     

Some properties of the Lagrange multiplier μ in density functional theory

Some new properties of the Lagrange multiplier μ introduced through the normalization constraint on ρ in the variations of energy density functionals are determined. Through arguments concerning the homogeneity properties of these functionals with respect to μ, it is demonstrated that at the point of variation μ = μ₀ = E₀/N, where E₀ is the ground state energy and N is the total particle number. It is also shown that the value of μ₀ is independent of the normalization imposed on ρ. The interpretation of μ₀ as a chemical potential is discussed in the light of these findings.     

Excess thermodynamic properties of the ethylene carbonate–trifluoroethyl methyl carbonate and propylene carbonate–trifluoroethyl methyl carbonate systems at T = (298.15 or 315.15) K

The deviation in excess thermodynamic parameters such as molar volume (V^E ), viscosity ( η^E), dielectric constant (ϵ^E ), Gibbs energy of activation of the viscous flow (G ^* E ) and surface tension ( γ^E) have been determined for propylene carbonate and 2,2,2-trifluoroethyl methyl carbonate (TFMC) mixtures atT =  298.15 K and for ethylene carbonate and TEMC mixtures at T =  313.15 K. All quantities were plotted against mole fraction over the whole concentration range. Polynomial regressions have been fitted with the results. The strength and the nature of the interactions between like and unlike components have been discussed.     

Application of the energy gap law to the decay of charge transfer excited states,solvent effects

Values of non-radiative decay rate constants (k_nr) and emission energies (E_cm) have been obtained for Os(Phen₃)²⁺ in a series of solvents and the results are consistent with the energy gap law. For hydroxylic solvents like water or methanol related studies suggest the existence of strong, specific contributions to the vibrational trapping energy of the solvent.     

Mechanisms of the hydrogen atom and the phenyl group migration in the molecule of heptaphenylcycloheptatriene

In terms of the density functional theory using the B3LYP functional, 1,2,3,4,5,6,7-heptaphenylcycloheptatriene was shown to be the most stable in the boat conformation of the cycloheptatriene ring with the H atom in the equatorial position. 1,5-Sigmatropic shifts of the H atom along the seven-membered ring perimeter take place when it is in the axial position through the asymmetric transition state with the barrier ΔE ^≠ _ZPE = 28.7 kcal mol^?1. The H atom can attain the axial position upon inversion of the seven-membered ring, which is accompanied by the orthogonal turn of the phenyl group at the sp³-hybridized C atom (ΔE ^≠ _ZPE = 22.6 kcal mol^?1). The energy barrier to the circular rearrangement of the H atom (ΔE ^≠ _ZPE = 32.2 kcal mol^?1) explains formation of isomers during the high-temperature synthesis of di(p-tolyl)pentaphenylcycloheptatriene. The barrier to the 1,5-sigmatropic shifts of the phenyl group is 19.7 kcal mol^?1 higher than that for the competing shifts of the H atom.     

Evaluation of metal hydride thermograms by a differential-correction technique

A least-squares linear-Taylor differential-correction technique has been used for the rapid evaluation of thermogravimetric curves obtained during the decomposition of magnesium hydride, iron—titanium hydride and lanthanum—nickel hydride. For magnesium hydride and iron—titanium hydride the Avrami—Erofe'ev equation fits the experimental data, thus indicating that nucleation is the rate-determining step under thermogravimetric conditions. For lanthanum—nickel hydride a combination of the Avrami—Erofe'ev equation and the phase boundary movement equation fits the data up to a fractional decomposition of 0.8. For magnesium hydride decomposition the activation energy E and the pre-exponential factor Z are dependent on the hydrogen pressure (E = 101.2 kJ mole^?1 and Z = 8.96 × 10⁷ at 0.30 MPa, while E = 66.3 kJ mole^?1 and Z = 4.77 × 10⁷ at 0.11 MPa). For iron—titanium hydride (E = 28.4 kJ mole^?1) and lanthanum—nickel hydride (E = 13.4 kJ mole^?1) the values are independent of pressure.     

The Conductance- and Capacitance-Frequency Characteristics of the Rectifying Junctions Formed by Sublimation of Organic Pyronine-B on p-Type Silicon

The rectifying junction characteristics of the organic compound pyronine-B film on a p-type Si substrate has been studied. The pyronine-B has been sublimed on the top of p-Si surface. The barrier height and ideality factor values of 0.79±0.04 and 1.13±0.06 eV for this structure have been obtained from the forward bias current-voltage (I-V) characteristics. From the low capacitance-frequency (C-f) characteristics as well as conductance-frequency (G-f) characteristics, the energy distribution of the interface states and their relaxation time have been determined in the energy range of (0.53−E_v)-(0.79−E_v) eV taking into account the forward bias I-V data. The interface state density N_ss ranges from 4.93×10¹⁰ cm⁻² eV⁻¹ in (0.79−E_v) eV to 3.67×10¹³ cm⁻² eV⁻¹ in (0.53−E_v) eV. Furthermore, the relaxation ranges from 3.80×10⁻³ s in (0.53−E_v) eV to 4.21×10⁻⁴ s in (0.79−E_v) eV. It has been seen that the interface state density has an exponential rise with bias from the midgap towards the top of the valence band. The relaxation time shows a slow exponential rise with bias from the top of the valence band towards the midgap.     

Excess enthalpies and (vapour + liquid) equilibrium data for the binary mixtures of dimethylsulphoxide with ketones

Excess enthalpies (H^E), at ambient pressure and T = 298.15 K, have been measured by using a solution calorimeter for the binary liquid mixtures of dimethyl sulphoxide (DMSO) with ketones, as a function of composition. The ketones chosen in the present investigation were methyl ethyl ketone (MEK), methyl isobutyl ketone (MIBK), and cyclohexanone (CH). The H^E values are positive over the entire composition range for the three binary mixtures. Furthermore, the (vapour + liquid) equilibrium (VLE) was measured at 715 Torr for these mixtures, of different compositions, with the help of Swietoslawski-ebulliometer. The experimental temperature-mole fraction (t-x) data were used to compute Wilson parameters and then used to calculate the equilibrium vapour-phase compositions as well as the theoretical points for these binary mixtures. These Wilson parameters are used to calculate activity coefficients (γ) and these in turn to calculate excess Gibbs free energy (G^E). The intermolecular interactions and structural effects were analyzed on the basis of the measured and derived properties.     

Densities and viscosities for binary mixtures of phenetole with 1-pentanol, 1-hexanol, 1-heptanol, 1-octanol, 1-nonanol,and 1-decanol at different temperatures

Density (ρ) and viscosity (η) values of the binary mixtures of phenetole+1-pentanol, + 1-hexanol, + 1-heptanol, + 1-octanol, + 1-nonanol, and + 1-decanol over the entire range of mole fraction at 293.15, 298.15, 308.15, and 318.15 K have been measured at atmospheric pressure. The excess molar volume (V^E), viscosity deviations (Δη), and excess Gibbs energy of activation (G*^E) have been calculated from the experimental measurements. These results were fitted to Redlich and Kister polynomial equation to estimate the binary interaction parameters. The viscosity data were correlated with equations of Grunberg and Nissan, Hind et al., Frenkel, and McAllister. While the excess molar volumes of phenetole+1-pentanol, + 1-hexanol are positive, the remaining binary mixtures are negative. The viscosity deviations and excess Gibbs energy of activation are negative for all investigated systems. As the chain length of 1-alkanols increases, both viscosity deviations and excess molar volume values decrease while excess Gibbs energy of activation value increase. The temperature has no effect on excess molar volume, slight effect on excess Gibbs energy of activation, and significant effect on viscosity deviations. The calculated functions have been used to explain the intermolecular interaction between the mixing components.     

Resonance-enhanced multiphoton ionization of molecular hydrogen via the E,F1Σg+ state: Photoelectron energy and angular distributions

Photoelectron energy and angular distributions are measured for the 2+1 multiphoton ionization process H₂ X¹Σ_g⁺ (ν = 0,J) + 2hv → E,F¹Σ_g⁺(ν_E,J_E = J) + hν → H₂⁺X²Σ_g⁺ (ν⁺) + e^?, for ν_E = 0, 1, or 2 and for J_E = 0 or 1 of the inner well of the double-minimum E,F state. Although a strong preference is found for ν⁺ = ν_E, the detailed H₂⁺ vibrational distribution does not exhibit Franck-Condon behavior, and the photoelectron angular distributions vary markedly with both the J_E value of the intermediate state and the ν⁺ value of the ion.     

Physical Properties of Binary Liquid Systems: Ethanoic Acid/Propanoic Acid/Butanoic Acid with Cresols

Density, viscosity and surface tension of nine binary liquid systems: ethanoic acid, propanoic acid and butanoic acid with o-cresol, m-cresol and p-cresol have been determined at 298.15, 308.15 and 318.15 K over the complete compositional range. From the experimental results the excess values of molar volume (V ^E), viscosity (η ^E), Gibbs free energy for the activation of flow (ΔG ^E) and surface tension (σ ^E) were evaluated. The excess values were fitted to the Redlich–Kister type equation using a nonlinear regression technique. The Grunberg–Nissan parameter, d, was also calculated. From the sign and magnitude of the V ^E, η ^E, ΔG ^E, σ ^E, and d values, it is concluded that specific interactions are present in all of the nine binary mixtures under study. V ^E is negative for carboxylic acid–cresol mixtures at all temperatures and over the entire composition range. The values of η ^E, ΔG ^E and σ ^E are positive over the whole range of composition and increase with increasing temperature at a constant mole fraction of the carboxylic acid, confirming the existence of specific interactions in these binary mixtures. Further, the viscosity data of the binary systems were fitted to various theoretical/empirical models. The binary viscosity data is well represented by the Auslander model. Surface tension data were fitted to various theoretical/empirical models. The binary mixture surface tension data are well represented by the model given by Zihao and Jufu.     

Intermolecular interactions in methyl formate-ethanol mixtures at 303–313 K according to ultrasonic data

Density (ρ), viscosity (η), and ultrasonic velocity (U) have been measured for a binary mixture composed of methyl formate and ethanol at 303, 308, and 313 K. The adiabatic compressibility (β), acoustic impedance (Z), free length (L _f ), free volume (V _f ), internal pressure (π _i ), viscous relaxation time (τ), and Gibbs free energy (ΔG) were calculated from the experimental data. The excess values of these parameters (β ^E , Z ^E , L _f ^E , V _f ^E , π _i ^E , τ ^E , and ΔG ^E ) have also been calculated using the determined parameters and interpreted in terms of molecular interactions. The deviations in the sign and values of these excess parameters from the ideal mixing reveal the nature of intermolecular interactions between components of the mixture.     

Molecular beam chemiluminescence XI: kinetic and internal energy dependence of the NO + O3 → NO2*,→ NO23 reaction

Seeded supersonic NO beams were used to study the kinetic energy dependence of both the electronic (NO₂^*) and vibrational (NO₂³) chemiluminescence of the NO + O₃ reaction. In addition the electronic CL is found to be enhanced by raising the NO internal temperature. This is shown to be due to enhanced reactivity of the NO(²Π,_{$\text{3}\text{2}$}) fine structure component. By difference NO(²Π_{$\text{1}\text{2}$}) is concluded to yield predominantly groundstate NO₂³. The excitation function for NO₂^* formation from NO(²Π_{$\text{3}\text{2}$}) is of the form σ_{$\text{3}\text{2}$}(E) = C(E/E₀ - 1)ⁿ over the 3–6 kcal energy range where n = 2.4 ± 0.15, C = 0.163 Ų and E₀ = 3.2 ± 0.3 kcal/mole. Vibrational IR emission from NO₂³ has an energy dependence different from electronic NO₂^* emission, confirming that emitters are formed predominantly in distinct reaction channels rather than via a common precursor (either NO₂^* or NO₂³). The short wavelength cutoff of the CL spectra recorded at elevated collision energies E ? 15 kcal/mole corresponds to the total available energy. These and literature results are discussed in the light of general properties of the (generally unknown) ONO₃ potential energy surfaces. The formation of electronically excited NO₂^* rather than energetically preferred O₂ (¹ Δg) (Gauthier and Snelling) can be rationalized in terms of surface hopping near a known intersection of potential energy surfaces more easily than by vibronic interaction in the asymptotic NO₂ product.     

A simple reliable approximation for isotropic intermolecular forces. A critical test using HH(3Σu+) as a model

A simple semi-empirical approximation for the exchange energy (E_x), coupled with a tractable representation of the Coulomb energy (E_C), has been found to yield very accurate results for the isotropic part of the interaction energy (E_int = E_x + E_C) between two closed shell systems. The expression for E_int is based on the knowledge of the first order Coulomb energy and the first three terms in the asymptotic long range expansion of the second order Coulomb energy for the interaction and contains but one adjustable parameter which occurs in E_x. The usefulness of this approach for evaluating E_int is tested critically by using the non-bonded H(1s)H(1s) (³Σ_u⁺) interaction as a model (accurate values of the total interaction energy, the exchange energy, and various orders of Coulomb energies, are available for a wide range of R for this system). The results obtained for both E_int and (dE_int/dR) are inremarkable agreement with the exact results of Kotos and Wolniewicz for R > 3 a_o. Since the law of corresponding states for inert gas pairs holds equally well for the HH(³Σ_u⁺) interaction, our analysis of this simple system yields valuable information on the reliability of the approach for other van der Waals dimers.     

Comparison of four methods of integration in the context of their application in calculations of the surface activity of an organic compound and the excess electrochemical Gibbs energy of mixing in the adsorbate state

Four methods of integration, used alternatively in the determination of the activity coefficients of an adsorbed species from experimental interfacial tension measurements, have been compared. Statistical Fisher-Snedecor F-tests have been used to estimate the improvements offered by the methods investigated and to choose the best one. The method which incorporated the trapezoidal rule of integration proved to be the most suitable in the context examined. Deviations of the calculated activity coefficients from those predicted by theoretical equations are presented. In addition, the implications of the improvements achieved in calculations of the excess electrochemical Gibbs energy of mixing of the surface solution, ΔḠ^E/RT, are discussed. The magnitude and distribution of errors δ(ΔḠ^E) related to the calculations are shown. It is concluded that the mean variance of this thermodynamic function can be of the order of 10⁻⁶ (mean standard deviation 0.001) and that the deviations are randomly distributed. This represents, on the average, about a 20-fold improvement over the method proposed earlier [M. Karolczak, J. Phys. Chem., 89 (1985) 1556], not regarding the advantages resulting from the elimination of a systematic error inherent in this method.     

Influence of the nature of solvent and substituents on the oxidation potential of 2,2,6,6-tetramethylpiperidine 1-oxyl derivatives

The influence of solvent (DMF, MeCN, and water) and R1, R2 substituent nature on the formal oxidation potential (E°´) of 4-R1,R2-2,2,6,6-tetramethylpiperidine 1-oxyls (1a—f) on a glass carbon electrode was studied by cyclic voltammetry. It was shown that for all the solvents the observed dependence had the form E°´ = ρ″σ″ + b, where σ″ is the substituent constant. The b values decreased with an increase of the solvent solvating ability, while the values ρ″ are similar for all the solvents, surpassing the corresponding values for nitroxyls of the imidazoline series with substituents at position 3, which can be interpreted as an abnormally strong influence of the substituent remote from the reaction center in 1a—f. The experimental values E°´ were linearly correlated with the reaction free energy values (ΔG) calculated by DFT B3LYP and MP2 for the gas phase contribution and by HF/PCM for the contribution of solvation effects. When applying the B3LYP and the HF/PCM approaches in combination, the dependence of ^E°´ on Δ^G for all the considered solvents was described by a linear correlation equation with a slope close to unity and a constant term which was close to the theoretical value of the absolute potential of the reference electrode used.     

Regression analysis of dependences of adsorption potential shifts on the charge in systems (Tl-Ga)/[N-methylformamide + mc KI + (1 − m)c KClO4], (Tl-Ga)/[N-methylformamide + mc KBr + (1 − m)c KClO4] and (Tl-Ga)/[N-methylformamide + mc KCl + (1 − m)c KClO4]

By the regression analysis of dependences of the adsorption potential shift (E _ads) on the electrode charge in systems (Tl-Ga)/[NMF + 0.1m M KI + 0.1(1 ? m) M KClO₄], (Tl-Ga)/[NMF + 0.1m M KBr + 0.1(1 ? m) M KClO₄], and (Tl-Ga)/[NMF + 0.1m M KCl + 0.1(1 ? m) M KClO₄] with the following m fractions of the surface-active anion: 0.05, 0.1, 0.2, 0.5, and 1, the adsorption parameters are calculated in terms of two models based on the Frumkin isotherm both considering the free adsorption energy as a quadratic function of the electrode charge, where one model takes into account the diffuse layer and the other ignores it. It is shown that for the studied electrode charges q ≤ 2 μC/cm², both models provide equal accuracy in calculating E _ads in the systems under study.     

The electron correlation cusp

The Kais function is an exact solution of the Schrödinger equation for a pair of electrons trapped in a parabolic potential well with r ₁₂ ^?1 electron-electron interaction. Partial wave analysis (PWA) of the Kais function yields E _L = E + C₁(L + \-C ^?1 ₂)^?3 + O(L ^?5) where E is the exact energy and E _L the energy of a renormalized finite sum of partial waves omitting all waves with angular momentum ? > L. Slight rearrangement of an earlier result by Hill shows that the corresponding full CI energy differs from E _L only by terms of order O(L ^?5) with FCI values of C ₁ and \-C ^?1 ₂ identical to PWA values. The dimensionless \-C ₂ parameter is weakly dependent upon the size of the physical system. Its value is 0.788 for the Kais function, and 0.893 for the less diffuse helium atom, and approaches \-C ₂→ 1 in the limit of an infinitely compact charge distribution. The ?th energy increment satisfies an approximate virial theorem which becomes exact in the high ? limit. This analysis, formulated to facilitate use of the Maple system for symbolic computing, lays the mathematical ground work for subsequent studies of the electron correlation cusp problem. The direction of future papers in this series is outlined.