Band intensities in the infrared spectra of metal carbonyl complexes: Chromium,molybdenum and tungsten hexacarbonyls

The absolute integrated intensities for IR absorption bands of M(CO)₆ (M = Cr, Mo, W) were measured. The calculations of dipole moment derivatives of the molecules were performed using a procedure suggested by L. S. Mayants and B. S. Averbukh. The effective atomic charges of M(CO)₆ are estimated and discussed.     

An effective atomic charge model for infrared intensities

Infrared intensities, in particular the dipole derivatives with respect to internal (symmetry) coordinates derived from the intensities, can be explained in terms of an effective atomic charge model which includes both the equilibrium charges and their first-order fluxes. For diatomic molecules it is found that most of the intensity arises from the equilibrium charges in the case of the hydrogen halides, but conversely, in CO, most of the intensity is due to the charge flux. The parameters found can be nicely related to elementary bonding theory.In small symmetrical polyatomic molecules the number of parameters is sufficiently restricted by symmetry and charge conservation that the parameters would be uniquely determinate except for the ambiguity in sign of the experimental dipole derivatives. The examples of AB₂ (D_∞h and C_2v), AB₃ (D_3h and C_3v), and AB₄ (Td) are discussed in detail; a simple generalization for molecular ions is included.For nonpolar molecules, the effective equilibrium charges are determined by the motion (not the equilibrium value) of the electronic centroid.     

High order vibrational matrix elements for diatomic molecules; dipole moment function and transition moments of CO

The fifth and sixth-order contributions to the vibrational matrix elements are obtained for the transitions v→v'(v'?v+4) using an eight power internuclear Dunham potential and a quartic power series expansion of the dipole moment function. The results for the dipole moment coefficients M₀ to M₄ of CO and the transition moments R_v^v' (with v=5, 10, 20) deduced from a calculation including succesively third, fourth, fifth and sixth-order perturbation theory are compared. The validity of these results is discussed.Using a quintic dipole moment function, general expressions for the vibrational matrix elements corresponding to the transitions v→v'(v'? v+5) are also presented and the influence of these contributions on the calculation of the dipole moment coefficients as well as the hot band transition moments of CO is shown.     

Study of the electronic structure of M(CO)5Cl complexes (M = Mn, Re) using X-ray spectroscopy and density-functional theory

The electronic structure of M(CO)₅Cl metal complexes (M = Mn, Re) has been investigated by X-ray emission spectroscopy. The obtained X-ray emission C Kα, OKα, Cl Kβ₁, MnLα, and MnKβ₅ spectra for Mn(CO)₅Cl and ReLβ₅ spectra for Re(CO)₅Cl have been interpreted on the basis of the quantum-mechanical calculations by the method of density-functional theory, using the Gaussian-98 program. The investigation of Mn(CO)₅Cl and Re(CO)₅Cl showed similarity of the electronic structure of both complexes. Only small differences have been revealed in the energy structure and orbital occupancies of the atomic orbitals of the corresponding molecular orbitals; these differences are caused by the difference of the type of metal ions and the molecule geometry. On the basis of the performed quantum-mechanical calculations, theoretical X-ray emission spectra have been constructed, which reproduce well the characteristic features of the corresponding experimental spectra of M(CO)₅Cl metal complexes (M = Mn, Re).     

Modes of natural vibration for magnetic domains

We analyze wall-vibration modes for the case of plane parallel stripe domains in a uniaxial film whose easy axis is normal to the film plane, using Landau-Lifshitz equations carried to the limit of vanishing wall thickness. We take into account long-range dipole interactions and wall-moment twist due to stray fields from magnetic charges on the film surfaces. The small-amplitude wall displacement q(k, z) depends on the position coordinate z normal to the film plane, and on a two dimensional wave vector k parallel to the film plane. Numerically computed natural frequencies v_n(k) depend on the number of nodes n(=0, 1, 2 …) in the dependence of q on z. Surface and bulk modes are distinguished by the z-dependence of computed eigenmodes q_n(k, z). The spectrum of computed natural frequencies compares favorably with available experimental data.     

Influence of hydrogen on PtSiO2Si structures

It is shown that hydrogen in the ambient gives rise to a dipole layer at the PtSiO₂ interface and to drifting charges in the oxide. These reversible effects were studied with internal photoemission, polarisation currents and quasistatic C(V)-measurements.     

Vibration-rotation matrix elements for diatomic molecules; vibration-rotation interaction functions Fv′v (m) for CO

General expressions for the fourth-order vibrational matrix elements are obtained for the transitions v → v′ (v ? v′ v + 4) using a sixth-power internuclear potential and a quartic dipole moment function. The results for the dipole moment coefficients M₀ to M₄ of CO and for some transition moments R^v′_v deduced from a calculation including successively second, third and fourth order perturbation theory are compared.Using the rotational potential function expanded through the cubic term as a perturbation, we have also obtained general expressions for the vibration-rotation matrix elements. The vibration-rotation interaction functions F^v′_v (m) are calculated for the transitions v → v′ (v = 0, 10, 20 and v ? v′ ? v + 4) of CO and the coefficients C, D, E and G of the quartic polynomials fitting these functions are deduced. Taking account of uncertainties in the matrix elements R⁰₀ to R⁴₀, an error estimate for the coefficients of F²₀(m) and F³₀(m) is given.     

Gravitational charges,f-gravity and hadron masses

Two types of fundamental gravitational charges are suggested by quantization of the angular momentum (i.e. J=n?, wheren is an integer or half integer) occurring in the uncharged and charged Kerr metrics. These charges turn out to bee/√a ande/a, wheree is the unit electric charge anda the fine structure constant. The use of strong (f) gravity leads to corresponding fundamental massesM ₁(f) ～2.2×10^?24 g andM ₂(f)～2.3×10^?23 g. It is postulated that the hadrons are composed of these fundamental entities (christened oms here). Thus mesons arediomic particles and baryons aretriomic particles. This has a close resemblance to the quark model but here we deal with gravitational charges. The charges constituting hadrons are bound together by strong (f) gravity which is super strong compared to nuclear forces. Various hadron masses are obtained as the vibrational excitations of these composite units. The above model is capable of accounting for quantum numbers such as spin, baryon number, strangeness and isospin.     

Interfacial auger transitions in oxidised sodium and magnesium

A study of the oxidation of sodium and magnesium under precisely controlled U.H.V. conditions using Auger electron spectroscopy has revealed the presence of Auger transitions which may be interpreted as arising from the interface between the oxide and the underlying metal. These Auger peaks have been assigned transitions of the type: M¹(L_2,3) M(V) O¹(L) where M¹ and O¹ are ionic levels present in the oxide and one of the final state holes M(V) is in the conduction band. The experimentally observed Auger energies agree well with those calculated for the proposed transitions. It is expected that transitions of this type might occur in other metal—oxide systems.     

Mean-square displacements of metal and boron atoms in crystal lattices of rare-earth hexaborides

The intensities of the I₄₁₀ and I₄₁₁ reflections of nine rare-earth hexaborides MB₆ (M=La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy) are experimentally studied in the temperature range 4.2–300 K. The mean-square displacements of metal and boron atoms are calculated from the temperature dependences of the intensities I₄₁₀(T) and I₄₁₁(T). The characteristic temperatures of the metal (θ_M) and boron (θ_B) sublattices of rare-earth hexaborides are determined in the Debye approximation. It is found that the characteristic temperatures decrease with an increase in the atomic number of the metal.     

Components of the low-temperature heat capacity of rare-earth hexaborides

The temperature dependence of heat capacity C _p(T) was studied for nine rare-earth hexaborides MB₆(M=La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, and Dy) at temperatures of 5–300 K. Using the correspondence principle for lattice heat capacities of isostructural compounds, the lattice contribution C ₁(T) and the excess contribution ΔC(T) to the heat capacity of the hexaborides were determined. The lattice heat capacity C ₁(T) is represented as the sum of the Debye contributions of the metal and boron sublattices: C ₁(T)=C _M (T)+6C _B(T). The Debye temperatures π_M and π_B of the metal and boron sublattices were determined. The anomalies in the excess heat capacity ΔC(T)=C _p (T)?C ₁(T) are related to the magnetic ordering effects, the Schottky contribution, and the Jahn-Teller effect.     

On the Relative Intensity-Concentration Relationship of Carbonyl Bands in the Solution Infrared Spectra of Metal Carbonyl Compounds of C4v Symmetry

The theory on the relative intensities of CO stretching bands of metal carbonyl compounds of C^4v symmetry has been advanced by orgel, inter alios. ² For complexes of formula M(CO)₅Xⁿ [a = -1, 0), three infrared active bands are expected, 2A₁ + E. The two A₁ bands consist of modes which are predominantly vibration of the CO trans to X (A₁ ⁽¹⁾) and the symmetrical stretch of the four equatorial CO's (A^{1 (2)}). The A₁ ⁽²⁾ band is nearly forbidden, and owes its intensity to the contribution of the axial CO stretch to the normal mode. The end result of this coupling between axial and radial CO stretching symmetry modes would appear to be an aid in assigning the bands in the carbonyl stretching region to the appropriate symmetry modes; the relative intensities are weak (A₁ ⁽²⁾), strong (E), and medium (A₁ ⁽¹⁾) Although this weak-strong-medium pattern is invariably observed in the spectra of     

String quantization in accelerated frames and black holes

We quantize a closed bosonic string in a light-cone gauge in Rindler (uniformly accelerated) space-time and apply it to the Schwarzschild-Kruskal manifold. Inertial and accelerated particle states of the string associated to positive frequency modes with respect to the inertial and Rindler times respectively, are defined. There is a stretching effect of the string due to the presence of an event horizon. We explicitly solve the dynamical constraints leaving as physical degrees of freedom only those transverse to the acceleration. Different mass formulae are introduced depending on whether the centre of mass of the string has uniform speed or uniform acceleration. The expectation value of the Rindler (Schwarzschild) number-mode operator in the string around state (tachyon) results equal to a thermal spectrum at the Hawking-Unruh temperature T_s=α/2π (∼ M_Pl(M_Pl/M)^1/(D−3), where M is the black hole mass). We find T₀=M′/2π where M′ is the accelerated ground state string mass and T₀ the temperature T_s in dimensionless frequency units. Correlation functions of string coordinates and vertex operators and their Fourier transforms in accelerated time (string response functions) are computed and their thermal properties analyzed.     

Moments de transition vibrationnelle des molecules diatomiques. Intensite des raies rovibrationnelles des bandes 0→2 et 0→3 et fonction dipolaire de CO

General expressions for the radial wavefunctions and the rotationless matrix elements of the dipole moment for the transitions 0→0 to 0→4 are obtained using a fifth-power internuclear potential, a quartic dipole moment function, and third-order perturbation theory. Line intensities in the 0→2 and 0→3 bands of CO have been measured for pressures varying from 2 to 5 atm. Using the values of the vibrational transition moments |R₀²| and |R₀³| deduced from our measurements and the values of |R₀⁰|, |R₀¹| and |R₀⁴| previously given, we evaluate the coefficients M₀ to M₄ of the dipole-moment function for CO.     

Intensity,transition moment,and bandshapes for the second overtone of compressed CO

Infrared spectra of the CO second overtone absorption band have been studied for pressures up to 156 bar. The absolute intensity, obtained from direct measurements of the total band, is found to be (1.27 ± 0.04) × 10^-2cm^-2Am^-1 at 298 K. Using the vibrational moments for the ground state and the transitions 0–1 to 0–4, we have evaluated the coefficients M₀ to M₄ of the quartic dipole moment function for CO and the coefficients of the vibration-rotation interaction functions. The normalized 0–3 band contours of compressed CO were first generated by summing the pressure-broadened rotational lines with Lorentz profiles. A discrepancy appears between calculated and observed bandshapes and increases with density. An empirical model, which involves the sum of CO self-broadened lines with profile described as the product of a Lorentz function by a fitted exponential function, gives reasonable agreement with the experiments. The interference effects resulting from overlapping lines have been estimated within the impact approximation.     

Adequate representation of the dipole moment function for diatomic molecules and the matrices of vibration-rotation transition moments

An exponential representation of perturbations is used as a basis of the perturbed Morse oscillator approach which is applied, in a matrix form, for calculating the radial matrix elements for diatomic molecules. An analytic procedure is developed to deduce an exponential-power series expansion for the dipole moment function M(r) from experimental spectral intensities. It is shown that for real anharmonic molecules, the series expansion in powers of e^ar (α being the Morse parameter) is an adequate form for representing transition operators, just as the usual series expansion in powers of internuclear distance r is adequate for the case of a harmonic oscillator, and it is equivalent to a series expansion in vibrational wavefunctions. An exponential-power series expansion is derived as well for a model dipole moment function which has a correct long-range dependence and limit. To exemplify the accuracy and efficiency of the technique proposed, the (40 × 40) matrices of vibration-rotation transition moments 〈vJ|M(r)|v′J′〉(v, v′ = 0, 1, …, 39) have been calculated for the ground state of CO. Typical results of these computations are presented (up to v = 35, J = 100, and v′ ? v = 1–4) to illustrate the dependence of vibration-rotation interaction functions on the vibrational and rotational quantum numbers.     

Comparative analysis of the phonon modes in AgNbO<Subscript>3</Subscript> and NaNbO<Subscript>3</Subscript>

The lattice dynamics of silver niobate AgNbO₃ and sodium niobate NaNbO₃ is calculated from first principles. The unstable modes (i.e., tilting of oxygen octahedra and ferroelectric atomic displacements) in silver and sodium niobates are analyzed. It is shown that the existence of ferroelectric modes is associated primarily with the instability of the atomic positions of silver and sodium in the crystal lattice. The dynamic charges in the structure of silver and sodium niobates are determined. According to the first-principles calculations, both silver and sodium niobates in the ground state (T = 0) are characterized by ferroelectric atomic displacements and frozen tilting of oxygen octahedra, with the only difference being that the tilting modes of the oxygen octahedra in silver niobate correspond to the M point of the Brillouin zone, whereas those in sodium niobate are attributed to the R point of the Brillouin zone. The results of these calculations are in good agreement with experimental data.     

Electrical conductivity and complex electric modulus of titanium doped nickel-zinc ferrites

The samples Ni_1+x−yZn_yTi_x Fe_2−2xO₄; y=0.1, 0.0≤x≤0.5 were prepared in a single-phase spinel structure as indicated from X-ray analysis. Electrical conductivity and dielectric measurements at different temperatures from 300 K to 600 K in the frequency range from 42 Hz to 5 MHz have been analyzed. The relation of conductivity with temperature revealed a semiconductor to semimetallic behavior as Ti⁴⁺ concentration increases. The conduction mechanism depends mainly on the valence exchange between the different metal ions in the same site or in different sites. The dielectric constant as a function of temperature and frequency showed that there is a strong dependence on the compositional parameter x. The electrical modulus has been employed to study the relaxation dynamics of charge carriers. The result indicates the presence of correlation between motions of mobile ion charges. The activation energies extracted from M′(ω) and M″(ω) peaks are found to follow the Arrhenius law. The electrical conductance of the samples found to be dependent on the temperature and frequency.     

Transferability of dipole moment derivatives: Calculation of absolute rotational contributions for symmetrical molecules

It is shown that Polo's method for the calculation of the D^?1 and G^?1 matrices can be extended to the calculation of the absolute rotational contributions involved in the molecular dipole moment derivatives in terms of symmetry coordinates. The method applies to both stretching and bending modes. The method is outlined for AB₃ (C_3v) molecules.     

Systematics of vibrational intensities for “diatomic” molecules: Approximate formulas

Several approximations are discussed which enable one to estimate electric dipole moment transition matrix elements for diatomic molecules based on a very limited amount of experimental data. For strongly polar molecules, a simplistic point-charge dipole model in which there is no vibrational charge flux predicts a simple relation between the permanent moment, M₀, and its derivative with respect to internuclear separation, M₁. This is found to be approximately valid for a surprisingly large number of polar molecules. Next, approximate matrix elements for the fundamental and overtone bands are presented for a linear dipole moment function. Finally, systematic trends for molecules having similar electronic structures are investigated and combined with the approximations discussed above in order to estimate the transition moments for several molecules of astrophysical interest. An extension to the ν₃ fundamental and overtone bands of CH₄ is suggestive that some of these ideas may be applicable to certain polyatomic molecules as well.