The estimation of equilibrium molecular structures from zero-point rotational constants

The approximate equation I_e = 2I₈ - I₀, where I_e, I₈, and I₀ are, respectively, the equilibrium, substitution and zero-point moments of inertia of a molecule, can be derived from a first order treatment of isotope effects, and is valid for linear, symmetric or asymmetric tops. By means of this equation it is possible to estimate the equilibrium structure of a molecule from the zero-point rotational constants of several isotopes. The advantage of this “mass-dependence” (r_m) method over the conventional r_e method is that it is insensitive to the perturbations and resonances that frequently affect excited vibrational states. The main disadvantages are that a large number of isotopic molecules may be necessary and that the above equation is not sufficiently accurate for hydrogen-deuterium isotope effects.A detailed comparison between r_m and r_e of CO shows that the slight difference of about 2 × 10^?4Å between the two bond lengths is due mainly to the difference in the contributions of the electrons. The r_m method has also been applied to the triatomic molecules N₂O, OCS, SO₂ and HCN. For N₂O and SO₂ the results are in excellent agreement with the most recent r_e structures. For OCS there is a significant difference between the r_m structure and the present r_e structure. This difference is as yet unexplained. The poor results for HCN confirm the general expectation that the r_m method cannot be applied to hydrides without further modification.     

The development of a new Morse-oscillator based rotation-vibration Hamiltonian for H3+

The rotation-vibration Hamiltonian for an equilateral triangular X₃ molecule is derived in terms of the three curvilinear stretching coordinates Δr_i, and expanded in the form of a power series in the variables y_i = 1 ? exp(-aΔr_i), where a is a molecular parameter obtained from the potential function. The reason for the use of the variable y_i is twofold: Stretching potentials exhibit a much stronger convergence in the y_i than in the Δr_i, and a Hamiltonian expressed in the y_i can be diagonalized in a straightforward fashion using a Morse-oscillator basis set as we do here. Using a published ab initio potential surface we have expanded it as a polynomial in the y_i, and have calculated variationally the rotation-vibration energies of H₃⁺ and D₃⁺ using a symmetry-adapted Morse-oscillator-rigid symmetric top basis set. The results indicate that an expansion of the potential function to quartic terms in the y_i might be adequate, and that satisfactorily converged energies can be obtained with a relatively small basis set. The molecule H₃⁺ is the simplest polyatomic molecule. Inspection of the Appendix of this paper shows that the rotation-vibration Hamiltonian used here is one of the more complicated ones.     

The predictive use of the configurational co-ordinate model for luminescent centres

In the configurational co-ordinate model of a luminescent centre the displacement (Δr) of the excited state curve relative to the ground state plays an important role: for large values of Δr non-luminescent centres are formed, while for a low or zero value of Δr luminescent centres with a high quenching temperature are formed. The relative value of Δr can be deduced indirectly from the quenching temperature of the luminescence, but this involves a number of approximations which may not always be valid. The Δr has been calculated directly for a series of fluoride phosphors activated by Mn⁴⁺ from the intensity distribution of vibronic progressions which are present in the emission spectrum. The value of Δr thus obtained is influenced by the host lattice in a predictable way, and the quenching temperature of the phosphors correlate well with this independently determined value. The value of Δr along the e_g (Jahn-Teller active) co-ordinate is about twice as great as that along the a_1g co-ordinate. This may play an important role in nonradiative processes. The value of Δr along the other co-ordinates is too small to be calculated accurately.     

AB initio energy band structure of polysulfur nitride, (SN)x

All electron energy band structure is reported for an infinite one-dimensional model of polysulfur nitride, (SN)_x, using the ab initio LCAO Hartree-Fock method. The calculated values of the effective mass and density of states at the Fermi level are ?0.72 m_e and 0.06 states/(eV spin molecule), respectively. An appreciable amount of charge transfer (0.30 e) from sulfur to nitrogen was obtained. Finally, comparison is made with the results of a semi-empirical version of the same method.     

The variation of the electronic transition moment, Re, in the intensity theory of diatomic molecules

The electronic transition moment functions, R_e(r_v′v″), have been compiled, and their variation with the r-centroid has been investigated. Connections between the Λ-quantum numbers, the multiplicities, Δr_e, and the variation of R_e(r_v′v″) were not found.     

The use of scaled moments of inertia for structural calculations

A procedure for obtaining molecular structural parameters from microwave spectral data is described. The method uses the same set of experimental ground state moments of inertia used for a substitution structure determination, but is based upon a least-squares fit of moments which are obtained by scaling the experimental I₀ values. The scaling is performed in such a way that the resulting moments of inertia, I_m^γ are comparable to Watson's I_m moments and are thus close to the equilibrium moments. Initial tests and evaluation suggest that the method may lead to structural parameters which are better approximations to the r_e structure than those obtained by the conventional r₀ or r_s methods.     

Structure of dichlorine monoxide as studied by microwave spectroscopy. Determination of equilibrium structure by a modified mass dependence method

The microwave spectra of four isotopic species of dichlorine monoxide (OCl₂) have been observed, and the rotational constants have been obtained. The r_m structure for each isotopic species has been determined by Watson's method. The equilibrium structure has been estimated by taking proper averages of r_m structures to be $\text{r}{}_{\mathrm{e}}\text{(OCl) = 1.69587(7)}\text{A}\text{?}$ and ∠_eClOCl = 110.886(6)°. The general applicability and the merit of the present method for estimating the equilibrium structure are pointed out.     

Theoretical evaluation of the effective work functions for positive-ionic and electronic emissions from polycrystalline metal surfaces

Effective work functions (φ⁺ and φ^e) for positive-ionic and electronic emissions from polycrystalline metals of Nb, Mo, Ta, W and Ir are calculated according to our theoretical model by using those published data on both fractional surface area (F_i) and local work function (φ_i) of each metal surface composed of several patchy faces (1, 2, …, i). Comparison between the theoretical values thus obtained and those experimental data published to date yields the conclusions as follows. (1) With a slight error of less than ∼0.1 eV, the value of φ^e calculated with each of the metals is in fair or good agreement with that determined by experiment. (2) Such agreement is found also with φ⁺ for W. (3) In a typical case of W, where the degree of monocrystallization (δ_m) corresponding to the largest among the values of F_i is less than ∼0.5, the thermionic contrast (Δφ* ≡ φ⁺ − φ^e) is found again to be nearly equal to both theoretical and experimental values reported previously. (4) Each of the five metals shows that Δφ* at δ_m = 0.68-0.95 is smaller than Δφ* at δ_m < 0.5. (5) This result strongly supports our theoretical prediction that Δφ* decreases gradually to zero as δ_m increases beyond ∼0.5 up to ∼1. (6) Particularly, such a surface which has δ_m ≥ 0.96 exhibits Δφ* ≈ 0, apparently equivalent to the so-called “monocrystalline surface (δ_m = 1)”. These results lead to the conclusion that our theoretical model is valid for evaluating the effective work functions probably with a slight error of less than ∼0.1 eV, irrespective of both the surface species and the range of δ_m. In addition, our simple model makes it possible to analyze the mechanism of change in φ⁺ and φ^e according to the change in surface characters of both φ_i and F_i.     

On the Determination of the Equilibrium Structure of the PH3 Molecule

Values of the r_e and α_e equilibrium structural parameters of the PH₃ molecule have been determined on the basis of experimental data on the fundamental bands of the PH₂D and PHD₂ species only, without any knowledge of the force-constant-type parameters of the PH₃ molecule. The functions of the equilibrium rotational parameters A^e, B^e, and C^e have been determined. These functions are totally independent of the values of any resonance interaction parameters. Then these functions have been used to determine r_e and α_e constants. The obtained values r_e=(1.416 776±0.000 164) Å and α_e=(93.56±0.29)° differ a little from those found in the earlier literature.     

Quantitative relation between the thermionic contrast of metal surfaces and their degree of monocrystallization

For better understanding the peculiarities of work function, a simple model is devised to calculate the effective work functions (?⁺ and ?^e) for positive-ionic and electronic emissions from polycrystalline surfaces, which have a work function range from the maximum (?_max) to the minimum (?_min). Analysis of the theoretical results thus obtained and also of experimental data published to date enables us to find the quantitative relation between the thermionic contrast (Δ?^* ≡ ?⁺ − ?^e) and the degree of monocrystallization (δ_m), thereby yielding the three formulae of (1) Δ?^* = c for 0 < δ_m ? 1/2 (polycrystal), (2) Δ?^* = 4 cδ_m (1 − δ_m) for l/2 ? δ_m ? 1 (polycrystal), and (3) Δ?^* = 0 for δ_m = 1 (monocrystal). For a given surface consisting of a number of patchy faces (i), δ_m corresponds to the largest among its fractional surface areas (F_i) having different values of local work function (?_i). In a typical case of tungsten, the constant of c is evaluated theoretically to be 0.53 ± 0.09 eV, which well agrees with 0.59 ± 0.06 eV determined experimentally by many workers and also which satisfies the essential condition of Δ?^* ≦ c < ?_max − ?_min ≈ 0.8-1.0 eV. Our theoretical model is quite simple, but it is very useful for (1) evaluating both ?⁺ and ?^e with an uncertainty of less than ±0.1 eV, (2) finding the quantitative relation between Δ?^* and δ_m for actual surfaces of both poly- and monocrystals, and also (3) getting a substantial clue as to the problem how the effective work functions are governed by the surface characteristics of both F_i and ?_i.     

The Ground State Spectroscopic Parameters and Equilibrium Structure of PD3

Infrared spectra of PD₃ have been measured in the 20-320 cm⁻¹ range and in the region of the ν₂/ν₄ and ν₁/ν₃ fundamental bands near 750 and 1690 cm⁻¹, respectively, with a resolution of ca. 0.0025 cm⁻¹. Furthermore, submillimeter-wave spectra covering the J=4-3, 13-12, and 14-13 clusters in the vibrational ground state were recorded. The observed ΔJ=+1 rotational lines were augmented by about 5500 ground state combination differences formed from transitions belonging to the fundamental bands. Of these, 1300 involved perturbation-allowed lines with ΔK≠0. These data and observations taken from the literature were appropriately weighted and fitted to 14 ground state molecular constants. The A and B reductions of the rotational Hamiltonian were found to be equivalent. Improved effective ground state and equilibrium structures were determined for both PH₃ and PD₃; the equilibrium structures, r_e (PH)=141.1607(83) pm and α_e (HPH)=93.4184(95)° and r_e (PD)=141.1785(57) pm and α_e (DPD)=93.4252(68)°, are in good agreement.     

Molecular structure of phosgene as studied by gas electron diffraction and microwave spectroscopy: The rs,rm, and re structures

The microwave spectra of eight isotopic species of COCl₂ have been observed, and the following rotational constants have been obtained: An analysis of the rotational constants has resulted in the r_s and r_m structures. The equilibrium structure, r_e, has been estimated by combining the r_m parameters derived according to Watson's method and the r_e bond distances estimated in our recent electron-diffraction and spectroscopic studies to be $\text{r}{}_{\mathrm{e}}\text{(CO}\text{) = 1.1756 ± 0.0023}\text{A}\text{?}$, $\text{r}{}_{\mathrm{e}}\text{(CCl}\text{) = 1.7381 ± 0.0019}\text{A}\text{?}$, ∠_eClCCl = 111.79 ± 0.24°.     

Large amplitude bending motion in CsOH, studied through ab initio-based three-dimensional potential energy functions

The large-amplitude bending motion in CsOH, a ‘classical’ molecule whose microwave spectrum was first recorded in 1967, has been studied ab initio. The three-dimensional potential energy surface has been calculated at the RCCSD(T)_DK3/[QZP + g ANO-RCC (Cs, O, H)] level of theory and employed in MORBID calculations of the rotation-vibration energies and intensities. The ground electronic state is ¹Σ⁺ with the equilibrium structure r_e(Cs-O) = 2.3930 Å, r_e(O-H) = 0.9587 Å, and ∠_e(Cs-O-H) = 180.0°. The O-H moiety is bound to Cs by an ionic bond and the molecule can be described as Cs^δ+(OH)^δ-. Hence, the bending potential is shallow and gives rise to large-amplitude bending motion. The ro-vibrationally averaged structural parameters, determined as expectation values over MORBID wavefunctions, are 〈r(Cs-O)〉₀ = 2.3987 Å, 〈r(O-H)〉₀ = 0.9754 Å, and 〈∠(Cs-O-H)〉₀ = 163°. Although the averaged structure in the vibrational ground state is far from being linear, the Yamada-Winnewissi-linearity parameter for CsOH is γ₀≈-1.0, the value characteristic for a linear molecule.     

Anomalous X-ray scattering studies on superionic glassy (As2Se3)-(AgX) systems (X = halides)

Anomalous X-ray scattering experiments for glassy room-temperature superionic conductors (As₂Se₃)_0.4 (AgI)_0.6 and (As₂Se₃)_0.4(AgBr)_0.6 were performed close to the As, Se, Ag, and Br K edges using a third-generation synchrotron radiation facility, ESRF. The differential structure factors, Δ_iS(Q), were obtained from detailed analyses, indicating that Δ_AsS(Q) and Δ_SeS(Q) of both the glassy superionic semiconductors are similar to those of glassy As₂ Se₃ except the prepeak in Δ_SeS(Q). The Δ_AgS(Q) spectrum of (As₂Se₃)_0.4 (AgI)_0.6 looks molten salt-like. However, the Δ_Ag S(Q) of (As₂Se₃)_0.4(AgBr)_0.6 glass have quite different features from that of (As₂Se₃)_0.4 (AgI)_0.6 glass in the low Q range, and the Δ_BrS(Q) has even a pre-shoulder around 13 nm^? 1 unlike molten salts. In the differential pair distribution functions Δ_ig(r) obtained from the Fourier transforms of Δ_iS(Q), the first peaks of Δ_Asg(r) and Δ_Seg(r) show no correlation with those of Δ_Agg(r) and Δ_Brg(r), and vice versa. From these results, it can be concluded that a pseudo-binary mixture of the As₂Se₃ network matrix and AgX-related ionic conduction pathways is a good structural model for these superionic glasses. Differences between the AgBr- and AgI mixtures were found in the second-neighbor structures around the Ag atoms, which may reflect those in the crystal structures of the AgX salts.     

On the electronic properties of the sulfur nitride polymer (SN)x

Results of an ab initio LCAO Hartree-Fock crystal orbital calculation are reported for (SN)_x using a double-zeta type atomic basis set. In contrast with previous minimal basis calculations the width of the metallic half-filled band is only ～ 4 eV in this study. The calculated effective mass (1.7m_e), electron state density [0.14/(ev spin molecule)] and transferred charge (～0.4e from sulfur to nitrogen) are also in good agreement with experiment.     

Optical spectra of high-symmetry isomers 60(CH3-r 6-H)n at n=3, 6

Earlier, we found the energies of formation and the electron band structures of the fullerene molecule C₆₀ and its methylated and hydrogenated chemical derivatives with saturated r ₆ bonds of the type C₆₀(CH₃-r ₆-H)_n with n from 1 to 6. Based on the self-consistent molecular-orbital method, we found the energies of singlet and triplet excitations for each molecule by the ΔSCF technique. We compared the electron structure of the fullerene molecule with experimental data and other theoretical calculations and showed that the semiempirical quantum-chemical technique used in our work satisfactorily explains the experimental photoluminescence spectra of fullerene-containing star-shaped polystyrenes. Partial or complete removal of the dipole inhibition for the transitions in isomers that are formed upon chemical saturation of double bonds makes it possible to follow changes in the electron structure of the pπ shell of the fullerene molecule by spectroscopic techniques. Specific optical spectra of the first excited singlet states (spectra of absorption, luminescence, and excitation of luminescence) as well as phosphorescence of the first spin-triplet state are described.     

The effect of Cu substitution on the A1g mode of La0.7Sr0.3MnO3 manganites

We report on the first Raman data of Cu substituted La_1−ySr_yMn_1−xCu_xO₃ (0≤x≤0.10 and 0.17≤y≤0.3, accordingly in order to have the same Mn⁴⁺/[Mn⁴⁺+Mn³⁺] ratio), collected in the frequency range 100-900 cm⁻¹ and at room temperature, with parallel (e_i∥e_s) and crossed (e_i⊥e_s) polarizations of the incident (e_i) and scattered (e_s) light. Spectra were fitted with a Drude-Lorentz model, and peaks at 190-220 and 430 cm⁻¹, together with two broad structures centered at near 500 and 670 cm⁻¹, have been found. We also have observed that the A_1g mode is substantially shifted with increasing Cu substitution. The A_1g phonon shift is a linear function of the tolerance factor t and the rhombohedral angle α_r, thus following the structural changes of the MnO₆ octahedra in the system.     

Intensities of rotational lines in first overtone bands for axially symmetric molecules of the group C3v

The interaction of vibration and rotation is considered in the computation of the intensities of rotational lines in the first overtone bands of axially symmetric molecules of the group C_3v. The calculation utilizes the contact transformation method through first order of approximation as outlines by Hanson and Nielsen. General formulas for the intensities of the lines in the first overtone bands 2ν_n and 2ν_m are obtained, where n and m denote normal modes of species A₁ and E, respectively. It is found that to this order of approximation the usual selection rules ΔJ = 0, ±1 and ΔK = 0 are observed for the parallel overtone band 2ν_n. For the overtone band 2ν_m, the selection rules are more complicated, being ΔJ = 0, ±1; Δl_m = 0 and ΔK = 0, Δl_m = ±2 and $\text{Δ}\text{K = ?1}$, or Δl_m = ±2 and ΔK = ±2.     

Quantum interference effects in a multi-driven transition Fg = 3 ↔ Fe = 2

We calculated and studied the quantum coherence effects of a degenerate transition F_g = 3 ↔ F_e = 2 system interacting with a weak linearly polarized (with σ_± components) probe light and a strong linearly polarized (with σ_± components) coupling field. Due to the competition between the drive Rabi frequency and the Zeeman splitting, electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) are appeared at the different values of applied magnetic field in both cases that the Zeeman splitting of excited state Δe is smaller than the Zeeman splitting of ground state Δg (i.e., Δe < Δg) and Δe > Δg. It is shown that the resonance is broader and contrasts are higher for Δe < Δg than that for Δe > Δg at the same Rabi frequencies of probe and coupling fields.     

Head-on collision of dust-ion-acoustic solitons in electron-dust-ion quantum plasmas

In this paper, we study the head-on collision between two dust-ion-acoustic (DIA) solitons in quantum electron-dust-ion plasma. Using the extended Poincaré–Lighthill–Kuo (PLK) method, we obtain the Korteweg–de Vries (KdV) equations, the phase shifts and the trajectories after the head-on collision of the two DIA solitons. We investigate the effect of quantum diffraction parameters for electrons and ions (H _e, H _i), the Fermi temperature ratio (σ) and the dust charged number density (n _d0) on the phase shifts. Different values of μ?=?z _d0(n _d0/n _i0) and μ _d?=?z _d0(m _i/m _d) are taken to discuss the effects on phase shifts, where z _d0 denotes the dust charge number, n _j0 represents the equilibrium number density and m _j is the mass of the jth species (j?=?e, i, d for electrons, ions and dust particles, respectively). It is observed that the phase shifts are significantly affected by the plasma parameters.