Third-order theory of the line intensities in the allowed and forbidden vibrational-rotational bands of C3v molecules

A third-order theory of the intensities of the allowed and “forbidden” (perturbation-allowed) transitions to the fundamental vibrational levels of C_3v semirigid molecules has been worked out by using the method of contact transformations applied to the electric dipole moment operator. Explicit expressions have been obtained for the linestrengths of the allowed (Δk = 0, ±1) as well as forbidden (Δk = ±2, ±3, ±4) transitions from the ground vibronic state to the fundamental vibrational levels of C_3v molecules. The treatment takes into account all the important Coriolis and anharmonic interactions in a C_3v molecule, including the effect of the “2, 2” and “2, −1” l-type interactions and the Δk = ±3 interactions on the intensities of the allowed and forbidden vibrational-rotational transitions. The expressions for the linestrengths of the allowed and forbidden transitions are given here in a form suitable to fit the experimental data on the intensities in the vibrational-rotational spectra of C_3v molecules.     

The effect of temperature on libron frequencies in molecular crystals: Implications for TTF-TCNQ

Results for the effect of pressure and oemperature on lattice-phonon frequencies in six crystals (As₄S₄, S₈, S₄N₄, C₁₀H₈, C₁₄H₁₀, C₁₆H₁₀) have been analyzed to separate the phonon-excitation-driven (“explicit”) and the thermal-expansion-driven (“implicit”) contributions to dv/dT. The data establish that the volume-driven implicit effect dominates the temperature dependence of external-mode frequencies in molecular crystals. This finding has a bearing upon recent proposals for the role of librons in the electron transport of TTF-TCNQ.     

Analysis of the rotational spectrum of C3v molecules by using factorization and diagonalization of the energy matrix: Application to CH3C15N

A method is given for the analysis of the rotational spectrum in the ground and excited states of C_3v molecules; it consists in a direct diagonalization of the energy matrix including all elements whose contribution can become significant for the analysis up to the sixth order of approximation.The method of factoring the energy matrix into four submatrices A₁, A₂, E, E, according to the symmetry species of the full point group C_3v, is given. The programm enables the calculation of the rotational frequencies and also carries out by a least-squares method the fitting of the molecular constants for vibrational states v = 0 (ground state) and v_E = 1, 2, 3, and 4, separately or simultaneously over several of these states.The analysis of the rotational spectrum of CH₃C¹⁵N in the v₈ = 0, 1, 2 states is given as an example.     

C 60 and the icosahedral group Ih: Simplification methods and group-theoretical applications

Group-theoretical methods are used to induce “global” distortions of C ₆₀ from basis function(s) of a single “local” distortion in two cases: (1) The 60 vibrational modes arising from radial displacements of carbon atoms are found in terms of basis functions of A′, the one-dimensional symmetric representation of C_s; (2) The 24 vibrational modes arising from tangential displacements of hypothetical atoms placed at pentagon centers are found in terms of basis functions of E ₁, the vector irreducible representation of C_5v . The induction process is simplified by an icon notation (v) or (vμ) which uniquely labels the operations in I_h if μ,v = 0, 1, 2, 3, 4 and under/over lining of a digit is included. These icons describe the transformations IUS^vTS^μ of Felix Kline referred to a five-fold z-axis and two-fold x-axis and serve to label and “distinguish” symmetrically equivalent points of the truncated icosahedron.     

Stark spectroscopy with the CO laser: The ν3 fundamental band of H2CO

The ν₃ fundamental band of H₂CO (CH₂ scissoring motion) has been studied by means of CO laser Stark spectroscopy and conventional infrared absorption spectroscopy. The primary aim of the work was to determine the dipole moment of H₂CO in the v₃ = 1 state, and the value determined was 2.3250 ± 0.0025 D. The spectrum was analyzed with the inclusion of the Coriolis interactions among ν₃, ν₄, and ν₆ so that “true” rotational constants were determined for ν₃; “effective” constants obtained by ignoring these interactions were also determined. The ν₃ band origin was determined to be 1500.174 ± 0.002 cm^?1. The H₂CO spectrum was also used as a means of determining the frequencies of some ¹³C¹⁶O and ¹²C¹⁸O laser lines in the 1500 cm^?1 region relative to ¹²C¹⁶O lines.     

Effective Hamiltonian for degenerate vibrational states in symmetric top molecules

A mixed matrix-operator form of the effective rotational Hamiltonian has been discussed for the degenerate vibrational states of symmetric top molecules. In this scheme, a rotational contact transformation can be applied to the effective Hamiltonian such that the operators of the “2, +2,” “2, −2,” and “2, −1” l-type interactions as well as the operators of the Δk = ±3 and ±4 interactions are eliminated from the first-order terms of the expansion of the rotational Hamiltonian in terms of the small parameter λ. The results have been used to discuss the correlation between various interaction parameters in the effective rotational Hamiltonian for the doubly degenerate fundamental vibrational levels of semirigid symmetric top molecules. For example, for C_3v or D₃ molecules, the parameter of the “2, −1” interaction is correlated with other parameters and cannot be determined separately by fitting the experimental data (unless there are certain accidental resonances between vibrational-rotational levels).     

Normal Vibrations of Water in 1:1 Complexes

IR spectra of water in 1:1 complexes (HOH…B) show a characteristic change of the vibration frequencies v₁, v₂ and v₃ for differently strong bases (B). The normal vibrations in different complexes are calculated from the frequencies and the force constants f_OH, f_α, f_OH,OH. The normal vibrations show that v₃ (1:1) becomes the “free” and v₁ (1:1) the “bonded” OH vibration. The degree of coupling in these systems can be deduced directly from the observed band separation. For a base like water the degree of coupling in 1:1 complexes is about 40%.     

Surface-enhanced Raman spectroscopy of electrochemically characterized interfaces; potential dependence of Raman spectra for thiocyanate at silver electrodes

Surface-Enhanced Raman Spectra have been obtained for thiocyanate anions at silver electrodes following an oxidation-reduction cycle (ORC) as a function of electrode potential and electrolyte composition and compared with the extent of thiocyanate adsorption determined under the same conditions from differential capacitance-potential data. A spectrograph equipped with an optical multichannel analyzer (OMA) detector and a scanning spectrometer were used to make the Raman measurements. Spectra were obtained over the frequency range 100–2200 cm^?1, where all three normal vibrations, CN stretching (v_CN, 2090–2120 cm^?1), CS stretching (v_CN, 735 cm^?1), NCS angle bending (δ_NCS, 450 cm^?1) occur, along with a low frequency vibration attributed to a metal-ligand stretching mode (v_ml, 200–215 cm^?1) arising from a silver-sulfur surface bond. Both v_CN and v_ML decreased in frequency as well as intensity as the potential was made more negative in the region ?100 to ?700 mV versus Ag/AgCl for bulk thiocyanate concentrations of one millimolar and above, even though the thiocyanate surface concentration remained close to a monolayer throughout. By means of rapid time-resolved spectral measurements following potential steps using the OMA, the decrease of the intensity and frequency of the v_CN mode with increasing negative electrode potential was separated into a rapid “reversible” component and a slower “irreversible” decay. The latter component is attributed to the decay of Raman-active sites associated with the dissipation of metastable silver clusters formed during the ORC, that are prevented from rearranging at more positive potentials due to the presence of surrounding anionic adsorbate.     

Heat capacity and velocity of sound in the YbMgCu<Subscript>4</Subscript> “light” heavy-fermion system

This paper reports on a measurement of the heat capacity at constant pressure (C _p ) in the temperature range 3–320 K and the sound velocity (v) at 77 K for the “light” heavy-fermion compound YbMgCu₄. The present experimental data on C _p and v of YbMgCu₄, combined with our earlier phonon thermal conductivity data for YbMgCu₄ in the range 5–300 K, have been used to calculate the phonon mean free path l in this compound. The temperature dependence of l obtained is found to be characteristic of classical amorphous materials.     

Microwave l-type resonance transitions of the v4 = 1 state in PF3: Detailed interactions and molecular structure

Observation of the direct l-type resonance transitions in the microwave spectrum of the v₄ = 1 state of PF₃ has been extended to J = 36. The w-type interaction, (Δl = 0, ΔK = 6), has been found from measurements on the “forbidden” Stark trasitions in the $\text{K}\text{= 3}$ series. Also in this series a close accidental degeneracy was found between J = 30, $\text{K}\text{= 3}$ and 0, leading to new zero-field “forbidden” transitions through the r-type interaction (Δl = 2, ΔK = ?1) and to the determination of the C rotational constant. Nine spectroscopic parameters were determined using 140 observed frequencies including two “forbidden” trasitions. After suitable correction the B and C constants were used to determine the r₀, r_z, and r_e structures for PF₃. The equilibrium structure is estimated to be P-F = 1.561 ± 0.001 Å and ∠FPF = 97.7 ± 0.2°.     

Microwave spectrum and hydrogen bonding in 1-aziridineethanol

From its microwave spectrum, 1-aziridineethanol,

$\text{CH}{}_2\text{CH}{}_2\text{NCH}{}_2\text{CH}{}_2\text{OH}$

is found to have a gauche OCCN configuration, maintained by an OH?N-type hydrogen bond. The normal species rotational constants (MHz), A = 8528.87(25), B = 2069.74(2), and C = 2020.41(2), are consistent with a small (～6°) distortion from the “staggered” configuration about the central CN bond. Assuming a “normal” hydroxyl group, the hydroxy d₁ data suggest a decrease in the O?N distance upon bridge deuteration of ～0.003 Å. The dipole moment is 2.77(5) D, with 2.34(3), 1.45(6), and 0.3(3) D “a,” “b,” and “c” components, respectively.     

Spin-spin and spin-other-orbit effects of optical spectra and the spin-Hamiltonian parameters for Cr ions in MgO crystals

An extended complete diagonalization method/microscopic spin-Hamiltonian (CDM/MSH) program has been developed, which is applicable for d³ ions at sites of tetragonal symmetry type I (C_4v, D_2d, D₄, D_4h) and trigonal symmetry type I (C_3v, D₃, D_3d). The Hamiltonian includes the spin-spin (SS) and spin-other-orbit (SOO) magnetic interactions besides the spin-orbit (SO) magnetic interaction usually taken into account. Utilizing the extended CDM/MSH program, the optical spectra, the spin-Hamiltonian (SH) parameters of the ground state ⁴B₁, and the splitting δ(²E) of the first excited ²E state for Cr³⁺ (3d³) ions at C_4v symmetry sites in MgO crystals have been successfully investigated. It is found that although the SO magnetic interaction is the most important one, the contributions to the SH parameters and the optical spectra from the SS and SOO magnetic interactions for Cr³⁺:MgO crystals are appreciable and should not be omitted, especially reaching 27.8% for the zero field splitting parameter D.     

Microwave spectrum of tropone

The microwave spectrum of tropone (2,4,6-cycloheptatriene-1-one) has been obtained and assigned. The observation of a statistical weight intensity alternation indicates that the molecule has C_2v symmetry. Relative intensity measurements show the molecule to possess a low wavenumber vibration whose 1-0 interval is 60 ± 20 cm^?1. The dipole moment is found to be 4.1 ± 0.3 D by the “rate-of-growth” method.     

Intensity measurements in freon bands of atmospheric interest

The absolute intensities of the i.r. absorption bands, which are located in the atmospheric window region, of CFCl₃ (“Freon-11”) and CF₂Cl₂ (“Freon-12”) have been measured at 300°K. Our best estimates for these parameters are: for CFCl₃ (“Freon-11”), S_v = 635±36 cm^-2atm^-1 (9.2μ band), S_v = 1536±45 cm^-2atm^-1 (11.8μ band); for CF₂Cl₂ (“Freon-12”), S_v = 718±14 cm^-2atm^-1 (8.7μ band), S_v = 1136±22 cm^-2atm^-1 (9.1μ band), and S_v = 1302±40 cm^-2atm^-1 (10.9μ band).     

C42+的几何构型和Jahn Teller效应

用从头计算法QCISD/6-311G得到了C₄²⁺分子的10种不同的几何构型,其中包括C_s,C_∞v,C_2v,D_2h,D_∞h,D_4h,D_2d,C_3v等不同的构型.计算表明C₄²⁺的T_d构型不能稳定存在,详细讨论了T_{d 关键词： 几何构型 4}²⁺')" href="#">C₄²⁺ Jahn Teller效应     

Temperature dependence of fluorescence quantum yields of some side-substituted anthracene sulphonates

Of the four anthracene sulphonates (Na-salt), anthracene-1-sulphonate (1-AS), anthracene-2-sulphonate (2-AS) and anthracene-1, 5-disulphonate (1, 5-AS) show temperature dependence of φ_f, whereas for anthracene-1, 8-disulphonate (1, 8-AS) φ_f is independent of temperature. E_a for 1-AS, 2-AS and 1, 5-AS are 939 cm^?1, 1144 cm^?1 and 445 cm^?1, respectively. A low energy T_nπ¹ level supplied by ?SO^?₃ group could be responsible for efficient ISC in 1, 8-AS of symmetry C_2v. The possibility of tunnelling due to molecular distortion i.e. “geometry factor” cannot be ruled out also.