Simplified Hartree-Fock-Roothaan calculations of superhyperfine interactions for [VF6]4- and [CrF6]3- complexes - comparison with experiment

We apply a simplified Hartree-Fock-Roothaan Hamiltonian to the calculation of the superhyperfine interaction for [VF₆]^4- and [CrF₆]^3- in KZnF₃. We obtain a satisfactory agreement with EPR measurements.     

Analysis of the ν2 + ν3 band of 12CH4 and 13CH4

The ν₂ + ν₃ bands of ¹²CH₄ and ¹³CH₄ occurring in the region 4400–4650 cm^?1 have been studied from spectra recorded with a high-resolution Fourier transform spectrometer (resolution better than 0.01 cm^?1). Champion's Hamiltonian expansion, Canad. J. Phys.55, 1802 (1977), is applied to the problem of the two interacting F₁ and F₂ vibrational sublevels of this type of a band. As the P branch of ν₂ + ν₃ is strongly overlapped by neighboring bands, a combination-difference method, adapted to tetrahedral XY₄ molecules has been developed to help assignments of lines. A fit of 700 transitions has been performed using 13 new effective constants in the case of ¹²CH₄. In the case of ¹³CH₄, 532 transitions have been fit to 18 constants. The known parameters, relative to the vibrational ground state and the ν₃ state for both methanes, and the ν₂ state for ¹²CH₄ were fixed throughout. Most of the perturbed levels, up to J′ = 12, are well reproduced and the general agreement between experimental and calculated transitions is satisfactory with standard deviations of 0.047 cm^?1 (¹²CH₄) and 0.041 cm^?1 (¹³CH₄). The results (order of magnitude of obtained (ν₂ + ν₃) parameters and comparison of observed and computed intensities) indicate that the ν₂ + ν₃ band is perturbed by many other bands.     

Cooperative Jahn-Teller ordering and magnetic structure - pyridine-N-oxide complexes of Cu2+: Cu(ONC5H5)6X2 [X = ClO−4, BF−4]1

Pyridine-N-oxide complexes CuL₆X₂ [L: C₅H₅NO ; X: BF^?₄(I), ClO^?₄(II)] with trigonal unit cells at 298 K and CuL₆²⁺ octahedra in approximately cubic primitive arrangement exhibit dynamic to static Jahn-Teller phase transitions to pseudopetragonal modifications at ≈ 90 K (I) and below 70 K (II). It found by single crystal and powder EPR-spectroscopy, that the low-temperature β-phases are characterised by a cooperative Jahn-Teller order of elongated CuO₆-octahedra, which is ferrodistortive (I) and antiferrodistortive (II) respectively. These orbital order patterns are in agreement with the symmetries of the magnetic structures found for the two complexes.     

Diode laser line strength measurements of the (ν4 + ν5)0 band of 12C2H2

A diode laser spectrometer that was operated in sweep integration mode was used to measure individual line strengths for 17 R-branch transitions of the (ν₄ + ν₅)⁰ combination band of ¹²C₂H₂ at 7.4 μm. Analysis of these results gives a band strength S_v = 64.4 ± 2.0 cm^?2 atm^?1 at 296 K. Line-broadening parameters for several of these transitions were determined by using both N₂ and He as broadening gases.     

The ν2, 2ν2, 3ν2, ν4, and ν2 + ν4 bands of 15NH3

The ir absorption of gaseous ¹⁵NH₃ between 510 and 3040 cm^?1 was recorded with a resolution of 0.06 cm^?1. The ν₂, 2ν₂, 3ν₂, ν₄, and ν₂ + ν₄ bands were measured and analyzed on the basis of the vibration-rotation Hamiltonian developed by V. ?pirko, J. M. R. Stone, and D. Papou?ek (J. Mol. Spectrosc.60, 159–178 (1976)). A set of effective molecular parameters for the ν₂ = 1, 2, 3 states was derived, which reproduced the transition frequencies within the accuracy of the experimental measurements. For ν₄ and ν₂ + ν₄ bands the standard deviation of the calculated spectrum is about four times larger than the measurements accuracy: a similar result was found for ν₄ in ¹⁴NH₃ by ?. Urban et al. (J. Mol. Spectrosc.79, 455–495 (1980)). This result suggests that the present treatment takes into account only the most significant part of the rovibration interaction in the doubly degenerate vibrational states of ammonia.     

The ν2 + ν4 and 2ν2 isotropic Raman bands of 12CH4

The purely isotropic Raman spectrum of the ν₁ band, the ν₂ + ν₄ band (enhanced through interaction with ν₁), and the 2ν₂ band of ¹²CH₄ was obtained with a spectral resolution of 0.30–0.35 cm^?1 from exposures with different orientations of the linearly polarized exciting light. The ν₂ + ν₄ and 2ν₂ bands show partially resolved rotational structure. The spectra are interpreted in terms of a model which takes explicitly into account vibrational and rovibrational interactions with other vibrational states, using molecular constants determined primarily from infrared spectra. The computed contours are in excellent agreement with the experimental ones and the observed and calculated peak wavenumbers agree within one tenth of the spectral resolution limit, except for a small region near the ν₁ band. The good overall agreement represents an independent check on the overall correctness of the previously reported molecular constants. A detailed discussion is given of the contributions to the intensities of individual transitions from the three transition moment matrix elements, which in an isolated-band model are the intensity parameters of the ν₁, 2ν₄, and 2ν₂ isotropic bands, respectively.     

Jahn-Teller analysis of the 3T1(P) absorption band of Ni2+ in GaP

Comparison between experimental absorption due to the ${}^3\text{T}{}_1\text{(F)?}{}^3\text{T}{}_1\text{(P)}$ transition of substitutional Ni²⁺(d⁸) in GaP and theoretical predictions based on the Jahn-Teller model is presented. Numerical solution of the Hamiltonian, in which spin-orbit interaction and T₂-mode Jahn-Teller coupling are included, is in very good agreement with the energy position and intensities of the observed absorption lines.     

Core polarization of Cu2+ ions in [Cu(H2O)6]2+ complexes

An alternative interpretation of the experimental spin-Hamiltonian of Cu²⁺: LMN on the basis of M.O. theory is proposed. The calculated value for the core polarization of Cu²⁺ is 20% higher than the one previously assumed.     

Laser stark spectroscopy of the ν4 + ν8 − ν8 band of CH3C15N: Fermi resonances with 4ν84, 4ν82, and (ν7 + ν8)2

Laser Stark spectra for the ν₄ + ν₈ ? ν₈ parallel band of CH₃C¹⁵N were measured by using CO₂ and N₂O lasers in the 10-μm region. About 300 resonances have been assigned to 102 rovibrational transitions with J′ <- 16 and ?9 ≤ kl ≤ +9. Anomalies observed around kl = ?6 and +8 were proved to be due to the Fermi interactions with 4ν₈² and 4ν₈⁴, respectively. Another Fermi interaction with (ν₇ + ν₈)² was necessary to account for the anomaly around kl = ?6. Observed data were analyzed by the method of least squares, and precise molecular constants have been obtained.     

Molecular constants for the interacting upper states of the ν1, ν3, 2ν2, ν2 + ν4, and 2ν4 bands in 12CH4

In a previous paper (J.-E. Lolck and A. G. Robiette, J. Mol. Spectrosc.88, 14 (1981)) a theoretical model for the interacting upper states of the ν₁, ν₃, 2ν₂, ν₂ + ν₄, and 2ν₄ bands in methane was described. The present paper summarizes the results obtained, using this model, in a comprehensive analysis of the five bands of ¹²CH₄ through J′ = 12. Values of 80 molecular constants, of which 17 correspond to vibrationally off-diagonal operators, are reported. In addition the computed energy levels of the v₃ = 1 state are compared to the experimental ones and to the result of the previous isolated band approach.     

CrO43- centers in NH4Al(SO4)2.12H2 O single crystals

Electron paramagnetic resonance and optical absorption spectra of radiation damage products of undoped and CrO₄^2- doped ammonium alum are studied. On X-irradiation at room temperature several paramagnetic species like CrO₄^3-, SO₃^? and O₃^? are formed in the doped crystals. In the undoped crystals SO₃^? and O₃^? are the major radiation damage products.     

The shape of the 11S0 − 21P1 Fano resonance in the H- photo-ionization continuum

The interaction between the discrete autoionized state 1s2p of negative hydrogen and the overlapping split-configuration continuum is described in terms of stationary perturbations of nonorthogonal states that are eigenstates of two different first-order approximations to the Hamilton operator for the system.The eigenfunctions for the split-configuration states are taken to be those of a free p electron outside a neutral hydrogen atom in the ground state. The eigenfunction adopted for the short-lived, closed 1s2p configuration is the product of two functions that belong to symmetric Hartree-Fock eigenfunctions for the 1s²¹S and 2p²¹D states, respectively. This eigenfunction defines that Hamilton-operator approximation, of which the 1s2p state is an eigenstate.An improved Hamilton operator defines two different, but not independent, perturbation functions, one of which is a measure of the instability of the 1s2p configuration. The width of the resonance is found, correspondingly, to be determined by the product of two different perturbation terms. They are calculated in a Hartree-type approximation and found to be small, in part due to an effect of the nonorthogonality of the unperturbed states.The mean position of the singlet and triplet P Fano resonances in the ground state absorption continuum of H^- is found to be close to that of the diffuse interstellar bands at λ4430 and λ4760, but the calculated distance is about four times that of the bands. With exchange neglected and the position of maximum absorption fixed at λ4430 the singlet P resonance is found to have a width of 43 Å at half maximum, a minimum on the short-wave-length side, and a top absorption coefficient of 7 × 10^-16 cm²/ion, corresponding to an f value equal to 0.27.Tables of Hartree-Fock functions for the 2s²¹S, and the 2p²¹S, ¹D and ³P states of H^-, calculated by Claus Ingemann-Hilberg, are given in an appendix.     

The pentad rotation-vibrational states of 12CD4: Wavenumber analysis of infrared and Raman spectra of the ν1, ν3, 2ν2, ν2 + ν4, and 2ν4 bands

The so-called pentad of ¹²CD₄ consists of the vibrational states v₁ = 1(symmetry A₁), v₃ = 1(F₂), v₂ = 2(A₁ + E), v₂ = v₄ = 1(F₁ + F₂), and v₄ = 2(A₁ + E + F₂). All states are located in the 1950 to 2250-cm^?1 region and all are strongly interacting. In the present work we have assigned more than 5000 infrared rotation-vibrational transitions and 163 isotropic Raman transitions from the vibrational ground state to the pentad. We have used infrared and Raman spectra of a resolution better than 0.01 cm^?1. From the experimental wavenumbers 2567 pentad rotation-vibrational energy levels with J ≦ 20 have been determined. These levels are reported in the paper. The levels have been used for refinements of the spectroscopic constants of two physically different effective Hamiltonians for the pentad states. For all levels with J ≦ 12 an unweighted standard deviation of 0.004 cm^?1 is obtained for both Hamiltonians, whereas the standard deviation increases more or less rapidly with J above 12 due to the imperfections of the Hamiltonians. The values of the spectroscopic constants of both Hamiltonians (85 and 106, respectively) are reported and the effects of the approximations are discussed.     

Strengths and lorentz broadening coefficients for spectral lines in the ν3 and ν2 + ν4 bands of 12CH4 and 13CH4

Line strengths and self- and nitrogen-broadened half-widths were measured for spectral lines in the ν₃ and ν₂ + ν₄ bands of ¹²CH₄ and ¹³CH₄ from 2870–2883 cm^?1 using a tunable diode laser spectrometer. From measurements made over a temperature range from 215 to 297 K, on samples of ¹²CH₄ broadened with N₂, we deduced that the average temperature coefficients n, defined as $\text{b}{}_{\mathrm{<mtext>L</mtext>}}{}^0\text{(T) = b}{}_{\mathrm{<mtext>L</mtext>}}{}^0\text{(T}{}_0\text{)(}\text{T}\text{T}{}_0\text{)}{}^{\mathrm{?n}}$, of the Lorentz broadening coefficients for the ν₃ and ν₂ + ν₄ bands of ¹²CH₄ were 0.97 ± 0.03 and 0.89 ± 0.04, respectively. A smaller increase is observed in line half-width with increasing pressure for E-species lines, for both self- and nitrogen-broadening, than for other symmetry species lines over the range of pressures measured, 70 to 100 Torr.     

Extended assignment and analysis of the ν2 and ν4 infrared bands of 12CH4

Infrared spectra of the ν₂ and ν₄ bands of ¹²CH₄ have been assigned up to J′ = 20 in the ν₄ band and J′ = 17 in the ν₂ band. Assignments are presented for over 1000 transitions ranging from 1123 to 1712 cm^?1, which involve 652 upper-state energy levels of the two bands. The 652 upper-state levels have been fitted with a weighted standard deviation of 0.0026 cm^?1, almost all levels being reproduced to within their experimental error, by a Hamiltonian for the coupled upper states containing 28 refining parameters and 4 fixed parameters. Calculated relative intensities are also tabulated and discussed in relation to recent experimental intensity measurements.     

Phonon coupled cooperative low-spin 1A1high-spin 5T2 transition in [Fe(phen)2(NCS)2] and [Fe(phen)2(NCSe)2] crystals

Heat capacities of [Fe(phen)₂(NCS)₂] and [Fe(phen)₂(NCSe)₂] were measured between 13⁵ and 375 K. A heat capacity anomaly due to the spin-transition from low-spin ¹A₁ to high-spin π₂ electronic ground state was found at 176·29 K for the SCN-compound and at 231·26 K for the SeCN-compound, respectively. Enthalpy and entropy of transition were determined to be ΔH = 8·60 ± 0·14 kJ mol^?1 and ΔS = 48·78 ± 0·71 J K^?1 mol^?1 for the SCN-compound and ΔH = 11·60 ± 0·44 kJ mol^?1 and ΔS = 51·22 ± 2·33 J K^?1 mol^?1 for the SeCN-compound. To account for much larger value of ΔS compared with the magnetic contribution, we suggest that there is significant coupling between electronic state and phonon system. We also present a phenomenological theory based on heterophase fluctuation. Gross aspects of magnetic, spectroscopic, and thermal behaviors were satisfactorily accounted for by this model. To examine closely the transition process, infrared spectra were recorded as a function of temperature in the range 4000 ? 30 cm^?1. The spectra revealed clearly the coexistence of the ¹A₁, and the ⁵T₂ ground states around T_c.     

[Co(CO2)n]+团簇的红外解离光谱实验和理论研究

本文利用红外光解离光谱研究了一价钴阳离子与二氧化碳之间的相互作用. 通过密度泛函理论计算得到[Co(CO₂)_n]⁺团簇的几何结构,并且模拟了它们的振动光谱与实验数值进行比较. 研究结果表明,在[Co(CO₂)_n]⁺(n=2∽6)团簇中,钴阳离子通过电四极矩静电作用以端点结合的方式与二氧化碳中的氧原子结合在一起. 团簇的红外光谱都集中在二氧化碳反对称伸缩的波数附近,并且随着团簇尺寸的变化出现蓝移,最后把[Co(CO₂)_n]⁺的红外光解离光谱与稀有气体贴附的[Co(CO₂)_n]⁺-Ar的红外光解离光谱进行了比较.     

Simultaneous analysis of the ν1, ν4, 2ν2, ν2 + ν5, and 2ν5 infrared bands of 12CH3F

The Fourier-transform spectrum of CH₃F from 2800 to 3100 cm^?1, obtained by Guelachvili in Orsay at a resolution of about 0.003 cm^?1, was analyzed. The effective Hamiltonian used contained all symmetry allowed interactions up to second order in the Amat-Nielsen classification, together with selected third-order terms, amongst the set of nine vibrational basis functions represented by the states ν₁(A₁), ν₄(E), 2ν₂(A₁), ν₂ + ν₅(E), 2ν₅⁰(A₁), and 2ν₅^±2(E). A number of strong Fermi and Coriolis resonances are involved. The vibrational Hamiltonian matrix was not factorized beyond the requirements of symmetry. A total of 59 molecular parameters were refined in a simultaneous least-squares analysis to over 1500 upper-state energy levels for J ≤ 20 with a standard deviation of 0.013 cm^?1. Although the standard deviation remains an order of magnitude greater than the precision of the measurements, this work breaks new ground in the simultaneous analysis of interacting symmetric top vibrational levels, in terms of the number of interacting vibrational states and the number of parameters in the Hamiltonian.     

High-resolution infrared and microwave spectroscopy of the ν4 and 2ν2 bands of 14NH3 and 15NH3

More than two thousand Stark resonances of the ν₄ and 2ν₂ band transitions of ¹⁴NH₃ and ¹⁵NH₃ were observed at Doppler-limited resolution with a CO laser. Fourier transform infrared spectroscopy on ¹⁵NH₃ is also carried out. Thirty-six new microwave transitions including seven perturbation-enhanced transitions are observed in the v₄ = 1 excited vibrational state of ¹⁴NH₃ and ¹⁵NH₃. Accuracies of all available spectroscopic data on the v₄ = 1 and the v₂ = 2 states are evaluated and analyses of the vibration-rotation spectra are performed. The Coriolis interaction between the closely lying v₄ = 1 a (antisymmetric level) and v₂ = 2 s (symmetric level) states is explicitly included in the analysis. Smaller Coriolis interactions between the v₄ = 1 a and the v₂ = 1 s states and between the v₂ = 2 s and the v₂ = v₄ = 1 a states (i.e., (v₁, v₂, v′₃, v′₄) = (0 1 0⁰ 1¹)) are also taken into consideration. The accuracy in determination of the principal molecular constants is 10^?6. The parameters thus obtained reproduce the frequencies of the vibration-rotation transitions and inversion transitions within the accuracy of 0.0024 cm^?1.     

Acetylene spectra with a tunable diode laser: (ν4 + ν5)0+−ν41fQ branches of 12C2H2 and 12C13CH2

The rotational structure of the Q branches of the (ν₄ + ν₅)⁰⁺?ν₄^1f bands of ¹²C₂H₂ and ¹²C¹³CH₂ at 13.7 μm has been observed in a natural sample of acetylene by using a tunable diode laser as a source in a high-resolution infrared grating spectrometer equipped with a precision grating drive. Altogether 23 lines from J = 6 to 28 for ¹²C₂H₂ and 15 lines from J = 6 to 20 for ¹²C¹³CH₂ have been identified. The observed full width at half maximum of the resolved lines of these Q branches is very close to the calculated Doppler width. Molecular constants ν₀ + B″, B′ ? B″ ? 2D″, D′ ? D″, and H′ ? H″ have been derived from the measured line positions of the rotational structure.