The CO dimer: new light on a mysterious molecule

The present state of research on the CO dimer is reviewed. In recent years, both infrared and millimeter-wave spectra have been measured and partially assigned by the use of combination differences. A microwave-millimeter wave double resonance experiment, reported here for the first time, provides independent confirmation of these assignments and the resulting (CO)₂ energy level scheme. In the double resonance experiment, the OROTRON spectrometer functions as a supersensitive intra-cavity millimeter-wave detector. We update the continuing, but difficult, experimental efforts in recording the spectra, the quest for secure assignments, and the construction of a consistent and reliable energy level scheme. Although at present we have only limited knowledge of some aspects of the CO dimer, such as its geometrical structure, we have succeeded in characterizing unambiguously nine “stacks” of ground state energy levels with “microwave accuracy” (∼0.1 MHz). Every energy level within a given stack exhibits the same symmetry: either A⁻ or A⁺. Only transitions between A⁺ and A⁻ levels are allowed, and consequently ordinary pure rotational transitions within a stack are forbidden. Transitions between stacks can be thought of as tunneling transitions, and the separation of the lowest energy A⁺ and A⁻ states corresponds to a value of for the effective “tunneling splitting” of the CO dimer. The stacks tend to fall into two groups, corresponding to “isomers” with effective inter-molecular separations of either 4.0 or 4.4 Å. The larger inter-molecular separation of the true ground state (4.4 Å) likely corresponds to a C-bonded configuration, while the low-lying excited state with the smaller separation (4.0 Å) likely displays an O-bonded geometry.     

The millimeter wave spectrum of the CO dimer

The millimeter wave spectrum of the isotopically substituted CO dimer, (¹³C¹⁶O)₂, has been studied for the first time, confirming and extending a recent infrared study. Eighty-seven transitions in the 77-180 GHz region have been assigned and analyzed in terms of a model-independent term value scheme involving 57 rotational levels with J=0-8. The levels can be classified into 7 “stacks” which have symmetry classifications of either A⁻/B⁺ or A⁺/B⁻ and K-values of either 0 or 1. For the normal isotope, symmetry and nuclear spin statistics cause alternate rotational levels to be missing, but for (¹³C¹⁶O)₂ all levels are present with an intensity alternation of 1:3 between A and B symmetries. The four A⁻/B⁺ stacks have not previously been observed, and the lowest of them establishes the tunneling splitting of (¹³C¹⁶O)₂ to be 3.769 cm⁻¹, slightly larger than the (¹²C¹⁶O)₂ value of 3.731 cm⁻¹. A large amount of precise experimental data is now available for the CO dimer, which should lead to greater theoretical insight into its structure and tunneling dynamics.     

The high resolution FTIR spectrum of the ν2 band of formaldehyde isotopomer H2CO

The Fourier transform infrared (FTIR) absorption spectrum of the ν₂ fundamental band of the formaldehyde isotopomer H₂¹³CO was recorded at an unapodized resolution of 0.0063 cm⁻¹ in the 1630–1780 cm⁻¹ region. Upper state (ν₂ = 1) rovibrational constants inclusive of three rotational, five quartic, and six sextic centrifugal distortion constants were accurately determined by assigning and fitting 447 unperturbed infrared transitions with a rms deviation of 0.00056 cm⁻¹ using Watson’s A-reduced Hamiltonian in the I^r representation. Analysis of new transitions measured in this work yielded more higher-order upper state constants with greater accuracy than previously reported. The band center of the A-type ν₂ band was found to be 1707.980943 ± 0.000058 cm⁻¹ while the calculated inertial defect Δ₂ of the H₂¹³CO molecule was 0.09581 ± 0.00004 μŲ.     

Rotational Analysis of the ÃA1-X?A1 Band System of Yttrium Dicarbide, YC2

The 000-000 and 3¹₀ bands of the 775-nm electronic transition of YC₂(òA₁←X?²A₁) have been studied at high resolution, using the laser-induced fluorescence from a supersonic jet expansion. Three types of experiment have been carried out. First, the complete rotational and hyperfine structures of the two bands were recorded. To measure the small asymmetry splittings in the K=2 levels of the X?²A₁ state, portions of the b-type 3¹₀ band were then recorded in the presence of a weak static electric field. Finally, a number of pure rotational transitions between the K=0 levels of the ground state were recorded by pump/probe microwave optical double resonance. A few small rotational perturbations occur in the upper electronic state but, omitting the perturbed lines, the combined data sets could be modeled using an effective Hamiltonian operator appropriate for the rotation, electron spin, and hyperfine structure of a rigid asymmetric top molecule. The molecule is confirmed as being “T-shaped,” where the Y atom is bonded to the side of a C₂ group; the rotational constants determined are for the òA₁, 3¹ level, A=1.76128, B=0.189949, C=0.170056 cm⁻¹, and for the X?²A₁, v=0 level, A=1.742731, B=0.201947, C=0.181285 cm⁻¹. Allowing for electron orbital corrections to the rotational constants, the geometrical structures are found to be òA₁ state, r (Y-C)=2.2795 Å, r (C-C)=1.2630 Å, ∠C-Y-C=32.17°; X?²A₁ state, r (Y-C)=2.1946 Å, r (C-C)=1.2697 Å, ∠C-Y-C=33.63°. A molecular orbital diagram is given for the states of YC₂ and the interpretation of the electron spin and hyperfine parameters is discussed.     

The ν12 band of ethylene-1-C (CCH4) by high-resolution FTIR spectroscopy

The Fourier transform infrared (FTIR) spectrum of the ν₁₂ fundamental band of ethylene-1-¹³C (or ¹³C¹²CH₄) was recorded with an unapodized resolution of 0.0063 cm⁻¹ in the wavenumber region of 1360-1520 cm⁻¹. Rovibrational constants for the upper state (ν₁₂ = 1) up to five quartic and two sextic centrifugal distortion terms were derived for the first time by assigning and fitting a total of 879 infrared transitions using a Watson’s A-reduced Hamiltonian in the I^r representation. The root-mean-square deviation of the fit was 0.00066 cm⁻¹. The ground state rovibrational constants were also determined by a fit of 523 combination-differences from the present infrared measurements, with a rms deviation of 0.00090 cm⁻¹. The A-type ν₁₂ band which is centred at 1439.34607 ± 0.00004 cm⁻¹ was found to be relatively free from local frequency perturbations. From the ν₁₂ = 1 rovibrational constants obtained, the inertial defect Δ₁₂ was found to be 0.242826 ± 0.000002 μŲ.     

High-resolution FTIR spectrum of the ν12 band of ethylene-d (C2H3D)

The infrared absorption spectrum of the ν₁₂ fundamental band of ethylene-d (C₂H₃D) has been recorded with an unapodized resolution of 0.004 cm⁻¹ in the wavenumber range of 1340-1460 cm⁻¹ using the Fourier transform technique. By assigning and fitting a total of 870 infrared transitions using a Watson’s A-reduced Hamiltonian in the I^r representation, three rotational and five quartic centrifugal distortion constants for the upper state (v₁₂ = 1) were determined for the first time. The rms deviation of the fit was 0.00044 cm⁻¹ which is close to the experimental precision of the absorption lines. The A-type ν₁₂ band centred at 1400.762811 ± 0.000041 cm⁻¹was found to be relatively free from local frequency perturbations. The inertial defect Δ₁₂ was found to be 0.20928 ±  0.00002 μŲ.     

The ν12 band of C2D4

The Fourier transform infrared (FTIR) absorption spectrum of the ν₁₂ fundamental band of ethylene-d₄ (C₂D₄) was recorded in the 1017-1137 cm⁻¹ region with an unapodized resolution of 0.0063 cm⁻¹. Upper state (v₁₂ = 1) rovibrational constants consisting of three rotational and five quartic constants were improved by assigning and fitting 2103 infrared transitions using Watson’s A-reduced Hamiltonian in the I^r representation. The band centre of the A-type ν₁₂ band is found to be 1076.98480 ± 0.00002 cm⁻¹. The present analysis covering a wider wavenumber range and higher J and K_c values yielded upper state constants including the band centre which are more accurate than previously reported. The rms deviation of the upper state fit is 0.00045 cm⁻¹. Improved ground state rovibrational constants were also determined from the fit of 1247 ground state combination differences (GSCD) from the presently-assigned infrared transitions of the ν₁₂ band of C₂D₄. The rms deviation of the GSCD fit is 0.00049 cm⁻¹. In the rovibrational analysis, local frequency perturbations were not detected even at high J and K_a values. The calculated inertial defect Δ₁₂ is 0.32551 ± 0.00001 μŲ. The line intensities of the individual transitions in the ν₁₂ band were measured and the band strength of 39.8 ± 2.0 cm⁻² atm⁻¹ was derived for the ν₁₂ band of C₂D₄.     

The AE-XA1 System of CaOCH3

We have recorded laser excitation spectra of the CaOCH₃ free radical in a laser ablation molecular beam apparatus, at a spectral resolution of about 0.010 cm⁻¹ and a rotational temperature estimated at 15 K. The two spin-orbit components of the A²E-X²A₁ 0₀⁰ origin band between 625 and 630 nm have been analyzed. Five main subbands were revealed, with ΔK=+1 and K″=0,±1,±2. There was clear evidence of lambda-doubling in the A²E_1/2-X²A₁ 0₀⁰ (F′₁) K′=+1←K″=0 component. A nonlinear least-squares fitting program based on the model developed by Endo et al. [Y. Endo, S. Saito, and E. Hirota, J. Chem. Phys.81, 122-135 (1984)] fit the experimental data (514 A-X lines, N″≤37) with a root mean square deviation of 0.003 cm⁻¹, using known molecular constants of the ground state. The main vibronic (T₀=15 925.1232(5) cm⁻¹), spin-orbit (aζ_ed=66.974 48(51) cm⁻¹), Coriolis (Aζ_t=5.437 30(24)) cm⁻¹, rotational (A=5.439 97(24) cm⁻¹, B=0.117 884(2) cm⁻¹), and fine structure constants (ε₁=−8.208(14)×10⁻³ cm⁻¹, h₁=1.50(12)×10⁻⁴ cm⁻¹, ε_aa=3.58(89)×10⁻³ cm⁻¹, ε_bc=3.20(76)×10⁻³ cm⁻¹) for the excited state have been obtained.     

Improved rovibrational constants for the ν12 band of C2H3D

The Fourier transform infrared absorption spectrum of the ν₁₂ fundamental band of ethylene-d (C₂H₃D) was recorded at an unapodized resolution of 0.0063 cm⁻¹ in the 1330-1475 cm⁻¹ region. Upper state (ν₁₂ = 1) rovibrational constants inclusive of three rotational, five quartic, and four sextic centrifugal distortion constants were improved by assigning and fitting 1444 infrared transitions using Watson’s A-reduced Hamiltonian in the I^r representation. The present analysis yielded more higher-order upper state constants than previously reported. The rms deviation of the fit is 0.00055 cm⁻¹. Improved ground state rovibrational constants were also determined from the combined fit of 2026 ground state combination differences (GSCD) from the assigned infrared transitions of the ν₁₂, ν₃ and ν₆ bands and 21 microwave frequencies of C₂H₃D. The rms deviation of the GSCD fit is 0.00047 cm⁻¹. The A-type ν₁₂ band is centered at 1400.76262 ± 0.00004 cm⁻¹. Local frequency perturbations were not detected in the analysis. The calculated inertial defect Δ₁₂ is 0.20809 ± 0.00003 μŲ.     

High-resolution FTIR measurement and analysis of the ν3 band of C2H3D

The Fourier transform infrared (FTIR) spectrum of the ν₃ band of C₂H₃D was measured at an unapodized resolution of 0.0063 cm⁻¹ in the 1240-1340 cm⁻¹ region. Rovibrational constants for the upper state (ν₃ = 1) up to five quartic and two sextic centrifugal distortion terms had been obtained by assigning and fitting a total of 1037 infrared transitions using a Watson’s A-reduced Hamiltonian in the I^r representation. The root-mean-square deviation of the fit was 0.00051 cm⁻¹. The ground state rovibrational constants were also determined by a fit of 674 combination differences together with 21 microwave frequencies from the present infrared measurements with a root-mean-square deviation of 0.00040 cm⁻¹. The upper state (ν₃ = 1) and ground state rovibrational constants of C₂H₃D represent the most accurate values obtained so far. The A-type ν₃ band, centred at 1288.788826 ± 0.000044 cm⁻¹ was found to be relatively free from local frequency perturbations. From the ν₃ = 1 rovibrational constants obtained, the inertial defect Δ₃ was 0.1619724 ± 0.0000001 μŲ.     

High-resolution infrared and theoretical study of the fundamental bands ν6, ν7, ν9 and ν13 of 1,2,3-thiadiazole

The Fourier transform gas-phase IR spectrum of 1,2,3-thiadiazole, C₂H₂N₂S, has been recorded with a resolution of ca. 0.003 cm⁻¹ in the 700-1100 cm⁻¹ spectral region. Four fundamental bands ν₆(A^/; 1101.8 cm⁻¹), ν₇(A^/; 1038.8 cm⁻¹), ν₉(A^/, 858.9 cm⁻¹), and ν₁₃(A^//; 746.2 cm⁻¹) have been analyzed using the Watson model in A-reduction. Two additional bands, ν₈ (A^/; 894.6 cm⁻¹) and ν₁₂(A^//; 881.2 cm⁻¹) were assigned by their weak Q-branches. Ground state rotational and quartic centrifugal distortion constants as well as upper state spectroscopic constants have been obtained from fits. A number of weak global and local interactions are present in the bands. The resonances identified were qualitatively explained by Coriolis type perturbations with neighboring levels. Ground state rotational and quartic centrifugal distortion constants, anharmonic frequencies, and vibration-rotational α-constants predicted by quantum chemical calculations using a cc-pVTZ basis and B3LYP methodology, have been compared with the present experimental data, where there is generally good agreement.     

Rotationally Resolved LIF Spectra of the AΣ-XΠr Transition of Jet-Cooled GeCl

The A²Σ⁺-X²Π_r band system of ⁷⁴Ge³⁵Cl has been rotationally resolved for the first time using isotopically enriched ⁷⁴GeCl₄ as the precursor in a pulsed discharge jet experiment. The previous vibrational analysis of W. J. Balfour and K. S. Chandrasekhar (1986, J. Phys. B19, L187-L191) has been verified from the observed isotopic splittings of both the chlorine and germanium isotopomers. The ²Π_1/2 components of three vibronic bands have been rotationally analyzed leading to revised values for the ground state rotational constant B″₀=0.154165(35) cm⁻¹ and the lambda-doubling constant p″₀=6.560(97)×10⁻³ cm⁻¹. We have experimentally determined the value of B′_e=0.118710(24) cm⁻¹ for the A²Σ⁺ state leading to an excited state equilibrium bond length of 2.44581(25) Å.     

Coherence-converted population transfer FTMW-IR double resonance spectroscopy of CH3OD in the OD-stretch region

Rotationally selected infrared spectra of jet-cooled CH₃OD have been recorded and analyzed in the OD-stretch region (2710-2736 cm⁻¹). The observed spectra are obtained by monitoring three E-species microwave transitions (1₋₁ ← 1₀ at 18.957 GHz, 2₋₁ ← 2₀ at 18.991 GHz, and 3₋₁ ← 3₀ at 19.005 GHz) in a narrowband cavity Fourier transform microwave spectrometer, using the background-free coherence-converted population transfer technique. Of the four upper state subbands observed, two (K′ = 0 and −2) are split by perturbations. The E-species deperturbed band origin is at 2718.1 cm⁻¹. The deperturbed reduced term values follow a pattern similar to the ground state. This allows the J′ = 0 torsional tunneling splitting to be estimated as 2.1 cm⁻¹, which can be compared to 2.6 cm⁻¹ in the ground state.     

ESR of Cu doped cadmium (II) formate dihydrate

Electron spin resonance (ESR) of Cu²⁺ doped cadmium formate dihydrate single crystal was studied at room temperature. Copper enters the lattice substitutionally and is trapped at two magnetically inequivalent sites. The observed spectra are fitted to a spin-Hamiltonian of rhombic symmetry with the following values of the spin-Hamiltonian parameters, Cu²⁺(I): g_x=2.097±0.002, g_y=2.1166±0.002, g_z=2.2887±0.002 and A_x=(140±2)×10⁻⁴ cm⁻¹, A_y=(151±2)×10⁻⁴ cm⁻¹, A_z=(239±2)×10⁻⁴ cm⁻¹, Cu²⁺(II): g_x=2.0843±0.002, g_y=2.1045±0.002, g_z=2.2742±0.002 and A_x=(141±2)×10⁻⁴ cm⁻¹, A_y=(158±2)×10⁻⁴ cm⁻¹, A_z=(267±2)×10⁻⁴ cm⁻¹. The ground state wave function of the Cu²⁺ ion in this lattice is evaluated. It is found that the ground state is predominantly |x²−y²〉. The g-factor anisotropy is also calculated and compared with the experimental value. With the help of the optical absorption study, the nature of bonding in the complex has been discussed.     

ESR and optical study of Cu-doped Bis(l-asparaginato)zinc(II)

The Electron spin resonance (ESR) study of Cu²⁺-doped Bis(l-asparaginato)zinc(II) has been done at room temperature. Two magnetically equivalent sites for Cu²⁺ have been observed. The spin-Hamiltonian parameters evaluated with the fitting of spectra to rhombic symmetry crystalline field are g_x=2.0341±0.0002, g_y=2.0649±0.0002, g_z=2.2390±0.0002, A_x=(51±2)×10⁻⁴ cm⁻¹, A_y=(75±2)×10⁻⁴ cm⁻¹and A_z=(169±2)×10⁻⁴ cm⁻¹. The ground state wave function of Cu²⁺ has also been determined. The g-anisotropy has been estimated and compared with the experimental value. Further with the help of optical study, the nature of bonding of metal ion with different ligands in the complex has been discussed.     

The infrared spectrum of the CO dimer

The infrared spectrum of (¹²C¹⁸O)₂ has been studied for the first time using a tunable diode laser spectrometer in the 2095 cm⁻¹ region to probe a pulsed supersonic jet expansion. Very dilute gas mixtures of CO in He were used, resulting in small consumption of ¹²C¹⁸O sample gas, as well as cold and simple spectra. The results were analyzed using a term value scheme to obtain model-independent energies for 7 rotational levels belonging to 2 stacks in the lower state, v_CO=0, and 22 levels belonging to 7 stacks in the upper state, v_CO=1. The two ground state isomers of the CO dimer were found to be separated by only 0.639 cm⁻¹ for (¹²C¹⁸O)₂. These results provide a foundation for future studies of the millimeter wave spectrum.     

A visible spectrum of jet-cooled rhodium monosulfide

The diatomic molecule RhS has been observed for the first time. It has been studied by high resolution laser-induced fluorescence spectroscopy in a supersonic molecular beam following reaction by laser-vaporized rhodium atoms with CS₂ doped in He. Electronic, vibrational, and rotational data have been collected. The RhS ground state has ⁴Σ⁻ symmetry with a second-order spin-orbit splitting of 47.43 cm⁻¹, indicating case (a) coupling at low J. Three bands in the 535-555 nm region have been rotationally analyzed and give a bond length in the ground state of 0.2059 nm. A vibrational frequency ω_e ≈ 485 cm⁻¹ is estimated from dispersed fluorescence measurements.     

Doping and temperature dependence of inversion symmetry breaking in La2−xSrxCuO4

The doping dependence of the Raman spectra of high quality La_2−xSr_xCu^16,18O₄ polycrystalline compounds has been investigated at low temperatures. It is shown that symmetry forbidden bands peaked at ∼150 cm⁻¹, ∼280 cm⁻¹, and ∼370 cm⁻¹ are activated in the (xx/yy) polarization Raman spectra due to the local breaking of the inversion symmetry mainly at low temperatures and for doping concentrations for which the compound is superconducting. The apparent A₁-character of the activated modes in the symmetry reduced phase indicates a reduction from the D_2h to C_2v or D₂ crystal symmetries, which associates the observed modes to specific IR-active phonons with eigenvectors mainly along the c-axis. The temperature and doping dependence of this inversion symmetry breaking and the superconducting transition temperature are very similar, though the symmetry reduction occurs at significantly higher temperatures.     

Crystal field energy levels of the laser crystal Gd3Ga5O12: Nd

The crystal field energy levels of laser crystal Gd₃Ga₅O₁₂: Nd³⁺ are calculated using the diagonalization (of energy matrix) method. From the calculations, the 93 observed crystal field energy levels are explained reasonably and the root-mean-square (r.m.s.) deviation σ(≈25.6 cm⁻¹) and the scalar crystal-field strength parameter Nv (≈3847 cm⁻¹) are obtained. The results are discussed.     

Fourier Transform Emission Spectroscopy of the FΣ-XΣ System of RuN

Emission spectra of RuN have been recorded at high resolution in the region 12 000-35 000 cm⁻¹ using a Fourier transform spectrometer. The molecules were excited in a ruthenium hollow cathode lamp in the presence of about 2.5 Torr of Ne and 5 m Torr of N₂. New bands with origins near 17 758.1, 18 866.4, 19 800.4 and 20 721.5 cm⁻¹ have been assigned as the 0-1, 0-0, 1-0, and 2-0 bands of a new ²Σ⁺-²Σ⁺ system with the lower state as the ground state. This transition has been labeled as F²Σ⁺-X²Σ⁺, with the F²Σ⁺ state arising from the 1σ²2σ²1π⁴1δ⁴4σ¹ configuration. A rotational analysis of these bands has been carried out and spectroscopic constants have been extracted. The principal equilibrium constants for the ground state of RuN are ΔG(1/2)″=1108.3235(22) cm⁻¹, B_e″=0.5545023(42) cm⁻¹, α_e″=0.0034468(57) cm⁻¹, r_e″=1.5714269(60) Å, while the equilibrium constants for the excited state are ω_e′=946.8471(40) cm⁻¹, ω_ex_e′=6.4229(14) cm⁻¹, B_e′=0.50085(21) cm⁻¹, α_e′=0.00375(10) cm⁻¹, r_e′=1.65345(34) Å. This transition is analogous to the E²Σ⁺-X²Σ⁺ system of RhC (W. J. Balfour et al., J. Mol. Spectrosc.198, 393 (1999)).