A rotation-torsion-vibration treatment with three-dimensional internal coordinate approach and additional FTIR spectral assignments for the CH3-bending fundamentals of methanol

A theoretical model has been developed to account for certain features of both newly observed and previously reported CH₃-bending subbands between 1450 and 1570 cm⁻¹ in the high-resolution Fourier transform infrared spectrum of CH₃OH [Can. J. Phys. 79 (2001) 435]. The features include (i) an apparent inversion of the rotationless E-A torsional splitting with respect to the ground state, i.e., the A state located above the E state, (ii) a pronounced upward slope in the K-reduced torsion-vibration energy pattern for the subband origins, and (iii) unexpected A₁/A₂ inversion of the K=2A and K=3AJ-rotational levels that led to ambiguity in identifying the vibrational mode as or . The model is an effective internal coordinate Hamiltonian constructed in G₆ molecular symmetry with the CH₃-bends coupled to each other and to torsion and including a- and γ-type Coriolis coupling. With this model, 33 out of 36 experimental upper-state K-term values for newly assigned , and ν₁₀ subbands plus previous ν₄ subbands have together been fitted successfully, employing 9 adjustable parameters and 17 fixed parameters to give a standard deviation of 0.14 cm⁻¹. The P_γ Coriolis term appears to be the leading cause of the upward shift in the K-reduced energies. When J-dependence is introduced via a rotational Hamiltonian including b- and c-type Coriolis terms in addition to molecular asymmetry, the observed A₁/A₂ inversion of the K=2A and 3A rotational levels can also be reproduced. Predictions using the fitted K-rotation-torsion-vibration Hamiltonian show an interesting Coriolis-induced crossover and mixing of the ν₅ and ν₁₀ torsion-vibration energy patterns. These predictions played a role in identifying two of the new ν₅ subbands in the crossing region, thereby helping to validate the model.     

New analysis of the Coriolis-interacting v2 and v5 bands of CH3Br and CH3Br

The and fundamental bands of CH₃⁷⁹Br and CH₃⁸¹Br have been studied by Fourier transform infrared spectroscopy with an unapodized resolution of 0.004 cm⁻¹, corresponding to an improvement of one order of magnitude compared to previous studies. For both isotopomers, some 2427 (2239) lines were newly assigned for the parallel and the perpendicular bands and, in addition, 80 perturbation-allowed transitions were also added. The ground-state axial rotational constants A₀ were redetermined from allowed and perturbation-allowed infrared transitions observed in the v₂ and v₅ bands around the local crossing. The A₀ values obtained for both isotopomers are more accurate but fully compatible with those obtained previously. Using those results, and the variation of the rotational constants with vibration, new accurate equilibrium constants A_e and B_e have been also determined for CH₃⁷⁹Br and CH₃⁸¹Br. The excited states v₂=1 and v₅=1 are coupled by Coriolis-type interactions (Δl=±1,ΔK=±1) and (Δl=?1,ΔK=±2), while the l₅=±1 levels of v₅ interact also through “l(2,2)”-type interaction (Δl=±2,ΔK=±2). The Coriolis coupling term was determined to be for CH₃⁷⁹Br and for CH₃⁸¹Br. All interaction parameters have been determined with higher accuracy, compared to previous studies. A total of 4213 (3704) line positions with J?68(64) and K?16(11) including all available data was fitted using 20 (18) parameters with a root-mean-square deviation of 0.0007 (0.0006) cm⁻¹ for CH₃⁷⁹Br and CH₃⁸¹Br, respectively. Two different but equivalent forms of reduced Hamiltonians with two different sets of constrained constants were successfully applied according to Lobodenko's reduction [J. Mol. Spectrosc. 126 (1987) 159]. The ratio of the transition moments, |d₂/d₅|=1.65, and a positive sign of the Coriolis intensity perturbation d₂×ζ₂₅×d₅ were determined. Therefore, it has been possible to generate an accurate prediction of the whole spectrum between 1200 and 1650 cm⁻¹, including Q branches.     

Stability of matter–antimatter molecules

We examine the stability of matter–antimatter molecules by reducing the four-body problem into a simpler two-body problem with residual interactions. We find that matter–antimatter molecules with constituents possess bound states if their constituent mass ratio m₁/m₂ is greater than about 4. This stability condition suggests that the binding of matter–antimatter molecules is a rather common phenomenon. We evaluate the binding energies and eigenstates of matter–antimatter molecules , and (K⁺μ⁻) − (μ⁺K⁻), which satisfy the stability condition. We estimate the molecular annihilation lifetimes in their s states.     

Fourier transform spectroscopy of chemiluminescence from the AΠ-XΣ system of SrO

The A^′1Π-X¹Σ⁺ near infrared system of strontium oxide (SrO) was observed at high spectral resolution by measuring the chemiluminescence from a Broida flow reactor using a Fourier transform spectrometer. In total, 32 bands from , , were measured within the spectral region at a resolution of . Vibrational levels of the upper state were observed up to v_A^′=4, and more than 5600 rotational lines were assigned. Incorporating previously published high resolution data for the A¹Σ⁺-X¹Σ⁺ system, a global fit to both data sets yields improved Dunham constants for the ground state and for the lower vibrational levels (v_A^′=0, 1, and 2) of the A^′1Π state. Because perturbations arising from interactions with the b³Σ⁺ and A¹Σ⁺ states affect the higher vibrational levels of the A^′1Π state more strongly, levels v_A^′=3 and 4 were represented by effective band constants in the fits. RKR potentials for the X¹Σ⁺,A^′1Π, and b³Σ⁺ states have been generated utilizing all the available data, Franck-Condon factors have been calculated for the A^′1Π-X¹Σ⁺ system, and A^′1Π∼b³Σ⁺ and A^′1Π∼A¹Σ⁺ perturbations are discussed.     

Stretch-bend combination polyads in the ÃAu state of acetylene, C2H2

Rotational analyses are reported for a number of newly-discovered vibrational levels of the S₁-trans (ùA_u) state of C₂H₂. These levels are combinations where the Franck-Condon active and vibrational modes are excited together with the low-lying bending vibrations, and . The structures of the bands are complicated by strong a- and b-axis Coriolis coupling, as well as Darling-Dennison resonance for those bands that involve overtones of the bending vibrations. The most interesting result is the strong anharmonicity in the combinations of (trans bend, a_g) and (in-plane cis bend, b_u). This anharmonicity presumably represents the approach of the molecule to the trans-cis isomerization barrier, where ab initio results have predicted the transition state to be half-linear, corresponding to simultaneous excitation of and . The anharmonicity also causes difficulty in the least squares fitting of some of the polyads, because the simple model of Coriolis coupling and Darling-Dennison resonance starts to break down. The effective Darling-Dennison parameter, K₄₄₆₆, is found to increase rapidly with excitation of , while many small centrifugal distortion terms have had to be included in the least squares fits in order to reproduce the rotational structure correctly. Fermi resonances become important where the K-structures of different polyads overlap, as happens with the 2¹3¹B¹ and 3¹B³ polyads (B = 4 or 6). The aim of this work is to establish the detailed vibrational level structure of the S₁-trans state in order to search for possible S₁-cis (¹A₂) levels. This work, along with results from other workers, identifies at least one K sub-level of every single vibrational level expected up to a vibrational energy of 3500 cm⁻¹.     

Probing the electronic structure of the nickel monohalides: Spectroscopy of the low-lying electronic states of NiBr and NiCl

Laser induced fluorescence and single vibronic level emission spectroscopy has been used to probe five low-lying electronic states (X²Π_3/2, A²Δ_5/2, X²Π_1/2, A²Δ_3/2 and B²) of NiBr and NiCl that arise from the 3d⁹ configuration of Ni⁺. Of these, for NiBr only the X²Π_3/2 and A²Δ_5/2 states have been previously observed experimentally, and a complete vibrational analysis of the low-lying states has not been reported for either molecule. In this work, term energies and a complete set of vibrational parameters were derived for all five electronic states for both NiBr and NiCl, and these are compared with recent high level ab initio calculations. In contrast to NiI, there are very few perturbations observed in the vibronic structure of these levels for either NiBr or NiCl. The data set derived in this work affords a detailed analysis of periodic trends in the Nickel monohalide series.     

High-resolution diode laser absorption spectroscopy of the O-H stretch overtone band (2,0,0)←(0,0,0) of the HO2 radical

The O-H stretching overtone (2ν₁) of the HO₂ radical was observed between 6603.2 to by using tunable diode laser absorption spectroscopy (TDLAS). About 1000 lines were observed in this region of which 491 transitions could be definitively assigned to the 2ν₁. The spectrum is observed to be an A/B hybrid band with band features of both a perpendicular and parallel nature. Transitions of the A-type bands with K_a^′=0-3, N^′?16 and transitions of the B-type bands with K_a^′=0,1, N^′?15 were assigned. The origin calculated from the best fit to the present spectrum is at which is ∼ higher than previously reported. The overtone spectrum is observed to be heavily perturbed, possibly by Fermi resonance with energy levels of the nearby (ν₂+5ν₃) state.     

The formaldehyde cation: Rovibrational energy level structure and Coriolis interaction near the adiabatic ionization threshold

Rotationally resolved pulsed-field-ionization zero-kinetic-energy photoelectron spectra of the 0⁰, 6¹ and 4¹ vibrational levels of the ground electronic state of the formaldehyde cation were recorded using a resonant three-color three-photon excitation scheme. The first adiabatic ionization energy of CH₂O (87793.33(1.30) cm⁻¹) and the rigid-rotor rotational constants (A⁺ = 8.874(8) cm⁻¹, B⁺ = 1.342(15) cm⁻¹, C⁺ = 1.148(18) cm⁻¹) of the vibronic ground state of CH₂O⁺ were derived. A strong a-type Coriolis interaction between the 6¹ and 4¹ vibrational levels was observed. The Coriolis coupling parameter and the deperturbed fundamental vibrational frequencies of the in-plane-rocking mode ν₆ and the out-of-plane bending mode ν₄ were determined to be 8.70(10) cm⁻¹, 823.67(30) cm⁻¹ and 1036.50(30) cm⁻¹, respectively. The intensity distribution of the photoelectron spectra was analyzed in the realm of a simple photoionization model.     

Laser spectroscopy of VS: hyperfine and rotational structure of the CΣ-XΣ transition

The (0,0) and (0,1) bands of the C⁴Σ⁻-X⁴Σ⁻ electronic transition of VS (near 809 and 846 nm, respectively) have been recorded at high resolution by laser-induced fluorescence, following the reaction of laser-ablated vanadium atoms with CS₂ under supersonic free-jet conditions. A least squares fit to the resolved hyperfine components of the rotational lines gives the rotational constants and bond lengths as C⁴Σ⁻: , ; X⁴Σ⁻: , . The electron spin parameters for the two states show that there are some similarities between the states of VS and those of VO, but the hyperfine parameters show that the compositions of the partly filled molecular orbitals are by no means the same. The ground state Fermi contact parameter of VS, b(X⁴Σ⁻), is only 58% of that of the ground state of VO, which implies that the σ orbital of the ground σδ² electron configuration has less than 50% vanadium 4s character. Similarly, the excited state Fermi contact parameter, b(C⁴Σ⁻), is very much smaller than that of VO. No local rotational perturbations have been found in the C⁴Σ⁻ state of VS, though an internal hyperfine perturbation between the F₂ and F₃ electron components at low N confuses the hyperfine structure and induces some forbidden (ΔJ=±2) rotational branches.     

Free states of the canonical anticommutation relations

Each gauge invariant generalized free state _A of the anticommutation relation algebra over a complex Hilbert spaceK is characterized by an operatorA onK. It is shown that the cyclic representations induced by two gauge invariant generalized free states _A and _B are quasi-equivalent if and only if the operatorsA ^1/2–B ^1/2 and (I–A)^1/2–(I–B)^1/2 are of Hilbert-Schmidt class. The combination of this result with results from the theory of isomorphisms of von Neumann algebras yield necessary and sufficient conditions for the unitary equivalence of the cyclic representations induced by gauge invariant generalized free states.Work supported in part by US Atomic Energy Commission, under Contract AT (30-1)-2171 and by the National Science Foundation.     

Experimental and theoretical study of the electronic states and spectra of PbLi

Gas phase emission spectra of the hitherto unknown free radical PbLi have been measured in the NIR range with a Fourier-transform spectrometer. The emissions were observed from a fast flow system in which lead vapor in argon carrier gas was passed through a microwave discharge and mixed with lithium vapor in an observation tube. Five electronic transitions have been found in the wavenumber range 3800-10 000 cm⁻¹. Bands from two excited states to the ground state were measured at high spectral resolution such that rotational analyses could be performed and accurate molecular parameters derived. In order to aid in the analysis of the experimental data, a series of relativistic configuration interaction calculations has been carried out to obtain potential curves for the low-lying states of PbLi and also electric dipole transition moments connecting them. As in the lighter molecules of this group, CLi and SiLi, the ground state of PbLi is found to be 3/2) with a spin splitting of about 2000 cm⁻¹. The first excited state is (A 1/2), and two observed band systems are assigned to the transitions A→X₁ and A→X₂. Two more excited states, (B 3/2) and C 1/2, are identified from the observed spectra with the help of the computed data, and their spectroscopic constants are determined. In contrast to PbH and PbF, the ab initio results indicate a very complicated low-energy electronic structure for the PbLi radical, with 19 bound electronic states calculated to lie below 3 eV.     

Vibration-internal rotation-overall rotation interactions in CH3OH. II. Vibration introduced τ-dependence to the reduced kinetic energy coefficient for internal rotation

Vibration-internal rotation-rotation interaction theory has been used to calculate the τ-dependence of F, the reduced kinetic energy coefficient for internal rotation for CH₃OH from molecular structure. The leading term is as a fraction of F⁰. Smaller terms are and then and for the symmetry breaking terms of the vibrationally distorted molecule. These terms have not been included previously in torsion-rotation anaylses for CH₃OH but should be compared with the fractional uncertainty in F⁰ of ±7×10⁻⁷. A rough estimate of the τ-independent vibrational contributions to F⁰ is of the order 4% with the largest contributors being the COH bend and OH stretch.     

High-resolution infrared and theoretical study of four fundamental bands of gaseous 1,3,4-oxadiazole between 800 and 1600 cm

The Fourier transform infrared spectrum of gaseous 1,3,4-oxadiazole, C₂H₂N₂O, has been recorded in the 800–1600 cm⁻¹ wavenumber region with a resolution around 0.0030 cm⁻¹. The four fundamental bands ν₉(B₁; 852.5 cm⁻¹), ν₁₄(B₂; 1078.5 cm⁻¹), ν₄(A₁; 1092.6 cm⁻¹), and ν₂(A₁; 1534.9 cm⁻¹) are analyzed by the standard Watson model. Ground state rotational and quartic centrifugal distortion constants are obtained from a simultaneous fit of ground state combination differences from three of these bands and previous microwave transitions. Upper state spectroscopic constants are obtained for all four bands from single band fits using the Watson model. The ν₄ and ν₁₄ bands form a c-Coriolis interacting dyad, and the two bands are analyzed simultaneously by a model including first and second order Coriolis resonance using the ab initio predicted Coriolis coupling constant . An extended local resonance in ν₂ is explained as higher order b-Coriolis type resonance with ν₆ + ν₁₀, which is further perturbed globally by the ν₁₅ + ν₁₀ level. A fit of selected low-J transitions to a triad model including ν₂(A₁), ν₆ + ν₁₀(B₁), and ν₁₅ + ν₁₀(A₂) using an ab initio calculated Coriolis coupling constant is performed.The rotational constants, ground state quartic centrifugal distortion constants, anharmonic frequencies, and vibration–rotational constants (α-constants) predicted by quantum chemical calculations using a cc-pVTZ and TZ2P basis with B3LYP methodology, are compared with the present experimental data, where there is generally good agreement. A complete set of anharmonic frequencies and α-constants for all fundamental levels of the molecule is given.     

Sub-Doppler high-resolution excitation spectroscopy of the S1 ← S0 transition of dibenzofuran

Rotationally resolved ultrahigh-resolution fluorescence excitation spectra of the S₁ ← S₀ transition of dibenzofuran have been observed using the technique of crossing a collimated molecular beam and the single-mode UV laser beam. 3291 rotational lines of the band and 3047 rotational lines of the band have been assigned. The band has been found to be a b-type transition, in which the transition moment is along the twofold symmetry axis of this molecule, and only the ΔK_a = ± 1 transitions were observed. The excited state is identified to be the S₁¹A₁(ππ^∗) state. In contrast with this, the band has been found to be an a-type transition in which the transition moment is along the long axis in plane. It indicates that the intensity of this vibronic band arises from vibronic coupling with the S₂¹B₂(ππ^∗) state. We determined the accurate rotational constants and the molecule have been shown to be planar both in the ground and excited states.     

The small signal gain and the saturation intensity measurement of the nitrogen-ion laser

A series oscillator-amplifier has been fabricated and optimized in order to determine the small signal gain and the saturation intensity of the N₂⁺ amplifying medium. Two plasmas, which are composed of a mixture of helium and nitrogen gases, have been produced under pressures of 2–5 atm by applying an electrical transverse discharge. The time delay between the two plasmas has been controlled by the gas pressure. To optimize the gain, the entrance time of the oscillator's output pulse into the amplifier was synchronized with the maximum population inversion in the amplifier. The gain coefficient () was obtained from 6 to 124, by varying the intensity of the input beam at the optimum pressure. The small signal gain and the saturation intensity have been calculated as 0.04, 0.07, 0.10 cm⁻¹ and 7.77, 13.33, 19.97 (kW cm⁻²) at 1.25, 1.70, 2.20 atm, respectively. The dominant wavelength of the nitrogen-ion laser corresponding to the B²∑_u(v = 0) → X²∑_g(v′ = 1) transition, 427.8 (nm) wavelength, was used in this work.     

Geometric form of the equations for the phase changes on reflection and transmission at a thin absorbing film

Abelès' equations for the phase changes on reflection and transmission, F_s, F_p, X_s and X_p at thin films have been rearranged into geometrical form in the ε₁, ε₂ plane. The contours of constant F_s and F_p are a series of circles whilst X_s and X_p can be represented by straight lines. When considering the same functions in the n, k plane, f_s and F_p become quartics in new axes, n′ and k′, obtained by rotating the n and k axes through an angle a given by tan . A similar transformation applied to X_s and X_p generates hyperbolae in the n′, k′ plane.     

Isotopic study of the transition of calcium monomethoxide using laser excitation and population depletion spectroscopy

High resolution excitation spectra have been obtained of the 0–0 band of the transition of four isotopologues, CaO¹²CH₃, CaO¹³CH₃, CaO¹²CD₃ and CaO¹³CD₃ of calcium monomethoxide. The deuterated species were found to have unexpectedly complicated spectra, and definitive rotational assignments were possible only from investigation by optical optical double resonance (OODR) population depletion spectroscopy. This confirmed the assignment of the CaO¹²CD₃ spectrum, and proved crucial in assigning the K-structure and spin components for CaO¹³CD₃. The state was found to be well described by the symmetric rotor model with C_3v symmetry for both hydride species but, for the deuterides, the K-structure and spin rotation splittings were irregular, especially for CaO¹³CD₃ where the K = 0 and 1 levels were heavily perturbed. The changes in the A constant determined for the hydride suggest that the CH₃ umbrella opens by 0.4°, i.e., 0.2° further on excitation to the state than on excitation to the lower-lying state (geometry change established in an earlier experiment by Crozet et al. [P. Crozet, A.J. Ross, C. Linton, A.G. Adam, W.S. Hopkins, R.J. Le Roy, J. Mol. Spectrosc. 229 (2005), 224–230]).     

High resolution infrared spectra of the first and second stretching overtone band systems of SbD3

The high resolution infrared spectrum of the mono-isotopic species ¹²³SbD₃ has been studied in the regions of the first and second Sb–D stretching overtones, from 2600 to 2800 cm⁻¹ and from 3900 to 4100 cm⁻¹, respectively. In both regions only two almost degenerate bands of similar intensity have been observed, one parallel and the other perpendicular, corresponding to the low-lying states in the manifolds of the excited vibrational states. These bands have been identified as 2ν₁(A₁)/ν₁ + ν₃(E) in the first overtone and 3ν₁(A₁)/2ν₁ + ν₃(E) in the second overtone band system. About 1700 transitions with have been assigned to the 2ν₁(A₁)/ν₁ + ν₃(E) and about 700 with to the 3ν₁(A₁)/2ν1 + ν₃(E) dyad. The transitions assigned to each dyad have been fitted simultaneously since the A₁/E excited states are affected by strong Coriolis and k-type perturbations treated explicitly in the model. Eventually, the extent to which the parameters resulting from the analyses fulfill the local mode theory requirements has been evaluated. Differently from SbH₃, the deuterated species does not reach true local mode behavior, even in the second overtone.     

Fourier-transform microwave and submillimeter-wave spectroscopy of chloroiodomethane, CH2ICl

Guided by a previous microwave study (9–35 GHz), the rotational spectrum of both chlorine isotopologues of chloroiodomethane in its vibrational and electronic ground state has been re-investigated in the microwave region and extended to the millimeter/submillimeter-wave region. Weak a-type transitions have been recorded by Fourier transform microwave spectroscopy below 20 GHz whilst strong b-type rotational transitions have been recorded between 15 and 646 GHz, corresponding to energy levels with J″ ≤ 108 and . Molecular constants including those describing the hyperfine structures owing to the two halogen atoms were accurately determined for both species from the least-squares analysis of a total of 1475 distinct transition frequencies (of which 906 belong to the CH₂I³⁵Cl isotopologue). The two sets of rotational constants allowed us to derive an r₀ structure of CH₂ICl.