Tetrahedral Splitting Research Articles

High resolution study of MGeH4 (M=76, 74) in the dyad region

The infrared spectrum of GeH4 (88.1% of 76GeH4, 11.5% of 74GeH4, and minor amounts of three other stable isotopic species in the sample) was measured in the 700–1080cm−1 region with a Bruker IFS 125HR Fourier transform interferometer (Nizhny Novgorod, Russia) and analyzed. 1922 transitions with Jmax.=26 were assigned to the ν4 and ν2 bands of 76GeH4 (ν2 is a symmetry forbidden absorption band, and its transitions appear in the spectrum only because of strong Coriolis interaction with the ν4 band). Rotational, centrifugal distortion, tetrahedral splitting, and interaction parameters for the ground, (0100) and (0001) vibrational states were determined from the fit of experimental line positions. The obtained set of parameters reproduces the initial experimental data with an accuracy close to experimental uncertainties. The result of analogous analysis of the 74GeH4 isotopologue (the number of assigned transitions is 788) is also presented.

Jet-cooled FTIR spectroscopy and analysis of the C–O stretch fundamental of Ni(CO) 4

Rovibrational spectra of the C–O stretch band (ν5) of Ni(CO)4 have been recorded at 0.006 cm− 1 resolution by coupling a low pressure continuous supersonic jet with a high resolution interferometer. The spectrum has been analysed thanks to the STDS software (see http://icb.u-bourgogne.fr/OMR/SMA/SHTDS/) that implements the tensorial formalism developed in the Dijon group for tetrahedral molecules. We obtain a very satisfying simulation thanks to an effective Hamiltonian expanded up to order 3. The asymmetry of the high-J lines is due to a small tetrahedral splitting and is well reproduced. The root mean square deviation is 0.96 × 10− 3 cm− 1. The Coriolis constant is somewhat larger than for other spherical-top carbonyls like Mo(CO)6 and W(CO)6 and, as a consequence, the level structure displays a standard three-branch structure, typical for triply degenerate fundamentals.

A perturbative calculation of the rovibrational energy levels of methane

The rovibrational energy levels of methane are determined from a quartic ab initio potential energy force field where the expansion coordinates are the Morse coordinates for the stretches and extension coordinates for the bends. Energies are calculated using canonical Van Vleck perturbation theory. Results are obtained for both rotation–vibration Hamiltonians expressed as functions of curvilinear and rectilinear normal coordinates. Second, fourth, and sixth order curvilinear results are compared with experimental results, and fourth order results for the rectilinear and curvilinear Hamiltonian are compared to each other. The calculated rovibrational levels are in good agreement with the experimental values for low J levels. The calculated rotational level splittings are in even better agreement with the experiment. In particular, the ground state tetrahedral splittings, which are as small as 10 −4 cm −1, are well reproduced by our calculations at sixth order.

D-to-s bonding in GaN

The interaction scheme for cubic GaN is constructed from the FP-LAPW density of states and scalar relativistic free-atom LDA eigenvalues. Orbital interactions responsible for the DOS distribution, indicated by interaction lines, show that, due to the Ga d-to-N s bonding the d states split into three subbands, displaying ds bonding, nonbonding, and antibonding properties. While nonbonding bands comprise d states of both and symmetry components, bonding and antibonding ds states originate exclusively from the -to-s orbital interactions. Due to the slight N p admixture, the relatively narrow band of nonbonding d states shows reversed tetrahedral splitting similar to that of fully occupied d states in II-VI semiconductors.

Lamb dip and infrared–radio frequency double resonance spectroscopy of 188OsO4

The frequency of seven rovibrational transitions in the ν3 band, Q branch of 188OsO4 have been measured with high accuracy. The spectrometer used consists of two CO2 lasers [∼3 W on the 10R(0)], the first of which is stabilized on the 4.3 μm fluorescence Lamb dip of the CO2 and the second on the saturated absorption dip of the rovibrational transitions of 188OsO4. The OsO4 transition frequencies are obtained combining the known frequency of the first laser with the measured frequency of the beat note between the two laser beams. For the assignment of the transitions the recent Fourier transform analysis by Bobin et al. [J. Mol. Spectrosc. 122, 229 (1987)] was used. The access to the 10R(0) laser line has made it possible to investigate, for the first time, the Q branch of the ν3 band of OsO4 in a sub-Doppler regime. Furthermore, the tetrahedral fine structure in the ground and in the ν3 state has been analyzed using the infrared–radio frequency double resonance technique. The tetrahedral splitting constants, Dt for the ground state and Z3t for the ν3 state, have been calculated with higher accuracy than in previous works.

Anharmonic cubic force field of methane

Anharmonic Klambda mu nu parameters of the CH4 molecule potential function are derived from the experimental rotational, tetrahedral splitting and resonance parameters of CH4 and CH2D2. As an illustration of the correctness of the potential parameters obtained, the original spectroscopic constants of CH4 and CH2D2 are theoretically reproduced. Calculations of the spectroscopic constants of CH3D and CHD3 molecules are also given for illustrations.

Local mode rotational structure in the (3000) Ge-H stretching overtone (“3ν 3”) of germane

The (3000) Ge-H stretching overtone band of germane, GeH 4 (conventionally described as 3ν 3) has been observed near 6130 cm −1 by Fourier transform infrared spectroscopy with a resolution of 0.01 cm −1. The rotational structure shows no sign of the tetrahedral splitting patterns normally characteristic of a spherical top. Instead the band exhibits a striking pseudo-symmetric-top structure. This had been predicted by Halonen and Robiette as the limiting case of a spherical top showing local-mode behaviour. The present results represent the first observation of this phenomenon.

Some effects of spin-orbit interaction on rotational levels and rotational line intensities in vibrationally unexcited 2A, 2E, and 2F electronic states of open-shell XY 4 molecules

Rotational energy levels in vibronic ground states of 2 A, 2 E, and 2 F electronic states of open-shell XY 4 molecules, as well as rotational line intensities for allowed transitions between such states, are discussed, including the effects of spin-orbit interaction and tetrahedral splittings. Jahn-Teller effects are assumed to be small, and are only taken into account implicitly, through their contributions to various parameters in the effective Hamiltonian. Qualitative information is obtained by considering several limiting-case coupling schemes among the electron spin angular momentum S, the electron orbital angular momentum L, and the pure rotational angular momentum R. These limiting cases are similar in spirit to Hund's coupling cases in diatomic molecules, but differ sufficiently from the latter to make detailed correspondences unhelpful. Quantitative information on rotational energy levels and line intensities is obtained numerically by diagonalizing a Hamiltonian matrix set up in a basis set characterized by uncoupled moleculefixed projections of S, L, and the total angular momentum J, and symmetrized so that all basis set functions belong to a definite species in the subgroup D 2 d of the true point group T d . Hamiltonian matrix elements are determined by ladder operator techniques. Three sample calculated spectra, corresponding to p( 2F 2)-s( 2A 1) , d( 2E)-p( 2F 2) , and d( 2F 2)-p( 2F 2) are presented. As one might expect, when the spin-orbit constant A is set equal to zero, then both qualitative and quantitative aspects of the rotational-electronic problem in open-shell XY 4 molecules can be mapped easily onto discussions of the rotation-vibration problem from the CH 4 literature.

Spectra of the ammonium radical: The Schuster band of ND 4

The Schuster band of ammonia occurs in many kinds of electric discharges through streaming ammonia if the pressure is not too low. While it is entirely diffuse for ordinary ammonia it shows a fairly clear structure (and an isotope shift) when produced with heavy ammonia (ND 3). Studies with intermediate isotopes show conclusively that there are four H atoms and a single N atom present in the molecule responsible for this spectrum, i.e., that it is due to the ammonium (NH 4) radical. An attempt is made to understand the structure of the ND 4 Schuster band in terms of a tetrahedral configuration of the molecule in both upper and lower state. By assuming that the lower state is the (predissociating) ground-state 3 s 2 A 1 of the molecule while the upper state is a 2 F 2 state derived from a 3 d electron it is possible to obtain quite a fair and detailed representation of the observed structure including partly resolved tetrahedral splittings in the upper state. The agreement of the wavenumber of the band origin with several recent ab initio calculations is not as good as one might wish and not as good as in the analogous case of H 3. This and other difficulties of the present interpretation of the spectrum are briefly discussed.

High-resolution spectroscopy of the 16-μm bending fundamental of CF 4

The 16-μm bending fundamentals ( ν 4) of 12CF 4, 13CF 4, and 14CF 4 have been observed at Doppler-limited resolution using a tunable PbSnSe semiconductor diode laser. The tetrahedral splittings of the rotational manifolds have been observed in all three branches, and in particular the dense and partially overlapping transitions in the Q branches have been resolved and assigned. A least-squares fit of the Hamiltonian, including off-diagonal terms, yielded five scalar and three tensor spectroscopic constants for each of the three isotopes. From these constants the upper-state rotational constant B 4 and the Coriolis constant ζ 4 have been calculated, together with some of the other molecular constants. An absorption feature at about 0.18 cm −1 to the red of the main Q branch of each isotopic species has been identified as the Q branch of ( ν 2 + ν 4) − ν 2, which is the transition that lases when CF 4 is pumped by a CO 2 laser at 9.4 μm (i.e., in ν 2 + ν 4).

The methane ν1(a1) vibrational state rotational structure obtained from high-resolution CARS-spectra of the Q-branch

The gaseous methane ν1(a1), Q-branch coherent anti-Stokes Raman scattering (CARS) spectra have been investigated at a resolution of 0.002 cm−1. A complex rotational structure of the resolved Q-branch has been experimentally observed. This structure can be ascribed to strong tetrahedral splitting of the rotational levels of the upper vibrational state, which possibly occurs due to Fermi resonance between the ν1(a1) and 2ν2(a1) vibrational energy levels which are close to each other. An assignment of the observed spectral lines has been made, yielding the rotational constants B, D, and Dt for the ν1(a1) vibrational state of the methane molecule. The absolute Raman frequency ν1 of the purely vibrational transition has been found.

The structure of Q branches in infrared-active fundamental-type bands of spherical-top molecules

In the absence of strong accidental resonance, the detailed energy-level structures of all Q branches of infrared-active fundamental-type bands in spherical-top molecules are prescribed, in the first approximation, by the value of the single parameter, β = v g , where v = Δ B eff Q and g is the tetrahedral or octahedral splitting constant. The Q branches of several heavy and light spherical tops are examined in this context, using energy-level diagrams, level cluster analysis, and computer graphics to simulate the superpositions of hundreds of absorption lines.

Vibrational anharmonicity in CF4

A simple anharmonic force field, consisting of a general quadratic force field in curvilinear coordinates, augmented with principal cubic and quartic valence-bond stretching force constants based on a Morse function, has been determined by least-squares adjustment to the vibrational energies of CF4. Since this model did not give a value of the cubic normal-coordinate force constant k344 in agreement with experiment, we considered a second force field identical to the first one except for the introduction of cubic stretch–bend–bend interaction force constants. These force fields have been used to calculate the tetrahedral anharmonic splittings of overtone and combination levels of CF4 and the calculated splittings have been compared with observed values determined by re-examining the previously published infrared spectra of CF4 in liquid–argon solution.

Doppler-limited spectra of the ν3 vibration of 12CH 4 and 13CH 4

The tetrahedral splittings in the P and R branches of the ν 3 band of natural methane have been examined with Doppler-limited resolution using a difference-frequency spectrometer. The spectra obtained by this difference-frequency mixer are compared to recent high-resolution grating spectrometer studies of 12CH 4 and enriched 13CH 4. The resolution, selectivity and precision are improved over the conventional methods. The mixing spectrometer utilizes tunable, narrow linewidth infrared radiation generated in the nonlinear optical crystal, LiNbO 3 as the beat frequency between a CW argon ion and a tunable dye laser. This spectrometer covers the 2.2 to 4.2 μm infrared spectrum with an instrumental resolution of 5 × 10 −4 cm −1 and continuous scans up to ∼1 cm −1 and with ir power ∼1 μW.

High resolution infrared measurements on the ν3 vibration-rotation band of 28SiH 4

The ν 3 vibration-rotation band of silane ( 28SiH 4) has been measured at high resolution (0.030–0.045 cm −1). The tetrahedral splitting has been partially resolved. The analysis of the band has yielded an improved set of molecular constants.

Theory of Microwave Transitions in the Vibronic Ground State of Tetrahedral Molecules

Vibration-rotation interactions in the motion of tetrahedral molecules, which are conventionally nonpolar in their ground vibrational and electronic states, permit pure rotational transitions. These transitions, which are electric dipole in nature, occur at microwave frequencies for the following changes in rotational quantum numbers: $\ensuremath{\Delta}J=0$ and $\ensuremath{\Delta}K=\ifmmode\pm\else\textpm\fi{}2$. General expressions for spectral line positions and absolute intensities are calculated for $J=0\ensuremath{-}20$. The effects of tetrahedral fine-structure splittings and nuclear-spin statistical weights have been included. Detailed results are established for methane, the prototype of molecules with tetrahedral symmetry. Possible competing transitions are discussed.

Theory of Pure Rotational Transitions in the Vibronic Ground State of Methane

It is shown that vibration-rotation interaction terms in the Hamiltonian of tetrahedral molecules like ${\mathrm{CH}}_{4}$ permit transitions, in the ground vibrational and electronic states, in which only the rotational quantum numbers change. Selection rules, spectral line positions, and absolute intensities are calculated. Effects of tetrahedral fine-structure splittings and nuclear-spin statistical weights are considered. Possible competing transitions are discussed.

The ν3 infrared bands of C 12H 4 and C 13H 4

The infrared spectrum of 92 mole % C 13H 4 was obtained over the region 2870–3130 cm −1 at a resolution of about 0.3 cm −1 and was compared with the spectrum of C 12H 4. The tetrahedral splitting was partly resolved and the splitting constants were determined by applying the theoretical treatments of Herranz and Hecht. With the aid of a partial analysis of the Q branch, and assuming a value for the ground-state rotational constant B 0, the molecular constants were obtained. Significant changes in going from C 12H 4 to C 13H 4 were observed for the following constants: Δ ν 0 = −9.95 cm −1; Δ B eff Q = +0.0027 cm −1; Δ α 3 = −0.0013 cm −1; Δ ζ 3 = −0.0088; as well as for some of the splitting constants. These changes are discussed and are shown to be generally in agreement with theoretical predictions using previously established force constants and harmonic frequencies. Expected vibrational frequency shifts, Δ ν, are tabulated for a number of vibrational modes; it is shown that analyses of C 13H 4 spectra will be useful in making assignments in the overtone region and may lead to more precise force constants for methane.

Theory of vibration-rotation interactions in spherical top molecules: Part I. A new overtone band

The possibility of a new overtone band in the infrared absorption spectrum of tetrahedral XY 4 molecules is investigated theoretically. This band is associated with the E vibrational part of the first overtone of an infrared active fundamental. The new band is active only through vibration-rotation interactions. Its intensity is very small compared to that of the F 2 vibrational part of the same overtone. Formulas for relative intensities and matrix elements of the Hamiltonian are calculated. The selection rules imply a single P, Q, and R branch. The tetrahedral splittings of the vibration-rotation levels are determined by only two parameters: D t and γ′ 3t ≡ 1 3 (Z 3s + 6Z 3t) . A possible favorable case for the observation of the band may be CD 4 at about 4700 cm −1. With the assumption that γ′ 3 t ⪢ D t , the tetrahedral splittings and relative intensities are calculated numerically through J = 7 for this case.

Infrared Absorption Spectrum of CD4 at 4500 cm—1

A high-resolution infrared absorption spectrum is presented for the region of the first overtone of the triply degenerate vibrational fundamental ν3 of CD4. The measured lines between 4430 and 4550 cm—1 are reproduced and tabulated. Comparisons are made between the tetrahedral splittings in this spectrum and those in the spectra ν3 and ν1+ν4 of CH4.