Perturbations in the vibration-rotation-torsion energy levels of an ethane molecule exhibiting internal rotation splittings

Various examples of perturbations in the vibration-rotation-torsion energy levels of an ethane molecule exhibiting internal rotation splittings are discussed, both from the point of view of the point group D_3d, appropriate when internal rotation tunneling effects cannot be observed, and from the point of view of the group $\text{G}{}_{36}{}^2$, appropriate when internal rotation tunneling in ethane leads to observable splittings in the spectrum. It is found, for perturbations allowed in both D_3d and $\text{G}{}_{36}{}^2$, that each of the two torsional components of the perturbed D_3d vibration-rotation level can in principle interact with a “corresponding” torsional component in the perturbing vibration-rotation level. It is found for perturbations forbidden in D_3d but allowed in $\text{G}{}_{36}{}^2$, which all occur between D_3d vibrational levels of different g, u parity, that only one of the two torsional components of the perturbed D_3d vibration-rotation level can interact with a corresponding torsional component in the perturbing vibration-rotation level. Some of the perturbations examined give intensity to otherwise forbidden transitions in such a way that perturbation-induced transitions can be used in conjunction with normally allowed transitions to determine the sum of the internal rotation splittings for two rotational levels differing in K by three units.     

The magnetic rotation spectrum of iodine monobromide

The MRS of IBr in the visible region of the spectrum has been studied at high resolution and a rotational and vibrational analysis is reported. The spectrum consists of short runs in J′ for several neighboring vibrational states of the mixed B, ${}^3\text{Π}{}_0{}^{\mathrm{+}}$, and $\text{B}\text{?}\text{′}$, 0⁺ electronic states. These results imply that only a small number of closely related rotational-vibrational states of the combined system have sufficiently long lifetimes to provide the sharp lines required for the appearance of a MRS. The values observed extend to higher energies similar results reported by Selin for the absorption spectrum.     

The ultraviolet absorption spectrum of thioformaldehyde

The spectra of H₂CS and D₂CS were surveyed over the wavelength region from 230 to 180 nm and four distinct absorptions were identified. These are assigned to transitions from the $\text{X}\text{?}{}^1\text{A}{}_1$ ground state to the $\text{B}\text{?}{}^1\text{A}{}_1\text{(π, π}{}^1\text{)}$, $\text{C}\text{?}{}^1\text{B}{}_2\text{(n, 3s)}$, $\text{D}\text{?}{}^1\text{A}{}_1\text{(n, 3p}{}_{\mathrm{y}}\text{)}$, and $\text{E}\text{?}{}^1\text{B}{}_2\text{(n, 3p}{}_{\mathrm{z}}\text{)}$ electronic states. A vibrational and rotational analysis of the second system was undertaken. The results indicate that the molecule is planar in the $\text{C}\text{?}{}^1\text{B}{}_2\text{(n, 3s)}$ state and that while the CH and CS bond lengths remain near their ground-state values, the HCH angle increases substantially.     

The visible absorption spectrum of NO2: A three-mode nuclear dynamics investigation

The vibronic band origins of the visible absorption spectrum of NO₂ are calculated theoretically with the aid of a simple model Hamiltonian for the coupled electronic and vibrational motions. Including all three vibrational modes in the calculation and using ab initio values of the relevant parameters, we obtain satisfactory qualitative agreement with experiment. In particular, the observed high density and irregular intensity distribution of the band origins is reproduced correctly by the calculation. The present results confirm unambiguosly that the anomalous vibronic structure of the ${}^2\text{B}{}_2\text{←}{}^2\text{A}{}_1$ transition is caused by strong nonadiabatic interactions between the ²B₂ and ²A₁ electronic states of NO₂. They also show that simple deconvolution procedures, which are often used to deperturb irregular spectra, are not applicable to the ${}^2\text{B}{}_2\text{←}{}^2\text{A}{}_1$ transition of NO₂. To further explore the strength of the nonadiabatic effects in NO₂, we calculate the mixing of the different electronic species in the vibronic eigenstates and compare it to several relevant experimental quantities.     

Near-uv spectra with fully resolved rotational structure of naphthalene and perdeuterated naphthalene

The combination of a single-frequency, tunable uv source with a well-collimated supersonic molecular beam and sensitive fluorescence detection has been used to obtain spectra with rovibronic resolution for some large organic molecules. The results of analysis of the 0₀⁰ and $\text{8}$₀¹ vibronic bands of the ${}^1\text{B}{}_{\mathrm{3u}}\text{←}{}^1\text{A}{}_{\mathrm{g}}$ electronic transition for naphthalene and naphthalene-d_g are presented. The obtained spectra are assigned using a rigid asymmetric rotor Hamiltonian and the structure in both the ground and electronically excited states is determined. The rotational temperature of the molecules cooled in the beam has been determined. The influence of the nuclear spin statistics on the line intensities is observed and discussed.     

Energy levels of low lying triplet states of N2 from infrared emission studies

A theoretical model used to describe the $\text{B′}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}$ and B³Π_g states of N₂ is presented. Using recently acquired high resolution spectra of the $\text{B′}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{→ B}{}^3\text{Π}{}_{\mathrm{g}}$ (0-0) band, rotational energy levels of the v = 0 vibrational levels of these two states are generated with this model. These levels are in excellent agreement with those obtained using a combination differences technique. The precision of the model generated levels is 0.01 cm^?1. The previously unpublished rotational levels of Dieke and Heath for the $\text{A}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, B³Π_g and C³Π_u states are referenced to the $\text{N}{}_2\text{X}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ (v = 0, J = 0) ground level and tabulated here. Estimates of the precision of their work are made.     

Zeeman effects in the visible 2B2 ← 2A1 system of NO2

The Zeeman effect facilitates certain rotational assignments in bands of the ${}^2\text{B}{}_2\text{-}{}^2\text{A}{}_1$ electronic system of NO₂. A partial analysis of two bands of this system is reported.     

Microwave spectrum of the IO radical

The two lowest rotational transitions of the IO radical in the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ ground electronic state have been observed by means of a Stark modulated spectrometer. The effective rotational constants in the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ state, the centrifugal distortion constant, the axial component of the magnetic hyperfine interaction, and the nuclear electric quadrupole coupling constant are determined accurately. It was necessary to take into account the second-order effects from the matrix elements off-diagonal in J for the analysis of the hyperfine structure. An equilibrium internuclear distance r_e is calculated to be 1.8677 ± 0.0028 Å from the effective rotational constant $\text{B}{}_0\text{(}{}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{)}$, combined with α₃ from the A²Π → X²Π transition.     

Nonadiabatic effects in the B, C, B′, and D states of H2

The Kolos-Wolniewicz potentials for the H₂$\text{B}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and C¹Π_u states were used together with the hypothesis of pure precession for the rotation-electronic interaction, to calculate the nonadiabatic energy levels of these states for J = 1 to 5. The complete coupling matrix was computed using accurate numerical vibrational wavefunctions. The calculated Λ-doubling of the v = 0 to 12 C vibrational levels generally agrees well with experimental values, and the nonadiabatic shifts in the B rotational constants qualitatively explain the difference between the theoretical and RKR potentials for this state.The interaction of the B′${}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and D¹Π_u states was also investigated, but only qualitatively since adiabatic potentials of sufficient accuracy do not exist for these states. The Λ-doubling of the Dv = 0 rotational levels agrees well with the experimental values. An appreciable “background” nonadiabatic shift in the B′ rotational constants was found. This shift, which is nearly 5 percent of B_v, is in addition to that of strong local two-level interactions and was not “deperturbed” in constructing the B′ RKR potential. The result is that the RKR turning points differ by about 0.04 au from the “true” adiabatic turning points. This conclusion is supported by a Hartree-Fock calculation of the B′ potential to the left of R_e.     

Determination of molecular constants of nitric oxide from (1-0), (2-0), (3-0) bands of the 15N16O and 15N18O isotopic species

The (1-0), (2-0), and (3-0) transitions of ¹⁵N¹⁶O and ¹⁵N¹⁸O are investigated. The wavenumbers of the rotation-vibration lines are reported for the overtone bands and the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{-}{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ (1-0) subband. It is shown that in the data reduction it is advantageous to calculate first merged spectroscopic constants ignoring the Λ-type doubling. The vibrational constants ω_e, ω_ex_e, ω_ey_e and the vibrational dependence of the rotational constants are determined. The study of ¹⁵N¹⁸O allows the determination of the equilibrium values of the centrifugal distortion correction A_De to the spin-orbit constant and of the spin-rotation constant γ_e from the isotopic invariance of the ratios $\text{A}{}_{\mathrm{<mtext>De</mtext>}}\text{B}{}_{\mathrm{<mtext>e</mtext>}}$ and $\text{γ}{}_{\mathrm{<mtext>e</mtext>}}\text{B}{}_{\mathrm{<mtext>e</mtext>}}$. It is found that $\text{A}{}_{\mathrm{<mtext>De</mtext>}}\text{B}{}_{\mathrm{<mtext>e</mtext>}}\text{= (?3.9 ± 1.3) × 10}{}^{\mathrm{?6}}$ and $\text{γ}{}_{\mathrm{<mtext>e</mtext>}}\text{B}{}_{\mathrm{<mtext>e</mtext>}}\text{= (?4.00 ± 0.05) × 10}{}^{\mathrm{?3}}$.     

Polarized absorption spectra of diphenylnitroxide

A polarization study of the low-lying electronic states of the diphenylnitroxide radical imbedded in a benzophenone single crystal is presented. Assignments are made for the first two electronic excited states: ${}^2\text{B}{}_2\text{(n → π}{}^1\text{)}$ at 569 nm and ${}^2\text{B}{}_1\text{(π → π}{}^1\text{)}$ at 431 nm. Vibronic coupling is invoked in inducing the $\text{n → π}{}^1$ transition. The electronic structure of the nitroxide bears some resemblance to the corresponding carbonyl. The delocalization of the π electrons is also discussed.     

The emission spectrum of B2

The emission spectrum of B₂ was reinvestigated under high resolution. Six bands of ¹¹B₂ (0-0, 1-1, 1-0, 2-1, 3-2, and 0–1) as well as four bands of ¹⁰B¹¹B (0-0, 1-0, 2-1, and 3-2) were rotationally analysed. Accurate rotational and vibrational constants were obtained. The triplet character of the transition (${}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{-X}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$) was unambiguously established for the first time and spin-spin interaction constant is obtained for the excited state.     

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 XY4 molecules

Rotational energy levels in vibronic ground states of ²A, ²E, and ²F electronic states of open-shell XY₄ 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_2d of the true point group T_d. Hamiltonian matrix elements are determined by ladder operator techniques. Three sample calculated spectra, corresponding to $\text{p(}{}^2\text{F}{}_2\text{)-s(}{}^2\text{A}{}_1\text{)}$, $\text{d(}{}^2\text{E)-p(}{}^2\text{F}{}_2\text{)}$, and $\text{d(}{}^2\text{F}{}_2\text{)-p(}{}^2\text{F}{}_2\text{)}$ 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 XY₄ molecules can be mapped easily onto discussions of the rotation-vibration problem from the CH₄ literature.     

Thioformaldehyde: Vibrational analysis of the Ã1A2-X̃1A1 visible absorption system

The electronic absorption spectra of thioformaldehyde and thioformaldehyde-d₂ have been obtained. A vibrational analysis of the discrete band system in the 6100-4400-Å region is reported. The type A origin bands are at $\text{16 394}\text{16 484}\text{cm}{}^{\mathrm{?1}}$ for $\text{CH}{}_2\text{S}\text{CD}{}_2\text{S}$, and are magnetic dipole allowed. The electronic transition is $\text{A}\text{?}{}^1\text{A}{}_2\text{-}\text{X}\text{?}{}^1\text{A}{}_1$ under the C_2v point group. Most of the intensity of the system is in type B bands, and is due to vibronic mixing with higher ¹B₂ states when the inversion mode ν₄ is excited. The molecule in the excited ¹A₂ state is “floppy-planar,” having a broad potential function with a barrier of the order of 20 cm^?1 to the inversion motion.     

The spectrum of HeNe+

Discharges through mixtures of helium and neon show two band groups near 4250 and 4100 Å as first observed by Druyvesteyn. These bands, assigned to the HeNe⁺ ion by Tanaka, Yoshino, and Freeman, have been studied under high resolution and have been fairly completely analyzed. The upper state of the transition is a very weakly bound state resulting from $\text{He}{}^{\mathrm{+}}\text{(}{}^2\text{S) +}\text{Ne}\text{(}{}^1\text{S}{}_0\text{)}$. There are two lower states resulting from the two components of $\text{Ne}{}^{\mathrm{+}}\text{(}{}^2\text{P) +}\text{He}\text{(}{}^1\text{S}{}_0\text{)}$. The upper of these two (${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$) is also very weakly bound while the lower of the two, the ²Σ⁺ ground state, has a dissociation energy of 0.69 eV and an r_e value of 1.30 Å. All bands in both band groups show four branches designated R_ff, Q_ef, Q_fe, and P_ee. From their analysis the rotational constants in the various vibrational levels of the three electronic states have been determined. While no spin splitting in the B²Σ⁺ state has been found the ground state X²Σ shows a very large spin splitting and the $\text{A}{}_2{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ state a very large $\text{Ω-type}$ doubling. The vibrational numberings in all these states were established by the study of the spectrum of ³HeNe⁺. At the same time the hyperfine structure observed in all lines of ³HeNe⁺ confirmed the nature of the upper state B²Σ⁺ as resulting from He⁺ + Ne, i.e., by charge exchange from the ground state. The ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ component of the ²Π state has not been observed, presumably because of low intensity.     

Rotational analysis of the NO2 6125-Å region

In the NO₂ 6125-Å region 135 transitions belonging to four bands have been assigned using laser-induced fluorescence. On the whole, the rotational structure of the four vibronic bands is well characterized by near-prolate symmetric top relations. The 6125 and 6126-Å bands perturb each other, the former having predominantly the character of the $\text{A}\text{?}{}^2\text{B}{}_2$ state, the latter the $\text{X}\text{?}{}^2\text{A}{}_1$ state; this parent-daughter relationship is recognized to occur else-where in the NO₂ visible spectrum.     

The ã3A2 ← X̃1A1 absorption spectrum of thioformaldehyde: A vibrational and rotational analysis

The results of a vibrational and rotational analysis of the banded $\text{a}\text{?}{}^3\text{A}{}_2\text{←}\text{X}\text{?}{}^1\text{A}{}_1$ transition in $\text{CH}{}_2\text{S}\text{CD}{}_2\text{S}$ are presented. Only three of the six vibrational modes are active in the spectrum with $\text{ν′}{}_2\text{=}\text{1320}\text{1012}$, $\text{ν′}{}_3\text{=}\text{859}\text{798}$, and $\text{2ν′}{}_4\text{=}\text{711}\text{516}\text{cm}{}^{\mathrm{?1}}$. The spin forbidden transition gains intensity primarily by a mixing of the ${}^1\text{A}{}_1\text{(π}{}^1\text{,π)}$ and ${}^3\text{A}{}_2\text{(π}{}^1\text{,n)}$ states. This is confirmed by a rotational analysis of the 0₀⁰ band of both isotopes. The rotational analysis shows that the coupling in the $\text{a}\text{?}{}^3\text{A}{}_2$ state is near Hund's case b and that the spin constants are nearly 10 times greater than those observed for CH₂O. A $\text{CNDO}\text{2}$ calculation shows that this difference is due to the greater spin orbit coupling of S in CH₂S and to the smaller energy differences between the $\text{B}\text{?}{}^1\text{A}{}_1\text{(π}{}^1\text{,π)}$, $\text{b}\text{?}{}^3\text{A}{}_1\text{(π}{}^1\text{,π)}$, $\text{X}\text{?}{}^1\text{A}{}_1$, and the $\text{a}\text{?}{}^3\text{A}{}_2\text{(π}{}^1\text{,n)}$ states. The r₀ structure calculated from the rotational constants is $\text{r}{}_{\mathrm{<mtext>CS</mtext>}}\text{= 1.683}\text{A}\text{?}$, $\text{r}{}_{\mathrm{<mtext>CH</mtext>}}\text{= 1.082}\text{A}\text{?}$, β_HCH = 119.6°, and α (out of plane) = 16.0°. A simultaneous fit of the vibrational levels in ν′₄ of CH₂S and CD₂S to a double minimum potential function yielded a barrier to molecular inversion of 13 cm^?1 and an equilibrium out-of-plane angle of 15°.     

Theoretical analysis of the centrifugal distortion contributions to the rotational spectra of 2Π diatomics

The centrifugal distortion contributions to the rotational energies of diatomic molecules are derived from the resolution of the vibration-rotation wave equation. The unknown radial dependence of the fine structure constants is taken into account by means of a Taylor expansion around the equilibrium distance. Hence, one obtains the expressions of the centrifugal corrections associated with each fine structure constant in terms of the equilibrium values of its radial derivatives. The case of ²Π states is examined in detail. The dependence of the centrifugal distortion effects upon the choice of the coupling scheme representation is exhibited and a ²Π energy matrix containing the centrifugal constants of any order is proposed. Such a matrix is appropriate to fit the data for any value of the rotational quantum number. The theoretical expressions of the energy levels are related to the experimental data and the correlations between the spin-orbit centrifugal and spin-rotation contributions are put in evidence. It is shown that very compact formulas can be derived allowing a straightforward evaluation of the successive radial derivatives of the spin-orbit function in terms of the spectroscopic data $\text{A}{}^{\mathrm{(1)}}\text{? ?α}{}_{\mathrm{A}}\text{(}\text{w}{}_{\mathrm{e}}\text{B}{}_{\mathrm{e}}\text{)}$; $\text{A}{}^{\mathrm{(2)}}\text{? ?(1 +}\text{α}{}_{\mathrm{B}}\text{w}{}_{\mathrm{e}}\text{2B}{}_{\mathrm{e}}{}^2\text{)A}{}^{\mathrm{(1)}}$; …. Application of these results to the case of several molecules is considered and discussed.     

Analysis of the perturbed NO22B2 ← 2A1 system in the 591.4- to 592.9-nm region based on sub-Doppler laser spectroscopy

Sub-Doppler excitation spectra of NO₂, covering four vibronic bands within the spectral range from 16 861 to 16 903 cm^?1, were measured with a resolution of down to 10 MHz in a collimated supersonic molecular beam. Unambiguous assignment of all prominent lines in the 42-cm^?1-wide interval of the ${}^2\text{B}{}_2\text{←}{}^2\text{A}{}_1$ excitation spectrum was achieved by recording for each excitation line at least four vibrational bands of the corresponding fluorescence spectrum with completely resolved rotational lines. From least-squares fits to the line positions in the excitation spectra the rotational, fine, and hyperfine structure of the ²B₂ state was analyzed. A perturbation analysis, based on information from both types of spectra, confirms earlier models of vibronic coupling with high-lying vibrational levels of the ²A₁ ground state and gives evidence for spin-orbit coupling. Possible models are discussed which may explain the observed perturbations.     

Further studies of the electronic and vibrational spectra of ND2: Improved molecular parameters for the 000 and 010 levels of the ground state

Improved molecular parameters for the 000 and 010 levels of the $\text{X}\text{?}{}^2\text{B}{}_1$ ground state of ND₂ have been obtained by a weighted least-squares treatment using published microwave-optical double resonance frequencies, laser magnetic resonance data, infrared-optical double resonance frequencies, and extensive new optical data for the $\text{A}\text{?}{}^2\text{A}{}_1\text{-}\text{X}\text{?}{}^2\text{B}{}_1$ absorption spectrum. Revised assignments are given for 13 LMR transitions, including 4 “hot” band transitions.