Forbidden rotational spectra of axially symmetric polar molecules

In this paper we consider the rotational transitions induced by centrifugal distortion in polar or quasipolar symmetric top molecules belonging to the point groups C_n and C_nv (n ≥ 3). It is shown that in this series only the molecules of point groups C₃, C_3v, C₄, and C_4v may possess rotational spectra induced by first-order centrifugal distortion. A general expression is given for the effective dipole moment operator and for its matrix elements. The peak absorption coefficients for some of the strongest ΔK = 3 transitions of the CH₃D molecule have been calculated and compared with the peak absorption coefficients of allowed transitions.     

Selection rules for rovibronic transitions in symmetric top molecules

A simple diagrammatic rule is presented for determining the rotational selection rules governing transitions between any pair of vibronic states in electric dipole spectra of symmetric top molecules. The rule is useful in cases where degenerate vibronic levels with first-order Coriolis splittings occur, because it gives immediately the selection rule for the (+l) and (-l) components in any degenerate state. The rule is also helpful in determining the symmetry species and the effective zeta constants in overtone and combination levels involving degenerate vibrations. Particular attention is devoted to the conventions concerning the signs of zeta constants.     

Spin-allowed and forbidden rotational intensities in doublet-doublet transitions in asymmetric top molecules

Spin-orbit coupling allows anomalous transitions in spectra involving states of the same degenerate multiplicity, due to the relaxation of the spin selection rule ΔΣ = 0. This effect is discussed for doublet-doublet transitions in asymmetric top molecules. All the nonvanishing and independent transition moments, including those responsible for the anomalous transitions, are determined by symmetry and time reversal arguments. Rotational intensities are given for transitions between case (b) near-symmetric top eigenstates.     

Forbidden rotational spectra of polyatomic molecules

Some of the pure rotational transitions of polyatomic molecules that are forbidden according to the rigid rotor selection rules may acquire intensity by a centrifugal distortion mechanism, in which the intensity depends on the dipole derivatives and on the displacements in the normal coordinates produced by centrifugal distortion. The structures of the predicted spectra are discussed for nonpolar molecules belonging to the point groups D_3h, D_n (n > 2), D_2d, and T_d. Some of the calculated R-branch lines of methane are stronger than some of the lines of HD already observed in the same frequency range. For polar molecules extra contributions to the intensity must be considered and are exemplified for the Δk = ±3 transitions of C_3v molecules. These forbidden rotational transitions may have some astrophysical importance.     

Spin-vibronic transition moments and rotational intensities in doublet-quartet transitions in asymmetric top molecules

Symmetry and time reversal arguments allow the rigorous determination of the nonvanishing and independent spin-vibronic transition moments for doublet-quartet transitions in asymmetric top molecules. Less strict additional relations, leading to a smaller number of independent parameters, are derived by considering an insight of the intensity borrowing mechanism in the case of weak spin-orbit interactions. In this case it is shown that there are either two or three independent transition moments in orthorhombic molecules, depending on the symmetry species of the vibronic wavefunctions involved in the transition.Case (b) selection rules are derived, and it is shown that rotational intensities in orthorhombic molecules can be obtained in all cases by squaring certain sums of either all real or all imaginary terms. A diagrammatical method is devised to identify the form and polarization of the nonvanishing transition moments as well as the symmetry species of the products of those vibronic pairs whose spin-orbit mixing contributes to a given transition moment.     

Effects of collisional interference of lines in the spectra of symmetric top molecules: III. Broadening of rotational transitions with a hyperfine structure

The peculiarities of the broadening of rotational transitions of molecules in the case where the spectrum exhibits a hyperfine structure caused by the nuclear quadrupole interaction are considered. The relaxation parameters of the components of a number of hyperfine multiplets of CH₃I molecules are calculated taking into account self-broadening, and calculations are compared with experiment.     

Jahn-Teller and L-uncoupling effects on rotational energy levels of symmetric and spherical top molecules

The effects of a small Jahn-Teller effect and of Coriolis L-uncoupling forces on the rotational energy levels of a degenerate electronic state are considered. In general the two types of mechanism make similar contributions to the energy levels, and can only be separated by the use of additional information such as the isotopic variation of the molecular parameters. The theory of the rotational energies is formulated in a way that is applicable to both symmetric and spherical top molecules. The expressions derived for symmetric tops reproduce the results of previous workers. For E or F electronic states of spherical tops, the rotational parameters are equivalent to those employed for the fundamental levels of degenerate vibrations, but they must be interpreted in terms of the form of the appropriate double or triple potential energy surface. Parameters calculated for the 3d²F₂-3s²A₁ transition of the ND₄ molecule from the ab initio potential surface of Havriliak and King do not agree well with the experimental values of Herzberg and Hougen.     

Bifurcation in the rotational spectra of nonlinear symmetric triatomic molecules

A microscopic theory is proposed for bifurcation in the rotational spectra of nonlinear AB₂-type molecules. The theory is based on a study of small-amplitude vibrational and precessional motion near the stationary states of a rotating molecule. Bifurcation leads to the formation of fourfold clusters of levels in the upper parts of the rotational multiplets, disruption of the symmetry of the molecule, and a transition from normal to local valence vibrations. The role of the centrifugal force of inertia in the development of these effects is clarified. Bifurcation and the accompanying phenomena are studied in the hydride molecules H₂O, H₂S, H₂Se, and H₂Te using empirical molecular potentials. Zh. éksp. Teor. Fiz. 112, 1239–1256 (October 1997)     

Effective Hamiltonian for degenerate vibrational states in symmetric top molecules

A mixed matrix-operator form of the effective rotational Hamiltonian has been discussed for the degenerate vibrational states of symmetric top molecules. In this scheme, a rotational contact transformation can be applied to the effective Hamiltonian such that the operators of the “2, +2,” “2, −2,” and “2, −1” l-type interactions as well as the operators of the Δk = ±3 and ±4 interactions are eliminated from the first-order terms of the expansion of the rotational Hamiltonian in terms of the small parameter λ. The results have been used to discuss the correlation between various interaction parameters in the effective rotational Hamiltonian for the doubly degenerate fundamental vibrational levels of semirigid symmetric top molecules. For example, for C_3v or D₃ molecules, the parameter of the “2, −1” interaction is correlated with other parameters and cannot be determined separately by fitting the experimental data (unless there are certain accidental resonances between vibrational-rotational levels).     

Theory of higher-order stark effect of symmetric top molecules

The Stark effect formula for symmetric top molecules, which is correct to the fifth order of an external electric field, is given. The formula is applicable to linear molecules without or with electronic angular momenta coupled in Hund;s case a. Numerical tables are given for the special case of linear molecules without any electronic angular momentum. The effect of centrifugal stretching is considered to the first order. It is shown that our perturbation formula, which is correct to the sixth order of an external electric field, is good even when μE/B is about 1.     

Rotational selection rules for doublet-quartet transitions in asymmetric top molecules

Selection rules on the rotational structure of doublet-quartet transitions in asymmetric top molecules are discussed on the basis of the spin-orbit coupling mechanism, rather than by symmetry arguments, and some additional rules are found with respect to a previous work. In the case that the combining doublet and quartet states are appreciably mixed only with levels directly connected to them by the spin-orbit operator, it turns out that, except for the very low values of the rotational quantum numbers, branches with |ΔN ? ΔJ| > 1 are essentially forbidden. Thus, branches with ΔN = ± 3 (T and N branches) are not expected to be observable. In this case, it is found also that in a high magnetic field transitions with ΔM_s = ±2 are forbidden, and only ΔM_s = 0, ±1 bands are expected to occur. All these restrictions are removed if the combining states are also appreciably contaminated by states indirectly connected to them by the spin-orbit operator, through intermediate levels.     

Forbidden vibrational-rotational transitions and Herman-Wallis factors in fundamental IR bands of symmetric-top molecules

Within the theory of coupled schemes of ordering of vibrational-rotational interactions, the operator of the effective dipole moment of single-quantum vibrational transitions is represented in the form of an infinite series in vibrational (normal coordinates and conjugate momenta) or rotational variables (components of the total angular momentum). Mechanisms of activation of infrared-inactive totally symmetric vibrations in molecules of the D _2a , D _3h , C _3h , D _n (n ≥ 3), S ₄, T, T _a , and O symmetries and forbidden vibrational-rotational transitions in IR bands of active vibrations have been studied. The group-theoretic analysis of tensor parameters in higher-order effective dipole moments of single-quantum vibrational transitions in axially symmetric molecules has been performed. The strengths of allowed transitions and forbidden transitions in fundamental and hot IR bands of axially symmetric molecules are calculated with allowance for the Herman-Wallis factors. For effective dipole moments of multiquantum transitions in molecules, models are developed in the form of infinite series in rotational variables and in the form of Padé approximants.     

Rotational energy levels of symmetric top molecules in 2 E states

Expressions are derived for the rotational energy levels of a symmetric top molecule in a ² E state which take into account a spin-orbit interaction and vibronic Jahn-Teller interactions. Some group theoretical aspects of the Jahn-Teller problem for a general symmetric top molecule are discussed. In addition, the overall selection rules and formulae for the relative intensities of rotational lines in a ² A-² E transition are derived and the possibility of applying them to two recently published experimental examples is considered.     

Non-resonant absorption by a dilute gas of symmetric top molecules

A simple kinetic theory of non-resonant absorption by a dilute gas of symmetric top molecules is presented. Attention is focussed on the case where absorption occurs in the presence of static magnetic and electric fields. The macroscopic polarization of interest is found to behave differently in the two cases, but the lineshape has the same simple lorentzian form to a very good approximation. The predictions of the present theory agree with recent experimental observations, and the discrepancies of a previous kinetic theory are analysed and shown to be removable.     

Forbidden transitions in homopolar isotopically unsymmetric diatomic molecules and the dipole moment of HD

The theoretical expressions for the intensities of forbidden rotational and rotation-vibration spectra of homopolar isotopically unsymmetric diatomic molecules, made allowed by the breakdown of the Born-Oppenheimer approximation, are derived. The results are applied to HD and it is shown that among the previously overlooked contributions to the dipole moment of the molecule there is one with a very significant value in the direction H^?D⁺. A rotationally dependent contribution arising from centrifugal distortion is extremely small. The intensities of the fundamental and overtone bands of HD are also considered.     

“Forbidden” rotational spectra of symmetric-top molecules: PH3 and PD3

A millimeter-wave spectrometer having a sensitivity of 4 × 10^?10 cm^?1 in the 2-mm region has been constructed for observation of extremely weak millimeter-wave spectra of gases. It has been used to measure J → J, K = 0 ← 3 transitions in PH₃ and J → J, K = 0 ← 3 as well as K = ±1 ← ±4 transitions in PD₃. The B₀ and C₀ spectral constants (in MHz) are: for PH₃, B₀ = 133 480.15 ± 0.12 and C₀ = 117 488.85 ± 0.16; for PD₃, B₀ = 69 471.10 ± 0.03 and C₀ = 58 974.37 ± 0.05. The effective ground-state values obtained for the bond angle and bond length are: for PH₃, $\text{r}{}_0\text{(}\text{A}\text{?}\text{) = 1.420}{}_0$ and $\text{α}{}_0\text{(}{}^{\mathrm{o}}\text{) = 93.34}{}_5$; for PD₃, $\text{r}{}_0\text{(}\text{A}\text{?}\text{) = 1.417}{}_6$ and $\text{α}{}_0\text{(}{}^{\mathrm{o}}\text{) = 93.35}{}_9$. The corresponding zero-point-average values were calculated to be: for PH₃, $\text{r}{}_{\mathrm{z}}\text{(}\text{A}\text{?}\text{) = 1.4269}{}_9\text{± 0.0002}$ and $\text{α}{}_{\mathrm{z}}\text{(}{}^{\mathrm{o}}\text{) = 93.228}{}_7$; for PD₃, $\text{r}{}_{\mathrm{z}}\text{(}\text{A}\text{?}\text{) = 1.4226}{}_5\text{± 0.0001}$ and $\text{α}{}_{\mathrm{z}}\text{(}{}^{\mathrm{o}}\text{) = 93.256}{}_7\text{± 0.004}$. For both species, the equilibrium values are $\text{r}{}_{\mathrm{e}}\text{(}\text{A}\text{?}\text{) = 1.4115}{}_9\text{± 0.0006}$ and $\text{α}{}_{\mathrm{e}}\text{(}{}^{\mathrm{o}}\text{) = 93.32}{}_8\text{± 0.02}$.     

Multilevel rotational transitions in the intermediate stage of three-photon ionization of molecules

Ionization and dissociation of diatomic molecules induced by a weak field (after preliminarily populating an intermediate level) and by intense, linearly polarized monochromatic radiation have been studied. Field-induced mixing of rotational components of various electronic-vibrational states of molecules (such as CO, NO, etc.) at field strength f∼10⁻⁴–10⁻⁵ atomic units can lead to migration among states with different angular momenta J. Therefore, ions with rotational momenta J ⁺ much higher than those prescribed by selection rules for three-photon absorption can be formed from molecules in the ground state. The possibility of selective formation of ions with J ⁺≫1 and zero projection of the angular momentum on the polarization vector of the external electromagnetic radiation has been investigated. Zh. éksp. Teor. Fiz. 111, 1624–1632 (May 1997)     

Forbidden transitions in a magneto-optical trap

We report the first observation of a nondipole transition in an ultracold atomic vapor. We excite the 3P-4P electric quadrupole (E2) transition in 23Na confined in a magneto-optical trap, and we demonstrate its application to high-resolution spectroscopy by making the first measurement of the hyperfine structure of the 4P(1/2) level and extracting the magnetic dipole constant A=30.6+/-0.1 MHz. We use cw optical-optical double resonance accompanied by photoionization to probe the transition.     

Effects of collisional interference of lines in the spectra of symmetric top molecules: II. Self- and foreign-gas-broadening of rotational spectral lines

The theory outlined in the first part of the study is applied to an analysis of self-broadening and broadening by foreign gases of spectral lines for a number of symmetric top molecules with a high potential barrier to the inversion vibration. In all cases considered, the results obtained are in better agreement with the experimental data than previous theoretical results; however, in some cases, the discrepancy is rather large. Possible reasons are discussed and the acute need for experimental data obtained with modern equipment is noted.     

Forbidden transitions in anisotropic electron-nucleus interactions

Forbidden transitions in electron-nucleus systems are treated by perturbation theory for an arbitrary shape of the spin-spin interaction tensor.