Group theoretical treatment of the planar internal rotation problem in (HF)2

The HF dimer is believed to exhibit an internal rotation tunneling process between two planar but nonlinear equilibrium configurations, during which tunneling the roles of the hydrogen-bonded and the free hydrogen atom are interchanged. This process can be represented schematically with labeled atoms as H_lF_aH₂F_b ? F_aH_lF_bH₂, and gives rise to a permutation-inversion group G₄ containing four operations. In the present work the vibration-rotation-tunneling problem in (HF)₂ is treated group theoretically in three ways: (i) by allowing tunneling only through a trans planar C_2h intermediate, (ii) by allowing tunneling only through a cis planar C_2v intermediate, and (iii) by considering the trans and cis tunneling processes both to occur, though not necessarily with the same probability. The molecular symmetry groups used for these treatments are (i) the point group C_2h, (ii) the point group C_2v, and (iii) a double group, which might be thought of as $\text{G}{}_4{}^2\text{= C}{}_{\mathrm{2h}}{}^2\text{= C}{}_{\mathrm{2v}}{}^2$. Nonplanar tunneling paths are not considered, since the internal axis method (IAM) coordinate system used here cannot easily be adapted to nonplanar internal rotation motions in this molecule. Various-details of energy level diagrams, symmetry species for operators, selection rules for spectroscopic transitions, and statistical weights are presented for the (HF)₂ tunneling problem, as well as some speculation on the general question of when point groups, permutation-inversion groups, or double groups are preferable for treating large-amplitude vibrational motion problems.     

Calculation of centrifugal distortion constants for diatomic molecules from RKR potentials

Expressions are developed for computing the centrifugal distortion constants D_v, H_v, and L_v directly from the Rydberg-Klein-Rees rotationless potential of a diatomic molecule. These expressions involve summations over integrals of the wavefunctions of all neighboring vibrational levels. Application is made to the X¹Σ⁺ state of CO and the $\text{X}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state of O₂. In these applications, we have neglected the contributions of the continuum wavefunctions. For higher vibrational levels, particularly those near the dissociation limit, this approximation would be expected to fail. For the lowest vibrational levels of an electronic state, this method gives the same results for D_v, H_v, and L_v as the Dunham relations. However, for intermediate vibrational levels the present method is an improvement since expressions for only a few coefficients of the Dunham expansion are available. The use of D_v and H_v values calculated from Rydberg-Klein-Rees potentials in an iterative improvement of the reduction of spectroscopic data is described.     

l-type doubling transitions in Δ states of OCS

Molecular beam electric resonance spectroscopy has been used to measure the l-type doubling transitions in carbonyl sulfide. Transitions in J = 4 to J = 20 have been observed for the (02²0) vibrational state and for J = 1 and J = 2 for the (03¹0) state. The data has been analyzed to give the v = 2 energy separation $\text{E}{}_{\mathrm{<mtext>\Delta </mtext>}}{}^0\text{- E}{}_{\mathrm{<mtext>\Sigma </mtext>}}{}^0\text{= ?5.7861(2) + 8.36(1) × 10}{}^{\mathrm{?5}}\text{J(J + 1)}\text{cm}{}^{\mathrm{?1}}$, and the vibrational dependence of q to be 86.52(9)(v₂ + 1) KHz. The dipole moment of the (02²0) vibrational state is 0.6936(3) D.     

The dipole moment of thioformaldehyde in its singlet and triplet π1 − n excited states

Laser-induced fluorescence excitation has been used to measure Stark splittings of selected lines in the $\text{A}\text{?}{}^1\text{A}{}_2\text{-}\text{X}\text{?}{}^1\text{A}{}_1$ and $\text{a}\text{?}{}^3\text{A}{}_2\text{-}\text{X}\text{?}{}^1\text{A}{}_2$ band systems of H₂CS in electric fields up to 13 kV/cm. The derived excited state a-axis dipole moments are 0.820 ± 0.007 D for the 4¹ level of the ¹A₂ state; 0.838 ± 0.008 D for the zeroth vibrational level of ¹A₂; and 0.534 ± 0.015 D for the zeroth vibrational level of the ³A₂ state. These results are compared with the corresponding values of H₂CO, and interpreted in terms of the changing localization of the π and $\text{π}{}^1$ orbitals accompanying electronic excitation.     

Revised molecular constants,RKR potential,and long-range analysis for the B3Π(0u+) state of Cl2, and rotationally dependent Franck-Condon factors for Cl2 (BX1Σg+)

Literature data for the line frequencies of the B³Π(0_u⁺) ← X¹Σ_g⁺ transition of Cl₂ are fitted directly by least squares to obtain new molecular constants. The constants from individual bands are merged to obtain single-valued estimates of the rotational constants for each vibrational level of the B state. The results are combined with recent data from the B → X system in emission to obtain new RKR turning points for the B and X states, and Franck-Condon factors for the B-X system. The new constants are also used to provide revised long-range parameters for Cl₂(B) which differ from those of earlier work. In particular, the coefficient C₅ of the leading term in the inverse-power long-range potential is now found to be $\text{C}{}_5\text{= 1.16(2) × 10}{}^5\text{A}\text{?}{}^5\text{cm}{}^{\mathrm{?1}}$. Theoretical results for the variation of centrifugal distortion parameters for levels near dissociation are tested for D_v and H_v, and an extrapolation based on this behavior is used to facilitate determination of reliable B_v and G(v) values for the highest observed B-state levels.     

The 3540-Å electronic transition of malonaldehyde,a tunneling hydrogen-bonded molecule

Revised and more complete vibrational assignments are made for the 3540-Å $\text{π}{}^1\text{← n}$ band system of malonaldehyde. The $\text{0}{}^{\mathrm{+}}\text{0}{}^{\mathrm{?}}$ tunneling splitting is found to be 19 ± 11 cm^?1 for the $\text{nπ}{}^1$ state and this represents a 7-cm^?1 decrease relative to the ground electronic state. The tunneling splitting and the Franck-Condon envelope of intensities in the 185-cm^?1 upper-state progression suggest that the ${}^1\text{B}{}_1\text{(nπ}{}^1\text{)}$ state is significantly less tightly hydrogen-bonded than the ground ¹A₁ state.     

The emission spectra of H35Cl+, H37Cl+, D35Cl+, and D37Cl+ in the region 2700–4100 Å

The $\text{A}{}^2\text{Σ}{}^{\mathrm{+}}\text{-X}{}^2\text{Π}$ emission spectrum of HCl⁺ has been measured and analyzed for four isotopic combinations. These analyses extend previous work and provide rotational constants for the v = 0–2 levels of the ground state and for the v = 0–9 levels of the excited state. RKR potentials have been determined for both states, although the upper state could not be fitted precisely to such a model. Calculated relative intensities based on these potentials demonstrated that the electronic transition moment must change rapidly with lower state vibrational quantum number. Although considerable caution should be exercised in applying the concept of equilibrium constants to the $\text{A}{}^2\text{Σ}{}^{\mathrm{+}}$ state, the following are the best estimates of these constants (in cm^?1) for the $\text{X}{}^2\text{Π}$ state of H³⁵Cl⁺: B_e = 9.9406, ω_e = 2673.7, A_e = ? 643.7, and $\text{r}{}_{\mathrm{e}}\text{= 1.315}\text{A}\text{?}$. For the $\text{A}{}^2\text{Σ}{}^{\mathrm{+}}$ state of H³⁵Cl: T_e = 28 628.08, B_e ～ 7.505, ω_e ～ 1606.5, and $\text{r}{}_{\mathrm{e}}\text{= 1.514}\text{A}\text{?}$.     

Acetylene fluorescence

Previously unobserved acetylene ${}^1\text{A}{}_{\mathrm{u}}\text{(}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{) →}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ fluorescence occurs following 1933-Å ArF laser excitation of C₂H₂ or C₂H₄ and their deuterated analogs in solid Ne and Ar hosts at 4.2 K. Acetylene is a photolysis product of matrix-isolated ethylene. Ground-state vibrational levels as high as ν″₃ = 30 of the degenerate ν₃ bending vibration are observed for C₂D₂. Only ν₃ is appreciably active in the fluorescence. The negative ν₃ anharmonicity, previously observed in the gas phase, also occurs in Ne host. Consideration of rotational selection rules indicates that the Ne host strongly hinders free rotation about the low-moment-of-inertia $\text{a}\text{?}$ axis in the excited state.     

Vibration-rotation spectrum of HCF (X̃1A′) by laser-induced fluorescence

The vibration-rotation spectrum of the HCF molecule was observed by laser-induced fluorescence with an Ar⁺ laser. The laser line of 514.5 nm coincided with two rovibronic transitions, ^rR₁(9) and ^pQ₅(9) for $\text{A}\text{?}{}^1\text{A″(020)-}\text{X}\text{?}{}^1\text{A′(000)}$. The spectrum consisted of the progression of bending vibrational mode ν₂. The rotational lines were fully resolved for each of the vibronic bands. The analysis yielded the vibrational and rotational parameters for both the ground and the excited vibronic states. The rotational parameters of the $\text{X}\text{?}{}^1\text{A′}$ state were obtained for four vibrational levels [(0v₂0), v₂ = 0 – 3].     

The 280-nm absorption system of benzoyl fluoride

Benzoyl fluoride exhibits a weak, discrete absorption system in the region 290 – 260 nm. Vibrational structure associated with the C₆H₅COF and C₆D₅COF isotopes has been analyzed in detail. The C₆H₅COF and C₆D₅COF origin bands lie at 35 685 and 35 829 cm^?1, respectively. The intensity in the spectrum is principally associated with two progressions, ν′₁₉, the breathing vibration of the benzene ring and ν′₂₄, a COF in-plane bend, and sequence bands involving the COF torsion motion ν₃₆. The $\text{C}{}_6\text{H}{}_5\text{COF}\text{C}{}_6\text{D}{}_5\text{COF}$ν₁₉, ν₂₄, and ν₃₆ vibrational frequencies are respectively 1005/-, $\text{376}\text{357}\text{,}\text{and}\text{57}\text{55}\text{cm}{}^{\mathrm{?1}}$ in the ground state and $\text{950}\text{919}\text{,}\text{348}\text{331}\text{,}\text{and}\text{89}\text{85}\text{cm}{}^{\mathrm{?1}}$ in the excited state. The barriers to rotation of the COF group are estimated from the torsional frequency data to be 1450 and 3450 cm^?1 in the ground and excited electronic states, respectively.     

Selenium dioxide: Rotational analysis and Franck-Condon calculations for the 3130 Å 1B2-X̃1A1 absorption system

Band contour analyses of the absorption bands of ⁷⁸Se¹⁶O₂ and ⁸⁰Se¹⁶O₂ at 2949 Å, assigned to the 1₀³ transition (King and McLean, in press), show that they are type A, with transition moment directed in-plane and parallel to the line joining the oxygen nuclei. The electronic transition responsible for the B absorption system of the molecule is therefore ${}^1\text{B}{}_2\text{-}\text{X}\text{?}{}^1\text{A}{}_1$ under the C_2v point group. The contour analysis gives the excited state bond angle as 101.0°, and the bond length as 1.74 Å. The latter value is confirmed by Franck-Condon calculations. There is therefore an increase in bond length and a decrease in bond angle upon electronic excitation. This agrees with the predictions of molecular orbital theory.     

Rotational analysis of the A2Πu-X2Πg Second Negative band system of O2+

Existing high-resolution data for the $\text{O}{}_2{}^{\mathrm{+}}\text{A}{}^2\text{Π}{}_{\mathrm{u}}\text{- X}{}^2\text{Π}{}_{\mathrm{g}}$ Second Negative band system have been analyzed using a nonlinear least-squares fit that employs numerically diagonalized Hamiltonians. Values for the full set of molecular constants of the A²Π_u and X²Π_g states are obtained for the first time. In addition to values for ν₀(v′, v″), B_v, and D_v, the values for the spin-orbit coupling constants A_v are determined for both states. For the X²Π_g state, which is near Hund's case (a), the agreement between these A_v″ values and those predicted by theory is good. However, for the A²Π_u state, which is much nearer to case (b), these A_v′ values and theory disagree both in magnitude and in variation with vibrational level. The A²Π_u state is an inverted state for vibrational levels v′ ≤ 5 and is a regular state for levels v′ = 6–8 (the upper limit of present high-resolution data). Λ-doubling parameters are determined for the X²Π_g state, the only state where Λ-doubling is statistically significant. Spin-rotation interaction is not statistically significant for either state. Dunham Y_i0 and Y_i1 expansion coefficients are determined for each state. Theoretical D_v values calculated from RKR potentials are used to improve the B_v values in the reduction of the data.     

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.     

Vibrational assignments in the electronic spectra of thiazyl fluoride

The first assignments of ν₂, largely SF stretching mode, have been made for the $\text{A(}{}^1\text{A″)}$ and $\text{a(}{}^3\text{A″)}$ states of NSF. The fundamental frequencies are respectively 707 and 673 cm^?1. New hot band assignments are reported and the observed vibrational envelopes of hot band progressions display multiple maxima in agreement with the calculated Franck-Condon envelopes. A number of weak unassigned bands remain in the singlet spectrum which must be associated with either multiple quanta of ν₂′, another electronic state or both.     

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.     

Nonadiabatic effects in the ground state of the hydrogen molecule

A sum-over-states procedure is used in the ab initio evaluation of the matrix elements needed for a nonadiabatic treatment of the ground electronic state of H₂. Bunker's (J. Mol. Spectrosc.42, 478 (1972)) semiempirical value for the nonadiabatic parameter l₁ = 0.130 ± 0.006 is in agreement with the present calculation, which therefore supports the interpretation of the difference between theoretical adiabatic and experimental vibrational energies as being due to nonadiabatic effects. The same techniques are used to evaluate the expectation value of $\text{?}{}^2\text{?R}{}^2$ in the H₂ ground electronic state. Finally, it is pointed out that an average energy denominator used in several recent treatments of nonadiabatic effects in H₂ is in error by roughly a factor of two. The correct average energy denominator reflects that the sums have large contributions from states in the electronic continuum.     

Dye laser site selection spectroscopy on U6+ luminescent molecular centers in LiF-U3O8 crystals

The polarized excitation and emission spectra of the U⁶⁺ molecular centers giving the most intense emission lines at 18 940 cm^?1 and 19 285 cm^?1 are presented and analyzed in detáil. From the polarization experiments, it is shown that the symmetry of the centers is C_4v and that the symmetries of the observed electronic states are Γ₂, Γ₁ and Γ₅. Finally, an electronic model is proposed which associates the emission and excitation lines of the U⁶⁺ centers in the visible region to transitions between the fundamental state $\text{Γ}{}_1\text{(6p}{}^6\text{,}{}^1\text{S)}$ and the states of the excited configuration $\text{6p}{}^5\text{(}{}^2\text{P}\text{3}\text{2}\text{) 7s}$.     

The HH1Σg+ state of hydrogen: Adiabatic calculation of vibronic states in H2, HD,and D2

The nuclear-mass-dependent diagonal corrections to the electronic energies of the $\text{H}\text{H}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ state of hydrogen are computed in the range 1.25 ≤ R ≤ 11 a.u. The correction energy goes through a pronounced peak near R = 3 a.u., which is discussed in terms of the character of the electronic wavefunction. The rovibrational structures of H₂, HD, and D₂ in the adiabatically corrected double-minimum potential curves of these isotopes in the $\text{H}\text{H}$ state are presented. Comparison with experimental data indicates the presence of appreciable nonadiabatic perturbations.     

The dipole moment of the FO radical

The electric dipole moment of the FO radical (${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$) has been directly measured by observing its saturated absorption laser magnetic resonance spectrum (v = 1 ← 0) in the presence of a moderate electric field. The resulting dipole moment [μ(v = 0) = 0.0043(4) D, μ(v = 1) = 0.0267(9) D] is extremely small, and shows a large relative change with vibrational state. The sign of the dipole moment is the same for the two vibrational states. Previous failures to detect microwave or gas phase EPR spectra of FO are fully explained by this small dipole moment.     

Predissociation of the Schumann-Runge bands of O2

The predissociation line broadening in the Schumann-Runge bands of O₂ is interpreted through an ab initio calculation of the pertinent repulsive potential energy curves and spin-orbit matrix elements. The ab initio results provide an overall qualitative picture of the predissociation which is further refined through a detailed comparison of calculated level shifts and widths with experimental data. The position of the dominant repulsive curve is also deduced by a deperturbation of the level shift in the second vibrational difference. The predissociation is dominated by the ⁵Π_u state crossing the $\text{B}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}$ state around 1.875 Å with a spin-orbit matrix element of 65 cm^?1. The ¹Π_u and ³Π_u states have small spin-orbit matrix elements and play only minor roles in the predissociation. The calculated and experimental widths are in good agreement for low and high vibrational levels. The apparent experimental widths between v = 5 and 11 are shown to be inconsistent with the theoretical analysis, the difference probably being due to line blending.