Schematic representation of the equilibrium configuration of (CH3)2SO (DMSO) according to ab initio computations; 27 the three principal axes of inertia cross at the center of mass, axes B and C (vertical) lie in the symmetry plane. Reproduced with permission from A. Cuisset, L. Nanobashvili, I. Smirnova, R. Bocquet, F. Hindle, G. Mouret, O. Pirali, P. Roy, and D. A. Sadovskií, Chem. Phys. Lett.492, 30 (Year: 2010)10.1016/j.cplett.2010.04.042. Copyright 2010, Elsevier B.V. A. Cuisset, O. Pirali, and D. A. Sadovskií, Phys. Rev. Lett.109, 094101 (Year: 2012)10.1103/PhysRevLett.109.094101. Copyright 2012, American Physical Society.
Spectrum (lower trace, blue) of the ν23 and ν11 fundamental bands of DMSO observed using the AILES beamline of the SOLEIL synchrotron (P = 0.06 Torr, L = 150 m, Δν = 0.00015 cm−1, 700 scans, 46 h of acquisition) by Cuisset et al., 1,2 and predicted transitions (stick spectrum, upper trace, black). The amplitude scaling of the two traces is independent; the experimental unresolved ν11 Q-branch takes nearly the full height of the plot. The insets (top) represent the lowest vibrational energy levels of DMSO in cm−1 according to our measurements for ν11 and ν23 and the harmonic frequencies computed by GAUSSIAN. 27 Gray lines represent dipole inactive states and their overtones, arrows show the transitions analyzed in this work.
Classical rotational energy of DMSO in the ν23 fundamental vibrational excited state (a) and the ground state (b) with angular momentum J = 50. The surfaces are drawn in slightly rotated coordinates (J a , J b , J c ) of Fig. 1 . In both plots, the energy is given, up to the same fixed additive constant and scale, by the radial distance from the origin as function of the position of the instantaneous axis of rotation. Equidistant sets of constant energy are stripe painted to display more clearly the shape of the surfaces. We see a deep minimum along the J c axis (vertical) and very shallow height variations in the equatorial area. The animation shown in DMSOsRE-animj.gif of the supplementary material 24 illustrates the evolution of the rotational energy of ν23 as J varies on the interval [30, 60]. Adapted from Ref. 3 .
Absorption spectrum of the ν23 and ν11 fundamentals of DMSO in the rigid symmetric top approximation at 298 K. Different branches of the perpendicular band 0 → ν23 and parallel and perpendicular components of the 0 → ν11 band are color coded.
Reciprocal multiplets Q P(35) and Q R(33) of the 0 → ν11 spectrum. Gray line shows the observed FT-FIR spectrum; blue and orange sticks mark computed intensities for dipole moment components μ c (dominant ‖ component) and μ b (⊥ component); K c or K a assignments for most prominent lines are displayed on top of the sticks in blue or brown, respectively. Note that the presence of many weaker lines of other bands obscures the μ b -transitions in this region.
The μ c multiplet Q R(7) and the neighboring μ b transitions R R(J) with J = 10…12 and K c = J, J − 1, … in the 0 → ν11 spectrum. The observed FT-FIR spectrum is shown by gray solid line; blue and orange sticks mark computed intensities for dipole moments μ c (‖ component) and μ b (⊥ component). For the Q R(7) lines, their K c or K a assignments are displayed on top of the blue sticks in blue or brown, respectively; for the R R(J) lines, the assignments are given in red on top of the orange sticks.
Errors (theory–experiment) in reproducing rotational transitions in the ν11 FIR band. Red and blue represent A and C-type levels, respectively.
Rotational structure of the vibrational state ν11 of DMSO reconstructed using parameters in Table I . Energies (level dashes) are shown after subtracting the average classical ground state rotational energy ; observed levels are marked by longer dashes; bold solid lines represent energies of classical stationary axes of rotation (relative equilibria), the neighboring state ν23 is indicated in gray. A dashed line marks locally perturbed ν11 levels with K = 15–16 and J = 30…40.
Errors (theory–experiment) in reproducing rotational transitions in the Q P(35) sub-branch of 0 → ν11 exhibiting a local perturbation of ν11 near K = 15–16 for J = 34.
Assignment of the reciprocal R Q K−1 and P Q K+1 sub-branches in the 0 → ν23 spectrum, see Sec. ??? . (a) Quasi-linear dependence of R Q K−1 and PQ K+1 sub-branch heads on K := K′ c . (b) Reduced frequency plot (Loomis-Wood diagram) of P Q K+1 sub-branch lines. (c) Centered reduced frequencies of P Q K+1(J) sub-branch lines with K = 11. (d) Errors in the combination differences for P Q K−1(J) and R Q K+1(J) with K = 11.
Reciprocal multiplets R Q 10(J) and P Q 12(J) with K = 11 in the 0 → ν23 spectrum, cf. Fig. 10(a) . Gray line shows the observed FT-FIR spectrum; sticks mark computed intensities for the dipole moment μ a (⊥ component); J assignments are displayed on top of the sticks.
Errors (theory–experiment) in reproducing rotational transitions in the ν23 FIR band. Red and blue represent A and C-type levels, respectively.
Rotational structure of the vibrational state ν23 of DMSO reconstructed using parameters in Table I . Energies (horizontal dashes) are shown after subtracting the average classical ground state rotational energy ; observed levels are marked by longer dashes; bold solid lines represent energies of classical stationary axes of rotation (relative equilibria), the neighboring state ν11 is indicated in gray.
Upper part of the rotational multiplet of the ν23 fundamental vibrational state of DMSO, cf. Fig. 13 . Energies are shown after subtracting the classical energy of rotation about the unstable stationary axis B. Horizontal dashes mark quantum levels; bold solid lines represent energies of classical stationary rotations, the levels of the neighboring state ν11 are indicated in gray. Circles mark level sequences engaged in the X-type quadruplet formation. Reproduced by permission from A. Cuisset, O. Pirali, and D. A. Sadovskií, Phys. Rev. Lett.109, 094101 (Year: 2012)10.1103/PhysRevLett.109.094101. Copyright 2012, American Physical Society.
Latitudinal tilt φ (degrees) of new axes X of stationary rotation in the ν23 state of DMSO, cf. Fig. 3(a) .
Vibration-rotation parameters (MHz) of the effective Hamiltonian of DMSO in the model of isolated vibrational states; the value of a parameter for the vibrational state ν k equals the sum of values in columns |0⟩ and ν k , e.g., . *Parameters of the ground state fixed to zero.
Summary of the analysis of the spectroscopic data for DMSO used in our work: For each band, we give the total number of assigned lines, the values of the total angular momentum J, the estimated unweighted σu and weighted σw standard errors of the fit, and the number of assigned lines with errors above ±2σ.
Frequencies (cm−1) and observed–calculated errors (Err.) (10−3 cm−1) of the assigned lines in the far IR ν23 ← 0 spectrum of DMSO, which involve the quadruple rotational states of type X of the fundamental vibrational excited state ν23.
Comparison of experimental and estimated frequencies (cm−1) of bending vibrational modes of DMSO; G-h and G-a refer to harmonic and anharmonic frequencies computed using GAUSSIAN03, 27 see Appendix A of the supplementary material. 24 The experimental frequencies of ν13 and ν24 are obtained from the intensities of the respective MW satellite bands relative to those in the 0 ← 0 band; 57 the ν12 frequency comes from the liquid state Raman spectrum. 35
Article metrics loading...
Full text loading...