Quantum monodromy in NCNCS - direct experimental confirmation.

Since the first confirmation of quantum monodromy in NCNCS (B. P. Winnewisser et al., Report No. TH07 in 60th International Symposium on Molecular Spectroscopy, Columbus, OH, (2005) and B. P. Winnewisser et al., Phys. Rev. Lett., 2005, 95, 243002) we have continued to explore its implications for the quantum structure of molecules. To confirm quantum monodromy bending-vibrational + axial-rotational quantum energy level information is needed. This was not directly available from the pure a-type rotational transitions available in 2005. The confirmation of quantum monodromy therefore had to be based on the fitting of the Generalised SemiRigid Bender (GSRB) model to the experimental rotational data. The GSRB is a physically motivated model and was able to extract the required information based on the changes of the rotational energy level structure upon excitation of the bending vibration and of the axial rotation. These results were, in some sense, predictions. Our goal here was to obtain a fully experimental and unambigous confirmation of quantum monodromy in NCNCS. This involved a series of experimental campaigns at the Canadian Light Source (CLS) synchrotron. To coax the required information out of the masses of spectral data that had been obtained a variety of techniques had to be used. The result is that we can now confirm, without recourse to a theoretical model, the existence of quantum monodromy in the ν7 bending mode of NCNCS. As a side benefit we also confirm the power of the GSRB model to extract the required information from the previously available data. The predictions previously provided by the GSRB were surprisingly accurate. Only a slight augmentation of the model was required to allow us to refit it including the new data, while maintaining the quality of the fitting for that data previously available. We also present a very basic introduction to the idea of monodromy and to how the GSRB was used.

Pursuit of quantum monodromy in the far-infrared and mid-infrared spectra of NCNCS using synchrotron radiation.

Quantum monodromy has a dramatic and defining impact on all those physical properties of chain-molecules that depend on a large-amplitude bending coordinate, including in particular the distribution of the ro-vibrational energy levels. As revealed by its pure rotational (a-type) spectrum [B. P. Winnewisser et al., Phys. Chem. Chem. Phys., 2010, 12, 8158-8189] cyanogen iso-thiocyanate, NCNCS, is a particularly illuminating exemplar of quantum monodromy: it clearly shows the distinctive monodromy-induced dislocation of the ro-vibrational energy level pattern for its low-lying bending mode. This dislocation centers on a lattice defect in the energy vs. momentum map of the ro-vibrational levels at the top of the barrier to linearity, and represents an example of an excited state quantum phase transition [D. Larese and F. Iachello, J. Mol. Struct., 2011, 1006, 611-628]. To complete the data, so far limited to ΔJ = +1 transitions, we decided to measure the high-resolution far-infrared band of the large-amplitude bending vibration ν7, and, if possible, mid-infrared bands. This Perspectives article presents our ongoing progress towards this goal, beginning with the description of how to predict line positions and intensities of the a- and b-type bands of the large amplitude bending mode using the Generalized-SemiRigid-Bender (GSRB) Hamiltonian for NCNCS and ab initio dipole moment functions [B. P. Winnewisser et al., Phys. Chem. Chem. Phys., 2010, 12, 8158-8189]. We include background information about synchrotron physics to clarify the advantages and limitations of that radiation source for our experiments. Details of the chemical preparation and sample handling, leading to the realization that NCNCS is 50 kJ mol(-1) lower in energy than its isomer S(CN)2 [Z. Kisiel et al., J. Phys. Chem. A, 2013, 117, 13815-13824] are included. We present the far-infrared and mid-infrared spectrum of NCNCS obtained at the Canadian Light Source synchrotron, using the IFS 125HR Bruker Fourier transform spectrometer. Eight of the fundamental vibrational modes of NCNCS have now been observed at high resolution. Initial analyses of the data confirm band assignments and demonstrate the accuracy of the predictions.

Rotation and rotation-vibration spectroscopy of the 0+-0- inversion doublet in deuterated cyanamide.

The pure rotation spectrum of deuterated cyanamide was recorded at frequencies from 118 to 649 GHz, which was complemented by measurement of its high-resolution rotation-vibration spectrum at 8-350 cm(-1). For D2NCN the analysis revealed considerable perturbations between the lowest Ka rotational energy levels in the 0(+) and 0(-) substates of the lowest inversion doublet. The final data set for D2NCN exceeded 3000 measured transitions and was successfully fitted with a Hamiltonian accounting for the 0(+) ↔ 0(-) coupling. A smaller data set, consisting only of pure rotation and rotation-vibration lines observed with microwave techniques was obtained for HDNCN, and additional transitions of this type were also measured for H2NCN. The spectroscopic data for all three isotopic species were fitted with a unified, robust Hamiltonian allowing confident prediction of spectra well into the terahertz frequency region, which is of interest to contemporary radioastronomy. The isotopic dependence of the determined inversion splitting, ΔE = 16.4964789(8), 32.089173(3), and 49.567770(6) cm(-1), for D2NCN, HDNCN, and H2NCN, respectively, is found to be in good agreement with estimates from a simple reduced quartic-quadratic double minimum potential.

Far-infrared spectrum of S(CN)2 measured with synchrotron radiation: global analysis of the available high-resolution spectroscopic data.

The high resolution Fourier transform spectrum of the chemically challenging sulfur dicyanide, S(CN)2, molecule was recorded at the far-infrared beamline of the synchrotron at the Canadian Light Source. The spectrum covered 50-350 cm(-1), and transitions in three fundamentals, ν4, ν7, and ν8, as well as in the hot-band sequence (n + 1)ν4 - nν4, n = 1-4, have been assigned and measured. Global analysis of over 21,300 pure rotation and rotation vibration transitions allowed determination of precise energies for 12 of the lowest vibrationally excited states of S(CN)2, including the five lowest fundamentals. These results constitute an extensive set of benchmarks for ab initio anharmonic force field calculations and the observed and calculated vibration-rotation constants and anharmonic frequencies are compared. The semiexperimental equilibrium, r(e)(SE), geometry of S(CN)2 has also been evaluated. In the course of the measurements, new information concerning the physical chemistry of S(CN)2 has been obtained.

Analysis of the FASSST rotational spectrum of NCNCS in view of quantum monodromy.

Quantum monodromy has a strong impact on the ro-vibrational energy levels of chain molecules whose bending potential energy function has the form of the bottom of a champagne bottle (i.e. with a hump or punt) around the linear configuration. NCNCS, cyanogen iso-thiocyanate, is a particularly good example of such a molecule and clearly exhibits a distinctive monodromy-induced dislocation of the energy level pattern at the bending-rotation energy at the top of the potential energy hump. Indeed, NCNCS [B. P. Winnewisser et al., Phys. Rev. Lett. 2005, 95, 243002] and the water molecule [N. F. Zobov et al., Chem. Phys. Lett. 2005, 414, 193-197] were the first two molecules for which experimental confirmation of quantum monodromy was obtained. We used the fast scan sub-millimetre spectroscopic technique (FASSST) to extend the measurements and spectral analysis to pure rotational transitions (end-over-end) in bending vibrational states lying well above the monodromy point. The analysis of 9204 lines assigned to 7 vibrational states, presented here, shows that the topological properties of the bending potential function are mapped onto every aspect of the ro-vibrational energy levels involving excitation of the quasi-linear bending vibration. In order to model the large amplitude dynamics of such a molecular system, and also to achieve some insight beyond satisfactory parameters for reproducing the spectrum, we used the generalized semi-rigid bender (GSRB) Hamiltonian, which is described in some detail. This Hamiltonian provides a good description of the energy levels over the seven bending states observed, coming close to experimental accuracy. Due to high J values of the measured rotational transitions (J

Experimental confirmation of quantum monodromy: the millimeter wave spectrum of cyanogen isothiocyanate NCNCS.

We have made energy-momentum maps for the experimental end-over-end rotational energy and the two-dimensional bending vibrational energy, both of which confirm the dominating effects of nontrivial quantum monodromy in cyanogen isothiocyanate. Accidental resonances in the rotational spectra yield accurate intervals between bending states.

The A Matrix in Molecular Vibration-Rotation Theory.

Crawford's A matrix in the theory of molecular vibrations is, in a sense, the inverse of Wilson's B matrix, but is not unique because B is rectangular. We consider the general form of A and then use the Eckart conditions to obtain the solution A = M(-1)B(T)G(-1), which has been widely used. Although the internal-coordinate harmonic force constants f = A(T)F(X)A, where F(X) are the Cartesian force constants, are superficially isotope-dependent, we show that this dependence vanishes. More generally, solutions of the form A = WB(T)(BWB(T))(-1), where W is an arbitrary nonsingular square matrix, are shown to give an f matrix that is independent of W. Copyright 2001 Academic Press.