Semirigid Bender Research Articles

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.

GSRB rotation and rovibration intensities for: The bent HOCl molecule, and for: Quantum monodromy in NCNCS

Considerable work has gone into identifying and delineating the effects of quantum monodromy on molecules. Recently this included consideration of transition intensities of the NCNCS molecule using ab initio electric dipole moment functions in the Generalised SemiRigid Bender (GSRB) model [M. Winnewisser et al. PCCP 16, 17373-17407 (2014)]. In that work a discrepancy between the observed and calculated spectra was discovered. The purpose of the present work is to identify the source of that discrepancy - is it due to the physics of monodromy itself or are other issues involved? To investigate this we use the same theoretical approach for the simpler molecule HOCl. This allows us to identify a programming error affecting the b-type rovibrational transitions. We show that the NCNCS spectrum calculated with the corrected GSRB model does reproduce the experimental spectrum for pure rotational transitions within the ν7 large amplitude bending vibrational states, starting from the ground state and progressing through levels at the monodromy energy and beyond, while also reproducing the a-type υ:1←0rovibrational spectrum. However, the discrepancy with regard to the b-type rovibrational transitions remains. We discuss possible reasons for this discrepancy. In the course of this work we obtain a good GSRB model for the bending vibration-rotation levels of the atmospherically important HOCl molecule and its isotopologues. With ab initio calculations of the electric dipole moment function the GSRB calculates the rotation and bending rovibrational spectrum of HOCl in agreement with other determinations and with experiment. Using the physically constrained GSRB model, errors in tabulated transitions (including in the HITRAN database) were easily identified.

Hybrid calculation of the partition functions of prolate top molecules: Using HOCl as the test case

The partition function of a molecule can be obtained by a direct sum-over-states (SOS) calculation using the molecule’s quantum energy levels. These energies can be those obtained by a model fitted to experimental data. For molecules with “exotic” behaviour (such as large amplitude vibrational motion) physically motivated models can be required. Often, however, such models can be limited in the range of quantum levels that can be reliably calculated, making a converged SOS calculation impractical. Here we present a hybrid approach for prolate top molecules. Our hybrid approach allows the simple extension from a limited SOS calculation to a good approximation for the infinite sum limit. This is achieved by adding easily calculated closed-form corrections to the limited SOS result. We test our approach using the Generalised SemiRigid Bender (GSRB) program as the physically motivated model. HOCl serves as a good test case because for it the GSRB model can extend to high enough levels for convergence of the direct SOS calculation. Then, by limiting the range of GSRB calculated rotational levels included in the SOS, we confirm our hybrid approach. The technique we present here should be particularly applicable to quasilinear molecules, including those exhibiting quantum monodromy. The Appendix presents step-by-step instructions for implementing this hybrid procedure. Also presented there is a brief discussion of how to adapt the hybrid technique to approximately account for rotational or vibrational dissociation in the case that that is necessary.

Ro-torsional energy correlation between the high barrier and free-internal-rotor limits: The case of the skew chain molecule HSOH

Skew-chain molecules, such as HSOH, exhibit exotic behavior due to coupling of torsion and rotation. In particular, the torsional tunneling splittings vary cyclically in magnitude with axial rotational quantum number, K, with a period depending on the ratio of the moments of inertia for their end moieties. Although successfully modeled using a variety of approaches (algebraic, reduced-dimensional, and full-dimensional) a conceptual understanding of this cyclic variation for HSOH has not been presented. We do this here, using the reduced-dimension Generalized Semi-Rigid Bender (GSRB) approach to establish the correlation between states at the free-rotor (zero-barrier) limit and those at the more physical high-barrier limit. In this context we present the symmetries and appropriate quantum numbers for the states in these two limiting cases. We show that the cyclic variation of the magnitude of the torsional splittings originates in the energy level-structure in the zero-barrier limit combined with the correlation to the high-barrier limit. This allows us to give a simple recipe for calculating the period of this cyclic variation in any such skew-chain molecule, based only on the moments of inertia of the two end moieties.

ChemInform Abstract: The Microwave Spectrum and Semirigid Bender Analysis of Isocyanatoethyne, HCCNCO.

Abstract Isocyanatoethyne, HCCNCO, has been prepared and its microwave spectrum recorded. The molecule behaves as a slightly asymmetric prolate rotor, the spectrum indicating deviations from linearity in the equilibrium structure. Vibrationally excited states with up to three quanta of the CNC bending mode were observed, allowing analysis of the spectrum to be carried out using a semirigid bender model. The results of this analysis give the following structural parameters: r(CC) = 1.2237 (20) A , r(CN) = 1.3025 (54) A , r(NC) = 1.2139 (60) A , r(CO) = 1.1741 (48) A , ∠(CNC) = 140.67 (48)° and, ∠(NCO) = 170.02 (93)°, with all other bond angles assumed to be 180°. The barrier to linearity was calculated to be 537.2(5.4) cm−1.

Torsion–rotation coupling and the determination of the torsional potential energy function of HSOH

Hindered torsional motion in a molecule such as HSOH leads to tunnelling splittings. Lying between the simpler limiting cases of strongly hindered torsion (the "we can simply neglect the tunnelling" limit) and that of free internal rotation (the "tunnelling pair of levels are just different vibrational states" limit) HSOH is particularly challenging due to strong and inherent torsion-rotation coupling. The low symmetry due to the different terminal moieties, SH and OH, further enriches the energy level pattern by allowing a systematic mixing within each quadruplet of torsion- and asymmetry-doubled levels. This mixing, which varies in a systematic manner with angular momentum quantum numbers, can reach 50% and is in addition to the mass-dependent and quasicyclic variation of the tunnelling splittings. We show that a carefully implemented reduced-dimension model, the Generalised SemiRigid Bender (GSRB), combined with a few modest ab initio calculations, is sufficient to account for the bulk of these physical effects. We also point out the reversal of energy pairing of torsional levels with increased energy. That is, at low torsional energy the lowest of the torsional level pair is the symmetric level while at high torsional energy it is the antisymmetric level which is the lowest. Finally, we present a purely empirical determination of the tunnelling splittings for K = 0, 1, 3, 4, and 5.

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</= 116), the least squares fitting procedure was applied not directly to the measured frequencies, but to effective constants derived from fitting the transition frequencies to a set of polynomials in J(J + 1) yielding effective B(eff) and D(eff) constants. The GSRB wave functions are used to show that the expectation values of any quantity which varies with the large amplitude bending coordinate will also have monodromy-induced dislocations. This includes the electric dipole moment components. High level ab initio calculations not only provided the molecular equilibrium structure of NCNCS, but also the electric dipole moment components mu(a) and mu(b) as functions of the large-amplitude bending coordinate. Calculated expectation values of these quantities for individual ro-vibrational levels show the now recognizable monodromy pattern. Finally, a generalization of the quasi-linear parameter gamma(0) is suggested.

Renner–Teller interactions in the dissociative recombination of HCO+

The formalism developed in the preceding paper for vibrational autoionization via Renner-Teller active vibrations is adapted to treat dissociative recombination and applied to the reaction of HCO(+)+e(-). Existing spectroscopic data on the rovibrational structure of the HCO(+) (2)Sigma(+) ion and the HCO 3ppi (2)Pi Rydberg state are fitted by using the semirigid bender model to extract the parameters required to calculate the autoionization and electron capture widths. The results of this simple model are in good agreement with more detailed first principles calculations of the dissociative recombination cross section and confirm the earlier conclusion that coupling due to the Renner-Teller interaction is largely responsible for the observed dissociative recombination cross section at electron energies below approximately 0.1 eV.

The hidden kernel of molecular quasi-linearity: Quantum monodromy

Chain molecules with one low-lying bending mode provide a set of model species for the exploration of quantum monodromy in quasi-linear molecules. Recent work on water [N.F. Zobov et al., Chem. Phys. Lett. 414 (2005) 193–197] and NCNCS [B.P. Winnewisser et al., Phys. Rev. Lett. 95 (2005) 243002.] have shown that the topology of the energy–momentum maps of such molecules follows closely the predictions based on the mathematical concept of non-trivial monodromy. From existing data and new calculations which extrapolate beyond the existing data for several species, we can now present the topological properties of the bending-rotation energy–momentum maps of a range of molecules, from rigidly linear to rigidly bent. The generalized semi-rigid bender (GSRB) Hamiltonian used for the extrapolations is reviewed, and the mathematical concepts required to define the monodromy perspective are presented. Furthermore, it is shown that the energy–momentum map for the end-over-end rotational energy, represented by the effective rotational constant B or B ¯ , has previously unremarked properties which, like the basic bending-rotation energy–momentum map, are robust across the whole set of molecules studied. The molecules discussed are OCCCS, NCCNO, HCNO, OCCCO, ClCNO and BrCNO, NCNCS, HCCNCO, NCNCO and NCSCN.

Bending energy level structure and quasilinearity of the X̃+B13 ground electronic state of NH2+

The bending level structure of the quasilinear X+ 3B1 ground electronic state of the amidogen cation NH2+ was studied by pulsed-field-ionization zero-kinetic-energy photoelectron spectroscopy using a near-infrared vacuum-ultraviolet two-photon ionization sequence via selected rovibronic levels of the A 2A1 state of NH2. The careful selection of the intermediate levels permitted to optimize the transition intensities to the lowest vibrational levels of the cation in the photoionization step and to overcome the low sensitivity of previously employed single-photon ionization schemes. For the first time, all bending levels of the cationic ground state with quantum numbers upsilon2,lin + < or =4, N+ < or =4, and /K+/ < or =2 could be observed, enabling a detailed characterization of the large-amplitude bending vibration. The rotational structure corresponds to that of an effectively linear molecule in all observed vibrational levels. The bending vibrational structure which shows marked deviations from a harmonic behavior was analyzed in terms of a semirigid bender model. The bending potential function was obtained from a fit to the experimental data. The height of the barrier at the linear geometry and the bond angle at the potential minimum were determined to be 231.8(22) cm(-1) and 152.54(4) degrees , respectively, and all bending levels are located above the maximum of the barrier.

High-resolution infrared spectroscopic determination of the nν5±n vibrational energies of HCCN and DCCN

The high-resolution infrared kinetic spectra of HCCN and DCCN have been recorded, the former between 3395 and 3481 cm−1 and the latter in the 2517–2593 cm−1 region. A total of four dominant Q branches were observed and have been subsequently assigned to the ν1+2ν5±2←ν5±1, ν1+3ν5±3←2ν5±2 bands of the two isotopomers. The band origins have been determined to be 3420.666(1), 2544.743(2), 3460.912(2), and 2573.480(1) cm−1 respectively. These new values have been used in conjunction with the previously obtained ν1+2ν5±2←2ν5±2 band origins of HCCN and DCCN to obtain 2ν5±2←ν5±1 vibrational energies of 212.822(1) and 133.106(1) cm−1 for HCCN and DCCN, respectively. Semirigid bender calculations of the energy levels of these molecules have been carried out. By adjusting the height of the barrier to linearity, excellent agreement with experimental data has been attained.

On the Anharmonic XCN Bending Modes of the Quasilinear Molecules BrCNO and ClCNO

The millimeter-wave spectra of the unstable halofulminates BrCNO and ClCNO were recorded at room temperature in several frequency intervals between 52 and 230 GHz. Besides rotational transitions in the vibrational ground state, transitions in numerous thermally excited states of the XCN bending mode (X = Br or Cl) could be observed. The irregular sequence of these satellites indicated that in both molecules, the XCN bending mode is highly anharmonic. Indeed, the XCNO molecules exhibit truly quasilinear behavior. From semirigid bender analyses of the rotational data, the effective potential functions and their barriers to linearity were determined. The barrier heights were found to be 130.82 (56) cm-1 for BrCNO and 166.86 (84) cm-1 for ClCNO, resulting in quasilinearity parameters γ0 of +0.362 and +0.416, respectively.

On the Low-Lying CCN Bending Mode of the Nearly Linear Molecule NCCNO

The low-lying CCN bending mode of cyanofulminate, NCCNO, was characterized by rotational spectroscopy in the millimeter-wave and submillimeter-wave range as well as by rovibrational spectroscopy in the far-infrared range. The spectra exhibit the gross features of a linear molecule. However, a closer qualitative analysis regarding the low-lying CCN bending mode revealed significant deviations from a harmonic bending mode that is normally found in a linear molecule. This result was confirmed by a quantitative analysis of the combined data with an effective Hamiltonian for a linear molecule. In linear molecule notation, the term value of the first excited state ν7 is 80.524 182 (10) cm-1, and the term values for the l7 = 0 and l7 = 2 levels of the second excited state 2ν7 are 166.118 254 (16) and 164.604 243 (22) cm-1. A semirigid bender analysis of our data, including rotational transitions of the isotopomers 15NCCNO, N13CCNO, NCC15NO, and NCCN18O observed in natural abundance, yielded a considerable quartic contribution to the effective CCN bending potential function V(ρ)/cm-1 = 747.40 (81) × (ρ/rad)2 + 959.2 (24) × (ρ/rad)4.

ν 1 and ν1+ν5 of DCCN: Determination of the ν5 energy and the quasilinearity of DCCN

The high resolution infrared spectrum of DCCN in the region of 2385–2530 cm−1 has been investigated using infrared kinetic spectroscopy. The CD stretching fundamental, ν1,together with the closely related hot bands, ν1+ν5−ν5,ν1+2ν5±2−2ν5±2, and ν1+2ν50−2ν50 have been observed and assigned. In addition the combination band, ν1+ν5, was observed. When the information provided by this perpendicular band is combined with that provided by ν1+ν5−ν5, the vibrational energy of ν5 is accurately determined to be 74.845(2) cm−1. This measurement, when combined with the ab initio and semirigid bender calculations of Malmquist et al., gives a barrier to linearity of 280 cm−1. Generally, fine structure splittings are not resolved for any levels except those belonging to the upper l- or K-type doubling components of ν1+ν5. This fine structure splitting is most strongly exhibited in the Q-branch of the ν1+ν5 band where it is 0.039 cm−1.

A New Perspective on Isomerization Dynamics Illustrated by HCN → HNC

We discuss the role of delocalized states in isomerization dynamics and illustrate the ideas by considering isomerization in HCN. We analyze results from an earlier study, where HCN was treated as a semirigid bender, and isomerization was induced by collision with an Ar atom. That analysis is applied here to three-dimensional HCN, using exact three-dimensional wave functions, obtained using a slight modification of a previous global potential based on high-quality ab initio calculations.

Amino groups in nucleic acid bases, aniline, aminopyridines, and aminotriazine are nonplanar: Results of correlated ab initio quantum chemical calculations and anharmonic analysis of the aniline inversion motion

The amino group nonplanarity in nucleic acid bases, aniline, aminopyridines, and aminotriazine was investigated by ab initio methods with and without inclusion of correlation energy utilizing medium and extended basis sets. For all the systems studied, the amino group was found to be nonplanar and the coupled cluster method [CCSD(T)] ‘‘nonplanarities’’ and inversion barriers slightly higher than their second-order many-body perturbation-theory (MP2) counterparts. To assess the reliability of the calculations, inversion splittings for aniline and aniline-ND2 were evaluated by solving a two-dimensional vibrational Schrödinger equation for the large-amplitude inversion and torsion motions, while respecting the role of small-amplitude C–N stretching and H–N–H bending motions. Because a large number of points is required for the description of the aniline potential energy surface, the Hartree–Fock (HF) method with 6-31G* basis set was utilized. The vibrational calculations were performed within the framework of the semirigid bender Hamiltonian of Landsberg and Bunker. Excellent agreement between experimental and theoretical inversion-torsion frequencies for fundamental, overtone, and combination modes was found, which gives strong evidence for the adequacy of the theoretical model used in general, and potential energy surface in particular. Similarity between the HF, MP2, and CCSD(T) aniline inversion barriers and amino group nonplanarities gives us confidence that the MP2 and CCSD(T) inversion barriers and amino group nonplanarities of the DNA bases, aminopyridine, and aminotriazine, are close to the actual values which are still experimentally unknown.

Methanol as a Flexible Model

A method based on the semirigid bender and the flexible model approaches has been developed for internal rotation in methanol. For construction of the torsion Hamiltonian matrix aK-dependent trigonometric variational basis set adapted toC3vsymmetry was employed. It allowed easy and unambiguous labeling of the torsion–rotational energy levels and it was computationally efficient as well. It was found that when certain idealized cases of structure variation with torsional angle are considered, an unusual splitting of theA1andA2energy levels occurs in the extreme case of a free rotor. It was shown how the results of theab initiocalculations forC3v(M) molecules could be linked to the developed flexible model using the approximation of equality of the torsional angle ρ and the average of the three top-frame dihedral angles τeff. An analysis of the process of determining the methanol molecular geometry employing the developed model was performed. Two of the zero-order parameters were fixed at the values obtained from electron diffraction measurement and the remaining zero-order parameters and some of the parameters describing variation of the geometry during torsion as well as the potential energy function were determined for variousJmax. The fitted values for the bending semirigidity parameters were found to be broadly consistent with those from the MO calculations, while the fitted bond stretching parameters were generally in poor agreement.

Chemical reaction jet spectroscopy, molecular structure, and the bending potential of the à 1A″ state of monofluorosilylene (HSiF)

The jet-cooled laser induced fluorescence excitation spectrum of the à 1A″–X̃ 1A′ band system of HSiF has been observed with the chemical reaction jet technique. Vibrational analysis of the spectrum gave upper state fundamental vibrational frequencies of ν1=1547 cm−1, ν2=558 cm−1, and ν3=857 cm−1. Seven bands in the spectrum were recorded at high resolution and rotationally analyzed, providing excited state molecular constants. The upper state vibrational and rotational bending levels were fitted to a semirigid bender model to obtain the equilibrium geometry and the potential energy barrier to linearity. Due to correlations in the parameters, it was necessary to fix the bond angle at the ab initio value of 114.5°. The resulting fitted model yielded re(Si–F)=1.602 Å, re(Si–H)=1.548 Å with a potential energy barrier to linearity of 9130 cm−1.

The v4 large-amplitude bending potential of HNCO as determined by a semirigid bender analysis of the ground state rotational spectra

The ground state microwave, millimeter wave, and far-infrared spectroscopic data ( J < 10) of HNCO and its isotopomers were analyzed using the semirigid bender (SRB) Hamiltonian. The geometry of the molecule and the potential energy function of the large-amplitude HNC-bending motion were determined by a non-linear least-squares fitting procedure. The barrier to the linear configuration was found to be 1899 cm −1, which is much lower than the previously reported value. The parameters determined for the molecular structure are in excellent agreement with the r s values.

Collision induced isomerization of a semirigid bender hydrogen cyanide

The isomerization of a hydrogen cyanide molecule from a localized HCN state to a localized HNC state is formulated as a bimolecular scattering process. The scattering partner is Ar, and the intermolecular interaction potential is written as a pairwise summation of Lennard-Jones potentials. The parameters of this potential are optimized to yield the correct Ar–hydrogen cyanide van der Waals structure. The intramolecular isomerization potential is based on an approximate reaction path through a three-dimensional ab initio potential, and HCN/HNC is treated as a semirigid bender. Eighty molecular eigenstates are calculated, and used as a coupled-channel basis in a scattering calculation in which the hydrogen cyanide rotation is treated in the infinite order sudden approximation. Transition probabilities and cumulative reaction probabilities to HNC states from initial HCN states are focused on; however, some results to final delocalized states are also presented. The bimolecular isomerization rate constant is presented over a wide temperature range. The energy transfer between Ar and initial HCN states is also briefly examined, as a function of the initial relative translational energy.