Torsional Levels Research Articles

Impact of Molecular Conformation on Barriers to Internal Methyl Rotation: The Rotational Spectrum of m-Methylbenzaldehyde

The ground state spectrum of m-methylbenzaldehyde (m-MBA) was measured with a chirped-pulse Fourier transform microwave (CP-FTMW) spectrometer. The methyl rotor on m-MBA introduces an internal rotation barrier, which leads to splitting of the torsional energy level degeneracy into A and E states. Ab initio calculations predict a low torsional barrier for both the O-cis and O-trans conformers, resulting in a large doublet splitting up to several gigahertz in the frequency spectrum. The rotational constants, distortion terms, and V(3) values for both species have been determined from the ground state rotational spectrum using the BELGI-C(s) fitting program. There are significant differences in the torsional potential for the O-cis and O-trans m-MBA conformers. Molecular orbitals and resonance structures for each conformer are analyzed to understand the difference in torsional barrier height as well as the irregular shape of the O-trans torsional potential.

ChemInform Abstract: Molecular-Beam Optothermal Spectrum of the OH Stretching Band of Methanol.

Abstract The OH stretching fundamental band, ν1, of CH3OH has been recorded with sub-Doppler resolution using a molecular-beam optothermal spectrometer. The low effective temperature (∼6 K) of the molecular beam greatly reduces the spectral congestion from hot torsional vibrations and high rotational levels seen at room temperature, permitting an essentially complete assignment. a fit to a global hindered internal-rotor Hamiltonian, and identification of several perturbations and their likely perturbers. The observed linewidths are ∼15 MHz yielding an upper limit to any intramolecular vibrational relaxation rate.

ChemInform Abstract: Methyl Rotor Effects in 3- and 5-Methylindole

The fluorescence excitation spectra of jet-cooled 5-methylindole, 5-methylindole complexed with He, 2 He, and water, 3-methylindole, and 3-(methyl-d 3 )indole are presented. Methyl torsional transitions are assigned for all species, and barriers are fit for the 1 L b state. Two-photon contours reveal strong internal-overall rotation interaction in 5-methylindole based on a significant broadening of the q Q branch for e symmetry torsional levels

Tuning for Performance and Stability in Systems of Nearly Tautochronic Torsional Vibration Absorbers

This paper considers the dynamic response and performance characteristics of a special class of centrifugal pendulum torsional vibration absorbers. The absorbers of interest are designed by selection of the path that their center of mass follows, such that their dynamics are linear or nearly so, out to large amplitudes of motion, thereby avoiding the nonlinear-induced detuning that typically accompanies such responses. These order-tuned, tautochronic or isochronic, absorbers have been the subject of previous investigations, including analyses of the synchronous and certain nonsynchronous responses of systems comprised of a set of identical absorbers. The analysis and experiments have demonstrated that the synchronous response of such absorber systems can experience an instability that results in nonsynchronous responses in which a subset of absorbers have significantly larger amplitude than the corresponding synchronous response. In this study, we present results that generalize these stability results to include absorbers whose dynamics differ slightly from tautochronic by varying the absorber path such that both linear and nonlinear perturbations of perfect tuning are included. It is shown by analysis and verified by simulations that the perfect tuning case is quite special, specifically that the instability described above occurs for tunings very close to ideal and that the synchronous response can be made stable over the entire feasible operating range by employing small levels of linear and/or nonlinear detuning. Such detuning is known to have the additional benefit of resulting in smaller absorber responses and an attendant larger operating range albeit at the expense of absorber performance in terms of attenuating rotor torsional vibrations. The main conclusion of these results is that one can select a very small amount of detuning to avoid this undesirable instability and that such detuning does not have a significant effect on absorber effectiveness. The analytical results derived also provide a quantitative means of predicting synchronous absorber response amplitudes and the associated rotor torsional vibration levels, as well as the stability properties of these responses, results are very useful for the design of absorber systems.

Rotational and Vibrational Cooling in Pulsed High-Pressure Molecular Beam Expansions from 3 bar into the Supercritical Regime

Experiments employing pulsed high-pressure (< or = 90 bar) supersonic jet expansions into a laser REMPI time-of-flight mass spectrometer are presented. Due to the very short opening time of the high-pressure valve, a compact arrangement with moderate pumping speed requirements is sufficient, which can be used up to 50 Hz repetition frequency, still maintaining an operating pressure in the expansion chamber of ca. 10(-4) mbar. p-Fluorotoluene was used as a rotational and vibrational "molecular thermometer" to characterize the cooling capabilities of high-pressure pulsed argon and CO(2) expansions into vacuum, spanning a wide range of stagnation pressures into the supercritical regime. Rotational and torsional temperatures were deduced from the contour of the S(0) --> S(1)(0-0) transition by an asymmetric-top/free-internal-rotor simulation and compared with the results of a simpler rigid-rotor asymmetric-top fit. The experiments show that average rotational temperatures of ca. 1-2 K in argon and 13-15 K in CO(2) can be reached at the highest pressures studied. The population of higher |m| torsional levels of p-fluorotoluene is clearly demonstrated by the appearance of characteristic features on the blue edge of the contours, which are more pronounced in the warmer CO(2) expansions. While the rotational temperatures in argon expansions compare well with estimated gas dynamical terminal translational temperatures, there are considerable differences in the case of CO(2). Still, the degree of internal cooling reached with CO(2) is sufficiently low, so that a setup of this kind might provide good opportunities for future studies of thermally labile low-volatile molecules to cool them to cryogenic temperatures low enough to achieve a sufficient simplification of their spectra.

The HOOH UV spectrum: Importance of the transition dipole moment and torsional motion from semiclassical calculations on an ab initio potential energy surface

The absorption cross section of HOOH, a starting point for larger ROOH, was calculated using the "Wigner method." Calculations use the Wigner transform of ground state wave functions and classical approximations for excited state wave functions. Potential energy and transition dipole moment surfaces were calculated using the equation-of-motion coupled-cluster singles and doubles method over an extended Franck-Condon region. The first two O-O stretches and the first five HOOH torsional levels are included. This study also addresses two fundamental questions about ROOH photodissociation. The long wavelength A(1)A:B(1)B excited state preference has been measured from dynamics experiments, but a Franck-Condon overlap explanation has not been directly verified. A moderate barrier to HOOH torsional motion and excited state dynamics affect the temperature dependence in the UV spectrum. Based on these initial findings for HOOH, photodissociation of large ROOH cannot be eliminated as an important factor for ozone and particulate matter production seen in both ambient and laboratory studies.

Asymmetric-top molecules containing one methyl-like internal rotor: Methods and codes for fitting and predicting spectra

This paper is a review of various effective Hamiltonians, methods and codes dealing with asymmetric-top molecules containing one internal rotor with C 3 v (or close to C 3 v ) symmetry. It aims at helping high-resolution spectroscopists to find the most appropriate method(s) and code(s) to assign and fit their internal rotor spectra. The topics included are: description of some of the available effective Hamiltonians, methods (PAM, Principal Axis Method, RAM, Rho-Axis Method and IAM, Internal-Axis Method) and codes to deal with internal rotor spectra (JB95, ERHAM, XIAM, SPFIT/SPCAT/IAMCALC and BELGI). The methods are also classified by the way they are dealing with the set of torsional states associated with the internal rotation large amplitude motion: globally or locally. Examples are given of internal rotors treated by each of those codes with root-mean-square deviations, J max, torsional bath levels involved, and parameters obtained to allow the reader to choose the appropriate method for his study. More details are given for the RAM method used in BELGI, with series of examples. Some user-manual-like hints for running the fits are also given.

Torsional energy levels of nitric acid in reduced and full dimensionality with ElVibRot and Tnum

The internal rotation (nu(9)) of nitric acid is studied using several ab initio models including 1D models and full dimensionality (9D) ones. For the 9D calculations, an adiabatic separation between the large amplitude motion, i.e. the torsion, and the eight other modes is performed. The potential energy surface is calculated at CCSD(T) level with a triple zeta atomic basis set and is expanded in a Taylor series up to the second-order along the torsional path. The vibrational calculations are performed with the codes ElVibRot and Tnum. Our main results show that the torsional energy levels and the corresponding tunneling spliting are in good agreement with the experimental ones. Furthermore, the resonance between 2nu(9) and nu(5) (NO(2) in-plane bending) is also well described with full dimensionality models.

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.

Effect of spiral reinforcement on flexural-shear-torsional seismic behavior of reinforced concrete circular bridge columns

This paper investigates the behavior of reinforced concrete (RC) circular columns under combined loading including torsion. The main variables considered in this study are the ratio of torsional moment to bending moment (T/M) and the level of detailing for moderate and high seismicity (low and high transverse reinforcement/spiral ratio). This paper presents the results of tests on seven columns subjected to cyclic bending and shear, cyclic torsion, and various levels of combined cyclic bending, shear, and torsion. Columns under combined loading were tested at T/M ratios of 0.2 and 0.4. These columns were reinforced with two spiral reinforcement ratios of 0.73% and 1.32%. Similarly, the columns subjected to pure torsion were tested with two spiral reinforcement ratios of 0.73% and 1.32%. This study examined the significance of proper detailing, and spiral reinforcement ratio and its effect on the torsional resistance under combined loading. The test results demonstrate that both the flexural and torsional capacities are decreased due to the effect of combined loading. Furthermore, they show a significant change in the failure mode and deformation characteristics depending on the spiral reinforcement ratio. The increase in spiral reinforcement ratio also led to significant improvement in strength and ductility.

Seismic performance of circular RC columns subjected to axial force, bending, and torsion with low and moderate shear

Test results of reinforced concrete (RC) circular columns under cyclic bending and shear, cyclic pure torsion, and various levels of combined cyclic bending, shear, and torsion complimented with finite element (FE) results are presented in this paper. The main variables considered in this study are the ratio of torsion-to-bending moment ( T / M ) , and the aspect ratio ( H / D ) of the column or bending moment to shear ( M / V ) (to simulate low or moderate shear). The aspect ratio of the column determines the level of flexure–shear interaction. Under combined loadings, the columns were tested at torsion-to-bending moment ratios of 0.2 and 0.4 with aspect ( H / D ) ratios of 6 and 3. This work analyzed the effect of an increase in aspect ratio with respect to several behaviors. Specifically, the significance of the level of shear on the failure modes and its effect on the torsional and bending strength under combined loadings is investigated. Test results demonstrate that there was no appreciable change in flexural or torsional capacities with decrease in aspect ratio as was observed in the FE analysis. However, results show a significant change in the failure mode and deformation characteristics due to reduction in aspect ratio.

Brief ischaemia reduces testicular lipid peroxidation following susequent ischaemia: An evidence for ischaemic preconditioning

Brief periods of ischaemia followed by reperfusion protect tissues like the brain and heart from subsequent ischaemic episodes. Similar effects in the testis has not been adequately studied despite the fact that the testis is subject to ischaemia-reperfusion phenomena of clinical importance during testicular torsion. The present study was designed to investigate whether the testis exhibits ischaemic pre-conditioning. In the first part of the experiment, 85 adult male Sprague-Dawley rats were divided into five groups. In the first group, testicular malondialdehyde levels was determined as the control. In four groups, right sided testicular torsion was induced by twisting the testes and spermatic cord in a counter-clockwise direction through 720 degrees for 15, 30, 45 and 60 minutes. Five of the animals in each group had testes removed for determination of MDA levels, while the remaining had torted testes de-torted and orchidopexied. After 2, 4 and 6 weeks, five animals in each group had the right testes again twisted through 7200 for 15, 30, 45 and 60 minutes and de-torted. Animals were then sacrificed and testes collected for estimation of MDA. In the second part of the experiment, the above procedure was repeated except that intra-peritoneal melatonin 1 mg/kg was administered before de-torsion. Following retorsion after two weeks, MDA levels were significantly reduced from the control after 30, 45 and 60 minutes of torsion but not after 15 minutes of torsion. There was no significant difference between testicular MDA levels at initial torsion and subsequent levels following re-torsion if melatonin was administered at initial torsion. The testis exhibits ischaemic preconditioning which is abolished by melatonin.

Rotational Contour Analysis of Jet-Cooled Methyl Hydroperoxide Action Spectra in the Region of the 2νOH and 3νOH Bands

State-selected photodissociation is used to record the partially rotationally resolved action spectra of CH(3)OOH in the region of its first and second OH-stretching overtones (2nu(OH) and 3nu(OH)) under free-jet expansion conditions. From an analysis of the rotational band contours for the OH-stretching states and their corresponding COOH torsion combination bands, effective rotational constants and transition dipole moment orientations are determined for the vibrational eigenstates. The level splitting between the lowest symmetric and antisymmetric pair of COOH torsion levels, 0(+) and 0(-), associated with the 2nu(OH) overtone state is found to be approximately 3.9 cm(-1). Comparison of spectra in the region of the 2nu(OH) and 2nu(OH) + nu(COOH) bands in CH(3)OOH and CD(3)OOH reveals that the spectral features in CH(3)OOH are substantially more perturbed compared to those of its deuterated counterpart, suggesting that modes involving the methyl rotor contribute significantly to promoting intramolecular vibrational energy redistribution (IVR) in CH(3)OOH. Furthermore, a comparison of the average rotational line widths in both CH(3)OOH and CD(3)OOH for the 2nu(OH) and 2nu(OH) + nu(COOH) bands appears to suggest that at these energies, adding one quanta of low-frequency COOH torsional motion does not enhance the IVR rate relative to that of the pure OH-stretching overtone.

Energy levels and partition functions of internal rotation: Analytical approximations

A simple numerical method that has considerably simplified the calculations of torsional energy levels is proposed for one-dimensional barriers of arbitrary shape. The internal rotation constant is also permitted to vary as a function of torsional angle. In two limiting cases of high and low barriers, analytical expressions for hindered rotor state energies have been obtained. The partition function of internal rotation is then evaluated by eigenvalue summation. The derived analytical formula for the partition function of free internal rotation gives reasonable values down to the lowest temperatures. Analytical approaches give a better insight into the physical nature of the problem solvable by a rigorous method.

Analysis and fit of the high-resolution spectrum of the Ã1A u– [formula omitted]1A g LIF spectrum of the two-equivalent-top molecule biacetyl

The jet-cooled laser-induced visible fluorescence excitation spectrum of the à 1 A u (S 1)– X ˜ 1 A g ( S 0) transition in biacetyl (CH 3 C( O) C( O) CH 3) exhibits a long progression in the torsional vibrations of the two equivalent methyl tops in this molecule, whose structure has previously been described and qualitatively understood using local mode ideas applied to the two equivalent methyl rotor torsions together with the G 36 symmetry species A 1, A 2, A 3, A 4, E 1, E 2, E 3, E 4, and G. In the present rotational analysis, we have assigned a G 36 symmetry species, two local-mode torsional quantum numbers, and the usual three asymmetric rotor quantum numbers J KaKc to the upper and lower torsion–rotation levels involved in the observed transitions, relying heavily on comparison of quantum-beat patterns to determine transitions with a common upper state. These torsion–rotation transitions were then globally fit using a two-equivalent-top computer program, which was written in the principal axis system of the molecule and which uses a free-rotor basis set for each top, a symmetric-top basis set for the rotational functions, and a single-step diagonalization procedure. We can fit 411 lines involving 16 torsional sublevels from states with zero to three quanta of torsional excitation in the excited electronic state, using 24 parameters to obtain a standard deviation of 0.0045 cm −1, which is quite satisfactory, but inclusion in the fit of 440 transitions from all 17 rotationally assigned torsional levels increases the standard deviation by some 25%. The present fit gives a value of V 3 = 238 cm −1 for the threefold barrier height in the excited electronic state, in reasonable agreement with earlier studies.

High torsional vibrational energies of H2O2 and CH3OH studied by MULTIMODE with a large amplitude motion coupled to two effective contraction schemes

We have introduced the theory of the Reaction Path Hamiltonian into the variational scheme MULTIMODE, for the calculation of vibrational energy levels of polyatomic molecules which have a single large amplitude motion (for which the classic example is hydrogen peroxide). As with all MULTIMODE calculations, the greatest difficulty is the size of the CI matrix. The algorithm is now enhanced to include user-defined contraction schemes in order to probe high-energy regions of the potential energy surface. Furthermore an increased efficiency in matrix element evaluation is reported. High torsional levels of hydrogen peroxide and methanol are reported; those for hydrogen peroxide are consistent with an ‘exact’ variational procedure in valence coordinates, whilst those for methanol are predictions based on a recently-derived potential energy surface. The coupling between the torsional mode and the remaining normal modes is highlighted. These ‘technical’ advances open up the use of MULTIMODE for the study of vibrations in larger systems.

Exterior wide beam–column connections in existing RC frames subjected to lateral earthquake loads

In this paper, the seismic performance of reinforced concrete exterior wide beam–column connections with shallow spandrel beams lightly reinforced for torsion and moderate levels of gravity loads was investigated experimentally. The study focuses on existing frames designed and detailed according to construction practices used over ten years ago in the moderate-seismicity Mediterranean area. The results can be useful for assessing the seismic vulnerability of older structures and orienting seismic retrofit alternatives. Two 3/5 scale test models representative of exterior sub-assemblages in a prototype six-story building were subjected to gravity-load levels typical of those acting during an earthquake, and quasi-static cyclic lateral loads until failure. The performance was studied in terms of strength, displacement, ductility and energy dissipation capacity. The data are analyzed in conjunction with the results of previous tests. The specimens exhibited a “strong column–weak beam” type of flexural yielding mechanism. The average drift ratios at first yielding of the wide beam longitudinal reinforcement, δ y o , and at failure, δ u , were 2.2% and 4.5% respectively; the displacement ductility ratio μ was approximately 2.2. Comparison to similar connections without added gravity loads showed that moderate levels of gravity loading increased δ y o by about 40%, and decreased by a similar percentage the value of μ and the energy dissipated in each half cycle of displacement expressed in terms of an equivalent viscous damping ratio. Finally, two approaches for estimating the wide-beam flexural capacity are examined.

Vibronic spectra, ab initio calculations, and structures of conformationally non-rigid molecules of oxalyl halides in the ground and lowest excited electronic states. Part I: Reanalysis of the 3680Å and 4100Å absorption systems of oxalyl chloride

The vapor-phase absorption spectrum of oxalyl chloride in the 3000–4180 Å region has been re-examined at high resolution. Singlet–singlet A ˜ 1 A u ← X ˜ 1 A g and singlet–triplet a ˜ 3 A u ← X ˜ 1 A g electronic transitions of the trans- conformer found in the spectrum are in agreement with earlier works [W.J. Balfour, G.W. King, J. Mol. Spectrosc. 26 (1968) 384–397; ibid. 27 (1968) 432–442]. Torsion levels of trans -oxalyl chloride in the ground X ˜ 1 A g and excited A ˜ 1 A u and a ˜ 3 A u states were found for the first time. Ab initio calculations of structures for conformers of oxalyl chloride in the ground and lowest excited electronic states explain the absence of second conformer transitions in the vibronic absorption spectrum.

Intramolecular Dynamics of RS−SR′ Systems (R, R′ = H, F, Cl, CH3, C2 H5): Torsional Potentials, Energy Levels, Partition Functions

The equilibrium and cis and trans geometric structures of a series of disulfides RS-SR' (HSSH, HSSF, HSSCl, HSSCH3, HSSC2H5, FSSF, ClSSCl, ClSSF, CH3SSCH3, C2H5SSC2H5) have been studied using both density functional theory (B3LYP/6-311++G(3df, 3pd)) and second-order Møller-Plesset perturbation theory (MP2(FU)/aug-cc-pVTZ). The effects of internal rotation on the structural parameters have been analyzed and the torsional potentials around the S-S bond have been compared with experimental and theoretical information, when available, as well as with the analogues of the peroxydic family. Torsional levels were calculated, and their distribution as a function of temperature was determined, obtaining partition functions. This information is of interest for statistical approaches to equilibrium properties and to rates of processes in which torsional anharmonicity is relevant. It is also required for recent atmospheric modeling studies and also for prototypical chiral separation experiments, in view of a possible dynamic mechanism for chirality exchange by molecular collisions. In general, barriers for such processes are higher than for the corresponding peroxides, and accordingly, rates for chirality change are estimated to be consistently smaller.

Rotationally resolved photoelectron spectroscopic study of the Jahn–Teller effect in allene

The pulsed-field-ionization zero-kinetic-energy photoelectron spectra of allene (C(3)H(4)) and perdeuterated allene have been recorded from the first adiabatic ionization energy up to 2200 cm(-1) of internal energy in the cations at a resolution sufficient to observe the full rotational structure. The intensity distributions in the spectra are dominated by vibrational progressions in the torsional mode, which were analyzed in the realm of a two-dimensional model of the Emultiply sign in circle(b(1) plus sign in circleb(2)) Jahn-Teller effect in the allene cation [C. Woywod and W. Domcke, Chem. Phys. 162, 349 (1992)]. Whereas the rotational structure of the transitions to the lowest torsional levels (0(0) and 4(1)) are regular and can be qualitatively analyzed in terms of a simple orbital ionization model, the rotational structure of the spectra of the 4(2) and 4(3) levels are strongly perturbed. The photoelectron spectrum of C(3)H(4) also reveals several weak vibrational bands in the immediate vicinity of these levels that are indicative of (ro)vibronic perturbations. A slight broadening of the transitions to the 4(1) levels compared to that of the vibronic ground state and the increase of the number of sharp features in the rotational structure of the spectrum of the 4(2) level point at the importance of large-amplitude motions not considered in previous treatments of the Jahn-Teller effect in the allene cation.