Oblate Top Research Articles

Virtual indentation of the empty capsid of the minute virus of mice using a minimal coarse-grained model.

A minimal coarse-grained model for T=1 viral capsids assembled from 20 protein rigid trimers has been designed by extending a previously proposed form of the interaction energy written as a sum of anisotropic pairwise interactions between the trimeric capsomers. The extension of the model has been performed to properly account for the coupling between two internal coordinates: the one that measures the intercapsomer distance and the other that gives the intercapsomer dihedral angle. The model has been able to fit with less than a 10% error the atomic force microscopy (AFM) indentation experimental data for the empty capsid of the minute virus of mice (MVM), providing in this way an admissible picture of the main mechanisms behind the capsid deformations. In this scenario, the bending of the intercapsomer dihedral angle is the angular internal coordinate that can support larger deformations away from its equilibrium values, determining important features of the AFM indentation experiments as the elastic constants along the three symmetry axes of the capsid and the critical indentations. From the value of one of the parameters of our model, we conclude that trimers in the MVM must be quite oblate tops, in excellent agreement with their known structure. The transition from the linear to the nonlinear regimes sampled in the indentation process appears to be an interesting topic for future research in physical virology.

Rotation of CH3+ Cations in Helium Droplets.

Observation of the free rotation of molecules in helium droplets enabled microscopic study of interaction of quantum rotors with a superfluid environment at T = 0.4 K. This work extends studies of rotation in helium to molecular cations, such as methenium, CH3+. The spectrum of the v3 band of CH3+ around 3130 cm-1 has three prominent peaks assigned to the rotational structure of the band. While the free CH3+ is an oblate top, in helium it behaves as a prolate top. This effect is ascribed to the strong binding of two He atoms along the figure axis of the ion. Our results indicate that the other He atoms within the first solvation shell remain fluxional and in disparity with the widely accepted model of a rigid He "snowball" surrounding ions.

Theoretical Spectroscopic Characterization at Low Temperatures of Dimethyl Sulfoxide: The Role of Anharmonicity.

The structural and spectroscopic parameters of dimethyl sulfoxide (DMSO) are predicted from CCSD(T)-F12 calculations that can help to resolve the outstanding problem of the rovibrational spectroscopy. DMSO is a near oblate top that presents a trigonal pyramidal geometry. Rotational parameters are determined at the equilibrium and in selected vibrational states. For the ground state, the rotational constants were calculated to be A0 = 7031.7237 MHz, B0 = 6920.1221 MHz, and C0 = 4223.3389 MHz, at few megahertz from the previous experimental measurements. Ab initio calculations allow us to assert that DMSO rotational constants are strongly dependent on anharmonic effects. Asymmetry increases with the vibrational energy. Harmonic frequencies, torsional parameters, and a two-dimensional potential energy surface (2D-PES) focused to describe the internal rotation of the two methyl groups are determined at the CCSD(T)-F12 level of theory. For the medium and small amplitude motions, anharmonic effects are estimated with MP2 theory getting an excellent agreement with experimental data for the ν11 and ν23 fundamentals. Torsional energies and transitions are computed variationally form the 2D-PES that denotes strong interactions between both internal tops. The vibrationally corrected V3 torsional barrier is evaluated to be 965.32 cm(-1). The torsional splitting of the ground vibrational state has been estimated to be lower than 0.01 cm(-1). Although the ν13 torsional fundamental is found at 229.837 cm(-1) in good agreement with previous assessment, there is not accord for the low intense transition ν24. A new assignment predicting ν24 to lie between 190 and 195 cm(-1) is proposed.

Algebraic treatment of alpha-cluster nuclei

I discuss an algebraic treatment of alpha-cluster nuclei in the framework of the Algebraic Cluster Model. It is suggested to treat 12C as an oblate top with symmetry (equilateral triangle) and 16O as a spherical top with tetrahedral symmetry (regular tetrahedron). The structure of the rotational bands is a consequence of the underlying symmetry, and can be used to help determine the geometrical configuration of the α-particles.

The structure of the Hoyle state via a measurement of the 'Hoyle Rotational Band' in 12C

We have measured the 12C(γ, 3α) reaction with an Optical Time Projection Chamber (O-TPC) detector operating with the CO2(80%) + N2(20%) gas mixture and gamma-ray beams from the HIγS facility of the TUNL at Duke. We measured complete angular distributions (between 9.1 – 10.7 MeV) from which we determine the cross section yield curve and E1-E2 relative phases leading to an unambiguous identification of the second 2+ state in 12C at 10.03(11) MeV. The observed spectrum of 12C below 12 MeV including the 2+2 observed in this work resembles the rotation-vibration spectrum predicted for a triangular shape oblate spinning top in which the Hoyle state is the first vibrational breathing mode of the triangular three alpha particle system. The predicted rotation-vibration spectrum of a triangular shape oblate spinning top (with a D3h symmetry) allows us to compare the moment of inertia of the predicted Hoyle rotational band to the ground state rotational band and in this way extract the model radius parameter of the Hoyle state of 3.22(8) fm ( time the r.m.s. radius of the ground state) which is close to the radius extracted from 12C(x,x') data.

The structure of the Hoyle state and its 2+partner state in12C

We have measured the 12C(γ, 3α) reaction with an Optical Time Projection Chamber (O-TPC) detector operating with the CO2(80%) + N2(20%) gas mixture and gamma-ray beams from the HIγS facility of the TUNL at Duke. We measured complete angular distributions (between 9.1 – 10.7 MeV) from which we determine the cross section yield curve and E1 – E2 relative phases leading to an unambiguous identification of the second 2+ state in 12C at 10.03(11) MeV. The observed spectrum of 12C below 12 MeV including the 22+ state observed in this work resembles the rotation-vibration spectrum predicted for a triangular shape oblate spinning top in which the Hoyle state is the first vibrational breathing mode of the triangular three alpha-particle system. We also observed a hint of the 23+ state which is predicted by the U(7) model as a member of the 1- bending mode band, but the existence of this 23+ is yet to be confirmed. The predicted rotation-vibration spectrum of a triangular shape oblate spinning top (with a D3h symmetry) allows us to compare the moment of inertia of the predicted Hoyle rotational band to the ground state rotational band and in this way extract the (large) rms radius of the Hoyle state of 3.22(8) fm. We compare the deduced rms radius with recent ab-initio theories and cluster models as well as the radius extracted from 12C(p, p′) data.

Microwave survey of the conformational landscape exhibited by the propeller molecule triethyl amine

Conformational studies with quantum chemical methods yielded for the most stable conformer of triethyl amine a propeller-like structure belonging to the point group C(3), which corresponds to an oblate top. The microwave spectrum of this conformer with (14)N hyperfine splitting of all rotational transitions was assigned and molecular parameters were determined. The rotational constants were found to be A = B = 2.314873978(11) GHz, the (14)N quadrupole coupling constant χ(cc) = -5.2444(07) MHz. The observed spectrum could be reproduced within experimental accuracy. The standard deviation of a global fit with 48 rotational transitions is 1.5 kHz. The propeller-like structure seems to be energetically favorable and therefore also typical for related systems like triethyl phosphine, triisopropyl amine, tri-n-propyl amine, and tri-tert-butyl amine. Furthermore, the rotational transitions of two isotopologues, (13)C(2) and (13)C(5), could be measured in natural abundance and fitted with an excellent standard deviation. The C rotational constants could be determined to be 1.32681(96) GHz and 1.32989(18) GHz for the (13)C(2) and (13)C(5) isotopologues, respectively.

Centrifugal distortion analysis of the rotational spectrum of aziridine: Comparison of different Hamiltonians

Previous measurements of rotational spectrum of aziridine up to 1.85 THz have been supplemented by new data in 225–660 GHz frequency range. A total of 1465 transitions (915 of them are newly assigned ones) with maximum values of J = 59 and K c = 50 were fit to a standard Watson Hamiltonian using the S- and A-reductions and the representations I r and III r . Although aziridine is an asymmetric oblate top, the combination ( A, III r ) gives the worst results. From the point of view of the convergence of the Hamiltonian, the best results are obtained with the combination ( S, III r ). It is explained that the failure of the combination ( A, III r ) is due to the large value of the parameter σ = ( 2 C - A - B ) / ( A - B ) which makes some sextic centrifugal distortion constants much too large impeding the convergence of the Hamiltonian. It is also shown that the calculation of the centrifugal distortion constants from a force field is sometimes an ill-conditioned operation. Finally, the use of a non-reduced Hamiltonian (with six quartic centrifugal distortion constants) was successful in the particular case thanks to the method of predicate observations.

Choice of the reduction and of the representation in centrifugal distortion analysis: A case study of dimethylsulfoxide

The millimeter-wave and submillimeter-wave spectra of dimethylsulfoxide have been measured up to 660 GHz, corresponding to maximum values of J = 70 and K c = 68. A total of 3331 transitions (corresponding to 2133 distinct frequencies) were fit to a standard Watson Hamiltonian using the S- and A-reductions and the representations I r and III r . Although dimethylsulfoxide is an asymmetric oblate top, the combination ( A, III r ) gives the worst results. From the point of view of the convergence of the Hamiltonian, the best results are obtained with the combination ( S, III r ) but the least-squares system of normal equations is better conditioned with representation I r . These results are compared to those obtained for a few typical molecules.

Orientation of dipole molecules and clusters upon adiabatic entry into an external field

The induced polarization of a beam of polar clusters or molecules passing through an electric or magnetic field region differs from the textbook Langevin-Debye susceptibility. This distinction, which is important for the interpretation of deflection and focusing experiments, arises because instead of acquiring thermal equilibrium in the field region, the beam ensemble typically enters the field adiabatically, i.e., with a previously fixed distribution of rotational states. We discuss the orientation of rigid symmetric top systems with a body-fixed electric or magnetic dipole moment. The analytical expression for their "adiabatic-entry" orientation is elucidated and compared with exact numerical results for a range of parameters. The differences between the polarization of thermodynamic and "adiabatic-entry" ensembles of prolate and oblate tops, and of symmetric top and linear rotators, are illustrated and identified.

CLASSICAL MECHANICS OF DIPOLAR ASYMMETRIC TOP MOLECULES IN COLLINEAR STATIC ELECTRIC AND NONRESONANT LINEARLY POLARIZED LASER FIELDS: ENERGY-MOMENTUM DIAGRAMS, BIFURCATIONS AND ACCESSIBLE CONFIGURATION SPACE

We study classical energy-momentum (E-m) diagrams for rotational motion of dipolar asymmetric top molecules in strong external fields. Static electric fields, nonresonant linearly polarized laser fields, and collinear combinations of the two are investigated. We treat specifically the molecules iodobenzene (a nearly prolate asymmetric top), pyridazine (nearly oblate asymmetric top), and iodopentafluorobenzene (intermediate case). The location of relative equilibria in the E-m plane and associated bifurcations are determined by straightforward calculation, with analytical results given where possible. In cases where analytical solutions cannot be obtained, we resort to numerical solutions, while keeping a geometrical picture of the nature of the solutions to the fore. The classification we obtain of the topology of classically allowed rotor configuration space regions in the E-m diagram is of potential use in characterization of energy eigenstates of the corresponding quantum mechanical problem.

A new graphical version of STROTAB: The analysis and fitting of singlet–triplet spectra of asymmetric top molecules in the prolate or oblate limits

The original version of STROTAB has been modified to run under Microsoft Windows using the C++ programming language. The new version takes full advantage of the Microsoft Foundation Classes available within the Microsoft Visual C++ Version 6 development environment. Specifically, windows can be created that edit the input file, summarize the results of the least-squares fit, display the calculated and observed spectra, display whole or partial sections of the calculated spectra as a stick or Gaussian de-convoluted spectrum. A listing of the rotational quantum numbers in the cases (a) and (b) limits for each of the displayed lines is provided. A branch annotating routine provides a quick visual guide to the assignment of the spectrum. A new eigenvalue sorting method has been added as an option that complements the existing method based on the eigenvector coefficients. The new sorting method has eliminated some difficulties that may arise using the existing “Least Ambiguous Method”. The program has been extended to handle near-oblate asymmetric tops using a type III r representation. New version summary Title of program: STROTAB Version number: 2 Catalogue identifier:ADCA_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADCA_v2_0 Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland Reference in CPC to previous version: 93 (1996) 241–264 Catalog identifier of previous version: ADCA Authors of previous version: R.H. Judge, E.D. Womeldorf, R.A. Morris, D.E. Shimp, D.J. Clouthier, D.L. Joo, D.C. Moule Does the new version supersede the original program: Yes Computers for which the program is designed and others on which it has been tested: Pentium Xenon, Pentium Pro and Later Operating systems or monitors under which program has been tested: Windows 98, Windows 2000, Windows XP Programming language used in the new version: ANSI C, C++, Microsoft Foundation Class (MFC) No. of lines in distributed program, including test data, etc.:11 913 No. of bytes in distributed program, including test data, etc.: 2 816 652 Memory required to execute with typical data: 7 Meg No of bits in a word: 16 No of processors used: 1 Has the code been vectorized or parallelized?: No No. of bytes in distributed program, including test data, etc.: ∼3.2 MB (compressed) Distribution format: zip file Additional keywords:near oblate top, bootstrap eigenvalue sorting, graphical environment, band contour Nature of physical problem: The least-squares/band contour fitting of the singlet–triplet spectra of asymmetric tops of orthorhombic symmetry using a basis set appropriate to the symmetric top limit (prolate or oblate) of the molecule in either Hund's case (a) or case (b) coupling situations. Method of solution: The calculation of the eigenvectors and eigenvalues remains unchanged from the earlier version. An option to sort the eigenvalues of the current J by fitting them to regular progressions formed from earlier J values (bootstrap method) can be used as an option in place of the existing method based on eigenvector coefficients. Reasons for the new version: The earlier version can only handle oblate tops by diagonalizing using the prolate limit. This has turned out to be unacceptable. An improved method of sorting eigenvalues under certain conditions is also needed. A graphical interface has been added to ease the use of the program. Summary of revisions: The Hamiltonian can now be constructed in a limit appropriate the representation for of the molecule. Sorting by an alternate method is now offered. Numerous graphical features have been added. Restrictions on complexity of the problem: The rotational quantum number restrictions are J ⩽ 255 and K (or P) ⩽127. The allowed transition frequency minus the band origin frequency must be in the range of ±10 000 cm −1. Up to five decimal places may be reported. The number of observed lines is limited by the dynamic memory and the amount of disk space available. Only molecules of symmetry D 2h, D 2 and C 2v can be accommodated in this version. Only constants of the excited triplet state may be varied.

Assignment of Infrared and Far-Infrared Transitions ofCH2CF2

Starting from the Watson A-reduced Hamiltonian and considering theinfrared transitions with ΔKa = 0, ΔKc = ±1 (A-type)or ΔKa = ±1, ΔKc = ±1 (B-type), and thefar-infrared transitions with ΔKa = 0,±2 and ΔKc = ±1, we calculate all the possible infrared absorption andfar-infrared emission transitions of the ν4 and ν9 bandsof 1,1-difluoroethylene (CH2CF2) pumped by 10P10 and 10P12 CO2laser lines. We assign four previously unassigned CH2CF2far-infrared laser lines (291.3 µm, 339.3 µm, 349.5 µmand 657.9 µm), where Ka and Kc represent the quantum number Kof the limiting prolate top and the limiting oblate top, respectively.The 291.3 µm line is identified as being generated from the cascadetransition. The assignment of the 288.5µm line by Laffertyet al. (J. Mol. Spectrosc. 87(1981)416) is also confirmed.

Semiclassical description of purely rotational recurrences for collisionless asymmetric top molecules: new results

A semiclassical approach, based on the discrete WKB approximation, is developed for the description of purely rotational recurrences in thermal ensembles of collisionless asymmetric top molecules. Exact non-perturbative expressions are derived for the periods of the J-, H-, and K-type transients. These formulas automatically account for the phenomenon of increasing the period of the J-type transients for oblate asymmetric tops and decreasing that for prolate asymmetric tops in parallel with the enhancement of molecular asymmetry. The asymmetry corrections are demonstrated to magnify the period of the K- and H-type transients, irrespective of the form of the molecular top. The polarity of the A- and C-type transients is established. New kinds of transients are predicted and characterized by their periods and polarity. The most important of these is demonstrated to be the P-type transients arising for planar molecules.

Approximation for sums and densities of state of vibrations coupled with symmetric top K-rotor

The energy of a symmetric top rotor depends on quantum numbers J and K. In unimolecular rate theory the energy of the K-rotor, i.e. the K-dependent part of the symmetric top rotor energy, may be considered under some conditions as “active”, i.e. mixed with vibrational energy and thus contributing to the sum and density of vibrational states of the molecule, subject to the restriction − J ⩽ K ⩽ + J. In these cases proper evaluation of the sum/density of vibrational plus active K-rotor states at specified energy and J involves a summation of sums/densities over all the allowed Ks, a computationally intensive exercise. This work proposes simple and accurate approximations that require only trivial machine time. For the prolate symmetric top, the K-dependence of vibrational + rotational sum/density of states is approximated by a truncated Gaussian, and for the oblate top by a hyperbolic cosine. In each case the necessary parameters are obtained by a fit to smoothed “exact” vibrational sums/densities at K = 0 and one, or at most two, other values of K. The approximations are tested on a selection of typical symmetric top molecules at several energies and values of J with satisfactory results. The use of symmetry numbers is briefly invoked.

Microwave and Millimeterwave Spectrum of 1,1-Difluoroethylene and the Vibrational Mode ν10 from FT-IR Spectroscopy

Abstract Pure rotational spectra of 1,1-Difluoroethylene (1,1-DFE) in the vibrational ground state (GS) and in excited vibrational states (EVSs) have been investigated by double resonance modulation (DRM) microwave spectroscopy in the range from 12 GHz to 40 GHz, and by millimeterwave spectroscopy in the range from 90 to 260 GHz. In addition to the GS spectrum, rotational transitions have been observed for the EVSs ν10 = 1, and 2, ν12 = 1, ν6 = 1, ν11 = 1, ν4 = 1, and ν9 = 1. Along with other IR bands up to 1400cm-1 , the fundamental vibrational band ν10 = 1 ← 0 has been observed by FT-IR spectroscopy and has been analysed to yield ν10 0 = 436.8851 cm-1. Rotational constants and quartic distortion constants were deduced for all observed states. In addition, sextic distortion constants were obtained for the GS and for the EVSs ν10 = 1, 2, ν6 = 1, and ν12 = 1 by computer fits of combined microwave and millimeterwave data to Watson's A-reduced Hamiltonian in Ir representation. The S-reduced Hamiltonian in IIIr representation may be considered more appropriate for the calculation or the fitting of the transitions because 1,1-DFE is a near oblate asymmetric top. Thus, for comparison, results are given for both the A- and the S-reduction.

Collision induced far infrared spectrum of cyclopropane

Rotational collision-induced absorbance has been observed in the far I.R. spectra of cyclopropane samples and cyclopropane-argon mixtures. The part of the spectrum due to the polarizability and quadrupolar and octapolar field is calculated using the literature values of the molecular properties for this oblate symmetric top. Prolate and oblate top molecules are shown to have excess observed absorbance at different frequencies. The excess absorbance is analysed in terms of violations of the multipolar selection rule, ΔK = 0, which is caused by asymmetrical interactions during collisions.

ChemInform Abstract: THE MICROWAVE SPECTRUM OF 1‐PYRAZOLINE

The microwave spectrum of 1-pyrazoline has been observed from 18 to 40 GHz in the six lowest states of the ring-puckering vibration. It is an a-type spectrum of a near oblate asymmetric top. Each vibrational state has been fitted to a separate effective Hamiltonian, and the vibrational dependence of both the rotational constants and the quartic centrifugal distortion constants has been observed and analyzed. The v = 0 and 1 states have also been analyzed using a coupled Hamiltonian; this gives consistent results, with an improved fit to the high J data. The preferred choice of Durig et al. [J. Chem. Phys. 52, 6096 (1970)] for the ring-puckering potential is confirmed as essentially correct, but the A and B inertial axes are shown to be interchanged from those assumed by Durig et al. in their analysis of the mid-infrared spectrum.

The microwave spectrum of 1-pyrazoline

The microwave spectrum of 1-pyrazoline has been observed from 18 to 40 GHz in the six lowest states of the ring-puckering vibration. It is an a-type spectrum of a near oblate asymmetric top. Each vibrational state has been fitted to a separate effective Hamiltonian, and the vibrational dependence of both the rotational constants and the quartic centrifugal distortion constants has been observed and analyzed. The v = 0 and 1 states have also been analyzed using a coupled Hamiltonian; this gives consistent results, with an improved fit to the high J data. The preferred choice of Durig et al. [ J. Chem. Phys. 52, 6096 (1970)] for the ring-puckering potential is confirmed as essentially correct, but the A and B inertial axes are shown to be interchanged from those assumed by Durig et al. in their analysis of the mid-infrared spectrum.

Raman band contours. II: Symmetric top molecules

AbstractThe general theory of Raman band contours of symmetric tops is discussed briefly, and a program for the calculation of the band contours for the degenerate bands of prolate and oblate symmetric tops is described. The band contours as a function of the Coriolis coupling constant, zeta, have been computed for the range ζ = −1.0 to + 1.0 and for values of beta (A/B–1) ranging from −0.5 (planar oblate top) to + 3.0. The results, which are presented in tabular and graphical form, can be used to determine approximate values of zeta from the contours of unresolved bands for molecules in which the selection rules are restricted to ΔK = ± 1 or ΔK = ± 2. Limitations and sources of error are discussed.