Derivation of the nonrigid rotation-large-amplitude internal motion Hamiltonian of the general molecule

The nonrigid (effective) rotation-large-amplitude internal motion Hamiltonian (NRLH) of the general molecule with one or more large-amplitude vibrations has been derived to the order of magnitude κ²T_VIB. The derivation takes advantage of the idea of a nonrigid reference configuration and uses the contact transformation method as a mathematical tool. The NRLH has a form fairly similar to that of the effective rotation Hamiltonian of semirigid (i.e., normal) molecules. From a careful examination of the Eckart-Sayvetz conditions and of the Taylor expansions of the potential energy surface in terms of curvilinear displacement coordinates, three types of large-amplitude internal coordinates of different physical meaning (effective large-amplitude internal coordinates, real large-amplitude internal coordinates, and reaction path coordinates) are described. To test the ideas and the formulas the effective bending potential function of the C₃ molecule in its ground electronic and ground stretching vibrational state is calculated from the ab initio potential energy surface given by W. P. Kraemer, P. R. Bunker, and M. Yoshimine (J. Mol. Spectrosc. 107, 191–207 (1984)). The calculations were carried out by using either the effective or the real large-amplitude bending coordinate of C₃. The NRLH theory is compared to the nonrigid bender theory at a theoretical level as well as through the results of the test calculations.     

Quantum states of hydrogen transfer and vibration in malonaldehyde

New ab initio results on the 21D potential energy surface of malonaldehyde and a quantum mechanical treatment of the hydrogen transfer motion and its interaction with all vibrations are presented. An explicit approximate reaction path, close to the minimum energy path but matching the reactive normal mode near equilibrium, allows one to predict the ground state tunnelling frequency even when using small basis sets. With a barrier of 1144 cm^?1 (3.27kcal mol-¹) the tunnelling splitting is predicted to be 22.0cm^?1 for the parent species and 3.8 cm^?1 for the species deuterated in the hydrogen bond, in good agreement with the observed values 21.6 and 2.9 cm^?1, respectively. Predicted energy levels for excited states of the hydrogen transfer motion and for the non-reactive vibrations suggest a re-examination of the vibrational spectra and an extension of the number of vibrational factors in the basis set to improve the results for the vibrationally excited states.     

Normal Coordinate Analysis of 3-Bromo-1,3-Dinitroazetidine

Abstract

The infrared spectrum of 3-bromo-1,3-dinitroazetidine was interpreted with the aid of normal coordinate calculations. A seventy-two parameter modified valence field was used in those calculations, and the observed wave numbers were fit with an average error of 2.5 cm^?1. An assignment of the bands in terms of symmetry coordinates is given. Many of the force constants were transferred to 1-acetyl-3,3-dinitroazetidine to aid in normal coordinate calculations for that compound.     

High resolution FTIR spectroscopy of CH2DF: analysis of the v 3 and v 4 interacting bands

The high resolution (0.004cm^?1) Fourier transform infrared spectrum of the monodeuterated form of methyl fluoride, CH₂DF, has been recorded and analysed in the v ₃ and v ₄ band region around 1420cm^?1. Both bands, coming from A′ symmetry vibrations, have a/b hybrid character, although in v ₃ the b-type component prevails over the a-type. The rotational structure has been analysed using a dyad model including c-type Coriolis coupling and high order vibrational resonance between these states. Accurate upper state molecular parameters and interaction terms have been obtained by fitting about 3270 assigned transitions to Watson's A-reduced Hamiltonian in the I^r representation. In addition, from a simultaneous fit of ground state combination differences coming from this analysis and 42 literature microwave transitions, an improved and more complete set of ground state constants, including three new sextic centrifugal distortion terms (Φ_JK, Φ_KJ and Φ_K), has been derived.     

Primary and secondary isotope effect on tunnelling in malonaldehyde using a quantum mechanical scheme

Primary and secondary isotope effect on tunnelling in malonaldehyde is investigated with reduced-dimensional quantum mechanical models in the saddle-point normal coordinates, where the Hamiltonian takes the imaginary-frequency normal model as the reaction coordinate and uses the relaxed potentials to approximate the normal modes not explicitly included. Our two-dimensional (2D) results of the ground-state tunnelling splitting (Δ₀), as well as the ratio of the Δ₀ in malonaldehyde to that in its isotopologues, are in reasonably good agreement with available experimental data. The experimental deduction about the appreciable impact of secondary isotope effect on tunnelling is further confirmed. Moreover, we find that in most isotopologues, the fundamental excitation of the ring-deformation normal mode, explicitly included in the 2D model, shows a large enhancement of tunnelling relative to the Δ₀.     

Microwave and low-frequency vibrational spectra of bullvalene

The microwave spectrum of bullvalene has been investigated in the region 18–40 GHz. In addition to transitions in the ground vibrational state, transitions arising from five excited vibrational states below 600 cm⁻¹ have also been observed. A combination of microwave intensity measurements and infrared and Raman data has been utilized to assign these vibrations. Three of the vibrations are E-type modes at 241, 355, and 588 cm⁻¹. One is an A₁-type mode at 445 cm⁻¹, and another is an A₂-type at 266 cm⁻¹. The microwave spectrum indicates the presence of a first-order Coriolis interaction for the E modes at 241 and 588 cm⁻¹. The first-order Coriolis coupling constant q = 0.557 MHz for the 241 cm⁻¹ vibration. The spectral results are consistent with C_3v symmetry for bullvalene.     

High resolution infrared synchrotron study of CH2D81Br: ground state constants and analysis of the ν5, ν6 and ν9 fundamentals

The high resolution infrared absorption spectrum of CH₂D⁸¹Br has been recorded by Fourier transform spectroscopy in the range 550–1075?cm^?1, with an unapodized resolution of 0.0025?cm^?1, employing a synchrotron radiation source. This spectral region is characterized by the ν₆ (593.872?cm^?1), ν₅ (768.710?cm^?1) and ν₉ (930.295?cm^?1) fundamental bands. The ground state constants up to sextic centrifugal distortion terms have been obtained for the first time by ground-state combination differences from the three bands and subsequently employed for the evaluation of the excited state parameters. Watson's A-reduced Hamiltonian in the I^r representation has been used in the calculations. The ν ₆?=?1 level is essentially free from perturbation whereas the ν ₅?=?1 and ν ₉?=?1 states are mutually interacting through a-type Coriolis coupling. Accurate spectroscopic parameters of the three excited vibrational states and a high-order coupling constant which takes into account the interaction between ν₅ and ν₉ have been determined.     

Anharmonic force field for methanol

An ab initio quartic anharmonic force field for methanol has been calculated at the equilibrium position using the CCSD(T) method for the structure and the harmonic potential energy surface, and the MP4(SDQ) method for the anharmonic part of the surface. A triple zeta basis set was employed with symmetrized curvilinear internal valence coordinates in all calculations. The internal coordinate force field constants have been transformed into force constants in the dimensionless normal coordinate representation for various isotopomers. Vibrational term values for CH₃OH, CH₃OD, CD₃OH, and CD₃OD have been obtained using second order perturbation theory. Particular care has been devoted to the inclusion of Fermi resonance interactions between different vibrational states. A good accuracy has been achieved in the calculation of the fundamentals for all the isotopomers, the mean absolute error being 5.8 cm^?1.     

A vibrational spectroscopic investigation of rhodanine and its derivatives in the solid state

Raman and infrared spectra are reported for rhodanine, 3‐aminorhodanine and 3‐methylrhodanine in the solid state. Comparisons of the spectra of non‐deuterated/deuterated species facilitate discrimination of the bands associated with N H, NH₂, CH₂ and CH₃ vibrations. DFT calculations of structures and vibrational spectra of isolated gas‐phase molecules, at the B3‐LYP/cc‐pVTZ and B3‐PW91/cc‐pVTZ level, enable normal coordinate analyses in terms of potential energy distributions for each vibrational normal mode. The cis amide I mode of rhodanine is associated with bands at ∼1713 and 1779 cm⁻¹, whereas a Raman and IR band at ∼1457 cm⁻¹ is assigned to the amide II mode. The thioamide II and III modes of rhodanine, 3‐aminorhodanine and 3‐methylrhodanine are observed at 1176 and 1066/1078; 1158 and 1044; 1107 and 984 cm⁻¹ in the Raman and at 1187 and 1083; 1179 and 1074; 1116 and 983 cm⁻¹ in the IR spectra, respectively. Copyright © 2010 John Wiley & Sons, Ltd.     

Calculation of spectroscopic parameters and vibrational overtones of methanol

A high-level quartic ab initio potential energy surface of methanol has been used to calculate spectroscopic constants of the ¹²CH₃OH molecule. These include coefficients of quartic anharmonic resonance terms, Darling-Dennison constants, for stretching states. A model expressed in terms of dimensionless normal coordinates has been employed in the calculation of O—H and C—H stretching vibrational states in high-overtone regions. Both cubic Fermi and quartic Darling-Dennison anharmonic coupling terms have been included in the model in order to take into account strong resonances between different states. The nonlinear least-squares method has been used to optimize some of the model parameters employing experimental term values of ¹²CH₃OH as data. Vibrational assignments are suggested for the first C—H stretching overtone region.     

High-resolution Fourier-transform infrared spectroscopy of the ν1 and ν8 fundamental bands of sulphur tetrafluoride (SF4)

The vibration-rotation spectra of the ν₁ and ν₈ fundamental bands of ³²SF₄ have been observed using Fourier-transform infrared spectroscopy. The band centre of the c-type ν₁ symmetric sulphur-equatorial-fluorine stretching vibration was observed at 891.6 cm^?1 and that for the b-type ν₈ asymmetric sulphur-equatorial-fluorine stretching vibration at 864.6 cm^?1. In total, 2044 rovibrational transitions have been assigned. Analysis of the spectra showed that the rotational states of the ν₁ = 1 and ν₈ = 1 upper vibrational levels are coupled by an a-type Coriolis interaction. This coupling has been treated both using perturbation theory and by the explicit inclusion of an appropriate Hamiltonian matrix element in a combined fit of the data for both bands. Spectroscopic parameters have been determined for the ground, ν₁ = 1 and ν₈ = 1 vibrational levels. Weaker transitions resulting from difference bands and the fundamental bands of the ³⁴SF₄ isotopomer have been identified but could not be assigned, because of the density of lines in the room-temperature spectrum. The possibility that discrepancies between the observed and predicted spectra of the ν₁ fundamental may result from either a Coriolis interaction with the states of another vibrational level, or the effects of intramolecular exchange of axial and equatorial fluorine atoms is considered. The discussion is supported by theoretical calculations which show that the likely path for intramolecular exchange is via a C _4v transition state.     

The Degenerate Vibrations of BCl3, BBr3 and BI3 with Application of Keating Coordinates

The experimental works of vibrational spectroscopy and normal coordinate analyses for BCl₃, BBr₃ and BI₃ are reviewed extensively. Harmonic force fields of the E' species are produced using isotopic frequencies and Coriolis constants as additional data, respectively. The usefulness of Keating coordinates versus valence coordinates as basis of force field approximations is discussed. The conclusions are not unequivocal, but they go in favour of the Keating coordinates when the reliability of the different computations is taken into account. Boron trichloride is treated specifically in some detail. Final force fields are proposed for the title molecules with the aid of the mass influence on Coriolis constants.     

Anharmonic potential function of 1,1-dichloroethylene

A simple anharmonic potential containing 18 quadratic, 6 cubic, and 6 quartic constants is proposed to fit 124 vibrational frequencies of 1,1-dichloroethylene and its ³⁷Cl isotope in the region from 10 000 to 350 cm^?1. The level patterns in the first and the second overtone regions of the CH₂ stretching vibrations are explained by the absence of large higher-order interaction terms between the two CH stretching coordinates.     

Boron Trifluoride: Application of the Keating Bendings to the Degenerate Vibrations

The harmonic force field of the E' species of BF₃ is studied. The Keating force field (KFF) is defined in analogy with the familiar VFF and CFF. In this connection three different coordinate sets are introduced. All of them contain bond stretchings. In addition, the valence coordinates include ordinary (Decius') bendings, the central coordinates nonbond stretchings, and Keating coordinates the Keating's bendings.

The experimental data of vibrational frequencies and Coriolis constants are reviewed extensively, as well as previous normal coordinate analyses. The different coordinate sets are tested for their usefulness as basis of force field approximations. For this purpose two different sets of experimental data are applied. The general conclusion goes in favour of the Keating coordinates.     

The adiabatic approximation as a diagnostic tool for torsion-vibration dynamics

The adiabatic separation of large-amplitude torsional motion from small-amplitude vibrations is applied as an aid in interpreting the results of fully coupled quantum calculations on a model methanol Hamiltonian. Comparison is made with prior work on nitromethane [D. Cavagnat, L. Lespade, J. Chem. Phys. 106 (1997) 7946]. Even though the torsional potentials are very different, both molecules show a transition from adiabatic to diabatic behavior when the CH stretch is excited to ν_CH = 4 or higher. In the adiabatic approximation, the effective torsional potentials for the various CH stretch vibrational states do not cross, but the CH vibrational amplitude moves from one bond to the next as a function of torsional angle. In the diabatic approximation, the effective torsional potentials do cross, but the distribution of the CH vibrational amplitude remains approximately constant in the vicinity of the crossing. The transition to diabatic behavior is promoted by the normal mode to local mode transition, and the relevant adiabatic and diabatic effective torsional potentials are determined by the torsion-vibration coupling. The torsion-vibration couplings in the four overtone manifolds considered (methanol OH, CH, nitromethane CH, and hydrogen peroxide OH) are large, reaching 265-500 cm⁻¹ by ν_XH = 6, and are of generally similar magnitude. The largest torsion-vibration couplings involve the first Fourier term in the torsional angle (cosγ for the CH stretch in methanol and the OH stretch in HOOH), whereas higher Fourier terms (cos2γ in nitromethane and cos3γ for the OH stretch of methanol) result in somewhat weaker coupling. Nonadiabatic matrix elements in methanol couple the torsional and vibrational energies and they exhibit a slow fall-off with coupling order.     

An ab initio investigation of the potential function of PH3

Ninety-three points on the potential energy surface of the ground electronic state of the phosphine molecule (with energies up to 12 000 cm⁻¹ above equilibrium) have been calculated ab initio using second-order many-body perturbation theory. A polynomial potential function (quartic in the in-plane coordinates and containing up to 12th-order terms in the out-of-plane coordinate) has been fitted to these points using the reduced inversion potential and standard polynomials. Using the nonrigid invertor Hamiltonian with this function, rotation-vibration energies have been calculated and found in reasonable agreement with experiment. The results are believed to be helpful in the determination of a realistic experimental potential function of the phosphine molecule over a wide range of values for the out-of-plane motion coordinate.     

Sextic force field of nitrous oxide

The sextic force field in the curvilinear internal coordinates has been studied for the nitrous oxide molecule from the spectroscopic data of ¹⁴N₂¹⁶O, ¹⁴N¹⁵N¹⁶O, and ¹⁵N¹⁴N¹⁶O. The bands below 6600 cm⁻¹ have been used. The force constants in the internal coordinates are converted to those in dimensionless normal coordinates by two successive transformations. The vibration Hamiltonian matrix for each symmetry species of a given isotopic species has been constructed from the harmonic oscillator basis functions, and it is then diagonalized numerically to give the vibrational energy levels and the wavefunctions. The latter have been used for the evaluation of ratational constants. The least-squares refinement has been very successful in the present study, and it is shown that the general quartic force field supplemented by the quintic and sextic stretching diagonal force constants estimated from the Morse function, provided that the terms up to sextic are kept in the dimensionless normal coordinate space, well reproduces the spectroscopic constants such as the vibrational levels, rotational constants, l-type doubling constants, and centrifugal distortion constants. The spectroscopic constants of the isotopic molecules which are excluded from the refinement process are also in good agreement with the computed ones. The bond dissociation energies of the NN and NO bonds estimated from the present results have been critically examined.     

Infrared spectra of the Kr—CO and Xe—CO van der Waals complexes

The infrared spectra of the weakly bound complexes Kr—CO and Xe—CO have been studied in the region of the CO stretching vibration (4.7 μm) using a high-resolution tuneable diode laser probe. The complexes were observed in a long path (200 m) low temperature (76 K) gas cell (Kr—CO) and in a pulsed supersonic jet expansion (Kr—CO and Xe—CO). Previous long path cell measurements on these complexes at lower resolution analysed only the K = 0 and 1 stacks of rotational levels in the ground intermolecular vibrational state. The new data extend up to K = 3 (Xe—CO) or 4 (Kr—CO), and also include K = 0 and 1 stacks in the excited bending state, ν₂ = 1. The bending frequencies for Kr—CO and Xe—CO (in the ν_co = 1 upper state) were determined to be 13.156cm_?1 and 13.794cm^?1, respectively. Detailed molecular parameters were determined to describe the rotational energy levels of each complex using a simple empirical Hamiltonian. These results enable parameters to be compared for the entire series of rare gas—carbon monoxide complexes, from He—CO to Xe—CO. Also they will guide the future development and evaluation of accurate intermolecular potential energy surfaces for Kr—CO and Xe—CO.