Vibrating rotator calculations

Watson, J.K.G. Vibration-rotation calculations for H3+ using a Morse-based discrete variable representation, Can. J. Phys. 1994, 72, 702-13 ... 

For a RRKM calculation without any approximations, the complete vibrational/rotational Flamiltonian for the imimolecular system is used to calculate the reactant density and transition state s sum of states. No approximations are made regarding the coupling between vibration and rotation. Flowever, for many molecules the exact nature of the coupling between vibration and rotation is uncertain, particularly at high energies, and a model in which rotation and vibration are assumed separable is widely used to calculate the quantum RRKM k(E,J) [4,16]. To illustrate this model, first consider a linear polyatomic molecule which decomposes via a linear transition state. The rotational energy for tire reactant is assumed to be that for a rigid rotor, i.e. 

H1] Qiu Y and Bai Z 1998 Vibration-rotation-tunneling dynamics of (HF)2 and (HCI)2 from fulldimensional quantum bound state calculations Advances in Moiecuiar Vibrations and Coiiision Dynamics, Voi. i-ii Moiecuiar dusters ed J Bowman and Z Bai (JAI Press) pp 183-204... 

Molecular enthalpies and entropies can be broken down into the contributions from translational, vibrational, and rotational motions as well as the electronic energies. These values are often printed out along with the results of vibrational frequency calculations. Once the vibrational frequencies are known, a relatively trivial amount of computer time is needed to compute these. The values that are printed out are usually based on ideal gas assumptions. 

C) The error in AE" /AEq is 0.1 kcal/mol. Corrections from vibrations, rotations and translation are clearly necessary. Explicit calculation of the partition functions for anharmonic vibrations and internal rotations may be considered. However, at this point other factors also become important for the activation energy. These include for example ... 

So, the calculation of the shape of an IR spectrum in the case of anticorrelated jumps of the orienting field in a complete vibrational-rotational basis reduces to inversion of matrix (7.38). This may be done with routine numerical methods, but it is impossible to carry out this procedure analytically. To elucidate qualitatively the nature of this phenomenon, one should consider a simplified energy scheme, containing only the states with j = 0,1. In [18] this scheme had four levels, because the authors neglected degeneracy of states with j = 1. Solution (7.39) [275] is free of this drawback and allows one to get a complete notion of the spectrum of such a system. 

Fully Coupled Six-Dimensional Calculations of the Water Dimer Vibration-Rotation-Tunneling States with a Split Wigner Pseudo Spectral Approach. 

It is well established that the average lengths of CH bonds are consistently 0.003 to 0.004 A longer than the corresponding CD bonds in the ground vibrational state (see Fig. 12.1, its caption, and Section 12.2.3). It remains only to establish the dipole moment derivative, (9p/9r), at the equilibrium bond length. That is available from theoretical calculation or spectroscopic measurement (via precise measurements of IR intensities of vibration-rotation bands). Calculations based on Equation 12.7 yield predicted dipole moment IE s in reasonable agreement with experiment. 

Fig, 19. Infrared spectra of the symmetric CHj bend mode of ethylidyne (CCHj) on Pt(l 11) at 82 K and 300 K. The dotted lines are calculated assuming a vibrational-rotational coupling. Inset shows the suggested orientation. (Reproduced by permission from Malik et... 

We examine the derivation of information about molecular structure and properties from analysis of pure rotational and vibration-rotational spectral data of diatomic molecular species on the basis of Dunham s algebraic formalism, making comparison with results from alternative approaches. According to an implementation of computational spectrometry, wave-mechanical calculations of molecular electronic structure and properties have already played an important role in spectral reduction through interaction of quantum chemistry and spectral analysis. 

Although transformation of coefficients pj into coefficients qj is readily practicable, the resulting values for CO adopt unwieldy magnitudes. Chackerian and Tipping [141] fitted a function of the latter form from experimental and theoretical (computations of molecular electronic structure) information in judicious combination, according to which they calculated vibration-rotational matrix elements for transitions in bands 5-0 and 6-0 fitting the latter values with formula 84 yielded the values of quantities presented above. Rational functions, such as those in formulae 92 - 94 or others, transcend the spirit of Dunham s approach because their construction incorporates physical knowledge of a quantity that is superfluous for invocation of a mere truncated polynomial. 

S.P.A. Sauer, J. Oddershede, J.F. Ogilvie, Evaluation of parameters in radial functions from rotational and vibration-rotational spectra and calculation of rotational and vibrational g... 

Computational spectrometry, which implies an interaction between quantum chemistry and analysis of molecular spectra to derive accurate information about molecular properties, is needed for the analysis of the pure rotational and vibration-rotational spectra of HeH in four isotopic variants to obtain precise values of equilibrium intemuclear distance and force coefficient. For this purpose, we have calculated the electronic energy, rotational and vibrational g factors, the electric dipolar moment, and adiabatic corrections for both He and H atomic centres for intemuclear distances over a large range 10 °m [0.3, 10]. Based on these results we have generated radial functions for atomic contributions for g g,... 

Recent microwave data for the potential interstellar molecule Sis is used together with high-level coupled-cluster calculations to extract an accurate equilibrium structure. Observed rotational constants for several isotopomers have been corrected for effects of vibration-rotation interaction subsequent least-squares refinements of structural parameters provide the equilibrium structure. This combined experimental-theoretical approach yields the following parameters for this C2v molecule re(SiSi) = 2.173 0.002A and 0e(SiSiSi) = 78.1 O.2 ... 

The purpose of this report is to demonstrate the ease with which highly accurate equilibrium structures can be determined by combining laboratory microwave data with the results of ab initio calculations. In this procedure, the effects of vibration-rotation interaction are calculated and removed from the observed rotational constants, Aq, Bq and Cq. The resulting values correspond to approximate rigid-rotor constants and and are thus inversely... 

---