Linear rotor

Because of the very prolate nature of many dimers, their Stark effects can often be simply analyzed with the linear rotor expression ... 

The special cases of the symmetric rotor and the linear rotor can be performed by using or neglecting the appropriate quantum numbers in the general expression given above. 

A.I.Maergoiz, E.E.Nikitin, and J.Troe, Diabatic/adiabatic channel correlation diagrams for two linear rotors with long-range dipole-dipole interaction. Z Phys.Chem. 176,1 (1992)... 

IV. Valence interaction between atoms and linear rotors. J. Chem. Phys. 108, 5265 (1998)... 

Maergoiz, A.I., Nikitin E.E., Tree, J., Ushakov V.G. Classical trajectory and statistical adiabatic channel study of the dynamics of capture and unimolecular bond fission (1996) a) I. Ion-dipole capture, J. Chan. Phys. 105, 6263-6269 b) n. lon-quadrupole capture, ibid. 6270-6276 c) HI. Dipole-dipole capture, ibid. 6277-6284 (1998) d) IV. Valence interactions between atoms and linear rotors, J. Chem. Phys. 108, 5265-5280 e) V. Valence interactions between two linear rotors, ibid. 9987-9998 (2002) g) VI. Properties of transitional modes and specific rate constants H.EJ), J. Chem. Phys. 117, 4201-4213. 

In this paper we give an overview of the mean-field theory of phase transitions in coupled rotors with particular attention to the issues of reentiance, other quantum anomalies, and meta-stability. We comparatively analyze coupled planar rotors (two-dimensional model) and coupled linear rotors (three-dimensional). We show that the dipolar potential does not exhibit the reentrance anomaly, whereas the quadmpolar one does. The phase transition turns out to be second order in all cases except for the linear rotors in a quadmpolar potential where it is first order. We also investigate the effects of the crystal field in the case of the linear rotor model with quadmpolar potentials the crystal field causes the appearance of critical points which separate lines of the phase diagram where the transition is first order from regions where there is no... 

Figure 6. Phase diagram for linear rotors, X=1 and X=2, with several values of the crystal field in the case of the latter.

For the systems without erystal field, the two features identified in the previous seetion in the ease of the planar rotors, namely the stronger ordering tendeney in the X=1 ease, and the reentrant phase transition in the X=2 case are present in the case of linear rotors as well. 

Figure 9. Entropy of the ordered state and at fixed values of the order parameter for the system of linear rotors withX=2 at a crystal field of Uj=0.018, Ug=12.00. The inset shows the order parameter.

In the absence of the crystal field the quantum melting phase transition is second order for planar rotors, first order for linear rotors. When a crystal field is turned on the phase transition is absent for planar rotors, whereas a more... 

We have presented a eomparative review of the mean-field theory of different types of eoupled rotors. We have eonsidered planar and linear rotors in dipolar and quadrupolar potentials. 

A second implication of the collective, moleculelike model concerns the states with excitation in the bending mode. The bending mode of the linear rotor-vibrator is of course doubly degenerate. Hence, there are two independent states with one quantum of bending, which should be very similar to one another and should differ markedly from the state with no excitation as with all first excited vibrational states, their probability distributions should be zero at the potential minimum where the density of the unexcited state is a maximum. In this case, the implication is that the two first excited bending states... 

If we compare Eq. (4.78) with Eq. (4.73), it is clear that the algebraic three-dimensional model provides the correct rotational spectrum of a rigid linear rotor, where the (vibrational) angular momentum coefficient, ggg, is described by the algebraic parameters A 2 and A j2- The J-rotational band is obtained by recalling in Eq. (4.12), the branching law... 

To be more specific, let us consider the explicit form of in the linear rotor case (neglecting /-doubling effects, which we discuss later) ... 

P13.23 Refer to the flow chart in Fig. 12.7 in the text. Yes at the first que.stion (linear ) leads to linear point groups and therefore linear rotors. If the molecule is not linear, then yes at the next question (two or more C with n > 2 ) leads to cubic and icosahedral groups and therefore spherical rotors. If the molecule is not a spherical rotor, yes at the next question leads to symmetric rotors if the highest C has > 2 if not. the molecule is an asymmetric rotor. 

D17.1 An approximation involved in the derivation of all of these expressions is the assumption that the contributions from the different modes of motion are separable. The expression = kT/hcB is the high temperature approximation to the rotational partition function for nonsymmetrical linear rotors. The expression q = kT/hcv is the high temperature form of the partition function for one vibrational mode of the molecule in the haimonic approximation. The expression (f- =g for the electronic partition function applies at normal temperatures to atoms and molecules with no low lying excited electronic energy levels. 

Evidcintly the rotational structure of the band of a spherical rigid rotor is similar i,o that of a perpendicular (X) band of a lineal rigid rotor. The two types of bands of a. symmetric rotor are more complex. The paralhd ( ) typo of Itand, for which AK = 0, will, however, bo similar in structure to that of a spherical lotor or a perpendicular (X) band in a linear rotor. For a perpendicular (X) band, however, the position of the Q branch is dependent both upon the initial value of K in the transition and upon the sign of AK, as can be seen from the following expressions ... 

A18. The Memory-Function-Modeled Self-Diffusion Coefficient and Velocity Autocorrelation Function for Stockmayer Fluids of Linear Rotors. 

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