Rotations in diatomics

In this chapter, we extend our treatment of rotation in diatomic molecules to nonlinear polyatomic molecules. A traditional motivation for treating polyatomic rotations quantum mechanically is that they form a basis for experimental determination for bond lengths and bond angles in gas-phase molecules. Microwave spectroscopy, a prolific area in chemical physics since 1946, has provided the most accurate available equilibrium geometries for many polar molecules. A background in polyatomic rotations is also a prerequisite for understanding rotational fine structure in polyatomic vibrational spectra (Chapter 6). The shapes of rotational contours (i.e., unresolved rotational fine structure) in polyatomic electronic band spectra are sensitive to the relative orientations of the principal rotational axes and the electronic transition moment (Chapter 7). Rotational contour analysis has thus provided an invaluable means of assigning symmetries to the electronic states involved in such spectra. 

Rotations in Diatomics 396 Rotations in Polyatomics 400 BIOSKETCH Stewart Novick 402 Spectroscopy of Rotational States 406 TOOLS OF THE TRADE Radio Astronomy 408... 

There is no internal rotation in diatomic and linear molecules)... 

Pekeris C L 1934 The rotation-vibration coupling in diatomic molecules Phys. Rev. 45 98 Slater J C and Kirkwood J G 1931 The van der Waals forces in gases Phys. Rev. 37 682... 

This Schrodinger equation relates to the rotation of diatomic and linear polyatomic molecules. It also arises when treating the angular motions of electrons in any spherically symmetric potential... 

As in diatomic molecules the structure of greatest importance is the equilibrium structure, but one rotational constant can give, at most, only one structural parameter. In a non-linear but planar molecule the out-of-plane principal moment of inertia 4 is related to the other two by... 

The rotational selection rule for vibration-rotation Raman transitions in diatomic molecules is... 

Hence, the problem is reduced to whether g(co) has its maximum on the wings or not. Any model able to demonstrate that such a maximum exists for some reason can explain the Poley absorption as well. An example was given recently [77] in the frame of a modified impact theory, which considers instantaneous collisions as a non-Poissonian random process [76]. Under definite conditions discussed at the end of Chapter 1 the negative loop in Kj(t) behaviour at long times is obtained, which is reflected by a maximum in its spectrum. Insofar as this maximum appears in g(co), it is exhibited in IR and FIR spectra as well. Other reasons for their appearance are not excluded. Complex formation, changing hindered rotation of diatomic species to libration, is one of the most reasonable. 

He assumed that a pair of electrons is shared between two atoms in diatomic hydrogen and in other molecules, like methane. The electrons were modeled as a girdle of electrons rotating in a circle at a right angle to the axis connecting two atoms. 

Pekeris, C. L. (1934), The Rotation-Vibration Coupling in Diatomic Molecules, Phys. Rev. 45, 98. 

A diatomic molecule with fixed bond length R rotating in the absence of any external potential is described by the following Schrodinger equation ... 

C.C. Brau and R.M. Jonkman. Classical Theory of Rotational Relaxation in Diatomic Gases. J. Chem. Phys., 52 477,1970. 

J.G. Parker. Rotational and Vibrational Relaxation in Diatomic Gases. Phys. Fluids, 2 449-462,1959. 

Cameron system of, 298 fundamental IR band of, table of, 174 rotational transitions of, table of, 168 Carbon-13 NMR, 356-357 Cartesian displacement coordinates, 236 Case (a) coupling, 188-189, 212 Case (b) coupling, 190-191,212 Cayley, A., 78, 387 Center of symmetry, 53 Central-force problem, 38 Centrifugal distortion in diatomics, 158,166-167 in polyatomics, 213, 216, 218 Chain rule, 20-21 Characters ... 

This type of energy exchange in an autoionization process may correspond with the behavior of a kicked rotator in classical mechanics, which is known to exhibit chaos. It would be worthwhile to consider an autoionization process of a simple diatomic molecule in its Rydberg states to understand experimentally the essential dynamics of a quantum system, whose classical counterpart exhibits chaos. 

I 2.1 Rotational Energy Levels of Diatomic Molecules, K I 2.2 Vibrational Energy Levels of Diatomic Molecules, 10 I 2.3 Electronic Stales of Diatomic Molecules, 11 I 2.4 Coupling of Rotation and Electronic Motion in Diatomic Molecules Hund s Coupling Cases, 12 1-3 Quantum States of Polyatomic Molecules, 14... 

Vibrational Population in Diatomic Molecules, 18 I 4.2 Rotational Population in Diatomic Molecules, 19 I 4.3 Thermal Contribution to Photolysis and Fluorescence. 21)... 

Absorption and Emission Spectra of Small Molecules. In diatomic molecules the number of vibrational and rotational levels is small, so that their energy spacing remains relatively large. Their absorption spectra are therefore line spectra which correspond to transitions to stable , associative excited states, but if a dissociative excited state is reached then the absorption spectrum becomes a continuum since such states have no vibrational levels. 

In addition to the processes just discussed that yield vibrationally and rotationally excited diatomic ions in the ground electronic state, vibrational and rotational excitations also accompany direct electronic excitation (see Section II.B.2.a) of diatomic ions as well as charge-transfer excitation of these species (see Section IV.A.l). Furthermore, direct vibrational excitation of ions and molecules can take place via charge transfer in symmetric ion molecule collisions, as the translational-to-internal-energy conversion is a sensitive function of energy defects and vibrational overlaps of the individual reactant systems.312-314... 

Such high rotationally excited states in diatomic systems play a significant role in understanding molecular processes occurring in interstellar space [49]. For the specific system of H2+, these rotationally hot states can be produced for instance by the dissociation of CH42+ dications [50]. 

Each of the potentials shown in Figure 12.5 supports at least one bound or quasi-bound state which can be labeled by quantum numbers (j, Cl, J). These zeroth-order states correspond to almost free rotation of HF within the van der Waals complex with quantum numbers j = 0,1,2,... and Cl = 0,1,2,..., min(j, J). In analogy with the nomenclature for electronic states, they are termed E and n for Cl = 0 and 1, respectively. For j = 1 and Cl = 0 the diatom rotates in the plane defined by the three atoms. In contrast, for j = 1 and Cl = 1 it rotates in a plane perpendicular to the intramolecular vector R. As J increases, the centrifugal potential h2[J(J + 1) + j(j + 1) — 2Cl2]/2mR2 increases as well and eventually Veff(R j,Cl,J) becomes purely repulsive and the sequence of bound or quasi-bound states breaks off. 

Hougen, J.T. (1970). The Calculation of Rotational Energy Levels and Rotational Line Intensities in Diatomic Molecules (National Bureau of Standards (U. S.), Monograph 115, Washington D.C.). 

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