Rotational ground state

We tend to give the letter J to the rotational quantum states. The rotational ground state has a rotational quantum number of J and the excited rotational quantum number is J. To be allowed (in the quantum-mechanical sense), the excitation from J to J must follow... 

The proviso T = 0 signifies that AB is in its electronic, vibrational, and rotational ground states and has no translational energy. The word isolated indicates the perfect gas model. The minimum energy condition ensures that AB+ is also in its electronic, vibrational, and rotational ground states and the translational energies of AB+ and e are both zero it also indicates that the products in reaction 4.1 do not interact, that is, they also conform with the perfect gas model. 

Amides possess planar or almost planar structures (1 and 2). Their rotational ground state is stabilized because the amino group is a strongly electron-donating group and the carbonyl function is strongly electron accepting. Excellent reviews on this topic have been published (28,29,30), and should be consulted by readers interested in amide rotation. 

Expectation Values of the Deuteron-Proton Distance, rd-p, the Deuteron-Electron Distance, rd-e, and the Proton-Electron Distance, r e, and Their Squares for the Vibrational Levels of HD" in the Rotational Ground State"... 

Closed shell molecules in the rotational ground state have no net magnetic dipole moment m apart from nuclear magnetic dipole moments. However, when molecules rotate with angular momentum /, they acquire a net rotational magnetic moment... 

It is interesting to note the near-absence of absorption in the translational band of pure para-hydrogen. At the temperature of the measurement (20.8 K), all para-H2 molecules are in the rotational ground state (J = 0) which is optically isotropic. The optical properties of these molecules are thus much like those of He atoms. No translational ab-... 

At the lowest temperature where the para-H2 and ortho-H2 concentrations are in thermal equilibrium, the rotational ground state and the lowest excited state (J = 0 and 1) are about equally populated, hence the comparable line intensities at 354 and 587 cm-1 at 77 K. With increasing temperature, the J = 1 state is more highly populated, and states with J > 1 are increasingly populated as well, at the expense of the J = 0 ground state, so that the So(l) line shows up much more prominently than So(0) at the higher temperatures. Profiles obtained at temperatures T > 100 K may similarly be fitted by simple three-parameter model profiles if one accounts for the higher So(J) and Qo(J) lines, J > 1, as well. Very satisfactory fits of the laboratory data have resulted [15]. The profiles of the individual lines vary with temperature. Fairly accurate empirical spectra may be constructed, even at temperatures for which no measurements exist, when the empirical temperature dependences of the three BC parameters are known, see Chapter 5 below. 

Fig. 11.8. Rotational state-distributions of OH(2n3/2) originating from the 193 nm photolysis of H2O in the Ooo rotational ground state within the 10 0) vibrational manifold. The results for the A and the A" A-doublets are drawn on the same scale. Adapted from Hausler, Andresen, and Schinke (1987).

Once again, it is difficult to be sure that both the reagent and the product are in their electronic, vibrational, and rotational ground states. Indirectly, one can measure electron affinities by using crossed atomic and molecular beams—for example, Cs beam collisional ionization ... 

In o-H2, the two nuclear spins appear as coupled to form an I(total) = 1 species, with three states having Mj= —1, 0, +1 respectively. Thus it is NMR-active.45 Furthermore, only rotational states with odd quantum numbers can be occupied. Thus the rotational ground state has N=1 a triplet of states. In other words, o-H2 can never stop rotating, about any axis perpendicular to its molecular axis n. 

Only rotational states with even quantum numbers N can be occupied. Thus the rotational ground state has N=0 a singlet. It follows that hydrogen gas is a mixture of components in a 3 1 ratio of abundance, and that o-H2 molecules continue to rotate even when cooled, when unimpeded. 

Wasserman, E. Yaga-, W. A. Kuck, V. J. EPR of CH2 a substiantiaUy bent and partially rotating ground state triplet, ChertL Phys. Lett. 1970, 7,409-413. 

In the following numerical experiment we show that it is possible to demonstrate the difference between locahzed and resonant rotor dynamics with Csl molecules. At time t = 0 the molecules are prepared in their rotational ground state ( 4 (t = 0)) = J = 0, M = 0)). For t > 0 they are exposed to a string of microwave pulses. The control parameters r and k determine the repetition frequency and the strength of the pulses. In order to be able to compare with the results for the planar kicked rotor discussed in Section 5.3, we choose k = 5 and r = 1 (for the nonresonant case) and r = 7t/3 (for the resonant case). This choice of control parameters translates into a driving frequency oi u = 1/T w 9 GHz and a field strength of q w IkV/cm. For the pulse shape we choose... 

A feature of London s paper is its emphasis on the zero-point motion of electrons it is the intermolecular correlation of this zero-point motion that is responsible for dispersion forces. London s Section 9 extends the idea of zero-point fluctuations to the interaction of dipolar molecules. If their moment of inertia is small, as it is for hydrogen halide molecules, then even near the absolute zero of temperature when the molecules are in their non-rotating ground states, there are large fluctuations in the orientation of the molecules and these become correlated in the interacting pair. 

Scheme 9 provides (using 47 for purposes of illustration) molecular detail for the concepts outlined in Fig. 21. In essence, the proof of principle for the molecular motor starts with 47a. Compound 47a is one of three low-energy rotational isomers (rotamers) about the axle connecting the triptycene and helicene components (47b is a second low-energy rotamer). Rotamer 47a is activated by reaction with phosgene to give the isocyanate 49. Isocyanate 49 is chemically armed to react with the OH group in the hydroxypropyl tether attached to the helicene, but, in the rotational ground state 49, the isocyanate...

Next, we consider the scattering signal when the molecule is in a nonstationary excited state obtained by excitation out of the initial stationary vibrational-rotational ground state. 

Above we only studied excitation of Nal out of the rotational ground state. In practice, one usually starts with a Boltzmann distribution of initial rotational... 

Thus, an inversion is always found if the vibrational and rotational temperatures differ such that Tyib exceeds Ta0t sufficiently to satisfy this inequality. This is illustrated in Fig. 2 for the case NV=NV-1- The situation here corresponds to an infinite vibrational temperature Tvtb= In the extreme case of such an inversion TRot- -0 and Tvib > 0, all the molecules in the various vibrational states are found in the rotational ground state J =0. It can be seen that inversion then exists for the P(l) transitions (J =0- -J — 1). As this discussion shows, inversion can exist of some J values can only as long as the vibrational temperature is positive (Tvib < °°)-This is called a partial population inversion. If Tvib attains a negative value, all J transitions may show inversion. This situation, called a total inversion, can arise only if Nv>Nv-i. 

An explanation of the bifurcation can be found from the angular density (lower panel of Fig. 36). Because we start from the rotational ground state, the first excitation step prepares a wavepacket with the rotational quantum number 7=1. Then, the density, initially, is proportional to Tio(0,0) cos (0) 2. It is seen that the density changes with time and that a depletion at angles smaller than 7i/2 occurs, which goes in hand with a concentration of density at a value of n. It is now straightforward to find a classical interpretation of the (radial) density bifurcation in regarding the classical force which stems from the external field interaction and acts in the radial direction ... 

Figure A3.12.1. Schematic potential energy profiles for three types of unimolecular reactions, (a) Isomerization, (b) Dissociation where there is an energy barrier for reaction in both the forward and reverse directions, (c) Dissociation where the potential energy rises monotonically as for rotational ground-state species, so that there is no barrier to the reverse association reaction. (Adapted from [5 ].)... 

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