Zeeman effect rotational

A. Klesing, D. H. Sutter, and F. Stroh, /. Mol. Spectrosc., 148, 149 (1991).High-Resolution Rotational Zeeman Effect Study cf Isocyanogen, CNCN, Combined with Quantum Chemical Calculations. 

This term describes the rotational Zeeman effect, that is, the coupling between the external field and the magnetic moment of the rotating nuclei. We note that there is no corresponding vibrational contribution since R a k is zero. The physical reason for this lack is that it is not possible to generate vibrational angular momentum in a diatomic molecule because it possesses only one, non-degenerate, vibrational mode. 

The direction of the magnetic field defines the space-fixed p = 0 (or Z) direction. Equation (8.239) represents a very simplified version, in that it neglects the nuclear and rotational Zeeman effects, as well as the second-order effects of spin-orbit coupling, none of which are negligible. Nevertheless (8.239) will allow us to derive theoretical values for the first-order effective g-factors, for comparison with the experimental spectra [43]. The required matrix elements of (8.239) in a case (b) hyperfine-coupled basis are as follows ... 

Pure rotational and vibrational Raman spectra of At2 Raman spectroscopic study of kinetics of Ar, formation in a supersonic expansion seeded with Nj Electronic absorption spectrum of HgAr Rotational Zeeman effect in ArHBr t HgCl2 collision complex formed in harpoon reaction of Hg with Clj investigated via excitation of the HgCL van der Waals complex... 

Papers have appeared concerned with (i) the migratory aptitude of 2-furyl relative to vinyl and ethyl groups. In the vapor phase on alumina the order is the same as that in acidic solvents457 (ii) the effect of complex-ation with BC1, or TCNQ upon the aromaticity of furan,458 (iii) the molecular rotational Zeeman effect in 3-methylfuran459 and (iv) microwave and H-NMR spectra and the molecular dimensions of furan when held in a nematic phase provided by methoxybenzenene azophenylcaproate 460... 

B. The Analysis of Rotational Zeeman Effect Spectra in Asymmetric... 

D. The Rotational Zeeman Effect of Linear Molecules and Zeeman... 

E. The Rotational Zeeman Effect in Molecules Containing Quadrupole... 

From these equations it is obvious that it is possible, at least in principle, to determine the electric dipole moment of a molecule from the rotational Zeeman effect data of two isotopic species (see Fig. II,1). If the isotopic substitution causes a parallel shift of the principle axis system a p=av + Aa, b p = bp- - Ab, c p—Cp->r Ac, etc., where Aa is the a-coordinate of the center of mass of the daughter molecule referred to the principal axes of the parent molecule, the corresponding equations are given by... 

Fig. II.3. Effect of fluorine substitutions on the out-of-plane minus average in-plane component of the magnetic susceptibility are shown for several aromatic rings. The difference between the Cotton-Mouton and the rotational Zeeman effect data is probably due to the neglect of the field dependence of the electric polarizability in the analysis of the Cotton-Mouton data. Note that the difference in the results for 1,2- and 1,3-difluorobenzene indicates that the ring current quenching effects of substituents strongly depend on their position...

Fig. III.2. Electromagnet used for the rotational Zeeman effect measurements at Kiel. The upper yoke may be lifted by hydraulic jacks in order to insert spacers on top of the side yokes for different gap widths. Bearings in the side yokes are to allow for lateral access of the gauss-meter probe tip. The power connections (/mu = Amps, each coil) arc visible at the right front side. The overall length of the gap is 250 cm and the maximum field at a gap width of 6 cm is close to 21 kG, and at a gap of 0.6 cm the field is 31 kG...

Consider the rotational Zeeman effect of ethyleneoxide as an example for an asymmetric top molecule. The first investigation of the rotational Zeeman effect of ethyleneoxide has been carried out by the authors and W. Hiittner in 1968. In the meantime, the Zeeman splittings were remeasured with improved accuracy in an attempt to determine the sign of the electric dipole moment from the change of the g-values and rotational constants upon isotopic substitution (compare Chapter II). All numerical values will be taken from this later work 9). 

Quite generally, the analysis of the rotational Zeeman effect of asymmetric top molecules may be broken up into a sequence of three steps ... 

In the course of a typical rotational Zeeman effect investigation of an asymmetric top molecule 40 to 100 Zeeman satellites of different rotational transitions are recorded with both AM=0 and AM = 1 selection rules. According to Eq. (III. 13), this corresponds to a set of 40 to 100 linear equations from which the g-values and susceptibility anisotropies are calculated by a least squares procedure. As an illustration. Fig. III.12 shows recordings of the 2i2 - -22i rotational transition of ethylene oxide in exterior magnetic fields close to 25 kG. The +2.259... 

In a certain respect the einalysis of the rotational Zeeman effect may appear simpler in the case of symmetric top molecules as compared to the asymmetric top case, since the angular momentum eigenfunctions with K... 

The small modification due to electronic shielding of the exterior field is negligible in most cases of interest here. As will be demonstrated below, at field strengths close to 30 kG as are generally used in rotational Zeeman effect studies, the magnetic field can uncouple the nuclear spin from the overall rotation. Thus, we will use the uncoupled basis in order to set up the matrix of... 

D. H. S. would also like to thank his friends and colleagues H. Dreizler, A. Guamieri, E. Hamer, L. Engelbrecht, W. Czieslik, and J. Wiese for many helpful discussions on the rotational Zeeman effect. 

The components of the g tensor of the rotational magnetic moment gga =-0.213 0.005, gbb = -0.058 0.002, gcc = -0.068 0.002, In units of the nuclear magneton, were obtained from the first-order rotational Zeeman effect. The sign was chosen by consideration of the two resulting sets of molecular quadrupole moments (g>0 Implies Q to be unreasonably large) [1,3, 26, 27] see also the tables of magnetic constants of asymmetric top molecules [4]. 

Two magnetic susceptibility anisotropies were directly measured by the molecular rotational Zeeman effect as 2xaa-Xbb Xcc=-19-9 0.6 and 2xbb Xaa-Xcc=+12.8 1.2 [1]. Also see the microwave spectral tables [11]. The effect of intramolecular charge transfer on the diamagnetic components Xm was studied [2]. x= -13.19 and the components Xxx= -16.74, Xyy= -11.53, and Xzz= 11-30 (x OH, molecule in xz-plane) were calculated by a finite perturbation method (see below) with a gauge invariant Gaussian basis set. x 16 follows from the Pascal additivity rule [3]. 

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