Open orbits

If the picture is correct then we see that the observed order of activation energies which is largest for molecular reactions, small for radical-molecule reactions and nearly zero for radical-radical reactions, falls into a 1 1 relation with the acid-base model. The radical-radical reactions have the open orbital and the electron donor, hence little promotion energy to form an attractive pair. The radical-molecule reactions have one open orbital but require polarization of the molecule in order to form the complimentary acid or base. For the molecule-molecule addition type reaction, complimentary polarization of both species must take place for an attractive transition state to form and the activation energy is the highest. 

The aim of this article is to show that the new quasi-two-dimensional organic conductor p -(BEDO-TTF)5[CsHg(SCN)4]2 [hereafter called (BEDO)CsHg] (BEDO-TTF - bis-(ethylenedioxy)tetrathiafulvalene) which contains closed and open orbits displays rather complicated oscillatory spectra associated with magnetic breakdown (MB) and quantum interference (QI) effects. Tight binding band structure calculations for this compound are proposed to characterise its Fermi surface. The aim of the article includes also an investigation of the optical conductivity anisotropy with polarized infrared reflectance spectra. 

The closed orbit on the left represents a system in vibration (also called libration) and the open orbit on the right corresponds to rotation. Vibra-... 

In the reconstructed FS the original quasi-lD bands disappear under the SDW potential but a new pair of open sheets tilted by against the original ones appear. Small lens-like closed orbits (Ai) remain which may be separated by only small energy barriers from the open orbits. Therefore, it is suggested... 

In all cases, however, a pronounced increase in the rate of recombination occurs with increasing pressure, corresponding to a three-body process of rate coefficient a,. As opposed to the close similarity of the (Xj values, the values of a, were found to increase by two orders of magnitude in going from iso pentane to water vapor. The magnitude of a, could in fact be directly related to the efficiency of the different molecules at exchanging energy with electrons while within the coulomb well, which results in closed rather than open orbits. 

In Ref. 20 several choices of a Fock operator for a general CASSCF reference state were discussed. They were all constructed such that for our high-spin example, the f" Fock matrix is obtained for the open orbitals. These modified Fock operators were constructed with the aid of a matrix K, defined as... 

A diradical is a molecule with two open orbitals, each containing one electron. Consider as an example twisted ethylene D2d symmetry, see Fig. 3.9). The HOMO is a degenerate e-orbital, occupied by two electrons. Construct the diradical states for this molecule, and determine their symmetries. 

The Yb metal was the first rare earth metal studied with the de Haas-van Alphen measurement. Tanuma et al. (1967) purified a piece of raw metal by the vacuum distillation method. A single crystal specimen was obtained by spark cutting a large grain in a vapor condensed ingot. The resistivity ratio of the specimen was not reported. The crystal structure was determined to be fee by X-ray analysis at room temperature. Two de Haas-van Alphen frequencies were observed, and the authors suggested that they came from two separate pieces of Fermi surface. Datars and Tanuma (1968) deduced from magnetoresistance measurements at 1.3 K with fields up to 20 KG that there were no open orbits in Yb. Therefore, they concluded that Yb is semimetallic with two small, closed pieces of Fermi surface. ... 

When some of the cyclotron orbits are not closed but form open orbits, the magnetoresistance increases quadratically and depends on the current direction as... 

Ap/p H cos a, where a is the angle between the current direction and the open orbit direction in -space. This is true regardless of the state of compensation. 

If we count the number of valence electrons in a primitive cell, most of the lanthanide compounds are even in number, meaning that they are compensated metals. In this case the transverse magnetoresistance increases as /f" (I 2) for a general direction of the field. Note that the integer n is not equal to 2 because the high-field condition is not fully satisfied in the real compounds. When the magnetoresistance saturates for a particular field direction, often a symmetrical direction, there exist some open orbits whose directions are parallel to JxH, namely a=Ji/2 in -space. 

Experimentally the current direction is fixed to a crystal symmetry axis of the sample and the sample is slowly rotated under constant magnetic field which is perpendicular to flie current direction. The presence of open orbits is revealed by (a) spikes against a low background for the uncompensated metal and (b) dips against a large background for the compensated metal. 

Magnetoresistance measurements were done for RBg. Reflecting the multiply connected Fermi surface, open orbits were observed for LaBg, PrBg and NdBe (Onuki et al. 1989d). 

Magnetoresistance experiments (Sellmyer et al. 1975) confirmed that YZn is an uncompensated metal with a multiply connected Fermi surface which favors open orbits, at least, along the (110) direction. These results are consistent widi the results of band calculations mentioned above. 

Fig. 41. (a) Angular and (b) field dependencies of the magnetoresistance in LaSnj (Umehara et al. 1991a). Open orbits occur in the stippled region in (a). The solid lines connecting the data are guidelines. 

On the other hand, the magnetoresistance of CeSns in fig. 43 increases in the all field directions (Umehara et al. 1990), indicating compensated carriers and the absence of open orbits in CeSna, which may be compared to the uncompensated state of LaSns. These results indicate that Ce is tetravalent, Ce, confirming the itinerant nature of die 4f electron. 

The results of magnetoresistances for LaSna and CeSna are consistent with the results of the band calculations mentioned above (Hasegawa and Yamagami 1991, Hasegawa et al. 1990). The multiply connected band 8 Fermi surface in LaSna favors the experimentally observed open orbits. All of the Fermi surfaces in CeSna are closed ones, in good agreement widi the compensated metal of CeSna without open orbits. 

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