The approximate symmetry of the band is due to the fact that Bi — Bq, that is, the vibration-rotation interaction constant (Equation 5.25) is small. If we assume that B = Bq = B and neglect centrifugal distortion the wavenumbers of the i -branch transitions, v[i (J)], are given by [Pg.149]

To better appreciate the effects of approximate symmetries, the consequences of exact symmetries are examined first. [Pg.8]

Another term for approximate symmetry is broken symmetry. The symmetry breaking factor is whatever factor is responsible for the deviation of e from zero. As an example, any crystal has broken translational symmetry. The exact symmetry limit is an infinite crystal, obviously unattainable in practice. [Pg.8]

Antibiotic Cation Number of coordinating oxygen atoms ) /approximate symmetry of coordination sphere Approximate shape and size of complex Ref. [Pg.121]

XRD analysis of (n-BuLi)e (291b) reveals that the cluster of six Li atoms has an approximate symmetry (trigonal antiprismatic), with the six w-Bu groups placed around the axis of rotation. Each Li atom is coordinated to four Li atoms, one a-C and one /3-C atom the conformation of the six n-Bu groups is such that the a-C atom is coordinated to the three Li atoms of a face of the distorted octahedron and the fi-C atom to one of them only ". [Pg.385]

The structure of compound 133 (Fig. 12) was determined by X-ray diffraction. It has an approximate symmetry with planar nitrogen atoms. An N—N unit is shared by the two five-membered rings, which are not planar. The torsion angles Si8-Nl 1-Nl 1 -Si8 and Sil2-Nll-Nll -Sil2 are found to be -45° and -37°. (See Table XX.) [Pg.39]

From Equations (6.27) and (6.28) it follows that the zero gap, v[/ (0)J — v[P(l)], is 4B and that the spacing is 2B between adjacent P-branch lines and also between adjacent P-branch lines, hence the approximate symmetry of the band. [Pg.150]

In connection to control in dynamics I would like to take here a general point of view in terms of symmetries (see Scheme 1) We would start with control of some symmetries in an initial state and follow their time dependence. This can be used as a test of fundamental symmetries, such as parity, P, time reversal symmetry, T, CP, and CPT, or else we can use the procedure to discover and analyze certain approximate symmetries of the molecular dynamics such as nuclear spin symmetry species [2], or certain structural vibrational, rotational symmetries [3]. [Pg.377]

We have here kept the description of the radiative decay rates fairly general and did not discuss their exact relations to the vibronic states (in particular within the Franck-Condon approximation). This description is sufficient for our purpose here and more adapted to the generalization to the case of MEF. It is nevertheless worth mentioning that there is an approximate symmetry between the transitions for absorption Sg(0) —> S 0) ) and those [Pg.30]

Not too many theories have been formulated from this point of view and some of the more interesting cases are at the speculative stage of development. Even so, it is remarkable how some of the most enigmatic of natural phenomena have no convincing explanation apart from broken-symmetry theories. Included are the initiation or nucleation of phase transitions, superconductivity (T4.5.1), the arrow of time (entropy) and the cosmic imbalance between matter and antimatter. The beauty of the world, indeed seems to lie in approximate symmetries. [Pg.38]

Note that interpretations of the time-reversal experiments are only valid in strictly euclidean space-time. This condition is rarely emphasized by authors who state that all laws of physics are time-reversible, except for the law of entropy. Fact is that entropy is the only macroscopic state function which is routinely observed to be irreversible. One common explanation is to hint that entropy is an emergent property of macro systems and hence undefined for microsystems. Even so, the mystery of the microscopic origin of entropy remains. A plausible explanation may be provided if the assumed euclidean geometry of space-time is recognized as an approximate symmetry as demanded by general relativity. [Pg.12]

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