Symmetry linear molecules

Linear molecules belong to the axial rotation group. Their symmetry is intermediate in complexity between nonlinear molecules and atoms. 

Atoms, linear molecules, and non-linear molecules have orbitals which can be labeled either according to the symmetry appropriate for that isolated species or for the species in an environment which produces lower symmetry. These orbitals should be viewed as regions of space in which electrons can move, with, of course, at most two electrons (of opposite spin) in each orbital. Specification of a particular occupancy of the set of orbitals available to the system gives an electronic configuration. For example,... 

Finally, for linear molecules in Z states, the wavefunctions can be labeled by one additional quantum number that relates to their symmetry under reflection of all electrons through a ay plane passing through the molecule s Coo axis. If F is even, a + sign is appended as a superscript to the term symbol if F is odd, a - sign is added. 

For non-linear molecules of the spherical or symmetric top variety, pf j(Rg) (or dpf j/dRa) may be aligned along or perdendicular to a symmetry axis of the molecule. The selection rules that result are... 

The point group is derived from by the inclusion of U , therefore, all linear molecules with a plane of symmetry perpendicular to the axis belong to D f. Acetylene... 

In Section 4.3.f it was shown that there are 3N — 5 normal vibrations in a linear molecule and 3N — 6 in a non-linear molecule, where N is the number of atoms in the molecule. There is a set of fairly simple rules for determining the number of vibrations belonging to each of the symmetry species of the point group to which the molecule belongs. These rules involve the concept of sets of equivalent nuclei. Nuclei form a set if they can be transformed into one another by any of the symmetry operations of the point group. For example, in the C2 point group there can be, as illustrated in Figure 6.18, four kinds of set ... 

As for diatomic molecules (Section 7.2.5.2) fhe vibrational (vibronic) transitions accompanying an electronic transition fall into the general categories of progressions and sequences, as illustrated in Figure 7.18. The main differences in a polyatomic molecule are that there are 3A — 6 (or 3A — 5 for a linear molecule) vibrations - not just one - and that some of these lower the symmetry of the molecule as they are non-totally symmetric. 

For a removal attempt a molecule is selected irrespective of its orientation. To enhance the efficiency of addition attempts in cases where the system possesses a high degree of orientational order, the orientation of the molecule to be added is selected in a biased way from a distribution function. For a system of linear molecules this distribution, say, g u n ), depends on the unit vector u parallel to the molecule s symmetry axis (the so-called microscopic director [70,71]) and on the macroscopic director h which is a measure of the average orientation in the entire sample [72]. The distribution g can be chosen in various ways, depending on the physical nature of the fluid (see below). However, g u n ) must be normalized to one [73,74]. In other words, an addition is attempted with a preferred orientation of the molecule determined by the macroscopic director n of the entire simulation cell. The position of the center of mass of the molecule is again chosen randomly. According to the principle of detailed balance the probability for a realization of an addition attempt is given by [73]... 

There is evidence that the reactions can take place by all three mechanisms, depending on the structure of the reactants. A thermal [ 2, + 2s] mechanism is ruled out for most of these substrates by the orbital symmetry rules, but a [ 2s + mechanism is allowed (p. 1072), and there is much evidence that ketenes and certain other linear molecules in which the steric hindrance to such an approach is... 

The final expression is the classical limit, valid above a certain critical temperature, which, however, in practical cases is low (i.e. 85 K for H2, 3 K for CO). For a homonuclear or a symmetric linear molecule, the factor a equals 2, while for a het-eronuclear molecule cr=l (Tab. 3.1). This symmetry factor stems from the indistinguishable permutations the molecule may undergo due to the rotation and actually also involves the nuclear partition function. The symmetry factor can be estimated directly from the symmetry of the molecule. 

If a linear molecule contains a center of symmetry, the quantum number J is restricted to either odd or even values. Thus, the sum in Eq. (58) is composed of two parts that approach the same value as J increases, viz-... 

For linear molecules that lack a center of symmetry, Eq. (58) is applicable and at temperatures significantly greater than the rotational temperature , 9 s= h2/%n2lk, the sum in Eq. (58) can be replaced by an integral. This... 

For linear molecules or ions the symbols are usually those derived from the term symbols for the electronic states of diatomic and other linear molecules. A capital Greek letter E, n, A, O,... is used, corresponding to k — 0,1,2,3,..., where A. is the quantum number for rotation about the molecular axis. For E species a superscript + or - is added to indicate the symmetry with respect to a plane that contains the molecular axis. 

Methylzinc hydride was formed by the insertion of excited zinc atoms, in their 3Pi state, into the C-H bond of methane in an argon matrix.229 The MeZnH product was characterized on the basis of its infrared spectrum and determined to be a linear molecule with C v symmetry. The band at 1866.1 cm-1 is due the Zn-H stretch, while the band at 565.5 cm-1 was assigned to the Zn-C stretching vibration. Additional bands for isotopically labeled species were also reported. 

Linear molecules belong to one of two symmetry types. The first is typified by HCN, which has the... 

Linear molecules having a different symmetry type are typified by C02, which has the structure... 

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