Molecular symmetry center

In some studies of pure N2 solids more realistic potentials have been used by considering electrostatic interaction in addition. The electrostatic interaction sites are positive charges of q = cj2 = 0.313e at distances 1.044 A away from the molecular center-of-mass on the molecular symmetry axis and negative charges = /4 = —0.313 e at distances 0.874 A respectively [143-145]. 

Therefore, ionization events occurring at lower I.P. appear more interesting since they involve the d-type metal-centered orbitals and correspond to the dn configurations in the ligand-field splitting patterns appropriate to the molecular symmetry of M(CO)n, Thus we have one ionization band with multiplet structure, at 7.52 and 7.88 eV, from the t%g configuration of octahedral V(CO)6 (21), one narrow band at 8.42 eV from in octahedral Cr(CO)6 (22), two bands of equal intensity at 8.60... 

Next consider Sx and S2 axes. Since the only kind of reflection that sends the momental ellipsoid into an equivalent configuration is one in a plane containing two principal axes, a molecular symmetry plane contains two of the principal axes and is perpendicular to the third. A molecular center of symmetry coincides with the center of mass, which is the point of intersection of the three principal axes. 

If this molecule is assumed to consist of two benzene rings placed on either side of the chromium atom so that their planes are parallel and their Cb axes colinear, the molecular symmetry may be Z)w or depending on whether the rings are staggered or eclipsed. X-ray study of the crystalline compound shows that the chromium atom is at a center of inversion so that in the crystalline state at least the molecular point group is D<. There is evidence from infrared and Raman spectra that the molecule has D symmetry in solution. 

Just as with vibronically allowed transitions, in symmetry groups in which all Cartesian axes are not equivalent (noncubic groups), it is found that, in general, transitions will be allowed only for certain orientations of the electric vector of the incident light. One class of compounds in which this phenomenon has been studied both theoretically and experimentally consists of trischelate compounds such as tris(acetylacetonato)M(III) and tris(oxalato)M(III) complexes. In these complexes the six ligand atoms form an approximately octahedral array but the true molecular symmetry is only Dy Since there is no center of symmetry in these molecules, the pure electronic selection rules might be expected to be dominant. 

Johnson and Rice used an LCAO continuum orbital constructed of atomic phase-shifted coulomb functions. Such an orbital displays all of the aforementioned properties, and has only one obvious deficiency— because of large interatomic overlap, the wavefunction does not vanish at each of the nuclei of the molecule. Use of the LCAO representation of the wavefunction is equivalent to picturing the molecule as composed of individual atoms which act as independent scattering centers. However, all the overall molecular symmetry properties are accounted for, and interference effects are explicitly treated. Correlation effects appear through an assigned effective nuclear charge and corresponding quantum defects of the atomic functions. 

The molecular symmetry number (a) is a measure of the rotational degeneracy of the molecule. It is defined as the number of indistinguishable positions that can be obtained by rigidly rotating the molecule about its center mass. Symmetry numbers for spherical, conical, and cylindrical molecules, shapes with infinite axes of rotation, have o values of approximately 200, 20, and 20, respectively. Chemicals with no axes of symmetry have o = l. 

Naphthalene. Since Z = 2, the molecule occupies a site of symmetry I in other words, there is an inversion center in the middle of the C4a-C8a bond. With reference to the atom numbering system shown below, the asymmetric unit can be taken as one of the right (1 1,4a), left (5-8,8a), upper (1,2,7,8,8a) or lower (3,4,4a, 5,6) half of the molecule. Note that the idealized molecular symmetry P>2h of naphthalene is not fully utilized in the solid state, and some of the chemically identical bond distances and bond angles have different measured values. 

Hexamethylbenzene, CeMe6, exists as a plastic phase I above 383 K, a room-temperature phase II, and a low-temperature phase III below 117.5 K. Both phase II and phase III crystallize in space group PI with Z = L The molecule is therefore located at an inversion center, and the site symmetry I is much lower than the idealized molecular symmetry of >6h- The asymmetric unit consists of one-half of the molecule. 

The all-iron(III) nature of 22 and 23 was determined by Mossbauer spectroscopy. In [Fe4(L7)4] (22), four octahedrally coordinated iron centers constitute the apices of a tetrahedron, and the four tripodal, tris(bidentate) ligands (L7)3 are centered above the triangular faces of the tetrahedron [86]. Hence, 22 has nearly / -molecular symmetry, and the crystals are composed as racemic mixtures of homoconfigurational (A,A,A,A)/(A,A,A,A)-/ac stereoisomers. There is no evidence that the cavity of the tetrahedron hosts a guest (Fig. 8, top) [49, 62, 91-99]. 

Complex [Fe6(L8)6] (23) can be described as having idealized D3-molecular symmetry. The iron centers define the apices of a distorted trigonal antiprism in which six tripodal, tris(bidentate) ligands (L8)3 make up the equatorial faces, leaving the top and bottom triangles unoccupied. All six iron(III) ions are... 

In principle, all the six-membered ferric wheels [Fe6CI6(LM l7)6] (39) are isostructural and have idealized S g-molecular symmetry. However, there are fundamental differences concerning their crystal packing. For example, all the disk-like molecules of 39a are arranged in parallel and are piled in cylindrical columns, with all the iron centers superimposed. Each column is surrounded by six parallel columns, which are alternately dislocated by 1/3 c and 2/3 c against the central one (Fig. 13). 

A second 7r interaction between that it orbital of the organic group and a molecular orbital of a symmetry centered on the metal fragment (Fig. 11), although of less energy than the former tt interaction, results in a calculated bond order between M and Ca of between 2 and 3 and, more importantly, indicates that rotation of the vinylidene unit about the M-Ca bond should be facile. This prediction is easily deduced from the lone pair... 

The character tables of Tables 7.6 and 7.7 are best explained by example. For instance, consider the bent molecule NO2, which belongs to point group Czv, and choose a minimum basis-set of atomic orbitals centered on the three atoms (Fig. 7.7). To exploit the molecular symmetry, it is wise to orient the molecule with the z axis bisecting the ONObond angle and with the x axis normal to the N02 molecular plane. Consider what will happen to the column vector representing 2px orbitals centered on the three atoms 2px(N), 2px 0A), 2px(0B) ... 

Fig. 11 Relative size and orientation of dipole moment vectors of the ground state black) and the excited states JMLCT (bJA ), 3IL (b3A"), and 3MLCT (a3A") of [Re(Etpy)(CO)3(bpy)]+, projected onto the optimized ground-state molecular structure. Dipole moment vectors originate in the center of charge calculated using Mulliken population analysis. They lie in the molecular symmetry plane. (Calculated by TD-DFT G03/PBE0/vacuum at the optimized ground state geometry.) Reproduced with permission from [76]...

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