For the linear XYZ molecule, with two non-degenerate and one doubly degenerate vibrations, one Bg value and three a values must be determined [Pg.12]

For bent XYZ molecules there are several possible choices of geometrical variables, as discussed in Chapter 3. [Pg.98]

Figure 2. The space-fixed (XYZ) and body-fixed xyz) frames in a diatomic molecule AB. The nuclei are at A and B, and 1 represents the location of a typical electron. The results of inversions of their SF coordinates are A A, B B, and 1 1, respectively. After one executes only the reinversion of the electronic SF coordinates, one obtains 1 — 1. The net effect is then the exchange of the SF nuclear coordinates alone. |

Figure 4.15 Schematic representation of a portion of the spectrum of a bent XYZ local-mode molecule. |

As discussed in Ref. [1], we describe the rotation of the molecule by means of a molecule-fixed axis system xyz defined in terms of Eckart and Sayvetz conditions (see Ref. [1] and references therein). The orientation of the xyz axis system relative to the XYZ system is defined by the three standard Euler angles (6, (j), %) [1]. To simplify equation (4), we must first express the space-fixed dipole moment components (p,x> Mz) in this equation in terms of the components (p. py, p along the molecule-fixed axes. This transformation is most easily done by rewriting the dipole moment components in terms of so-called irreducible spherical tensor operators. In the notation in Ref. [3], the space-fixed irreducible tensor operators are [Pg.214]

In order to represent 3D molecular models it is necessary to supply structure files with 3D information (e.g., pdb, xyz, df, mol, etc.. If structures from a structure editor are used directly, the files do not normally include 3D data. Indusion of such data can be achieved only via 3D structure generators, force-field calculations, etc. 3D structures can then be represented in various display modes, e.g., wire frame, balls and sticks, space-filling (see Section 2.11). Proteins are visualized by various representations of helices, / -strains, or tertiary structures. An additional feature is the ability to color the atoms according to subunits, temperature, or chain types. During all such operations the molecule can be interactively moved, rotated, or zoomed by the user. [Pg.146]

Table 6 Total atomic population Gt on atom i in some linear XYZ molecules with different basis sets424 |

The ab initio calculations produce values of fiy, i.e., the components of the electronically averaged dipole moment along the x y z axes defined above. In order to calculate molecular line strengths, however, we must determine, as functions of the vibrational coordinates, the dipole moment components along the molecule-fixed axes xyz (see equation (23)) defined by Eckart and Sayvetz conditions [1]. [Pg.221]

If the moments / of more than one species are required to determine the molecular structure, this averaging is no longer feasible. The -structure must then be obtained by direct calculation (or by a least-squares fit, if possible) using a substitution data set composed in a completely balanced manner of complementary sets of isotopomers. The linear XYZ molecule, e.g., is a problem which must be treated in this way. This restructure is still expected to approximate the restructure better than the restructure does. [Pg.109]

The first zinc enzyme to be discovered was carbonic anhydrase in 1940, followed by car-boxypeptidase A some 14 years later. They both represent the archetype of mono-zinc enzymes, with a central catalytically active Zn2+ atom bound to three protein ligands, and the fourth site occupied by a water molecule. Yet, despite the overall similarity of catalytic zinc sites with regard to their common tetrahedral [(XYZ)Zn2+-OH2] structure, these mononuclear zinc enzymes catalyse a wide variety of reactions, as pointed out above. The mechanism of action of the majority of zinc enzymes centres around the zinc-bound water molecule, [Pg.198]

Let us now investigate the effects which the two different models proposed for the activated state have upon the quantities kjk a, The difference in degeneracy between the two models will introduce a change of ten per cent at the most on account of the small magnitude of l+J(Wj,+ ) /24. In considering the contributions of the entropy terms to i/ 2a finds, from Lechner s formulas for the vibrations of a bent XYZ molecule, that the ratio (vi rather insensitive to [Pg.56]

The anticodon region consists of seven nucleotides, and it recognizes the three-letter codon in mRNA (Figure 38-2). The sequence read from the 3 to 5 direction in that anticodon loop consists of a variable base-modified purine-XYZ-pyrimidine-pyrimidine-5h Note that this direction of reading the anticodon is 3 " to 5 whereas the genetic code in Table 38—1 is read 5 to 3 since the codon and the anticodon loop of the mRNA and tRNA molecules, respectively, are antipar-allel in their complementarity just like all other inter-molecular interactions between nucleic acid strands. [Pg.360]

As a particular example of materials with high spatial symmetry, we consider first an isotropic chiral bulk medium. Such a medium is, for example, an isotropic solution of enantiomerically pure molecules. Such material has arbitrary rotations in three dimensions as symmetry operations. Under rotations, the electric and magnetic quantities transform similarly. As a consequence, the nonvanishing components of y(2),eee, y 2)-een and y,2)jnee are the same. Due to the isotropy of the medium, each tensor has only one independent component of the xyz type [Pg.564]

See also in sourсe #XX -- [ Pg.116 , Pg.117 ]

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