Standard orientation

The nonlinear response of an individual molecule depends on die orientation of the molecule with respect to the polarization of the applied and detected electric fields. The same situation prevails for an ensemble of molecules at an interface. It follows that we may gamer infonnation about molecular orientation at surfaces and interfaces by appropriate measurements of the polarization dependence of the nonlinear response, taken together with a model for the nonlinear response of the relevant molecule in a standard orientation. 

This section displays positioning of the atoms in the molecule used by the program internally, in Cartesian coordinates. This orientation is chosen for maximum calculation efficiency, and corresponds to placing the center of nuclear charge for the molecule at the origin. Most molecular properties are reported with respect to the standard orientation. Note that this orientation usually does not correspond to the one used in the input molecule specification the latter is printed earlier in the output as the Z-matrix orientation. ... 

The dipole moment is broken down into X, Y, and Z components. In this case, the dipole moment is entirely along the Z-axis. By referring to the standard orientation for the molecule, we realize that this is pointing away from the oxygen atom, which is... 

What is the standard orientation of the molecule In what plane do most of the atoms lie ... 

The RR and SS forms both have a dipole moment of 2.8 debye along the negative Z-axis. To locate this within the molecule, we need to examine the standard orientation. Here is the output for the RR form ... 

Gaussian output indicates the number of basis functions for a molecule in its output, just below the standard orientation ... 

The Optimized Parameters are the predicted bond lengths (named Rn), bond angles (An) and dihedral angles (Dn) for the optimized structure. The applicable atom numbers are in parentheses. Atoms in the molecule are numbered according to their order in the molecule specification section. These center numbers also appear in the Cartesian coordinates for the optimized strucmre expressed in the standard orientation which follows the listing of the optimized parameters. 

In addition to the frequencies and intensities, the output also displays the displacements of the nuclei corresponding to the normal mode associated with that spectral line. The displacements are presented as XYZ coordinates, in the standard orientation ... 

The tensor is given in lower-triangular format (i.e. a. standard orientation. The Approx polarizability line gives the results of the cruder polarizability estimate using sum-over-states perturbation theory, which is suggested by some older texts. 

The tensors are again in lower triangular (tetrahedral) format, expressed here in the standard orientation. 

This table gives the displacements for the normal mode corresponding to the imaginary frequency in terms of redundant internal coordinates (several zero-valued coordinates have been eliminated). The most significant values in this list are for the dihedral angles D1 through D6. When we examine the standard orientation, we realize that such motion corresponds to a rotation of the methyl group. 

Examining the standard orientation for the molecule verifies that angles A8 through AlO and dihedral angles D7 through DIO involve the atoms in question. ... 

The standard orientation for the molecule, and specifically the coordinates of the atoms of interest. Sometimes, the atomic numbers alone are enough to identify the atoms you want, but for larger systems, the center numbeis will be needed to pick out specific atoms within the standard orientation. Their coordinates will enable you to characterize the expected components of the displacement for the motion under investigation. 

System Standard Orientation (Cj, C2) Expected Displacement Scaled Frequency Peak Number... 

System Molecular Formula Center s (C,0) Standard Orientation (C,0) Exp. Displ. Scaled Freq. Peak ... 

Here is the stationary point found by the optimization, in its standard orientation ... 

From the standard orientation, we see that the plane of the molecule is the XY plane. Both orbitals are composed of only p components, indicating that they are Jt orbitals. Thus, this excited state corresponds to the Jt— Jt transition. 

The standard orientation is the coordinate system used internally by the program as it performs the calcula on, chosen to optimize performance. The origin is placed at the molecule s center of nuclear charge. Here, the oxygen atom sits on the Y-axis above the origin, and the two hydrogen atoms are f ced below it in die XY plane. 

In order to demonstrate what the various types of turns actually look like, Figs. 31 through 34 show stereo views of turn examples from real structures that have angles very close to the defining values for each type. Type III is illustrated for completeness, but it cannot be distinguished from type I by inspection unless it is part of a continuing 310-helix. Types IV and V are not shown, because type IV is a miscellaneous category and there are no ideal cases of type V (see Fig. 36). The turns are all shown in approximately the same standard orientation with the mean plane of the four a-carbons in the plane of the... 

Three distinct structural types are available for a tetracoordinated fragment a square planar structure of symmetry, a nonplanar square pyramid with C4t> symmetry, a nonplanar structure with Cjv symmetry (which would result from the removal of two cis ligands from an octahedral MLg), and the tetrahedral structure of symmetry Td- These are shown in Figure 13.5 in the standard orientation. The orbitals of the Z>4/, structure... 

Example /. The net of vertical and horizontal reflection lines is rather obvious, as are the twofold axes. The fourfold axes may be slightly less obvious. Once they are found, however, it becomes clear that we need to turn the pattern 45° in order to put it into the standard orientation for one of the square symmetries, / 4, p4m, or p4g. Since we have seen the net of reflection lines we know it must be either p4m or / 4g, and when we note that the reflection lines pass between, not through, the fourfold axes we conclude that it is p4g. The presence of the two different nets of glide lines, only one net passing through the fourfold axes, is not obvious. The reader should convince himself that they are there. The second diagram in column C shows one example of each type of glide, g, takes brick AB to A B while g takes brick... 

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