All phenyl groups are planar, as is the cyclopentadiene ring of the dihydropentalene skeleton. Overcrowding at the fluorine position causes some deviations from the normal bond angles in the cyclopentene ring. Approximate values for the lengths of these axes were obtained from oscillating photographs, and the angles between the .. reciprocal axes were measured on an optical goniometer.
These weights were then used in the final least-squares refinement stages where they corresponded to the quantity Vw. In the following discussion, uniform structure factor, normalized uniform structure factor, and uniform scattering factors will be used. This large number of reflections would make direct application of the method described in the previous section excessively laborious.
The following relationships regarding the symbolic signs developed in the course of sign determination. So many sharp peaks were present in the E-map that no meaningful interpretation could be made without the help of the electron density map.
Signs determined from sign relationships
The signs (obtained from the structure factor calculation) of the 2,296 reflections with sin2e IA 2 < 0. 55 • The refinement was continued by the method of least squares (11) on the IBM 7094 computer with the 11Triclinic Least Squares program" (ref. 5, chapter 6) written by Dr. The initial stage of the refinement consisted of 15 least-squares cycles limited to the 609 reflections for which.
This R is larger than the previous values because all data was used in the structure factor calculation. All spatial parameters for the carbon atoms and hydrogen atoms were then placed into a separate 33 X 33 matrix for each phenyl group. remaining spatial parameters for the carbon atoms of the dihydropentalene skeleton and the two fluorine compounds were placed in a 30 × 30 matrix. 146 were used in the final cycle of least squares refinement because their calculated F's were greater than the minimum observable F. Consequently, only 3,577 of the 6,017 recorded reflections were used in the final cycle of least squares refinement.
The final atomic coordinates in terms of fractions of cell edges are listed in Table VIII, along with the shifts in the coordinates calculated in the last cycle, and the a's that are cal-. The final values for the anisotropic temperature parameters are listed in Table IX, together with the corresponding shifts calculated in the last cycle and the a's.
Spacial parameters
A negative sign in the sec-. o s. about c. second column indicates a "minor axis, 11 and the numerical value· following the negative sign is the minimum observable F .. after a vaiue in the second column means that the reflection in question has a weight of zero in given least squares refinement As indicated in Table VIII, the shifts for the hydrogen parameters in the last cycle 6£ the least squares refinement were of the same order of magnitude as the standard deviations Since the refinement therefore did not reach convergence with respect to the hydrogen not, there is no reason to list individual C-H distances and C-.
The longest and shortest C-H distances are 1. All other bond distances and angles are shown in Figures 2 and 3. Figures 2 and 3 show the molecule viewed along a direction in the plane defined by axes ~ and)?, and perpendicular to axis b. Except for the five-membered ring containing C(2), the ring systems of DHB form well-defined planes. The numbering of these surfaces is shown in figure 5. The direction cosines and deviations. of these planes) of the individual atoms are given in Table XI.
Least- squares planes
As expected from the sp2 .. hybridization of C{3) and C{4), the deviations from level VII are smaller than from level VII'. The angle between the normal to the two planes, VII and VIII, of the dihydropentalene skeleton is 28° 35', which is a consequence of the sp3. The phenyl rings, as expected from steric considerations, are rotated from 36° 55' to 88° 351 with respect to the corresponding rings of the dihydropentalene skeleton.
The angle of 28° 35' between the perpendiculars of planes VII and VIII is, for all practical purposes, the angle between the p-orbitals of C(4) and C(5). The reduced overlap does not appear to be severe enough to prevent conjugation between the C(3.) = C(4) double bond and the cyclopentadiene ring. The C-C bond distances in DHB clearly demonstrate the relationship between the hybridization of the carbon atoms involved and the bond distance.
This effect is discussed by Dewar and Schmeisling (4), · and the "expected" values with which the distances in DHB are compared are taken from their average values. However, it is not surprising that the C-F distances in DHB are longer than expected for a CF. The planarity of the phenyl rings requires that the average of the internal C-C-C bond angles in the phenyl rings is .120 0, A-meas-.
There is no reliable structural data for a cyclopentene ring with which to compare the angles in ring VII; however, except for the angles around C(l), they appear normal. The anisotropic temperature factors in Table IX were converted to thermal vibration ellipsoids by the method of Waser (29) with the "Temperature Ellipsoids. Program" (reference 5, chapter . 12) which. A qualitative examination of these results shows remarkable thermal vibrational anisotropy, , for the carbons in the phenyl rings.
Although no quantitative vibration analysis was performed, indications of rigid body vibrations and oscillations can be seen in Table XIII. Rings II, III, IV and VI exhibit the same type of oscillation, but in addition they oscillate along an arc:c perpendicular to each ring plane.
Ellipsoids of thermal vibration
A LOW TEMPERATURE REFINEMENT OF THE CYANURIC TRIAZIDE STRUCTURE
The crystal structure of cyanuric triazide (1, 3, 5-triazido- 2, 4, 6-triazine) was investigated independently by Hughes (5) and Knaggs (2, 8). In general, the overall molecular configuration was the same in both these works, but the following differences were noted: 1) Hughes found that the two crystallographically different C-N bonds in the triazine ring are of equal length, while Knaggs found them to be unequal life; 2) Hughes reported a nonlinear azide.
Crystallooraphlc 6
This R is large because new temperature factors are used instead of the negative ones from B2. All shifts in the final least-squares cycle were less than one-tenth of the respective standard deviations. The terminal azide nitrogen, N(5), (see Figure 5 for atom numbering) showed the largest deviation from the plane of the triazine ring.
The positions of the atoms defined by least squares are shown in Fourier for an asymmetric unit with x' s. A is indicated at the centers of atoms within the ring and the first nitrogen, N(3), of the azide groups. The noise appeared to be concentrated in the plane of the molecule and was significantly lower throughout the rest of the unit cell.
Despite the short distance between N(3) and atom H, the interaction between N(l) and N(4) together with similar interactions involving C(Z) (which is omitted in figure 7 to avoid overcrowding the drawing ), causes the angle N( l)-C(2)-N(3) 'i 119. N( l') is the nitrogen in the triazine ring related to N( 1) by the operation; of the b axis. The following programs and subroutines were written in the Macro Assembly Program (MAP) language (4) as part of the CRYRM crystallographic computer system (1.
Both operations (scaling and Howells, Phillips, and Rogers calculation) can be performed simultaneously during the second pass of the data. Chemical evidence (8, 9) indicates the ability of the two molecular halves to pass over each other in the thermochromic transition. Therefore, even with phenyl groups, which are perpendicular to the plane of the naphthacene core, considerable tension is noticeable in the structure.
Only B 6H from the BnHn series. Other interesting structures have been observed in the carborane series, Bn C. The following carboranes are known: B. 6 carboranes are isoelectronic with the. 18, should be observed on the low field side of the multiplet in the spectrum of B-2. Molecular scale models (see Figures 6 and 7, reference 7) show that one of the hydrogen atoms on both the 1 and .
