Semitopological Representation of Electronic Structure of Complex Boron Hydrides and Ions Using styx Numbers S. K. Dikshit and Ramsharan Singh 1. I. T. Kanpur 208016,India Several forms of equations of balance for boron hydridesL4 have been suggested. These equations pertain to orbital, electron, and hydrogen balance. By using these three equations, it is possible to derive a set of styx values for a given boron hydride, its ion or pseudoborohydride (e.g., C4H7+which is isoelectronic with B&-). The equations of balance do not always give unequivocal answers, but they do assist us by limiting the structure to be considered. In choosing the best structures, the following additional considerations are found u s e l l . 1. Every pair of adjacent B's muat be bonded to each other through a E B , EH-B, or E E B bond. 2. Pairs of B atoms bonded by a B-B bond may not also be bonded to one another by the followingbonds.
3. Nonadjacent pairs of B atoms may not be bonded by frame-
work bonds. 4.Other aspects being equal, the preferred structureis the one with the highest symmetry. From given sets of styx values for a particnlar boron hydride, the most appropriate set is chosen and corresponding to that set the most symmetrical structures are drawn. For example, in case of B5H9three sets of styx numbers are possible solutions: 2302, 3211,and 4120. Based on additional considerations mentioned above, the first two solutions are eliminated. leavinrc the 4120 structure. All ~ o s s i hle semitopological representations corresponding tb sty1 n the fiimre for pentaborane. set of 4120 are ~ v e in Of the valence structures presented above, i t is evident that no single structure of B5H9adequately reflects its molecular symmetry, C4".In order to presume such symmetry, resonance forms must be considered. When the valence strncture is drawn using an open bond,
two symmetry-equivalent forms are required. When the structure is drawn using a closed bond,
four symmetry-equivalent structures are required to presume molecular symmetry. Thus, the entire group of symmetry-equivalent structures taken together represent the symmetry of the B5
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Journal of Chemical Education
All possible semitopological representations corresponding to styx set of 4120.
framework. AC4operation yields each successive structure from the urecedine one. Of course. the existence of several symmetry-equivalent structures wrresponds to electron delocalization. The semitopological scheme has its limitations. For the symmetrical closed structures and even for the larger and more symmetrical open structures, i t becomes difficulkif not impossible-to write simple satisfactory structures given above. One structure for a given hydride (ion)may be inwmpatible with the high symmetry of the molecule. The dficnlty can be overcome by treating the structure as resonance hybrid of several canonical structures. With increasing size and symmetry, however, this sort of approach becomes very cumbersome. Because all canonical stmctures will not be equivalent, it becomes desirable to employ a n MO description, wnsistent with the full molecular symmetry and naturally incorporating delocalization.
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'~berhardt,W. H.: Crawford, B. L. Jr.; Lipsmmb, W. N. J. Chem. Ph s 1 9 5 4 , Z 989. {ibcomb, W. N. J. Phys. Chem. 1958, 62,381. 3Muetterties,E. L. Boron Hydride Chemistw Academic Press: New York 1975, p. 90. 4Grenda. S. C. J. Chem. Educ. 1989.66,639.
