The Boron Hydrides

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The diagrams of the experimentally determined structures of diborane, tetraborane, pentaborane and decaborane were obtained from Chemistry With Inorganic Qualitative Analysis, Moeller, Bailar, Kleinberg, Guss, Castellion, and Metz; Illustrations by Rino Dussi; page 835, figure 27.10; Copyright 1980 by Academic Press.

Okay, not exactly nuclear data, but it is of interest to chemists, and it might be useful in testing the shell models. I spent some time studying the boron hydrides because of boron's semiconducting properties and its unique electron-deficient bonds. Its the oddball stuff that leaps out at you and promises you discoveries, if only you can figure it out, and boron is clearly one of these oddballs. The pages above were originally published in my 1989 report, Time and Geometry: A Geometrical Unification of the Four Forces. At the time I did not yet have a solution for boron, but as you can see, I was trying to gleen insights into the boron nucleus from its bond geometry. (I never liked that shared electron junk in the chemistry books, seemed to me like a lot of dancing around to prop up an inadequate physical model.) I had already worked out a theory concerning the hybridization of metallic bonds I called "linearization," and in these diagrams I was attempting to apply the technique to the boron hydrides to see if it would adequately explain the geometric properties of the molecules. I hoped in the process to acquire some insights into the string geometry of boron's nuclear structure. But, because I did not yet have the nuclear geometry of boron, and could make no firm conclusions, and presented the data to physicists rather than chemists, the work was pretty much ignored.

The bottom line on these old diagrams is that I haven't found the time to go back and check the shell models against them. There may be pinning errors on them. At the time I did these I was not aware of too many shell structures, and I thought that all covalent bonds were mediated by radical strings and were doubly-pinned bonds. That turns out not to be the case. Singly-pinned and un-pinned covalent bonds seem to be available also, the doubly-pinned bond would likely be shorter and stronger than a singly-pinned bond, and the un-pinned would be largely ionic and less rigidly spaced. I recall that there were things that troubled me about these models. I do have them un-folded pretty good, and the electron count and positioning are good, but the string configurations of the covalent bonds may be incorrect. I think the linearized bonds (daisy-chains) are correct. A couple of shell stacking and pinning solutions for boron will tell the story, it would also be enormously helpful if somebody could verify which isotope(s) of boron were involved... that information was noticeably and frustratingly absent from the chemistry texts I perused. Oh, you might also notice a modified Lewis diagram in the images. I put the dots down to indicate electron positions. If this theory pans out, additional enhancements to the Lewis diagrams might be convenient, to indicate the pinning status of covalent and ionic bonds.

B10: An Interesting Discovery

05JUL97: As it turns out, I missed my 04JUL97 publication date. Its just as well, with all eyes focused on Mars, I doubt I would have made much of a splash. I knew I was going to be a bit late, so I went ahead and built a stacked shell model for B10. (I needed a shell-stacking example anyway.) As you can see, the stacked shells of P5-42P (upper shell) and N5-41P (lower shell) match the structure of both Boron atoms in the B2H6 configuration, and the two atoms on either end of the B4H10 configuration shown in the first figure above, and maybe all four of them if that extended bond length between the middle two boron atoms is not the result of hybridization. (I'm not a chemist, so I'm a bit sketchy on bond lengths and stuff.) As I was viewing this stacked shell solution, I realized that if I increased the frequency of the strings in the outer shell (or conversely, decreased the frequency of the strings in the inner shell), I could stack the neutron shell over the proton shell, yielding two hybridized orbitals and one normal lobe. It looks as though all the Boron Hydrides can be explained simply by the order of shell stacking of the B10 nucleus. If true, all the Boron atoms in the Pentaborane and Decaborane molecules are stacked with the neutron shell on top, or so it would appear from my early attempts to map the bonding strings of the Boron Hydrides. I mapped these molecules while searching for clues to the solution of P5 and N5 shells, in ignorance of what would result. It is surprising to me that the shell stacking order of Boron 10 appears to be so easily inverted. So, an interesting test of the predictions of this model would be to isolate the boron hydrides, and determine the isotope of boron involved. The model suggests they can all be fashioned with B10 nucleons. The B11 nucleus can come in a few flavors, one of which has 5 P.V.B.'s on the proton shell (P5-35P) and combines with one of the N6 polar star shells, yielding a configuration in which none of the orbitals are likely to be linearized, another having only two P.V.B.'s (P5-42P) combined with the spherical N6 shell solution (N6-30) which I would expect to typically serve as the lower shell, so again, not likely to hybridize an orbital. None of the solution sets I've found for the N6 shell require P.V.B.'s with the exception of the exotic N6-42S Belt-Sinusoidal solution. (And if you find one of those, I'd like to hear about it.) So, if its B11, it will most likely have 2, 5, or in the odd case of N6-42S, 4 or 7 pinned strings, but not 3 as in B10. Of course, it is the electrons the nucleus attracts that pin to the strings, and a nucleus can have more pinned strings than it has electron pairs to utilize them. The geometry of the boron hydrides might be achieved with B11, but there would be no hybridized orbitals unless the P5 shell takes the interior position, and then the hybridization might still not arise as the N6 and P5 shells cannot be stacked into complementary shell configurations. So, it is most likely that B10 is the primary isotope of boron involved in fabricating the boron hydrides.

Please note the hybridized orbital. Also note that the pinning of the radical strings are preferentially placed to turn this into a complementary shell model. The hybridized orbital is the one pinned to the lower nuclear shell, regardless of where you choose as its pinning site. Hybridization, in this case, metallic linearization of the bonding string, occurs because the pinned string is sandwiched between two quarks in adjacent complementary shells. This flattens the lobe, essentially squeezing the lepton string in the charge currents off the two Up quarks. (Remember that pinning of a string only emulates a Down quark, its a way the particle can "fudge" its cosmological spreadsheet, the quarks which have pinned strings are still essentially Up quarks at the fine structural level.) To maintain the complementary shell structure, if you move the hybridized orbital on the lower shell to a different up quark, you'll have to re-locate the pinning site of the displaced lobe on the upper shell. Keep in mind that the pinning sites are somewhat flexible, and the photo's above represent a B10 nucleus which can pin its orbitals three different ways, but those three results all have one linearized and two normal lobes. Inverting the shell order as described above will yield three more pinning solutions, but in that situation all the solutions will have two hybridized (from the lower shell) and one normal orbital lobe (from the upper shell).

Stereograms of Boron 10

Copyright 1997, 1999 by Arnold J. Barzydlo
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