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Downloaded by UNIV OF CALIFORNIA SAN DIEGO on September 28, 2016 | http://pubs.acs.org Publication Date: January 1, 1966 | doi: 10.1021/ba-1966-0054.ch002
The Feasibility of Predicting Properties of N, F Oxidizers by Quantum Chemical Calculations JOYCE J. K A U F M A N , LOUIS A . B U R N E L L E , and J O N R. H A M A N N Research Institute for Advanced Studies, Martin Co., Baltimore, M d .
In this research on N, F compounds we examined such properties as relative stabilities, possible existence of new species, ionization potentials, electron affinities, π-bonding, and charge distributions through extended Hückel LCAO -MO calculations and through analysis of the calculated wave functions and energy levels. It has been possible to: (1) predict the order of the N — F bond lengths in NF , NF , trans-N F and cis-N F and of the N—N bond lengths in cis- and trans-N F (before knowing experimental results); (2) predict the greater stability of cis-N F relative to transN F ; (3) reproduce the experimental ionization potential of NF ; (4) predict the order of the symmetric N—F stretch frequencies in NF , NF , trans-N F , N F , and cis-N F ; (5) verify the supposition of π-bonding in NF and NF leading to a greater N — F bond dissociation energy in these species than in NF . 2
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' T ' h i s research conducts a quantum chemical investigation of energetic N , F compounds to provide insight into the fundamental bonding and behavior of these species. This insight is necessary for guiding and plan ning the overall experimental research project in the oxidizer field. Our original theoretical interest in N , F compounds was stimulated by the observation of an apparently anomalous pattern i n bond dissocia tion energies of some of these compounds. I n 1961 at an American Chemical Society Symposium on Chemical Bonding i n Inorganic Systems, C. B . Colburn of Rohm and Haas at Huntsville mentioned that while the Ν—H dissociation energies i n N H were D ( H N — H ) > D ( H N — H ) > D ( N — H ) , i n N F the order was D ( F N — F ) < D ( F N — F ) . A t that time we postulated that the reason must largely be caused b y the fact that 3
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Holzmann; Advanced Propellant Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1966.
2.
KAUFMAN ET AL.
9
Predicting Ν, F Oxidizers
although there is virtually no ^-bonding i n N F , there must be a consider able amount of F - » Ν îr-bonding i n N F which is planar (15). (Our subsequent calculations have confirmed this F -> Ν π-bonding i n N F . ) ir-Bonding i n N F would increase the N—F bond strength over that i n N F . The close agreement of ionization potentials of N F and N H were also predicted as being caused by F —> Ν ττ-bonding i n N F and N F . ( Incidentally, it seemed likely that there would also be F - » Ν ττ-bonding in Ν—F, which has also been corroborated subsequently by our calcula tions. ) In this class of compounds, there are many interesting properties whose solutions, using approximate wave functions, may yield sufficiently accurate results to permit interpretation of the desired phenomena. F o r this reason we have performed calculations using the semiempirical "ex tended H u c k e l method," modified to include a seemingly more justifiable physical interpretation of the matrix elements as well as iterative processes which introduce a measure of self-consistency. W e shall discuss this method i n detail later, present some results of the calculations, and show their good agreement with experimental results. 3
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Downloaded by UNIV OF CALIFORNIA SAN DIEGO on September 28, 2016 | http://pubs.acs.org Publication Date: January 1, 1966 | doi: 10.1021/ba-1966-0054.ch002
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Calculational Techniques Good, rigorous S C F calculations on polyatomic molecules are long, difficult, and tedious to program and inevitably expensive i n computer time. What we needed was a simple semiempirical approximate method for three-dimensional molecular orbital calculations. In recent years increasing use has been made of an extended H u c k e l type L C A O - M O method for calculating wave functions and energies of three-dimensional molecules (as opposed to molecules having separable τΓ-systems). This extended Hiickel-type method is based on a technique apparently originally introduced by Wolfsberg and Helmholz (23) and used over the years by Longuet-Higgins (18), extensively by Lipscomb and co-workers, (8, 9, 12, 16, 17) especially by Hoffman (8, 9, 10, 11) as well as by Ballhausen and Gray ( J ) . F r o m a molecular orbital φ* built up as a linear combination of atomic orbitals χ Γ
τ
and by applying the variation principle for the variation of energy, the following set of equations for the expansion coefficients is obtained. («r + ESrr)c + £ T
(β„
-
ES ,)c. = 0 r
ffâs
s = 1,2 ...
M where M is the number of atomic orbitals
Ε = energy
Holzmann; Advanced Propellant Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1966.
(2)
ADVANCED PROPELLANT CHEMISTRY = SxSxÀv
S
r9
Hrr =» a
r
Downloaded by UNIV OF CALIFORNIA SAN DIEGO on September 28, 2016 | http://pubs.acs.org Publication Date: January 1, 1966 | doi: 10.1021/ba-1966-0054.ch002
/f
re
= 0„ =
= overlap integral
(3)
= SxSWxAv = Coulomb integral fxr*3Cxdv
(4)
= Resonance integral (r 5* J )
(5)
χ is an effective one-electron Hamiltonian representing the kinetic energy, the field of the nuclei, and the smoothed-out distribution of the other electrons. The diagonal elements are set equal to the effective valence state ionization potentials of the orbitals i n question. The off-diagonal ele ments, H can be evaluated i n several ways as follows: ( 1 ) I n the early work on the boron hydrides the relationship r89
H. r
= K'S„
(6)
with K! = —21 e.v. was used. However, one was forced to use inordi nately high values of K! owing to the requirement that K' be smaller than any diagonal matrix element ( L — H + R ) ( I S ) . ( 2 ) A better approximation was to set Hr. = O.SK(Hrr +
and to use Κ = (1.75-2.00) ( W - f f )
H„)S„
(7)
(23)
(3) A similar expression, H. r
=ΐκ"(Η„.Η„)-ν*ς„
(8)
which differs only i n second order and has certain computational ad vantages, has also been used ( I ). (4) Cusachs reported (4) that the repulsive terms i n the W-H model which assumes that electron repulsion and nuclear repulsion cancel n u clear-electron attraction, consist of one-electron antibonding terms only. Cusachs noted Ruedenberg's observation that the two-center kinetic energy integral is proportional to the square of the overlap integral rather than the first power. Cusachs used this to develop the approximation: H„
-
s„(2
-
14,1)
(9)
which contains no undetermined parameters and avoids collapse. (5) A t Istanbul F u k u i (5) also reported a new scheme H„
-
j i (H„
+ H)
+ K^S
m
(10)
r9
for approximating the off-diagonal elements. Since the valence state ionization potentials are known to be func tions of the electron population at that atom, we have introduced iterative schemes for calculating H such as Equations 11 and 12: rr
=
-
Kara*'*
OD
~ (»r. ~ 9r ' W R l
a
where R is the iteration cycle number, r refers to orbital a on atom r, m is the occupation number for that orbital i n the ground state, q is some function of the population i n that o r b i t a l and W is an empirical constant. a
Ta
r
