5546
Journal of the American Chemical Society
101:19
1 September 12, 1979
Molecular Mechanics and ab Initio Studies of the Structures, Heats of Formation, Conformations, and Strain Energies of Azoalkanes James Kao* and Tai-Nang Huang Contribution from the Research School of Chemistry, Australian National University, Canberra, A.C. T. 2600, Australia. Received April 3, I979
Abstract: Ab initio molecular orbital theory has been employed to investigate the structures, energies, and conformations of trans- and cis-methyldiazene, trans-azomethane, diazetine, pyrazoline, 1,2,4,5-tetraazacyclohexa-I ,4-diene, and trans,tmnsI ,2,4,5-tetraaza-l ,4-pentadiene. A force field has been developed, on the basis of available experimental and theoretical (ab initio) data. to permit molecular mechanics calculations on azoalkanes. Structures, heats of formation, strain energies, and conformations of more than 50 molecules studied by the developed force field are presented. Extensive comparison is made with previous results for analogous alkenes and some striking features are revealed.
provide necessary information for the force-field development. Introduction Most of the previous theoretical studies have been primarily AZOcompounds, characterized by the -N=N- functional concerned with the diimine m ~ l e c u l e . ” -Secondly, ~~ we present group, have attracted considerable attention in the literature.’ a force-field method for azoalkanes, which is developed on the The area of interest almost covers every branch of chemistry. basis of experimental and theoretical results. Thirdly, appliFor example, there has been great interest in azo compounds cations of the present molecular mechanics to a study of conas powerful and selective reducing agents,2 as sources of free formations, structures, heats of formation, and strain energies radical^,^ for study of thermal and photochemical fragment a t i ~ nand , ~ for a model study of unimolecular reaction t h e ~ r y . ~ of a wide range of azoalkanes are reported and discussed. Finally, extensive comparison is made with the available results The transition-metal chemistry of azo compounds has also been for the isoelectronic and structurally related alkenes. a productive and active field of researchS6Furthermore, theoretical chemists have been interested in the mechanism of the Computational Aspects and Results trans-cis isomerization of d i a ~ e n e s .However, ~ despite the Ab Initio Calculations. The results presented here were obactivity in this area, experimental thermochemical and tained using the modified version of the GAUSSIAN 70 system structural data for azo compounds are rather limited, as of program^.^^**^ Geometrical optimization was carried out compared with their isoelectronic alkene analogues. Such inusing a direct search procedure26 and the minimal STO-3G formation is desirable in order to have a better understanding basis set.27 Structural parameters** of the planar forms of of azo chemistry. dimethylenediazene (diazetine, l),trimethylenediazene (pyAn alternative source of such data is from theoretical calrazoline, Z),and 1,2,4,5-tetraazacyclohexa-1,4-diene (3) were culations. Recently, the a b initio molecular orbital theory has fully optimized. The geometry of the boat form of 1,2,4,5proven useful in systematic studies of equilibrium geometries, tetraazacylohexa- 1,4-diene (4) was also fully optimized with electric dipole moments, charge distributions, relative energies, the exception that the C-H bond lengths were taken from the and conformational analysis of a variety of small compounds.8 theoretical (STO-3G) structure of the planar form. All However, the computation time required for a b initio calcustructural parameters for the eclipsed N N C H conformations lations is a t present a major practical problem to the applicaof trans- and cis-methyldiazene (5 and 6) were fully optimized tion of this method to large molecules. Furthermore, there is assuming C3c local symmetry for the methyl group. The poa sizable error in the calculated total energy (which is directly tential barrier hindering rotation of the methyl group was related to the heat of formation), although it is occasionally studied for both cis- and trans-methyldiazenes by optimizing possible to derive correct heats of formation from theoretical the N I - C I bond length and the N Z N I C Iand N I C I H I , ~ , ~ ~ ~ heats of reactions in conjunction with experimental enthalpies bond angles of the staggered forms while the rest of the paof f ~ r m a t i o n . ~ rameters were kept the same a s in the optimized eclipsed The molecular mechanics (MM) or force field methodlo has forms.30 The obtained structural parameters for 1-6 and total been shown to be a very reliable, fast, and efficient way of energies are shown in Chart I. Also included in Chart I are determining molecular structures, energies, and other propseveral previous result^'^.'^ obtained with the STO-3G basis erties for a wide variety of compounds.10-16A handicap of the set and they are shown for easy comparison. molecular mechanics method lies in the fact that it is an emA flexible rotor geometric model similar to the one used in pirical method and hence a great amount of accurate data must methyldiazenes was employed in the study of the rotational be available for a given class of compounds before the method potential function along the Cl-N 1 bond of trans-ethyldiazene can be developed.1° For instance, it is certainly difficult to (11). Thus, only three parameters ( N I - C I , N ~ N I C Iand , develop a reliable force field for azo compounds simply on the N ,C1C23’)were optimized while other structural parameters basis of the existing experimental data. were derived from the STO-3G optimized geometries of A promising theoretical approach to study geometries and trans-methyldiazene and ethane.32 Conformations with the energies of large molecules would therefore seem to be a dihedral angle C$ equal to 0 ( N N C C syn), 60,90, 1 IO, 1 IS, 120, combined utilization of the a b initio and molecular mechanics methods. In this work, we first report several a b initio calcu- and I 80° were examined. The obtained rotational potential function is plotted in Figure I and the structural and energetic lations, these calculations being carried out essentially to data are presented in Table I . l o 5 The rotational potential surface of trans,trans- 1,2,4,5-te* 12.022. Energy Laboratory, Massachusetts Institute of Technology. Cambridge. traaza-l,4-pentadiene (12) was also investigated using a Mass. 02139. 0002-7863/79/ 1501-5546$0l .OO/O
0 1979 American Chemical Society
Kao, Huang
/
Molecular Mechanics a n d a b Initio Studies of Azoalkanes
5547
Chart I. Calculated STO-3G Structural Parameters
C,.
-147 13593 oy
(6)
-T
~W
h
I
C",
--
-10s 73067 OY
(9)
(I 1)
(12)
flexible rotor model. The possible rotational isomerism, referring to the syn,syn ( N C N N ) Czu conformation, was examined by moving the two azo groups by 60' (or smaller) intervals. For each conformation, the N I C I N ~N, ~ N I C Iand , N ~ N ~ angles C I were optimized, while the C-N and H-N bond lengths and the H N N and H C H bond angles were assigned fixed values of 1.512 A, 1.060 A, 104.9', and 109.5O, respectively, on the basis of previous results for trans-methyldiazene and trans-ethyldiazene. Furthermore, the azo groups were taken to be planar and the H C H plane was assumed to bisect the N C N angle throughout. The structural variations and calculated relative energies are presented in Table II,IoS while the rotational potential energy surface obtained in this manner is depicted in Figure 2. In order to obtain a reasonable theoretical estimate for the NSp2-Csp3stretching force constant, calculations using the extended 4-31G basis set33 were carried out on trans-azomethane. The 4-3 IG set is the larger and probably more reliable for molecular energetics, but, because of the computational expenses, only four parameters ( N I = N ~ , C I - N I , N ~ N I C Iand , N I C I H ~ J . of , ~ trans-azomethane ) (9) wereoptimized. The C-H bond length was taken from the 4-31G optimized geometry of methane32and the HCH bond angles were kept at 109.5O. The calculated total energy is - 187.770 34 au while the optimized structural parameters are 1.222 A, 1.460 A, 115.7O, and 177.6O, respectively, for the N I = N ~ and C I - N I bond lengths and the N ~ N I Cand I N I C I H I , an~,~ gles.
The Molecular Mechanics Method Geometries. The Allinger 1973 force field described pre-
C-
-165 71652 OY
(IO)
-+Figure 1. Calculated potential functions describing internal rotation (4) about the CSp3-Nsp2bond in trans-ethyldiazene (TED) and ris-ethyldiazene (CED).
-+*Figure 2. The theoretical (STO-3G) rotational potential surface for trans,trans-l,2,4,5-tetraaza1,4-pentadiene (see text for discussion).
v i o ~ s l y was ~ ~ used ~ . ~as~ a starting point to extend these force field calculations to a study of azo hydrocarbons. The Allinger 1973 force field is one of the six force fields for which extensive usageloa~l1-I5has been reported and is currently in use
Journal of the American Chemical Society
5548 Table 111. Force-Field Parametersn
van der Waals Parameters for the Hill Equation Y*. A E . kcal mol-’ atom 1.700 1.200 1.200
Nsp2
H LP
0.039 0.040 0.025
Natural Bond Lengths and Stretching Force Constants lo, A k,, mdyn A-l dipole, D b bond Nspz=Nsp~ Nsp2-Csp3 Nsp2-H
1.250 1.480 1.029 0.500
Nsp2-L~
0.00
10.72 3.95 5.23 4.60
- 1.75 - 1S O 0.60
Natural Bond Angles and Bending Force Constants angle typeC 80, deg kg, mdyn A rad-2 NSp2-Nsp2-Csp3 N~~z-N~~z-H NSp~-Nsp2-Lp Csp3-NSp2-L~ H-Nsp2-Lp
NSp2-C,p3-Nsp2
0 1 2 0 1 2 0
Nsp2-Csp3-Csp3 N ,p2-CsP3-
H
1
2
107.00 108.30 126.70 126.30 125.00 108.27 109.31 109.00 109.47 110.51 1 10.20 108.50 108.51 107.90
0.38 0.36 0.36 0.36 0.36 0.38 0.38 0.38 0.38 0.38 0.38 0.24 0.24 0.24
out-of- lane bending constant for Nsp2-Nsp2-X mydn
8: rad-2
bonds = 0.05
Stretch-Bend Constants angle
kts, mdyn rad-]
Nsp2-Nsp2-Csp3 Nsp~--Csp~-Csp3 Nsp2--Nsp2-H Nsp2-Csp3-H Nsp2--N,p2Lp CSp3-Nsp2-L~
0.12 0.12 0.04 0.04 0.00 0.00 0.00
H-NS~Z-LP
Torsional Parameters (kcal mol-]) dihedral angle VI V2 Csp3- Nsp2-NSp2-Csp3 C,p3-Nsp~-Nsp2-L~ C,p3-Nsp2-N,p2-H Lp-Nsp2-Nsp2-
Lp
H-NSp2-Nsp2-Lp H-Nsp2-Nsp2-H
C,p3-Csp3--Nsp2-LP H-Csp3-Nsp2-Lp N ,p2-Csp~-N 5p2- Lp H -C,p3-Nsp2-Nsp2 Csp3-Cspl-Nsp2-Nsp2 N,p2-CSp3-Nsp2-Nsp2 c,p3-csp3-Csp3-Nsp2 NSp2-Csp3-Csp3-Nsp2 H -Csp3-Clp3-Nsp2
-6.60 0.00 -4.99 0.00 0.00 -3.38 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
14.00 14.00 14.00 14.00 14.00 14.00 0.00 0.00 0.00 0.00 0.00 -0.20 0.00 0.00 0.00
v3
0.00 0.00 0.00 0.00 0.00 0.00 1.95 1.95 1.95 0.00 0.70 1.20 0.53 0.53 0.53
Heat of Formation Parametersd (kcal mol-]) N,,2=N
5p2
Nspz-H
Nsp2-C Ns,2-CH3
46.758 -5.054 4.07 I 1.299
Nsp2-CH
