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A simple procedure for quantitative predictions of the CC framework bond distances and angles in n-hydrocarbons
Journal of Molecular Structure (Theochem), 139 (1986) 125-144 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
A SIMPLE PROCEDURE FOR QUANTITATIVE PREDICTIONS OF THE C-C FRAMEWORK BOND DISTANCES AND ANGLES IN n-HYDROCARBONS*
LOTHAR SCHAFER, KHAMIS SIAM and JOHN D. EWBANK Department of Chemistry 72701 (U.S.A.)
and Biochemistry,
University
of Arkansas,
Fayetteville,
AR
EIJI OSAWA Chemistry
Department,
Hokkaido
University,
Sapporo
060 (Japan)
ABSTRACT The structures of four conformations of n-pentane, and of ten conformations of nhexane were determined by ab-initio gradient geometry refinements on the 4-21G level. The results are used to demonstrate the efficacy of a simple empirical procedure to predict the C-C bond distances and C-C-C angles of long-chain n-hydrocarbons from small molecules. Specifically, the C-C bond distances of n-pentane and n-hexane are predicted from those of n-butane (published previously) with a most frequent error of 0.001 a, and a maximum error of 0.003 A, while the C-C-C angles of n-hexane are predicted from n-pentane with a typical deviation of 0.1” in unstrained conformational states, and a maximum deviation of 0.5” in strained conformations. It is expected that the procedure is generally effective in quantitative structural predictions of the C-C framework of the low energy conformational states of n-hydrocarbons regardless of chain length. INTRODUCTION
The current paper is a continuation of our structural work on hydrocarbons which so far has involved some n-hydrocarbons [l-3], strained cyclic systems [4, 51, and cyclohexane derivatives [6, 71. For this study we have refined the structures of four conformations of n-pentane, and of ten conformations of n-hexane, in order to explore one possibility of predicting structural parameters of long chain hydrocarbons from smaller systems. The 4-21G basis [8] was used for the geometry refinements with Pulay’s gradient method [ 91 and program [lo]. It was our specific goal to determine the accuracy with which it is possible to predict the C-C bond distances of n-pentane and n-hexane from those of n-butane published previously [ 11, and the C-C-C angles of n-hexane from those of n-pentane. The C-C bonds of n-butane can be classified into sufficiently generalised types, from which the bond distances of larger systems *Paper No. 53 in the series: Ab Initio Studies of Structural Features Not Easily Amenable to Experiment. 0166-1280/86/$03.50
o 1986 Elsevier Science Publishers B.V.
126
can be modelled; for C-C-C angles, n-pentane is the smallest system from which a comprehensive set can be derived that is sufficient for parameter predictions. We refer to previous comparisons [ll-131 of 4-21G calculations with experimental results to estimate the general accuracy of the structures derived in this paper. RESULTS
AND DISCUSSION
Notation Throughout this discussion, the following notation will be used. The C-C-C-C torsional angles are r1 = Cl-C2-C3-C4, r2 = C2-C3-C4-C5, and r3 = C3-C4-C5-C6. They are designated A, or G+, when their values are in the vicinity of 180” (A), or either k60” or +90” (Gk), and each conformation is characterized by the A or G symbol for its C-C-C-C torsions. Thus, in form (AG+) of pentane, 7 1 is in the vicinity of 180”, and 72 is in the vicinity of +60” ; and in form (G - G + G -) of n-hexane, 71, 72, and 73 are close to -90°, + 60” and -go”, respectively. In each C-C-C-C torsional angle, we identify an internal (i) and an external (e) C-C bond distance. For example, C2-C3 is internal and Cl-C2 is external in rl. In n-pentane or n-hexane, some C-C bond distances must be multi-labelled. For example, C2-C3 in n-pentane is both i to 71 and e to 72; and C3-C4 in n-hexane is simultaneously e to TV and 73 and i to r2. A similar notation holds for C-C-C angles. When both legs of a bond angle are part of a given torsion, the angle is labelled “internal” (i). When only one leg of a bond angle is part of a torsion, it is termed “external” (e). Thus, C5-C4-C3 is e to pi and i to 72 in n-pentane; and e to TV and i to both 72 and 73 in n-hexane. These examples also show that, for systems larger than butane, the C-C-C angles must be multi-labelled and, furthermore, that n-butane does not contain all the angle types which are needed to describe long-chain systems. A complete set of all i or e labels, followed by the value (in degrees) of the torsional angle involved, is needed for each parameter to identify its type. That is, parameter type is determined by all the associations, i or e, of a given parameter with the C-C-C-C torsions of a system, and by the conformational states of the latter. Thus, bond angle C4-C3-C2 in nhexane, conformation (G + AA), is i(60)i(MO)e(180), because it is i to TV and 72 and e to TV, while the magnitudes of these torsions in this conformation are close to 60”, 180” and NO”, respectively. The characteristic torsional angles and conformational energies for npentane and n-hexane are given in Tables 1 and 2. The 4-21G optimized structures for both compounds are listed in Tables 3-5. Symmetric and asymmetric forms are listed together, even though this leads to some redundant entries for the symmetric forms, because this provides the fastest way
127 TABLE 1 Characteristic torsional angles (“), and total (E) and relative (AE) energies for four 4-21G optimized conformations of n-pentane Conformation
4-3-2-l
5-4-3-2
E
(kcal mol-’ ) (AA) (AG+) (G+G+) tG+G-)
180 176.9 61.4 64.6
0.0 0.86 1.63 3.69
-122,949.57 -122,948.71 -122,947.94 -122,945.88
180 65.7 61.4 -93.8
tktal mol-’ )
TABLE 2 Characteristic torsional angles (“) and total (E) and relative energies optimized conformations of n-hexane Conformation
(AAA) (G + AA) (AG + A) (AG-G-0) (G--G-) (G--G+) (G -G - 0) (AG-G+) (G-G-G+) (G-G+ G-)
4-3-2-l
180.0 66.3 176.6 -175.6 -66.0 -67.0 -61.6 -172.9 -62.7 -93.8
5-4-3-2
6-5-4-3
(AE)
E
(kcal mol-’ ) 180.0 176.7 67.0 -61.8 -172.9 -179.8 -59.2 -65.4 -66.5 64.8
180.0 179.6 176.5 -61.1 -66.0 67.3 -61.6 92.2 91.7 -93.0
for ten 4-21G
-147,394.41 -147,393.55 -147,393.53 --147,392.74 -147,392.70 -147,392.60 -147,391.98 -147,390.71 -147,389.85 -147,387.68
rk:al mol-’ ) 0.0 0.86 0.88 1.67 1.71 1.81 2.43 3.70 4.56 6.73
to determine specific parameter changes between corresponding segments of symmetric and asymmetric conformations. In the last phase of the refinements, the symmetry of some forms was affected by slight rounding effects, but these were not corrected because they are insignificant. Differences between different parameter types of n-butane (4-21G values from ref. 1) and n-pentane are given in Tables 6 and 7. The C-C bond distances of n-pentane and n-hexane, predicted from those of n-butane, are compared with the 4-21G optimized values in Table 8; the C-C-C angles of n-hexane, predicted from those of n-pentane, are compared with the 4-21G optimized values in Table 9. Atom numbering is explained in Figs. l-3 and the conformational dependence of bond distances and angles in n-butane on the C-C-C-C torsion is documented in Figs. 4 and 5, which are based on the 4-21G values of ref. 1.
128 TABLE3 Structural parameters (bond distances in A, anglesin degrees) forthe 4-21G optimized geometriesofthe n-pentane conformations(AA),(AG+),(G+G+)and (G+G-)
(AA) 2 6 7 8 3 9 10 4 11 12 5 13 14 15 16 17 6 7 7 8 8 8 3 9 9 10 10 10 4 11 11 12 12 12 5 13 13 14 14 14 15 16 16 17 17 17 3
1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 2
2 2 6 2 6 7 1 1 3 1 3 9 2 2 4 2 4 11 3 3 5 3 5 13 4 4 15 4 15 16 1
6
1.5408 1.0835 1.0839 1.0839 1.5415 1.0850 1.0850 1.5415 1.0858 1.0858 1.5408 1.0850 1.0850 1.0835 1.0839 1.0839 111.08 110.68 108.12 110.68 108.12 108.05 112.37 109.46 109.23 109.46 109.23 106.95 112.73 109.25 109.25 109.25 109.25 106.94 112.37 109.23 109.46 109.23 109.46 106.95 111.08 110.68 108.12 110.68 108.12 108.05 180.0
(AG+ 1
(G + G +)
(G+ G-1
1.5412 1.0832 1.0839 1.0838 1.5423 1.0832 1.0852 1.5445 1.0856 1.0859 1.5418 1.0851 1.0847 1.0834 1.0840 1.0822 111.07 110.61 108.15 110.65 108.19 108.06 111.94 109.17 109.95 109.47 109.11 107.08 114.00 108.48 108.74 109.27 109.25 106.87 113.67 109.18 109.55 108.63 108.76 106.82 110.61 110.50 108.10 111.44 107.88 108.20 -179.9
1.5413 1.0835 1.0841 1.0825 1.5453 1.0849 1.0834 1.5453 1.0856 1.0856 1.5413 1.0834 1.0849 1.0835 1.0841 1.0825 110.62 110.56 108.10 111.40 107.88 108.15 113.54 108.86 108.13 109.62 109.93 106.56 115.25 108.51 108.71 108.71 108.51 106.83 113.54 109.93 109.62 108.13 108.80 106.56 110.62 110.56 108.10 111.40 107.88 108.15 175.5
1.5411 1.0838 1.0838 1.0819 1.5461 1.0851 1.0852 1.5528 1.0854 1.0849 1.5432 1.0844 1.0849 1.0839 1.0809 1.0840 110.39 110.79 108.06 111.39 107.75 108.34 114.93 108.68 108.18 109.23 108.81 106.70 115.12‘ 109.39 109.43 107.37 108.61 106.56 114.18 108.74 107.91 109.42 109.78 106.51 110.57 111.83 108.09 110.24 107.99 108.00 173.6
129 TABLE 3 (continued)
(AG+1
(AAl 3 3 9 9 9 10 10 10 4 4 4 11 11 11 12 12 12 5 5 5 13 13 13 14 14 14 15 15 15 16 16 16 17 17 17
2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5
1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4
7 8 6 7 8 6 7 8 1 9 10 1 9 10 1 9 10 2 11 12 2 11 12 2 11 12 3 13 14 3 13 14 3 13 14
60.0 -59.8 58.1 -62.0 178.3 -58.8 -178.9 61.4 176.9 -61.6 55.6 55.6 177.1 -65.8 -60.6 60.9 178.1 65.7 -173.2 -56.9 -57.0 64.2 -179.5 -173.1 -52.0 64.3 176.2 -61.4 55.1 56.5 179.0 -64.6 -63.8 58.6 175.1
59.9 -59.9
58.5 -61.7 178.6 -58.5 -178.6 61.7 180.0 -58.3 58.3 58.3 180.0 -63.3 -58.3 63.3 180.0 180.0 -58.3 58.3 58.3 180.0 -63.3 -58.3 63.3 180.0 180.0 -58.5 58.5 59.9 -178.6 -61.7 -59.9 61.7 178.6
(G+ Gt) 55.8 -64.5 55.1 -64.7 175.0 -61.1 179.2 58.9 61.4 -177.8 -61.8 -60.8 60.1 176.0 -176.6 -55.8 60.2 61.4 -176.6 -60.8 -61.8 60.2 176.0 -177.8 -55.8 60.1 175.5 -61.1 55.1 55.8 179.2 -64.7 -64.5 58.9 175.0
(G t G-) 54.0 -66.7 52.3 -67.4 172.0 -63.8 176.6 55.9 64.6 -173.8 -58.2 -59.1 62.6 178.1 -174.3 -52.7 62.8 -93.8 29.9 145.8 145.7 -90.7 25.3 29.7 153.4 -90.7 -178.5 -57.5 58.2 61.0 -178.0 -62.3 -59.2 61.8 177.5
TABLE 4 Structural parameters (bond distances in A, angles in degrees) for the 4-21G optimized geometries of the n-hexane conformations (AAA), (G + AA), (AG + A), (AG -G-) and (G - AG-)
(AAN 2 7 8 9 3
1 1 1 1 2
1.5405 1.0839 1.0834 1.0839 1.5416
(G+AN 1.5417 1.0841 1.0836 1.0823 1.5447
(AG + A) 1.5412 1.0839 1.0833 1.0839 1.5424
(AG-G-) 1.5413 1.0838 1.0833 1.0840 1.5420
(G--G-) 1.5416 1.0824 1.0836 1.0841 1.5450
130 TABLE 4 (continued)
10 2 11 2 4 3 12 3 13 3 5 4 14 4 15 4 6 5 16 5 17 5 18 6 19 6 20 6 71 81 81 91 91 91 3 2 10 2 10 2 11 2 11 2 11 2 4 3 12 3 12 3 13 3 13 3 13 3 5 4 14 4 14 4 15 4 15 4 15 4 6 5 16 5 16 5 17 5 17 5 17 5 18 6 19 6 19 6
2 2 7 2 7 8 1 1 3 1 3 10 2 2 4 2 4 12 3 3 5 3 5 14 4 4 6 4 6 16 5 5 18
(AAA)
(G+AA)
(AG+ A)
(AG-G-)
(G--G-)
1.0850 1.0850 1.5416 1.0858 1.0858 1.5416 1.0858 1.0858 1.5405 1.0850 1.0850 1.0833 1.0839 1.0839 110.71 111.12 108.09 110.71 108.00 108.09 112.35 109.48 109.22 109.48 109.21 106.94 112.72 109.20 109.30 109.20 109.30 106.94 112.72 109.31 109.19 109.31 109.21 106.94 112.35 109.23 109.49 109.21 109.47 106.95 111.11 110.71 108.10
1.0851 1.0847 1.5422 1.0856 1.0858 1.5422 1.0840 1.0860 1.5408 1.0849 1.0851 1.0833 1.0839 1.0839 110.54 110.63 108.07 111.44 108.18 107.85 113.60 109.51 109.18 108.80 108.69 106.84 113.89 108.75 108.61 109.18 109.30 106.87 112.37 110.01 108.84 109.23 109.17 107.07 112.33 109.25 109.50 109.21 109.46 106.94 111.08 110.66 108.14
1.0852 1.0833 1.5446 1.0859 1.0856 1.5424 1.0856 1.0859 1.5412 1.0833 1.0852 1.0833 1.0839 1.0839 110.66 111.05 108.12 110.69 108.05 108.16 111.95 109.46 109.13 109.14 109.97 107.07 113.97 109.27 109.29 108.49 108.74 106.83 113.97 108.74 108.49 109.29 109.27 106.83 111.95 109.97 109.14 109.13 109.46 107.07 111.05 110.66 108.12
1.'0835 1.0852 1.5454 1.0857 1.0842 1.5456 1.0857 1.0856 1.5413 1.0835 1.0849 1.0836 1.0825 1.0841 110.70 111.07 108.16 110.65 108.04 108.12 111.97 109.11 109.92 109.47 109.22 107.03 113.97 108.52 108.22 109.29 110.02 106.53 115.34 108.59 108.70 108.64 108.46 106.77 113.59 109.96 109.56 108.15 108.80 106.53 110.62 111.41 107.84
1.0848 1.0851 1.5430 1.0842 1.0858 1.5450 1.0858 1.0842 1.5416 1.0851 1.0848 1.0836 1.0824 1.0841 111.47 110.67 107.82 110.59 108.14 108.03 113.56 108.80 108.66 109.51 109.23 106.86 113.48 108.85 110.03 108.69 108.56 107.03 113.48 108.55 108.69 110.03 108.85 107.03 113.57 109.23 109.51 108.65 108;79 106.86 110.67 111.47 107.82
131 TABLE4(continued)
(AA-41 20 20 20 3 3 3 10 10 10 11 11 11 4 4 4 12 12 12 13 13 13 5 5 5 14 14 14 15 15 15 6 6 6 16 16 16 17 17 17 18 18 18 19 19 19 20 20 20
6 6 6 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6
5 18 19 17 18 19 17 18 19 17 18 19 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5
1 10 11 1 10 11 1 10 11 2 12 13 2 12 13 2 12 13 3 14 15 3 14 15 3 14 15 4 16 17 4 16 17 4 16 17
110.70 108.10 108.01 59.9 180.0 -59.9 -178.6 -58.5 61.6 -61.7 58.5 178.6 180.0 58.3 -58.3 -58.3 180.0 63.4 58.3 -63.4 180.0 180.0 58.4 '-58.4 -58.4 180.0 63.2 58.3 -63.3 180.0 180.0 58.3 -58.3 -58.3 180.0 63.4 58.4 -63.3 -179.9 180.0 58.5 -58.5 59.9 -61.7 -178.6 -59.9 178.6 61.6
(G+ AA) 110.65 108.14 108.06 56.4 176.1 -63.9 178.8 -61.5 58.4 -64.8 54.9 174.9 66.3 -56.2 -172.4 -172.4 65.1 -51.1 -56.1 -178.7 65.1 176.7 55.3 -60.9 -61.9 176.8 60.5 55.4 -66.0 177.8 179.6 57.5 -59.0 -58.7 179.2 62.7 58.0 -64.1 179.3 179.9 58.3 -58.6 59.8 -61.8 -178.7 -60.0 178.5 61.5
(AGt
A)
110.69 108.16 108.05 59.9 179.9 -59.9 -179.0 -58.9 61.2 -62.1 58.0 178.1 176.6 55.2 -61.9 -60.9 177.8 60.6 55.3 -66.1 176.8 67.0 -55.5 -171.8 -171.8 65.6 -50.6 -55.5 -178.1 65.6 176.5 55.2 -60.9 -62.0 176.7 60.6 55.2 -66.1 177.8 180.0 58.0 -58.9 59.9 -62.1 -179.0 -59.9 178.1 61.3
(AG-G-O) 110.62 108.08 108.15 60.1 -179.7 -59.7 -178.0 -57.8 62.3 -61.2 59.0 179.1 -175.6 63.0 -54.2 -54.9 -176.4 66.5 60.9 -60.6 -177.7 -61.8 177.4 61.4 60.5 -60.4 -176.4 176.2 55.4 -60.6 -61.1 176.7 60.9 62.1 -60.1 -175.9 178.0 55.8 -59.9 -174.9 61.7 -54.4 65.2 -58.2 -174.3 -55.2 -178.6 65.3
(G--G-) 110.59 108.03 108.14 64.0 -176.0 -56.3 -174.9 -54.9 64.8 -58.4 61.6 -178.7 -66.0 172.8 56.5 56.9 -64.4 179.4 173.1 51.9 -64.3 -172.9 64.9 -51.9 -51.9 -174.1 69.1 64.9 -57.3 -174.1 -66.0 173.2 56.9 56.6 -64.3 179.5 172.8 51.9 -64.3 -176.0 61.6 -54.8 64.0 -58.4 -174.8 -56.3 -178.7 64.8
132 TABLE5 Structural parameters (bond distances in A, anglesin degrees) forthe 4-21G optimized geometriesof the n-hexane conformations(G--G+), (G-G-G-), (AG-G+), (G-G-G+)and(G-G+G-)
21 71 81 91 3 2 10 2 11 2 4 3 12 3 13 3 5 4 14 4 15 4 6 5 16 5 17 5 18 6 19 6 20 6 712 812 817 912 917 918 321 10 2 1 10 2 3 11 2 1 11 2 3 11 2 10 43 2 12 3 2 12 3 4 13 3 2 13 3 4 13 3 12 54 3 14 4 3 14 4 5 15 4 3 15 4 5 15 4 14 65 4 16 5 4 16 5 6 17 5 4 17 5 6
(G--G+)
(G-G-G-)
(AG-GG+)
(G-G-G+)
(G-G+G-)
1.5416 1.0822 1.0836 1.0841 1.5455 1.0848 1.0852 1.5426 1.0860 1.0837 1.5455 1.0860 1.0837 1.5416 1.0848 1.0852 1.0836 1.0841 1.0822 111.55 110.62 107.79 110.55 108.16 108.04 113.74 108.72 108.60 109.54 109.19 106.82 113.57 109.16 109.22 108.36 109.31 107.00 113.56 109.24 109.16 109.30 108.37 107.01 113.73 108.61 108.71 109.19 109.54
1.5414 1.0825 1.0836 1.0841 1.5451 1.0849 1.0837 1.5463 1.0858 1.0840 1.5451 1.0840 1.0858 1.5414 1.0837 1.0849 1.0836 1.0825 1.0841 111.43 110.64 107.84 110.59 108.14 108.07 113.57 108.80 108.20 109.53 109.96 106.53 115.21 108.47 108.22 108.82 109.30 106.47 115.21 169.30 108.82 108.22 108.47 106.47 113.57 109.96 109.53 108.20 108.80
1.5415 1.0838 1.0833 1.0840 1.5420 1.0828 1.0849 1.5466 1.0860 1.0859 1.5524 1.0855 1.0849 1.5433 1.0845 1.0850 1.0839 1.0840 1.0808 110.68 111.05 108.17 110.67 108.05 108.12 111.76 109.01 109.88 109.44 109.41 107.23 115.45 108.33 108.10 108.99 108.94 106.66 115.41 109.43 109.41 107.25 108.44 106.52 114.24 108.63 107.86 109.44 109.83
1.5412 1.0821 1.0836 1.0842 1.5446 1.0852 1.0826 1.5478 1.0861 1.0857 1.5522 1.0840 1.0852 1.5433 1.0846 1.0850 1.0839 1.0841 1.0807 111.50 110.66 107.90 110.48 108.12 108.05 113.56 108.64 107.93 109.90 110.10 106.43 116.74 108.11 108.17 108.64 108.14 106.61 115.33 110.28 109.57 106.77 108.20 106.25 114.60 108.49 107.78 109.38 109.74
1.5432 1.0810 1.0840 1.0839 1.5524 1.0838 1.0846 1.5490 1.0852 1.0856 1.5521 1.0856 1.0853 1.5432 1.0846 1.0839 1.0808 1.0839 1.0840 111.88 110.11 107.96 110.69 108.09 107.98 113.96 110.12 109.73 107.76 108.53 106.42 116.77 108.30 106.72 109.16 109.03 106.35 116.78 109.07 109.16 106.71 108.26 106.36 114.03 108.48 107.74 109.71 110.13
133
TABLE 5 (continued) (G-AGt) 17 5 18 6 19 6 19 6 20 6 20 6 20 6 321 3218 3219 102 1021 1021 112 112 112 43 43 43 123 12 3 12 3 133 13 3 13 3 54 54 5 4 144 14 4 14 4 154 15 4 15 4 65 6 5 65 165 16 5 16 5 175 17 5 17 5 186 18 6 18 6 196 19 6 19 6 206 20 6 20 6
16 5 5 18 5 18 19 7
1
7 8 9 7 8 9 1
1 1 1 2 210 211 2 1 2 10 2 11 2 1 2 10 2 11 3 2 312 313 3 2 3 12 3 13 3 2 3 12 3 13 4 3 414 415 4 3 4 14 4 15 4 3 4 14 4 15 5 4 5 16 5 17 5 4 5 16 5 17 5 4 5 16 5 17
106.82 110.62 110.55 108.04 111.55 107.79 108.16 64.1 -175.9 -56.3 -174.8 -54.8 64.8 -58.4 61.6 -178.8 -67.0 171.8 55.7 55.2 -66.0 177.8 171.4 50.2 -66.0 -179.8 58.1 -58.7 -57.7 -179.8 63.4 59.1 -63.0 -179.8 67.3 -54.9 -171.1 -171.6 66.3 -49.9 -55.4 -177.6 66.2 176.0 54.9 -61.5 56.4 -64.7 178.9 -64.0 174.9 58.5
(G-G-G-) 106.53 110.64 111.43 107.84 110.59 108.07 108.14 64.8 -175.2 -55.5 -174.6 -54.6 65.1 -58.5 61.5 -178.8 -61.6 177.5 61.5 59.8 -61.1 -177.0 175.3 54.4 -61.6 -59.2 179.3 63.7 63.7 -57.9 -173.4 179.3 57.7 -57.9 -61.6 175.3 59.9 61.5 -61.6 -177.0 177.5 54.4 -61.0 -175.2 61.5 -54.6 64.9 -58.5 -174.6 -55.4 -178.8 65.1
(AG-Gt) 106.54 110.52 110.25 107.98 111.90 108.06 108.01 60.5 -179.4 -59.3 -177.9 -57.7 62.4 -60.9 59.3 179.4 -172.9 66.0 -51.5 -51.5 -172.7 69.8 64.2 -57.0 -174.5 -65.4 173.1 57.5 58.5 -63.0 -178.6 173.6 52.1 -63.4 92.2 -31.7 -147.5 -147.3 88.8 -27.1 -31.4 -155.3 88.9 177.8 57.0 -58.8 58.5 -62.3 -178.1 -61.7 177.4 61.7
(GyG-G+) 106.52 110.46 110.31 107.93 111.97 107.96 108.08 64.5 -175.4 -55.8 -175.4 -55.3 64.4 -59.3 60.8 -179.6 -62.7 176.8 61.1 59.5 -61.0 -176.8 174.8 54.3 -61.5 -66.5 171.4 56.3 58.3 -63.8 -178.9 173.3 51.2 -63.9 91.7 -33.4 -148.8 -147.8 87.1 -28.3 -32.0 -157.1 87.5 176.9 56.1 -59.6 57.7 -63.2 -178.8 -62.7 176.4 60.8
(G-G+ 106.43 111.92 110.66 108.07 110.11 107.97 107.97 59.6 -60.4 -179.7 -64.2 175.8 56.5 -179.9 60.1 -59.2 -93.8 30.2 146.1 145.8 -90.2 25.7 30.4 154.4 -89.7 64.8 -174.0 -59.5 -59.5 61.7 176.2 -174.0 -52.8 61.7 -93.0 31.2 146.6 146.9 -88.8 26.6 31.1 155.3 -89.3 60.2 -179.3 -63.7 -179.2 -58.7 57.0 -59.9 60.6 176.2
G-)
134 TABLE 6 4-21G optimized typesa
parameters of n-butane and differences between different parameter
Parameter
Type
C2-C3 C2-C3 Cl-C2 Cl-C2
i(180) i(180) e(180) e(180)
C3-C2-C1 C3-C2--Cl
i(180) i( 180)
Value
Type
1.5416 1.5416 1.5405 1.5405 112.37 112.37
i( 60) i( 90) e(60) e(90) i(60) i( 90)
Diff.
Value 1.5444 1.5499 1.5414 1.5417
+ 0.003 + 0.008 + 0.001 + 0.001
113.81 112.65
+1.4 + 0.3
aBond distances in A, bond angles in degrees [ 11. The type symbols are explained in the text. TABLE 7 Differences between different C-C-C Parameter
Type
C3-C2-C1
(AA): (AA): (AA):
C4-C3-C2
(AA): (AA): (AA):
C5-C4-C3
(AA): (AA):
angle types in various conformations
Value
Type
112.37
(AG+ ):
112.37
(G + G+):
112.37
(G+ 0):
i(180) i(180) i(180) i(180) i(180) i(180)
112.73
(AG+):
112.73
(G+ G+):
112.73
(G+ G-):
e(180) i( 180) e( 180) i(180)
112.37
(AG+):
112.37
(G+ G-):
i(180) e(180) i(180) e( 180) i(180) e(180)
of n-pentanea
Value i(180) e(60) i(60) e(60) i(60) e(90) i( 180) i( 60) i(60) i( 60) i(60) i( 90) e(180) i(60) e(60) i(90)
Diff.
111.94
-0.4
113.54
+ 1.2
114.93
+ 2.6
114.00
+1.3
115.25
+ 2.5
115.12
+ 2.4
113.67
+1.3
114.18
+1.8
a4-21G values are from this study. Type symbols are explained in the text.
Definition of parameter increments for structure predictions When the number of carbon atoms in the open chain of an n-hydrocarbon exceeds four, the C-C bond distances and angles of the all-anti states seem to be relatively independent of chain length. In nonane, for example, the distances, Cl-C2, C2-C3, C3-C4 and C4-C5 are (4-21G values, in A, from ref. 3) 1.5408, 1.5415, 1.5418, and 1.5418, respectively; and the angles,
135 TABLE 8 Predicted and calculated C-C n-hexanea n-Pentane (AA) 'Type
bond distances for various conformers of n-pentane and
(G+G+)
(AG+) Value
Pred.
Type
CalC.
(G+G-)
Type
Pred.
CalC.
Type
Pred.
talc.
Cl-C2
e(180) 1.541
e(180) 1.541
1.541
e(60)
1.542
1.541
e(60)
1.542
1.541
C2-C3
i(180) 1.541 e(180)
i(180) 1.542 e(60)
1.542
i(60) e(60)
1.545
1.545
i(60) e(90)
1.545
1.546
C3-C4
e(180) 1.541 i(180)
e(180) 1.544 i(60)
1.544
e(60) i(90)
1.550
1.553
c4-c5
e(180) 1.541
e(60)
1.542
1.542
e(90)
1.542
1.543
(AAA)
(G+AA) Type
Pred.
CalC.
Type
Pred.
C&h.
n-Hexane
Type
value
(AG+A)
(AG-G-) Pred.
ale.
Type
Cl-C2
e(180) 1.540
e(60)
1.541
1.542
~~(180) 1.540
1.541
e(180) 1.540
1.541
C2-C3
i(180) 1.542 e(180)
i(60) 1.545 e(180)
1.545
i(l80) 1.543 e(60)
1.542
i(180) 1.543 e(60)
1.542
c3-c4
e(180) 1.542 i(180) e(180)
e(60) 1.543 i(180) e(180)
1.542
e(180) 1.545 i(60) e(180)
1545
e(180) 1.546 i(60) e(60)
1.545
c4-c5
eU80) 1.542 i(180)
e(180) 1.542 i(180)
1.542
e(60) i(60)
1.546
1.546
C5-C6
e(180) 1.540
e(180) 1.540
1.541
e(60)
1.541
1.541
n-Hexane
(G-AG--) TYPO
Pred. Calc. 1.541 1.542
(G-AG+)
(G-G-G-)
Type
hed.
e(60)
Calc. Type
Pred.
(AG-G+) Calc. Type
Pred. Calc.
Cl-C2
e(60)
1.541
1.542 e(60) 1.541
1.541 e(180) 1.540 1.541
C2-C3
i(60) 1.545 1.545 e(180)
i(60) 1.545 e(180)
1.545 i(60) 1.546 e(60)
1.545 i(180) 1.543 1.542 e(60)
c3-c4
e(60) 1.544 1.543 i(180) e(60)
e(60) 1.544 i(180) e(60)
1.543 e(60) 1.547 i(60) e(60)
1.546 e(180) 1.546 1.547 i(60) e(90)
c4-c5
e(60) i(90)
1.551 1.552
C5-C6
e(90)
1.541 1.543
n-Hexane
(G-G-G+)
(G-G+G-)
5pe
Pred.
talc.
TYpe
Pred.
talc.
Cl-C2
e(60)
1.541
1.541
e(90)
1.541
1.543
C2-C3
i(60) e(60)
1.546
1.545
i(90) e(60)
1.551
1.552
c3-c4
e(60) i(60) e(90)
1.547
1.548
e(90) i[60) e(90)
1.547
1.549
c4-C5
e(60) i(90)
1.651
1.552
C5-C6
e(90)
1.541
1.543
aThe predicted values were obtained by the empirical procedure described in this paper. The calculated values are 4-21G results from this study. Distance types are explained in the text. Values determined by symmetry are omitted.
i(l80)
113.6
113.6
Pred.
e(60) i( 90)
e(60) i( 60) i(90)
114.1
115.0
114.6
115.3
i( 90) i(60) e(90)
i(90) i(60) i( 60) e(90)
116.7
113.6
et601 116.5
113.5
et601
i(60)
116.4
114.1
Pred.
Type
Pred.
Calc.
i( 60) i( 180) e(60)
i( 60) e( 180)
Type
Type
113.6
115.3
114.0
112.0
Calc.
(G-G+G-)
113.5
115.2
113.9
111.9
Pred.
(G-AG-)
(G-G-G+)
e(60) i(60)
e(180) i( 60) i( 60)
i(180) i( 60) e(60)
i(180) e(60)
Type
(AG-C+)
116.8
114.0
Calc.
113.5
113.6
Calc.
*The predicted values were obtained by the empirical procedure described in this paper. The calculated values are the 4-21G results from Tables 4 and 5. Type symbols are explained in the text. Values determined by symmetry are omitted.
114.2
114.1 e(60) i(90)
111.8
C6-C5-C4
111.9
115.4
dW
115.1
115.2
113.6
e(180) i(60) i(90)
115.1
113.5
Calc.
c5-C4-c3
i(60) i( 60) e(60)
e(60)
i(60)
Pred.
115.4
113.6
113.6
Calc.
Type
Pred.
Type
115.3
i(60) i(180) e(60)
C4-C3-C2
113.7
Calc.
113.6
Pred.
)
114.0
111.9
Calc.
i(180) i(60) e(90)
i(60) e(l80)
C3-C2-Cl
Type
114.0
111.9
Pred.
(AG-G+
(G-AG+
Parameter
i( 180) i(60) e(180)
i(180) e(60)
Type
(AG+ A)
of n-hexane*
(G-G-G-)
112.3
112.3
e(180) i(180)
112.3
e( 180) i(180)
C6-C5-C4
)
112.4
112.3
e(60) i(180) i( 180)
112.7
113.9
114.0
e( 180) i(180) i(180)
c5-C4-c3
113.6
113.6
i( 60) i(180) e(180)
Calc.
Pred.
112.7
i( 180) i( 180) e(180)
C4-C3-C2
Type
i( 60) e(180)
Value
(G+ AA)
angles in various conformations
112.3
i( 180) e(180)
Type
(AAA)
C3-C2-Cl
Parameter
Calculated and predicted C-C-C
TABLE 9
137
HB\ /HgH32\ ,H13 H5,C 1/“\
H6’
\ H7
/c41H
H9,Hl0
14
H6,
H7#j’ H8
ic3\ Hl0 Hll
Fig. 1. Atom numbering for n-butane.
Hla
H/1’
H14 H15
I H9
Hli
z? \c3/c4\
HI{
h2
,HlS ” H\17H16
Fig. 2. Atom numbering for n-pentane.
H18 \ ,H19
t 4/ \c5/c6iH20
H7,c l/c2\c3/ H8’
ic
H1\3/nl4
h3
Hi/s A17
Fig. 3. Atom numbering for n-hexane.
Cl-C2-C3, C2-C3-C4, C3- C4-C5, and C4-C5-C6 are (4-21G values, in degrees, ref. 3) 112.4, 112.7,112.7, and 112.7, respectively. These values are practically identical with those calculated here for n-pentane (AA) and n-hexane (AAA). Therefore, it seems that the framework of the all-anti forms of n-hydrocarbons can be considered practically constant and essentially known. It may thus serve as a reference from which parameter increments can be measured which incorporate the bond distance and angle changes which accompany the transitions of a system from the most stable all-anti state to other points of its conformational energy surface. In Figs. 4 and 5 the changes in bond distances and angles are plotted which occur in n-butane during a complete rotation of TV,These plots illustrate the concept of “local geometry” [ll, 141: the magnitudes of the structural parameters of a molecule are local at a given point of its potential energy surface, i.e., they can differ significantly for different combinations of its torsional angles. For n-hydrocarbons and C-C-CC torsions, Figs. 4 and 5 indicate that internal C-C bonds vary more with conformation than external C-C or C-H bonds; and that significant conformational variations must also be expected for internal C-C-C angles. In Tables 6 and 7 differences are listed for various parameter types of nbutane and n-pentane which are found between their values in different torsional states. Thus, when a C-C bond is i( 60) in n-butane, it is 0.003 _i$longer than when it is i( 180). Similarly, an i(60) i(60) C-C-C angle in n-pentane is 2.5” more extended than the i(180) i(180) type. We expect that parameter increments of this kind, i.e., differences between the different specified parameter types, in n-hydrocarbons are relatively independent of. chain length, except in the strained states of large systems, when long-range non-bonded interactions are the source of special effects.
138
BUTRNE BOND
OISTRNCES
H9-C2 H8-C2 H7-Cl H6-Cl .
/
‘HS-Cl I 1c2-Cl
C3-C2
0
60
120
180
240
300
3 i0
Fig. 4. The variation of some bond distances of n-butane with the torsional angle 7 = Cl-C2-C3-C4. Each curve represents the differences of a parameter relative to its value at 7 = 0”. Different curves are plotted_ with the same scale on offset zero-lines.
These considerations form the basis of our empirical procedures for parameter prediction, which involves the following steps. (1) For each C-C bond distance and angle determine its type, i.e., the complete set of labels, i(T1) or e(ri), in agreement with the convention put forth in the previous section. (2) For each parameter which is associated with a ri # 180°, find the appropriate increment from Tables 6 (for C-C bonds) and 7 (for C-C-C angles) which has to be added to its value in the all-anti state, to predict its magnitude in a different state. (3) If a parameter is multi-labelled and more than one of the associated 7i’S differ from 180”, find the correction for each Ti, and use the sum of all the corrections as the effective parameter increment. Some of the parameters and their increments in Tables 6 to 9 have been rounded to three significant decimals for distances, and one for angles. Carrying a larger number of digits might affect the accuracy in some cases,
139
BUTRNE BOND
RNGLES
H9-C2-C3
H8-C2-C3
H7-Cl
-C2
H6-Cl-C2
HS-Cl-C2
C3-C2-Cl
I
60
120 180 240 300 360
Fig. 5. The variation of some bond angles of n-butane with the torsional angle 7 = ClC2-C3-C4. Plot format is as in Fig. 4.
but it is not practically meaningful. The accuracy of the simple procedure described cannot be expected to be better than a few thousandths of an A and approximately 0.5”. This is sufficient for most practical purposes and even exceeds the current performance of experimental techniques in resolving single parameters in systems of this kind. For the same reason, geometry optimization for this study was terminated when the largest residual forces were reduced to 0.001 aJ A-’ for bond distances and 0.001 aJ rad-’ for bond angles. That is, in some cases errors due to incomplete optimization may amount to a few tenthousandths of an A and a few hundredths of a degree. The listing of parameter increments in Tables 6 and 7 was limited to the exact values of Ti = 60’, 90”, and 180”. By a few degrees, some of the torsions in the optimized geometries are not exactly at these values. In most cases these deviations are of little significance for the magnitudes of the increments. The largest ones are found for C3-C2 in n-butane in the region of i(90) to i(lOO), where the distance changes are 0.0004 A per degree of ri; and for C3-C2-Cl, in the region i(60) to i(70), where the changes are
140
-0.05” per degree of ri. Thus, using variable increments rather than a constant set, might affect the outcome of some predictions by a few thousandths of an W and a few tenths of a degree; i.e., these factors are approximately within the error limits pursued. This approach was also chosen, because we want to explore the possibility of predicting the framework of n-hydrocarbons without knowing their torsional angles exactly, except for their classification into (A), (G+), or (G-). In this context, it may be significant to note that the magnitudes of the torsional angles in n-pentane and n-hexane depend on the torsional sequence in a characteristic way. For example, in the combination of (A) with (G), the (G) torsions are often close to about 66”, except when, in n-hexane, this combination is also part of a (G+ G+ ) or (G - G-) arrangement. In that case, the values for (G) are close to about 61” as in (G + G+) of n-pentane. Similarly, in many (AG) combinations, the (A) torsions are close to 176” rather than 180”; and in (G + G-), one of the torsions is consistently at 93’. Even though we have not searched for the exact torsional minima, one is led to believe that these trends also exist in long-chain systems. In (G + G-) combinations, specifically, the 90” correction should always be applied to that torsional degree of freedom, whose displacement from 60” relieves the strain of the system. The above defines the basis of our procedure. If systems with special and unusual torsions are desired to be investigated, standard geometry functions [ 15, 161, i.e., analytic representations of torsionally-dependent parameter variations, should be employed for predictions of this kind. The procedure is expected to be effective, whenever bond distances and angles primarily depend on changes in torsions with which their relationship is e or i, while longer-ranging interactions are not so important. This condition is found, for example, by comparing the (AAA) and (G + AA) forms of n-hexane: when a torsion is changed at one end of the system, the structure at the other end is affected little. A second condition for the procedure to be effective is the additive nature of the parameter increments which are encountered, when a parameter is associated with several torsions for which simultaneous changes occur. In previous predictions of some structural parameters in polyfunctional systems [15, 161, the additivity has been found approximately to hold. In the following sections we shall test to what extent these considerations are applicable to n-hydrocarbons. Details of parameter
predictions
Since the C-C bonds of n-butane are both of type i and e, they can be used to estimate the bond distance trends in the larger systems, n-pentane and n-hexane. Among the results (Table 8), the following examples are particularly interesting. In n-pentane and n-hexane Cl-C2 is always exclusively of type e. In agreement with the changes found for the e-type C-C bond of n-butane, the
141
variations of Cl-C2 with 71 are always small. In n-pentane, C3-C2 is i to r1 and e to r2. Thus, in comparing (AA) with (AG+ ), the small change of an external bond is observed for this parameter. However, in going from (AA) to (G + G+ ) or (G + G-), the relatively large change of the i-type C-C! bond plus the e-type variation is observed. C3-C4 in n-pentane is e to 71 and i to r2. In comparing (AA) with (AG+), the expected i-type change is approximately found. In going from (AA) to (G+ G+), both the e-type and i-type changes are accumulated. An additional increment is found for C3-C4 in (G+ G-), because r 2 is in the vicinity of 90”, and the unusually long distance of 1.550 A results (calculated 1.553 A). In this conformation the most extended C-C bond range, from 1.541 to 1.553 A, is encountered. The multi-label cases of n-hexane are also of particular interest. C3-C4 is e(180) i(180) e(180) in (AAA). When it changes to e(180) i(60) e(180) in (AG + A), the i-type increment is found. In forms such as (AG - G-), where C3-C4 is e(180) i(60) e(60), or in (G-G-G+), where it is e(60) i(60) e(90), the additivity of the simultaneous parameter changes again is approximately confirmed. This result supports the view that systems larger than hexane may also be predicted in this way. Since the C-C-C angles of n-butane are only type i, n-pentane is the smallest system that can be used to define a comprehensive set of angle types, which can be applied to larger systems. In the determination of angle increments, the following details are important. The angles in n-pentane are all double-labelled. In n-hexane, the C-C-C angles can have two or three labels; and four labels are possible in still larger systems. The n-hexane double-label angles, C3-C2-Cl and C6-C5-C4, in all forms either have magnitudes which are very close to the corresponding types of n-pentane, or they can be easily predicted. An apparent complication arises, when the double-label increments of n-pentane are used to predict triple-label parameters, because the desired end result has to be approached in several steps for which different options may exist. For example, the transition of C4-C3-C2 in (AAA), where it is i(180) i(180) e(180), to (G-G-G-), where it is i(60) i(60) e(60), can be achieved by first applying the increment for i( 180) i( 180) e( 180) + i( 180) i(60) e(60) (using the C3-C2-C1 increment of +1.2”, for i(180) e(180) in (AA) to i(60) e(60) in (G + G+), Table 7) followed by i( 180) i(60) e(60) + i(60) i(60) e(60) (using the i( 180) i(60) C4-C3-C2 increment from (AG+ ) to i(60) i(60) in (G + G+), + 1.2”, Table 7), yielding a total increment of 2.4”; or it can be achieved by the sequence i( 180) i( 180) e( 180) + i( 180) i( 180) e(60) + i(180) i(60) e(60) + i(60) i(6C) e(60), with the corrections (all from Table 7) -0.4” (C3-C2-Cl from (AA) to (AG+)), +1.6” (C3-C2-Cl from (AG+) to (G+ G+)), and +1.2” (C4-C3-C2 from (AG+) to (G + G+)), also yielding a total increment of 2.4”. In the second sequence, proceding from i(180) i(180) e(60) + i(60) i(60) e(60), by using the (AA) to (G+ G+) increment for C4-C3-C2 (+2.5”), would not have been correct for the followingreason. Each triple angle label consists of two pairs which are made up of the first
142
two labels, and of the second and third, respectively. Therefore, when a single torsional angle changes for a triple-labelled C-C--C angle, two label pairs may be affected which are different. For example, in the transition i( 180) i( 180) e(60) + i(180) i(60) e(60), there is a change of two pairs, i(180) i(180) + i( 180) i(60) and, at the same time, of i( 180) e(60) + i(60) e(60), even though only one torsion has changed. Question is now as to whether this single torsional variation requires the sum of two increments, or only one, and if only one, which of the changing pairs should be chosen to define the increment. The answer is provided by the following observation. When the C-C-C angle in n-butane changes from i(180) to i(60), the increment is + 1.4’. In n-pentane, i( 180) + i(60) transitions in a pair have very similar increments, if the second label in the pair is either i(180), e( 180), or i(60). However, if the second label is e(60), there is an additional increment of +0.3’. Thus, Table 7, (AA) to (AG+) is +1.3” for both the i(180) i(180) + i(180) i(60) and the i( 180) e(180) --f i(60) e(180) combinations; and +1.2” for i(180) i(60) in (AG+) to i(60) i(60) in (G+ G+). However, for C3-C2-Cl and the transition i(180) e(60) in (AG+) to i(60) e(60) in (G + G+), the increment is + 1.6”. Therefore, the double-labelled increments of n-pentane can be used to find the triple-labelled angles in n-hexane without any further correction, if the labels which change in a pair are adjacent to a third label which is either i(180), i(60), or e(180), but not e(60). We shall illustrate this principle by giving a number of examples. For i(180) i(180) e( 180) -+ i(180) i(60) e( 180), change one pair, either i( 180) i( 180) + i(180) i(60), or i(180) e(180) -+ i(60) e(180), for an increment of +1.3” (C4-C3-C2 or C5-C4-C3, respectively, (AA) to (AG+), Table 7). This change is the same as for i(180) i(180) e(180) -+ i(60) i(180) e(180). For i(180) i( 180) e(180) -+ i(180) i(60) e(60), go i( 180) e(180) + i(60) e(60) (+1.2”, C3-C2-Cl, (AA) to (G+ G+), Table 7); do not go via the forbidden route i(180) i(180) e(180) + i(180) i(180) e(60) (pair i(180) e(180) + i(180) e(60), C3-C2-Cl, (AA) to (AG+), Table 7, -0.4”), followed by i(180) i(180) e(60) + i(180) i(60) e(60) (pair i(180) i(180) + i(180) i(60), C4-C3-C2, (AA) to (AG+), +1.3”), because the last step implies the change of a label in a pair which is adjacent to e(60). The last sequence can be followed only, if the additional +0.3” correction is applied, which holds for such a change. For i(180) i(180) e( 180) + i(60) i( 180) e( 60), first the pair i(180) i(180) is changed to i(60) i(180), then the pair i(180) e(180) is changed to i(180) e(60), yielding a total increment of +1.3” 0.4” = +0.9”. When a label in a pair is changed at the side which is not adjacent to another label, the increment determined for this pair can always be applied without any further correction. As a last example, we present the derivation of C4-C3-C2 in (G - G-G+ ) and (G- G + G-). For the former, the transition is i(180) i(180) e(180) + i(180) i(60) e(90) + i(60) i(60) e(90). The last pair was changed first, using C3-C2-Cl in (AA) to (G + G-); followed by a change in the first pair, using C4-C3-C2 in (AG+ ) to (G + G+ ); and the total correction is + 3.8”.
143
For the latter, the transition is i(180) i( 180) e( 180) + i(180) i(60) e(90) + i(90) i( 60) e(90) (last pair changed first, using C3-C2-Cl in (AA) to (G+ G-); followed by changing the first pair, using C4-C3-C2 in (AG+) to (G + G-); and the total increment is +3.7”). No label in any pair was changed in these steps that was not adjacent to either i( 180), i(60), or e(180); except for those which are not adjacent to any other one. In the same fashion, all the angles of Table 9 were obtained. The specified rules seem sufficient for the present cases, to eliminate ambiguous sequences which arrive at the same terminal labels with different increments. Whereas, it cannot be ruled out that such ambiguities may arise in larger systems, the success in predicting triple-labelled parameters from dual labels makes it likely that also quadruple-labelled angles in longer chains can be estimated in this way. CONCLUSIONS
So many structural trends have been predicted correctly by the analysis presented above that it is difficult to believe that the results are fortuitous. At the same time, this empirical procedure is so simple that further tests concerning its general extension are desirable. In any case, for n-pentane and n-hexane, the C-C bond distances have been successfully estimated from those of n-butane, with a most frequent error of 0.001 A, and a single maximum deviation of 0.003 A, for a distance range extending 0.012 A from 1.541 to 1.553 A. Similarly, the C-C-C angles in n-hexane were predicted from those of n-pentane with a most typical accuracy of 0.1” in unstrained cases, and a maximum deviation of 0.54 for a total angular range of nearly 5”. It is a particular point of interest that, even in forms with the combination G+ G-, in which non-bonded interactions come into play which do not exist in n-butane, the agreement is nevertheless satisfactory. At the same time, the fact that the largest discrepancies are found for the strained cases, and (G-G + G-), should serve as a warning that (G+ G-), (G- G--G+), in the strained conformations of large systems, where non-bonded interactions cannot be estimated from the current data, the predictions may become inaccurate. Among the strained systems are those with (G + G-) sequences, for which the 90” or 60” status might be complicated to predict in long chains. Any uncertainty of this kind implies the possibility of additional errors of 1-2” and 0.005 A, which may still leave the method competitive with current experimental resolution. Compared to experimental results, the 4-21G parameters of n-hydrocarbons are rather accurate. A correction of -0.008 A relates aliphatic 4-21G bonds to electron-diffraction, r g, parameters [12], while the calculated and experimental C-C-C angles are practically the same [ 121. One is thus tempted to believe that the procedure described in this paper will provide realistic structural estimates for the low energy forms of a whole class of compounds.
144
There is growing evidence [ 15, 161 that similar results can be expected for hetero-systems. Further reports of our ongoing studies will be reported elsewhere. ACKNOWLEDGEMENT
Support by NSF grant ISP-8011447
is gratefully acknowledged.
REFERENCES 1 N. L. Allinger, L. Schafer, K. Siam, V. J. Klimkowski and C. Van Alsenoy, J. Comput. Chem., 6 (1985) 331. 2 J. N. Scarsdale, C. Van Alsenoy and L. Schafer, J. Mol. Struct. (Theochem), 86 (1982) 277. 3 J. N. Scarsdale, H. L. Sellers, L. Schafer and N. L. Allinger, J. Comput. Chem., 3 (1982) 269. 4 C. Van Alsenoy, J. N. Scarsdale and L. Schafer, J. Chem. Phys., 74 (1981) 6278. 5 C. Van Alsenoy, J. N. Scarsdale and L. SchZfer, J. Comput. Chem., 3 (1982) 53. 6 N. S. Chiu, J. D. Ewbank and L. Schafer, J. Mol. Struct. (Theochem), 86 (1982) 397. 7 V. J. Klimkowski, J. P. Manning and L. SchHfer, J. Comput. Chem., 6 (1985) 570. 8 P. Pulay, G. Fogarasi, F. Pang and J. E. Boggs, J. Am. Chem. Sot., 101 (1979) 2550. 9 P. Pulay, Mol. Phys., 17 (1969) 197. 10 P. Pulay, Theor. Chim. Acta, 50 (1979) 299. 11 L. Schafer, J. Mol. Struct., 100 (1983) 51. 12 L. Schafer, C. Van Alsenoy and J. N. Scarsdale, J. Mol. Struct. (Theochem), 86 (1982) 349. 13 V. J. Klimkowski, J. D. Ewbank, C. Van Alsenoy, J. N. Scarsdale and L. Schafer, J. Am. Chem. Sot., 104 (1982) 1476. 14 L. Schafer, C. Van Alsenoy and J. N. Scarsdale, J. Chem. Phys., 76 (1982) 1439. 15 L. Schafer, J. D. Ewbank, K. Siam, V. J. Klimkowski and C. Van Alsenoy, J. Mol. Struct. Theochem), 133 (1985) 281. 16 L. Schafer, J. D. Ewbank, C. Van Alsenoy, V. J. Klimkowski and K. Siam, J. Mol. Struct. (Theochem), 135 (1986) 141.
A SIMPLE PROCEDURE FOR QUANTITATIVE PREDICTIONS OF THE C-C FRAMEWORK BOND DISTANCES AND ANGLES IN n-HYDROCARBONS*
LOTHAR SCHAFER, KHAMIS SIAM and JOHN D. EWBANK Department of Chemistry 72701 (U.S.A.)
and Biochemistry,
University
of Arkansas,
Fayetteville,
AR
EIJI OSAWA Chemistry
Department,
Hokkaido
University,
Sapporo
060 (Japan)
ABSTRACT The structures of four conformations of n-pentane, and of ten conformations of nhexane were determined by ab-initio gradient geometry refinements on the 4-21G level. The results are used to demonstrate the efficacy of a simple empirical procedure to predict the C-C bond distances and C-C-C angles of long-chain n-hydrocarbons from small molecules. Specifically, the C-C bond distances of n-pentane and n-hexane are predicted from those of n-butane (published previously) with a most frequent error of 0.001 a, and a maximum error of 0.003 A, while the C-C-C angles of n-hexane are predicted from n-pentane with a typical deviation of 0.1” in unstrained conformational states, and a maximum deviation of 0.5” in strained conformations. It is expected that the procedure is generally effective in quantitative structural predictions of the C-C framework of the low energy conformational states of n-hydrocarbons regardless of chain length. INTRODUCTION
The current paper is a continuation of our structural work on hydrocarbons which so far has involved some n-hydrocarbons [l-3], strained cyclic systems [4, 51, and cyclohexane derivatives [6, 71. For this study we have refined the structures of four conformations of n-pentane, and of ten conformations of n-hexane, in order to explore one possibility of predicting structural parameters of long chain hydrocarbons from smaller systems. The 4-21G basis [8] was used for the geometry refinements with Pulay’s gradient method [ 91 and program [lo]. It was our specific goal to determine the accuracy with which it is possible to predict the C-C bond distances of n-pentane and n-hexane from those of n-butane published previously [ 11, and the C-C-C angles of n-hexane from those of n-pentane. The C-C bonds of n-butane can be classified into sufficiently generalised types, from which the bond distances of larger systems *Paper No. 53 in the series: Ab Initio Studies of Structural Features Not Easily Amenable to Experiment. 0166-1280/86/$03.50
o 1986 Elsevier Science Publishers B.V.
126
can be modelled; for C-C-C angles, n-pentane is the smallest system from which a comprehensive set can be derived that is sufficient for parameter predictions. We refer to previous comparisons [ll-131 of 4-21G calculations with experimental results to estimate the general accuracy of the structures derived in this paper. RESULTS
AND DISCUSSION
Notation Throughout this discussion, the following notation will be used. The C-C-C-C torsional angles are r1 = Cl-C2-C3-C4, r2 = C2-C3-C4-C5, and r3 = C3-C4-C5-C6. They are designated A, or G+, when their values are in the vicinity of 180” (A), or either k60” or +90” (Gk), and each conformation is characterized by the A or G symbol for its C-C-C-C torsions. Thus, in form (AG+) of pentane, 7 1 is in the vicinity of 180”, and 72 is in the vicinity of +60” ; and in form (G - G + G -) of n-hexane, 71, 72, and 73 are close to -90°, + 60” and -go”, respectively. In each C-C-C-C torsional angle, we identify an internal (i) and an external (e) C-C bond distance. For example, C2-C3 is internal and Cl-C2 is external in rl. In n-pentane or n-hexane, some C-C bond distances must be multi-labelled. For example, C2-C3 in n-pentane is both i to 71 and e to 72; and C3-C4 in n-hexane is simultaneously e to TV and 73 and i to r2. A similar notation holds for C-C-C angles. When both legs of a bond angle are part of a given torsion, the angle is labelled “internal” (i). When only one leg of a bond angle is part of a torsion, it is termed “external” (e). Thus, C5-C4-C3 is e to pi and i to 72 in n-pentane; and e to TV and i to both 72 and 73 in n-hexane. These examples also show that, for systems larger than butane, the C-C-C angles must be multi-labelled and, furthermore, that n-butane does not contain all the angle types which are needed to describe long-chain systems. A complete set of all i or e labels, followed by the value (in degrees) of the torsional angle involved, is needed for each parameter to identify its type. That is, parameter type is determined by all the associations, i or e, of a given parameter with the C-C-C-C torsions of a system, and by the conformational states of the latter. Thus, bond angle C4-C3-C2 in nhexane, conformation (G + AA), is i(60)i(MO)e(180), because it is i to TV and 72 and e to TV, while the magnitudes of these torsions in this conformation are close to 60”, 180” and NO”, respectively. The characteristic torsional angles and conformational energies for npentane and n-hexane are given in Tables 1 and 2. The 4-21G optimized structures for both compounds are listed in Tables 3-5. Symmetric and asymmetric forms are listed together, even though this leads to some redundant entries for the symmetric forms, because this provides the fastest way
127 TABLE 1 Characteristic torsional angles (“), and total (E) and relative (AE) energies for four 4-21G optimized conformations of n-pentane Conformation
4-3-2-l
5-4-3-2
E
(kcal mol-’ ) (AA) (AG+) (G+G+) tG+G-)
180 176.9 61.4 64.6
0.0 0.86 1.63 3.69
-122,949.57 -122,948.71 -122,947.94 -122,945.88
180 65.7 61.4 -93.8
tktal mol-’ )
TABLE 2 Characteristic torsional angles (“) and total (E) and relative energies optimized conformations of n-hexane Conformation
(AAA) (G + AA) (AG + A) (AG-G-0) (G--G-) (G--G+) (G -G - 0) (AG-G+) (G-G-G+) (G-G+ G-)
4-3-2-l
180.0 66.3 176.6 -175.6 -66.0 -67.0 -61.6 -172.9 -62.7 -93.8
5-4-3-2
6-5-4-3
(AE)
E
(kcal mol-’ ) 180.0 176.7 67.0 -61.8 -172.9 -179.8 -59.2 -65.4 -66.5 64.8
180.0 179.6 176.5 -61.1 -66.0 67.3 -61.6 92.2 91.7 -93.0
for ten 4-21G
-147,394.41 -147,393.55 -147,393.53 --147,392.74 -147,392.70 -147,392.60 -147,391.98 -147,390.71 -147,389.85 -147,387.68
rk:al mol-’ ) 0.0 0.86 0.88 1.67 1.71 1.81 2.43 3.70 4.56 6.73
to determine specific parameter changes between corresponding segments of symmetric and asymmetric conformations. In the last phase of the refinements, the symmetry of some forms was affected by slight rounding effects, but these were not corrected because they are insignificant. Differences between different parameter types of n-butane (4-21G values from ref. 1) and n-pentane are given in Tables 6 and 7. The C-C bond distances of n-pentane and n-hexane, predicted from those of n-butane, are compared with the 4-21G optimized values in Table 8; the C-C-C angles of n-hexane, predicted from those of n-pentane, are compared with the 4-21G optimized values in Table 9. Atom numbering is explained in Figs. l-3 and the conformational dependence of bond distances and angles in n-butane on the C-C-C-C torsion is documented in Figs. 4 and 5, which are based on the 4-21G values of ref. 1.
128 TABLE3 Structural parameters (bond distances in A, anglesin degrees) forthe 4-21G optimized geometriesofthe n-pentane conformations(AA),(AG+),(G+G+)and (G+G-)
(AA) 2 6 7 8 3 9 10 4 11 12 5 13 14 15 16 17 6 7 7 8 8 8 3 9 9 10 10 10 4 11 11 12 12 12 5 13 13 14 14 14 15 16 16 17 17 17 3
1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 2
2 2 6 2 6 7 1 1 3 1 3 9 2 2 4 2 4 11 3 3 5 3 5 13 4 4 15 4 15 16 1
6
1.5408 1.0835 1.0839 1.0839 1.5415 1.0850 1.0850 1.5415 1.0858 1.0858 1.5408 1.0850 1.0850 1.0835 1.0839 1.0839 111.08 110.68 108.12 110.68 108.12 108.05 112.37 109.46 109.23 109.46 109.23 106.95 112.73 109.25 109.25 109.25 109.25 106.94 112.37 109.23 109.46 109.23 109.46 106.95 111.08 110.68 108.12 110.68 108.12 108.05 180.0
(AG+ 1
(G + G +)
(G+ G-1
1.5412 1.0832 1.0839 1.0838 1.5423 1.0832 1.0852 1.5445 1.0856 1.0859 1.5418 1.0851 1.0847 1.0834 1.0840 1.0822 111.07 110.61 108.15 110.65 108.19 108.06 111.94 109.17 109.95 109.47 109.11 107.08 114.00 108.48 108.74 109.27 109.25 106.87 113.67 109.18 109.55 108.63 108.76 106.82 110.61 110.50 108.10 111.44 107.88 108.20 -179.9
1.5413 1.0835 1.0841 1.0825 1.5453 1.0849 1.0834 1.5453 1.0856 1.0856 1.5413 1.0834 1.0849 1.0835 1.0841 1.0825 110.62 110.56 108.10 111.40 107.88 108.15 113.54 108.86 108.13 109.62 109.93 106.56 115.25 108.51 108.71 108.71 108.51 106.83 113.54 109.93 109.62 108.13 108.80 106.56 110.62 110.56 108.10 111.40 107.88 108.15 175.5
1.5411 1.0838 1.0838 1.0819 1.5461 1.0851 1.0852 1.5528 1.0854 1.0849 1.5432 1.0844 1.0849 1.0839 1.0809 1.0840 110.39 110.79 108.06 111.39 107.75 108.34 114.93 108.68 108.18 109.23 108.81 106.70 115.12‘ 109.39 109.43 107.37 108.61 106.56 114.18 108.74 107.91 109.42 109.78 106.51 110.57 111.83 108.09 110.24 107.99 108.00 173.6
129 TABLE 3 (continued)
(AG+1
(AAl 3 3 9 9 9 10 10 10 4 4 4 11 11 11 12 12 12 5 5 5 13 13 13 14 14 14 15 15 15 16 16 16 17 17 17
2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5
1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4
7 8 6 7 8 6 7 8 1 9 10 1 9 10 1 9 10 2 11 12 2 11 12 2 11 12 3 13 14 3 13 14 3 13 14
60.0 -59.8 58.1 -62.0 178.3 -58.8 -178.9 61.4 176.9 -61.6 55.6 55.6 177.1 -65.8 -60.6 60.9 178.1 65.7 -173.2 -56.9 -57.0 64.2 -179.5 -173.1 -52.0 64.3 176.2 -61.4 55.1 56.5 179.0 -64.6 -63.8 58.6 175.1
59.9 -59.9
58.5 -61.7 178.6 -58.5 -178.6 61.7 180.0 -58.3 58.3 58.3 180.0 -63.3 -58.3 63.3 180.0 180.0 -58.3 58.3 58.3 180.0 -63.3 -58.3 63.3 180.0 180.0 -58.5 58.5 59.9 -178.6 -61.7 -59.9 61.7 178.6
(G+ Gt) 55.8 -64.5 55.1 -64.7 175.0 -61.1 179.2 58.9 61.4 -177.8 -61.8 -60.8 60.1 176.0 -176.6 -55.8 60.2 61.4 -176.6 -60.8 -61.8 60.2 176.0 -177.8 -55.8 60.1 175.5 -61.1 55.1 55.8 179.2 -64.7 -64.5 58.9 175.0
(G t G-) 54.0 -66.7 52.3 -67.4 172.0 -63.8 176.6 55.9 64.6 -173.8 -58.2 -59.1 62.6 178.1 -174.3 -52.7 62.8 -93.8 29.9 145.8 145.7 -90.7 25.3 29.7 153.4 -90.7 -178.5 -57.5 58.2 61.0 -178.0 -62.3 -59.2 61.8 177.5
TABLE 4 Structural parameters (bond distances in A, angles in degrees) for the 4-21G optimized geometries of the n-hexane conformations (AAA), (G + AA), (AG + A), (AG -G-) and (G - AG-)
(AAN 2 7 8 9 3
1 1 1 1 2
1.5405 1.0839 1.0834 1.0839 1.5416
(G+AN 1.5417 1.0841 1.0836 1.0823 1.5447
(AG + A) 1.5412 1.0839 1.0833 1.0839 1.5424
(AG-G-) 1.5413 1.0838 1.0833 1.0840 1.5420
(G--G-) 1.5416 1.0824 1.0836 1.0841 1.5450
130 TABLE 4 (continued)
10 2 11 2 4 3 12 3 13 3 5 4 14 4 15 4 6 5 16 5 17 5 18 6 19 6 20 6 71 81 81 91 91 91 3 2 10 2 10 2 11 2 11 2 11 2 4 3 12 3 12 3 13 3 13 3 13 3 5 4 14 4 14 4 15 4 15 4 15 4 6 5 16 5 16 5 17 5 17 5 17 5 18 6 19 6 19 6
2 2 7 2 7 8 1 1 3 1 3 10 2 2 4 2 4 12 3 3 5 3 5 14 4 4 6 4 6 16 5 5 18
(AAA)
(G+AA)
(AG+ A)
(AG-G-)
(G--G-)
1.0850 1.0850 1.5416 1.0858 1.0858 1.5416 1.0858 1.0858 1.5405 1.0850 1.0850 1.0833 1.0839 1.0839 110.71 111.12 108.09 110.71 108.00 108.09 112.35 109.48 109.22 109.48 109.21 106.94 112.72 109.20 109.30 109.20 109.30 106.94 112.72 109.31 109.19 109.31 109.21 106.94 112.35 109.23 109.49 109.21 109.47 106.95 111.11 110.71 108.10
1.0851 1.0847 1.5422 1.0856 1.0858 1.5422 1.0840 1.0860 1.5408 1.0849 1.0851 1.0833 1.0839 1.0839 110.54 110.63 108.07 111.44 108.18 107.85 113.60 109.51 109.18 108.80 108.69 106.84 113.89 108.75 108.61 109.18 109.30 106.87 112.37 110.01 108.84 109.23 109.17 107.07 112.33 109.25 109.50 109.21 109.46 106.94 111.08 110.66 108.14
1.0852 1.0833 1.5446 1.0859 1.0856 1.5424 1.0856 1.0859 1.5412 1.0833 1.0852 1.0833 1.0839 1.0839 110.66 111.05 108.12 110.69 108.05 108.16 111.95 109.46 109.13 109.14 109.97 107.07 113.97 109.27 109.29 108.49 108.74 106.83 113.97 108.74 108.49 109.29 109.27 106.83 111.95 109.97 109.14 109.13 109.46 107.07 111.05 110.66 108.12
1.'0835 1.0852 1.5454 1.0857 1.0842 1.5456 1.0857 1.0856 1.5413 1.0835 1.0849 1.0836 1.0825 1.0841 110.70 111.07 108.16 110.65 108.04 108.12 111.97 109.11 109.92 109.47 109.22 107.03 113.97 108.52 108.22 109.29 110.02 106.53 115.34 108.59 108.70 108.64 108.46 106.77 113.59 109.96 109.56 108.15 108.80 106.53 110.62 111.41 107.84
1.0848 1.0851 1.5430 1.0842 1.0858 1.5450 1.0858 1.0842 1.5416 1.0851 1.0848 1.0836 1.0824 1.0841 111.47 110.67 107.82 110.59 108.14 108.03 113.56 108.80 108.66 109.51 109.23 106.86 113.48 108.85 110.03 108.69 108.56 107.03 113.48 108.55 108.69 110.03 108.85 107.03 113.57 109.23 109.51 108.65 108;79 106.86 110.67 111.47 107.82
131 TABLE4(continued)
(AA-41 20 20 20 3 3 3 10 10 10 11 11 11 4 4 4 12 12 12 13 13 13 5 5 5 14 14 14 15 15 15 6 6 6 16 16 16 17 17 17 18 18 18 19 19 19 20 20 20
6 6 6 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6
5 18 19 17 18 19 17 18 19 17 18 19 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5
1 10 11 1 10 11 1 10 11 2 12 13 2 12 13 2 12 13 3 14 15 3 14 15 3 14 15 4 16 17 4 16 17 4 16 17
110.70 108.10 108.01 59.9 180.0 -59.9 -178.6 -58.5 61.6 -61.7 58.5 178.6 180.0 58.3 -58.3 -58.3 180.0 63.4 58.3 -63.4 180.0 180.0 58.4 '-58.4 -58.4 180.0 63.2 58.3 -63.3 180.0 180.0 58.3 -58.3 -58.3 180.0 63.4 58.4 -63.3 -179.9 180.0 58.5 -58.5 59.9 -61.7 -178.6 -59.9 178.6 61.6
(G+ AA) 110.65 108.14 108.06 56.4 176.1 -63.9 178.8 -61.5 58.4 -64.8 54.9 174.9 66.3 -56.2 -172.4 -172.4 65.1 -51.1 -56.1 -178.7 65.1 176.7 55.3 -60.9 -61.9 176.8 60.5 55.4 -66.0 177.8 179.6 57.5 -59.0 -58.7 179.2 62.7 58.0 -64.1 179.3 179.9 58.3 -58.6 59.8 -61.8 -178.7 -60.0 178.5 61.5
(AGt
A)
110.69 108.16 108.05 59.9 179.9 -59.9 -179.0 -58.9 61.2 -62.1 58.0 178.1 176.6 55.2 -61.9 -60.9 177.8 60.6 55.3 -66.1 176.8 67.0 -55.5 -171.8 -171.8 65.6 -50.6 -55.5 -178.1 65.6 176.5 55.2 -60.9 -62.0 176.7 60.6 55.2 -66.1 177.8 180.0 58.0 -58.9 59.9 -62.1 -179.0 -59.9 178.1 61.3
(AG-G-O) 110.62 108.08 108.15 60.1 -179.7 -59.7 -178.0 -57.8 62.3 -61.2 59.0 179.1 -175.6 63.0 -54.2 -54.9 -176.4 66.5 60.9 -60.6 -177.7 -61.8 177.4 61.4 60.5 -60.4 -176.4 176.2 55.4 -60.6 -61.1 176.7 60.9 62.1 -60.1 -175.9 178.0 55.8 -59.9 -174.9 61.7 -54.4 65.2 -58.2 -174.3 -55.2 -178.6 65.3
(G--G-) 110.59 108.03 108.14 64.0 -176.0 -56.3 -174.9 -54.9 64.8 -58.4 61.6 -178.7 -66.0 172.8 56.5 56.9 -64.4 179.4 173.1 51.9 -64.3 -172.9 64.9 -51.9 -51.9 -174.1 69.1 64.9 -57.3 -174.1 -66.0 173.2 56.9 56.6 -64.3 179.5 172.8 51.9 -64.3 -176.0 61.6 -54.8 64.0 -58.4 -174.8 -56.3 -178.7 64.8
132 TABLE5 Structural parameters (bond distances in A, anglesin degrees) forthe 4-21G optimized geometriesof the n-hexane conformations(G--G+), (G-G-G-), (AG-G+), (G-G-G+)and(G-G+G-)
21 71 81 91 3 2 10 2 11 2 4 3 12 3 13 3 5 4 14 4 15 4 6 5 16 5 17 5 18 6 19 6 20 6 712 812 817 912 917 918 321 10 2 1 10 2 3 11 2 1 11 2 3 11 2 10 43 2 12 3 2 12 3 4 13 3 2 13 3 4 13 3 12 54 3 14 4 3 14 4 5 15 4 3 15 4 5 15 4 14 65 4 16 5 4 16 5 6 17 5 4 17 5 6
(G--G+)
(G-G-G-)
(AG-GG+)
(G-G-G+)
(G-G+G-)
1.5416 1.0822 1.0836 1.0841 1.5455 1.0848 1.0852 1.5426 1.0860 1.0837 1.5455 1.0860 1.0837 1.5416 1.0848 1.0852 1.0836 1.0841 1.0822 111.55 110.62 107.79 110.55 108.16 108.04 113.74 108.72 108.60 109.54 109.19 106.82 113.57 109.16 109.22 108.36 109.31 107.00 113.56 109.24 109.16 109.30 108.37 107.01 113.73 108.61 108.71 109.19 109.54
1.5414 1.0825 1.0836 1.0841 1.5451 1.0849 1.0837 1.5463 1.0858 1.0840 1.5451 1.0840 1.0858 1.5414 1.0837 1.0849 1.0836 1.0825 1.0841 111.43 110.64 107.84 110.59 108.14 108.07 113.57 108.80 108.20 109.53 109.96 106.53 115.21 108.47 108.22 108.82 109.30 106.47 115.21 169.30 108.82 108.22 108.47 106.47 113.57 109.96 109.53 108.20 108.80
1.5415 1.0838 1.0833 1.0840 1.5420 1.0828 1.0849 1.5466 1.0860 1.0859 1.5524 1.0855 1.0849 1.5433 1.0845 1.0850 1.0839 1.0840 1.0808 110.68 111.05 108.17 110.67 108.05 108.12 111.76 109.01 109.88 109.44 109.41 107.23 115.45 108.33 108.10 108.99 108.94 106.66 115.41 109.43 109.41 107.25 108.44 106.52 114.24 108.63 107.86 109.44 109.83
1.5412 1.0821 1.0836 1.0842 1.5446 1.0852 1.0826 1.5478 1.0861 1.0857 1.5522 1.0840 1.0852 1.5433 1.0846 1.0850 1.0839 1.0841 1.0807 111.50 110.66 107.90 110.48 108.12 108.05 113.56 108.64 107.93 109.90 110.10 106.43 116.74 108.11 108.17 108.64 108.14 106.61 115.33 110.28 109.57 106.77 108.20 106.25 114.60 108.49 107.78 109.38 109.74
1.5432 1.0810 1.0840 1.0839 1.5524 1.0838 1.0846 1.5490 1.0852 1.0856 1.5521 1.0856 1.0853 1.5432 1.0846 1.0839 1.0808 1.0839 1.0840 111.88 110.11 107.96 110.69 108.09 107.98 113.96 110.12 109.73 107.76 108.53 106.42 116.77 108.30 106.72 109.16 109.03 106.35 116.78 109.07 109.16 106.71 108.26 106.36 114.03 108.48 107.74 109.71 110.13
133
TABLE 5 (continued) (G-AGt) 17 5 18 6 19 6 19 6 20 6 20 6 20 6 321 3218 3219 102 1021 1021 112 112 112 43 43 43 123 12 3 12 3 133 13 3 13 3 54 54 5 4 144 14 4 14 4 154 15 4 15 4 65 6 5 65 165 16 5 16 5 175 17 5 17 5 186 18 6 18 6 196 19 6 19 6 206 20 6 20 6
16 5 5 18 5 18 19 7
1
7 8 9 7 8 9 1
1 1 1 2 210 211 2 1 2 10 2 11 2 1 2 10 2 11 3 2 312 313 3 2 3 12 3 13 3 2 3 12 3 13 4 3 414 415 4 3 4 14 4 15 4 3 4 14 4 15 5 4 5 16 5 17 5 4 5 16 5 17 5 4 5 16 5 17
106.82 110.62 110.55 108.04 111.55 107.79 108.16 64.1 -175.9 -56.3 -174.8 -54.8 64.8 -58.4 61.6 -178.8 -67.0 171.8 55.7 55.2 -66.0 177.8 171.4 50.2 -66.0 -179.8 58.1 -58.7 -57.7 -179.8 63.4 59.1 -63.0 -179.8 67.3 -54.9 -171.1 -171.6 66.3 -49.9 -55.4 -177.6 66.2 176.0 54.9 -61.5 56.4 -64.7 178.9 -64.0 174.9 58.5
(G-G-G-) 106.53 110.64 111.43 107.84 110.59 108.07 108.14 64.8 -175.2 -55.5 -174.6 -54.6 65.1 -58.5 61.5 -178.8 -61.6 177.5 61.5 59.8 -61.1 -177.0 175.3 54.4 -61.6 -59.2 179.3 63.7 63.7 -57.9 -173.4 179.3 57.7 -57.9 -61.6 175.3 59.9 61.5 -61.6 -177.0 177.5 54.4 -61.0 -175.2 61.5 -54.6 64.9 -58.5 -174.6 -55.4 -178.8 65.1
(AG-Gt) 106.54 110.52 110.25 107.98 111.90 108.06 108.01 60.5 -179.4 -59.3 -177.9 -57.7 62.4 -60.9 59.3 179.4 -172.9 66.0 -51.5 -51.5 -172.7 69.8 64.2 -57.0 -174.5 -65.4 173.1 57.5 58.5 -63.0 -178.6 173.6 52.1 -63.4 92.2 -31.7 -147.5 -147.3 88.8 -27.1 -31.4 -155.3 88.9 177.8 57.0 -58.8 58.5 -62.3 -178.1 -61.7 177.4 61.7
(GyG-G+) 106.52 110.46 110.31 107.93 111.97 107.96 108.08 64.5 -175.4 -55.8 -175.4 -55.3 64.4 -59.3 60.8 -179.6 -62.7 176.8 61.1 59.5 -61.0 -176.8 174.8 54.3 -61.5 -66.5 171.4 56.3 58.3 -63.8 -178.9 173.3 51.2 -63.9 91.7 -33.4 -148.8 -147.8 87.1 -28.3 -32.0 -157.1 87.5 176.9 56.1 -59.6 57.7 -63.2 -178.8 -62.7 176.4 60.8
(G-G+ 106.43 111.92 110.66 108.07 110.11 107.97 107.97 59.6 -60.4 -179.7 -64.2 175.8 56.5 -179.9 60.1 -59.2 -93.8 30.2 146.1 145.8 -90.2 25.7 30.4 154.4 -89.7 64.8 -174.0 -59.5 -59.5 61.7 176.2 -174.0 -52.8 61.7 -93.0 31.2 146.6 146.9 -88.8 26.6 31.1 155.3 -89.3 60.2 -179.3 -63.7 -179.2 -58.7 57.0 -59.9 60.6 176.2
G-)
134 TABLE 6 4-21G optimized typesa
parameters of n-butane and differences between different parameter
Parameter
Type
C2-C3 C2-C3 Cl-C2 Cl-C2
i(180) i(180) e(180) e(180)
C3-C2-C1 C3-C2--Cl
i(180) i( 180)
Value
Type
1.5416 1.5416 1.5405 1.5405 112.37 112.37
i( 60) i( 90) e(60) e(90) i(60) i( 90)
Diff.
Value 1.5444 1.5499 1.5414 1.5417
+ 0.003 + 0.008 + 0.001 + 0.001
113.81 112.65
+1.4 + 0.3
aBond distances in A, bond angles in degrees [ 11. The type symbols are explained in the text. TABLE 7 Differences between different C-C-C Parameter
Type
C3-C2-C1
(AA): (AA): (AA):
C4-C3-C2
(AA): (AA): (AA):
C5-C4-C3
(AA): (AA):
angle types in various conformations
Value
Type
112.37
(AG+ ):
112.37
(G + G+):
112.37
(G+ 0):
i(180) i(180) i(180) i(180) i(180) i(180)
112.73
(AG+):
112.73
(G+ G+):
112.73
(G+ G-):
e(180) i( 180) e( 180) i(180)
112.37
(AG+):
112.37
(G+ G-):
i(180) e(180) i(180) e( 180) i(180) e(180)
of n-pentanea
Value i(180) e(60) i(60) e(60) i(60) e(90) i( 180) i( 60) i(60) i( 60) i(60) i( 90) e(180) i(60) e(60) i(90)
Diff.
111.94
-0.4
113.54
+ 1.2
114.93
+ 2.6
114.00
+1.3
115.25
+ 2.5
115.12
+ 2.4
113.67
+1.3
114.18
+1.8
a4-21G values are from this study. Type symbols are explained in the text.
Definition of parameter increments for structure predictions When the number of carbon atoms in the open chain of an n-hydrocarbon exceeds four, the C-C bond distances and angles of the all-anti states seem to be relatively independent of chain length. In nonane, for example, the distances, Cl-C2, C2-C3, C3-C4 and C4-C5 are (4-21G values, in A, from ref. 3) 1.5408, 1.5415, 1.5418, and 1.5418, respectively; and the angles,
135 TABLE 8 Predicted and calculated C-C n-hexanea n-Pentane (AA) 'Type
bond distances for various conformers of n-pentane and
(G+G+)
(AG+) Value
Pred.
Type
CalC.
(G+G-)
Type
Pred.
CalC.
Type
Pred.
talc.
Cl-C2
e(180) 1.541
e(180) 1.541
1.541
e(60)
1.542
1.541
e(60)
1.542
1.541
C2-C3
i(180) 1.541 e(180)
i(180) 1.542 e(60)
1.542
i(60) e(60)
1.545
1.545
i(60) e(90)
1.545
1.546
C3-C4
e(180) 1.541 i(180)
e(180) 1.544 i(60)
1.544
e(60) i(90)
1.550
1.553
c4-c5
e(180) 1.541
e(60)
1.542
1.542
e(90)
1.542
1.543
(AAA)
(G+AA) Type
Pred.
CalC.
Type
Pred.
C&h.
n-Hexane
Type
value
(AG+A)
(AG-G-) Pred.
ale.
Type
Cl-C2
e(180) 1.540
e(60)
1.541
1.542
~~(180) 1.540
1.541
e(180) 1.540
1.541
C2-C3
i(180) 1.542 e(180)
i(60) 1.545 e(180)
1.545
i(l80) 1.543 e(60)
1.542
i(180) 1.543 e(60)
1.542
c3-c4
e(180) 1.542 i(180) e(180)
e(60) 1.543 i(180) e(180)
1.542
e(180) 1.545 i(60) e(180)
1545
e(180) 1.546 i(60) e(60)
1.545
c4-c5
eU80) 1.542 i(180)
e(180) 1.542 i(180)
1.542
e(60) i(60)
1.546
1.546
C5-C6
e(180) 1.540
e(180) 1.540
1.541
e(60)
1.541
1.541
n-Hexane
(G-AG--) TYPO
Pred. Calc. 1.541 1.542
(G-AG+)
(G-G-G-)
Type
hed.
e(60)
Calc. Type
Pred.
(AG-G+) Calc. Type
Pred. Calc.
Cl-C2
e(60)
1.541
1.542 e(60) 1.541
1.541 e(180) 1.540 1.541
C2-C3
i(60) 1.545 1.545 e(180)
i(60) 1.545 e(180)
1.545 i(60) 1.546 e(60)
1.545 i(180) 1.543 1.542 e(60)
c3-c4
e(60) 1.544 1.543 i(180) e(60)
e(60) 1.544 i(180) e(60)
1.543 e(60) 1.547 i(60) e(60)
1.546 e(180) 1.546 1.547 i(60) e(90)
c4-c5
e(60) i(90)
1.551 1.552
C5-C6
e(90)
1.541 1.543
n-Hexane
(G-G-G+)
(G-G+G-)
5pe
Pred.
talc.
TYpe
Pred.
talc.
Cl-C2
e(60)
1.541
1.541
e(90)
1.541
1.543
C2-C3
i(60) e(60)
1.546
1.545
i(90) e(60)
1.551
1.552
c3-c4
e(60) i(60) e(90)
1.547
1.548
e(90) i[60) e(90)
1.547
1.549
c4-C5
e(60) i(90)
1.651
1.552
C5-C6
e(90)
1.541
1.543
aThe predicted values were obtained by the empirical procedure described in this paper. The calculated values are 4-21G results from this study. Distance types are explained in the text. Values determined by symmetry are omitted.
i(l80)
113.6
113.6
Pred.
e(60) i( 90)
e(60) i( 60) i(90)
114.1
115.0
114.6
115.3
i( 90) i(60) e(90)
i(90) i(60) i( 60) e(90)
116.7
113.6
et601 116.5
113.5
et601
i(60)
116.4
114.1
Pred.
Type
Pred.
Calc.
i( 60) i( 180) e(60)
i( 60) e( 180)
Type
Type
113.6
115.3
114.0
112.0
Calc.
(G-G+G-)
113.5
115.2
113.9
111.9
Pred.
(G-AG-)
(G-G-G+)
e(60) i(60)
e(180) i( 60) i( 60)
i(180) i( 60) e(60)
i(180) e(60)
Type
(AG-C+)
116.8
114.0
Calc.
113.5
113.6
Calc.
*The predicted values were obtained by the empirical procedure described in this paper. The calculated values are the 4-21G results from Tables 4 and 5. Type symbols are explained in the text. Values determined by symmetry are omitted.
114.2
114.1 e(60) i(90)
111.8
C6-C5-C4
111.9
115.4
dW
115.1
115.2
113.6
e(180) i(60) i(90)
115.1
113.5
Calc.
c5-C4-c3
i(60) i( 60) e(60)
e(60)
i(60)
Pred.
115.4
113.6
113.6
Calc.
Type
Pred.
Type
115.3
i(60) i(180) e(60)
C4-C3-C2
113.7
Calc.
113.6
Pred.
)
114.0
111.9
Calc.
i(180) i(60) e(90)
i(60) e(l80)
C3-C2-Cl
Type
114.0
111.9
Pred.
(AG-G+
(G-AG+
Parameter
i( 180) i(60) e(180)
i(180) e(60)
Type
(AG+ A)
of n-hexane*
(G-G-G-)
112.3
112.3
e(180) i(180)
112.3
e( 180) i(180)
C6-C5-C4
)
112.4
112.3
e(60) i(180) i( 180)
112.7
113.9
114.0
e( 180) i(180) i(180)
c5-C4-c3
113.6
113.6
i( 60) i(180) e(180)
Calc.
Pred.
112.7
i( 180) i( 180) e(180)
C4-C3-C2
Type
i( 60) e(180)
Value
(G+ AA)
angles in various conformations
112.3
i( 180) e(180)
Type
(AAA)
C3-C2-Cl
Parameter
Calculated and predicted C-C-C
TABLE 9
137
HB\ /HgH32\ ,H13 H5,C 1/“\
H6’
\ H7
/c41H
H9,Hl0
14
H6,
H7#j’ H8
ic3\ Hl0 Hll
Fig. 1. Atom numbering for n-butane.
Hla
H/1’
H14 H15
I H9
Hli
z? \c3/c4\
HI{
h2
,HlS ” H\17H16
Fig. 2. Atom numbering for n-pentane.
H18 \ ,H19
t 4/ \c5/c6iH20
H7,c l/c2\c3/ H8’
ic
H1\3/nl4
h3
Hi/s A17
Fig. 3. Atom numbering for n-hexane.
Cl-C2-C3, C2-C3-C4, C3- C4-C5, and C4-C5-C6 are (4-21G values, in degrees, ref. 3) 112.4, 112.7,112.7, and 112.7, respectively. These values are practically identical with those calculated here for n-pentane (AA) and n-hexane (AAA). Therefore, it seems that the framework of the all-anti forms of n-hydrocarbons can be considered practically constant and essentially known. It may thus serve as a reference from which parameter increments can be measured which incorporate the bond distance and angle changes which accompany the transitions of a system from the most stable all-anti state to other points of its conformational energy surface. In Figs. 4 and 5 the changes in bond distances and angles are plotted which occur in n-butane during a complete rotation of TV,These plots illustrate the concept of “local geometry” [ll, 141: the magnitudes of the structural parameters of a molecule are local at a given point of its potential energy surface, i.e., they can differ significantly for different combinations of its torsional angles. For n-hydrocarbons and C-C-CC torsions, Figs. 4 and 5 indicate that internal C-C bonds vary more with conformation than external C-C or C-H bonds; and that significant conformational variations must also be expected for internal C-C-C angles. In Tables 6 and 7 differences are listed for various parameter types of nbutane and n-pentane which are found between their values in different torsional states. Thus, when a C-C bond is i( 60) in n-butane, it is 0.003 _i$longer than when it is i( 180). Similarly, an i(60) i(60) C-C-C angle in n-pentane is 2.5” more extended than the i(180) i(180) type. We expect that parameter increments of this kind, i.e., differences between the different specified parameter types, in n-hydrocarbons are relatively independent of. chain length, except in the strained states of large systems, when long-range non-bonded interactions are the source of special effects.
138
BUTRNE BOND
OISTRNCES
H9-C2 H8-C2 H7-Cl H6-Cl .
/
‘HS-Cl I 1c2-Cl
C3-C2
0
60
120
180
240
300
3 i0
Fig. 4. The variation of some bond distances of n-butane with the torsional angle 7 = Cl-C2-C3-C4. Each curve represents the differences of a parameter relative to its value at 7 = 0”. Different curves are plotted_ with the same scale on offset zero-lines.
These considerations form the basis of our empirical procedures for parameter prediction, which involves the following steps. (1) For each C-C bond distance and angle determine its type, i.e., the complete set of labels, i(T1) or e(ri), in agreement with the convention put forth in the previous section. (2) For each parameter which is associated with a ri # 180°, find the appropriate increment from Tables 6 (for C-C bonds) and 7 (for C-C-C angles) which has to be added to its value in the all-anti state, to predict its magnitude in a different state. (3) If a parameter is multi-labelled and more than one of the associated 7i’S differ from 180”, find the correction for each Ti, and use the sum of all the corrections as the effective parameter increment. Some of the parameters and their increments in Tables 6 to 9 have been rounded to three significant decimals for distances, and one for angles. Carrying a larger number of digits might affect the accuracy in some cases,
139
BUTRNE BOND
RNGLES
H9-C2-C3
H8-C2-C3
H7-Cl
-C2
H6-Cl-C2
HS-Cl-C2
C3-C2-Cl
I
60
120 180 240 300 360
Fig. 5. The variation of some bond angles of n-butane with the torsional angle 7 = ClC2-C3-C4. Plot format is as in Fig. 4.
but it is not practically meaningful. The accuracy of the simple procedure described cannot be expected to be better than a few thousandths of an A and approximately 0.5”. This is sufficient for most practical purposes and even exceeds the current performance of experimental techniques in resolving single parameters in systems of this kind. For the same reason, geometry optimization for this study was terminated when the largest residual forces were reduced to 0.001 aJ A-’ for bond distances and 0.001 aJ rad-’ for bond angles. That is, in some cases errors due to incomplete optimization may amount to a few tenthousandths of an A and a few hundredths of a degree. The listing of parameter increments in Tables 6 and 7 was limited to the exact values of Ti = 60’, 90”, and 180”. By a few degrees, some of the torsions in the optimized geometries are not exactly at these values. In most cases these deviations are of little significance for the magnitudes of the increments. The largest ones are found for C3-C2 in n-butane in the region of i(90) to i(lOO), where the distance changes are 0.0004 A per degree of ri; and for C3-C2-Cl, in the region i(60) to i(70), where the changes are
140
-0.05” per degree of ri. Thus, using variable increments rather than a constant set, might affect the outcome of some predictions by a few thousandths of an W and a few tenths of a degree; i.e., these factors are approximately within the error limits pursued. This approach was also chosen, because we want to explore the possibility of predicting the framework of n-hydrocarbons without knowing their torsional angles exactly, except for their classification into (A), (G+), or (G-). In this context, it may be significant to note that the magnitudes of the torsional angles in n-pentane and n-hexane depend on the torsional sequence in a characteristic way. For example, in the combination of (A) with (G), the (G) torsions are often close to about 66”, except when, in n-hexane, this combination is also part of a (G+ G+ ) or (G - G-) arrangement. In that case, the values for (G) are close to about 61” as in (G + G+) of n-pentane. Similarly, in many (AG) combinations, the (A) torsions are close to 176” rather than 180”; and in (G + G-), one of the torsions is consistently at 93’. Even though we have not searched for the exact torsional minima, one is led to believe that these trends also exist in long-chain systems. In (G + G-) combinations, specifically, the 90” correction should always be applied to that torsional degree of freedom, whose displacement from 60” relieves the strain of the system. The above defines the basis of our procedure. If systems with special and unusual torsions are desired to be investigated, standard geometry functions [ 15, 161, i.e., analytic representations of torsionally-dependent parameter variations, should be employed for predictions of this kind. The procedure is expected to be effective, whenever bond distances and angles primarily depend on changes in torsions with which their relationship is e or i, while longer-ranging interactions are not so important. This condition is found, for example, by comparing the (AAA) and (G + AA) forms of n-hexane: when a torsion is changed at one end of the system, the structure at the other end is affected little. A second condition for the procedure to be effective is the additive nature of the parameter increments which are encountered, when a parameter is associated with several torsions for which simultaneous changes occur. In previous predictions of some structural parameters in polyfunctional systems [15, 161, the additivity has been found approximately to hold. In the following sections we shall test to what extent these considerations are applicable to n-hydrocarbons. Details of parameter
predictions
Since the C-C bonds of n-butane are both of type i and e, they can be used to estimate the bond distance trends in the larger systems, n-pentane and n-hexane. Among the results (Table 8), the following examples are particularly interesting. In n-pentane and n-hexane Cl-C2 is always exclusively of type e. In agreement with the changes found for the e-type C-C bond of n-butane, the
141
variations of Cl-C2 with 71 are always small. In n-pentane, C3-C2 is i to r1 and e to r2. Thus, in comparing (AA) with (AG+ ), the small change of an external bond is observed for this parameter. However, in going from (AA) to (G + G+ ) or (G + G-), the relatively large change of the i-type C-C! bond plus the e-type variation is observed. C3-C4 in n-pentane is e to 71 and i to r2. In comparing (AA) with (AG+), the expected i-type change is approximately found. In going from (AA) to (G+ G+), both the e-type and i-type changes are accumulated. An additional increment is found for C3-C4 in (G+ G-), because r 2 is in the vicinity of 90”, and the unusually long distance of 1.550 A results (calculated 1.553 A). In this conformation the most extended C-C bond range, from 1.541 to 1.553 A, is encountered. The multi-label cases of n-hexane are also of particular interest. C3-C4 is e(180) i(180) e(180) in (AAA). When it changes to e(180) i(60) e(180) in (AG + A), the i-type increment is found. In forms such as (AG - G-), where C3-C4 is e(180) i(60) e(60), or in (G-G-G+), where it is e(60) i(60) e(90), the additivity of the simultaneous parameter changes again is approximately confirmed. This result supports the view that systems larger than hexane may also be predicted in this way. Since the C-C-C angles of n-butane are only type i, n-pentane is the smallest system that can be used to define a comprehensive set of angle types, which can be applied to larger systems. In the determination of angle increments, the following details are important. The angles in n-pentane are all double-labelled. In n-hexane, the C-C-C angles can have two or three labels; and four labels are possible in still larger systems. The n-hexane double-label angles, C3-C2-Cl and C6-C5-C4, in all forms either have magnitudes which are very close to the corresponding types of n-pentane, or they can be easily predicted. An apparent complication arises, when the double-label increments of n-pentane are used to predict triple-label parameters, because the desired end result has to be approached in several steps for which different options may exist. For example, the transition of C4-C3-C2 in (AAA), where it is i(180) i(180) e(180), to (G-G-G-), where it is i(60) i(60) e(60), can be achieved by first applying the increment for i( 180) i( 180) e( 180) + i( 180) i(60) e(60) (using the C3-C2-C1 increment of +1.2”, for i(180) e(180) in (AA) to i(60) e(60) in (G + G+), Table 7) followed by i( 180) i(60) e(60) + i(60) i(60) e(60) (using the i( 180) i(60) C4-C3-C2 increment from (AG+ ) to i(60) i(60) in (G + G+), + 1.2”, Table 7), yielding a total increment of 2.4”; or it can be achieved by the sequence i( 180) i( 180) e( 180) + i( 180) i( 180) e(60) + i(180) i(60) e(60) + i(60) i(6C) e(60), with the corrections (all from Table 7) -0.4” (C3-C2-Cl from (AA) to (AG+)), +1.6” (C3-C2-Cl from (AG+) to (G+ G+)), and +1.2” (C4-C3-C2 from (AG+) to (G + G+)), also yielding a total increment of 2.4”. In the second sequence, proceding from i(180) i(180) e(60) + i(60) i(60) e(60), by using the (AA) to (G+ G+) increment for C4-C3-C2 (+2.5”), would not have been correct for the followingreason. Each triple angle label consists of two pairs which are made up of the first
142
two labels, and of the second and third, respectively. Therefore, when a single torsional angle changes for a triple-labelled C-C--C angle, two label pairs may be affected which are different. For example, in the transition i( 180) i( 180) e(60) + i(180) i(60) e(60), there is a change of two pairs, i(180) i(180) + i( 180) i(60) and, at the same time, of i( 180) e(60) + i(60) e(60), even though only one torsion has changed. Question is now as to whether this single torsional variation requires the sum of two increments, or only one, and if only one, which of the changing pairs should be chosen to define the increment. The answer is provided by the following observation. When the C-C-C angle in n-butane changes from i(180) to i(60), the increment is + 1.4’. In n-pentane, i( 180) + i(60) transitions in a pair have very similar increments, if the second label in the pair is either i(180), e( 180), or i(60). However, if the second label is e(60), there is an additional increment of +0.3’. Thus, Table 7, (AA) to (AG+) is +1.3” for both the i(180) i(180) + i(180) i(60) and the i( 180) e(180) --f i(60) e(180) combinations; and +1.2” for i(180) i(60) in (AG+) to i(60) i(60) in (G+ G+). However, for C3-C2-Cl and the transition i(180) e(60) in (AG+) to i(60) e(60) in (G + G+), the increment is + 1.6”. Therefore, the double-labelled increments of n-pentane can be used to find the triple-labelled angles in n-hexane without any further correction, if the labels which change in a pair are adjacent to a third label which is either i(180), i(60), or e(180), but not e(60). We shall illustrate this principle by giving a number of examples. For i(180) i(180) e( 180) -+ i(180) i(60) e( 180), change one pair, either i( 180) i( 180) + i(180) i(60), or i(180) e(180) -+ i(60) e(180), for an increment of +1.3” (C4-C3-C2 or C5-C4-C3, respectively, (AA) to (AG+), Table 7). This change is the same as for i(180) i(180) e(180) -+ i(60) i(180) e(180). For i(180) i( 180) e(180) -+ i(180) i(60) e(60), go i( 180) e(180) + i(60) e(60) (+1.2”, C3-C2-Cl, (AA) to (G+ G+), Table 7); do not go via the forbidden route i(180) i(180) e(180) + i(180) i(180) e(60) (pair i(180) e(180) + i(180) e(60), C3-C2-Cl, (AA) to (AG+), Table 7, -0.4”), followed by i(180) i(180) e(60) + i(180) i(60) e(60) (pair i(180) i(180) + i(180) i(60), C4-C3-C2, (AA) to (AG+), +1.3”), because the last step implies the change of a label in a pair which is adjacent to e(60). The last sequence can be followed only, if the additional +0.3” correction is applied, which holds for such a change. For i(180) i(180) e( 180) + i(60) i( 180) e( 60), first the pair i(180) i(180) is changed to i(60) i(180), then the pair i(180) e(180) is changed to i(180) e(60), yielding a total increment of +1.3” 0.4” = +0.9”. When a label in a pair is changed at the side which is not adjacent to another label, the increment determined for this pair can always be applied without any further correction. As a last example, we present the derivation of C4-C3-C2 in (G - G-G+ ) and (G- G + G-). For the former, the transition is i(180) i(180) e(180) + i(180) i(60) e(90) + i(60) i(60) e(90). The last pair was changed first, using C3-C2-Cl in (AA) to (G + G-); followed by a change in the first pair, using C4-C3-C2 in (AG+ ) to (G + G+ ); and the total correction is + 3.8”.
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For the latter, the transition is i(180) i( 180) e( 180) + i(180) i(60) e(90) + i(90) i( 60) e(90) (last pair changed first, using C3-C2-Cl in (AA) to (G+ G-); followed by changing the first pair, using C4-C3-C2 in (AG+) to (G + G-); and the total increment is +3.7”). No label in any pair was changed in these steps that was not adjacent to either i( 180), i(60), or e(180); except for those which are not adjacent to any other one. In the same fashion, all the angles of Table 9 were obtained. The specified rules seem sufficient for the present cases, to eliminate ambiguous sequences which arrive at the same terminal labels with different increments. Whereas, it cannot be ruled out that such ambiguities may arise in larger systems, the success in predicting triple-labelled parameters from dual labels makes it likely that also quadruple-labelled angles in longer chains can be estimated in this way. CONCLUSIONS
So many structural trends have been predicted correctly by the analysis presented above that it is difficult to believe that the results are fortuitous. At the same time, this empirical procedure is so simple that further tests concerning its general extension are desirable. In any case, for n-pentane and n-hexane, the C-C bond distances have been successfully estimated from those of n-butane, with a most frequent error of 0.001 A, and a single maximum deviation of 0.003 A, for a distance range extending 0.012 A from 1.541 to 1.553 A. Similarly, the C-C-C angles in n-hexane were predicted from those of n-pentane with a most typical accuracy of 0.1” in unstrained cases, and a maximum deviation of 0.54 for a total angular range of nearly 5”. It is a particular point of interest that, even in forms with the combination G+ G-, in which non-bonded interactions come into play which do not exist in n-butane, the agreement is nevertheless satisfactory. At the same time, the fact that the largest discrepancies are found for the strained cases, and (G-G + G-), should serve as a warning that (G+ G-), (G- G--G+), in the strained conformations of large systems, where non-bonded interactions cannot be estimated from the current data, the predictions may become inaccurate. Among the strained systems are those with (G + G-) sequences, for which the 90” or 60” status might be complicated to predict in long chains. Any uncertainty of this kind implies the possibility of additional errors of 1-2” and 0.005 A, which may still leave the method competitive with current experimental resolution. Compared to experimental results, the 4-21G parameters of n-hydrocarbons are rather accurate. A correction of -0.008 A relates aliphatic 4-21G bonds to electron-diffraction, r g, parameters [12], while the calculated and experimental C-C-C angles are practically the same [ 121. One is thus tempted to believe that the procedure described in this paper will provide realistic structural estimates for the low energy forms of a whole class of compounds.
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There is growing evidence [ 15, 161 that similar results can be expected for hetero-systems. Further reports of our ongoing studies will be reported elsewhere. ACKNOWLEDGEMENT
Support by NSF grant ISP-8011447
is gratefully acknowledged.
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