Norbornan.e (bicyclo[2.2.l]heptane) and its derivatives have been extensively studied by chemical and physical methods. Since norbornane represents an important strained molecule, particular attention was payed tci its geometry1 and bonding properties2• However, no vibrational analysis of norbornane or its derivatives has been undertaiken. Only partly analysed vibrational spectra are reported3• Therefore we find des~rable to undertake a complete vibrational analysis of norbornane and its deuterated species

A. Rubčić

M. Randić

Z. Meić

English

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CROATICA CHEMICA ACTA CCACAA 46 (1) 25-30 (1974) CCA-813 YU ISSN 0011-1643 547.51 Note Vibrational Spectra and Force Constants of Bicyclic Molecules. I. Norbornane and Norbornane-d4 z. Meic, M. Randie*, and A . Rubcic* Institute »Ruiter Boskovic«, POB 1016, 41001 Zagreb, and *Faculty of Science and Mathematics, University of Zagreb, Marulicev trg 19/II, 41000 Zagreb, Croatia, Yugoslavia Received September 10, 1973 Norbornan.e (bicyclo[2.2.l]heptane) and its derivatives have been exten-sively studied by chemical and physical methods. Since norbornane represents an important strained molecule, particular attention was payed tci its geo-metry1 and bonding properties2• However, no vibrational analysis of norbor-nane or its derivatives has been undertaiken. Only partly analysed vibrational spectra are reported3• Therefore we find des~rable to undertake a complete vibrational analysis of norbornane and its deuterated species. Norbornane belongs to the C2v point group1• The orientation of the molecule in cartesian coordinates, the numbering of carbon atoms, as well as all the bonds and angles with which the internal valence coordinates are a:ssociated are presented in Fig. 1. The 3N - 6 = 51 fundamental vibrations are distributed among the irreducible representations of the C2v point group as foUows: I "' I I I ,'X --- - - · - ~ y Fig. 1. Schematic view of norbornane molecule with the symbols of bond lengths, bond angles and orientation in the cartesian coordinate system. 26 Z. MEIC ET AL. Of these only A1, B1 and B" modes are active in the infrared, but all the fundamentals are active in Raman spectroscopy. However, there are in all 62 internal coordinates, among which 11 redundancies exist. The redundant coordinates are distributed among the irreducible representations as follows : r vib = 5 A1 + 1 A 2 + 3 B1 + 2 B 2 The recognition of redundancy conditions is not trivial in molecules of such compleX,ity. The local redundancies are easy to define. However, there is a number of cyclic redundancies which are not so obvious. For instance, an unexpected condition is the linear dependence of the following internal conrdinates: 6J1, 6J2, 6)3 and 8 4 in the A1 species. Another example is the combination of R00, R' 00 and 8 2 in the B2 species. But it is not essential to solve all the redundancies, since in the calculation the corres-ponding frequencies appear as zeros, if all internal coordinates are used. The complete set of symmetry coordinates will be reported in a later paper4 • The standard procedure of Wilson5 and Eliashewich6 was followed in evaluating the G-matrLx elements. The geometrical model used was based on electron difraction data1• all RcH = 1.12 A <}: c~ C2 C3 = 103° <}: C1 C7 C4 = 93° <}: HC1 C2 = 119° dihedral angle = 1130 All the HCH angles, ho'Never, were assumed tetrahedral. In addition to the parent compound, there are 15 distinct deuterated species possessing the same C2v ,symmetry (Fig. 2). It is generally considered tha1t the best available Fig. 2. The normal and all the possible symmetrically deuterated norbornanes belonging to the C 2v point group. valence force field for saturated hydrocarbons is the one obtained by Snyder and Schachtshneider7• It was successively applied to several saturated cyclic molecules by the same authors7• Hence, we assumed it as the initial force · fields for the moderately strained norbornane. In Table I are listed the signi-VIBRATIONS OF NORBORNANE 27 ficant force constants taken from the paper of Snyder and Schachtschneider. Using the force constants of Table I we have calculated th e vibrational fre-K d = 4.554 mdyn A-1 K8 = 4.588 K R = 4.387 K R'= 4.337 H II = 0.550 mdyn A-1 rad-2 H Y = 0.656 H~ = 0.657 H00 = 1.130 H 'I! = 1.084 F R = 0.101 mdyn A-1 F R y = 0.328 mdyn rad -1 FRw = 0.417 FRy' = 0.079 F Y = -0.021 mdyn A rad-2 F qi = -0.041 F Y' 0.012 F Y"' = -0.031 TABLE I (C,CH2,C) (C,C,C,CH) (H2C,CH2) (H2C,CH) (C,CH2,C) (C,CH2,C) (C,C,C,CH) (C,CH2,C) (C,C,C,CH) (C,C) (C,C) (C,C) (C,C,H) (C,C) (C,C,C,) (C,C) (C,C,H) (C,C,H) (C,C,H') (C,C,C) (C,C,C') (C,C,H) (C,C,H ') (C,C,C) (C,C,H) C-H stretch C-H C-C C-C CH2 bend CCH CCH CCC CCC st retch-stretcl:> stretch-bend bend-bend " quencies for the molecules 1, 2, 3, 5 and 8 of i'ig. 2. However, a t present only infrared spectras of 1 and 3 are available for comparison with calculated values. The observed, i.e. without the IR inactive A2 species, and calculated fundamentals are lis ted in Table II. No. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 'Vex p. _ cm-1 2950 l 2850 1455 1450 1310 1252 1138 1068 948 888 815 752 390 'Vealed. cm-1 Ai 2926 2908 2856 2853 1512 1455 1317 1260 1157 1068 967 891 807 689 397 TABLE II Norbornane C7H12 (1) flv No. cm-1 1. 2. 3. 4. + 57 5. + 5 6. + 7 7. + 8 8. + 19 9. 0 10. + 19 11. + 3 - 8 -63 + 7 'Vexp. 'Vealed . flv cm-1 cm-1 cm-1 A2 2930 2853 1400 1319 1288 1176 1124 1017 957 567 93 28' Z. MEIC ET AL. No. ·I Yexp. I Y calcd. l:w I 1' calcd. 6.v 6.v No. cm-1 cffi-i cm-1 cm-1 cm-1 cm-1 B1 B2 1. 2950 } 2937 1. 2950 } 2929 2. 2902 2. 2924 3. 2850 2858 3. 2850 2854 4. 1449 1457 + 8 4. 1450 1453 + 3 5. 1310 1302 - 8 5. 1310 1325 + 15 6. 1310 1291 -19 6. · 1237 1246 + 9 7. 1208 1225 + 17 7. 1138 1149 + 11 8. 1138 1159 + 21 8. 1105 1117 + 12 9. 1105 1093 -12 9. 988 989 + 1 10. 1020 1013 - 7 10. 920 912 - 8 11. 870 854 -16 11. 797 800 + 3 12. 707 12. 338 359 + 21 13. 282 ----Norbornane-d4 C7HsD4 (3) A1 A2 1. 2950 } 2908 1. 2897 2. 2892 2. 2139 3. 2850 2857 3. 1307 4. 2120-) 2138 4. 1301 2210 5. ,1455 1511 + 56 5. 1259 6. 1325 1333 + 8 6. 1122 7. 1273 1276 + 3 7. 1010 8. 1235 1215 -20 8. 908 9. 1149 l139 -10 9. 862 10. 950 961 +11 10. 535 11. 883 900 + 17 11. 8~ 12. 797 789 - 8 13. 752 685 -67 14. 692 677 -15 15. 379 372 - 7 B1 B2 1. 2950 l 2904 1. 2950 l 2929 2. 2850 2895 2. 8 '2891 3. 2120- 2148 3. 2120- 2131 2210 . 2210 4. 1310 1312 3 4. 1310 1304 -11 5. 1295 1292 - 3 5. 1273 1288 + 15 6. 1254 1252 - 2 6. 1254 1243 -11 7. 1202 1198 -4 7. 1083 1118 + 34 8. 1070 1096 + 26 8. 1030 1004 - 27 9. 983 989 + 6 9. 925 930 + 5 10. 922 917 - 5 10. 810 815 + 5 11. 775 773 - 2 11. 655 669 + 14 12. 664 12. 347 347 0 13. 250 VIBRATIONS OF NORBORNANE 29 Generally, the difference between experim·ental and calculated wave-numbers for most vibrational modes is within · ± 20 cm-1. However, several A1 modes in the CH2 deformation and skeletal bending regions show larger differences for both molec,ules 1 and , 3. The preliminary investigation thus reveils that the force constants of Snyder and Schachtschneider are also fairly adequate for describing moderately strained polycyclic hydrocarbons. They may even be used for quantitative predictions, although some disa-greement . between the experimental arid calc'ulated frequencies' should' be expected for strained parts of a molecule. The forms of normal modes and the potential energy distribution (PED) show; for instance, that the largest deviations are associated with v5 of both isotopes corresponding to the CH2 scissorirt,g at the b11idge position, and Y14 of l as well as v1 3 of 3, which correspond to the C1 C7 C4 deformation 1respecti-vely. The most important 'force constants for these vibrations are H 6 = 0.550 and Hw = 1.130 mdyn A- 1 rad-2 . Because of the geometry used (8 4 = 93° and not tetrahedral for which the force constant H ~ · is applicable) force con-stant H '° has to be increased to the vqlue of 2.13 , mdyn A-1 rad-2, thus increa,sing the wavenumber //H = 685 to 752 cm-1, and Hb has 'to be.-decreased from 0.550 t·o 0.490 mdyn A-1 rad-2 thus decreasing the wavenumber 115 = 1512 to 1455 cm-1. The complete refinement of the original force field will be reported later. A more detailed study of these molecules should be supported by the assignment of numerous bands in the CH stretching region, which are still ambiguous. The synthesis of molecules 2, 5 and 8 is in progress and the band contour analyses of the gas phase infrared s pectra, as well as the depolarisation degrees of the Raman bands8, will provide sufficient experimental data for the complete and accurate vibrational analysis. This work will be reported in future. Acknowledgement. We are indebted Prof. D. E. Sunko and Mr. M. Tomic, Za-greb, for the samples of norbornane and norbornane-d4• Our thanks are also due to Prof. D. Hadzi, Ljubljana, who enabled the recording of IR spectra on Perkin--Elmer M521 in his laboratory. REFERENCES 1. Y. Morino, K. Kuchitsu, and A. Yokozeki, Bull. Chem. Soc. Jap. 40 (1967) 1552 ; G. D a 11 in g a and L. H. Tone man, Rec. Trav. Chim. Pays-Bas 87 (1968) 795; J. F. Chi an g, C. F. W i 1 cox, Jr., and S. H. Bauer, J. Amer. Chem. Soc. 90 (1968) 3149 ; A. Yoko z e k i and K. Kuch its u, Bull. Chem. Soc. Jap. 44 (1971) 2356, and references cited therein. 2. e.g. G. K 1 op man, J . Amer. Chem. Soc. 91 (1969) 89; N. Bodor and M. J. S. Dewar, J. Amer. Chem. Soc. 92 (1970) 4270 ; M. Randie andD. Stefanovic, J. Chem. Soc. A (1968) 755; Z. B. Ma ks i c and M. E ck er t - Ma ks i c, Croat. Chem. Acta. 42 (1970) 433. 3. D. Roberts, W. Bennet and F. Armstrong, J. Amer. Chem. Soc. 72 (1950) 3329; D. Ki v e 1 son, S. Wins t e in, P . Bruck and R. L. Hansen, J. Amer. Chem. Soc. 83 (1961) 2938; M. Avram, G. D. Mate es cu and I. I. Po g any, Rev. Chim. Acad. Repub. Pop. Roum. 7 (1962) 665; V. T. A 1 e k-s any an, Z. B. Barino v a, G. N. Z hi z hi n, K h. E. Ster in, N. A. Be h-k ova and A. F. P 1 ate, Zh. Strukt. Khim. 4 (1963) 28. 4. Z. M e i c, A. R u b c i c and M. R a n d i c, in preparation. 5. E. B. W i 1 son, Jr., J. C. Decius and P. C. Cross, Molecular Vibrations, McGraw-Hill, New York 1955. 30 Z. MEIC ET AL. 6. M. V. Vo 1 k est e in, M. A. E 1 i ash e vi ch and B. I. S t e pa no v, Kolebanya Molekul, GITTL, Moscow 1949. 7. R. G. Snyder and J. H. Schacht sch n eider, Spectrochim. Acta ?1 (1965) 169. 8. Z. Mei c, D. E. S u n k o and M. Tomi c, Ln preparation. SAi~ETAK Vibracijski spektri poteneijalne keruttante biciklickih molekula. I. Norbornan i norbornan-d4. z . .Meic, M. Randie i A. RubCic Analizirana su svojstva unutra~njih koordinata norbornana na temelju simetrije C2v. Primjenom prosjecnoga potencijalnog polja za zasiCene ugljikovodike Snyder--Schachtschnei:dera izracunane su vibracij1ske frekvencije za vise razlicitih izotopa norbornana. Raspolozivi eksperimentalni podaci 1nfracrvenih spektara zadovolja-vajuce se slazu s izracunanim vrijednostima. INSTITUT •l;iUDER BOSKOVIC« i PRIRODOSLOVNO-MATEMATICKI FAKULTET, SVEUCILISTA U ZAGREBU, nooo ZAGREB Prirnljeno 10. rujna , 1973. 

Vibrational Spectra and Force Constants of Bicyclic Molecules. I. Norbornane and Norbornane-d4

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