Balasubramanian, V

Ramaswamy, K

English

IACS Institutional Repository

Ind .... J. PloY" 43, 735-741 (1969) Force field for germylacetylene By K. RAMASWAMY AND V. BALASUBRAMANIAN Department of Physi08, Annamalai University, Annamal.inag" ( Received 7 November 1969. ) Approximate (orce field for a:ermyillcetylene was attempted using the kinematic methods suggested by Torkington (1949) and Heltan: & Castano (l966). The former method was found to give " satisfB.~toty force field for this lUolecule. INTRODUCTION The well known basic equations (Wilson, 1955) in molecular force field calculations are, LL = G ... (1) LFL = A ... (2) and GFL = LA ... (3) whete L Is the transformation matrix between the set of symmetry coordi-nates and the normal coordinates, F and G refer to the potential and inverse kinetic energy matrices and A a diagonal matrix with the element A, = 4,'" 'e', where VI is the k" vibrational wavenumber and 'is the velocity of light in em seC-'. It is seen from the above equations that the matrix L assumes importance in the determination of a unique set of force cons-tants. The kinematic methods (Tarkington 1949, Herronz & Castano 1966 and Biles 1966) are those which give the values of the L matrix elements consistent with the equatio~s (1) to (3), purely from the geometry of the molecule Without nny assumptions regarding the force constants. In a previous paper (Ramaswamy & Balasubramanian 1969) approximate force fields for the germvl halides using the above kinematic methods were attempted and Tarkington's methDd was found to give a better approxi-mation to the correct force field for the two heavier molecules GeH,Br and GeH,I while the method suggested by Herranz & Castano gave a close approximation to the correct force field for the two lighter molecules GeH,Cl and GeH.F. This paper deals with the force field for germylacety-lene by the first two method •. POTBNnAL ENERGY CONSTANTS In the method suggested by Tarkington (1949) the product of the matrices G ~nd 1 is triangular and the L matrix obtained as ,pe eigen ( 7l~ I 736 K. Ramaswamy and V. Balasubramanian vector of OF is also triangular. In the method suggested by Herranz &. Castano (1966) the L matrix is defined as, L = BM1I2 li .. ·(4) where B is an orthogonal matrix which diagonalises 0 and M is a diagonal matrix with the reciprocals of the eigen values of 0 as its elements. Germylacetylene belongs to the 0" point group and its infrared spec-trum was reported by Lovejoy & Baker (1967). Its microwave spectrum was given by Thomas & Laurie (1966). The structural data and the vibra-tional frequencies used in the calculations are given in table 1. The symmetry coordinates used are the same as those of Sathianandan & Mar-grave (1963). The values of important valence force constants obtained in the two methods are presented in table 2. TABLE 1. OBSERVED FREQUENCIES IN WAVE NUMBERS AND STRUCTURAL PARAMETERS FOR GeH,CCH Observed frequencies Structural data inem"'l (Thorn., & Laurie, (Lovejoy & Baker, 1967) 1966) ---., species e species d{Ge.H) ~ 1.521 A v, 331) 5 'ro 2117,2 ·;:;(Ge-Cj~-lR96A·-v, 2120,0 v, 886.0 r,(C-C) := I 208 A v, 2060.0 1', 67),0 r,(C-H) = 1056 A 1', 843.8 "0 64),8 «(H·Ge-H) = 1C9" 54' " 5300 1,10 216,4 ~(IHJe-C) = 109" 2' ~(Ge·C·C) = 180' O(C,C.H) = J 80' MEAN AMPLITUDES The various bonded mean amplitudes were calculated by the method of Cyvin (1959) and the nonbonded ones by the method of Ramaswamy et al (1962). The important mean amplitudes obtained in the first method arc given in table 3. Force ,peld for germylacetylene TABLE 2, VAL~NCE PORCE CONSTANTS IN MDYN PORIA GeH,CCH Valence force Method P MethodUb constant fro 6,1161' 6.2609 f., 16.4557 24.1624 I., 3.1112 7.4759 fd 2.6276 2.6286 Irrr, 1.2742 2.5m !'lrD 1.6183 11.4762 fr,d 0.0135 0.0964 Idd 0.0146 0.0156 f .. -I .... 0.1905 0.1957 fa - faa 0.1951 0.2050 I. 0.1775 0,1939 .r. 0.0739 0.0906 Id~ 0,0059 0.0181 jdp 0.0056 0.0264 'Method of 'Progressive rigidity' suggested by Torkington bMethod of 'characterec;tic set or valence coordi-n,tes' suggested by Herran. and Castano, • As under table 3 TABLE 3. VIBRATIONAL MEAN AMPLITUDES OP GeH,CCH AT 298.16'K. Mean amplitude. for similar types of Mean bonds in dlffereI1t molecules. Pair amplitudes Mean Molecule -- Reference--(iI) amplitude. (A) C-H 0.0740' 0.0743 C,H, Bakken (1958) C::;H 0.0366 0.0357 C,H, Bakken (1958) Ge·C 0.0484 Ge·H 0.0895 0.0895 GeH. Cyvin (1968) H ... H. 0.1540 0.1525 GeH, Cyvin (1968) H ... C 0.1318 'Thi. number of significant figures is retaiDQd to s~9uro ip~~1 90nalstencr in the calculations, 737 738 K. Ramaswamy and V. Balasubramanian ROTATIONAL DISTORTION CONSTANTS The centrifugal stretching constants DJ , D.x and DK were calculated using the relations given by De Alti et al (1965). The values are presented in table 4. TABLE 4. ROTATIONAL DISTORTION CONSTANTS IN KcfsEC. fOR GeH,CCH -~~----. --------Quantily Calculated Observed DJ 0.6565' 26.6906 802.9760 38 CORIOLIS COUPLING CONSTANTS The C< values for the perpendicular modes of vihrEtion were calculated using the relations given by Meal & Polo (1965). The values are presented along with the experimentally observed values. The t sum rule for this molecule is, ... (5) where, 1 A and 1 B are the principal components of the moment of inertia tensor. TABLE 5. CORIO LIS COUPLING CONSTANTS t fOR IlBRMYLACETYLENE Calculated Observed C. 0.0183' -0.052 t, -0.2043 -0.266 C. 1.0000 C. 0.2579 0.364 C. " 0.9503 Ee, 2.0222 • As under labl~ 3 Force fiela for germylacetyltne 739 DISCUSSION The method of Torkington (1949) gives for the C::=C stretching and C-H stretching force constant values of 16.4557 mdyn/A and 6.1161 mdynlA while the method given by Herranz & Castano (1966) gives the values of 24.1624 mdyn/A and 6.2609 mdyn/A, respectively. The first set is comparable with the values of 15.80 mdyn/A and 6.442 mdyn/A obtained by Daykin BI a! (1962) for methylacetylene and 15.59 mdyn/A and 5.87 mdyn/A of Duncan (1964) for silylacetylenc. For Ge-C bond stretching we obtain values of 3.1112 mdyn/A' and 7.4759 mdyn/A in the two methods, respectively.The fIrSt value is closer to the value of 2.87 mdynlA obtained by Clark & Weber (1966) for methylgermane. The second method gives an abnormally high value of 11.4762 mdyn/.1 for the inter-action force constant /'1'" The other bendmg, stretching and interaction force constants are of comparable magnitude in both the methods as seen from table 2. They are also consistent With the values obtained for germyl-halides in our previous study. The second method gives quite large values for the various force constants of the linear skeleton Ge - C::=C-H, barring the C-H stretching. High values for interaction force constants were also obtained by Ramaswamy & Srinivasan (1967. 1969) for the linear molecules like cyanoacetylene, diacetylene and dicyanoacetylene. They attributed these high values to the high degree of conjugation, and electron transfer in those molecules. Here the linear skeleton Ge-C=C - H is not a conjugated system and hence the second method is quite unsatisfactory in describing the force field for this molecule. So the other molecular constants were found using only the L matrix obtained in the first method. From table 3 it is seen that the mean amplitudes of vibration for dIe bonds C-H(0.0740/A) and C==C (0.0366.1) are comparable with the values of 0.0743A and 0.0357J. obtained by Bakken (1958) for c.Ht. The bonded Ge-H (0.0895A) and the nonbonded H ... H(0.1540A) mean amplitudes are also comparable to the values of (0.0895.1) and (0.1525,4) for GeH, obtained by C)'Vin (1968). These values are also consistent with the values obtained for germylhalides in our earlier study. The value of the centrifugal stretching constant DJI{ (26.6906 kc/sec) Is low compared to the value of 38 kc/sec obtained by Thomas & Laurie (1966) from microwave studies of germylacetylene. The difference might be due to the approximate description of the normal modes. Lovejoy &. Baker (1967) from the analysis of perpendicular band Contour. of the -infrared spectrum of germylacetylene reported the values of ii, i, and it' From the awn rule, i. + ilo was calculated to be 1.975, 740 K. Ramaswamy and V. Balasubramaruan Further, they predicted t, and ~IO to be approximately equal and slightly less than one. In similar molecules like silylacetylene (Reeves .1 o;! 1964) and methylacetylene (Thomas & Thompson 1968) the sum of the above two corresponding t elements is 1.89. For methylacetylene the two {'s have the values of 1 and 0.89 respectively. The values t, (1) and tlO (0.95) of the present study are close to those predicted by Lovejoy & Baker (1967). The value of t. (0.0183) and {, (-0.2043) are consistent with the values obtained for similar motions in the germylhalides. As for the germylhalides, here also the individual' values differ from the observed values. The' sum rule is thus verified. CONCLUSION Of the two kinematic methods the above study shows the method of 'Progressive regidity' suggested by Torkington as the most satisfactory in describing the force field for this molecule. However, as shown by the values of the {elements and the centrifugal stretching constant, the solu-tion to the force field is only an approximate one. This may be due to the approximate L matrix which is derived entirely from the geometry of the molecule. ACKNOWLEDGEMENT One of the authors (V. B.) is grateful to the Council of Scientific and Industrial Reseatch, New Delhi, for financial assistance by the award of a Junior Research Fellowship. REFERENCES B.kken 1. 19SB Acta Ch,m. Scand., 12, 594. Bile, F. 1966 Acta. Ohim. Acad. Sri. Hung., 47, 53. Cyvin S. J. 1959 Ace •. CIt,m. Scand., 13, 2135. 1968 Molecular tJibrnh.o718 and Mean Bquare amplUudtU, UJ'6WB1'8uet fer lagel, 0.1 •• Clark A. &; Alfon. Weber. 1%6 J. Chem. Phy'" 45. 1759. Daykin P. N., Sundaram, S. &; Clevel.nd F. F. 1962, J. Ch,,,.. Phy •. , 37, 1087. Duncan J. L. 1964 Sp"troohim. Aw. 20, 1807· Ginn CorIo De AI'i Vinido 0.1 ... 0 & Oiacomo Co,Ia 1965 Sp,CI,oo.;m AoIG 21,649. Herron: J. &; Cast.no P. 1966 SpccertJohim. Acta, 22, 1965. Lovejoy, R. W. &; Baker D. R. 1967 J. Ch.m. PhI/ •• , 46, 65B. Mo.1 J. H. &; Polo S. R. 1956 J. CI"m. Phy •. , 24, 1119. llallll.wBmy K. &; Bala.ubramanian Y. Ind. J. PIIy •• (In prell) Foroe jUltrl/or germylaoetylene R. ..... wamy [C. Sathlanandan K. '" Cleveland P. P. 1962 J. Mol. B,oaIry., 9, 101. RatDI"".my [C. '" Srlnlv •• an [C. 1961 A.,'. J. ClI,m., 11, 515. 1969 Awl . • 1. Oh.m., 22, liB S.thi.nandan [C. '" Margravo ). L. 196J J. M.l. 81'.011, .• 10, 442. Thoma. I!. C. " Laurie W. 1966 J. CA.m. Pay,., 44 2602 Thoma. R,. [C. & Thomp,on H. W. 1968 Bp.otroch, ... A.Ia, 14A. U3? Tarkington P. 1949 J. OMm. Pky •• , 17, 1026. 741 Wilaon E. S. )r., Declu. j. C. Ii< Cro" P. C. 1955 M.r .... lar Vi~ra&; .... , M.Gr ... Hilt New Yo, •. 

Force Field for Germylacetylene

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Force Field for Germylacetylene

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