324
SAN-ICHIRO MIZUSHIMA, YONEZO MORINOAND TAKEHIKO SHIMANOUCHI
Optically Active Derivatives of' Phosphine and Arsine.-The time of inversion 7 is very simply related to the splitting in the ground state A. by the equation 7 = 1/2A0c, where A. is in cm.-1 and c is the velocity of light, For instance in NH3 this time is 2.5 x 10-11 set. and is accepted as the reason that no optically active derivates of trivalent nitrogen have ever been made. The corresponding times for PHI and AsHa come out to be 2.3 x
Vol. 56
sec. and 1.4 years. For AsD3 the time is however 3.5 X lo7years, the inversion time being very sensitive to the masses of the atoms attached t o the apical atom. Thus one might expect optical activity associated with trivalent arsenic. Evidence for this has been given by Lesslie and Turnerlo and and Mann". (IO) M. J. Lesslie and E. E. Turner, J . Chem. SOC.,1170 (1934); 1051,1268 (1935); 730 (1g36). (11) J. Chatt and F. G. Mann. ibid., 1184 (1940).
SOME PROBLEMS OF INTERNAL ROTATION BY SAN-ICHIRO MIZUSHIMA, YONEZO MORINOAND TAKEHIKO SHIMANOUCHI Chemical Laboratory, Faculty of Science, Tokyo University, Hongo, Tokyo, J a p a n Received DBcembeT 96, 1961
We have studied by the infrared, Raman, dielectric and electron diffraction investigations the structure of many molecules with regard to. the internal rotation about the C-C axis. B comparing the experimental results obtained for molecules with various rotating groups (XHZC-CH~Y, XHZC-COY,XO&COX, X(CH&C-C(CH&X, XaC-CXa and XaS!-SiX3 where X and Y denote C1, Br, OH and C H d we arrived a t the followinp:conclusions concernme: the nature of the hinderme: uotential for the internal rotation. If there is no appreciable double b&d character in C-C bond, the steric force betwTeb atoms contained in different movable groups plays the most important role in determining the main feature of the potential curve: e.g., the positions of potential minima, corresponding to the stable configurations and the positions of potential maxima or of the potential barrier. The stable molecular configurations determined by this force would not be greatly changed by other conceivable forces as electrostatic force, hydrogen bond, etc., which would only affect such a quantity as the energy difference between the stable configurations. The intermolecular forces which are responsible for the change in equilibrium ratio of stable configurations cannot also change the main feature determined by the steric force.
Based on the experimental results of Raman effect,lp2 infrared a b ~ o r p t i o ndielectric ,~ constant44 and electron diffraction6 we have determined the stable configurations of rotational isomers which differ from one another in azimuthal angle of internal rotation about single bonds as axes. Some of the experimental results so far obtained in our laboratory are summarized in Table I.6 We believe that our conclusion for the configurations of these molecules is very sound, since we have applied various experimental methods as stated above. We shall now discuss several problems of internal rotation, especially those concerning the nature of the hindering potential based on these experimental data. Although this potential has been discussed theoretically by several
6
(I) Mizushima, Morino and Higasi, Physik. Z . , 36,905 (1934); Sei. P a p . Inst. P k y s . Chem. Res. Tokyo, 26,159 (1934); Mizushima, Morino and Nojiri, Nature, 137, 945 (1936); Mizushima, Morino and Kubo, Physik. z., 38, 459 (1937). (2) Mizushima, Morino, Watanabe, Shimanouchi and others, Sei. P a p . Inel. Phys. Chem. Res. Tokyo, 89, 387, 396 (1942); 40, 87. 100 (1942); 42, 1, 5, 27 (1944): J. Chem. Pkys., 18, 754, 1516 (1950); Mizushima, Morino and Takeda, ibid., 9, 826 (1941); Mizushima, Morino, Watanabe, Shimanouchi and Yamaguchi, ibid., 17, 691 (1949); Katayama, Shimanouchi, Morino and Mizushima, ibid., 18, 506 (1950). (3) Shimanouchi, Tsuruta and Mizushima, Sei. P a p . Inst. Phys. Chem. Res. Tokyo, 42, 51 (1946): Mizushima, Morino, Shimanouchi and Kuratani, J. Chem. Phys., 17, 838 (1949). (4) Watanabe, Mizushima and Morino, Sci. P a p . Inst. Phys. Chem. Rea. Tokyo, 39, 401 (1942); Watanabe, Miaushima and Mashiko. ibzd., 40, 425 (1943). (5) Yamaguchi, Morino, Watanabe and Mizushima, Sci. P a p . Inst. P h y s . Chem. Res. Tokyo, 40, 417 (1943); Morino, Yamaguchi and Lliaushiina, ibid., 42, 5 (1944); Morino and Iwasaki, J , Chem. Pkus., 17,216 (1949). ( 0 ) Similar studies have also been made by Pitzer, Glockler, Bernstein, Gwinn, Sheppard. Cleveland and others and their results are generally in good agreement with ours.
investigator^,^ it is desirable to discuss the experimental material more extensively. The data shown in Table I confirm our previous conclusion that the most important force in determining stable configurations of rotational isomers is the steric repulsion between two groups rotating against each other about a single bond as axis. For example, the fact that the molecules, of the type of XH&-CH2Y have rotational isomers of the same configurations (Le., the trans and the gauche forms8) irrespective of the dipole moment values of C-X and C-Y bands reveals that the steric repulsion is far more important than the electrostatic force. This conclusion is also compatible with the experimental result that the internal rotation of C13C-CC13 is hindered considerably (the height of the potential barrier amounting to about 10 kcal./mole), while that of C1&%SiC13 is almost free. In the eclipse formQ of C13C-CC13 corresponding to the potential maximum of the internal rotation, the distance between the two chlorine atoms, one contained in one ChCroup and the other in the other group, is 2.72 while that of C13SiSiC13is 3.20 A. The fact that such a minor difference in the interatomic distance in these two molecules results in a large difference in internal rotation suggests that the most important force must be the steric repulsion which is
1.
( 7 ) Glockler, Rev. Mod. Phys., lS, 112 (1943). (8)The trans form is the configuration in which X and Y atoms of XHnC-CHzY are a t the farthest distance apart and the oauehe form can be obtained from the trans forin by an internal rotation of about
120'. (9) The eclipse form of ClrC-CCla is the configuration in wliich all the three CI atoms of one ClsC-group eclipse the three GI atonis other ClrC-group when viewed along the C-C axis.
011
the
SOMEPROBLEMS OF INTERNAL ROTATION
March, 1952
325
TABLE I STABLE CONFIUURATIONS O F ROTATIONAL ISOMERS Figurw in parentheses denote the energy difference between the rotational isomers in kcal./mole -
Molecule
CIHzC-CH&I
Solid state
trans
BrH2C-CH2Br
lrans
CIH.C-CH2Br
trans
CIHsC-CHJI
lrans
CH~CHZ-CH~CH~
trans
CH3CHrCIIzCI
trans
HOHZC-CH~CI
gauche
C1H:C-COCI
trans
BrHZC-COCl
trans
cIoc-cocI
trans
Gaseous state
Liquid state
trans gauche (ca . O ) trans gauche ( 0 . 7 ) lrans gauche trans gauche trans gauche trans gauche trans gauche trans gauche trans gauche
4
trans gauche (1.2) trans gauche (1.4)
tram gauche lrans gauche trans gauche trans gauche
.
trans gauche (0.8) trans (0.95) gauche trans gauche (1.0) trans gauche (1.6) tram gauche (1.0)
Br( CH&C-C( CH3)2Br
CI(CH~)~C-C(CH~)SCI ClsC-CCI, C13Si-SiCla
CCh Solution
Staggered Almost free rotation
Almost free rotation
very sensitive to the variation of interatomic distance. (This force is inversely proportional to the 12th power of interatomic distance.) Concerning the steric repulsion in CI3C-CC1, we should like to note that in the staggered formlo (or the stable form) the distance between two nearest chlorine atoms on different movable groups is almost equal to the sum of the van der Waals radii of two chlorine atoms, yhile in the eclipse form this distance becomes 2.72 A. a t which there must be a considerable repulsion. This is the most important reason why the eclipse form corresponds to the potential maximum of internal rotation. In the stable configurations, therefore, the repulsive potential tends to take as low value as possible and the repulsive force may become of the same order of magnitude as the electrostatic force, hydrogen bonding, etc. This would be seen, for example, from the value of the energy difference of the rotational isomers of Br(CH3)2C-C(CH3)2Br ( A E = 1.6 kcal./mole) which is even greater than that of BrH2C-CH2Br ( A E = 1.4 kcal./mole). As the CH3-group has almost the same van der Waals radius as the Br-atom, AE of Br(CH2)2CC(CH3)%Brcannot be so large, if only the steric repulsion would contribute to the energy difference between the rotational isomers. In such a case we have, therefore, to consider an important contribution of the electrostatic force to AE. It is, however, evident that even in stable configurations we cannot neglect the steric repulsion. This will be seen, for example, from the difference of AE between CIH2C-CH2CI ( A E = 1.2 kcal./
mole) and BrH2C-CH2Br (AE = 1.4 kcal./mole) shown in Table I. The contribution of electrostatic force to AE in the dichloride must be greater than that in the dibromide, since the bond moment of C-CI is almost equal to that of C-Br and the induction effect in the dichloride is smaller than that in the dibromide." Therefore, the fact that A E of ClH2C-CH&l is smaller than that of BrH2CCHzBr shows that there is a considerable contribution of the steric repulsion to AE of such rotational isomers. It would be very interesting, if we could determine the ratio of the steric part to the electrostatic part of the hindering potential. The value of Ah' (= 0.8 kcal./mole) of n-butane may tell us the approximate magnitude of the steric part of AE of BrH2C-CH2Br, since n-butane is a non-polar substance and the van der Waals radius of the CH2-group is almost equal to that of the Br-atom as stated above. I n such a substance as C1H2C-CH20H an internal hydrogen bond is formed between the two rotating groups. This bond lowers the energy of the gauche form to make it more stable than the trans form which otherwise would be always the lower energy form in the case of molecules of the type of XH2C-qH2Y (see Table I). However, the internal hydrogen bond is not 60 strong as to shift the gauche position up to the cis position. . In the case where the internal rotation axis acquires a double bond character to a considerable amount, the situation may become quite different from what we have stated above. Among the
(10) The staggered form of ClaC-CCh is the configuration in which the projection of one C-CI bond upon the plane perpendioular to C-C axis is midway between those of two C-CI bonds i n the other half of the molecule.
(11) This would be seen from the difference in the moment value ~e of the gauche molecule between the dichloride and the dibromide. LQ. of CIHpC-CHpCI waa found to be 2.55 D , while pg. of BrHsCCHzBr was 2.0 D.
326
WALTERF. EDGELL AND THOMAS R. RIETHOF
I
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substances shown in Table I ClOC-COCI provides different configurations with the change of stat'e.1p2 us with such an example. For this substance the For example, for ClH2C-CH2Cl the gauche molecule trans form is found to be the stable configuration, becomes more abundant in the liquid state than in wfiich would not be the case, if the steric repulsion the gaseous state a t the same temperature, while in is the predominant factor in determining the stable the solid state this molecule disappears almost configuration. The stability of the trans form in completely (see Table I). Such a change in equilithis case is due on one hand to the single bond- brium ratio must be explained in terms of the interdouble bond resonance of the structure of O=Cmolecular forces as was already discussed in our C=O and on the other hand to the fact that the previous papers. However, as we can see from steric repulsion between two C1-atoms is much Table I, the intermolecular force is not so strong greater than that between C1- and 0-atoms. as to change greatly the positions of maxima and So far we have mainly discussed the molecular minima of the hindering potential which is deterconfigurations and their energy differences in the mined mainly by steric repulsion in case there free state. We have, however, often reported the is no considerable single bond-double bond resoconsiderable change of the equilibrium rattio of nance.
THE CALCULATION OF VIBRATIONAL FREQUENCIES OF MOLECULES WITH MANY ATOMS ANR LITTLE SYMMETRY. I. SIMPLE DERIVATIVES OF SYMMETRICAL MOLECULES BY WALTERF. EDGELL AND THOMAS R. RIETHOF Department of Chenaistry, Purdue University, La.fayetle, Indiana Receiued December 86, 1961
The use of approximate normal coordinates is suggested as a basis for the calculation of vibrational frequencies in the more complicated molecules. Two basically similar methods have been proposed. The first, which takes advantage of the existence of group fre uencies, has not been tested sufficiently. The second method dealing with molecules which may be regarded as simple jerivatives of symmetrical molecules, is tested numerically with simple examples.
Introduction One of the most potent devices in the analysis of vibrational spectra is the calculation of the fundamental modes of vibration of a molecule based on a mechanical model. All of our progress in the correlation of observed frequencies with types of motion of the various component elements of structure of a molecule has its origin in such calculations. Fundamentally the use of infrared and Raman spect,ra iii qualitative structural analysis rests upon this base. Because of the high order of the matrices and determinants involved in the practical application of the methods so far developed, such calculations have been limited to molecules containing few atoms and of relatively high degree of symmetry. The extension of the methods of theoretical infrared and Raman spectroscopy t o complex molecules depends upon the penetration of this barrier. A tremendous wealth of information available in spectra is as yet untapped because we do not recognize its correlation with structure and environment. There is no reason why one should not apply the same methods to penicillin and cortisone as are nom applied to methane and ethyl alcohdl. Two fundamentally similar methods of extending vibrational calculations to complex molecules have been outlined recent1y.l They involve perturbation methods based upon the use of normal coordinates as a practical tool in numerical calculations. Such a use of normal coordinates has been (1) Walter F. Edgell, Paper No. 16,Sixty First Session of the Iowa Academy of Science, Inorganic and Physical Chemistry Section, April, 1949.
neglected except in the application to the isotope e f f e ~ t . ~The ? ~ first and simpler method applies to molecules which may be considered as a simple derivative of a molecule possessing greater symmetry. Examples would be cyclic C4F7C1 considered as a derivative of cyclic C4Fs or C2F6C1 and CFzClCFzCl as derivatives of C2Faand CsHbC1 as a derivative of CGHB. The second method regards a complex molecule as being built up of basic structural units such as methyl and ethyl groups, benzene rings, etc., joined together by coupling links. It puts the concept of group frequencies upon a quantitative basis. While it will be relatively simple in actual application, this method requires considerable ground work including the calculation of numerous tables for its practical use. The present communication deals with the numerical test of the first method. No loss in generality and considerable savings in labor are involved by restricting the test to simple molecules. Normal coordinates by definition yield a unit matrix for the kinetic energy matrix and a diagonal potential energy matrix whose elements are the square of the (circular) frequencies of vibration. Unfortunately frequencies of vibration must be calculated first before normal coordinates can be obtained. However it can ,be predicted that the normal coBrdinates for a molecule like cyclic C4F7C1 will be similar to those for the molecule cyclic C4Fs. The use of the normal coordinates of the latter or parent molecule in setting up the expressions for the former or derivative molecule will (2) Walter F. Edgell,
J. Chem. P h ~ s . 13, , 306 (1925). (3) Ibid., 13, 539 (1945).
