3692 The Journal of Physical Chemistry, Vol. 92, No. 12, I988 TABLE I VJkJ mol‘’ 9.93 0.5 9.43 13.F 4.6‘
-V4/kJ mol-’
utar/cm-‘
9.0 6.2 5.91 10.8‘ 11.Y
104 125
uba:/cm-’
ref 1 3. 26 2 4 5
68 59 53 13 79
5Sd b b
“The value of the reduced rotational constant B = 0.413 cm-l in formula 2 was taken from ref 2. * N o t calculated. V, and V4 are values obtained by fitting expression 1 to the potential curves given in ref 4 and 5 . d 2 0 transition.
-
most cases only the leading terms in the expansion are considered depending on the nature of the internal operation (Le., its symmetry). For biphenyl the potential for internal rotation can be expressed in the form V(6) = Y2V2(1 -cos 26)
+ 1/2V4(l -cos
46)
(1)
A number of authors obtained the potential function for internal rotation by using various experimental methods’-3 as well as quantum chemistry The values V, and V4 for some different proposed potentials are given in Table I, and we can see a substantial difference in the value of proposed constants by various authors. Even more pronounced is the difference in the torsional frequencies, which are also given in Table I. For a high barrier the torsional mode is well-approximated by small oscillations about the potential minima. It means that the frequency of the torsional oscillations is simply determined by the second derivative of V”of the torsional potential at minima and by the reduced torsional constant B.I9s2O Vhar
= (2V’Y?)’/2
(2)
The results for vhar obtained by using different potentials are given in Table I. The probable cause for discrepancies between frequencies given by various authors and those obtained via the simple formula (2) is due to the different methods used. It appears that using the Wilson GF method tends to give very high torsional frequencies of the order of 100-130 cm-’. The reason for such high torsional frequencies is connected to the definition of the torsional coordinate in the polyatomic molecules.2’,22 There is (19) Lister, D. G.; Macdonald, J. N.; Owen, N . L. Internal Rotation and Inversion; Academic: London, 1978. (20) Fataley, W. G.; Harris, R. K.; Miller, F. A,; Witkowski, R. E. Soectrochim. Acta 1965. 21, 231. (21) Hildebrandt, R. L. J . Mol. Spectrosc. 1972, 4 4 , 599. (22) Williams, I. H. J . Mol. Spectrosc. 1977, 66, 288.
Additions and Corrections a great deal of confusion on this problem, and it turns out that the usual definition of the s vectors with four atoms taking part in the definition should be replaced by a new one in which all atoms taking part in the torsional motion are considered. A very illuminating discussion on this subject is given by Hildebrandt,2’ who pointed out the difference in values for the torsional constant for ethane given by different authors. A similar discussion would be applicable to the biphenyl molecule, and use of an appropriate torsional internal coordinate would redefine the diagonal element in the G-’ matrix and would result in a lower torsional frequency. The problem of the frequency of a torsional mode in a crystal (i.e., libration of phenyl ring) is more complicated because the effective potential for the torsion consists of two parts: the intramolecular one (usually described by the function V(6))and the intermolecular one (usually described within the frame of some semiempirical atom-atom potential model). It should be noted that, in the absence of intermolecular potential, the harmonic torsional frequency for a planar geometry via formula 2 is imaginary (because of V”< 0). It means that such a molecular geometry is unstable with respect to small torsional displacements from a planar geometry ( 6 = 0’). It is the intermolecular interaction which in fact stabilizes the planar geometry in the crystal. The balance between intramolecular potential (which has a minimum for dihedral angle of approximately 40’) and intermolecular potential (which has a minimum for dihedral angle of 0’) is very delicate, and external influences such as t e m p e r a t ~ r eand ~ ~ pressure2425 tend to change it. Any realistic model for the calculation of the torsional frequency of biphenyl in the crystal should take into account both contributions. As a conclusion, we can point out that from e~perimental”-’~ and the~retical*~-’* investigations the torsional mode of biphenyl in crystal is near 70 cm-’. The problem of torsional modes of free molecules (gas phase and solution) is not well-understood, and probably some additional clarifications are needed. Registry No. Biphenyl, 92-52-4. (23) Cailleau, H.; Moussa, F.; Mons, J. Solid State Commun. 1979, 31, 521. (24) Kirin, D.; Chaplot, S. L.; Mackenzie, G. A.; Pawley, G. S. Chem. Phys. Lett. 1983, 102, 105. (25) Cailleau, H.; Girard, A,; Messager, J. C.; Delugeard, K.; Vettier, G. Ferroelectrics 1984, 54, 251. (26) Almeningen, A.; Bastiansen, 0.;Fernholt, L.; Cyvin, S. J.; Samdal, S. J . Mol. Struct. 1985, 128, 59.
Ruder BoSkoviE Institute
D. Kirin
P.O.Box 1016 41 001 Zagreb, Yugoslavia
ADDITIONS AND CORRECTIONS 1986, Volume 90
1987, Volume 91
William L. Jorgensen* and Jiali Gao: Monte Carlo Siqulations of the Hydration of Ammonium and Carboxylate Ions.
Keith Consani: Infrared Bands of Acetone in Solid Argon and the Structure I1 Clathrate 2-Acetylene/Acetone/ 17-Water.
Page 2176. Structure 11 is incorrect. It should be R
H
- -’0
\ N,?! H ’ ~ H
I1
H
Page 5586. The CH3 antisymmetric deformation band columns in Table I should be as follows: TABLE I
H‘
2C2D2/ acetone/ 17H20
2C:H2/ acetone/ 17D20
approx mode’
gas’
MI (Ar, 1:700)
C H , antisym deform.
1454 1435 1410
1451.7 (w) 1449.5 (w) 1449.3 (w) 1429.4 (m) 1430.9 (m) 1430.8 (m) 1406.9 (w) 1412.9 (m) 1412.8 (m)
