DIPOLEMOMENT OF ~ E E X Z O Q U I N O N E
Aug. 5, 195s
An isotopic tracer study of the oxidation of chloride ion by chlorate ion has been described b y Taube and Dodgen.I2 They propose a mechanism to account for their results CI- f '2103-
2H'
=
+ Ci-cl('
H,O
0
rapid arid reversible
(14)
The fact that the chlorate-water exchange is not induced during the oxidation of chloride by chlorate is in disagreement with reaction 14. However the existence of the unsymmetrical intermediate cl-cl \ ri.j I i . i \ i , i,etn trt.,Ltecl ;iccordin; lc, t l u . I , r < r r < l u i i .
fi-brrizoqiiinone cas:ly iuidergoes photocheriiicLil r i r i i ~ c t i , ~ i:it i rooiii trrnperatiirc hydruquitionc o r cjuinhyiiiii!l a m o u n t s o f thebe i r n r i i i r i t i o coiild havc bcilii ])rwcrit a i i d .in'cct t l i c
to be
[ l!l.j4).
C O I I Z I ~ I C I C I II l C l
c
DIPOLEMOMENT OF p-BENZOQUINONE
Aug. 5 , 1958
sp orthonormalized hybrids which can be built up from the 2s and the 2p orbitals can be written as follows (reference system in Fig. 1) tl = (s) cos
tz t3
= (s)
=
sin
CY
cy
sin p cosy
+
(pz) cos a sin p sin? (py) sin cy - (pl) cos
cy
cos p
I
0-C!
n
c,=o
sin @ cosy - (pz) sin a sin p sin? (py) cosa - (pa) sin a cos p
(s) cos p cos;'
t4 = (sj s i n r
-
-
(pL) cos p sin-/
+ (pz) cosy
+ (p.)
sin p
(1)
Here (s) and (px) (p,) (pz) stand for the Slater nodeless orbitals defined as
3881
I
+A4
X
J
Y
Fig. 1.--Reference system used it1 the calculation. Coordinate axes centered on t h e oxygen atoms. Tlic molecule lies in the (2,31) plane.
hybrids defined by eq. 1 with CY = n / 4 and p = ~ / 2 and ; it is easily found t h a t in these conditions the resultant of the orbital dipole moments is always zero. The Action of the External Field.-Let us consider however the molecule under the action of an L , L external electric field alternating with frequency with 6 =- - n 2 lower than the frequency of the molecular vibrations. The influence of this field is isotropic on the 2 being the effective charge of the atom. The meaning of the hybridization parameters two carbonyl groups, acting on both in the same sense, can be approximately illustrated by the statements whatever the actual orientation of the niolecule that: a determines the angle between tl and t z ; (unless this is aligned with its long axis parallel to they are symmetrical only when a = ~ / 4 p; de- the field, a very small percentage of the time in a termines the angle of the plane of tl and t z with z- random distribution). The non-bonding lone pair axis and the amount of deformation of the orbital electrons, which are doubtless the most polarizable t a ; y determines the amount of sp hybridization of of the molecule, will have their average position the orbital t d and the angle between z-axis and t3. displaced off to the same side of the molecular plane, I t has been pointed out by C o ~ l s o n 'that ~ one of and this effect may be described in a first approxithe consequences of hybridization is a displace- mation as a deformation of the atomic orbitals of ment of the centroid of the electronic charge of the the oxygen atom. The whole molecule may thereorbital from the nuclear center of the atom. This fore be considered perturbed in such a way t h a t the gives rise to an orbital dipole moment, whose result- induced charge asymmetry gives origin to a dipole a n i depends on the hybridization of the atom and on moment component along z-axis, pZ, different from its bonding condition in the molecule. I n order to zero. A general expression for the p z of each oxygen evaluate the dipole moment i t is necessary to determine the-charge centroid of each orbital. The atom can be calculated from eq. 4 using the cencoordinates ti = fij Ti, si for the centroid Ci of the troid coordinates given in the Appendix; the result orbital ti are obtained easily through the integrals is p8
being any one of the coordinates x, y and z. Their expression is given in the Appendix. The components of the orbital dipole moments are then easily evaluated from the definition
m& (4) with qi the charge of the orbital t i . This relationship enables one to calculate the resultant of the orbital dipole moments as soon as the state of the oxygen atom in the molecule is specified. In the present case, referring to Fig. 1, the orbital t4 is constantly directed along the x-axis and is involved in the a-bond of the carbonyl group; t 3 is used in the T-bond; tl and t z are occupied by the lone pair electrons. Because the hybrids in the bonds must show the correct behavior with respect to all the symmetry operation of the molecule, the oxygen atom in the unperturbed p-benzoquinone molecule will have ,uLs(i' =
(14) C . A . Coulson, Proc. R o y . SOC.( L o i s d o n ) , A207, 63 (1951).
= A ( q , - 2e) sit1 p cos p cosy
(5)
Here we have set 41 = q 2 = 2e, the charge in each lone pair orbital; and 03 = g,l the charge in the oxygen orbital involved in the a-bond of the carbonyl group in the actual condition of the molecillc in the presence of the field. Assuming now that the component pLBhas the same magnitude for the two oxygen atoms, the total contribution to the moment along z-axis is 2 p z . Using eq. 4 it is also easily shown t h a t no other contribution needs to be taken into account because one always has p y = 0 and the ,uLxcomponents, although in general different from zero, cancel each other. The resultant induced moment of p-benzoquinone, under the conditions described above, is thus MR = 2pLz and can be written MR = A(q1
- 2e) sin 2 p cosy
(f: j
Because the orbital t 4 is intermediate between a pure p and a trigonal sp hybrid, ( 2 / 3 ) 1 / 2 6 cosy 1; and in a direct approximate calculation of the T electron distribution in p-benzoyuinone,15a16it has
