E. R. LIPPINCOTT, G. NAGARAJAN, AND J. M. STUTMAN
78
Polarizabilities from the 8-Function Model of Chemical Binding. 11. Molecules with Polar Bonds1
by E. R. Lippincott, G. Nagarajan, and J. M. Stutman Department of Chemistry, University of Maryland, College Park, Maryland
?207@
(Received May 3,1966)
The b-function potential model and the corresponding derivation yielding bond parallel and perpendicular polarizability contributions are briefly outlined. The calculated values of the bond and molecular polarizabilities are herein determined for 174 molecules with polar bonds having from five to thirteen residual atomic degrees of “polarizability” freedom and are in good agreement with the available experimental values. A brief discussion of the chemical significance of some of the results is given.
Introduction Several first principles attempts have been made in the past to calculate polarizabilities from quantum mechanical models, all with limited success and very narrow appljcability. Sources of the difficulties encountered in these problems may be summarized to be of one of two categories: (1) The potential energy for the unperturbed molecule is in reality 1‘ sum of electron-electron and nucleus-nucleus repulsive terms and electron-nucleus attractive terms. It is obvious that, if one assumes a real potential, one must resort to approximate mathematical solutions as soon as the number of particles is greater than two. It is further well known that these approximate solutions very rapidly become intractable even for modern high-speed computers as the number of particles increases. (2) The perturbing field potentia1 complicates the situation even more, and an exact solution to the wave equation becomes impossible practically. Difficulty 2 cannot be overcome if one wished to determine polarizabilities, susceptibilities, etc. Therefore, the only area of simplification available is the potential describing the unperturbed molecule. The b-function potential model, initiated by Frostza and modified by LippincottlZbyields encouraging calculated values of De, we, weze, and re for many diatomics and bonds of polyatomi~s.~The model assumes that a t each nucleus there exists a potential which is infinite and that everywhere else the potential is zero. The integral of the potential over all space, however, is finite and equal to a parameter which we call the ((8The Journal of P h y s k l Chemistry
function strength” or ‘%educed electronegativity” and is analogous to the “effective nuclear charge” of Slater. At each nucleus, then, a &function wave function is generated representing the probability amplitude of the electron for this isolated nucleus. These d-function atomic orbitals then are linearly combined to form molecular orbitals with the restriction that atoms may interact two at a time and only if bonds are believed to exist between the atoms. The major advantage of a d-function model lies in its one-dimensional nature. We consider each bond to be a separate onedimensional entity, and, since the potential has a nonzero value at only two points along any given bond, the problems of calculation are trivial. It is the aim of the present investigation to extend the calculations of polarizabilities for molecules with polar bonds in order to test further how far the polarizability could be a useful criterion in testing the accuracy of the d-function model of chemical binding adopted.
The &FunctionPotential Model The potential energy for the n-electron problem is taken to be the sum of single &function potentials, each having the following form for a diatomic system (1) This research was supported by a Materials Science Program from the Advanced Research Projects Agency, Department of De-
fense, and the National Institutes of Health Physical Chemistry Training Program. (2) (a) A. A. Frost, J . Chem. Phys., 22, 1613 (1954): 21,985 (1955); 25, 1150 (1956); (b) E.R.Lippincott, ibid., 23, 603 (1955);26, 1678 (1957). (3) E. R. Lippincott and M. 0. Dayhoff, Spectrochim. Acta, 16, 807 (1960).
POLARIZABILITIES FROM &FUNCTION MODELOF CHEMICAL BINDING
i) +
79
+ i)]
The bond-region electron contribution is calculated using a linear combination of atomic &function wave functions representing the two atoms involved in the where x is the coordinate of motion along the interbond; i.e., the expectation value of electronic position nuclear axis, a is the &function spacing, AI and A2 are squared (z2)along the bond axis is calculated, and this the &function strengths or reduced electronegativities is used to obtain this “bond-region” polarizability: (REN’s) for nucleus 1 and 2, respectively, g is the unit allb = 4 n A 1 2 ( l / a o ) ( ( ~ ~ where ) ) ~ , A12 is the root-mean&function strength (the value for the hydrogen atom), square &function strength of the two nuclei, a. is the and 6(x) is a 6 function whose properties are 6(z) = 0 radius of the first Bohr orbit of the atomic hydrogen, n is the bond order, and (zz)is the mean-square posiwhen x # 0,6(r) = m when x = 0, and (x)& = 1 tion of a bonding electron and may be expressed as for any argument x of 6. Thus, for the case in ques(z2)= (R2/4)4- (1/2cR1?). Here R is the internuclear tion the potential is zero everywhere except at the 6distance at the equilibrium position. In the case that function positions, i.e., x = a / 2 and x = -a/2. the bond is of the heteronuclear type, a polarity corThe solution to the Schroedinger equation for the rection is necessary to produce the ionic character molecular problem yields separate wave functions for believed to exist in reality. Then a!/,= q b u where the bonds and the ith bond wave function has the form u = exp[-(1/4)(Xl - X z ) 2 ] . Here X is Pauling’s as electronegativity.4 The nonbond-region electron contribution all. is calculated from the fraction of the given atom not involved in bonding and its atomic polarizability; and the whereN = [(2//c,)(lf exp(-cc,a) f ac,e~p(-c~a)]-’/~ basis for such calculation is the Lewis-Langmuir and ci = (-ZEJ1/’. Here Et is the separated atom octet rule modified by Linnett6 as the double quartet energy for the ith particle. Frost’s &function branchof electrons. Let us consider the molecule ing condition2”can then be used to obtain the following X. expression for the homonuclear case c, = A g [ 1 f HXClX * exp (- cia) 1, where plus and minus signs correspond to X . the attractive :tnd repulsive states, respectively. By combining the above equation with A = (-2Et)’/’, in the ground state where the “dots” represent the elecone may have and the trons with spin quantum number of “crosses” represent the electrons with spin quantum lim cf = Ag = (-2E,)”Zuam number of - 1 / 2 or vice versa. If C1 in its ground atomic state has seven electrons, then for this molecule the Lippincott and Dayhoffa bypam the problem of obnonbond-region electron contribution is alln = (6/7). taining the ci for each individual electron by generating a%l since six of seven valence electrons of C1 are not a “super” one-electron situation from the corresponding involved in bonding according to the Linnett picture. n-electron situation. A resultant c is obtained written Thus, for a diatomic molecule the total parallel as CR and is assumed to account for all of the electrons component is cq = allp f1a1 f2az1 where f 1 , f2, a, in the system. For the homonuclear situation, CR = and a2 are the fraction of electrons not involved in A (nN)’l2where -4is the one-electron &function strength bonding and the atomic polarizabilities of atom 1 for the atom, n the principal quantum number, and N and atom 2, respectively. For polyatomic molecules, it is the number of electrons making contributions to the is obvious that bond angle considerations must be embinding or two times the column number in the periodic ployed to calculate these components (which can be table. Heteronuclear diatomics are readily treated achieved with very little difficulty). by forming a geometric mean molecular &function 8. Perpendicular Component. The &function strength as exlz = (cR~cR~)~”= nlniV1N2(A1A2)1’Z model being one dimensional, it was necessary to and then solving the wave equation as if the molecule obtain the perpendicular component by a contrived were homonuclear. but justifiable approach. This is discussed in detail The &FunctionModel and Polarizabilities by Lippincott and Stutman.6 Briefly, however, every 1. Parallel Component. The bond parallel component is obtained from contributions of two sources: (4) L. Pauling, “The Nature of the Chemical Bond,” Cornell Uni(a) bond-region electrons and (b) nonbond-region versity Press, Ithaca, N. Y.,1960. electrons according to the valence bond interpretation. ( 5 ) J. W.Linnett, J. Am. C h a . SOC.,83, 2643 (1961).
V
=
-[:A’gs(x
-
A2ga(z
s-+;
U+W
+
+
Volume 70,Number 1
January 1966
80
E. R. LIPPINCOTT, G. NAOARAJAN, AND J. M, STUTMAN
isolated atom is allowed to possess three degrees of polarizability freedom, and every bond which is formed between two atoms removes two of these degrees of freedom, with the exception that (1) if two bonds are formed from the same atom and exist in a linear configuration, then only three atomic degrees of freedom are lost and ( 2 ) if three bonds are formed from the same atom and exist in a plane, then only five atomic degrees of freedom are lost. Using these rules the sum of all of the perpendicular components of the molecule is given as
molecular polarizability is higher than the experimental one when the molecule is assumed to have a D3h symmetry while it is in good agreement with the experimental value when the molecule is assumed to have a CSV symmetry; Le., the calculated value for this symmetry is 26.45 X However, the assumption of a nonplanar geometry to the borane molecule violates the Jahn-Teller eff ect11J2being operative in this molecule. Hence, a further investigation is needed to establish correctly the structure of the borane molecule. The molecular polarizability of methyl cyanide is not much different from that of methyl isocyanide though there are changes in the bondregion as well as nonbond-region electron contributions
where cyj and X j are the atomic polarizability and the electronegativity of the jt,h atom, respectively, and n d f is the number of residual atomic polarizability degrees of freedom. Here i is the bond index and J' the atom index. Hence, the average polarizability is thus given as
Results
Table I: Observed and Calculated Polarizabilities (in 10-26 cm.8) for with Five Residual Atomic polarizability D~~~~~~ of needom Molecules
All0 5'20 ClZO SClZ SiFZ SnClz SnBrz
a ~ (calod.) :
49.81 23.78 47.71 70.65 23.45 95.14 120.30 165.13 126.83 153.79
U M (obsd.)
The molecules for which the bond and molecular polarizabilities have been calculated here from the 6SnL function po1,ential model are classified according to PbC12" 99.46 their numbers of residual atomic polarizability degrees PbBrz PbIz 202.42 of freedom, and the calculated values in TeClz 98.09 are given in Tables I to IX. Available experimental TeBrz 124.51 values of dielectric constants and refractive indices CHzNz 37.11 were used to obtain the molecular polarizabilities NOF 28.24 through the well-known Langevin-Debye and LorentzNOCl 44.67 NOBr 53.76 Lorenz equations, and these values in ~ m are . ~ NSF 35.98 given in Tables I to IX. The molecular structural data used for such calculations were taken from a S. S. Batsanov, "Refractometry and Chemical Structure," translated by P. P. Sutton from Russian to English, Consultants Sutton' and the recent electron diffraction and microBureau, New York, N. Y., 1961. wave studies. Whether diimide possesses a cis or trans configuration is irrelevant from the point of view of the &function potential model since both the number of residual atomic polarizability degrees of freedom as (6) E. R. Lippincott and J. M. Stutman, J . Phys. Chem., 68, 2926 (1964). well as the internuclear distances are the same for both (7) L. E. Button, "Tables of Interatomic Distances and Configuraconfigurations. A similar statement may be made tion in Molecules and Ions," Special Publication No. 11, The Chemifor difluorodiazine. I n accordance with the results cal Society, London, 1958. of microwavt: studiess-l0 for hydrogen azide, a bond (8) R. Kawley, K. V. L. N. Sastry, and M. Winnewisser, J . Mol. Spectry., 12, 387 (1964). order of 1.5 was used to the nitrogen-nitrogen bond (9) L. H.Jones, J. N. Shoolery, R. G. Shulman, and D. M. Yost, adjacent and 2.5 was used to the nitrogen-nitrogen J . C h a . Phys., 18, 990 (1950). bond nonadjacent to the nitrogen-hydrogen bond; (10) G. C. Dousmanis, T. M. Sanders, C. H. Tomes, and H. J. Zeiger, ibid., 21, 1416 (1953). and in the cases of hydrogen isocyanate and hydrogen (11) H.A. Jahn and E. Teller, Proc. Roy. SOC.(London), A161, 220 isothiocyanate, a bond order of 2 was used for all of (1937). the bonds except the nitrogen-hydrogen bond. I n (12) G. W. Castellan, J. Chem. Phys., 22, 536 (1954); 22, 1791 the case of the borane (BH3) molecule, the calculated (1954). The Jourrial of Physical Ch,emistry
POLARIZABILITIES FROM &FUNCTION MODELOF CHEMICAL BINDING
Table 11: Observed and Calculated Polarizabilities (in 10-16 cm.9 for Molecules with Six Residual Atomic Polarizability Degrees of Freedom Molecules
NH3" NF: NHFz NHClz NHzCl PH3" PF3 PCla' PBr3 PI3 PClzF FCN ClCN BrCN ICN NzHz N2F2 NHOz
ay
(calcd.)
18.49 28.32 25.41 56.61 38.58 41.24 29.02 91.40 121.06 180.29 67.25 25.49 41.63 49.86 63.17 25.61 31.00 28.49
a y (obsd.)
21.75 27.86
42.72 103.03
Table IV: Observed and Calculated Polarizabilities (in 10-21 cm.3) for Molecules with Eight Residual Atomic Polarizability Degrees of Freedom Moleoules
HCCH".~ HCCF HCCCl HCCBr NCCN",~ ClCCCl BrCCBr ICCI CH3OH" CHsSH CFaSH SiCbSH
N~HI~ BrF5 IFs NFOa HNOa'
SS
'
See footnote a of Table I. K. L. Ramaswamy, Proc. Indian Acad. Sci., A2, 364 (1935). H. E. Watson, Proc. Roy. SOC.(London), A117, 43 (1927). d U . Grassi, Novo Cimenlo, 10, 3 (1933). a
81
Sea
r r (calcd.) ~
O ~ M(obsd.)
34.14 32.05 50.86 59.77 44.11 65.01 82.95 113.43 31.17 52.41 52.02 119.62 31.80 63.84 60.18 44.87 37.28 231.29 332.26
34-00
47.15
32.49
34.55
38.40
a H. E. Watson, G. G. Rao, and K. L. Ramaswamy, Proc. Roy. SOC.(London), A143, 558 (1934). b H . E. Watson and K. L. Ramaswamy, z%id., A156, 144 (1936). H. E. Watson, G. P. Kane, and K. L. Ramaswamy, z%id., A156,130, 144 (1936). H. Braune and T. Asche, 2. physik. Chem., B14, 18 (1931). J. B. Miles, Phys. Rev., 34, 964 (1929). See footnote a of Table I.
'
Table III: Observed and Calculated Polarizabilities (in 10-" 0111.3) for Molecules with Seven Residual Atomic Polarizability Degrees of Freedom Molecules
PM (calcd.)
HBOz BH3a N02F NOzCl HN3 HNCO HNCS AlF3 &c13a AlBr3" A113a CW3 BrF3 HCOF COHzb COFz COClzC COBrz CSCl2 ClOaF NSFs
27.80 29.98 32.54 49.58 32.07 31.27 50.35 27.25 89.30 118.61 187.19 46.74 51.89 27.63 27.80 28.04 59.52 86.26 80.21 47.42 50.78
'
a y (obsd.)
25.56
89.43 124.46 199.08
27.74 65.78
See footnote a of Table I. E. C. Hurdk and C. P. Smyth, J. Am. Chem. SOC.,65, 89 (1943). C. P. Smyth and K. B. McAlpine, ibid., 56, 1697 (1934). a
Table V : Observed and Calculated Polarizabilities (in lo-% cm.3) for Molecules with Nine Residual Atomic Polarizability Degrees of Freedom Molecules
BHaCO Bz03Q BZS3 H2SOa4 NHzNOz NHzCHO CHzCOb CHzNz CHsPHe CHaNHz' CHsAsFz CaHed CH&N" CHsNC CFaCN SiHsCN GeHaCN
ax (calcd.)
44.33 42,24 117.52 49.12 41.53 36.58 40.46 44.02 60.60 37.24 58.65 56.98 44.50 44.74 44.71 66.73 72.85
UM
(obsd.)
40.34 53.73
43.59 40.81 60.23 43.98
"See footnote a of Table I. b N . B. Hannay and C. P. Smyth, J . Am. Cbm. Soc., 68, 1357 (1946). ' R. Sanger, 0. Steiger, and K. Gachter, Helv. Phys. Acta, 5, 200 (1932). See footnote a of Table IV. e See footnote c of Table 111.
Volume 70,Number 1 January 1966
E. R. LIPPINCOTT, G. NAGARAJAN, AND J. M. STUTMAN
82
Table VI: Observed and Calculated Polarizabilities (in 10-26 cm.3) for Molecules with Ten Residual Atomic Polarizability Degrees of Freedom Molixules
C2H4" CzF4 CzCh CzBr4 czI4
l11-CJ32F2 Cis-CzIIzFz I,1-C2HzC12 Cis-CZIIzCl; trans-CzHnClz" trans-C:2HzBrzd cis-C2€[21zd CzH8 C2H3Cle C~H~BI.* CzH31B CnHF3 CzHCl: C2HBr.ld C2H2FC1 C&Bd31" CnClzI
CXM
(calcd.)
41.76 41.99 105.83 141.83 194.18 40.23 41.01 75.99 76.07 76.06 92.16 120.06 40.85 59.53 74.14 87.64 41.02 92.28 133.76 57.72 90.52 147.37
a~ (obsd.)
40.97
80.44 81.47 103.58 139.19 61.82 73.31 93.12
M o1ecules
CH3CCH"'* CH3CCC1 CH8CCBr CHSCCI CF3CCH SiH8CCH CHd CN )z (CH3)20" (CH3)zS (CHdSe C~H~OH~
C~H~SH* CzH60Cl6 COHCCH C2H402' CzH4OS CzH3F30
CH~NO~~ 132.40 91.85
See footnotes a and b of Table IV. * A. A. Maryott, M. E. Hobbs, and P. M. Gross, J . Am. Chem. Soc., 63, 659 (1941). See footnote a of Table I. 'N. A. Lange, "Handbook of Chemistry," Handbook Publishers Inc., Sandusky, Ohio, 1952. e J. A. C. Hugill, I. E. Coop, and L. E. Sutton, Trans. Faraday SOC.,34, 1518 (1938). a
to the parallel components. In the case of the ethylene series, there are no significant differences in the molecular polarizability values between the cis and trans configurations. A slight change is observed only in the bond-region electron contributions to the parallel coniponents owing to the difference in the internuclear distances adopted. A similar situation is also observed in the cases of 1,2-dichloropropane and 2,2-dichloropropanemolecules. The values of bond parallel components may be compared from one molecular system to another having similar chemical bonds with the same as well as different bond orders. The values of bond parallel components in 10-25 ~ m for . ~ the C-C bond are 16.90 in propyne, 19.93 in methyl cyanide, 17.28 in acetyl cyanide, and 17.01 in ethylene oxide; the values for the C=C bond are 22.39 in allene and 22.55 in ketene; the values for the C=C bond are 24.18 in diacetylene, 24.39 in propyne, 24.49 in propynal, 23.96 in acetylene, and 24.38 in silylacetylene; the values for the G O bond are 13.96 in ethylene oxide, 12.98 in methyl alcohol, and 13.09 in acetic acid; the values for the C=O The Journal of Physical Chemistry
Table VII: Observed and Calculated Polarizabilities (in 10-16 cm.3) for Molecules with 11 Residual Atomic Polarizability Degrees of Freedom
C3H3C1 C3H3Br C3H3I
ay
(oalcd.)
52.03 68.36 75.62 89.45 51.28 73.62 64.18 50.05 73.28 86.79 50.78 70.75 68.16 53.90 53.51 72.88 52.28 54.84 72.75 79.58 94.04
(obsd.)
CZM
55.48
52.70
50.64 73.74 70.53 51.12 55.91
"See footnote c of Table IV. bF. J. Hieger and H. H. Wenzke, J. Am, Chem. SOC.,60, 2115 (1938). 'L. G. Groves and S. Sugden, J . Chem. SOC.,1779 (1937). * See footnote u of Table I. C. T. Zahn, Physik. Z., 33, 525 (1932). C. T. Zahn, Phys. Rev., 37, 1516 (1931).
'
bond are 17.52 in formamide, 16.68 in hydrogen isocyanate, and 17.56 in oxalyl chloride; and the values for the C=N bond are 22.57 in cyanogen, 22.58 in methyl cyanide, 23.27 in methyl isocyanide, and 23.18 in fluorine cyanide. These clearly indicate that the parallel components can be transferred from one molecular system to another having similar chemical bonds with nearly identical internuclear distances in the two different molecules. The small changes in the value of the parallel component from one molecular system to another may be due to the slightly different values of the internuclear distances as the parallel component is roughly proportional to the fourth power of the internuclear distance. Since the perpendicular component is a linear combination of atomic polarizabilities and is independent of the internuclear distance, the perpendicular component will always be transferable from one molecular system to another having similar chemical bonds irrespective of the accuracy in the value of the internuclear distance. The values of the bond parallel components in cm.3 are 15.03 for the C-N bond in methyl isocyanide, 22.23 for the C=N bond in diazomethane, 23.27 for
POLARIZABILITIES FROM &FUNCTION MODELOF CHEMICAL BINDING
Table VIII: Observed and Calculated Polarizabilities (in 1 0 - 2 5 cm.3) for Molecules with 12 Residual Atomic Polarizability Degrees of Freedom
83
Table IX : Observed and Calculated Polarizabilities (in 10-26 cm.3) for Molecules with 13 Residual Atomic Polarizability Degrees of Freedom
a y (calcd.)
CH3COCN CF3SFs
a y (calcd.)
59.86 87.30 188.41 55.29 69.39 141.16 78.54 120.68 85.25 56.21 53.95 60.93 80.12 63.87 56.55 63.92 103.38 123.25 64.89 79.05
54.49 74.08 181.61 84.21 59.48 65.06 83.72 63.55 81.36 88.47 105.14 100.09 98.65 112.53 83.81 63.30 74.77 97.79
'See footnote c of Table 111. 'See footnote d of Table VI. K. L. hmaswamy, Proc. Indian Acad. Sei., A2, 364, 630 See footnote e of Table VII. G. A. Barclay, R. J. W. (1935). Le Febre, and B. M. Smyth, Trans. Faraday SOC.,46, 812 (1950). L. G. Groves and s. Sugden, J . Chem. SOC.,158 (1937).
'
the C=N bond in methyl isocyanide, 16.77 for the N-N bond in nitramide, 18.59 for the N=N bond in diazirine, and 20.49 for the N=N bond in Nz molecule. The values, as is expected, increase with bond order. The values of the bond parallel components for the C-C multiple bonds are in the increasing order roughly in the ratio 17 :22 :24; the values for the C-N multiple bonds are in the ratio 15:22:23; and for the N-N multiple bonds the ratio is 17:19:20. If the a and u electrons contribute equally to the bond parallel component, the values for the double and triple bonds should be two and three times the value for the single bond. Actually they are much less, which shows that the contribution to the parallel component by the electrons occupied in the 7r orbital is much less than that of the electrons occupied in the u orbital. Further, it is interesting to note that in all three of the above cases, the increment in bond polarizability from u --t Q 'X is greater than that from u 7r + u 27r. Apparently, the extra electron pair is incorporated into the bond region in such a way as to be effectively shielded from any applied field and thus generates a T system. This more stable system relative to the u
+
+
+
+
ay (obsd.)
64.19 62.33 82.42 93.91 114.52 101.44 102.23 84.01 63.80 96.29
C. T. Zahn, Physik. Z., 33, 686 (1932). See footnote c of See footnote c of Table V. See footnote f of Table IV. Table VIII. ' P. C. Mahanti, Phil. Mag., 20, 274 (1935). E. C. Hurdk and C. P. Smyth, J . Am. Chem. Soc., 64, 2829 (1942). A. A. Maryott, M. E. Hobbs, and P. M. Gross, ibid., 63, 659 (1941). See footnote a of Table I. 'See footnote b of Table V. M. Kube, Sci. Papers Inst. Phys. Chem. Research (Tokyo), 29, 122 (1936).
could probably account for the slow rate of electrophilic addition reactions of acetylenic systems relative to the ethylenic systems. Except for a very few cases where the molecular dimensions are uncertain, the calculated molecular polarizabilities are in good agreement with the experimental values. Thus, the present investigation further indicates that the &function potential model is useful in estimating molecular polarizabilities.
Appendix Sample calculations of bond and molecular polarizabilities for a diatomic molecule C12 and a polyatomic molecule acrylonitrile are given here. Cl,Molecule. C1-C1 = 1.988 8.,Acl = 0.753 a.u., = 13.88 x io-25 Cm.', xcl = 3.0, n d f = 4. CR
= (3 X 14)"*(1.4234)(108)= 9.225
(z') =
=
(R2/4)
+ ('/zcR')
X lo8 cm.-I
= 0.9939 X
4nA(1/@)((z2))2= (4)(1) (0.753) (0.98788)/(0.529) = 56.248 X
cm.2
CM.~
Volume 70, Number 1 Januuty 1966
E. R. LIPPINCOTT, G. NAGARAJAN, AND J. M. STUTMAN
84
Ball, = B j a j = (12)(13.88)/7 = 23.794 X
8 2 a l = '&f(zXj2QIj)/(BXj2)= (4)(249.84)/18
+
~ m . ~
( x 2 ) = 0.46112 X 10-l6 cma2
allb = (4) (2) (0.757) (0.21263)/(0.529) = =
55.52 X
24.342 X
~ m . ~
~ m . ~
For the C=N bond ~ m . ~ 45.187 X (z2) = 0.34579 X 10-la cm.2 The experimental value of the molecular p~larizability'~ ailb = (4)(3)(0.8377)(0.11957)/(0.529) is 46.10 x 10-25 ~111.~ which is in good agreement with 22.722 X ~ m . ~ the above calculated value. Z q P = 82.279 X ~ m . ~ Acrylonitrile. C-H = 1.07 8., C-C = 1.445 &, C=C = 1.34 8.,C=N = 1.154 8.,A H = 1.00 a.u:, Zcq. = (2)(7.43)/5 = 2.972 X ~ m . ~ Ac = 0.846 a.u., A N = 0.927 a.u., a~ = 5.92 X Z 2 a ~= (12)(328.5666)/(40.98) = ~ m . ac ~ , = 9.78 X ~ m . QN ~ , = 7.43 X XR = 2.1, XC = 2.5, X N = 3.0, ?&df = 12. 96.213 X ~ m . ~ For the C-H bond a~ = (1/3)(2allD f 2Qlln 2 2 a l ) = {z2) = 0.31547 X 10-l6 cm.2 60.488 X CM.~ allb = (4)(1)(0.8701)(0.09952)/(0.529) = The experimental value of the molecular p~larizabilityl~ 6.548 X 10-25 ~ m . is~ 61.816 X C M . which ~ is also in good agreement with the above calculated value. The polarity corallb = a j j , ~= (6.548)(0.961)(10-25) = rection for the CEN bond is not introduced because 6.293 X ~ m . of ~ greater electronic distribution in the bond region. The &function strengths for the bonds of the polyFor the C-C: bond atomic molecule have been obtained as described by (x2) = 0.53423 X cm.2 Lippincott and Dayhoff . 3 cqlb = (4) (1) (0.757)(0.2854)/(0.529) = 16.336 X 0311.~ (13) K. G. Denbigh, T T U ~Faraday S. SOC.,36, 936 (1940). aM =
(1/3)(za/lb
za/in
f 221)
+
For the C=C bond
The J O U Tof~Physical chemistry
(14) E. C. Hurdis and C. P. Smyth, J . Am. C h m . SOC.,65, 89 (1943).
