Spectrochhics Acta.1967,Vol.2SA,pp. 1489to 1497. Persamon Preea Ltd. Printed inNorthern Ireland
A transferable force-field for out-of-plane vibrations of chlorinated benzenes J. R. SCHERER Western Regional Research Laboratory, Agricultural Research Service U.S. Department of Agriculture, Albany, Cslifornis 94710 (Received 22 June 1966) Abstract-A twenty-three parameter force-fieldis found to reproduce 176 observed out-of-plane fundamentals of benzene and chlorinated benzenes to within 15 cm-l with an average error of 3.5 cm-l. The force-constents which overlap the benzene molecule agree with the accepted Miller-Crawford values. The diagonal constants for CH bend and CC1 bend decrease with substitution at adjacent ring positions and the C---C-C-C torsion constsnt increases with substitution at the central C-C bond. The values of o, m and p interaction constants between yo-, (X = H, Cl) coordinates are found to deviate only slightly from those found for benzene. Inconsistencieswere uncovered in the vibrational assignmentsof o-C,D,Cl,, C&D&l end 1,2,3,4. CsHsCI,; certain fundamentals in these molecules are reassigned.
THE goal of this work is to determine a transferable potential-function for a series of related substituted benzenes that tests existing vibrational assignments and also provides physically meaningful normal coordinates that explain the substituent dependence of the out-of-plane vibrations of these molecules. The transferability of valence force constants (VFF) has been demonstrated for the planar vibrations of benzene and chlorinated benzenes [l]. While the average difference between observed and calculated planar modes for this series of molecules was N&S cm-l, earlier studies of 1,3,5-trihalogenated benzenes [2,3] indicated that a better frequency fit should be possible for the out-of-plane vibrations. In the present study, the assumption of force-constant transferability leads to an average frequency fit of N f3.5 cm-l. GEOMETRICAL MODEL GAFNER and
HERBSTEIN [4] have
concluded from X-ray studies that o&o chlorine atoms in crystalline polychlorobenzenes probably do not deviate by more than 0.01 to 0.02 A from the plane of the ring. Their measurements on o-C,H,Br, [5] indicate that the planar angular displacement of the C-Br bonds is ~1.5” and they comment that it is not likely that the deviations would be greater in the chlorinated molecule. Recently, STRAND and Cox [6] have obtained electron diffraction data on gaseous C&Cl, and 1,2,4,5C,H,Cl, and have concluded that both [l] J. R. SCHERER, Spectrochim.Acta 20, 345 (1964). [2] J. R. SCHERER,J. EVANS, W. W. MUELDERand J. OVEREND,Spectrochim. Acta 18,67 (1962). [3] J. R. SCHERER,J. C. EVANSand W. W. MUELDER,Spectrochim. Acta 18,1579 (1962). [4] G. GARNERend F. H. HERBSTEIN,Acta Cryst. 13, 706 (1960). [B] G. GAFNERand F. H. HERBSTEIN,Mol. Phya. 1, 412 (1958). [6] T. G. STRANDand H. L. Cox, JR., J. Chem. Phy8. 44, 2426 (1966). 1489 21
J. R. SCHERER
1490
molecules are planar. They also find that the angle between the or& CC1 bonds in 1,2,4,5-C,H,Cl, is 62.8 f 0.4 degrees. In order to assess the dependence of the out-of-plane vibrations on these geometrical changes, a calculation of the vibrational frequencies of o-C,H,Cl, was made in which the C-Cl bond angles between the Cl atoms were each opened by 1.5”. The force-field will be discussed later. The deviations between the calculated frequencies (highest to lowest) of the distorted molecule and one that has 120’ bond angles are 0.0, 0.1, -0.1, -1.3 and 1.1 cm-l for the A, species and 0.2, 0.4, 1.2 and 0.7 cm-l for the B, species. We conclude that changes in kinetic energy arising from assumption of 120” C-C-Cl bond angles will not seriously affect our calculated frequencies. The Ccl, CH and CC [7] bond lengths were assumed to be 1.70, 1.084 and 1.397 A respectively. The observed frequencies of the chlorinated benzenes were taken from assignments by RANDLE and WHIFFEN [8], NONNENMACHER and MECKE [9], STOJILJKOVIC and WHIFFEN [lo] and SCHERER and EVANS [2,11]. SLOANE [12] has remeasured the far-infrared spectra of several chlorinated benzenes and has found bands at 115 cm-l in @J,H,Cl, (previously observed under single beam conditions at 125 cm-l), 98 cm-l in 1,2,3-C&H&Y, and 173 cm-l in C&l,. He also found no evidence for the C&Cl, band reported [lo] to be at 209 cm-l and we reassign the A, vibration to the 173 cm-l band. In the course of our calculations an inconsistency was found in the Scherer-Evans assignment of the A, species of o-C&D&l,. Their assignment placed the highest frequency A, CD bending mode at 705 cm-l whereas calculations, even with crudely refined force constants, indicate that the highest A, mode should be near 800 cm-l. In the present work no weight was given to the two highest A, modes and their calculated values were found to be 812 and 724 cm-l respectively. The 705 cm-l band is therefore reassigned to the second highest A, fundamental. The calculated value of the third highest A, fundamental of 1,2,3,4-C&H&l, was also found to be ~25 cm-l lower than an assignment by Scherer and Evans which was deduced from a combination band (2 x 530 N 1063). If a weak band at 1012 cm-l is considered the first overtone of the fundamental, the agreement with the calculaAn alternative assignment was given for the 1063 cm-l tion is nearly perfect. infrared band. In any event, the assignment of 530 cm-l is almost certainly incorrect and we expect the fundamental to be within 15 cm-l of 505 cm-l. NANNEY, BAILEY and LIPPINCOTT have recently published a vibrational ment of C,D,CI
assign-
[ 131. Results from early calculations were not in agreement with
A, fundamentals (760, 680 cm-l). Subsequent were carried out with the A, species given zero weight.
their assignment of the two highest
least-squares
refinements
[7] B. P. STOICHEFF, Can. J. Phy.9. 32, 339 (1954). [S] R. R. RANDLEand D. H. WELIFFEN, Molecular Spectrocrcopy,p. 111, Institute of Petroleum (1954). [9] G. NONNENMACHER and R. MECKE, Spectrochim. Acta 17, 1049 (1961). [lo] [ll] [12] [13]
A. J. H. T.
STOJILJKOVIC rend D. H. WHIFFEN, Spectrochim. Acta R. SCHERER and J. C. EVANS, Spectrochim. Acta 19, 1739 (1963). SLOANE, Private communication. R. NANNEY, R. T. BAILEY and E. R. LIPPINCOTT. Spectrochim. Acta 21, 1495 (1965).
A transferable force-field for out-of-plane
vibrations
1491
The results of our final calculations indicate that while all other calculated fundamentals in the series had errors less than 15 cm-i, the two highest A, modes deviated from the assignments by 20 and 37 cm-l respectively. Nanney et al. observe a very weak Raman line at 642 cm-r which they ascribe to a combination band. On the strength of our final calculations it seems preferable to assign the 642 cm-l Raman line to the second highest A, fundamental (which is Raman allowed) instead of the weak infrared (forbidden) band at 680 cm- l. In the H, molecule the infrared combination band involving the highest A, and B, CH deformations is strong enough to be easily detected (-1940 cm-l) [8]. Nanney et al. observed an infrared band at 1602 cm-l in the D, molecule which may be explained on the basis of the same This assigncombination if a value of 786 cm-i used for the highest A, fundamental. ment is in better agreement with our calculated value of 781 cm-l. The very weak infrared band observed at 760 cm-l may be due to incompletely deuterated material. FORCE-FIELD MODELS
Benzene MILLER and CRAWFORD [14] have determined a complete, eight parameter, symmetry valence force-field (SVFF) for benzene. Before extending this force-field to other molecules it must be decomposed into force-constants based on a set of coordinates that span the vibrational coordinate space of each molecule and whose The internal coordinates chosen by force-constants are, hopefully, transferable. MILLER and CRAWFORD* are particularly convenient for describing the substituent (X) dependence of a force-field because this dependence is limited, to a first approximation, to the Ay,, coordinates. The internal coordinates are defined as follows:
\
m Xi, the change in angle between the C,X, bond (X = H, / plane formed by the i-th carbon atom and its two adjacent carbon atoms i refers to a clockwise numbering of the ring positions ; Ari = A, in angle between the CI_lCiCi+l plane and the C,C,+,C,+, plane. The AYCX, =
constants
(indicated
like *A)
between ortho, meta andpara
Cl) and the (Ci__r,C,+l). the change interaction
AyCH coordinates
are
completely determined from the SVFF, but only the diagonal constant for Ari, one interaction constant between AT< and AT,, and two interaction constants between AyCH, and ATE may be obtained from the remaining transformation equations. Therefore, we arbitrarily set the long range interaction constants to zero. With respect to these assumptions, the Miller-Crawford valence force-field (MCVFF) is given in Table l(a). The units of all force constants are lo-l1 erg/rad2. The values in parenthesis are obtained by using presently accepted geometry [7] and observed frequencies [ 151. * A set of 24 torsional coordinates of the form CiCi+ICi+2CI+3, H,CiCi+,Ci+,, HiCiCi+lHGtl also spans the vibrational coordinate space of benzene. Eight force-constants may be deter-
mined for the non-redundant symmetry coordinates but the profusion of redundancies and the overlapping nature of the H,C,C,+,C,+, and HiC,C,+,Hi+, coordinates make a determination of a physically meaningful set of internal coordinate force constants impractical. [14] F. A. MILLER and B. L. CRAWFORD, JR., J. Chem. Phye. 14,282 (1946). [15] S. BRODERSEN and A. LANUSETH, Ma$. Fya. Skr. Dan Selak. 1, No. 7 (1959).
J. R. SCHERER
1492
KAKIUTI and SHIMANOUCHI[16] did a least-squares refinement of five benzene valence force constants using the observed frequencies of C,H, and C&D,, but their abbreviated force-field gave 20 cm-l errors in the hydrogen deformations of the B,, and E,, species. Their force-field (KSVPF) 1s * g iven in Table l(b). S=NOUCHI, KAKITJTI and GAMO [17] used the KSVFF to calculate approximate hydrogen deformation and ring deformation frequencies and normal coordinates of a series of The following least-squares refinement of the chlorinated substituted benzenes. benzenes improves the frequency fit for the hydrogen deformations, provides better descriptions of the skeletal modes and other low frequency vibrations because of inclusion of interaction with CC1 bending coordinates, and provides calculated frequencies and normal coordinates for all fully deuterated and some partially deuterated molecules. Table 1. Benzene valence force-constants in units of lo-l1 erg/rad2 (a) Miller-Crawford [14] (b) KakiutiShimanouchi [16] (c) this work Force constant type
(b)
(c)
0.441(0.444)
0.469
0.448
0.214(0.217)
0.350
0.259
(a)
-0.066(-0.068)
0.008(0.003)
-0.085
-
-0.072
0.003
-0.089(-0.089)
-0.023
- 0.065
-0.133(-0.141)
-0.197
-0.152
O.OSO(O.048)
-
0.035
Chlorinated benzenes Any force-field which implies a transferability of benzene force constants to chlorinated benzenes should satisfy a basic requirement : the force constants for the benzene molecule, that are obtained under the constraint of their transferability with chlorinated molecules, must agree with the force-constants that are obtained The following force-field meets this requirement and also solely from benzene. [IS]
Y. KAKIUTI and T. SHIMANOUCEU, J. Chem. Phys. 25, 1252 (1956). SHIMANOUCHI, Y. I(AICIUTI and I. GHO, J. Chem. Phys. 25, 1245 (1950).
[17] T.
A transferable force-field for out-of-plane
1493
vibrations
provides a satisfactory frequency fit to 176 observed fundamentals. The substituent dependence of the force-field is defined and the refined-force constants 4, are listed with their standard deviations (u(4)) in Table 2. The observed and calculated frequencies are listed in Table 3 and the observed frequencies that are starred have The weight matrix elements are proportional to l/1,,, been given zero weight. where I = 4rr2c2v2/N = (5.88852 x 10-‘)v2 mdyn/amu A and Y is in cm-l. The Cartesian displacements of each molecule have been calculated and stereo projections of the vibrating molecules have been prepared and are available on request [18]. Table 2. Benzene and chlorinated benzene force constants. Units are lo-l1 erg/rad2 Values in parenthesis represent one standard deviation, u{+} H
>I
H
0.448 (0.002)
H
H
Cl
H
H
*
Cl
-$H i
0.269 (0.009)
-0.072
_H
(0.001)
0
0
i
>I
Cl
>I
H
0.414 (0.002)
Cl
0.606 (0.010)
Cl
H
0.679 (0.007)
Cl
0.429 (0.002)
H
0.541 (0.007)
Cl
>I
Cl
>I
Cl
-$a % _H 0
Cl
-$a
0.269 (0.006)
0.347 (0.014)
H_
0
=H
0.006 (0.002)
HI
0
ICl
0.009 (0.003)
Cl m
0
m
0.003 (0.001)
-0.014 (0.002)
H
I
P’
o-
-*
-0.091 (0.002)
Cl
-0.066 (0.006)
Cl
0
i”
-0.162 (0.003)
I
Cl
0
%
0 mCl
-0.021 (0.003)
Cl
-0.016 (0.004)
0.035 (0.004)
_H 0
-0.065 (0.005)
_3
0
-0.184 (0.004)
Cl o-
[18] J. R. SCHERER, Stereo views of the non-planar deuterokotopes, available on request.
0.053 (0.005)
vibralions of chlorinated
benzene8 and
their
1494
J. R. SCHERER Table 3. Observed
Sym
obs.v
‘-3, A4s 675.0 % I 991.0 % E
*u
El,
E P”
707.0 849.0
Av
u{v}
078.4 -3.4 991.8 -0.8 5.6 10.2 -3.7 -1.3 10.2 -3.7 -1.3
2.8 2.6 2.9 2.2 2.3 2.2 2.2 2.3 2.2
-1.1 3.6 826.4 696.6 3.5 10.6 662.4 791.5 -2.5 352.4 -1.4 10.6 652.4 791.5 -2.6 352.4 -1.4
2.0 3.2 2.6 1.7 2.4 1.9 1.7 2.4 1.9
917.4
2.1 2.3 1.7 1.9 1.7 2.0 1.9 1.7 2.0
talc. Y
-% E 2” -% E t”
701.6 838.8 972.7 969.0 405.3 I404.0 849.01 838.8 972.7 969.0* 1404.0’ 405.3
830.0 599.0 863.0 1789.0 361.0 663.0* 7s9.0* 351.0*
498.1
E”
633.0
531.9
‘926.0
926.6
711.0 376.0 926.0* 711.0* 37&o*
703.1 377.4 926.5 703.1 377.4
966.0 830.0 400.0 985.0 902.0 740.0 682.0 467.0 196.0
961.1 827.6 405.7 984.0 898.1 737.4 687.7 469.1 197.6
3.9 2.4 -6.7 1.0 3.9 2.6 -5.7 -2.1 - 1.6
1.8 1.9 1.8 1.8 1.2 1.5 1.7 1.6 0.9
816.0 747.0 618.0 646.0 420.0 I 182.0
780.8 643.8 363.3 816.7 745.2 611.6 644.2 412.2 185.9
-0.7 1.8 6.4 1.8 7.8 -3.9
2.2 1.4 1.6 2.1 1.7 1.3 1.2 1.4 0.9
697.0
697.4
l
B,
C,D,Cl
BI
v
Av
u(v) Sym
A,
B1
i 976.0 855.0 695.0 604.0 154.0 f940.0 748.0 436.0 240.0
705.0* 606.0
t 145.0 766.0 681.0 E1 385.0 225.0
(891.0 631.0 212.0
B 1
A, i
Bl
-4.4 -1.5 -5.0 -0.7 3.2 4.0 1.1 -2.2 3.9
1.6 1.5 1.8 2.2 0.8 1.6 1.5 1.4 1.1
811.9 713.9 608.0 469.8 142.2 762.4 579.2 383.7 223.9
0.0 -8.9 -2.0 0.0 2.8 2.6 1.8 1.3 1.1
2.0 1.8 1.4 1.8 0.8 1.7 1.2 1.3 1.0
896.2 526.9 213.9 967.9 866.2 776.6 677.2 433.1 174.6
-4.2 6.1 -1.9 -1.9 2.8 -1.6 -3.2 -5.1 1.6
1.5 1.8 1.2 1.3 1.3 1.5 1.7 1.4 0.9
B,,
Au B,,
Av
u(v)
B1,
632.0 788.0 699.0 289.0 780.0 i 367.0 692.0 417.0
636.5 786.9 696.4 297.1 768.6 354.2 693.6 421.8 106.8
-4.5 2.1 2.6 -8.1 11.4 12.8 -1.6 -4.8
1.6 2.7 1.6 1.6 2.6 1.6 2.6 1.9 0.7
Bar
A” Bs,,
816.0 i 934.0 687.0* 298.0 951.0 I 407.0 819.0 486.0 115.0
863.0 662.0
A,” -
849.4 3.6 665.8 -3.8 141.8 6.2 876.3 -6.3 627.1 2.9 213.8 1.2 876.3 -6.3 527.1 2.9 213.8 1.2
2.2 2.2 1.1 1.7 1.8 1.3 1.7 1.8 1.3
i‘;g.; * 630.0 216.0 869.0* 630.0* 215.0’
I”
I”
-0.9 4.1 6.7 -2.9 3.2 3.2 -2.9 3.2 3.2
2.7 1.7 1.1 1.8 1.6 1.3 1.8 1.6 1.3
1,3,5-C,D,Cl, A,”
E”
E”
763.0 ( 634.0 148.0 ( 712.0 498.0 202.0 712.0* 498.08 202.02
763.9 629.9
141.3 714.9 494.8 198.8 714.9 494.8 198.8
1,3,&C,H,DCl, 731.0 494.4 198.7 801.4 737.6 626.3 640.0 378.1 167.6
1.7 1.2 1.7 1.8 1.4 1.3 1.4 1.2 0.9
A, (
B1
868.0 741.0 617.0 601.0
I
875.3 527.1 213.8 857.9 743.7 616.9 498.2 203.4 141.6
0.1 -2.7 1.1 2.8
1.7 1.8 1.3 1.6 1.6 1.7 1.5 1.3 1.1
1,3,5-C,D,HCl,
P-‘Z&W, B,,
talc. v
1,3,&C,H,CI,
A,
A,
ohs. v
NP,Cl, 979.4 866.5 700.0 604.7 150.8 936.0 746.9 437.2 236.1
m-C,D,Cl,
C,H,Cl -4,
do.
m-C,H,Cl, 0.6 -0.4 1.1 -0.6 7.9 -2.4 -0.6 7.9 -2.4
(918.0
I”
obs. v
frequencies for benzene and chlorinated refkement. U{V} represents the standard
o-‘&D&I, 497.0
Sym-C,H,D,
4”
Sym
calculated
o-C,H,Cl,
W, A P” %W
and
818.3 928.3 691.2 305.5 947.5 406.2 813.4 496.0 108.3
-3.3 6.7 -4.2 -7.6 3.5 0.8 6.6 - 10.0 6.7
1.9 2.3 2.2 1.5 2.2 1.9 2.1 2.1 0.7
A,
Bl
1713.0 600.0 201.0
714.9 494.8 198.8 866.7 756.3 579.3 604.0 208.4 141.4
-1.9 6.2 2.2 -3.7 -0.3 1.7 4.0
1.8 1.6 1.3 1.3 2.2 1.6 1.4 1.3 1.1
1495
A transferableforce-field for out-of-plane vibrations benzenes. The starred elements were given zero weight in the least-squares deviation of the calculated frequencies Sym
oba. v
talc. v
Av
A,
iO63.0
Bl
773.0 607.0 243.0 08.0
806.6
614.1 216.6 067.6 776.4 608.7 601.6 246.2 07.4
0.4 0.0 -3.6 -4.6 -3.4 -1.7 -3.2 0.6
1.6 1.6 1.3 1.3 1.3 1.7 2.2 1.6 0.6
-4,
BI
731.1 482.3 200.6 802.4 686.6 677.1 463.6 236.7 06.8
0.0 10.7 -2.6 -6.4 4.4 -1.1 0.6 0.3
1.7 1.6 1.2 2.3 1.6 1.1 1.8 1.6 0.6
063.1 866.6 826.1 689.4 649.7 440.6 311.3 170.3 106.6
-11.1 2.4 -14.1 -1.4 1.3 -6.6 -3.3 3.7 9.6
1.2 1.3 1.2 1.6 1.3 1.6 1.1 0.8 0.7
A”
1.7 1.3 1.6 1.6 1.0 1.3 1.1 0.8 0.7
793.3 734.0 682.1 600.2 604.6 384.7 301.6 171.1 103.6
A,
4
i ,808.O 667.0 241.0 111.0
A,
f B1
A,
B1
871.0 620.0 1216.0 860.0 602.0 660.0 316.0 147.0 80.0+
I
A,
’
Bl
B1, Bga A ” B,,
348.0 1860.0 681.0 226.0 600.0 ( 80.0* 878.0 442.0 140.0
038.8
706.6 606.0 311.4 94.2 816.6 663.9 241.3 106.9
1.2 0.4 26.0 -4.4 -7.6 3.1 -0.3 4.1
1.7 1.8 2.1 1.1 0.7 1.4 1.6 1.7 0.7
B,, B,, A = B,,
348.0 760.0 680.0 222.0 600.0 I so.o*
ob8.v
cda.v
Av
u{v}
1,2,4&C,HDCl, 781.3 674.6 464.6 301.8 04.1 676.2 614.8 231.6 106.1
2.4 2.0 1.6 1.1 0.7 1.7 1.8 1.6 0.7
1600.0 348.0
A,
870.0 746.0 636.0 414.0 210.0
B1 i
600.8 362.1 81.6 867.3 741.6 636.8 413.4 222.2 132.1
-0.8 -4.1
698.0 346.2 82.2 867.4 699.4 628.6 273.0 144.9 94.0
-1.0 -2.2
2.7 3.6 -0.8 0.6 -3.2
2.1 1.7 0.7 1.3 1.7 1.8 1.0 1.0 0.0
C,HCI, 816.7 616.3 216.3 868.3 688.4 663.0 316.2 142.3 86.8
-4.1 4.7 -0.3 0.7 3.6 -3.0 -0.2 4.1 -6.8
1.7 1.7 1.3 1.6 1.6 1.4 1.2 1.0 0.6
A,
B1
-4.4 1.6 -2.6 -1.0 6.1 0.1
1.8 1.6 0.7 1.3 2.1 1.9 1.2 1.1 0.8
C,DCl, 714.9 482.9 200.7 766.6 636.7 610.3 308.2 141.7 86.7
1.8 1.6 1.3 1.0 1.7 1.1 1.2 1.0 0.6
A,
B1
607.0 343.0 1742.0 666.0 490.0 267.0 146.0
698.0 346.2 82.2 744.0 663.8 486.7 261.6 144.1 94.7
-1.0 -2.2
167.6 706.4 106.4 330.1 694.6 82.1 330.1 694.6 82.7
16.6 -2.4 -9.4 0.0 -0.6 -2.1 0.0 -0.6 -2.1
-2.0 1.2 3.3 -4.6 0.0
1.8 1.6 0.7 1.0 2.1 1.6 1.1 1.1 0.8
CllC’, 362.1 866.2 682.7 227.7 600.8 81.6 868.4 447.6 132.7
-4.1 -6.2 -1.7 -2.7 -0.8 -1.6 9.6 -6.6 7.3
1.7 1.0 2.2 2.0 2.1 0.7 2.0 2.3 0.9
362.1 751.1 601.8 217.6 600.8 81.6 720.4 387.2 131.6
-4.1 8.9 -2.8 4.6 -0.8 -1.6 0.6 0.8 8.6
1.7 2.6 2.1 1.8 2.1 0.7 2.2 1.8 0.0
1,2,4,6-C,D,Cl,
1,2,3,4-C,H,Cl, 040.0 706.0 630.0* 307.0
(T(V)Sym
1,2,4,6-C,H,Cl,
1,2,4-C,D,Cl,
A”
Av
1,2,3,6-C,D,Cl,
1,2,4-C,H,Cl, 042.0 860.0 811.0 688.0 661.0 436.0 308.0 183.0 116.0
cahv
1,2,3,6-C,H,Cl,
1,2,3-C,D,Cl, 732.0 ( 403.0 108.0 706.0 600.0 676.0 464.0 237.0
oba. v
1,2.3,4-C,D,Cl,
1,2,3-C,H&l, 800.0 624.0* 212.0
a{v} Sym
A,, B =g El;. I ‘U Eln 1 ‘”
173.0 704.0 I 01.0* 340.0 I 694.0 ao.o* 340.0* 604.0* 80.0*
2.0 3.6 1.0 2.2 3.0 0.7 2.2 3.0 0.7
1496
J. R. SCHERER DISCUSSION
Several models which extended the MCVFF to chlorinated benzenes were tried but they were unsuccessful. A chronological account of each failure will not be given, but, we shall briefly describe the effect of some slight variations on our most successful force-field (Table 2). We shall use the weighted square-error sum, WSQER = 2 P,Aili2, as a measure of the overall frequency fit produced by least-squares refinement of a model. Pi is the weight matrix element for the i-th observed frequency and A& is the difference between observed and calculated frequency parameters. The WSQER for the refinement which yielded the twenty-three force constants in Table 2 is 0.5 x 1O-3 and the average frequency error is ~3.5 cm-l. A refinement of a twenty-one parameter force-field, constructed by removing the dependence of the ring torsional
force-constants
on the substituents X and Y, produced a 7-? WSQER = 0.6 x 1O-3 and an average frequency error of 4.0 cm-l. Further removal of the substituent dependence of the diagonal ycu and yccl force constants increased the WSQER to 2.2 x 1O-3 and gave an average frequency error of 6.8 cm-l. In another attempt, the dependence of all diagonal ycx and T force constants on neighboring substituents was eliminated, but, the interaction terms between m and r, yen and yccl coordinates were allowed to vary with the substitution between the coordinates viz. 4 %m = =?A?= The net para interaction sides of the ring i.e., HI(
9
@&
= ,/“;-w.
terms were assumed to be the average of terms from both Cl Cl F:
fi9nII = 1/2 (+,C:& + @&).
This twenty-six
parameter force-field had a WSQER = 1.4 x 1O-3 with an average frequency error of 5.8 cm-l. Adding substituent dependence in the AriAyi interaction terms of this model decreased the WSQER to 1.0 x 10e3 and the average frequency error to 5.2 cm-l. From these trials it appears that allowing substituent dependence of the diagonal force constants is far more effective in improving the fit to observed frequencies than placing this dependence completely in the interaction constants. The k3.5 cm-l fit obtained with the twenty-three parameter force-field of Table 2 is probably as good as we should expect considering the geometrical approximations and the simplicity of the potential function. We note that while the average difference between observed and calculated frequencies is 3.5 cm-l, the average standard We therefore adopt 5 standard deviations as a deviation [z a{~}/n) is ~1.6 cm-l. realistic measure of the errors in the calculated force constants. One standard deviation is shown in Table 2. The numerical magnitudes of the force constants which overlap benzene are compared with the MCVFF in Table l(c). The benzene force constants obtained in this study are within 5 o(d) of the Miller-Crawford force constants. The substituent
A transferable force-field for out-of-plane
vibrations
1497
dependence of the diagonal force constants is illustrated in Fig. 1 with uncertainties of 5 a($> and the MCVFF values are also indicated in this figure. We note that the diagonal constants for ~cn and yccl coordinates show a nearly linear dependence on the number of neighboring Cl atoms, and that the effect of Cl substitution in both cases is a lowering of the force constant. Conversely the CC torsion constants seem However, the high uncertainty for this force constants to increase with substitution. diminishes our confidence in the apparent curvature of this correlation.
1
I (4
I (b)
I (cl
Fig. 1. Substituent dependence of diagonal force constants. (a) no neighboring chlorine atoms (b) one neighboring chlorine atom (c) two neighboring chlorine atoms. Five standard deviations (50 ($1) in the force constants are indicated by the vertical bars.
A satisfying feature of this force-field is the close correspondence of the ortho, meta and para YcuYci and yclycl interaction constants to the related ~cu~cu interaction constants of benzene. Unfortunately, it is not yet possible to determine an eight parameter SVFF for C,Cl, because of the lack of suitable isotopic data. However, the present study is able to evaluate valence force constants which span C&l, because of the assumed transferability of these constants to other molecules and the use of collective vibrational frequency data. In general, the agreement of the final potential constants with those obtained for benzene lends support to our model. A discussion of the actual forms of the vibrations and their relation to group frequencies involving hydrogen and deuterium deformations, and skeletal modes will be presented in a subsequent report. AcknowWgements-The author wishes to thanlr Dr. J. OKEREND and Dr. J. SCFLWHTSCHNEIDER for supplying some of the FORTRAN computer programs used in this study.