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Molecular constants of dicyanoacetylene
Journal of Molecular Structure Elsevier Publishing Company, Amsterdam.
119
Printed in the Netherlands
MOLECULAR CONSTANTS OF DICYANOACETYLENE
K. VENKATESWARLU, Department
(Received
MARIAMMA
P. MA-I-HEW
AND
V. MALATHY
DEVI
of Physics, Kerala Uniuersity Centre, Ernakulam (India) April 26th, 1968)
ABSTRACT
The potential energy constants of dicyanoacetylene have been evaluated using a general valence force field. Applying the theory of mean-square amplitudes of vibration, the parallel and perpendicular mean square amplitudes have been calculated. The shrinkage effects are obtained for the different atomic distances. Coriolis constants are determined for the various possible couplings. The thermodynamic functions are estimated assuming a rigid rotor, harmonic oscillator approximation for the temperature of 100 to 1000” K.
INTRODUCTION
The dicyanoacetylene molecule is linear and symmetrical with the nitrogen atoms at its ends. It belongs to the D,, point group with the normal modes distributed as 3~: +2~,’ +27rg+27r,. Miller and Hannan’ have measured the IR and Raman spectra of dicyanoacetylene, and have given the assignment for eight of the nine fundamental frequencies. Later, Miller et al.’ again studied the IR and Raman spectra of dicyanoacetylene and have given the assignment of all vibrational fundamentals. Experimental evidence supports the linear configuration for the system corresponding to DA point symmetry. A normal-coordinate analysis for the potential constants had been carried out earlier’ for this molecule,
Fig. 1. Geometrical
configuratlon
o! dicyanozketylene. J. Mol. Structure.
3 (1969) li91128
120
K. VENKATESWARLU,
M. P. MATHEW,
V. M. DEVI
but no attempt has so far been made for the determination of other molecular constants. The present work deals with the determination of (1) force constants, (2) mean square amplitudes of vibration, (3) shrinkage constants, (4) Coriolis coupling constants and (5) thermodynamic properties for the molecule. The geometry of the molecule is represented in Fig. 1. The symmetry coordinates, which transform according to the characters of the point group concerned and satisfy the orthogonality and normalization conditions have been constructed. Using Meal and Polo ’ s ’ ‘3” vector method, the kinetic energy matrix elements are obtained. Those for the bending modes are obtained by the method of Ferigle and Meister4. The G elements thus obtained are essentially the same as those given by Miller and Hannanl except that they have been modified by proper scaling.
POTENTIAL ENERGY CONSTANTS
The force constants were calculated by Wilson’s I; and G matrix method5Their evaluation was repeated because the earlier workers’ did not calculate them on the basis of complete assignment of frequencies, and further, they are of value in the determination of Coriolis coefficients. Assuming a general valence type of potential function and neglecting certain interaction terms, the following F matrix elements are obtained:
0:
7rg
a,+species:
species:
species:
R,
species:
In the above expressions, fR, f, and fD are the valence force constants, associated with the internal coordinates CEN, C-C and CzC respectively; f, and fe represent respectively the angle bending force constants for N&-C and C-C.=C angles and the rest of the terms represent the interaction force constants associated with the respective internal coordinates.
MEAN-SQUARE
AMPLITUDES
OF VIBRATION
The elements of the symmetrized mean-square amplitude. matric are obtained6 on solution of the secular equation jZGwl -AEj = 0. The 2 matrix J. Mol. Structure,
3 (1969)
119-128
MOLECULAR
CONSTANTS
121
OF DICYANOACETYLENE
elements are identical to the R matrix elements given earlier. Considering the nonbonded atom pairs, the following additional mean square amplitudes are obtained in terms of Z matrix elements.
The generalised mean-square amplitudes which include the mean-square parallel and perpendicular amplitudes and the mean cross products are determined by the method of Morino and Hirota’. The following expressions are obtained for the parallel and perpendicular mean-square amplitudes for the various bonded and non-bonded atom pairs.
Bonded: 1. Nr=C
2. q-c,
<@a’> = <(W2> = =
= <(zs -cJ*> <(Ax)*> = <(x3 -~a)~>
= <(~3 -~4)*>
3. CEC <(W2>
= <(z‘+%)*> =
<@y12>
=
Non-bonded: 2. NI - - - C,
1. N,---N,
= <@I
-z21*>
=
<@42>
=
<(Ax)*>
=
<6wYZ)‘>
<@JO*>
= =
<(XI-xd*>
J. Mol. Structure, 3 (1969)
119-128
122
K. VENKATESWARLU,
4. N,
3. iv1 ---CT,
5. c3
V. M. DEVI
M. I’. MATHEW,
- - - c,
<@z12>
= ((~1 --d2>
afw2>
= <(z1-zd2>
=
= <@I -xJ2>
<(AY)~>
= <(VI -yd2>
<(Au)‘>
= <(VI -yd2>
---c,
7. c,
. - - c,
<(W’>
=
<(W2>
=
<(W2>
=
<(W2>
= <(x3 -M2>
<@Y>~>
= <(ys -yd2>
<@y12>
= <(YS -ud2>
Using the Z matrix elements and the transformation matrix A, such that A = M-r B’ G-‘, the generalised mean-square amplitudes are evaluated. The perpendicular mean-square amplitudes are equal for a given atom pair, and all the cross products vanish because of the symmetry of the molecule.
SHRINKAGE
EFFEC-I-
The shrinkage constants are determined for the molecule using the perpendicular mean-square amplitudes. The following shrinkages exist for the molecule. -_6
-_6
l---2
1*.*6
---_2t, R
r1...2
=
2(R+r)+D =
z1 .-.6
=R
71_..5
7R
7r
I...5
=
--6
I__.4
=
71-w-4 ~_---,
7R
7~
R+r
R
r
=
53 _ . _ 6
-_6
3.--6
3...5
=
27r
(1)
‘D
(2)
2r+D+R-R-r-i?
--6
-_6
27, -- r,, r D
OD
(3)
R+r+d-R-;-ii
27r
(4)
7D
(5)
2r+D-T-% .__‘j 73 _-_-_
=r
7D
r+D
r
D
(6)
where 713 = +<(Aqj)‘> <(AX,)‘>
+ t<(A~ii)~>,
and <(Ay,)” > representing
J. Mol. Structure,
3 (1969) 119-128
the perpendicular
mean-square
amplitudes.
MOLECULAR
CORIOLIS
CONSTANTS
COUPLING
OF
123
DICYANOACETYLENE
CONSTANTS
Application of Jahn’s rule* shows that the non-vanishing <-values are of type Fy which arise from (0: x rr*) and (crz x n,) couplings and of type c” arising from the couplings within tbe degenerate species. [-values are obtained from the relation f” = L- ’ Cz i- r, L being the normal-coordinate transformation matrix and C is the Coriolis C-matrix which is of the same form as the c-matrix, and the C” elements are derived by the vector method of Meal and Polo3. The C matrices are as follows:
a,+x
coupling:
7r,
s 6n
s 7a
-
-
p,Jr/R + &Jr/R - + JR/r) --dT2+ drIR+hW) --
S,
2
-cl&% p&/D/r+ drlD)l - - (h/r+ -p&JO/r
3
+ 2drjD)h
In general, C[ja = - C;rjb; i = 1,2,3; i = 6 and 7
a,+x
7r”
coupling: S 83
s 9n
S, pNdrIR+pc(drfR-k JRlr) I 1 -tCc~~~I~+~~~I~+~~I~)l ss C&
= -C~jb;
-
- mh 343h
i = 4 and 5;j = 8 and 9
ng x zg coupling : S 6b
S 7b ---
S’6a
~NTIR+~=[(~rlR+JRIr)2+Rlrl -
-
S 7a -p&/~r(~rlR-dRlr) --
- pc[dDlr(drlR + JR/r) --dRlr(dDlr+2drjD)1 pc [D/r +
(JDlr + drlD)‘I
-k~Rlr~~Dlr+h/rlD)l zIc,x 3r, coupling : S8b
S9b -
-
&a ~NrIR+~c,Wr+ drlR+~R21r)l --
S 9a
-pc[JDlr(Jr/R+JRIr)
-
-
-
-~c[~(~r/R+JRIr)+~~lrl 2pcDlr
+ JRDIrI J. Mol. Structure. 3 (1969) 119428
K. VENKATESWARLU,
124
M. P. MATHEW,
V. M. DEVI
The c-values are found to satisfy the following sum rule: For the tsz x By coupling, ii. G4LJ2
= i&&J2
and
= 1
iil(C&d’ =l$l(C~d2 =1
For the G,’ x xU coupling, c
1=4.5
(r&AJ)2 =
c
1=4.5
G6a)
2
’
=
1
and
c
i=4.5
(<;TA2 =
c
i=4.5
(G,x)’
= 1
and for the 7rgx 7~~and xTc,x nz, couplings all the diagonal zetas are unity and the off-diagonal elements vanish.
THERMODYNAMIC
QUANTITIEs
The thermodynamic functions are evaluated for the molecule using the observed fundamental frequencies. The values are reported from 100 to 1000” K, assuming a rigid rotor, harmonic oscillator approximation and also for the ideal gaseous state at one atmospheric pressure.
RESULTS
AND
DISCUSSION
The vibrational frequencies used are presented in Table 1. The interatomic distances are: C=N, 1.14 A; C-C, 1.37 A; GC, 1.19 A. The potential constants are given in Table 2. The normal C-C bond length is N 1.5 A and the corresponding force constant is N 5 mdynes A- ‘. In the present case the C-C bond length TABLE OBSERVED
1 VIBRATIONAL
FREQUENCIES
OF DICYANOACETYLENE
Species
Designation
Mode of vibration
us’
Vl % %
GN C-C CrC
stretch stretch stretch
C=N
stretch
a” c
v4 VS
5
J%l
C-C stretch
N&-C
bending
Frequencies 2290 692 2119 2241 1154
%
C-C&
bending
504 263
VS
N&-C C-C&
bending bending
472 107
%
%
J. Mol. Structure, 3 (1969) 119428
(Cm-‘)
MOLECULAR TABLE
CONSTANTS
125
OF DICYANOACETYLENE
2
~XRETCHING.
Symbol
BENDING
AND
~TERACTION
Force consrant
FORCE
Symbol
CONSTANTS
17.360
fRr
1.006
k
14.710 8.218
fRD
0.161 1.625
2
0.047 0.015 0.003
0.242 0.141 1.171
(mdyna ii-l)
Force constant
fR
2 A,
IN DICYANOACETYLENE
is abnormally small as is found in linear molecules. This accounts for the unusually high value of the C-C force constant. The stretching force constants of the present study are compared with those in dicyanodiacetylene and methyl cyanide in Table 3. TABLE
3
COMPARISON AND
OF THE FORCE CONSTANTS
OTHER MOLECULES
(mdynes
A-‘)
OF THE CzN,
C-C
AND
CaC
Compound
CEN
c-c
czc
NEC-CEGCEN N~C-CXLC~C-C~NP
17.630 16.550
8.218 8.395
14.710 14.845
H,C-C~N’”
17.880
5.130
BONDS IN
DICYANOACETYLENE
-
In the former case the carbon-carbon single bond is formed by linear sp-sp hybridization, whereas in the latter case it is formed by tetrahedral sp3-sp hybridization. Thus there is mores character in the former case resulting in the shortening of the bond length and a consequent enhancement of the force constant. The C=N and C=C force constants fall in the normal range. The frequencies calculated on the basis of the force constants obtained here are exactly the same as those observed. The mean-square amplitude values obtained for the molecule are given ‘in Table 4. The mean amplitude values for the various bonded and non-bonded pairs of atoins are reported in Table 5. The high stretching force constant value TABLE
4
,
MEAN-SQUARE
AMPLITUDES
Symbol
Mean-square amplitudes
OF VIBRATION
Symbol
(U’)
IN DICYANOA-LENE
Mean-square amplitudes
ORr %D
-0.oOo497 -0.OOOOO4
OD
0.001200 0.001750 0.001345
%D
-0.000536
a&z
0.023280
=ee
CR
Qr
a0 a cr
0.039455 -0.000174
(&>
=a
* %I3
-0.015555 -0.005616 0.001206 J. Mol.
Structure,
3 (1969) 119-128
126
K. VENKATESWARLU,
.TABLE
hi. P. MATHEW,
V.
hf. DEVI
5
hiBAN
AhfPLIl-UDE.5
Atom
pair
OF VIBRATION
FOR DICYANOACETYLENE
Mearr
AIOM pair
(ii)
Mean amplitude
ampiiiudes
Atom pair
Mean amplitudes
CrN
0.03465
N1.‘. N=
0.05244
N I‘__ G
0.0445
c-c
0.04183
N 1.‘.
G
0.05052
c 3.”
G
0.04852
crc
0.03667
N 1.”
G
0.04741
C 3”’
G
0.04499
TABLE
6
COMPARISON ACETYLENE
OF MEAN AMPLITUDES WITH
OF VIBRATION
OF
CsN,
C-C
C-C
CGC
0.03465
0.04183
0.03490 0.03613
0.04190 0.03829
0.03667 0.03530
CzN
NdS-CrC-C~N NsC-C=N= NzC-C&hC.dSCaN”
AND
CC%
BONDS
IN DICYANO-
7
GENERALISED
MEAN-SQUARE
AMPLITUDES
OF VIBRATION
Atom pair
<(A.#>
<(bF>
NrC
0.001200 0.001750 0.001345 0.002750 0.00255 1 0.002247 0.001981 0.002354 0.002024
0.021520 0.016654 0.012967
c-c ccc
(A)
OTHER CASES
Bond
TABLE
1
OF DlCYANOACElYLENE
(ii”)
= <@Y)*>
0.003537 0.016367 0.050239 0.054722 0.010461 0.020838
of the C-C bond produces a value of mean amplitude which is smaller than normal. The mean amplitude value decreases with increase of bond order as is seen in the case of the single and triple carbonxarbon bonds. A reverse effect is observed in the case of the force constants. Mean amplitudes increase with distance as is seen in the series UN,. . . C, < u&. . _Cs < uN1.. . C6 and UC,. . . c5 d uC3.. . cs - The mean amplitude values obtained in the present investigation are compared with those in dicyanodiacetylene and cyanogen in Table 6. The agreement is quite satisfactory. The generalised mean-square amplitudes are given in Table 7. In the case of non-bonded atom pairs, when the parallel mean-square amplitudes increase with distance, the perpendicular amplitudes show an opposite trend of variation. The shrinkage constants are presented in Table 8. Comparing the different N* * - C and C - . - C chains, it can be seen that the shrinkage constant increases with increase in distance as expected. >. Mol. Structure,
3 (1969) 119-128
MOLECULAR
TABLE
CONSTANTS
8
SHRINKAGE CONSTANTS IN DICXANOACETyLENE
Bond
Shrinkage
NS-CdZ-CzIU
0.072390 0.050857 0.028350 0.009230 0.032548 0.014920
NS-CsC-C NsC-CsC NsC-C c-csc-c c-es!
TABLE
9
CORIOLIS
COUPLING
CONSTANTS
ap’ x n, coupling
x nc,coupling
-Cx,
S:,,
=
-&,
0.0981
<$.9a =
-G
.9b
0.3599
g, ,7b = 0.00
I;& . 9b = 0.00
<; *9a =
-<;
,9b
0.9344
s=,, 6b = 0.00
q,
&a
=
-<;,,,
P3.6~1 =
-%=%
P 1.7a
-57,
0.1270
TY 2.7a =
4x2.7b
0.9900
g7=
-5’;,7b
0.9840 -0.1488
xg X 3rg coupling 0.9328
8b
-0.3604
<=,,
6b
&,,
=
1.00
= 1.00
*
x,
cgn
8b
&b
=
1.00
= 1.00 Rb = 0.00
*
--o-o644
10
THERMODYNAMIC
100 200 273.16 300 400 500 600 700 800 900 1000
IN DICXANOACFIYLENE
cz 8p=
-%33
TABLE
constant
coupling
=
=
(A)
a,+ xn,
TY 1.65
=
127
OF DICYANOACETYLENE
FUNCTIONS
12.94 18.21 20.82 21.57 23.66 25.16 26.37 27.40 28.26 28.99 29.61
OF DICYANOACETYLENE
10.02 12.86 14.66 15.25 17.11 18S8 19.78 20.79 21.69 22.45 23.12
33.52 41.37 45.65 47.09 51.71 55.70 59.21 62.59 65.19 67.77 70.21
(cal deg.-l mole-l)
43.54 54.23 60.31 62.34 68.82 74.28 78.99 83.08 86.88 90.22 93.33
The Coriolis coupling constants are presented in Table 9. They satisfy the required sum rules given earlier. The thermodynamic functions evaluated for the molecule for the ideal gaseous state at one atmospheric pressure are given in Table 10. J. Mol.
Srrucfure,
3 (1969) 119-128
128
K. VENKATESWARLU,
M. P. MATHEW,
V.-M. DEVI
ACKNOWLEDGMENT
Two of the authors (M.P.M. and V.M.D.) wish to thank the Council of Scientific and Industrial Research, Government of India, for the award of Senior Research Fellowships.
1 2 3 4 5 6
7 8 9 10 1I
A. MILLER AND R. B. HANNAN, J. Chem. Phys., 21 (1953) 110. A. MILLER, R. B. HANNAN AND L. R. COUSINS, J. Chem. Phys., 23 (1955) 2127. H. MEAL AND S. R. POLO, J. Chem. Phys., 24 (1956) 1119, 1126. M. FERIGLE AND A. G. MEI~TER,J. Chem. Phys., 19 (1951) 982. B. WILSON, JR.. J. Chem. Phys, 7 (1939) 1047,9 (1941) 76. S. J. Cwr~. Acta Pofytech. Scund., 6 (1960) 279. Y. MORINO ANLI E. HIROTA, J. Chem. Phys., 23 (1955) 737. H. J. JAHN, Phys. Rev., 56 (1939) 680. K. VENKHESWARLU, Y. ANANTHARAMA SARMA AND V. MALATHY DEVI, to be published. M. G. KRISHNA PILLAI AND F. F. CLEVELAND, J. Mol. S’ectry., 5 (1960) 212. S. J. CYVIN AND P. KLACBOE, Acru Chem. Stand., 19 (1965) 697.
F. F. J. S. E.
J. Mol. Srructure, 3 (I 969) 119-128
119
Printed in the Netherlands
MOLECULAR CONSTANTS OF DICYANOACETYLENE
K. VENKATESWARLU, Department
(Received
MARIAMMA
P. MA-I-HEW
AND
V. MALATHY
DEVI
of Physics, Kerala Uniuersity Centre, Ernakulam (India) April 26th, 1968)
ABSTRACT
The potential energy constants of dicyanoacetylene have been evaluated using a general valence force field. Applying the theory of mean-square amplitudes of vibration, the parallel and perpendicular mean square amplitudes have been calculated. The shrinkage effects are obtained for the different atomic distances. Coriolis constants are determined for the various possible couplings. The thermodynamic functions are estimated assuming a rigid rotor, harmonic oscillator approximation for the temperature of 100 to 1000” K.
INTRODUCTION
The dicyanoacetylene molecule is linear and symmetrical with the nitrogen atoms at its ends. It belongs to the D,, point group with the normal modes distributed as 3~: +2~,’ +27rg+27r,. Miller and Hannan’ have measured the IR and Raman spectra of dicyanoacetylene, and have given the assignment for eight of the nine fundamental frequencies. Later, Miller et al.’ again studied the IR and Raman spectra of dicyanoacetylene and have given the assignment of all vibrational fundamentals. Experimental evidence supports the linear configuration for the system corresponding to DA point symmetry. A normal-coordinate analysis for the potential constants had been carried out earlier’ for this molecule,
Fig. 1. Geometrical
configuratlon
o! dicyanozketylene. J. Mol. Structure.
3 (1969) li91128
120
K. VENKATESWARLU,
M. P. MATHEW,
V. M. DEVI
but no attempt has so far been made for the determination of other molecular constants. The present work deals with the determination of (1) force constants, (2) mean square amplitudes of vibration, (3) shrinkage constants, (4) Coriolis coupling constants and (5) thermodynamic properties for the molecule. The geometry of the molecule is represented in Fig. 1. The symmetry coordinates, which transform according to the characters of the point group concerned and satisfy the orthogonality and normalization conditions have been constructed. Using Meal and Polo ’ s ’ ‘3” vector method, the kinetic energy matrix elements are obtained. Those for the bending modes are obtained by the method of Ferigle and Meister4. The G elements thus obtained are essentially the same as those given by Miller and Hannanl except that they have been modified by proper scaling.
POTENTIAL ENERGY CONSTANTS
The force constants were calculated by Wilson’s I; and G matrix method5Their evaluation was repeated because the earlier workers’ did not calculate them on the basis of complete assignment of frequencies, and further, they are of value in the determination of Coriolis coefficients. Assuming a general valence type of potential function and neglecting certain interaction terms, the following F matrix elements are obtained:
0:
7rg
a,+species:
species:
species:
R,
species:
In the above expressions, fR, f, and fD are the valence force constants, associated with the internal coordinates CEN, C-C and CzC respectively; f, and fe represent respectively the angle bending force constants for N&-C and C-C.=C angles and the rest of the terms represent the interaction force constants associated with the respective internal coordinates.
MEAN-SQUARE
AMPLITUDES
OF VIBRATION
The elements of the symmetrized mean-square amplitude. matric are obtained6 on solution of the secular equation jZGwl -AEj = 0. The 2 matrix J. Mol. Structure,
3 (1969)
119-128
MOLECULAR
CONSTANTS
121
OF DICYANOACETYLENE
elements are identical to the R matrix elements given earlier. Considering the nonbonded atom pairs, the following additional mean square amplitudes are obtained in terms of Z matrix elements.
The generalised mean-square amplitudes which include the mean-square parallel and perpendicular amplitudes and the mean cross products are determined by the method of Morino and Hirota’. The following expressions are obtained for the parallel and perpendicular mean-square amplitudes for the various bonded and non-bonded atom pairs.
Bonded: 1. Nr=C
2. q-c,
<@a’> =
= <(~3 -~4)*>
3. CEC
= <(z‘+%)*> =
<@y12>
=
Non-bonded: 2. NI - - - C,
1. N,---N,
= <@I
-z21*>
=
<@42>
=
<(Ax)*>
=
<6wYZ)‘>
<@JO*>
= =
J. Mol. Structure, 3 (1969)
119-128
122
K. VENKATESWARLU,
4. N,
3. iv1 ---CT,
5. c3
V. M. DEVI
M. I’. MATHEW,
- - - c,
<@z12>
= ((~1 --d2>
afw2>
= <(z1-zd2>
=
= <@I -xJ2>
<(AY)~>
= <(VI -yd2>
<(Au)‘>
= <(VI -yd2>
---c,
7. c,
. - - c,
<(W’>
=
<(W2>
=
<(W2>
=
<(W2>
= <(x3 -M2>
<@Y>~>
= <(ys -yd2>
<@y12>
= <(YS -ud2>
Using the Z matrix elements and the transformation matrix A, such that A = M-r B’ G-‘, the generalised mean-square amplitudes are evaluated. The perpendicular mean-square amplitudes are equal for a given atom pair, and all the cross products vanish because of the symmetry of the molecule.
SHRINKAGE
EFFEC-I-
The shrinkage constants are determined for the molecule using the perpendicular mean-square amplitudes. The following shrinkages exist for the molecule. -_6
-_6
l---2
1*.*6
---_2t, R
r1...2
=
2(R+r)+D =
z1 .-.6
=R
71_..5
7R
7r
I...5
=
--6
I__.4
=
71-w-4 ~_---,
7R
7~
R+r
R
r
=
53 _ . _ 6
-_6
3.--6
3...5
=
27r
(1)
‘D
(2)
2r+D+R-R-r-i?
--6
-_6
27, -- r,, r D
OD
(3)
R+r+d-R-;-ii
27r
(4)
7D
(5)
2r+D-T-% .__‘j 73 _-_-_
=r
7D
r+D
r
D
(6)
where 713 = +<(Aqj)‘> <(AX,)‘>
+ t<(A~ii)~>,
and <(Ay,)” > representing
J. Mol. Structure,
3 (1969) 119-128
the perpendicular
mean-square
amplitudes.
MOLECULAR
CORIOLIS
CONSTANTS
COUPLING
OF
123
DICYANOACETYLENE
CONSTANTS
Application of Jahn’s rule* shows that the non-vanishing <-values are of type Fy which arise from (0: x rr*) and (crz x n,) couplings and of type c” arising from the couplings within tbe degenerate species. [-values are obtained from the relation f” = L- ’ Cz i- r, L being the normal-coordinate transformation matrix and C is the Coriolis C-matrix which is of the same form as the c-matrix, and the C” elements are derived by the vector method of Meal and Polo3. The C matrices are as follows:
a,+x
coupling:
7r,
s 6n
s 7a
-
-
p,Jr/R + &Jr/R - + JR/r) --dT2+ drIR+hW) --
S,
2
-cl&% p&/D/r+ drlD)l - - (h/r+ -p&JO/r
3
+ 2drjD)h
In general, C[ja = - C;rjb; i = 1,2,3; i = 6 and 7
a,+x
7r”
coupling: S 83
s 9n
S, pNdrIR+pc(drfR-k JRlr) I 1 -tCc~~~I~+~~~I~+~~I~)l ss C&
= -C~jb;
-
- mh 343h
i = 4 and 5;j = 8 and 9
ng x zg coupling : S 6b
S 7b ---
S’6a
~NTIR+~=[(~rlR+JRIr)2+Rlrl -
-
S 7a -p&/~r(~rlR-dRlr) --
- pc[dDlr(drlR + JR/r) --dRlr(dDlr+2drjD)1 pc [D/r +
(JDlr + drlD)‘I
-k~Rlr~~Dlr+h/rlD)l zIc,x 3r, coupling : S8b
S9b -
-
&a ~NrIR+~c,Wr+ drlR+~R21r)l --
S 9a
-pc[JDlr(Jr/R+JRIr)
-
-
-
-~c[~(~r/R+JRIr)+~~lrl 2pcDlr
+ JRDIrI J. Mol. Structure. 3 (1969) 119428
K. VENKATESWARLU,
124
M. P. MATHEW,
V. M. DEVI
The c-values are found to satisfy the following sum rule: For the tsz x By coupling, ii. G4LJ2
= i&&J2
and
= 1
iil(C&d’ =l$l(C~d2 =1
For the G,’ x xU coupling, c
1=4.5
(r&AJ)2 =
c
1=4.5
G6a)
2
’
=
1
and
c
i=4.5
(<;TA2 =
c
i=4.5
(G,x)’
= 1
and for the 7rgx 7~~and xTc,x nz, couplings all the diagonal zetas are unity and the off-diagonal elements vanish.
THERMODYNAMIC
QUANTITIEs
The thermodynamic functions are evaluated for the molecule using the observed fundamental frequencies. The values are reported from 100 to 1000” K, assuming a rigid rotor, harmonic oscillator approximation and also for the ideal gaseous state at one atmospheric pressure.
RESULTS
AND
DISCUSSION
The vibrational frequencies used are presented in Table 1. The interatomic distances are: C=N, 1.14 A; C-C, 1.37 A; GC, 1.19 A. The potential constants are given in Table 2. The normal C-C bond length is N 1.5 A and the corresponding force constant is N 5 mdynes A- ‘. In the present case the C-C bond length TABLE OBSERVED
1 VIBRATIONAL
FREQUENCIES
OF DICYANOACETYLENE
Species
Designation
Mode of vibration
us’
Vl % %
GN C-C CrC
stretch stretch stretch
C=N
stretch
a” c
v4 VS
5
J%l
C-C stretch
N&-C
bending
Frequencies 2290 692 2119 2241 1154
%
C-C&
bending
504 263
VS
N&-C C-C&
bending bending
472 107
%
%
J. Mol. Structure, 3 (1969) 119428
(Cm-‘)
MOLECULAR TABLE
CONSTANTS
125
OF DICYANOACETYLENE
2
~XRETCHING.
Symbol
BENDING
AND
~TERACTION
Force consrant
FORCE
Symbol
CONSTANTS
17.360
fRr
1.006
k
14.710 8.218
fRD
0.161 1.625
2
0.047 0.015 0.003
0.242 0.141 1.171
(mdyna ii-l)
Force constant
fR
2 A,
IN DICYANOACETYLENE
is abnormally small as is found in linear molecules. This accounts for the unusually high value of the C-C force constant. The stretching force constants of the present study are compared with those in dicyanodiacetylene and methyl cyanide in Table 3. TABLE
3
COMPARISON AND
OF THE FORCE CONSTANTS
OTHER MOLECULES
(mdynes
A-‘)
OF THE CzN,
C-C
AND
CaC
Compound
CEN
c-c
czc
NEC-CEGCEN N~C-CXLC~C-C~NP
17.630 16.550
8.218 8.395
14.710 14.845
H,C-C~N’”
17.880
5.130
BONDS IN
DICYANOACETYLENE
-
In the former case the carbon-carbon single bond is formed by linear sp-sp hybridization, whereas in the latter case it is formed by tetrahedral sp3-sp hybridization. Thus there is mores character in the former case resulting in the shortening of the bond length and a consequent enhancement of the force constant. The C=N and C=C force constants fall in the normal range. The frequencies calculated on the basis of the force constants obtained here are exactly the same as those observed. The mean-square amplitude values obtained for the molecule are given ‘in Table 4. The mean amplitude values for the various bonded and non-bonded pairs of atoins are reported in Table 5. The high stretching force constant value TABLE
4
,
MEAN-SQUARE
AMPLITUDES
Symbol
Mean-square amplitudes
OF VIBRATION
Symbol
(U’)
IN DICYANOA-LENE
Mean-square amplitudes
ORr %D
-0.oOo497 -0.OOOOO4
OD
0.001200 0.001750 0.001345
%D
-0.000536
a&z
0.023280
=ee
CR
Qr
a0 a cr
0.039455 -0.000174
(&>
=a
* %I3
-0.015555 -0.005616 0.001206 J. Mol.
Structure,
3 (1969) 119-128
126
K. VENKATESWARLU,
.TABLE
hi. P. MATHEW,
V.
hf. DEVI
5
hiBAN
AhfPLIl-UDE.5
Atom
pair
OF VIBRATION
FOR DICYANOACETYLENE
Mearr
AIOM pair
(ii)
Mean amplitude
ampiiiudes
Atom pair
Mean amplitudes
CrN
0.03465
N1.‘. N=
0.05244
N I‘__ G
0.0445
c-c
0.04183
N 1.‘.
G
0.05052
c 3.”
G
0.04852
crc
0.03667
N 1.”
G
0.04741
C 3”’
G
0.04499
TABLE
6
COMPARISON ACETYLENE
OF MEAN AMPLITUDES WITH
OF VIBRATION
OF
CsN,
C-C
C-C
CGC
0.03465
0.04183
0.03490 0.03613
0.04190 0.03829
0.03667 0.03530
CzN
NdS-CrC-C~N NsC-C=N= NzC-C&hC.dSCaN”
AND
CC%
BONDS
IN DICYANO-
7
GENERALISED
MEAN-SQUARE
AMPLITUDES
OF VIBRATION
Atom pair
<(A.#>
<(bF>
NrC
0.001200 0.001750 0.001345 0.002750 0.00255 1 0.002247 0.001981 0.002354 0.002024
0.021520 0.016654 0.012967
c-c ccc
(A)
OTHER CASES
Bond
TABLE
1
OF DlCYANOACElYLENE
(ii”)
= <@Y)*>
0.003537 0.016367 0.050239 0.054722 0.010461 0.020838
of the C-C bond produces a value of mean amplitude which is smaller than normal. The mean amplitude value decreases with increase of bond order as is seen in the case of the single and triple carbonxarbon bonds. A reverse effect is observed in the case of the force constants. Mean amplitudes increase with distance as is seen in the series UN,. . . C, < u&. . _Cs < uN1.. . C6 and UC,. . . c5 d uC3.. . cs - The mean amplitude values obtained in the present investigation are compared with those in dicyanodiacetylene and cyanogen in Table 6. The agreement is quite satisfactory. The generalised mean-square amplitudes are given in Table 7. In the case of non-bonded atom pairs, when the parallel mean-square amplitudes increase with distance, the perpendicular amplitudes show an opposite trend of variation. The shrinkage constants are presented in Table 8. Comparing the different N* * - C and C - . - C chains, it can be seen that the shrinkage constant increases with increase in distance as expected. >. Mol. Structure,
3 (1969) 119-128
MOLECULAR
TABLE
CONSTANTS
8
SHRINKAGE CONSTANTS IN DICXANOACETyLENE
Bond
Shrinkage
NS-CdZ-CzIU
0.072390 0.050857 0.028350 0.009230 0.032548 0.014920
NS-CsC-C NsC-CsC NsC-C c-csc-c c-es!
TABLE
9
CORIOLIS
COUPLING
CONSTANTS
ap’ x n, coupling
x nc,coupling
-Cx,
S:,,
=
-&,
0.0981
<$.9a =
-G
.9b
0.3599
g, ,7b = 0.00
I;& . 9b = 0.00
<; *9a =
-<;
,9b
0.9344
s=,, 6b = 0.00
q,
&a
=
-<;,,,
P3.6~1 =
-%=%
P 1.7a
-57,
0.1270
TY 2.7a =
4x2.7b
0.9900
g7=
-5’;,7b
0.9840 -0.1488
xg X 3rg coupling 0.9328
8b
-0.3604
<=,,
6b
&,,
=
1.00
= 1.00
*
x,
cgn
8b
&b
=
1.00
= 1.00 Rb = 0.00
*
--o-o644
10
THERMODYNAMIC
100 200 273.16 300 400 500 600 700 800 900 1000
IN DICXANOACFIYLENE
cz 8p=
-%33
TABLE
constant
coupling
=
=
(A)
a,+ xn,
TY 1.65
=
127
OF DICYANOACETYLENE
FUNCTIONS
12.94 18.21 20.82 21.57 23.66 25.16 26.37 27.40 28.26 28.99 29.61
OF DICYANOACETYLENE
10.02 12.86 14.66 15.25 17.11 18S8 19.78 20.79 21.69 22.45 23.12
33.52 41.37 45.65 47.09 51.71 55.70 59.21 62.59 65.19 67.77 70.21
(cal deg.-l mole-l)
43.54 54.23 60.31 62.34 68.82 74.28 78.99 83.08 86.88 90.22 93.33
The Coriolis coupling constants are presented in Table 9. They satisfy the required sum rules given earlier. The thermodynamic functions evaluated for the molecule for the ideal gaseous state at one atmospheric pressure are given in Table 10. J. Mol.
Srrucfure,
3 (1969) 119-128
128
K. VENKATESWARLU,
M. P. MATHEW,
V.-M. DEVI
ACKNOWLEDGMENT
Two of the authors (M.P.M. and V.M.D.) wish to thank the Council of Scientific and Industrial Research, Government of India, for the award of Senior Research Fellowships.
1 2 3 4 5 6
7 8 9 10 1I
A. MILLER AND R. B. HANNAN, J. Chem. Phys., 21 (1953) 110. A. MILLER, R. B. HANNAN AND L. R. COUSINS, J. Chem. Phys., 23 (1955) 2127. H. MEAL AND S. R. POLO, J. Chem. Phys., 24 (1956) 1119, 1126. M. FERIGLE AND A. G. MEI~TER,J. Chem. Phys., 19 (1951) 982. B. WILSON, JR.. J. Chem. Phys, 7 (1939) 1047,9 (1941) 76. S. J. Cwr~. Acta Pofytech. Scund., 6 (1960) 279. Y. MORINO ANLI E. HIROTA, J. Chem. Phys., 23 (1955) 737. H. J. JAHN, Phys. Rev., 56 (1939) 680. K. VENKHESWARLU, Y. ANANTHARAMA SARMA AND V. MALATHY DEVI, to be published. M. G. KRISHNA PILLAI AND F. F. CLEVELAND, J. Mol. S’ectry., 5 (1960) 212. S. J. CYVIN AND P. KLACBOE, Acru Chem. Stand., 19 (1965) 697.
F. F. J. S. E.
J. Mol. Srructure, 3 (I 969) 119-128