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Centrifugal distortion effects in the rotational spectrum of ethyl formate
Volume
70, number
2
CENTRIFUGAL
CHEhlICAL
PHYSICS
1 hlarch
LFi-lTEItS
DISTORTION EFFECTS IN THE ROTATIONAL
1980
SPECTRUM OF ETHYL FOE5MAI-E
Vijay Kumar KAUSHIK Department of Physics, Toyama Univemty. and Depamnent
Gofuku, Toyama-930. Japan of Physrcs, Zndum Znstitute of Technology. Kanpw 208016, Znndia
Recerved15 October 1979 The microwave rotational spectrum of ethyl formate has been analysed in the ground vibrational state and an excited vlbratronal state belongmg to the C-O torsional mode of nkatlon. l3e analysis gives effective rotational constants and quark centrifugal distortion constants. The calculated constants have been used to predict additional Q-bmch,J4 12 transihons.
1. Introduction The microwave rotational spectrum of ethyl formate was studied by Rrveros and Wdson [l] who estabhshed the existence of this molecule in two forms, namely gauche and tram forms. It was seen in their study that centrifugal distortion in the gauche form is much larger compared to that in the rrans Isomer. A srmdar feature has been observed in propyl chloride [2], propyl fluonde [3] and butyronitrile [4] , which also have gauche and tram forms. The problem of centrrfugal distortion analysrs of these molecules has recently been solved [5,6] _In the present investigation centrifugal drstortion constants have been calculated for ethyl for-mate in its ground vtbrational state and the u = 1 vrbrational state belonging to the C-O torsional mode of vibration.
2. Analysis of the spectrum Ethyl formate ISa near prolate asymmetric top. The ground-state spectrum consists of 32 transittons, and the C-O torsional mode spectrum consists of 22 rotational transitions. The observed spectrum [l] has been analysed using Watson’s [7] energy expression w= w. - $J2(J -dwJWoJ(J+
+ 1)2 - d&(J I)-dWKWo’PZ2>,
+ l)W;> - dKe) (11
tational constants 2, zand z_ The effective rotational -rvs constants A, B, C contain small centrifugal distortion corrections due to the R, centrifugal distortion term [7] ; dJ, CiJK, dK, dWJ and dwK are Watson’s set of centrifugal distortion constants. The constants obtamed as a result of the analysis are in table 2 and the agreement between calculated and observed frequencies can be seen in table 1. When the ground-state spectrum was subjected to analysis it was found that in spite of the fact that the number of observed lines is more for u = 0 than For u = 1, the standard deviation was much larger for the u = 0 state. This might be caused by experimental error m the frequency measurement or by inappropriate assignment of the observed lines. The spectrum was analysed carefully and a sequential elimination procedure was carried out simrlar to that used for nitric acid [8] and difhroramine [9 1. Each transition was eliminated from the analysis and was predicted through the constants obtained from the remaining transitions. This procedure helped to locate a single badly measured transition, 102,8-101,g; removal of this transition from the analysis reduces the standard deviation of the fit considerably. The quality of the fit was further improved by removing two other transitions, 53,243.1 and 3 2,1 -22,~, from the analysis. Removal of these transitions reduces the standard deviation of the fit from 43.4 kHz to 32.7 kHz. The standkd deviation of the fit is defined as
where W. is the energy of a rigid rotator with the ro317
1 March 1980
CHEMICAL PHYSICS LETTERS
Volume 70, number 2
Table 1 Ground and excited vibrational state transltions of the gauche form of ethyl formate u = 0 state
TransItion
20,2-lo.1
2 I.l--ll,O 2 1,2-11,l 2 2.0-11.1 21,2-lo,1 2 2.1-11,o 32.1-2~.~
a)
?v3-2cp2 1,2-2131
3 1,3-21,2 32.2
-22.1
32,2-31.3
4 2.2-32~ 40.4-30.3 41.3-31,~ 41.4-31.3 42,3-32,2 40.4-31,3 52,3-42,2
,
v=lstate
observed frequency @fHz)
calculated frequency (MHz)
14059.24 1473 148 13478.27 33841.22 19624.22 33 168.90 21337 85 0967.34 22067.24 20189.65 21157.56 21285.30 28614 94 27767 25 29364.08 26870 67 28174 02 22988 95
14059 231 14731.510 13478 235 33841.167
.
50,5-40,4
52,3-51.4 63,3-62.4 62.4-61,s 72,5-71,6 81.7-80.8 82,6_81,7 83.5-82.6
19624.22s
91*f5-go,9 102,8-101,9a)
;;:ti::;
123,g--122,lo
24506
-0 173 -0.147 0.031 -0 696 0.038
33168 969 21337.972 20976.33 1 22067.254 20189.650 21157 538 21285 307 28615 026 27767.250 29364 069 26870.660 28173 984 22988.937 (36004.078) (36604.106) 35440.993 35 159.736 30532.724 34414.446 16404 6 19 30364.441 16124 006 16311.482 22658.585 17085 660 27909 605 27100.981 20733 530 24506 405
35440 85 35 159 78 30532 69 34414.44 16404.61 30364.46 16123.98 1631156 22658 60 17085 64 27909.59
50,5-41*4
centrifugal distortion correction (MHz)
b,
40
-0.64 1 0 048 -0 535 -0 670 -0.166 0.142 -0.407 -0 784 -1.129 -1696 -0.595 -0.421 -1709 -2.464 -3 330 -0 255 -1.467 -3.029 -1.914 1989 3.726 2 357 1.575 -15.611 -1.192 12 351 -23 403 -16.728 11578
observed frequency (MHz)
caiculated frequency (MHz)
13832.88 14446 01 13293 53 34529.12 19783-79 33915.94
13832 883 14446 033 13293.492 34529 03 19783.779 33916 005 (20950.788) 20658.167 21644.756 19917.703 (20805.035) (22086.177) 28068 675 27379 682 28812 280 26516 897 27710 676 22169.250 35282 885 35934.781 (348 16.756) (34591.295) 29631 206 (33978 852) 17417.198 (32279.401) (17005.903) 16971 851 21412.145 17428.246 (30057 452) (25552.174) (20150 593) (25849 83 1)
20658.18 21644.68 19917.71
28068 68 27379.73 28812.25 26516 89 27710 69 22169.24 35282.9 1 35934.73
29631.23 17417 14
16971.91 21412 15 17428.22
centrifugal distortion correction (MHz)
b,
-0.225 -0 IS6 0.053 -1.132 0 042 -1075 0 219 -0.706 -0.809 -0 202 0.3 14 -0 656 -0.756 -1517 -2 116 -0 765 -0 374 -2 288 -2 783 -4.227 0.232 -1.697 -4.144 -2.621 2 900 4 067 3919 3.745 -19.145 1.380 16 387 -29.711 -15.020 28 870
a) TransItions not mcluded in the analysis b, The figures m parentheses xe predicted frequenaes.
(i=
Cgl(v’dc - v~,,,~/Nl/2, 1
(2)
3. Conclusion The constants
presented here wdl be helpful in pre-
where vIobs and vlalc are observed and calculated Fre-
dieting the rotational
quencies,
higher rotational
quantum
trifkgal distortion
effect
and N is the number
of transltions
in the analysis. The value of 0 for the C-O state is 40.1
318
kH2.
included torsional
distortion
constants
spectrum
of the molecule
numbers
with
for which the cen-
is large. Since the centrifugal
are directly
related to the force
Table 2 Rotational and centrifugal distortion constants of ethyl fomate Ground state
K a)
C-O
-0.8149
-0 8369
z (MHz)
9985.580
f 0.010
g (MHz)
3839.596
f 0 005
3755 641
f 0011
z (MHz)
3212.869
+0004
3 179.266
f 0.010
10245.938
lo do (MHz)
-0 38676 + 0 00391
-0.51971
dJK (MHz)
-0.26078
-0
dK mx)
-0
104 dWJ
f 0 01029
19072 * 0 01661
0 41726 r 0 02769
0.43575 f 0.12904
calculating
ground state
J1,
excited state
J_~ -JO, J series
I1.0-lo.1
6772 675
7066.617
21,1-lo,2
7444.955
7679.768
8535.877
3 I ~-30,s 4 1,3-40,4
10132 695
5 1.4-50,s
12322 355
12054 885
61,5-60,6
15 158.423
14592 542
8666 357 10098 956
71.6-70.7
18631 234
17726 245
101,9-100,lO
31792.767
30012.681
~ll,lo-llo,lI
36577 823
34650 605
121,11-120.12
41338 497
39339 608
J~,J_~-J~,J_I
series
18482.972
19506 667
17753 691
18812 699
42,2-4x,3
17004 648
18069 094
18538 320
18464.848
112,9-111,lO
23694 014
22528.981
122,10-121.11
27382.573
25605.093
o---21,1
92,7-s
53,
,8
J--J-J2,
[IO]
5-2 senes
33,0-32,1
32097.138
43,1-q2,2
31790 249
33478.598
53,2-52.3
31227.164
33012.469
73,4-72,s
29225.166
31275.303
93,6 --92,7
26581.946
28741.853
103,7-102,s
25441.729
27486.237
113,l3-112,9
24690 877
26465 988
33728.310
, these constants
force-field
constants
help!%1 in
might be [11,12]
.
The constants of table 2 have been used to predict additional Q-branch transitions,J < 12. The groundstate transitions were predicted with the constants obtamed from J < 8 transitions to check how accurateIy these constants can predict transitions up to J= 12. This shows that agreement in the predicted frequencies using J G 12 and J < 8 transition constants is within +-0.3 MHz. This has been done because excited-state transitions have been observed up to J = 8 and the coustants have been used to predict transitions with J < B2_ The predicted frequencies * are in table 3.
Acknowledgement The author
%,I--31.2
22
c 0.08937
40.1
constants
Predtcted frequency (MHz)
3 0.01369
0.17127 f 0.00404
32.7
Table 3 Predicted Q-branch transihons of ethy 1 formate
f 0.049
3 1365 + 0 04664
-0.16993
0.12620 f 0.00111
lo4 dwK U w-w
Traus~hon
torsional state
is grateful
to the Japan Society
for the
of Science (JSPS) and the Council of Scieutic and Industrial Research (CSfR, India) for !Znanciaf assistance, and would like to thank Professor Kojiro Takagi for his support and encouragement during this work. Promotion
* Only tranauons belonging to observed Q-branch series have been predicted.
References [ 11 J.M. Riveros and E-B. Wilson Jr., J. Cbem. Phys_ 46
39 (1963) 469. 319
Volume 70, number 2
CHEMICAL PHYSICS LETTERS
131 E. Hirota. J. Chem. Phys 37 (1962) 283. 141 E. Huota. J. Chem Phys. 37 (1962) 2918. IS] V.K. Kaushlk. Spectrochun. Acta 33A (1977) 463. [6] V.K. Kaushlk. Spectrochlm Acta 35A (1979) 851. [7] J.K.G. Watson. J. Chem Phys. 4.5 (1966) 1360. [Sl V.K Kaushik and P. Venkatcswarlu. Cbem. Phys Letters 48 (1977) I15.
320
1 Much
1980
[9] V-K. Kaushtk and P. Venkateswatlu, J. Mol. Spectry. 70 (1978) 1. [ 101 J E. WoIIrab. Rotational spectra and molecular structure (Academic Press. New York, 1967). [ 11) CA. Coulson and B&l. Deb, Intern. J. Quantum Chem 5 (1971) 411. 1121 A B. Anderson, J. Chem. Phys. 58 (1973) 381.
70, number
2
CENTRIFUGAL
CHEhlICAL
PHYSICS
1 hlarch
LFi-lTEItS
DISTORTION EFFECTS IN THE ROTATIONAL
1980
SPECTRUM OF ETHYL FOE5MAI-E
Vijay Kumar KAUSHIK Department of Physics, Toyama Univemty. and Depamnent
Gofuku, Toyama-930. Japan of Physrcs, Zndum Znstitute of Technology. Kanpw 208016, Znndia
Recerved15 October 1979 The microwave rotational spectrum of ethyl formate has been analysed in the ground vibrational state and an excited vlbratronal state belongmg to the C-O torsional mode of nkatlon. l3e analysis gives effective rotational constants and quark centrifugal distortion constants. The calculated constants have been used to predict additional Q-bmch,J4 12 transihons.
1. Introduction The microwave rotational spectrum of ethyl formate was studied by Rrveros and Wdson [l] who estabhshed the existence of this molecule in two forms, namely gauche and tram forms. It was seen in their study that centrifugal distortion in the gauche form is much larger compared to that in the rrans Isomer. A srmdar feature has been observed in propyl chloride [2], propyl fluonde [3] and butyronitrile [4] , which also have gauche and tram forms. The problem of centrrfugal distortion analysrs of these molecules has recently been solved [5,6] _In the present investigation centrifugal drstortion constants have been calculated for ethyl for-mate in its ground vtbrational state and the u = 1 vrbrational state belonging to the C-O torsional mode of vibration.
2. Analysis of the spectrum Ethyl formate ISa near prolate asymmetric top. The ground-state spectrum consists of 32 transittons, and the C-O torsional mode spectrum consists of 22 rotational transitions. The observed spectrum [l] has been analysed using Watson’s [7] energy expression w= w. - $J2(J -dwJWoJ(J+
+ 1)2 - d&(J I)-dWKWo’PZ2>,
+ l)W;> - dKe) (11
tational constants 2, zand z_ The effective rotational -rvs constants A, B, C contain small centrifugal distortion corrections due to the R, centrifugal distortion term [7] ; dJ, CiJK, dK, dWJ and dwK are Watson’s set of centrifugal distortion constants. The constants obtamed as a result of the analysis are in table 2 and the agreement between calculated and observed frequencies can be seen in table 1. When the ground-state spectrum was subjected to analysis it was found that in spite of the fact that the number of observed lines is more for u = 0 than For u = 1, the standard deviation was much larger for the u = 0 state. This might be caused by experimental error m the frequency measurement or by inappropriate assignment of the observed lines. The spectrum was analysed carefully and a sequential elimination procedure was carried out simrlar to that used for nitric acid [8] and difhroramine [9 1. Each transition was eliminated from the analysis and was predicted through the constants obtained from the remaining transitions. This procedure helped to locate a single badly measured transition, 102,8-101,g; removal of this transition from the analysis reduces the standard deviation of the fit considerably. The quality of the fit was further improved by removing two other transitions, 53,243.1 and 3 2,1 -22,~, from the analysis. Removal of these transitions reduces the standard deviation of the fit from 43.4 kHz to 32.7 kHz. The standkd deviation of the fit is defined as
where W. is the energy of a rigid rotator with the ro317
1 March 1980
CHEMICAL PHYSICS LETTERS
Volume 70, number 2
Table 1 Ground and excited vibrational state transltions of the gauche form of ethyl formate u = 0 state
TransItion
20,2-lo.1
2 I.l--ll,O 2 1,2-11,l 2 2.0-11.1 21,2-lo,1 2 2.1-11,o 32.1-2~.~
a)
?v3-2cp2 1,2-2131
3 1,3-21,2 32.2
-22.1
32,2-31.3
4 2.2-32~ 40.4-30.3 41.3-31,~ 41.4-31.3 42,3-32,2 40.4-31,3 52,3-42,2
,
v=lstate
observed frequency @fHz)
calculated frequency (MHz)
14059.24 1473 148 13478.27 33841.22 19624.22 33 168.90 21337 85 0967.34 22067.24 20189.65 21157.56 21285.30 28614 94 27767 25 29364.08 26870 67 28174 02 22988 95
14059 231 14731.510 13478 235 33841.167
.
50,5-40,4
52,3-51.4 63,3-62.4 62.4-61,s 72,5-71,6 81.7-80.8 82,6_81,7 83.5-82.6
19624.22s
91*f5-go,9 102,8-101,9a)
;;:ti::;
123,g--122,lo
24506
-0 173 -0.147 0.031 -0 696 0.038
33168 969 21337.972 20976.33 1 22067.254 20189.650 21157 538 21285 307 28615 026 27767.250 29364 069 26870.660 28173 984 22988.937 (36004.078) (36604.106) 35440.993 35 159.736 30532.724 34414.446 16404 6 19 30364.441 16124 006 16311.482 22658.585 17085 660 27909 605 27100.981 20733 530 24506 405
35440 85 35 159 78 30532 69 34414.44 16404.61 30364.46 16123.98 1631156 22658 60 17085 64 27909.59
50,5-41*4
centrifugal distortion correction (MHz)
b,
40
-0.64 1 0 048 -0 535 -0 670 -0.166 0.142 -0.407 -0 784 -1.129 -1696 -0.595 -0.421 -1709 -2.464 -3 330 -0 255 -1.467 -3.029 -1.914 1989 3.726 2 357 1.575 -15.611 -1.192 12 351 -23 403 -16.728 11578
observed frequency (MHz)
caiculated frequency (MHz)
13832.88 14446 01 13293 53 34529.12 19783-79 33915.94
13832 883 14446 033 13293.492 34529 03 19783.779 33916 005 (20950.788) 20658.167 21644.756 19917.703 (20805.035) (22086.177) 28068 675 27379 682 28812 280 26516 897 27710 676 22169.250 35282 885 35934.781 (348 16.756) (34591.295) 29631 206 (33978 852) 17417.198 (32279.401) (17005.903) 16971 851 21412.145 17428.246 (30057 452) (25552.174) (20150 593) (25849 83 1)
20658.18 21644.68 19917.71
28068 68 27379.73 28812.25 26516 89 27710 69 22169.24 35282.9 1 35934.73
29631.23 17417 14
16971.91 21412 15 17428.22
centrifugal distortion correction (MHz)
b,
-0.225 -0 IS6 0.053 -1.132 0 042 -1075 0 219 -0.706 -0.809 -0 202 0.3 14 -0 656 -0.756 -1517 -2 116 -0 765 -0 374 -2 288 -2 783 -4.227 0.232 -1.697 -4.144 -2.621 2 900 4 067 3919 3.745 -19.145 1.380 16 387 -29.711 -15.020 28 870
a) TransItions not mcluded in the analysis b, The figures m parentheses xe predicted frequenaes.
(i=
Cgl(v’dc - v~,,,~/Nl/2, 1
(2)
3. Conclusion The constants
presented here wdl be helpful in pre-
where vIobs and vlalc are observed and calculated Fre-
dieting the rotational
quencies,
higher rotational
quantum
trifkgal distortion
effect
and N is the number
of transltions
in the analysis. The value of 0 for the C-O state is 40.1
318
kH2.
included torsional
distortion
constants
spectrum
of the molecule
numbers
with
for which the cen-
is large. Since the centrifugal
are directly
related to the force
Table 2 Rotational and centrifugal distortion constants of ethyl fomate Ground state
K a)
C-O
-0.8149
-0 8369
z (MHz)
9985.580
f 0.010
g (MHz)
3839.596
f 0 005
3755 641
f 0011
z (MHz)
3212.869
+0004
3 179.266
f 0.010
10245.938
lo do (MHz)
-0 38676 + 0 00391
-0.51971
dJK (MHz)
-0.26078
-0
dK mx)
-0
104 dWJ
f 0 01029
19072 * 0 01661
0 41726 r 0 02769
0.43575 f 0.12904
calculating
ground state
J1,
excited state
J_~ -JO, J series
I1.0-lo.1
6772 675
7066.617
21,1-lo,2
7444.955
7679.768
8535.877
3 I ~-30,s 4 1,3-40,4
10132 695
5 1.4-50,s
12322 355
12054 885
61,5-60,6
15 158.423
14592 542
8666 357 10098 956
71.6-70.7
18631 234
17726 245
101,9-100,lO
31792.767
30012.681
~ll,lo-llo,lI
36577 823
34650 605
121,11-120.12
41338 497
39339 608
J~,J_~-J~,J_I
series
18482.972
19506 667
17753 691
18812 699
42,2-4x,3
17004 648
18069 094
18538 320
18464.848
112,9-111,lO
23694 014
22528.981
122,10-121.11
27382.573
25605.093
o---21,1
92,7-s
53,
,8
J--J-J2,
[IO]
5-2 senes
33,0-32,1
32097.138
43,1-q2,2
31790 249
33478.598
53,2-52.3
31227.164
33012.469
73,4-72,s
29225.166
31275.303
93,6 --92,7
26581.946
28741.853
103,7-102,s
25441.729
27486.237
113,l3-112,9
24690 877
26465 988
33728.310
, these constants
force-field
constants
help!%1 in
might be [11,12]
.
The constants of table 2 have been used to predict additional Q-branch transitions,J < 12. The groundstate transitions were predicted with the constants obtamed from J < 8 transitions to check how accurateIy these constants can predict transitions up to J= 12. This shows that agreement in the predicted frequencies using J G 12 and J < 8 transition constants is within +-0.3 MHz. This has been done because excited-state transitions have been observed up to J = 8 and the coustants have been used to predict transitions with J < B2_ The predicted frequencies * are in table 3.
Acknowledgement The author
%,I--31.2
22
c 0.08937
40.1
constants
Predtcted frequency (MHz)
3 0.01369
0.17127 f 0.00404
32.7
Table 3 Predicted Q-branch transihons of ethy 1 formate
f 0.049
3 1365 + 0 04664
-0.16993
0.12620 f 0.00111
lo4 dwK U w-w
Traus~hon
torsional state
is grateful
to the Japan Society
for the
of Science (JSPS) and the Council of Scieutic and Industrial Research (CSfR, India) for !Znanciaf assistance, and would like to thank Professor Kojiro Takagi for his support and encouragement during this work. Promotion
* Only tranauons belonging to observed Q-branch series have been predicted.
References [ 11 J.M. Riveros and E-B. Wilson Jr., J. Cbem. Phys_ 46
39 (1963) 469. 319
Volume 70, number 2
CHEMICAL PHYSICS LETTERS
131 E. Hirota. J. Chem. Phys 37 (1962) 283. 141 E. Huota. J. Chem Phys. 37 (1962) 2918. IS] V.K. Kaushlk. Spectrochun. Acta 33A (1977) 463. [6] V.K. Kaushlk. Spectrochlm Acta 35A (1979) 851. [7] J.K.G. Watson. J. Chem Phys. 4.5 (1966) 1360. [Sl V.K Kaushik and P. Venkatcswarlu. Cbem. Phys Letters 48 (1977) I15.
320
1 Much
1980
[9] V-K. Kaushtk and P. Venkateswatlu, J. Mol. Spectry. 70 (1978) 1. [ 101 J E. WoIIrab. Rotational spectra and molecular structure (Academic Press. New York, 1967). [ 11) CA. Coulson and B&l. Deb, Intern. J. Quantum Chem 5 (1971) 411. 1121 A B. Anderson, J. Chem. Phys. 58 (1973) 381.