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Magnetic hyperfine structure and centrifugal distortion in quadrupole spectra of 12CH3I and 13CH3I
JOURNAL OF MOLECULAR SPECTROSCOPY 1 I I, 344-35
1 (I 985)
Magnetic Hyperfine Structure and Centrifugal Distortion in Quadrupole Spectra of ‘*CH31 and 13CH31 B. D. OSIPOV’ AND hstilute of spectroscopy,
MICHAEL
N.
GRABOIS
USSR Academy of Sciences, Moscow Region. Troitzk 142092, USSR
state have been Quadrupole spectra of ‘2CH,‘271 and ‘%H, “‘I in the ground vibrational recorded at high resolution (1-2 KHz) using a radiofrequency-microwave double-resonance spectrometer. The magnetic structure of the quadrupole transitions has been resolved and analyzed. Spin-spin and spin-rotation interaction parameters have been determined, together with accurate values of the quadrupole coupling constants and their centrifugal corrections. Comparison with theory is made by using isotopic relations for the two species of iodomethane. Q 1985 Academic Press. Inc. INTRODUCTION
In our previous paper (I), we reported the results of the observation and analysis of the magnetic hyperfme structure in quadrupole transitions of ‘2CH3’271 in the ground vibrational state using a radiofrecfuency-microwave double-resonance spectrometer (2). The resolution obtained with this device, as in the case of molecular beam maser experiments (3) is about 1 KHz, which is the best achieved so far in microwave spectroscopy. It enabled us, in particular, to determine values for eqQo and its centrifugal corrections, xJ, xK, and Xd, which seem to be much more accurate than obtained before (4, 5). Precise determination of these molecular constants is important since, according to recent theory of centrifugal effects in the quadrupole hyperline structure, these constants may be used as additional data for quantum-chemical calculations (6, 7). This paper deals mainly with another isotopic species of methyl iodide, ‘3CH3’271, the molecular hyperfine constants of which little is known. The nonzero spin of the 13C nucleus makes the magnetic structure of the quadrupole spectra of 13CH31 more complex than that of 12CH31, and additional molecular parameters are involved in this case. The analysis of the spectra was simplified by use of the magnetic coupling constants for “CH31 already available (1). On the other hand, the quadrupole parameters for the two species of CH,I could be compared with each other by means of isotopic relations obtained by Aliev (7) which provide an opportunity for checking both the theory and the experiment. For these reasons, the molecular constants for “CH31 are also given in this paper (Table III). The previous unpublished experimental frequencies for 12CH31 are listed in Table I.
’ Deceased. 0022-2852185
$3.00
Copyright Q 1985 by Academic Press. Inc. All rights of reproduction in any form reserved.
344
QUADRUPOLE
SPECTRA
OF CHJ
345
TABLE I Observed
Quadrupole F;
F;
11
3/2
S/2
11
7/2
5/2
J
K
Transitions 3 ohs.
HWHU
179287.0 179290.7 291101.1 mm&.;
2:; :+. 2
2
l/2
3/2
1.5
2
2
3/2
S/2
1.5
2
2
9/2
7/2
1.5
2
2
S/2
7/2
1.5
3
3
3/2
5/2
1.0
3
3
S/2
7/2
1.5
3
3
II/2
9/2
1.5
4 7
3 4
1;;;
4
4
S/2
4
4
4
4
5
4
of 12CH31 Vc-%
-g.;;
301228:O
o:e 0.08 -0.82 0.25
276878.7
-0.01
226595.3 226584.8 226578.7
-0.05 -0.05 -0.05 -0.03 0.01 0.14 -;.A':
1::
wg
444641 .l 444655.3 444664.1 167288.9 pa&.;
1.5 1.5
28W5:2 l/2
1.5
7/2
9/2
1.5
13/2
11/2
1.5
15/2
13/2
1.5
l/2 9/2
912 II/2
1.5 1.5
5
13/2
ll/2
1.5
"7 2
9/2
11/2 II/2
:::
19/2
l7/2
2.0
:: 5
I
6
5
5
5/2
7/2
1.5
4
3
13/2
11/2
2.0
2: Note.
Fraquenciee
are
0:os -0.05
96478.9
-0.15
119779.4
-0.51
given in
KHz.
THEORY
The hyperfine Hamiltonian operator for the iodine nucleus operators:
for 13CH31 is a sum of the quadrupole coupling and of all the spin-rotation and spin-spin interaction
346
OSIPOV
AND
H = HQuad. + H,,_., + HI,“-., + H,,-,,,
+
GRABOIS
H,H--IH--IH
+
HI,-J
+
J&I,
+
f&w
2
( 1)
where J is the rotational angular momentum, Ic and I1 are spins of the carbon and iodine nuclei, and 13” is the total spin of the protons. The first two terms split each rotational level into a number of quadrupole sublevels; the other terms are responsible for the magnetic structure of each quadrupole sublevel. Calculation of the energies was carried out in the representation J + I, = F, F, + IxH= F2 F2 + Ic = F
(2)
Matrix elements of all but the last three terms in Eq. (1) are diagonal in F2 in this representation and may be obtained using Ref. (8), in which the hyperhne structure of NH3 is considered. For this reason, we give here only the matrix elements for interactions of the third spin in Eq. (2) [see, e.g. (9) where the HD170 hyperfine structure is analyzed]: (JF,F~FIH,,_,IJF;F;F’) X [J(J
+
= ~r,_~(- 1)J+h+h~+Ic+2Fi+Fi+Fl+F
1)(2J + I)(& + 1)(2Zc + 1)Zc(2F, + 1)(2F; + 1)(2F2 + 1)(2F; + 1)]“2 x {Z
(JF,F~FIHI,-,,IJF;F;F’) X
(
JF,FzF
= 1%,,lJ(2J
; {(Ic.J)(Iy.J) I
2
-
;}{;
;
:,,){T
;,
JF\}6,,*
111
+ (Iy*J)&.J)}
- (Ic.I,)(J*J)IJF;F;F’
>
,
(3)
where Y stands for 3H or L2 Interaction strengths of the individual terms in Eq. (1) can be written in the form: K2(4K2 - 1) eqQ=eqQ+x&I+ l)+xKK2+xd 3K2 - J(J+ 1) DI,-J
=
CN
D13”_-J= A +
(c, - CN)
+
K2
c ___
1)
J(J+
&
+ B&,1(- 1)
I i&a
K2 DIG_., = Ac + Cc ~ J(J+ 1) G-13,
=D,+D2
1) 2 &,(-l)‘+J+” 1) - 3K
J(J+ J(J+
* Equation (3) is given here only for determination of the constants D,,I, of the operators (IcJ), (1rJ) and (ICI,,) are available in Ref. (9).
and D,,J.
Matrix elements
QUADRUPOLE
&-I,
=
&-~a, =
SPECTRA OF CHJ
347
04
J(J+ 05
+
DJ
J(JS
1)
l)-
3K
2 &J(-l)l+J+”
03 DIH-IH-IH= 4
(4)
where v is the inversion quantum number (U = 0 or I), and where we use accepted notations for spin-rotation constants A, B, and C (L?),which should therefore be distinguished from the rotational constants. These strengths are defined by Eq. (3) and by other expressions for the matrix elements given in Ref. (9). The notations
TABLE II Observed Quadrupole Transitions of “CHJ J
K
F;
F;'
1
1
3/2
5/2
HwMl 1.5
9 obe. vc-vo 292565.3 %:E 292538:5
11
l/2
512
1.5
2
2
l/2
312
1.5
2
2
3/2
5/2
1.5
2
2
9/2
7/2
1.5
5 3 5
2 2 3
Y/2 1:;;
7/2 1;;;
2.0 :.g .
3
3
3/2
5/2
1.0
3
3
5/2
712
1.5
3
3
1112
Y/2
1.25
0.02 -0.07 -0.19
199939.2 216261.7 %:?; 21622616 %CZ 281580:2 z::*6' 226635:0 444770.4 444775.5 :w; 44476219
0.21 -0.19 0.43 -0.05 -0.08 -0.10 -0.03 -0.44 -0.15 0.23
-0.11
:x69.: 288954:6
4810'76.1 481071.4 :x",.: 202970:7 y&.: 264890:5
0.05 -0.08 0.01 0.30 -;A6 -0:06 -0.29 -0.02 -0.13 0.10 0.00 0.51 0.24 -0.27
lbte. Prequencies are given in KHZ.
348
OSIPOV AND GRABOIS
\_ v, KH[AE
444770
444750
FIG. 1. Observed (upper)and calculated (lower) profiles of the J = 3, K = 3, FI = 9/2 transition in 13CHJ. Lorentzian halfwidth, 1.25 KHz.
FL = I l/2
on the right-hand side of Eq. (4) are consistent with Ref. (8) with respect to the iodine and hydrogen nuclei. To obtain the accuracy required, perturbation theory through the fourth order in eqQO has been employed. In the higher-order terms we have used eqQO rather than the expression for eqQ from Eq. (4) valid for the matrix elements diagonal in J. Centrifugal constants DJ and DJK were taken into account for the calculation of rotational energies in denominators of the perturbation terms. Because of the comparable strengths of the proton and carbon magnetic interactions, partial diagonalization of the Hamiltonian was carried out in the subspaces with given Fi and F by solving quadratic secular equations. In the partially TABLE III Molecular ConStantSof ‘*CH$ ref. -Pa.
ref. (4)
(1)
-1934130.22(39)
-1934136
-1.546(22)
$J
$a CR
CK
-1934136(5)
-1.63(22) -38.2(61
-33.61(51)
x.K
ref. (2) -1.409(44) I
-38.1(10)
22.46(11)
22.9(23)
26.21(62)
17.411(86)
l-/.6(10)
17.405(58)
17.202(53)
17.0(46)
19.41(54)
A
-1.33(44)
C
-13.72(12) 0.972(30)
Dl
4.7?8(46)
n3/4
0.279(16)
C2 B
-0.444(13)
a constants the
laet
are digit
in
KHZ.
are
Staadard
shown
in
errOrB
parentheeee.
in
units
of
QUADRUPOLE
SPECTRA
349
OF CHJ
diagonalized basis thus obtained, all magnetic interactions were estimated in the first-order approximation. An exception was made for quadrupole transitions having a level in common with the relatively low-frequency transitions J = 3, K = 3, F, = 912 - 1l/2 and J = 3, K = 1, F, = 912 - 1l/2, for which second-order corrections (with matrix elements off-diagonal in F,) were also taken into account. Theoretical absorption profiles were represented, as usual, by superpositions of Lorentzian lines corresponding to all magnetic components. Relative intensities of the components were obtained by using matrix elements of the dipole moment in the representation chosen (9): (JF,F2FIpIJF’,F;F’) x
J+F;+F,+Fi+F2+F’+I~+l,~iI~il
= (-1)
[(2F + 1)(2F’ + 1)(2F, + 1)(2F’, + 1)(2F, + 1)(2F; + l)]“’
The unnecessary quantum numbers K and u have been omitted here and also in Eq. (3) but it must be noted that for states with K = 1 the intensities obtained by Eq. (5) are divided equally between the II = 1 - 0 and u = 0 - 1 components.
TABLE IV Molecular
Constants
of ‘%JH$
Calculated by least squares fitting AC
0.19(34)
A
-1.266
CC
17.38(53)
B
-0.421
eqQo
-1934232.71(34)
-31.63(24)
%K
$a CN
b
*
32.031
D7
BO
7119053.0(36) 5.78(10)
DJ
91.73125)
DJK
Calculatea
from
constents
for
_
b
-8.519
D5
0.28
4.770 0.618
D4
17.166(21)
CK
0.279
D3/4
16.530(31)
e
-13.787
D2
21.355(97)
-
0.972
Dl C
-1.443(89)
%J
b
Fixed in the least squares calculation
1
1 c
'2CHJ ,
Calculated from structural parametera
' Determined from rotational transitions and used in perturbation expansiane. Difference with the latest data (12) is not essential for this purpose a
In KHz.
One
standard deviation in parentheses.
350
OSIPOV AND GRABOIS TABLE V
Invariants for the Isotopic Substitution of C in CHJ Theoretical
Exper.
eXpl%&Wi0n
(x10-15)
ANALYSIS
‘&I31
9.76(4)
!xJ+fK+2rd 2J/B02
value
‘2cIi31
9.63(6)
27.5(4)
28.4(17)
OF EXPERIMENTAL
DATA
One of the observed quadrupole transitions is shown in Fig. 1. Inside the calculated line contour only the eight most intense components are represented. The total number of magnetic components for this quadrupole transition is 32, and the frequency interval occupied by them is about 240 KHz (for the same transition in 12CH31,there are only nine components in a span of 90 KHz). Under the assumption that isotopic substitution does not change the geometry of the molecule, values of D, ,D2,and D3 for 13CH31may be taken from the data for “CH31. The constants A and C were determined by using invariants (4 + C), (A/&), and (B/Be) also from the constants obtained in Ref. (I). The values of the carbon nucleus spin-spin interaction constants D4,D5, and 0, were obtained by using structural data from Ref. (IO) and formulas from Ref. (8). The remaining two magnetic constants, Ac and Cc, together with six quadrupole and spin-rotation parameters for the iodine nucleus, were obtained by nonlinear TABLE VI
Correlation Matrices for Molecular Constants of “CH31 and 13CH31 A
1
C
-0.993
Dl
-D3/4 D2 B
0.139 -0.015
1 -0.180
1
-0.016
o.z79
‘2CH3I 1
0.065
-0.069
0.056
0.037
1
0.177
-0.180
0.064
0.033
0.932
-0.087
0.075
-0.041
0.028
-0.028
0.039
0.082 -0.183 0.041
-0.071 0.176 -0.024
-0.095 0.108
-0.285
-0.103
-0.144
-0.116
-0.112
0.027 -0.192
1 1 0.034
1
XK
-0.050
0.030
0.140
tJ
-0.015
0.031
CFi
0.031
-0.015
CK
0.047
-0.094
0.210
-0.296
-0.954 -0.046
-0.048
0.215
1 -0.091
-0.066
CC wa0
0.067
0.151
-0.080
-0.022
AC
gd
-0.002
0.047 -0.004
0.349 -0.135
-0.248
1
-0.943
-0.033
0.287 -0.071
0.295
-0.052
0.178
‘3CH31
-0.335
-0.387
1
-0.883
-0.043
-0.150
-0.139
1
-0.381
1
-0.168 0.162
0.348
1 -0.291
0.103 0.056
0.569 -0.366
1 -0.435 0.135
1 -0.636
1
0.031 -0.077
1 -0.335
1
-0.153
-0.464
1
QUADRUPOLE
SPECTRA OF CH,I
351
least-squares fitting. Since the magnetic components are only partially resolved in the present work, the frequencies used were those of the maxima of the absorption profiles. This is similar to what was done in Ref. (11) except that a more effective method for the calculation of the least-squares coefficient matrix was employed by us (I). RESULTS AND DISCUSSION
The 13CH31 frequencies used are shown in Table II, and the constants obtained are given in Table IV, where the values of BO, DJ,and DJKare also given. Since the least-squares estimate u for the rms error of the frequency measurements is sufficiently small with respect to the linewidths, we did not try to improve the values of the parameters fixed in the least squares calculation. In Table V the expressions for the isotopic invariants mentioned in the Introduction are given together with their experimental values. Correlations between the parameters (Table VI) have been taken into account for the calculation of standard errors. Taking into consideration possible deviation from equality within a few percent (7). both isotopic relations are well satisfied. On the other hand, the value of (xJ + xK + 2xJ, which is zero for a diatomic molecule (6), is substantially nonzero in our measurements, a fact which was not evident from the less precise earlier data (4) cited in Ref. (6). This means that the diatomic model of CH31 discussed as an example in Ref. (6) is not valid within the accuracy obtained in the present work. ACKNOWLEDGMENT One of the authors (M.N.G.) thanks Dr. M. R. Aliev for helpful discussion of the manuscript. RECEIVED:
July
19, 1984 REFERENCES
1. B. D. OSIPOV AND M. N. GRABOIS, Opt. Spectrosc., in press. 2. B. D. OSIPOV, Pis’ma JETP 25, 14-17 (1977). 3. A. M. MURRAY AND S. G. KUKOLICH, J. Chem. Phyx 78. 3557-3559 (1983). 4. E. ARIMONDO, P. GLORIEUX. AND T. OKA. Phys. Rev. A 17, 1375-1393 (1978). 5. J. BURIE. D. BOUCHER, D. DANGOISSE, J. DEMAISON. AND A. DUBRULLE, Chem. Phys. 29, 323330 (1978); “Landolt-Bornstein” (K.-H. Hellwege. Ed.). New Series Group II, Vol. 14. Subvol. a. Chap. 2. Springer-Verlag. Berlin. 1982. 6. M. R. ALIEV AND J. T. HOUGEN, J. Mol. Specfrosc. 106, I lo-123 (1984). 7. M. R. ALIEV, private communication. 8. S. G. KUKOLICH. Phy.s. Rev. 156, 83-92 (1967): J. Chem Phys. 57, 869 (1972) (erratum). Y. J. VERHOEVEN, A. DYMANUS. AND H. BLUYSSEN, J. Chem. Phyx 50, 3330-3338 (1969). 10. J. L. DUNCAN AND P. D. MALLINSON, J. Mol. Spectrosc. 39, 471-478 (1971). 11. R. M. CARVEY. F. C. DE LUCIA, AND J. W. CEDERBERG,Mol. Phw. 31, 265-287 (1976). I-7. P. P. DAS, V. MALATHY DEW. AND K. NARAHARI RAO. J. Mol. Spectrosc. 86, 202-208 (1981).
1 (I 985)
Magnetic Hyperfine Structure and Centrifugal Distortion in Quadrupole Spectra of ‘*CH31 and 13CH31 B. D. OSIPOV’ AND hstilute of spectroscopy,
MICHAEL
N.
GRABOIS
USSR Academy of Sciences, Moscow Region. Troitzk 142092, USSR
state have been Quadrupole spectra of ‘2CH,‘271 and ‘%H, “‘I in the ground vibrational recorded at high resolution (1-2 KHz) using a radiofrequency-microwave double-resonance spectrometer. The magnetic structure of the quadrupole transitions has been resolved and analyzed. Spin-spin and spin-rotation interaction parameters have been determined, together with accurate values of the quadrupole coupling constants and their centrifugal corrections. Comparison with theory is made by using isotopic relations for the two species of iodomethane. Q 1985 Academic Press. Inc. INTRODUCTION
In our previous paper (I), we reported the results of the observation and analysis of the magnetic hyperfme structure in quadrupole transitions of ‘2CH3’271 in the ground vibrational state using a radiofrecfuency-microwave double-resonance spectrometer (2). The resolution obtained with this device, as in the case of molecular beam maser experiments (3) is about 1 KHz, which is the best achieved so far in microwave spectroscopy. It enabled us, in particular, to determine values for eqQo and its centrifugal corrections, xJ, xK, and Xd, which seem to be much more accurate than obtained before (4, 5). Precise determination of these molecular constants is important since, according to recent theory of centrifugal effects in the quadrupole hyperline structure, these constants may be used as additional data for quantum-chemical calculations (6, 7). This paper deals mainly with another isotopic species of methyl iodide, ‘3CH3’271, the molecular hyperfine constants of which little is known. The nonzero spin of the 13C nucleus makes the magnetic structure of the quadrupole spectra of 13CH31 more complex than that of 12CH31, and additional molecular parameters are involved in this case. The analysis of the spectra was simplified by use of the magnetic coupling constants for “CH31 already available (1). On the other hand, the quadrupole parameters for the two species of CH,I could be compared with each other by means of isotopic relations obtained by Aliev (7) which provide an opportunity for checking both the theory and the experiment. For these reasons, the molecular constants for “CH31 are also given in this paper (Table III). The previous unpublished experimental frequencies for 12CH31 are listed in Table I.
’ Deceased. 0022-2852185
$3.00
Copyright Q 1985 by Academic Press. Inc. All rights of reproduction in any form reserved.
344
QUADRUPOLE
SPECTRA
OF CHJ
345
TABLE I Observed
Quadrupole F;
F;
11
3/2
S/2
11
7/2
5/2
J
K
Transitions 3 ohs.
HWHU
179287.0 179290.7 291101.1 mm&.;
2:; :+. 2
2
l/2
3/2
1.5
2
2
3/2
S/2
1.5
2
2
9/2
7/2
1.5
2
2
S/2
7/2
1.5
3
3
3/2
5/2
1.0
3
3
S/2
7/2
1.5
3
3
II/2
9/2
1.5
4 7
3 4
1;;;
4
4
S/2
4
4
4
4
5
4
of 12CH31 Vc-%
-g.;;
301228:O
o:e 0.08 -0.82 0.25
276878.7
-0.01
226595.3 226584.8 226578.7
-0.05 -0.05 -0.05 -0.03 0.01 0.14 -;.A':
1::
wg
444641 .l 444655.3 444664.1 167288.9 pa&.;
1.5 1.5
28W5:2 l/2
1.5
7/2
9/2
1.5
13/2
11/2
1.5
15/2
13/2
1.5
l/2 9/2
912 II/2
1.5 1.5
5
13/2
ll/2
1.5
"7 2
9/2
11/2 II/2
:::
19/2
l7/2
2.0
:: 5
I
6
5
5
5/2
7/2
1.5
4
3
13/2
11/2
2.0
2: Note.
Fraquenciee
are
0:os -0.05
96478.9
-0.15
119779.4
-0.51
given in
KHz.
THEORY
The hyperfine Hamiltonian operator for the iodine nucleus operators:
for 13CH31 is a sum of the quadrupole coupling and of all the spin-rotation and spin-spin interaction
346
OSIPOV
AND
H = HQuad. + H,,_., + HI,“-., + H,,-,,,
+
GRABOIS
H,H--IH--IH
+
HI,-J
+
J&I,
+
f&w
2
( 1)
where J is the rotational angular momentum, Ic and I1 are spins of the carbon and iodine nuclei, and 13” is the total spin of the protons. The first two terms split each rotational level into a number of quadrupole sublevels; the other terms are responsible for the magnetic structure of each quadrupole sublevel. Calculation of the energies was carried out in the representation J + I, = F, F, + IxH= F2 F2 + Ic = F
(2)
Matrix elements of all but the last three terms in Eq. (1) are diagonal in F2 in this representation and may be obtained using Ref. (8), in which the hyperhne structure of NH3 is considered. For this reason, we give here only the matrix elements for interactions of the third spin in Eq. (2) [see, e.g. (9) where the HD170 hyperfine structure is analyzed]: (JF,F~FIH,,_,IJF;F;F’) X [J(J
+
= ~r,_~(- 1)J+h+h~+Ic+2Fi+Fi+Fl+F
1)(2J + I)(& + 1)(2Zc + 1)Zc(2F, + 1)(2F; + 1)(2F2 + 1)(2F; + 1)]“2 x {Z
(JF,F~FIHI,-,,IJF;F;F’) X
(
JF,FzF
= 1%,,lJ(2J
; {(Ic.J)(Iy.J) I
2
-
;}{;
;
:,,){T
;,
JF\}6,,*
111
+ (Iy*J)&.J)}
- (Ic.I,)(J*J)IJF;F;F’
>
,
(3)
where Y stands for 3H or L2 Interaction strengths of the individual terms in Eq. (1) can be written in the form: K2(4K2 - 1) eqQ=eqQ+x&I+ l)+xKK2+xd 3K2 - J(J+ 1) DI,-J
=
CN
D13”_-J= A +
(c, - CN)
+
K2
c ___
1)
J(J+
&
+ B&,1(- 1)
I i&a
K2 DIG_., = Ac + Cc ~ J(J+ 1) G-13,
=D,+D2
1) 2 &,(-l)‘+J+” 1) - 3K
J(J+ J(J+
* Equation (3) is given here only for determination of the constants D,,I, of the operators (IcJ), (1rJ) and (ICI,,) are available in Ref. (9).
and D,,J.
Matrix elements
QUADRUPOLE
&-I,
=
&-~a, =
SPECTRA OF CHJ
347
04
J(J+ 05
+
DJ
J(JS
1)
l)-
3K
2 &J(-l)l+J+”
03 DIH-IH-IH= 4
(4)
where v is the inversion quantum number (U = 0 or I), and where we use accepted notations for spin-rotation constants A, B, and C (L?),which should therefore be distinguished from the rotational constants. These strengths are defined by Eq. (3) and by other expressions for the matrix elements given in Ref. (9). The notations
TABLE II Observed Quadrupole Transitions of “CHJ J
K
F;
F;'
1
1
3/2
5/2
HwMl 1.5
9 obe. vc-vo 292565.3 %:E 292538:5
11
l/2
512
1.5
2
2
l/2
312
1.5
2
2
3/2
5/2
1.5
2
2
9/2
7/2
1.5
5 3 5
2 2 3
Y/2 1:;;
7/2 1;;;
2.0 :.g .
3
3
3/2
5/2
1.0
3
3
5/2
712
1.5
3
3
1112
Y/2
1.25
0.02 -0.07 -0.19
199939.2 216261.7 %:?; 21622616 %CZ 281580:2 z::*6' 226635:0 444770.4 444775.5 :w; 44476219
0.21 -0.19 0.43 -0.05 -0.08 -0.10 -0.03 -0.44 -0.15 0.23
-0.11
:x69.: 288954:6
4810'76.1 481071.4 :x",.: 202970:7 y&.: 264890:5
0.05 -0.08 0.01 0.30 -;A6 -0:06 -0.29 -0.02 -0.13 0.10 0.00 0.51 0.24 -0.27
lbte. Prequencies are given in KHZ.
348
OSIPOV AND GRABOIS
\_ v, KH[AE
444770
444750
FIG. 1. Observed (upper)and calculated (lower) profiles of the J = 3, K = 3, FI = 9/2 transition in 13CHJ. Lorentzian halfwidth, 1.25 KHz.
FL = I l/2
on the right-hand side of Eq. (4) are consistent with Ref. (8) with respect to the iodine and hydrogen nuclei. To obtain the accuracy required, perturbation theory through the fourth order in eqQO has been employed. In the higher-order terms we have used eqQO rather than the expression for eqQ from Eq. (4) valid for the matrix elements diagonal in J. Centrifugal constants DJ and DJK were taken into account for the calculation of rotational energies in denominators of the perturbation terms. Because of the comparable strengths of the proton and carbon magnetic interactions, partial diagonalization of the Hamiltonian was carried out in the subspaces with given Fi and F by solving quadratic secular equations. In the partially TABLE III Molecular ConStantSof ‘*CH$ ref. -Pa.
ref. (4)
(1)
-1934130.22(39)
-1934136
-1.546(22)
$J
$a CR
CK
-1934136(5)
-1.63(22) -38.2(61
-33.61(51)
x.K
ref. (2) -1.409(44) I
-38.1(10)
22.46(11)
22.9(23)
26.21(62)
17.411(86)
l-/.6(10)
17.405(58)
17.202(53)
17.0(46)
19.41(54)
A
-1.33(44)
C
-13.72(12) 0.972(30)
Dl
4.7?8(46)
n3/4
0.279(16)
C2 B
-0.444(13)
a constants the
laet
are digit
in
KHZ.
are
Staadard
shown
in
errOrB
parentheeee.
in
units
of
QUADRUPOLE
SPECTRA
349
OF CHJ
diagonalized basis thus obtained, all magnetic interactions were estimated in the first-order approximation. An exception was made for quadrupole transitions having a level in common with the relatively low-frequency transitions J = 3, K = 3, F, = 912 - 1l/2 and J = 3, K = 1, F, = 912 - 1l/2, for which second-order corrections (with matrix elements off-diagonal in F,) were also taken into account. Theoretical absorption profiles were represented, as usual, by superpositions of Lorentzian lines corresponding to all magnetic components. Relative intensities of the components were obtained by using matrix elements of the dipole moment in the representation chosen (9): (JF,F2FIpIJF’,F;F’) x
J+F;+F,+Fi+F2+F’+I~+l,~iI~il
= (-1)
[(2F + 1)(2F’ + 1)(2F, + 1)(2F’, + 1)(2F, + 1)(2F; + l)]“’
The unnecessary quantum numbers K and u have been omitted here and also in Eq. (3) but it must be noted that for states with K = 1 the intensities obtained by Eq. (5) are divided equally between the II = 1 - 0 and u = 0 - 1 components.
TABLE IV Molecular
Constants
of ‘%JH$
Calculated by least squares fitting AC
0.19(34)
A
-1.266
CC
17.38(53)
B
-0.421
eqQo
-1934232.71(34)
-31.63(24)
%K
$a CN
b
*
32.031
D7
BO
7119053.0(36) 5.78(10)
DJ
91.73125)
DJK
Calculatea
from
constents
for
_
b
-8.519
D5
0.28
4.770 0.618
D4
17.166(21)
CK
0.279
D3/4
16.530(31)
e
-13.787
D2
21.355(97)
-
0.972
Dl C
-1.443(89)
%J
b
Fixed in the least squares calculation
1
1 c
'2CHJ ,
Calculated from structural parametera
' Determined from rotational transitions and used in perturbation expansiane. Difference with the latest data (12) is not essential for this purpose a
In KHz.
One
standard deviation in parentheses.
350
OSIPOV AND GRABOIS TABLE V
Invariants for the Isotopic Substitution of C in CHJ Theoretical
Exper.
eXpl%&Wi0n
(x10-15)
ANALYSIS
‘&I31
9.76(4)
!xJ+fK+2rd 2J/B02
value
‘2cIi31
9.63(6)
27.5(4)
28.4(17)
OF EXPERIMENTAL
DATA
One of the observed quadrupole transitions is shown in Fig. 1. Inside the calculated line contour only the eight most intense components are represented. The total number of magnetic components for this quadrupole transition is 32, and the frequency interval occupied by them is about 240 KHz (for the same transition in 12CH31,there are only nine components in a span of 90 KHz). Under the assumption that isotopic substitution does not change the geometry of the molecule, values of D, ,D2,and D3 for 13CH31may be taken from the data for “CH31. The constants A and C were determined by using invariants (4 + C), (A/&), and (B/Be) also from the constants obtained in Ref. (I). The values of the carbon nucleus spin-spin interaction constants D4,D5, and 0, were obtained by using structural data from Ref. (IO) and formulas from Ref. (8). The remaining two magnetic constants, Ac and Cc, together with six quadrupole and spin-rotation parameters for the iodine nucleus, were obtained by nonlinear TABLE VI
Correlation Matrices for Molecular Constants of “CH31 and 13CH31 A
1
C
-0.993
Dl
-D3/4 D2 B
0.139 -0.015
1 -0.180
1
-0.016
o.z79
‘2CH3I 1
0.065
-0.069
0.056
0.037
1
0.177
-0.180
0.064
0.033
0.932
-0.087
0.075
-0.041
0.028
-0.028
0.039
0.082 -0.183 0.041
-0.071 0.176 -0.024
-0.095 0.108
-0.285
-0.103
-0.144
-0.116
-0.112
0.027 -0.192
1 1 0.034
1
XK
-0.050
0.030
0.140
tJ
-0.015
0.031
CFi
0.031
-0.015
CK
0.047
-0.094
0.210
-0.296
-0.954 -0.046
-0.048
0.215
1 -0.091
-0.066
CC wa0
0.067
0.151
-0.080
-0.022
AC
gd
-0.002
0.047 -0.004
0.349 -0.135
-0.248
1
-0.943
-0.033
0.287 -0.071
0.295
-0.052
0.178
‘3CH31
-0.335
-0.387
1
-0.883
-0.043
-0.150
-0.139
1
-0.381
1
-0.168 0.162
0.348
1 -0.291
0.103 0.056
0.569 -0.366
1 -0.435 0.135
1 -0.636
1
0.031 -0.077
1 -0.335
1
-0.153
-0.464
1
QUADRUPOLE
SPECTRA OF CH,I
351
least-squares fitting. Since the magnetic components are only partially resolved in the present work, the frequencies used were those of the maxima of the absorption profiles. This is similar to what was done in Ref. (11) except that a more effective method for the calculation of the least-squares coefficient matrix was employed by us (I). RESULTS AND DISCUSSION
The 13CH31 frequencies used are shown in Table II, and the constants obtained are given in Table IV, where the values of BO, DJ,and DJKare also given. Since the least-squares estimate u for the rms error of the frequency measurements is sufficiently small with respect to the linewidths, we did not try to improve the values of the parameters fixed in the least squares calculation. In Table V the expressions for the isotopic invariants mentioned in the Introduction are given together with their experimental values. Correlations between the parameters (Table VI) have been taken into account for the calculation of standard errors. Taking into consideration possible deviation from equality within a few percent (7). both isotopic relations are well satisfied. On the other hand, the value of (xJ + xK + 2xJ, which is zero for a diatomic molecule (6), is substantially nonzero in our measurements, a fact which was not evident from the less precise earlier data (4) cited in Ref. (6). This means that the diatomic model of CH31 discussed as an example in Ref. (6) is not valid within the accuracy obtained in the present work. ACKNOWLEDGMENT One of the authors (M.N.G.) thanks Dr. M. R. Aliev for helpful discussion of the manuscript. RECEIVED:
July
19, 1984 REFERENCES
1. B. D. OSIPOV AND M. N. GRABOIS, Opt. Spectrosc., in press. 2. B. D. OSIPOV, Pis’ma JETP 25, 14-17 (1977). 3. A. M. MURRAY AND S. G. KUKOLICH, J. Chem. Phyx 78. 3557-3559 (1983). 4. E. ARIMONDO, P. GLORIEUX. AND T. OKA. Phys. Rev. A 17, 1375-1393 (1978). 5. J. BURIE. D. BOUCHER, D. DANGOISSE, J. DEMAISON. AND A. DUBRULLE, Chem. Phys. 29, 323330 (1978); “Landolt-Bornstein” (K.-H. Hellwege. Ed.). New Series Group II, Vol. 14. Subvol. a. Chap. 2. Springer-Verlag. Berlin. 1982. 6. M. R. ALIEV AND J. T. HOUGEN, J. Mol. Specfrosc. 106, I lo-123 (1984). 7. M. R. ALIEV, private communication. 8. S. G. KUKOLICH. Phy.s. Rev. 156, 83-92 (1967): J. Chem Phys. 57, 869 (1972) (erratum). Y. J. VERHOEVEN, A. DYMANUS. AND H. BLUYSSEN, J. Chem. Phyx 50, 3330-3338 (1969). 10. J. L. DUNCAN AND P. D. MALLINSON, J. Mol. Spectrosc. 39, 471-478 (1971). 11. R. M. CARVEY. F. C. DE LUCIA, AND J. W. CEDERBERG,Mol. Phw. 31, 265-287 (1976). I-7. P. P. DAS, V. MALATHY DEW. AND K. NARAHARI RAO. J. Mol. Spectrosc. 86, 202-208 (1981).