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Magnetic susceptibility anisotropy and molecular quadrupole moment of fluoroacetylene
Volume
2, number
CHEMICAL PHYSICS LE:TTERS
8
MAGNETIC MOLECULAR
S’JSCEPTIBILITY
QUADRUPOLE
December I968
ANISOTROPY
MOMENT
OF
AND
FLUOROACETYLENE
*
R L. SHOEMAKER+* and W. H. FLYGARE Noyos Chemical Laboralory. Unic*eusify of Illinois. Uy&ana. Illinois. Received
USA
20 November
1968
The molectilar Zeeman effect has been observed in FC-‘CH under high resolution. The data yield the molecular g-value of gr = -0.0077 t 0.0002 and magnetic susceptibilitv anisotropy of xL - x,, = (0.861 z L 0.018) x 10-29 er,aiG%. The combination of these two results gives the molecular quadrupoIe moment in _, FCSCH of ‘+ = (3.96 5 0.14) x 10-26 esu cm2_
The molecular Zeeman effect in the J = 0 J = 1 rotational transition of FC=CH has been observed in a high magnetic field. Although the molecular Zeeman effect in FC=CH has been observed previously, only a small first order effect was
found
in that work
[l]_
In the present
work
we have been able to observe both first and second-order Zeeman effects. The first-order Zeeman effect provides a determination of the molecular g-value, and the second-order Zeeman effect provides a determination of the magnetic susceptibility anisotropy. The molecular g-value and the magnetic susceptibility anisotropy can then be combined to yield the molecular quadrupole moment in the center-of-mass coordinate system. Fluoroacetylene was syilthesized from fluoromaleic anhydride by the method of Middleton and Sharkey [2/, and used without furtiner purification. The electromagnet and microwave spectrometer
used
* This work was pariially supported b?_the Advanced -’ Research Projects Agency Grant SD-131 to the Ma:;;A%: Research Lzb0rator.v at the University of II-
.
transitions. The field is measured to an accuracy of better thzn 0.2% with a Rawson-Lush type 920
rotating coil gaussmeter which is periodically calibrated with an NMR gaussmeter. The theory of magnetic field interactions in a rotating molecule has been discussed previously 141. Although both the F and H nuclei have a spin of k, the coupling of these spins to the molecular rotation is much smaller than the resolution obtained in these experiments. Thus, the appropriate energy level expression is eq. (28) of ref. 141. For a iinear molecule this expression simplifies to: E(J.E;IJ
= E’(J)
in this work have been described
[3]. Briefly, the microwave spectrograph is a relatively standard high-resolution system with the high microwave frequencies phase stabilized to lower frequency oscillators. The magnet has either a 12 hy 72 inch fiat pole configuration or poles tapered to 2 inches over the full length of 72 inches. Ai%$z= *tl transitions are observed when the magnetic field is perpendicular to the electric field of the microwaves. An Xband cell in a 1.1 inch g&p allows a field of 27 000 hauss to be obtained_ By rotating the X-band elsewhere
_
** Nat&al 6lq.
waveguide by 90°, the magnet gap can be reduced to 0.6 inches and fields up to 30 000 gauss are observed. The magnetic field is now parallel to the electric field of the microwaves leading to 5M=O
Science Foundation predoctoral Fellow.
- lQQ&QJ
-
* 2 3+I(J+l) - bH [ @J-1)(=+3)
3 (x,-&I)*
(I)
EO(J) is the unperturbed rotational energy at zero field. H is the external magnetic field, p. is the nuclear magneton, J and dfJ are the rotational qua&m numbers, gA is the g-value perpendicuIar to the internuclear axis. and x, and 3, are the magnetic susceptibilities perpendicular and parallel to the internuclear axis. This expression neglects
the very small
effects
(symmetric
splittings of each component by less than 1 IrHz) produced by anisotropies in the nuclear magnetic shielding of H or F [4]. Eq. (I) readily yields the rotational frequencies in a.m.agnetic field. For J = 0 -J = 1 transition in FC=CH we obtain, for W_ I 0 selec-.
.-
Volume 2, number 8
CHEMICAL PHYSICS LETTERS
tion rules:
for Q,, for the two possible choices for the sign of g,
(2) The result for hill = 5.1 selection
g, negative:
h is Planck’s constant and z.~ois the zero field frequency. TheJ=OJ = 1 Ad1 = 0 transition in FC=CH was found to be shifted to a higher frequency by 148 rt 3 kHz in a field of 29 250 * 30 gauss. The AN = ll transition is split into a doublet. The splitting was 298 rt 9 kHz in a field of 25455 * rt 60 gauss and the center of the doublet was shifted 58 f 9 kHz lower in frequency than the zero-field result. From this data we obtain, using eqs. (2) and (3): = (0.861~0.018)
x low29 erg/G2
]gL 1 = 0.0077 * 0.0002.
(4) (5)
Since AN = +l and AM = -1 transitions cannot be distinguished in this experiment, only the magnitude of gL is obtained. This value of g1 is in agreement with the previously obtained value of 0.0071 f 0.0004 [l]. The magnetic susceptibility anisotropy is given here for the first time. The molecular quadrupole moment along a taxis is written as [5]
Q zz
=
] e] is the magnitude of the electronic charge, Z,, is the charge of the JIth nucleus, and the sum over JZis over all nuclei. The average in the second term is over the ground electronic state and the sum over i is over all electrons_ A general relation between the components of the molecular quadrupole moment tensor and the components of the molecular g-value and magnetic susceptibility tensors has been derived [6]. For a linear molecule we have:
rijej b9 - x I,) , Qt,=4&i (B, >f 4&(x, fel
Q,, = (3.96&0.14)
x lo-26esucm2 (6)
rules is g1 positive:
(X,-X,,)
December 1968
Q, = -$Q;, . (7)
B, is the rotational constant of the molecule. Mp is the mass of the proton, ~12is the mass of the electron, and c is the velocity.of light. Using the rotational constant of Tyler and Sheridan [7], the values of ]g,] and x,-x,, in eqs. (4) and (5), and eq, (7) gives two possible values
Q, = (7.78 f 0.14) x IO-26esu cm2 (9)
These molecular quadrupole moments are in the center *of-mass coordinate system. it is difficult to choose between these two vaIues for the molecular quadrupole moment. However. the g-value in acetylene (9, = -0.04903 f 0.00004) is known [8] to be negative and we would also expect the g-value in fluoroacetylene to be negative. Furthermore, we have recently measured the ]g i value and molecular quadrupole moment in m
611
Volume
2. number
CHEMICAL
8
PHYSICS
LETTERS
December
with the corresponding values of 3.0 x lo-l6 in IWO [12] and 4.5 x lo-l6 cm2 in OCS [3].
(10) Ushg restilt
+-he known molecular in eq. (8) gives (2
structure
IlO]
axis)
cm2 (11)
The bulk magnetic susceptibilib has not beer? measured in fluoroacetylene. However, it has Jeen estimated and confirmed by molecular orbizd calculations. The best value for (~2) is [ll] +2)
= 37.9 x 10 -16 cm2.
(12)
ilhus, by using eqs. (11) and (12) we have the iniividual components of the second moment of the :hzrge distribution. The results are (z2> = 31.0 x lo-l6
cm2,
3.5 x lo-l6
cm2.
(x2) =
(13)
t is difficult to access the uncertainty in these lumbers but 6-2) should be good to at least 20% nd &z2> should be good e of (r2j = 3.5 X lo-l6
to at least
15%.
cm2 compares
cm2
Founda-
and the
is the internuclear
- {A?> = (27.5 f 0.15j x lo-l6
The support of the National Science tion is gratefully acknowledged.
1968
The
val-
favorably
REFERENCES [l]
V. W. Weiss. H-D. Todd. Mei-Kuo Lo, H. S. Gutowsky and W-H_ Flygare. J. Chem_Phys. 47 (1967) 4021. [2] W. J. Middleton and W. H. Shzrkey. J. Am. Chem. sot. 81 (1959) 803. [31 W. H. Flygare. W. HUttner. R. L. Shoemaker and P. D. Foster. J. Chem. Phys. 49 (1969) to be published. [4] W. Htittner and W. H. Flygare. J. Chem. Phys. 47 (1967) 4137. [5] A. D. Buckingham. Quart. Rev. 13 (1959) 183. [6] W. Hiittner. Mei-Kuo Lo and W. H. Flpgare. J. Chem. Phys. 48 (1968) 1206. [7] T. K. Tyler and J. Sheridan. Trans. Faraday Sot. 5.9 (1963) 2661. [8] J. W. Cederberg. C. H. Anderson and N. F. Ramsey. Phys. Rev. 136 (1964) A960. [9] A. D. Buckingham. R. L. Disch and D.A. Dunmer. J. Am.Chem. Sot. 90 (1968) 3104. [lo) See ref. [7] or fig. 1 of ref. (I]. [ll] See eq. (11) and table 3 of ref. [l]. [IZ] W. H. F&are. R. L. Shoemaker and W. Hbttner. J. Chem. Phys. 50 (1969) to be published.
2, number
CHEMICAL PHYSICS LE:TTERS
8
MAGNETIC MOLECULAR
S’JSCEPTIBILITY
QUADRUPOLE
December I968
ANISOTROPY
MOMENT
OF
AND
FLUOROACETYLENE
*
R L. SHOEMAKER+* and W. H. FLYGARE Noyos Chemical Laboralory. Unic*eusify of Illinois. Uy&ana. Illinois. Received
USA
20 November
1968
The molectilar Zeeman effect has been observed in FC-‘CH under high resolution. The data yield the molecular g-value of gr = -0.0077 t 0.0002 and magnetic susceptibilitv anisotropy of xL - x,, = (0.861 z L 0.018) x 10-29 er,aiG%. The combination of these two results gives the molecular quadrupoIe moment in _, FCSCH of ‘+ = (3.96 5 0.14) x 10-26 esu cm2_
The molecular Zeeman effect in the J = 0 J = 1 rotational transition of FC=CH has been observed in a high magnetic field. Although the molecular Zeeman effect in FC=CH has been observed previously, only a small first order effect was
found
in that work
[l]_
In the present
work
we have been able to observe both first and second-order Zeeman effects. The first-order Zeeman effect provides a determination of the molecular g-value, and the second-order Zeeman effect provides a determination of the magnetic susceptibility anisotropy. The molecular g-value and the magnetic susceptibility anisotropy can then be combined to yield the molecular quadrupole moment in the center-of-mass coordinate system. Fluoroacetylene was syilthesized from fluoromaleic anhydride by the method of Middleton and Sharkey [2/, and used without furtiner purification. The electromagnet and microwave spectrometer
used
* This work was pariially supported b?_the Advanced -’ Research Projects Agency Grant SD-131 to the Ma:;;A%: Research Lzb0rator.v at the University of II-
.
transitions. The field is measured to an accuracy of better thzn 0.2% with a Rawson-Lush type 920
rotating coil gaussmeter which is periodically calibrated with an NMR gaussmeter. The theory of magnetic field interactions in a rotating molecule has been discussed previously 141. Although both the F and H nuclei have a spin of k, the coupling of these spins to the molecular rotation is much smaller than the resolution obtained in these experiments. Thus, the appropriate energy level expression is eq. (28) of ref. 141. For a iinear molecule this expression simplifies to: E(J.E;IJ
= E’(J)
in this work have been described
[3]. Briefly, the microwave spectrograph is a relatively standard high-resolution system with the high microwave frequencies phase stabilized to lower frequency oscillators. The magnet has either a 12 hy 72 inch fiat pole configuration or poles tapered to 2 inches over the full length of 72 inches. Ai%$z= *tl transitions are observed when the magnetic field is perpendicular to the electric field of the microwaves. An Xband cell in a 1.1 inch g&p allows a field of 27 000 hauss to be obtained_ By rotating the X-band elsewhere
_
** Nat&al 6lq.
waveguide by 90°, the magnet gap can be reduced to 0.6 inches and fields up to 30 000 gauss are observed. The magnetic field is now parallel to the electric field of the microwaves leading to 5M=O
Science Foundation predoctoral Fellow.
- lQQ&QJ
-
* 2 3+I(J+l) - bH [ @J-1)(=+3)
3 (x,-&I)*
(I)
EO(J) is the unperturbed rotational energy at zero field. H is the external magnetic field, p. is the nuclear magneton, J and dfJ are the rotational qua&m numbers, gA is the g-value perpendicuIar to the internuclear axis. and x, and 3, are the magnetic susceptibilities perpendicular and parallel to the internuclear axis. This expression neglects
the very small
effects
(symmetric
splittings of each component by less than 1 IrHz) produced by anisotropies in the nuclear magnetic shielding of H or F [4]. Eq. (I) readily yields the rotational frequencies in a.m.agnetic field. For J = 0 -J = 1 transition in FC=CH we obtain, for W_ I 0 selec-.
.-
Volume 2, number 8
CHEMICAL PHYSICS LETTERS
tion rules:
for Q,, for the two possible choices for the sign of g,
(2) The result for hill = 5.1 selection
g, negative:
h is Planck’s constant and z.~ois the zero field frequency. TheJ=OJ = 1 Ad1 = 0 transition in FC=CH was found to be shifted to a higher frequency by 148 rt 3 kHz in a field of 29 250 * 30 gauss. The AN = ll transition is split into a doublet. The splitting was 298 rt 9 kHz in a field of 25455 * rt 60 gauss and the center of the doublet was shifted 58 f 9 kHz lower in frequency than the zero-field result. From this data we obtain, using eqs. (2) and (3): = (0.861~0.018)
x low29 erg/G2
]gL 1 = 0.0077 * 0.0002.
(4) (5)
Since AN = +l and AM = -1 transitions cannot be distinguished in this experiment, only the magnitude of gL is obtained. This value of g1 is in agreement with the previously obtained value of 0.0071 f 0.0004 [l]. The magnetic susceptibility anisotropy is given here for the first time. The molecular quadrupole moment along a taxis is written as [5]
Q zz
=
] e] is the magnitude of the electronic charge, Z,, is the charge of the JIth nucleus, and the sum over JZis over all nuclei. The average in the second term is over the ground electronic state and the sum over i is over all electrons_ A general relation between the components of the molecular quadrupole moment tensor and the components of the molecular g-value and magnetic susceptibility tensors has been derived [6]. For a linear molecule we have:
rijej b9 - x I,) , Qt,=4&i (B, >f 4&(x, fel
Q,, = (3.96&0.14)
x lo-26esucm2 (6)
rules is g1 positive:
(X,-X,,)
December 1968
Q, = -$Q;, . (7)
B, is the rotational constant of the molecule. Mp is the mass of the proton, ~12is the mass of the electron, and c is the velocity.of light. Using the rotational constant of Tyler and Sheridan [7], the values of ]g,] and x,-x,, in eqs. (4) and (5), and eq, (7) gives two possible values
Q, = (7.78 f 0.14) x IO-26esu cm2 (9)
These molecular quadrupole moments are in the center *of-mass coordinate system. it is difficult to choose between these two vaIues for the molecular quadrupole moment. However. the g-value in acetylene (9, = -0.04903 f 0.00004) is known [8] to be negative and we would also expect the g-value in fluoroacetylene to be negative. Furthermore, we have recently measured the ]g i value and molecular quadrupole moment in m
611
Volume
2. number
CHEMICAL
8
PHYSICS
LETTERS
December
with the corresponding values of 3.0 x lo-l6 in IWO [12] and 4.5 x lo-l6 cm2 in OCS [3].
(10) Ushg restilt
+-he known molecular in eq. (8) gives (2
structure
IlO]
axis)
cm2 (11)
The bulk magnetic susceptibilib has not beer? measured in fluoroacetylene. However, it has Jeen estimated and confirmed by molecular orbizd calculations. The best value for (~2) is [ll] +2)
= 37.9 x 10 -16 cm2.
(12)
ilhus, by using eqs. (11) and (12) we have the iniividual components of the second moment of the :hzrge distribution. The results are (z2> = 31.0 x lo-l6
cm2,
3.5 x lo-l6
cm2.
(x2) =
(13)
t is difficult to access the uncertainty in these lumbers but 6-2) should be good to at least 20% nd &z2> should be good e of (r2j = 3.5 X lo-l6
to at least
15%.
cm2 compares
cm2
Founda-
and the
is the internuclear
The support of the National Science tion is gratefully acknowledged.
1968
The
val-
favorably
REFERENCES [l]
V. W. Weiss. H-D. Todd. Mei-Kuo Lo, H. S. Gutowsky and W-H_ Flygare. J. Chem_Phys. 47 (1967) 4021. [2] W. J. Middleton and W. H. Shzrkey. J. Am. Chem. sot. 81 (1959) 803. [31 W. H. Flygare. W. HUttner. R. L. Shoemaker and P. D. Foster. J. Chem. Phys. 49 (1969) to be published. [4] W. Htittner and W. H. Flygare. J. Chem. Phys. 47 (1967) 4137. [5] A. D. Buckingham. Quart. Rev. 13 (1959) 183. [6] W. Hiittner. Mei-Kuo Lo and W. H. Flpgare. J. Chem. Phys. 48 (1968) 1206. [7] T. K. Tyler and J. Sheridan. Trans. Faraday Sot. 5.9 (1963) 2661. [8] J. W. Cederberg. C. H. Anderson and N. F. Ramsey. Phys. Rev. 136 (1964) A960. [9] A. D. Buckingham. R. L. Disch and D.A. Dunmer. J. Am.Chem. Sot. 90 (1968) 3104. [lo) See ref. [7] or fig. 1 of ref. (I]. [ll] See eq. (11) and table 3 of ref. [l]. [IZ] W. H. F&are. R. L. Shoemaker and W. Hbttner. J. Chem. Phys. 50 (1969) to be published.