High resolution microwave studies of the magnetic properties of OCS

Volume 22, number 1

CfIEbIICAL

Harrison

PHYSICS

LETTERS

!S September

HIGH RESOLUTION

MICROWAVE

STUDIES

OF THE MAGNETIC

PROPERTIES

OF OCS*

LOi

TAFT, Pranab BHATTACHARYYA, Nelson SMITH** and BP. DA!LEY of Cher,zisrry, Colrrtnhia Ur~i~wsify. h’crr’ York. IVW York 100_‘7, US.!1

Dcparrrrwrzt

Reccivcd 3 1 >lay 1973 Rcvjscd manuscri$ rzceivcd 25 June 1973

A Hughresolution Zeeman microtvave spectrometer employing a sup?rconducting magncl. superhetcrodyne detcction, and a microwave resonant cavity absorption ccl1 was used to accurately measure :hc rotn!hnal magnetic mament and molecular magnetic susceptibility anisotropy of r60’ZC3ZS. &\f, = -cl Zecman transilions of thcI = 1 - 2 rotational absorption lint were studied, yielding the following rcsulcs: p, = -0.028860 i 0.000037, gl, = -0.026870 J:rom tllcsc data the molecular qundrupolc moment of 2 0.000037, ~x = (-9.363 2 0.016) X 1O-6 emu/molt. ‘60”C3’S has been cvaluarcd as O,, = (-0.773 + 0.023) X 1O-26 esu cm’.

1. tntmduction

In this experiment both the molecular g-factor the molc.cular magnetic susceptibility anisotropy

The magnetic properties of carborlyl sulphide have been studied in the past by various authors [ l-41 using both conventional microwave spectroscopy and molecular beam electric resonance. The molecular beam techniques give very precise results but are difficult and relatively inflexible and it has been found possible to study a much wider variety of molecules using microwave techniques. As part of a program to

OCS hale been evaiuated with considxabk

improve the microwave meihod so that it might produce data of a similar degree of precision as those ob.

no quadrupolar nucleii, the terms of interest are those due to the rotational magnetic moment(p) and the molecular magnetic susceptibility (z)_ The change in

tained using most beam techniques the molecule 16O17X32S has been restudied. OCS is important as a reference and there has been some disagreement among previously published results. The most recent version of the microwave spectrometer used employs superheterodyne detection, two phase-locked klystrons, a microwave resonant cavity as the absorption cell, and for the Zeeman studies, a superconducting magnet.

and of precision.

2. Theory Tile quantum mechanical theory for the magnetic properties of freely rotating 1X molecules IS readill available [j--7]. For ‘60lT3%. a linear rotor with

rotational enerW which OCS experiences when subject to an external magnetic field is therefore:

J(J+ x

[

1) - 3iyr;

(UJ+3)(2J_])

1

- w2

’

(1)

where go is the molecular g value fcr the rotational * This work was suoported in part by mants from the Army Research Office, Department of the-&my and The National Science Foundation. +* Present address: Department of Chemistry, Chflin University, Orangeburg, South Carolina 29115, USA.

state with quantum number J, MJ is the projection of J on the external magnetic field H, p,., is the nuclear magncton, and x,, and x1 are, re:pectiveIy, the components of the molecular magnetic susceptibility 113

Volume 22, number 1 _.. ‘_

tensor, x, in directions to the molecular axis.

15 September

CHEMICAL PHYSICS LETTERS

parallel

to and perpendicular

24325.923

1973

MHz

3. Experiment

For this study, a new microwave spectrometer was designed. Details of its operation and a description of its features will be given elsewhere. However, a few details should be mentioned here, in order to facilitate understanding of the magnetic field determination which is described below. The absorption cell, which is a cylindrical microwave resonant cavity, has a diameter of 2.03 cm and a length which is variable between zero and approsimately 7.5 cm. Due to the inhomogeneity of the magnetic field as described below, it was necessary to restrict the cavity length to approximately 1.3 cm. Under such conditions, the TE, L2 resonant mode is dominant and the J = 1 + 2 OCS microwave transition near 24325 MHz is readily observed.

4. Zeeman

spectra

Since our microwave resonant c?,Jity was designed to operate in the TEI IP mode, where p is a positive integer, the electric vector of the microwave radiation will be perpendicular to the external magnetic field (which is colinear with the axis of the cavity). Therefore, u (AM, = ?I) transitions are expected. The frequency, Y, of a particular line in the Zeeman spectrum of the J= 1 + 2 OCS rotational transition, is, from eq. (1):

++(Ax)H2[lW:

7 lQM, -93

,

(2)

where vo is the frequency of the unsplit line; the subscripts 1 and 2 refer to the lower and upper states, respectively, and Ax = (,Y_,,-x,). From eq. (2) one can deduce that the single J= 1 + 2 rotational line should split into six distinct lines in the presence of a strong external magnetic field. .The intensities of the Zeeman components will be in a ratio given.by (J’ + M; 5 l)(J’ f Mj), where J’ is the larger of,the two values of J, and Mj is the larger .pf the two values of MJ. Thus,.for the J = 1 + 2 OCS

Fig. I. X’hel= 1 - 2 rotational absorption line of ‘60’2C32S at uo = 24 325.923 f 0.001 MHz; the markers are at intervals of 486 l:Hz.

line, the relative intensities of peaks in both the 4M_, = +I and AMJ = -1 branches of the spectrum should be in the ratio 6:s: 1. Fig. I shows the zero-field J = 1 + 2 OCS line, which lrie have redetermined as having v. = 24325.923 f 0.001 MHz. The experimental conditions for the zero-field spectrum were: sample temperature: -40°C; sample pressure: approximately 6 microns. The haIf-width of the line was near 40 kHz. Eight sweeps were recorded. Fig. 2 shows the Zeeman pattern fo: the same transition with a magnetic field of approximately 63 kG; in this case the sample temperarure was -42°C and the sample pressure was 8 microns. The distance between the outermost peaks is greater than 5 MHz which enables one to make a deterrninstion of the peak frequencies to a standard deviation of about 1 kHz. Table 1 shows the frequency of each Zeeman component as well as its shift from the position of the zero-field line. In order to extract the molecular magnetic properties of interest from the spectra, the frequency shifts listed in table 1 were combined with eq. (2) and a ieast-squares analysis was performed, with the following results: p’,Hgl = -1.3778

f 0.001,

MHz,

(3)

p,,Hg2

= -1.37$

f 0.001,

MHz,

(4)

-9.204,

+ 0.004,

MHz .

(5)

(&)Ef2=

The average half-widths of the Zeeman components varieti behveen 60 and 85’kJ+z. This systematic variation of line width with frequency (depending on the

Volume 22, number 1

CH!XICAL

PHYSICS LETT6RS

15 September

1973

Theoretical

---_ 24x9

I 1 40

I I

--__ I-2

I

I

O-1

I-O

-l--z

O--l

Oa:inrr

24923

! zs

!J.y’

Experimental

Fig 2. Theoretically c;llculatad and experimentally observed &?TJ = ?I Zeeman spcctrcl or the/ = 1 - 2 16012C3’S sorption line at a magnetic field strength of ~63 kG; the frequency markers arc at intervals of 486 kHz. Table 1 Frequencies of the Zeeman components for the J = I -J = 2 transition of the ‘60’2C32S molecule (zero-field lint frcquency, IQ = 24 325.923 + 0.001 XlHZ) Transition Iv,-+Mj

Frequency (in hiHz)

Shift in frequency from v, (ir. MHz)

experimental O--I -1

i

-2

1-o O-1 l--L3 -14 0

243X.767-0.001 24324.288?0.001 24326.015rO.OOl ?4326.529+0.001 24 327.043 r 0.001 24328.798+0.002

C3lC.

-2.156~0.001~ -2.167 -1.63540.0014 -1.641 0.122e0.001‘$ 0.112 1.606~0.0014 0.589 1.120+0.001~ 1.116 2.875 f O.OOl, 2.868

values ofM, involved in the transition) can be shown to be due to the inhomogeneity in the magnetic field over the sample volume, since calculation of the expected contributions to line width due to Doppler (I 7 kHz), pressure (4 kHz), wall-collision ( 12 kHz), and modulation broadening (4 kHz), shows that these alone cannot account for the observed line widths. The asymmetric nature of the magnetic field distribution is apparent in non-lorentzian broadening of the individual Zeeman components of fig. 2. It is obvious that some thought must be given as to what value of His to be used in calcuIating the molecular magnetic properties of inte:est.

rotationA

ab-

The mean free path for OCS under the esperimental conditions is about 0.5 1 cm. This is snlall enough SO that a typical molecule will experience a few collisions and therefore a similar number of changes in rotationaL state as it traverses the cavity (diameter = 3.03 cm: length = 1.30 cm) ollce, over a period of time co%sponding to the half-life of the microwave transition being studied. Thus the average value of the magnetic field cannot be used in determining gl , g2., and Ax from eqs. (3), (4), and (5). Moreover, even if the mean free path were much greater than the cavity dimensions (if the sample pressure was much lower, for example). the most probable molecular velocity for OCS (approximately 250 mlsec) under the conditions of the experiment (temperature equal to -12°C) is too small to average out the inhomogeneities iu the magnetic field. In other words, in order to be able to use the average value of the magnetic fie!d in the caiculations, a typical OCS molecule must: (1) remain in the salne rotational state for a length of time equal to the halflife of the observed microwave transition, and (2) experience in that same length of time all possible magnetic field strengths present in the microwave cavity. In the present experiment neither condition is met. Thus one must calculate the most probsbIe value of the magnetic field for the cavity (Hmp): this is the value for which the product of the maIecuIar number 115

Vclumc 22, number

CHEMICAL

1

electric energy density

density times the microwave a ma,Crnum, i.e., E’(z, r, O)r = a maximum

,

PHYSICS

is

(6)

where z is the coordinate alang both the cavity and magnetic field axes (which are coincident) and r and 19are the remaining coordinates for a system of cylindrical symmetry with origin at the axial center of the magnet bore. H, is the value of the magnetic field which correspon z s to the frequency of the center of the spectral

rransition.

For the TEl

coordinates

z = kO.330

cm, r = 0.533

1q mode,

& cm.

U

mp has

15 September

LETTERS

1973

5. Discussion It is noted that the values of gl and g2 above are, within experimental error, identical. This fact can be rationalized by the following argument. The g-tensor can be considered to consist of two parts, an electronic and a nuclear contribution. It is the nuclear term which is most influenced by centrifugal distortional differences between the J = 1 and J = 2 rotational ievels, and hence it is here that we should look for reasons for gl not being equal to g2. For a li~enr molecule the nuclear g term is equal to:

A study of the magnetic field distribution was than made using a Hall-effect gaussmeter manufactured by F.W. Bell, Inc. The magnetic field points were measured to an accuracy of kO.05 kG. As expected, the

magnetic field distribution has cylindrical symmetry; i.e., H(z, f, 0) = H(z,r) for all values of 0. Over the cavity volume the magnetic field inhomogeneity is calculated to be iO.972. The value of the most probable magnetic field, which is the quantity of interest as far as evaluating the molecular magnetic properties of OCS, can be determined much more precisely than the apparent limits imposed by the magnetic field inhomogeneity, by the following method. A least-squares analysis is performed on the experimentally determined data points in the magnetic field distribution and an equation for H in terms of z and r is obtained. A set of magnetic field values is calculated using this equation, for the same points in space as in the experimentally determined magnetic field disrribution. These two sets of points are compared: and when the “fit” is satisfactory, a value of Hmp is calculated. As expected, the maihematical average of the measured field values, 17, is different from Hmp. The inter-

(7)

where Mp is the proton mass, 2, and IV, are the atomic and mass numbers of nucleus k, and )‘k and zk are the coordinates of nucleus k with respect to an origin at the molecular center of mass. Therefore, firs; order correction takes the form:

the

nal calibration of the gaussmeter was checked against a Varian 220 MHz NMR magnet and a deviation of to.14 kG was found. A maximum error of ~0.05 is assigned to H due to uncertainty in the readout the gaussmeter. Thus the most probable value of H = 62.63 * 0.05 kG. When this value of H is st%ted into eqs. (3), (4), and (5), the following are obtained: g1 = -0.028860

f 0.000037

,

g2 = -0.028870

+- 0.000037

,

AX = (-9.363 ,116’. :

due to centrifugal distortion, and the index X-’is added to providk for terms of type (nucleus 1) (nucleus 2). Ag will thus be zero when:

results shows

.. ,.

.:; :

1

that a correction

tog

due to centri-

would be negligible if the ratio of atomic number to mass number is the same for all nucleii in the molecule of interest. This is very nearly true for 16012c% fugal distortion

X 10m6 emu/mole

.:

sub-

where dYk and dzk are small changes in JJX_and zk

Eq. (10)

.. ‘.

,’ :,

f 0.01,)

kG of H is:

Volume 22, number 1

hlasured molecule

Table 2 magnetic and electric properties

of

‘60’2C32S

the

References

gJ=sll

this work [3! [II [41 this work I21

i3j

141 01,b,

-

this work

1973

and diamagnetic

(11) Measured value --

91- Xln)

The x-tensor has both paramagnetic cont;ibutions, xp and xd, such that:

---

Quantiry =g1

15 September

CHEMICAL PHYSICS L&TERS

-0.028860 -0.02R711 -0.02889 -0.028839

c f + +

0.000037 0.000040 0.00002 0.000006

= 0.016 J.35 f 02R -9.27 f 0.10

where the g subscripts indicate a tensor eIement along the gth molecular axis. The xp can be evaluated from a combination of the molecular g-tensor elements and the moiecular framework geometry [8] :

-9.363

-9.37 + 0.01 -0.773

+ 0.023

-2.10 ;:I

-0.88

+ 0.15

141

-0.786

2 0.014

a) In units of 1O+ erg/G2 mole; b) in unirs of 1 O-26 esu cm*.

Table 2 lists the values For g and x as determined by this investigation and by other authors. The highest magnetic field previously used was near 27 kG. Thus, in the present esperjment, the frequency shifts due to x are greater than those obtained earlier by a factor of more than 5. Consequently a significant improvement in accuracy over previous microwave studies have been achieved and the accuracy of the molecular beam work has almost been matched as leasr as far 3s x is concerned. It can be seen that our resulrs support the measurements of Leeuw and Dymanus and of Cederberg et al. Our experimental method is fundamentally different from that of Dymanus et al. and therefore the fact that our results and theirs agree witltin the respective limits of precision argues strongly that no systematic errors are present in either work. On the other hand theg value for 1601’C32S obtained by Flygare et al. differs from that of Dymanus et al. by 0.0003, more than three times Flygare et al.‘s published precision of +0.00004. This suggests the presence of a significant systematic error in Flygare et al.‘s work, perhaps in the measurement of the magnetic field. The value of Ax reported by Flygare et al. overlaps with that reported by Leeuw and Dymanus but with a precision limit approximately six times greater than that reported here. Therefore this work reduces the maximum value of a possible systematic err01 in the work of Dymanus et al. by a factor of six.

XP =f x x

EXPC_ YY

-e2N !!L+_c 4mc2 p

zp

;z ?

k

where e, N, ;?I, and c are respectively the electronic charge, Avogadro’s number, the electronic mass 2nd the speed of light, and J,, is the principal moment of inertia about the axis perpendicular to the molecular axis. Using molecular structural data from Gordy et al. [9], and our value for g1 yields: xy =(+186.392

k 0.002) X 10m6 erg/G’

mole,

(13)

xf = x& is zero for a linear molecule. The bulk magnetic susceptibility of liquid OCS has been determined as [IO] : ~=~(x,,+3-~J=

-32.4X

Thus we can evaluate

low6 erg/G’mole.

(141

xi, and x1:

x,, = -38.7

X IO- 6 ergj/G 2 mole ,

(15)

Xl = -29.3

X 10mh erg/C’

(16)

Further

mole

[4] :

(17)

Volume 22, number

1

CHEWICAL PHYSICS LETTERS

O,, = (-0.773

d = -e’rV Xl 4mc”

(O/C i

q = ercsr= $‘_” = -+o,,

tOiC(Xi’-Z,~)lO)=-41.71

?O.Ol

,

(21)

i

= t55.4,

(72)

i

(01C_Y,? IO) = t4.5 ,

(‘-3)

04)

,

[I ] J.W. Cederburg, C.H. Anderson and N.F. Ramsey, Phys. Rev. 136 (1964) A960. 12] H. Taft and BP. Dailey, J. Chem. Phys. 48 (1968) 597. [3J W.H. Flygnre, W. Hiittner. R.L. Shotmaker and P.D. Foster, J. Chcm. Phys. 50 (1959) 1714. (4 ] F.H. de Lecuw and A. Dymnnus, Chem. Phys. Letters 7 (1970) 288~ [S) J.R. Eshbach and h1.W.P. Strandberg, Phys. Rev. 85 (1952) 24. 16) B.F. Burke nnd M.W.P. Sirandbcrg, Phys. Rev. 90 (1953) 303. 171 IV. Hiittner and W.H. Flygze, J. Chem. Phys. 47 (1967) 4137. [S] W.H. Flygare, J. Chem. Phys. 42 (196.5) 1563. [9] IV. Gordy, W.V. Smith and R.F. Trnmbarulo, hlicrowave spectroscopy (Wloy, New York. 1953; Dover Publications. New York, 1966) pp. 347, 37 1. [IO J Lxrdolt-Bornstein, Zahlcnwertc und Ftmktionen, Vol. 2, part IO (Springer, Berlin, 1951) p. 66.

Thus:

.

13.8

-.

._:

:

,‘.” .,.

‘. ..-

..

”

_‘.’

‘.

.:

:.

:

... .

_,

(27)

References

All in units of lo- t6 cm2. In calculating some of the immediately preceding quantities it is apparent that no limits of error can be associated with them since thej; are derived using the value for jj given in eq. (14), which itself has no listed error limits. Among the most interesting molecular quantities which are calculable as a result of this experiment are the elements of the molecular quadrupole moment tensor, 6:

where G, = h/5n~Ix,,.

(26)

desired.

I

= 46.3

1973

It is apparent from table 2 that this result agrees with that of Leeuw and Dymanus [4], within experimental error, and that the error associated with value of B,, obtained from the present microwave work is much smaller than the earlier microwave experiments. Th: actual value for Bji is different from that of Leeuw and Dymanus (although they are in agreement within error limits) because of a numerical mistake made by those authors and confirmed by them in a private communication. The version of the microwave experiment reported here should be a useful alternative to beam techniques when high precision results are

all in units of 10e6 erg/G:! mole. And:

(01 &?lO, i

+ 0.023) X 10ez6 esu cm2 ,

(,T;+z;)10)

(20)

(01 Q30,

15 September