JOURNU W MOLEtlRAR SPECTROSCOPY 100,303-315 (1983)

Laser Magnetic Resonance of the O2 Molecule at 699 pm'

WATAKA MEUSHIMA dphysics. University of Cdorado. Bouhkr, Cdorodo 80309

K. M. EVENSON, J. A. M u m , AND D. A. JENMNGS Time and F r e p e n q Division. National Burmu of St&& M e r . Cdoraab 80303

AND

J. M. BROWN mri"nl of Chemistry, The University. Sayhamplon. so9 SNH, E n g M

A new highly sensitive far infrared optically pumped laser mrgn*ic ~csonana (LMR) spec- trometer bas facilitated the observation of 21 tnu~sitions in 4 at 699 - (428.6285 GHz). AU of tbcse tnnsitions invdvc N = 3 - 1 oftbe oxygen mdccule in i ts ekctronic ground state, X'Z;. Ofthev 21 L i q 10 ue due to tbe IQ, u = 0; 5 uc due totbe 'Q, n = 1; 5 arc due to the "O%, u = 0, md 1 set of 6 bypcrdae components is due to tbe %"O, u = 0. From the intensity of tbe obvrved lioa tbe sensitivity limit of this LhfR 5pcct"etcr is found to k h u t IO-' an-' at this frequency with a I-rec time constant.

INTRODUCIION

The first gas phase laser magnetic resonance (LMR) spectrum was observed by Evenson er al. (I) on the N = 5 - 3 transition of the oxygen molecule, 16@ (X3Z;, u = 0 ) using the 337-pm HCN laser line. The analysis was later refined by Mizushima m d. (2). Since then, four other rotational transitions of the '"0, molecule have been observed using the LMR technique, namely, the N = 15 - 13 and 23 - 21 transitions using H20 laser lines (J), and N = 17 - 15 and 21 - 19 transitions using D20 laser lines (4). All of these were observed in LMR spectrometers using electrical discharges for excitation. A new LMR spectrometer with optically pumped excitation has permitted the observation of some extremely weak transitions in oxygen at a wavelength of 699 pm (428.6285 GHz). The N -- 3 - 1 transitions of I6O2 and other isotopic species of this molecule are assigned in this paper. The N = 3 - 1 transitions of the I6O2 molecule have been observed by McKnight and Gordy (5) and Steinbach and Gordy (6) in submillimeter absorption spectroscopy. They reported an energy separation between the (N = J = 1) and (N = J = 3) states of 430.984697(60) GHr, which is confirmed by our pnscnt result. In addition to these transitions due to the 1602 molecule in the vibrational ground state (o = 0), we

Supported in pan by NASA Grant W-15,047.

303

observed transitions due to its isotopic Species: 160'70 and both in their natural abundance, 0.074 and 0.408%, rtspactively, and transitions due to in the u = 1 state. Amano and Hirota (7) observed the 6OGHz transitions for dl of these exapt those of I6O1'O; Endo and Mizushima (8) observed 60- and 1 19-GHt transitions of '601, in both u = 0 and 1 states; Steinbach and Gordy (9) observed microwave and submillimeter transitions of %%, and Cazzoli et uf. (10) observed microwave tran- sitions of '6O1'O and ''O"O.

!

4 EXPERIMENTAL DETAILS

A new FIR LMR spectrometer has been constructed in our NBS Boulder laboratory which is about five times more sensitive, allows more lines to lase, and is significantly easier to operate. The new spectrometer is shown in Fa 1. A 38-cm electromagnet with ring-shimmed hyperco pole caps produces a 7.5- homogeneous field region of five times greater length along the laser axis than that of our prtvious spectrometer, thus, it is about five times more sensitive. The new FIR cavity is 25 cm shorter and oscillates to wavelengths up to lo00 pm. Better overlap between pump and FIR laser yields a lower threshold of &ation and, consequently, a larger number of FIR lines. The improved overlap was accomplished with a nearly confocal mirror geometry, the insertion of the CO, pump at the beam waist, and the use of a cylindrical gold- coated py-rex tube as the CO, reflector. This cylindrical tube was found to double the output power in a FIR laser compared with the use of flat side mirrors. A l 0 - m i.d. goldcoated copper tube is used as the fmt cylindrical C Q beam focuser and is then followed by a series of consecutive refoci from the walls of the pyrex tube. Quartz is used for the spacers in the spectrometer to provide better thermal stability. For ease

Fki. 1. The new LMR sparometcr.

of operation, the micrometer, coupler. detector, CO, lascr grating, and gas handling system are all accessible fiom one side of the magnet. The beam splitter is rotatable about the laser axis so that the polaritation can be changed. The magnet controlled by a rotating coil is calibrated periodically with an NMR gaussmeter. The overall fractional uncertainty above 0.1 T is lo-'; below 0.1 T the absolute unceminty is 10-5 T.

ANALYSIS

' 6 0 2 (X'C,-, v = 0)

The theory of the rotational energy levels of the oxygen molecule in its electronic ground state, X32; is well established (11,12). It is found that all existing microwave (7, 8. 12), and submillimeter (5, 6) free field data of 1602 (X'Z;, v = 0) can be reproduced by taking the set of molecular parameters (8) shown in the first column of Table 1.

The EPR spectrum in the microwave region was observed by Baum a al. (13) who obtained value for the g factors of

81 = 2.004838(30), gr = 2.002025(20),

g, = 0.00012q12). (1)

We used these g factors and the molecular parameten in Table I to construct a I5 X 15 Hamiltonian matrix, including N = 1, 3, 5, 7, and 9 states for a given magnetic quantum number M and magnetic field B. The matrix was directly diag- onalized to obtain eigenvalues and eigenvectors. The values of the resonance fields shown in Table 11( 1) are obtained by comparing the differences between the lower and upper eigenvalues (corresponding to N = 1 and N = 3 states) with the laser fi-equency 428.6285 GHz. The rcscttability of the laser line gives the uncertainty of this value, 0.3 MHz.

TABLE 1

Vaiua of the Mdcculnr Rrametcrs UIcd in the CllcuLtion (X'Z; a t e )

~ ~~

1 43.100430 41.8306 40.707408 42.626398

D 1.436. lo-' 1.37. lo-' 1 .29r 10" 1 .489r 10"

A 59.5013489 59.50009 59.499097 59.646079

AD 5 . 8 3 0 5 1 lo-' 5-15. lo-' 5.3121 lo-' 6.325 71 10''

ADD 3.39~10-~' 1-51. 10-l'

T -0.2525875 -0.265114 -0 .238488 -0.253193

TD - 2 . 4 5 2 2 . - 2 . 4 . -6.19~10'~ -2.5241~10-~

A l l v a l u e s a r e i n C l l r

0 I

N 0 . d ”

0

N - m I n m

N O

* -

. c 0 - Y 4 . C . * Y

0 I L 4 .. - -

c 0

0 - a

n I C 0 1

n - c . h I - I - - - . * , !. . . - - L

, n: I O I

11

n l

Y ;I

e N h - - c 1 n n . * * * 0 0 . .

D O

n m - 0 e . - n 0

- n * * I N N I - n D O

n * ~

. .

D O

* N e n N .

0 .

0

c 0 -

o * 0

m i n -

n m 2 O. 0 .

0

0

0 - o * m -

0

. u m - a . o u D O

11

I o

W c c1

c e v

0 e 0

Q c a

I. e W e

* Y

U L Y

LI 0

c 0 4

2 0 c . e c Y

C

0 .

. e 0

Y e

C

b Y

0 I L 4

c

N -

306

* - n 0% I- ? ' N

- 4

- 1 * - o m

0

n n o n - o * 0

N N n c I. c n

0

0 O N N I n - . * 0

0 % -

e - * N m i

0

E. L, -

A

c . 0 0 0

I- - 0 4

0 U P

LMR OF 4 AT 699 rm

Y W 4

Y . 4

Y I

3 Q .- :I P I .

n m e - n n I W ' - "N' . . - 4

m - m - m i o n - n

m o I n n - 0 0 1

0 0

N * N

. .

- =. L,

.: I

N

I 5

0 H

Y . 5

0 U

Y

I

Y I S

Q

307

t l

308 MIzusHlMA ET AL.

c 0

Y d

9 c m . ., - i a

n * 1

I . . - e n

I L c . A 1 I

Y . . Y ., c Y 0

Y c -. r(

0

0

c - eB - U c Y

LI 0

Y c U c 0

0 Y

9 . C

n

* a = I 0 - - 9 . . d e

* Y

c .I-

s x -

o s 0 n o

U u a . a m * - O b

-.

d

L M R O F Q A T 6 9 9 p u 309

Because of the spin-axis coupling (the X tenn in the Hamiltonian), the Nquantum number, corresponding to the total mechanical angular momentum of the molecular frame, is not a good quantum number. Instead of N we (11) can use n to designate each state at zero field. In an external field even this quantum number n (and also N and J) is not a good quantum number. In Table XI we designate each state (upper or lower) by a set of two numbers J and M, wficre M is the magnetic quantum number while J indicates the value of J quantum number when the energy level is extrapolated to the zero field case adiabatically.

The Van Vleck transformation method in which we take a 3 X 3 matrix for each N state taking into account the effect of other N states by means of the second-order perturbation theory, and then diagonalize this small matrix, produces results which deviate from the experiment by as much as 10 MHz; therefore, this approach is not sufficiently accurate. The deviation is due to the small separation between the N = 1 and N = 3 triplets of only 430 GHz compared to the triplet spacing, 60 GHz.

1 I 1 I

0 s 699.4 pm. SP(34)

I

I I I . , ! 0 0.1 0.2 0.3 0.4 C

Bo. tesla 5

FIG. 2. Typical rcalrder uaa of the 699-pm LMR spectrr of oxygen gas. Inset is a d o n of B I Bo cpsc with the v a t i d d e amplified 100 tima showing hfs of W’o and one weak line of ‘Q in 0 = I state.

LMR OF 4 AT 699 31 1

N.1 J.2

.

Nr3 J.4

N = 3 J = i

uL = 428.6285 GHz / n

I I I 1 1 01 0 2 0.3 0.4

B (TI m. 4. Levck md kscr mrgnetic rcsonana for 'W'O ( X ' q 0 = 0.

The relative slope of each resonance line is calculated by diagonalizing the 15 X I5 matrix and is shown in Table Il in T m (10 G/GHz). The slope indicates how the resonance magnetic field shifts when the resonance frequency is increased by 1 THz. For example, we observed a width of 3.3 mT, on the 0.3034-T line, at about 133 Pa (1 Torr). Therefore, from the slope of - 1257 TFHz, we calculate a half-width of 10 -/Pa. The half-width of the N = 3 - 1 line is measured at zero- field (14) to be 12.1( 12) kHz/Pa in reasonable agreement with our result. However, the width of some of the narrower lines are caused by inhomogeneity of the magnetic field, rather than pressure broadening. To calculate the peak intenshy of each line we first calculate the matrix element

of the magnetic moment 2S/h in the transition using the eigenvectors obtained in diagonalizing the 15 X 15 matrix. The square of this matrix element, in units of the

*

FIG. 3. Tbe schematic cnagy kvel dipgnm 10 illustrate tbe magnetic resonance at 699 rm. All the N E 1 levels arc shifted up by the laser fnquency so that 8x1 rppropriatc kvd of N = 1 crossed the comsponding one of N = 3 at the rrsonana field of the tramition. Lev& for '"4, u = 0 (699.4 pm CH,OH; FIR LMR spectrum).

312 MIZUSHIMA ET Al"

Bohr magneton, 13.996106 GHz/T, is labeled SQDP and tabulated in Table 11 for each transition.

If we assume that each line is Larentzian with width parameter A (per Pa), then the absorption coefficient (peak intensity) at the resonance frequency Y (which is the laser frequency in our case) is given by

(2)

where P. is the number of molecules in the a state per unit volume at 1 Pa and pB is the Bohr magneton. This quantity, called the peak intensity, is tabulated in Table I1 in reciprocal centimeters assuming that A is 1 1.3 kHz/Pa (1.5 MHz/Torr) for all lines. We see that we have obscrved all stronger lines and that the weakest line we observed in the one at 0.2417 T with the peak intensity of 1.4 X

Figure 2 shows a typical chart recorder trace and Fig. 3 illustrates the energy levels of the two triplets (N = I and N = 3) as functions of the magnetic field for the I6O2, u = 0, molecule. The energy of the laser has been added to the N = 1 triplet; thus, the crossings corresponding to allowed transitions are the resonances.

a(@) = (~rdhCXp. - PblccWDP/A

cm-'.

w70 (x~z; , v = 0) In addition to the lines due to the ordinary oxygen molecule we have observed a

few &tiom of isotopically substituted oxygen molecules in their natural abundances. We observed the LMR line split into six hyperfine components with spacings of about 1.9 mT at 0.37 1 T with parallel polarization. This is due to the l6OI7O molecule in natural abundance (0.074%). The hyperfine structure is due to the I7O nucleus which has spin I = 5/2. Microwave transitions of this isotopic molecule was observed by caaoli ef al. (IO) in tnriched sample. Tbey report the value of the molecular parameten which we uscd with the g fktors of the '602 to calculate LMR spectrum shown in Table Il(2). The peak intenSity is calculated taking into account the natural abundance.

The peak intensity without hfi is 6.3 X cm-' for each component, which gives the sensitivity limit of the LMR spectrometer.

If we assume that the nuclear spin is completely decoupled by the external field, but that N and J quantum numbers can be assoCiated to the upper and lower states as (N = 3, J = 2) and (N = 1, J = 2), rrspectively, as seen in Fig. 4, then the spacing is given by ((5/6)b + (c/30))M&fJ, where b and c are the hfs coupling constants defined by Frosch and Foley (IS). From the observed spacing 3.82 mT and the calculated relative slope 0.0239 T/GHz of this line, we see that 1(5b/6) + (c/30)1 is 79.6 MHz, in very good agreement with Canoli a al. (IO) who rcported b = - 101.46 MHz and c = 139.68 MHz, which gin the spacing constant to be -79.89 MHz.

cm-', or 1.1 X

W B O (X';s,-, v = 0) Steinbach and Gordy (9) observed microwave transitions of the 160'80 molecule

and obtained the values of the molecular parameters as shown in Table I. We used these values and the g factors of the 1 6 4 molecule, and calculated the LMR spectrum shown in Table II(3). The agreement with five observed lines is quite good.

The natural abundance of this molecule, 0.408%, is multiplied by SQDP in obtaining the peak intensities shown in this table. The weakest line observed at 1.2457 T has the intensity of 5 x 1 0 - ~ cm-'.

.

w 7

LMR OF 4 AT 699 rm

0”

T 7

N

7 I(

* N II 7 7

C

n 7

313

314 MlzuSHIMA ET AL.

In Fw. 4 and 5 the &man energy levels of ’60”O and ‘60’*0, respectively, arr illustrated.

B a h k and Herzbe~ (16) observed vibrationally excited oxygen, and Albritton PI 01. (I 7) reanalyzed their results. Amano and Hirota (7) and Endo and Mizushima (8) observed some microwave lines due to this species and obtained the values of the molecular parameten. We calculated the LMR spec” using the last set of values and these values of the g factors given in (I). The results are shown in Table 11 (4).

The relative population of the u = 1 level is Hven by the Boltzmann factor exp(-€/kT), where € = 1556.2 cm-’. The peak intensities shown in Table Il(4) are calculated for T = 300 K. It is Seen that the line at 0.37964 T is observed within the hfs of ‘60”0 line centered at 0.371 1 T, and the intensity of that line is slightly larger than that of each component of hfs. The calculated peak intensity of this line, 2.0 X cm-’, is M e r than that of each hfs component, 1.1 X lo4 cm-’ in agreement with experiment. On the other hand we did not see a line predicted at 0.22816 T with peak intensity 0.7 X an-’. Therefore the sensitivity limit of this spectrometer is between 1.1 and 0.7 in lo4 c m - I .

The &man energy levels and resonance transitions of this species are shown in

,

Fs 6.

N = l J=2

N = 3 J = 4

N.3 J = i

e

- 1

1 CHz -7

,

I I I I I 0.1 0 2 0.3 0.4

B ( T I FIG. 6. Le& aod laser magnetic manana for ‘Q, (X’Z;) u = I .

Lh4R OF 4 AT 699 315

CONCLUSlON

All of the 21 observed LMR transitions arc nicely 8ssigned in this analysis. The calculation of the peak intensity has provided us With M estimation of the sendtivhy of the spectrometer as between 1.1 and 0.7 in an-’ at a wavelength of 700 pm witb a I-scc time constant. The spectrometer can also be used to measure pressure broadened linewidths.

RECEIVED: April 12, 1983

REFERENCES

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21, IO38-1WO (1968).

( 1972).

(1975).

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13. K. D. BAUER, R. A. KAMRR. AND C. D. L v m , Proc. R. Soe. (London) Ser. A S I , 565-574 (1956). 14. H. M. P l m , E. A. -EN, AND D. E. ~ N Z A , Mrophys. f. 15. R. A. FROSCH AND H. M. Fom. Bys. RN. 88, 1337-1349 (1952).

17. D. L. A L B ~ T O N , W. J. W w . A. L SCHMELTKOFF. AND R N. ZARE, J. Mol. Spafrosc. 46, 103-

Phy~ . Re. 143.31-32 (1966).

L49-L.51 (1981).

16. H. D. hBCOCK AND L. HERZIIERG. M&fl. f. lee, 167-190 (1948).

I I8 ( 1973).