zlfexp / JI ' CAL

Rotational Zeeman-Effect of [2,5-D2]-Furan

B . B A K *

Chemical Laboratory V of the University of Copenhagen

E . H A M E R , D . H . S U T T E R , a n d H . D R E I Z L E R

Abt. Chemische Physik im Institut für Physikalische Chemie der Universität Kiel

(Z. Naturforsch. 27 a, 705—707 [1972] ; received 22 January 1972)

The high-field first and second order rotational Zee- man-effect of [2,5-D2]-furan in the ground vibrational state has been investigated to supplement similar ear- lier measurements on furan1. The microwave spec- trum 2' 3 and structure2 of [2,5-D2]-furan are known.

The substance was prepared according to BAK ³ et al.

W e employed a conventional 33.3 kHz Stark-modulated spectrometer equipped with a high-field magnet4. Table 1 gives the measured lines. Zeeman satellites indicated by an asterisk have been omitted in the least squares fit used for the calculation of the jr-values and

the susceptibility anisotropics given in Table 2. From these values together with the bulk magnetic suscep- tibility5 and the structure of the nuclear frame the dia- gonal elements of the diamagnetic, paramagnetic and total magnetic susceptibility tensors igA, %ggv, Xgg) have been calculated (g = a, b, c; all tensor elements are referred to the principal axis system of the inertia tensor). From the g- and ^-tensor elements the values of the diagonal elements of the electric quadrupole tensor of the molecule, Qgg , and the second moments of the electronic charge distribution, ( 0 | 2 g ? | 0 ) ,

e

have been determined. They are included in Table 2.

For details see Ref. The sign of the ^-values given in Table 2 is based on the value of ( 0 | 2 c£ 2| 0 ) ,

E which should be positive. The set of ^-values with re- versed signs would result in a negative value of

<0 | 2 c£2 | 0 ) and was therefore discarded. For com-

e

parison the corresponding values of furan are listed also in Table 2. Since in Ref. 1 E Z « a «2 was errone- Table 1. Observed Zeeman spectrum of [2,5-Da] -furan. Those lines marked by an asterisk were not used in the least square fit.

Rotational Zero Field Magnetic Transition, Frequency Quantum

Magnetic Numbers Field Strength

[kG] [MHz]

Rel. Int. Zeeman-Shifts

zlfexp ^{/ JI ' CAL}

[MHz] [MHz]

Weighted A r^exp — 1 vCAI, Mean

Frequency [MHz] [kHz]

Ooo -> lit

13 319.470

H = 24.38 0 ^ - 1 2 - .165 - .173 8

1 2 .613 .604 9

H = 24.09 0 - > 0 1 - .422 - .422 - 1

2O2 -> 2xi

H = 24.08

2 i 2 22X

H = 22.49

H = 24.08

In -> 220

H - 22.48

H = 24.10

11 756.239

14 243.185

38 395.125

- 2

-1 0 0

2

1 -1 0 1

12

6 2

12

2 3

6

4 3

3.146 .721 1.488

- 3 . 1 1 2 - .891 - .058

.643 1.880 2.007 - 1.088

.908 1.158

3.106 .735 1.553 1.469 - 1 -> - 2 4 - 2.197 - 2.236

—2 - >

-1

^{4 - 1.575 - 1.586}

-1

^{6 - .540 - .537}

-1 ->

1 ->

^{0 0 6 6 j .532* .375 .495}

2 ->

1

^{4 .832* .859}

0 - >

1 ->

²

1

^{4 6 2.288 1.703 2.296 1.669}

—2 - > - 2 4 - 3.286 - 3.255

-1 -> -1 1

^{- .876 - .863}

1 1 1

^{— 1.627}

2 -> 2 4 1.700 1.726 3.128 .834 .091 .626 1.859 2.019 1.096 .940 1.193

.435

- 4 0 14 19 39

11

- 3 97 - 2 7 34

- 8

- 3 1 - 1 3

- 2 6

16 15 33 17

21 12 8

32 35

* Visiting Professor at Kiel University, Summer Semester 1970.

Rotational Zero Field Magnetic Rel. Int. Zeeman-Shifts Weighted A vexp — A Vcal

Transition, Frequency Quantum Mean A vexp — A Vcal

Magnetic Numbers A vexp A ^{f CA L} Frequency

Field Strength Frequency

[kG] [MHz] [MHz] [MHz] [MHz] [kHz]

lll-*2o2

H = 23.70

II = 25.23

loi 2i2 H = 22.42

H =- 25.28

lio -> 22i

2 ² I — > 3i2

H - 2 4 . 1 0

20 886.811

21891.152

31 386.501

3O3 -> 3i2 21 006.938 H = 22.47

36 700.796

1 0 2

- 1 - > 0 2 l - > 2 12 0 - > 1 6

- 1 6

- 1 -> - 2 12 l - > 1 3 0 - > 0 4 - 1 - * - 1 3

- 1.072 - .328 - .184

.116 .236 .824 - .987

.092³¹

}-

1.083 .327 .202 .096

.218

.798 .982 .106 .047 1 - > 0 2 - .850 - .867 - l - > 0 2 - .300 - .337

1 ->

0 - > 2

1 2

6 j - .013* - .064 - .009

( ) - > - 1 6 .100 .110

- 1 -> - 2 12 .735 .705 1 -> 1 3 - .833 - .839

0 4 - .220 - .229

- 1 -> - 1 3 - .103 — .106

.081

.049

- 2

- 3

-1

- 2

-1 0 0 1 1

2 2 3

6 6 10

10

12 12 12 12

10 10 6

6

- 2.795

— 2.610

\ — 1.207*

- .138 .173 .667

• 1.208*

1.403 2.001 2.496

2.782 2.588 1.157

1.218

.130 .186 .676 1.245 1.199 1.439 2.023 2.518

188

1.224

- 1

11 18 20

26

18 - 4 - 1 1

17 37 36 - 1 0

30 6 9 4 H = 22.40 0 - >

-1

^{6 - 1.674 - 1.643 - 3 1}

1 ->

^{0 2 - .915 - .900 - 1 5}

-1 ->

^{- 2 12 - .672 - .652 - 2 0}

0 - >

1 ->

²

1

^{12 6 .550 .892 .554 .896 - 4 - 4}

-1 ->

^{0 2 1.936 1.946} - 1 0

H = 24.10 0 - > 0 4 - .478 - .515 37

1 -> 1

^{3 .114 .141 26}

-1 -> -1

^{3 .819 8.39 20}

- 1 3 - 2 2 - 1 9 -13 - 9 -16 -36

22

22

2 l - > 2

1

^{5 8} J - .574* - .656 - .536

J-

^{.582 12}

0 9 - .198 - .200

J-

^.582

1 -> -1

^{8 .361 .352} 2 ⁹

2 -> - 2 5 1.140 1.121 19

ously taken as (30.20 ± 0.04) IJ instead of (31.31 + 0.01) Ä2, the values which depend on the molecular structure have been appropriately corrected.

Within the experimental uncertainties the magnetic susceptibilities of both furan and [2,5-D²]-furan are equal as may be predicted by theory 6.

From the differences between gx.rH and gXiP and be- tween gZz¹¹ and gzP it is in principle possible to de- termine the sign of the electric dipole moment 7' 8 ac-

cording to the following expression:

(and cycl.). (1) For the present work the z-axis has been chosen per- pendicular to the plane of the ring, while the y-axis coincides with the C²-axis of the molecule. Y and Z are the shifts of the center of mass due to the deutera-

Table 2. ^-values, susceptibilities in 10—6 erg/G2 Mol, structure sums in Ä2, molecular quadrupole moment in 10 — 28 esu cm2, second moment of the charge distribution in Ä2. — The calculated quantities marked by an asterisk differ from those obtained by SUTTER¹ et al., who erroneously used a value of Z^N AN2=30.20 + 0.04 A². For the two isotopic species the A- and 6-axis have changed under deuteration. The uncertainties of the ^-values and susceptibility anisotropics are the

standard deviations.

Furan [2,5-D2]-furan

*7aa = - 0.0911 ± 0.0007 GHB = - 0.07793 ± 0.0004 gbb = - 0.0913 ± 0.0002 sraa = - 0.08875 ± 0.00034 GCC = ± 0.0511 ± 0.0001 G^CC = + 0.04692 ± 0.00029

2 ZN A\ = 3 1 . 3 1 ± 0 . 0 1 * 2 ZNB2N = 3 1 . 3 8 ± 0 . 0 1

f Zⁿb^{2 n} = 32.62 ± 0.03 f a* = 32.61 ± 0.03

IZNCL= 0 2ZNC\= 0

2 Zaa

— Zbb — Xcc

= 43.0 ± 0.2 2

Xbb ~

Zaa —

Xcc =

43.4 ± 0.5 2 Zbb

— Zaa — Xcc =

34.4 ± 0.2 2 £a a — Zbb —

Xcc =

33.5 ± 0.6

t.8 ± 1.5

£(Xaa + + Xcc) = - 44.8 ± 1.5 £(*aa ± ^bb ± Xcc) =

4 = - 1 8 9 . 4 ± 1 . 9 Xbb = - 1 8 9 . 1 ± 1 . 8 Jfbb = - 1 8 7 . 2 ± 1 . 7 *

XL

- - 1 8 7 . 7 ± 1 . 9

= - 3 1 8 . 6 ± 1 . 7 *

xt

= - 3 1 8 . 7 ± 2 . 0 Zaa = 1 5 8 . 9 ± 0 . 3 Zbb = 1 5 8 . 7 ± 0 . 2 Zbb = 1 5 3 . 9 ± 0 . 1 *

xL

= 1 5 4 . 1 ± 0 . 1 zrc = 2 4 8 . 0 ± 0 . 1 * Xcc = 2 4 8 . 3 ± 0 . 3

* a a = - 3 0 . 4 ± 1 . 6

Xbb

= - 3 0 . 3 ± 1 . 7 Xbb = - 3 3 . 3 ± 1 . 6 Zaa = - 3 3 . 6 ± 1 . 7

Xcc

= - 7 0 . 6 ± 1 . 6

Xcc

= - 7 0 . 4 ± 1 . 9

Qaa.

= 0 . 2 ± 0 . 4

Q

bb = - 0 . 2 ± 0 . 5

^ b b = 5 . 9 ± 0 . 3

Qua,

= 6 . 4 ± 0 . 6

Qcc

= - 6 . 1 ± 0 . 4

Qcc

= - 6 . 2 ± 0 . 9

<«

2

>

= 3 7 . 2 8 ± 0 . 6 * <&2> = 3 7 . 3 9 ± 0 . 7

<ft

2

>

= 3 7 . 8 0 ± 0 . 6

<«

²

>

= 3 7 . 7 0 ± 0 . 7

< c2> = 6 . 8 4 ± 0 . 6 < C2> = 6 . 8 5 ± 0 . 7

tion, referred to the principal axis system of the parent molecule. (The positive 2/-axis points from the 0-nucleus towards the center of the molecule: Y = — 0.0233 Ä ; Z = 0.) G^gg are the rotational constants. For the non- deuterated species the values determined by BAK and coworkers 2 have been used, i . e . GXE = BE = 9246.61,

Gyy

R

= A

E

= 9446.96, and G

ZZH

= C

H

= 4670.88 (all

values in M H z ) . The rotational constants for the deu- terated species have been redetermined, using the zero- field transition frequencies given in Table 1. In view of the fact that only transitions with low J values have been measured the rigid rotor approximation has been used for the least squares fit. The following values have been obtained:

G

X3

P = A

D

= 9033.58

4

± 0.014 ,

Gyy° = ßD = 8160.748 ± 0.011 , and G^{2 2 D} = C^D = 4 2 8 5 . 8 5⁴± 0.010 M H z

(the uncertainties given are twice the standard devia-

1 D . H . S U T T E R a n d W . H . F L Y G A R E , J . A m e r . C h e m . S o c . 9 1 , 4 0 6 3 [ 1 9 6 9 ] .

2 B . B A K , D . CHRISTENSEN, W . B . D I X O N , L . H A N S E N - N Y - G A A R D , J . R A S T R U P - A N D E R S E N , a n d M . S C H O T T L Ä N D E R , J . M o l . S p e c t r . 9 , 1 2 4 [ 1 9 6 2 ] .

3 B . B A K , L . H A N S E N , a n d J . R A S T R U P - A N D E R S E N , F a r a d a y S o c . D i s c . 1 9 , 3 0 [ 1 9 5 5 ] .

4 D. H. SUTTER, Z. Naturforsch. 26 a, 1644 [1971].

5 LANDOLT-BÖRNSTEIN, Phys.-Chem. Tabellen, Vol. II, Part 10, Springer-Verlag, Berlin 1951.

tions). Although the differences in the ^-values are comparatively large for the two isotopic species so far measured, it is not possible to determine the sign of the electric dipole moment conclusively [|,M| = (0.661

i 0.006) D from Stark effect measurements⁹], since the change in the ^-values is largely compensated by the change in the rotational constants. If one inserts the appropriate values into Eq. (1) one arrives at ß y — + (2-6 ± 2.3) D (using the equation involving gXx), and f i y = + (0.5 ± 3 . 6 ) D (using the equation in- volving GZZ). This result may indicate that the negative charge associated with the electric dipole moment is at the oxygen side of the molecule. Recently, by an ab initio procedure, PALMER and GASKELL 10 calculated /j, = 0.64 D (negative end at o x y g e n ) .

The support of the Deutsche Forschungsgemeinschaft and the Fonds der Chemie is gratefully acknowledged. The calcu- lations were carried out at the computer center of the Univer- sity of Kiel.

6 J. H. VAN VLECK, The Theory of Electrical and Magnetic Susceptibilities, Oxford University Press 1932, p. 276.

7 C . H . T O W N E S , G . C . DOUSMANIS, R . L . W H I T E , a n d R . F .

SCHWARZ, Faraday Soc. Disc. 19, 56 [1955].

8 M E I - K U L O , V . W . WEISS, a n d W . H . F L Y G A R E , J . C h e m .

Phys. 45, 2447 [1966].

9 M. H. SIRVETS, J. Chem. Phys. 19, 1609 L [1951].

10 M. H. PALMER and A. J. GASKELL, Theor. Chim. Acta 23.

52 [1971].