The microwave spectra of ortho-fluorotoluene with the asymmetric internal rotors CH2D and CD2H

JOURNALOFMOLECULARSPECTROSCOPY

The Microwave

57,‘i-?4 (197.5)

Spectra of Ortho-Fluorotoluene with Internal Rotors CH,D and CD,H

the Asymmetric

D. SCHWOCH AND H. D. RUDOLPH Department

of Chemistry,

University

of Ulm, D 7900-Ulm,

Germany

The rotational spectra of a&- and ord2-ortho-fluorotoluene in the ground state of the methyl group torsion have been measured. The evaluation of the spectra has been based on the theory for the internal rotation of an asymmetric internal top formulated earlier by several authors. The barrier potential being threefold symmetric (Va), each torsional level consists of three nondegenerate substates, designated as sy and fasy. The sy-state is assigned to the conformation with the unique methyl hydrogen isotope within the molecular heavy-atom plane (sy-rotamer), while the fasy-states belong to the respective out-of-plane conformation (asy-rotamer). In the torsional ground state the level spacing between the fasy substates is very small and numerous accidental close degeneracies are present between the rotational level systems based on these torsional substates. The rotational levels involved are strongly perturbed by the coupling between molecular overall rotation and internal rotation. Large deviations from a rigid rotor spectrum and (+) ++ (-) intersystem (“tunneling”) transitions are observed. The spectrum of the asy-rotamer can be well reproduced by a “two-dimensional” 9 of which are determined by a fit to the Hamiltonian containing 11 “rotational constants,” spectrum. Several are sufficiently barrier-dependent to derive T/a. We obtain (in Cal/mole) 567 f 48 for a&-ortho-fluorotoluene, 711 f 40 for the ordr-isotope. The deviations from 649 Cal/mole for the normal isotope are appreciable, probably indicating shortcomings of the semirigid model. The sy-rotamer presents a rigid rotor spectrum.

INTRODUCTION

Molecular rotational spectra are known to show characteristic features when “largeamplitude” internal motions are present in the molecule. The absorption line splittings caused by the torsional-tunneling motion of an internal symmetric methyl top and the barrier data derived therefrom have been the subject of the majority of investigations. However, if both the internal top and the remaining molecular frame are asymmetric the moments of inertia of the molecule for overall rotation will become dependent on the instantaneous angle of internal rotation with an ensuing increase of spectral complexity. The interpretation of the more complicated spectra may on the other hand lead to a more crucial check on barrier dependent parameters and structural features. The theory for molecules with an asymmetric internal rotor has been developed by Quade and Lin (2) ; Meakin, Harris, and Hirota (2) ; and Hirota (3). It will be followed in the present study of the molecules adr- and adz-ortho-fluorotoluene having a partially deuterated methyl group, CHzD and CHD2, respectively. Our starting point was the investigation of the normal species of this molecule by Susskind (4) who found a barrier potential T13= 649 Cal/mole for the internal rotation of the symmetric methyl top. 47

Copyright @ 1975by Academic Press. Inc. All rights of reproduction in any form reserved.

48

SCHWOCH

AND

RUDOLPH

a) high barrier

WY)

(SY) c: low barrier

FIG. 1. (Above), Three possible D-positions in oldi-orthofluorotoluene for methyl top staggered with respect to CF bond. (Below), Splitting pattern of a rotational transition depending on internal rotation barrier potential. (a) High barrier: Rigid rotor spectra for sy-rotamer and asy-rotamer (twice intensity). (b) Intermediate barrier: spectrum of asy-rotamer splits due to interaction of molecular overall rotation and tunneling between equivalent methyl group positions. (c) Low barrier: Tunneling between all three D-positions, sy/asy-designation breaks down, deviations from rigid rotor spectra.

From the molecular conformation (Fig. l), one expects in the limit of a high internal rotation barrier two different rigid rotor spectra for each of the two molecular isotopes. One spectrum originates from the “sy-rotamer” with the unique methyl hydrogen isotope (D for CHzD-, H for CHDz-) within the heavy-atom plane of the molecule, the other spectrum from the “asy-rotamer” with the unique hydrogen outside this plane. The two rotamers have different rotational constants. In the asy-rotamer a tunneling of the unique hydrogen between the two equivalent out-of-plane positions may become noticeable for intermediate barriers and will then cause a splitting of the rotational transitions of the asy-spectrum. For still lower barriers the interconversion between the two different rotamers would have to be taken into account. For a barrier of the order of 650 Cal/mole spectra according to Fig. lb have been expected for both molecular isotopes and could be confirmed by the measurements. MOLECULAR The

semirigid

molecular

model

MODEL for

which

AND

HAMILTONIAN

a reasonable

structure

has

been

assumed

I) consists of two rigid parts, the planar frame represented by the substituted benzene ring and the much lighter partially deuterated methyl top. Both parts have c’lh symmetry with respect to the C-C bond axis about which they can rotate. It has been found practical (I) to adopt a coordinate axis’ system whose origin coincides with the molecular center of mass though it is fixed neither in the top nor in the frame. When top and frame rotate against each other the z-axis always remains parallel to the internal (Table

1Sign convention : z-axis points from center of mass to top. For (Y = 0 : y-axis points away from F-atom for o&-isotope, toward F-atom for &-isotope. x, y, z right-hand system. Directions given required for reproducing entries of Tables IIa and b.

MICROWAVE

SPECTRA

49

OF 0-FLUOROTOLUENE

rotation axis while the y-axis is parallel and the x-axis perpendicular with respect to the planar frame. The internal rotation angle CCis chosen to be zero when the symmetry planes of frame and top coincide. In the following only selected formulas (particularly those not given in the literature) will be presented with the aim of denoting and explaining the various structural quantities for which numerical values have been collected in Tables IIa and b. These values provide illustrative intermediate results and may serve as a check on the extensive computer calculations required to solve this and similar problems. The quantum mechanical energy operator of the semirigid molecule with an asymmetric top has been derived earlier (1, 2).

H = (l/2) C ~i,(+‘d’i -

1

(1,/2ijjC i,j

[g(ol)'~ij(ar)pj(oC)g(~)-i

p(a)-'~j(~)P,(~)g(~)']Pij(HR

+

+

(1)

+ (1/2)g(a)+ F, Pi((y)~ij(Ly)g(~)‘Pj(~)g(oO-i

+

+

V(a)

(1/21,')g(~)l~~,g(a)~~,g(~)-!

HRT)

(HT).

The summation runs over i, .i = x, y, z. The pij(oc) are the elements of the inverse a of a 3-dimensional (modified) inertial tensor I’(a). The elements of I’ have been given in closed form [Z, Eq. (S)] in terms of the known mass geometry of the molecule and at most the second powers of since and/or COW. The pij(oc) are most conveniently calculated by numerical inversion of I’ and expressed as Fourier series which turn out to be rapidly convergent. The Fourier coefficients of the pii calculated from the assumed structure of Table I have been collected in Tables IIa and b. The coefficients not listed have been checked and found to be negligible. g(a) is the determinant 1I’(a) 1= 1p(a) 1-l. The operators Pi are the components of the total angular momentum of the molecule, they are functions of the Eulerian angles which describe the rotation of the xyz-system with respect to space and their conjugate momenta. The components p; are those of the total angular momentum of the methyl top including both the effects of molecular overall and internal rotation. They have been shown to be (2) (pa since + sin@,),

pZ = (Iz’/21,‘). p, = (--1,‘MZ’).

(2)

(pa cow + ~cqa

pz = pa + b/2) (Pmcow + cowa), TABLE

STRUCTURE

BOND

LENGTHS

ASSUMED

FOR

(2):

I

ORTHO-FLUOROTOLUENE

ANGLES

('):

C(ring)

- C(ring)

1.391

HC(meth)H

109.5

C(ring)

- H

1.084

remainder

regular hexagon

C-F

1.348

Cfring)

- C(meth)

1.520

C(meth)

- I1

1.090

50

SCHWOCH

ANDIRUDOLPH

TABLE IIa ad,-ORTHO-FLUOROTOLUENE. INERTIAL AND RELATED QUANTITIES CALCULATED FROM STRUCTURE, TABLE I. Inertial Quantities Related to TOPS cf.(z), Eq.(5) (in amu 8') 1; = I' = 2.731 3(

4,

I’

z = 4.246

0,

n = 0.094 103

Fourier Series for Elements of Inverse Inertial Tensor (in MHz.1

Determinant of Inertial Tensor (in amu 3 X6) g(w) = )1'(oo(2= I&")/ -' = (1.447 16 + 0.002 -

0.009

75.cosu+

...

92.cosq

) - 107

Inverse Inertial Moment for Internal Rotation, Eq.(5) (in MHz) F(q) = 30 713.560 + 283.051.cosu + 67.629 -COS

...

2q+

(in MHz) Pseudopotential (2) Q(W) = 199.239 - 33.137.cosa + 137.2yl.cos 2W+

...

Rotation-Torsion Interaction, Eq.(6)

i x

Y z

q!') 1

q!o) 1

-2

439.778 987.839

-835.318 1585.039 -565.971

q!2) 1 -2.503

4.031 -1 .387

c&3) 1 -1.444

2.661 -0.793

type sin cos

CCS

I,‘, I,‘, and n are numbers [Z, Eq. (S)] to be calculated from the mass I,‘, geometry (seeTables IIa and b) ; I,’ is the reduced moment of inertia for the internal

where

rotation. p, denotes

43/&z.

In writing Eq. (1) use has been made of the fact that the

Pi, while obeying the commutation

relation CPz, P,] = --iP,, commute witha and pa. In the expansion of each of the pij(a) the constant leading term (where nonvanishing)

is very much larger than the a-dependent terms as is evident from Tables IIa and b. The a-independent Hamiltonian RR of an asymmetric rigid rotor may then be separated out of the first term of Eq. (1). HT is the energy operator of a fixed-axis hindered rotator or torsional oscillator, while B RT incorporates the second, Coriolis coupling, term of Eq. (1) as well as the remainder of the first term and represents the interaction between

HR and HT.

51

MICROWAVE SPECTRA OF 0-FLUOROTOLUENE TABLE

IIb

Oid2-ORTHO-FLUOROTOLUENE. QUANTITIESa '_

Inertial (in 1:

2_

amu

Quantities

(in

Series

8,

Ir z =

for

TOPS

5.308 b

Elements

RELATED TABLE

cf. (z),

of

7,

I.

Eq.(.5).

n = -0.074

588

Inertial

Tensor

Inverse

p!!) IJ

p(q) iJ

$3)

1

265.652

7

YY

299.396 2 977.050

6 3

2.5oj -0.001 -0.000

5 8 3

2.278

0

408.702

9

-0.001 0.403

0 5

2

YZ

zx Determinant g(a)

of

= /L'(a)I

Inertial

Tensor

= I@)/

-'

- 0.001

724.c6s2cx

Inverse

Inertial

=

type

1J

xx

zz XY

45

to

Related

AND

STRUCTURE,

MHz)

ij

A

FROM

22)

= I' = 2.706 Y

Fourier

INERTIAL

CALCULATED

-0.486 6 1.980 6 a.795 6 -0.987 5 1.721 7 -0.909 6 (in

amu'

COS COS COS sin COS sin

X6)

34 - 0.003

(1.529

o3*CosP(

+ lo7

+ . ..) Moment

for

Internal

Eq.(5)

Rotation,

(in MHz) = 24 672.785

F(W)

5

Pseudopotential pw

-6.

t

=

a

(2),

121.733

i

q!O) 1

x Y

-409.284

Note

that

Defining

axes

+ 39.764.~~~

Interactionbc

1

$2) 1

-646.149 203.735 431.144

-1.141

equations

.. .

Table

..a

qw1

0.865

-0.162 0.319 0.236

-0.692

y reversed

see

20( +

Eq.(6)

q!') 1

x and

2'Y+

Eq.(6)

+-25.067.~o5O:!~:ZM~;~.~o~

Rotation-Torsion

z -2 977.153

b

- 215.607*cosu

to

those

type sin

COS co?,

of ad,-isotope.

IIa.

Since the deuterium substitution in the methyl top should not affect the charge distribution in the molecule the conventional threefold barrier potential has been assumed also in the present case. V(a) = (V3/2) (1 - cask).

(3)

TORSIONAL EQUATION The torsional equation has been solved first. Since the components ,co.n,tam p,, HT may be written in a more compact form (2). 28T

=

pa2F(a)+

2&F(a)&+

F(+o,2+

p(a)+

1/3(1 -

pi [Eq. (2)] all

COshol).

(4)

52

SCHWOCH

AND

RUDOLPH

,

GHz

10.

+ SY 2.0 CD3

1.8

1.6

1.4 6

1.2

1.0 CHDZ

FIG. 2. Development (mu* hypothetical mass of mass changing hydrogen isotope) of energy sublevels (energies relative to that of lowest sublevel) +sy and fasy of the torsional ground state from the limiting symmetric methyl group to the adjacent ayswmetric case. Left: CH3 + CHzD; right: CD3 + CDzH. F(a)

of the inverse inertial moment for the internal from the pij(ol). For a molecule of the present structure

is one-quarter

calculated

F(a) = Uz’/2~z’hzz( a ) sin% + (ly’/21Z’)z~Uy (CX)cos201+ &.(a) -

(1,‘1,‘/21,‘2)~Z, (a) sina! COW+ (1,‘/21,‘)~,, -

rotation and can be we have obtained (1 + 98cosLy))

(a) sina (1 + n COW)

(IzI’l2IzI)PLyZ(o1)cosa!(I + n coscu) + (l/41*‘).

(5)

F(a) may be expanded in a pure cosine Fourier series (for the coefficients see Table IIa and b). The function p(a) whose lengthy form will not be explicitly reproduced here results from the operation of p, on the various a-dependent terms when going from HT of Eq. (1) to Eq. (4). p(o) has been named “pseudopotential” (2) because its effect is indistinguishable from that of the actual potential V(a). It vanishes for a symmetrical internal top and contributed negligibly2 to the torsional energies in ortho-fluorotoluene as is evident when the magnitudes of the Fourier coefficients of p(a) (Tables IIa and b) are compared with the potential amplitude 713 (of the order 6. lo6 MHz). The torsional energy matrix HT has been set up in the trigonometric basis sinmLy, cosma! (m = 0, 1, 2, . . .) to exploit the symmetry factorization. Elements with m up to 30 were included when numerically diagonalizing the matrix to obtain the lowest few torsional levels. Each torsional energy level v appears to be split into three nondegenerate substates. This is in contrast to the case of a symmetric internal rotor where a torsional state is split into one nondegenerate (A) and one degenerate (E) sublevel. It is illustrative to observe the development of the level triplet (which we designate as + sy, f asy) from the doublet (A, E) for a hypothetical gradual transition from the symmetric to the asymmetric internal top. Figure 2 presents the effects of a hydrogen mass change from a CHz- to a CHzD-top, and from a CDs- to a CD&top for the torsional ground state sublevels of ortho-fluorotoluene. In both cases two of the three sublevels eventually approach to form the f asy doublet of the tunneling oscillator represented 2 However, p(a) does become important when the potential is very much lower than in the present case as, e.g., with a&-para-fluorotoluene (6) (potential 13 Cal/mole) where agreement with the experimental torsional levels could not be achieved unless p(a) was included.

MICROWAVE

SPECTRA

OF O-FLUOROTOLUENE

53

by the asy-rotamer, while the well-separated single + sy-sublevel is to be assigned to the ground state of the sy-rotamer. (Note that in the CHtD case the f asy doublet connects with the A-sublevel and one component of the E-species of the CHa-rotor.) The f asy sublevel energy difference depends strongly on the barrier potential. EFFECTIVE

The rotational

and interaction

ROTATIONAL

OPERATOR [Eq.

part of the Hamiltonian

(l)] may be abbreviated

as ZYZ HR + HRT

=

(1/2)[C

ZYl.

pij(a)Pif'j +

Table

transitions

of

Qi(a)J’i],

i

i,i

Rotational

C

III

ad,-ortho-fluorotoluene,

D-in-plane

(sy-rotamer)

J

K

K+

J'

K' K' +

4

4

exP MHZ

10 648.316

exP - %alc MHZ

-0.055

2

2

1

1

1

3

0

3

2

12

8 630.867

3

1

3

2

12

8 802.249

0.050

3

0

3

2

0

2

9

110.690

o.or7

3

3

2

0

2

9 282.070

0.036

3

2

2

0

17 149.578

3

1 1 1

2

2

11

4

0

4

3

@

3

0

11 599.348

-0.007 -0.006 -0.150

4

1

4

3

0

3

2

3

3

2

2

13

431.651

0

14

847.038

1

3

3

-0.016

3

4

3

0.017

11 289.600 11 649.600

4

0.029

0.069

4

4

1

3

3

0

23

559.816

-0.008

4

4

0

3

3

23

702.592

0.032

19

177.740

0.066

5 6

3

1

2

4

3

1 1

5

5

i

4

19

362.420 389.968

0.026 -0.086

6

3

3

5

3

2

23

6

5

2

5

5

0

21

673.176

0.019

7

6

2

5

21

698.894

-0.006

7

1 6 2 6

6

2

5

21

737.790

-0.000

7

3

6

3

4

23

941.872

-0.006

a)

5

were 'talc rotational Bz2150.948,

calculated constants C=l283.713.

with (in

the MHz)

fitted

rigid

A=3121-553,

rotor

a)

54

SCHWOCH

where the Qi@) result from reducing y, z we have Qi (4 = - (Iz’lI,‘)C sinapi,(+,+ +pcrCOsolccig(~)]=

q&)p,

+

AND

RUDOLPH

the pi(a) [Eq.

(2)] to the operator p,.

p. sincw,b>l+

~is(~>pa+

For i = x,

(~,'I~,I>Ccow~(~)p~

~aPiz(~)l - dc@Wiz(~>~cz+

PaCO~Piz(a)l

paqib).

(6)

Introducing the ~~j(ol), qz(a) may be expressed as a pure sine Fourier series, p,(cu) and qz(cy) as pure cosine series (for the coefficients see Tables IIa and b). In principle, the energy operator Ha + Bar + Hr may then be set up in a product basis #a(Eulerian angles) .&(cx) formed from the known eigenfunctions J/R of the Table

Rotational

of

transitions

IV

&d2-ortho-fluorotoluene,

H-in-plane

(sy-rotamer)

J

KK -

+

J’

X’ -

K’ +

3

exP MHz

3

exP - Jcalca) MHz

2

2

0

1

1

1

11

852.556

2

2

1

1

1

1

10

760.769

3

3

0

2

2

1

17

725.254

0.108

2

2

0

17

349.504

0.108

0.050 -0.061

3

3

3

2

1 1

2

2

0

10

972.020

4

0

4

3

0

3

11

452.044

0.010

4

1

4

3

3

11

285.316

0.015

4

1

3

3

1 1

4

2

2

3

2

4

3

2

3

3

4

3

2

3

4

3

1

4

2

4 4 5

14

046.195

14

902.770

-0.017 0.042

13

741.240

0.067

20

118.555

0.044

2

21

896.850

2

13

065.012

3

1

23

910.984

3

0

23

817.936

-0.029

4

13

957.484

-0.038

3

16

712.008

2

2 1 1 1

3

2

3

3

2

4

0

3

4

1

3

1 1

5

4

0

4

4

3

17

359.962

-0.016

1

18

233.161

-0.027

113.614

5

2

4

4

1 1

5

3

2

4

3

5

-0.038

0.151 -0.001 0.092

0.065

5

3

3

4

3

2

17

5

4

4

4

0

17

408.418

5

4

4

3

2

27

578.504

5

5

1 1 1

0.048

4

4

0

30

186.134

-0.131

5

5

0

4

4

1

30

205.447

-0.055

5

4

2

5

3

3

10

328.304

-0.152

6

5

1

5

4

2

33

692.696

-0.056

-0.300 0.067

MICROWAVE

SPECTRA Table

J

IV

contiimed

J' K! K' +

K_ K+

J exp MHz

6

5

2

6 6

4 4

3 2

6

6

5 2

2 4

6

2

5

6 6 6 6 6

2 5 3 3 15 0 6 2 4

6 6 7 7 8

3 4 5 6 6

4 3 3 2

8

6

9

7

2

12

8

3 2 4

12

9

3

a)

5 5 5

5 4 4

1 2 1

5

4

1

5 5 5

2 3 14 2 4

5 5

3 2 14

5 6 6 6 7

15 15 2 5 3 4 4 4

7 8 8

5 5 5

3 3 4

9 12 12

6 7 8

3 5 4

5.5

OF O-FLUOROTOLUENE

3

exP-%alc MHZ

747.000

0.312

20 837.763 21 304.984

-0.039

33 524.158 21 777.654

-0.078

19 376.540 18 728.548

-0.042

355.256

0.176

20

22

19 123.880 16 415.851 y 012.200 11 082.504 10

837.592

12 878.038

0.083

0.056

0.001 -0.004 0.001 0.154 0.158 -0.021 -0.131

15 594.400

-0.399

14 790.795

-0.239

15 415.984

-0.277

18

-0.478

026.346 19 817.780 23 676.720

were calculated with the fitted rigid 'Jcalc rotational constants (in MHz) ~~3164.644,

a)

-0.928 -1.268

rotor

Bz2059.581, G1266.899.

rotational problem (conventionally the symmetric rotor wavefunctions SRR) and the torsional eigenfunctions $r just determined. However, as opposed to the torsional energy matrix &, the total energy matrix EZ, whose rank is (2J f 1) times as high, can no longer be directly diagonalized due to limited computer storage and a perturbation technique had to be used. First we compute the required torsional matrix elements of ~;j(cu) and Q~(cY),which are readily expressed only in the trigonometric basis sinnuu, cosnacr. With the aid of the transformation matrices stored away when solving the torsional problem, we find (Y’I&&) 1ZJ)and (0’ 1Q;(a) 1v), where each v divides into the fsy, fasy substates. Then a Van Vleck perturbation procedure is applied (3) which gives an “effective” rotational operator for a particular torsional state, e.g., the ground state. Whenever the fasy torsional ground state level doublet is nearly degenerate, the Van Vleck transformation must be aimed at the pair of levels simultaneously giving an effective rotational operator which is “two-dimensional” in appearance. We have, in agreement with the earlier treatment by Hirota (3), neglected all terms of higher than second order in the angular momentum components Pi.After a rotation xyz ---) xy’z’

SCHWOCH AND RUDOLPH

56

TABLE ROTATIONAL FROM

V

CONSTANTS ARR-FIT (in

OF TO

MHz)

Qd2-ortho-

Qd,-orthoFluorotoluene

Fluorotoluene

D-in-plane

H-in-plane

A

3 121.553

B

2

c

1 283.713

a

twice

SY-HOTAMERS

SPECTRA

150.948

fitting

O.Ola

3 164.644

+ 0.008

+ 0.006

2 059.581

+ 0.01

0.006

1 266.899

+ 0.01

+

+

errcars

of the axis system to eliminate P,P, + P,P, cross terms in each of the “diagonal blocks” of the effective fasy Hamiltonian, and upon the identification (xy’z’) = (&a), we obtain3

A+paz2+B+pa2+c+p,z H#ff

(v=O, +asy)=

R,,(P,Pc+PJ’,)+i&.P, +Rbc(PbPc+PcPb)+i&bPb

As,z+B_Pb2+C_p,z+Av,,,

1 I

.

(7)

Prior to the axis rotation all “rotational constants,” except the Q’S, consist of the torsional matrix elements of the respective Gus with contributions from Van Vleck perturbation sums in the Q;(a) added. The Q are simply the respective (v, asy+ 1Q;(a) 1ZJ,asy -) matrix elements. Explicit formulas have been given by Hirota (3). The rotational quantities depend on the barrier potential V3 which affects the torsional wavefunctions and hence the matrix elements. The effective rotational operator for the nondegenerate sy-substate is “one-dimensional” and, after a similar axis rotation, that of a rigid rotor. HReff(v, sy) = APa + BPb2 + CP?.

(8)

The eigenvalues of Eqs. (7) and (8) were evaluated in the SRR basis. The energy level arrangement generated by the fasy Hamiltonian [Eq. (7)j is approximated by the superposition of the eigenvalue systems of two slightly different asymmetric rigid 3Sign of &., &b reversed to that of (3).

MICROWAVE

SPECTRA

OF 0-FLUOROTOLUENE

57

rotors, the second system being displaced with respect to the first by the amount Avblb = Eaey_ - Easy+ of the torsional ground state. However, the two systems are coupled by the off-diagonal block with ensuing deviations from true rigid rotor level systems. Wherever this perturbation is sufficiently small, rotational transitions of significant intensity will occur only within each level system and the spectrum will consist of doublet lines which still roughly follow a rigid rotor pattern. When the coupling is strong, however, irregularly wide doublet splittings as well as intersystem (i.e., “tunneling”) transitions may be observed. Both cases are represented in the spectra measured. Table

Rotational

transitions

of

D-out-of-plane

J

K_ K+

J’ KI K:

J

VI

c&l-ortho-fluorotoluene, (asy-rotamer)

a) exP

MHZ

3

exP

-3

talc MHz

b)

+doublet exP MHZ

splitting CZllC MHZ

12 053.11 12 051.29

0.38 0.26

-1.82

-1.70

10 901.y7 10 900.43

0.18 0.28

-1.54

-1.65

0.36

0.36

-0.90

-0.84

-0.17 -0.16

-0.48

-0.49

11 300.10 11 292.36

-0.08 0.02

-7.74

-7.82

1

l3 479.58 13 473.42

0.16 0.25

-6.16

-6.25

0

3

11 739.00 11 738.28

0.09 -0.04

-0.72

-0.59

3

1

2

14 14

359.20 358.23

0.08 0.13

-0.98

-1.03

2

3

3

1

14 103.90 14 106.00

-0.10 0.03

2.10

1.97

3

1

3

3

0

14 561.85 14 564.25

-0.29 -0.14

2.40

2.25

5

4

2

5

3

3

lo 316.93 10 328.48

0.49 0.51

11.55

11.53

5

3

3

5

2

4

9 624.90 9 617.70

0.26 0.31

-7.20

-7.25

0.46 0.73

11.16

10.90

2

2

0

1

2

2

1

110

3

0

3

2

1

2

8 575.35 8 575.71

3

1

3

2

0

2

9 388.75 9 387.85

3

1

2

2

1

1

11 204.52 11 204.04

3

2

1

2

2

0

3

2

2

2

1

4

1

4

3

4

1

3

4

3

4

5

4

2-5 5

5

1

1

-0.12 -0.11 0.07 0.01

1

5

3

2

8 682.72 8 693.88

1

5

4

2

12 838.38 12 839.03

0.46 0.50

0.65

0.61

0

5

4

1

12 681.79 12 682.38

0.43 0.59

0.59

0.43

58

SCHWOCH AND RUDOLPH Table

J

K

K+

J'

K' K' +

9

VI

continued

exP MHZ

MHZ

-0.04 -0.00

+doublet exP MHz

splitting CdC

MHZ

5

4

2

4

4

1

17 757.60 17 756.88

6

4

3

6

3

4

10 895.09 10 914.67

0.32

6

5

2

6

4

3

12 752.51 12 742.37

0.63 0.47

-10.14

-9.98

6

5

1

6

4

2

12 099.00 12 088.34

0.59 0.55

-10.66

-10.62

6

6

1

6

5

2

15 683.92 15 684.88

0.61 0.58

0.96

0.9v

6

6

o

6

5

1

15 645.36 15 646.32

0.68 0.72

0.96

0.92

0.71

-0.72

-0.76

19.58

19.19

6

0

6

5

1

5

16 726.73 16 726.73

-0.33 -0.08

C)

-0.26

6

I

6

5

o

5

16 755.29 l6 755.29

0.05 0.3s

C)

-0.33

6

4

6

4

3 2

5 5

4 4

2

21 21

399.32 408.78

-0.10 -0.08

9.46

9.43

1

21 21

931.94 941.84

0.05 -0.01

9.90

9.96

21 21

313.52 312.20

0.13 -0.04

-1.32

-1.14

-0.99

-1.17

-a.52

-a.72

6

5

2

5

5

1

7

3

4

7

2

5

a 005.74 8 004.75

-0.02 0.16

7

4

4

7

3

5

11 957.52 11 949.00

0.36

7

5

3

7

4

4

12 844.16 12 862.49

0.50 0.72

16.33

18.11

7

5

2

7

4

3

10 989.48

006.40

0.49 0.55

16.92

16.86

7

6

2

7

5

3

15 486.24 15 486.72

0.48 0.50

0.48

0.46

7

6

1

7

5

2

15 279.92 15 279.92

0.69 0.55

C)

0.14

II

COMPUTER

0.16

PROGRAMS

A computer program was written, the first part of which computes from an assumed structure the Fourier series of the inertial quantities, solves the torsional problem for a prescribed Va, and calculates, for the torsional ground and first excited states, the rotational quantities that appear in the effective Hamiltonian [Eq. (7)]. The second part calculates the rotational spectrum for J up to 20 generated by this Hamiltonian, inclusive of intensities. It also determines by a least-squares fit to the experimental frequencies those values of the rotational quantities of Eq. (7) that best reproduce the spectrum. The comparison of the fitted values with those calculated by the first part of the program for a range of assumed VZ eventually yielded the actual barrier potential amplitude of orthofluorotoluene.

MICROWAVE

Table

J

7

K

6

K+

1

863

J' I?_ K:

6

6

0

VI continued

3 exP MHZ

a)

$

24 848.10 24

854

59

SPECTRA OF SFLUOROTOLUENE

847.06

15 310.64 15 282.96

_$ exP

CdC

MHZ

0.94 1.16

b) +doublet exP MHZ

splitting talc MHz

-1.04

-1.27

-27.68

-27.79

-0.45 -0.67

42.00

41.79

-28.80

-28.79

-0.46

-0.57

8

5

3

8

4

4

8

6

2

8

5

3

14 14

588.25 559.45

-0.60 -0.59

8

7

2

8

6

3

18 18

343.76 344.99

-0.56 -0.43

1.23

1.36

9

6

4

9

5

5

15 15

294.00 320.40

-0.78 -0.58

26.40

26.60

10

7

4

10

6

5

17 809.44 17 754.77

-0.33 -0.34

-54.67

-54.68

10

6

4

10

5

5

11 665.51 11 740.58

-0.64 -0.65

74.96

74.96

5

6

15 605.87 15 683.14

-0.33 -0.38

77.26

77.21

9 625.70 9 667.70

lo

6

5

13

11

7

4

11

6

5

15 605.87 15 640.06

-0.43 -0.51

34.19

34.12

12

7

5

12

6

6

13 743.37 13 852.92

-0.81 -1.44

109.55

109.74

12

7

6

12

6

7

17 880.11

17 993.10

-0.10 0.06

112.99

113.14

12

8

4

12

7

5

19 522.52 19 438.80

-0.42 -0.53

-83.72

-83.83

12

8

5

12

7

6

20 264.67 20

182.61

-0.16 -0.20

-82.07

-82.11 -2.29

13

9

4

13

8

5

22 22

837.22 834.81

0.16 0.28

-2.42

14

9

6

14

8

7

22 22

686.92 584.22

0.24 -0.19

-102.70

-103.13

14

9

5

14

8

6

21 21

962.81 858.00

0.52 0.16

-104.81

-105.18

The program has been checked against the torsional equation obtained for methanol CHSDOH and CHDzOH by Knapp and Quade (5) and against the rotational quantities and calculated spectra for propene CHzDCHCHz of Hirota (3) which were reproduced within a few KHz in the torsional ground and first excited states. The program was also successfully applied to the torsional energy eigenvalues of parafluorotoluene (6). EXPERIMENTAL

DETAILS

The adI- and adz-ortho-fluorotoluenes were purchased from Merck, Sharpe & Dohme, Canada, and checked by gas chromatography. Spectra were recorded between 8 and 35 GHz with a conventional 33 KHz-modulated Stark-spectrometer equipped with a 4 m length of adsorption cell with a cross section of 10 X 43 mm2. The vapor pressure

SCHWOCH AND RUDOLPH

60

Table

J

K

J' K' "1

K+

3

VI continued

a)

$

b) +doublet exP MHZ

-3 exP

exP MHz

CdC

MHz

splitting talc MHZ

14

8

7

14

7

8

20 121.26 20 264.74

0.16 0.48

143.47

143.80

14

a

6

14

7

7

15 868.00 16 006.73

-0.95 -0.54

138.73

139.14

15 10

5

15

9

6

25 305.65 25 302.27

0.32 0.45

-3.38

-3.26

16

9

a

16

8

9

22 339.02 22 505.88

0.43 0.95

166.87

167.39

16

9

7

16

8

8

18 040.22 18 201.05

-0.99 -0.41

160.84

161.42

16 lo

6

16

9

7

24 386.10 24 268.50

-1.06 0.32

-117.60

-118.34

16 10

7

16

9

8

25 083.74 24 968.13

0.90 0.53

-115.61

-115.99

1811

8

18 10

9

27 461.38 27 340.28

1.18 0.59

-121.10

-121.69

1811

7

1% 10

8

26 794.28 26 670.62

1.87 1.22

-123.66

-124.30

18 10

8

18

9

9

20 256.29 20 433.24

-0.73 -0.13

176.95

177.55

18 10

9

18

9 10

24 540.25 24 724.33

0.90 1.67

184.08

184.85

a)

The

rotational

the respective state

“1 cl

of the asymmetric

TheQcalc Table not

transitions tunneling

were

calculated

are listed substate

in the order

of the torsional

internal

rotor.

with

the fitted

constants

+,- of ground

of

X.

resolved

corresponded to a cell temperature near -50°C. High-resolution recordings were made with a scanning speed of 10 KHz/set, a detector diode current in the range of 100 PA, and a phase detector time constant near 10 sec. The spectra were extremely dense. With the exception of a few J: 2 + 3 transitions, well-resolved Stark lobes could not be observed. In several cases RF-MW double resonance measurements proved to be a useful tool for the identification or confirmation of transitions. ASSIGNMENT

AND METHYL

TOP CONFORMATION

As expected, asymmetric rigid rotor spectra due to a- and b-dipole moment components of almost equal magnitude were found for the two sy-rotamers. The lines recorded have been collected in Tables III and IV, the rotational constants in Table V. The two

MICROWAVE

SPECTRA

61

OF O-FLUOROTOLUENE

asy-rotamers presented doublet spectra (Tables VI and VII). Several lines departed appreciably from a rigid rotor pattern. Also, “forbidden,” i.e., intersystem, transitions were observed (Tables VIII and IX). The least-squares fit of the transition frequencies to a Hamiltonian of the type of Eq. (7) yielded the rotational quantities listed in Table X. The inertial defects A of all rotameric forms (Table XI) agree with the sy- or asyassignments. This evidence for the existence of well-defined rotamers allowed an application of Kraitchman’s equations which gave a staggered methyl top conformation with respect to the C-F bond. The corresponding conformation has been established also for ortho-chlorotoluene (7).

Table

Rotational

transitions

of Wd2-or‘tho-fluorotoluene,

H-out-of-plane

s

s’X;K:

K_K+

2

2

1

110

3

3

1

2

2

4

3

2

4

5

3

3

5

4

5

\J

VII

a) exP MHZ

(asy-rotamer)

b)

3 exP -VCdC #HZ

+doublet exp MHZ

splitting talc MHZ

lo 532.61 10 531.86

-0.35 -0.33

0

16 968.64 16 974.76

-0.49 -1.60

2

3

8 026.71 8 025.63

-0.11 -0.05

-1.08

-1.03

5

2

4

9 286.86 9 285.81

-0.09 -0.01

-1.05

-0.98

1

5

3

2

8 024.55 8 021.27

-1.15 -0.68

-3.29

-2.82

4

2

5

3

3

9 758.81 9 755.66

-0.33 -0.10

-3.15

-2.72

5

5

1

5

4

2

12 059.34 12 064.89

-0.32 -1.24

5.55

4.63

5

5

0

5

4

1

11 869.92 11 875.44

0.09 -0.84

5.52

4.59

5

3

2

4

3

1

18 579.19 18 579.19

-0.19 -0.25

5

4

2

4

4

1

17 17

6

3

4

6

2

5

11 020.21 11 019.14

6

4

3

6

3

4

10 392.30 10 390.82

-0.18 -0.03

6

5

1

6

4

2

ii.

11 225.17

-0.12 -0.83

4.91

4.20

6

5

2

6

4

3

11 991.49 11 996.82

-0.27 -1.27

5.33

4.33

6

6

I

6

5

2

14 723.69

0.69 -0.15

497.32 491.92

220.26

14 722.70

0.63 1.21

0.06 0.12

-0.75 6.12

C)

-0.73 5.01

-0.07

-5.40

-4.82

-1.07

-1 .oo

-1.49

-1.33

-0.99

-0.84

62

SCHWOCH AND RUDOLPH Table VIIcontinued

J

K_ K+

J' K' K' - +

v

a) exP MHZ

3

-3 exP

CdC

MHz

b) +doublet exP MHZ

splitting talc MHz

6

6

o

6

5

1

14 677.61 14 676.56

6

5

2

5

5

1

21 009.04 21 010.14

-0.93 -0.73 -0.43 -0.69

6

5

2

5

4

1

32 32

874.43 881.07

-0.46 -1.66

7

3

4

7

2

5

8 033.66 8 033.66

0.69 0.37

7

4

4

7

3

5

11 ii

523.89 522.62

-0.07 -0.02

-1.27

-1.22

7

5

2

7

4

3

10 095.50 10 092.30

-1.28 -0.82

-3.20

-2.74

7

6

1

7

5

2

14 263.74 14 270.76

0.30 -0.85

7.02

5.87

7

6

2

7

5

3

14 526.96 14 533.89

-0.26 -1.24

6.93

5.95

7

7

0

7

6

1

17 417.04 17 417.04

0.62 -0.18

C)

0.44

7

5

3

6

5

2

24 24

681.9% 673.65

-0.73 0.52

-8.33

-7.08

3

8

4

4

8 819.36 8 817.23

-1.03 -0.6%

-2.12

-1.78

-0.15 0.03

-1.82

-1.63

8

5

-1.05

-0.85

1.10

0.84

6.63

5.43

C)

-0.32

8

5

4

%

4

5

12 650.07 12 648.25

8

6

3

%

5

4

14 375.55 14 387.40

-0.09 -1.93

11.85

10.00

8

6

2

8

5

3

13 457.11 13 468.3%

0.28 -1.20

11.27

9.79

8

7

2

% 6

3

17 17

198.70 193.44

-0.24

-5.26

-4.54

17 17

133.54 128.19

-1.38 -0.61

-5.35

-4.57

20 20

138.30 138.30

-0.57 0.20

C)

0.76

8

7

1

8

6

2

8

8

0

8

7

1

0.24

SPECTRA OF ASY-ROTAMERS

Most of the doublet line splittings in the spectra of both asy-rotamers have magnitudes up to a few MHz which are similar to those found in the spectrum of the normal molecular isotope (4). However, considerably wider doublet separations have regularly been found for transitions (all of them bQ-type) where one of the levels involved is the member of a K-type level doublet which is split by an energy difference of the order Avtora.Figure 3 presents a typical level arrangement where one K-doublet member from the fasy stack of levels couples with its counterpart from the -asy stack with which it is nearly degenerate in zeroth order. The asymmetrical position of the line doublet arising from the particular transition in the +asy and -asy level system with respect to the hypothetical ARR frequency is worth noting. It is a consequence of the fact

MICROWAVE

SPECTRA OF 0-FLUOROTOLUENE Table

J

X

K+

J’

X’ -

K’ +

63

VIIcontinued

v exP MHz

a)

,,

_v

exP

talc MHz

b)

+doublet

splitting

exP

CdC

MHZ

MHZ

9

4

5

9

?

6

9 359.54 9 359.54

0.86 0.57

9

5

5

9

4

6

13 669.41

c.17 0.05

-1.34

-1.45

9

5

4

9

4

5

8 8

137.66 136.20

-0.54 -0.36

-1.47

-1.29

9

6

4

9

5

5

14 14

419.65 416.59

-0.39 -0.05

-3.06

-2.72

9

7

3

9

6

4

16 927.31 16 936.56

-0.24 -1.24

9.25

8.25

9

7

2

9

6

3

16 603.63 16 612.75

0.21 -0.77

9.11

a. 13

9

8

2

9

7

3

19 915.20 19 915.20

-0.29 0.25

c)

6

4

15 703.41 15 679.82

-2.10 -0.89

-23.58

-22.63

6

5

16 695.55 16 672.40

-0.32 0.51

-23.15

-22.32

0.90 -0.44

31.62

30.20

31.56

30.24

13 668.06

C)

-0.29

0.54

10

7

3

10

10

7

4

10

10

8

2

10

7

3

19 495.80 19 527.50

10

8

3

10

7

4

19 618.10 19 649.66

-0.17 -1.48

12

8

4

12

7

5

17 887.02 17 869.83

-1.61 -0.75

-17.19

-16.32

12

8

5

12

7

6

18 966.77 18 949.69

-0.64 0.52

-17.08

-15.92

12

9

3

12

8

4

21 21

857.49 885.10

o-73 -0.08

27.61

26.80

12

9

4

12

I3

5

21 22

992.18 019.89

0.03 -0.82

27.72

26.86

13

9

4

13

8

5

21 21

170.54 185.99

0.07 -0.24

15.44

15.14

13

9

5

13

8

6

21 21

581.68 597.50

-0.06 -0.54

15.82

15.34

that only one doublet member is heavily affected by the perturbation. For the same reason the Stark-patterns were distinctly different for the doublet members in this case, occasionally leading to a reversal of the Stark shift direction for the strongly perturbed member as was observed, e.g., for the (-) doublet member of the transition lOeb+ 10T4 of the CHzD-isotope. We have endeavored to include as many anomalous doublets as possible in our list of lines because the rotational quantities to be fitted, particularly Avtors, depended sensitively on these doublets, while the barrier potential T/‘ain turn depends on the significant evaluation of the rotational quantities. Even though the ARR level designation by K-K+ is only approximately correct for the eigenvalues of Eq. (7) for a particular J, we have adhered to this notation to which a (+) or (-) must be added depending on the particular (+) or (-) subblock to which

64

SCHWOCH

AND RUDOLPH

TableVIIcontinued

J

K

K+

J'

Ki

K:

J

a)

3

exP MHz

_$ exP

13 10

3

13

9

4

$2;;;*;i .

10

4

13

9

5

24 24

14

y

6

14

8

7

14

9

5

14

8

14

10

5

14

14

10

4

15

lo

b) +doublet

CdC MHz

splitting ca1c MHZ

exP MHz

0.49 -0.09

0.75

0.17

751.12 751.95

1.06 0.42

0.75

0.19

21 21

199.03 185.06

-0.17 0.41

-13.97

-13.40

6

20 20

058.89 044.19

-1.30 -0.49

-14.70

-13.89

y

6

24 24

330.25 35.9.75

-1.01 -2.23

29.50

27.98

14

9

5

24 24

181.25 208.75

0.25 0.65

27.50

27.90

5

15

9

6

23 23

413.20 432.88

-0.28 0.08

19.68

20.03

1510

6

15

9

7

23 23

854.32 874.48

0.04 0.19

20.16

20.28

16

lo

6

16

9

7

22 22

220.45 206.86

-0.71 -0.08

-13.59

-12.96

16

10

7

16

9

8

23 23

401.13 388.46

-0.01 0.29

-12.67

-12.37

1611

6

16

IO

7

26 26

636.01 664.47

-0.82 2.01

28.46

31.29

1711

6

17

lo

7

25 25

635.64 659.64

-1.09 0.82

24.00

25.91

1811

8

18

10

9

25 25

578.41 566.32

0.21 0.30

-12.09

-12.00

18

7

1811

8

28 28

914.61 947.38

0.23 3.47

32.77

36.01

6

1811

7

28 28

745.25 777.90

-1.42 1.82

32.65

35.90

13

12

1812

a)

The

rotational

transitions

the

respective

tunneling

state

b) c)

of

the

The

were

Vcalc Table X. not

asymmetric calculated

are

listed

substate internal with

of

in the

the

order

torsional

+,-

of

ground

rotor. the

fitted

constants

of

resolved

the eigenvalue belongs. We have found it practical to indicate the degree of interaction between the (+) and (-) asy subblocks by computing a “state mixing parameter” (smp) for each eigenvalue J, ILK+, (+) or (-), by adding up the squares of the amplitudes with which the SRR basis states of the counterpart block, (-) or (+), are contained in the particular eigenstate. The amplitudes are, of course, given by the respective

components

of the particular

eigenvector.

In the general

case, where the

MICROWAVE

SPECTRA

OF O-FLUOROTOLUENE

6.5

interaction between the (=t) subblocks is low, an smp of the order 0.02 is typical; however, in singular cases an smp approaching 0.5 was found for both isotopes, indicating nearly complete mixing and a formal breakdown of the (+) or (-) notation. An illustrative case is represented in Fig. 4, where the smp of the pair of levels, here still designated as 14*6(+) and 14,r(-), is 0.44 for both. While the pair would be very nearly degenerate in zeroth order, the actual energy difference is 300 MHz. The strong mixing leads to the existence of “forbidden” transitions which appear as “intersystem” transitions in Fig. 4, though it must be remembered that the (s) parity designation is no longer a good one for the above and similar pairs. It should be realized that none of the “forbidden” transitions shown in the figure are due to the molecular c-dipole moment which is negligibly small (less than 0.01 D) for the asy-rotameric forms of ortho-fluorotoluene. All transitions represented in the figure are b-type transitions, where each of

Table

VIII

O(d, -ortho-fluorotoluene, "Forbidden"

rotational

different

(+)-tunneling

torsional

ground

J

x

J’

K+

(+i

substates

state methyl

(asy-rotamer) transitions

of

the

between of

the

asymmetric

group

K: t-i X’

3 exp -%alc MHZ

10

5

5

10

6

5

11

916.48

0.58

lo

6

4

lo

5

6

15

432.24

0.51

12

6

6

12

7

6

14

013.75

1.04

12

7

5

12

6

7

17

723.04

0.04

12

7

5

12

a

5

20

453.06

0.50

12

8

4

12

7

6

19

252.20

0.25

14

7

7

14

8

7

16

167.84

14

a

6

14

7

a

19

964.88

-0.07 -0.32

0.52

14

a

6

14

9

6

22

883.98

14

9

5

14

a

7

21

663.10

16

a

a

16

9

a

la

371.80

16

9

7

16

a

9

22

174.27

-5.24

16

Y

0.05 0.25

7

16

IO

7

25

300.19

-0.79

16 10

6

16

9

a

24

054.35

-0.48

18

IO

9

20

619.07

-0.26

9

24

361.55

-0.68

a

27

703.02

-1.61

9

26

431.54

-0.85

9

18

18

lo

a

la

la

IO

a

1811

7

la

1811

a)

9

IO

The ~calc

were

constants

of

lo

calculated

Table

X.

with-the

fitted

rotational

a)

SCHWOCH AND RUDOLPH

66

Table

IX

O(d2-ortho-fluorotoluene, “Forbidden”

-rotamer)

transitions

different

(+)-tunneling

substates

torsional

ground

state

methyl

J

(c

rotational

of

the

between of

the

asymmetric

group

\I exP MHZ

K_ K+ (+)

8

5

3

8

6

3

13 505.76

8

6

2

8

5

4

14

3

exP -‘talc MHZ -1.40

338.22

-0.29 -0.27

10

6

4

10

7

4

15 656.77

10

7

3

lo

6

5

16 710.83

10

7

3

10

8

3

19 602.50

1.39 -1.15

10

8

2

10

7

4

19

543.12

1.74

12

7

5

12

8

5

17 829.24

-0.31

12

8

4

12

7

6

19 007.60

1.53

12

8

4

12

9

4

21 961.73

-1.49

12

9

3

12

8

5

21 915.46

1.39

13

8

5

13

9

5

21 253.68

0.12

13

9

4

13

8

6

21 514.40

0.40

14

8

6

14

9

6

19 985.58

0.15

14

9

5

14

8

7

21 258.28

14

9

5

14 10

5

24 283.65

14

10

4

14

9

6

24 254.53

lo

6

23 492.76

0.65 -1.42 0.87 -0.74

15

9

6

15

15

lo

5

15

9

7

23

IO

7

22 131.63

9

8

23

477.18

-0.41 -1.92

16

9

7

16

16

10

6

16

16

IO

794.08

6

1611

6

26

575.72

1611

5

16

IO

7

26

564.08

1811

7

18

12

7

28 848.20

18 12

6

1811

8

28 844.43

a)

The 'talc constants

were

calculated

of Table

with

the fitted

a)

0.02 0.72

0.31 1.82 -3.86 rotational

X.

the “zeroth-order forbidden” transitions, e.g., 1486(+) + 14~(-), “borrows intensity” from a corresponding “zeroth-order allowed” transition, e.g., 1481(-) + 1496(-). This is in contrast to the c-type transitions with parity change observed in the torsional ground state spectrum of 3-fluoropropene (Z), though of similar origin as the (+ ) + (-) transitions found in the first excited state spectrum of 3d-propene by Hirota (3). The relative intensities for transitions between energy levels of the rotational Hamiltonian Eq. (7) were calculated by subjecting the 2(2J + 1)-dimensional matrix of the a- and b-dipole moment components set up in the SRR-basis to a transformation by

MICROWAVE

SPECTRA

OF O-FLUOROTOLUENE

67

the diagonalizing matrices stored away when computing the eigenvalues of Eq. (7). The calculated intensities agreed well with those observed also in cases of strong perturbation. As is evident from Fig. 4, the combination of appropriate frequencies permits the application of various “spectroscopic sum rule” tests which were performed wherever possible and gave results within experimental accuracy, thus confirming the assignments. Since the frequencies of the “forbidden” transitions contain, in zeroth order, the ground state torsional energy difference Avtora, they are by far the most valuable lines for the accurate determination of this particular quantity in the fitting procedure. RF-MW

DOUBLE

RESONANCE

The search for forbidden transitions and anomalously wide doublets has been greatly aided by the application of RF-MW double resonance. For this purpose the amplitude modulated (33 KHz) RF pump power was connected to the Stark septum after the cell capacity had been roughly compensated by a coil. Pump frequencies between 4 and 1.5 TABLE ROTATIONAL FHOM

CONSTANTS

FIT OF EQ.( 7)

X OF ASY-HOTAMERS

TO SPECTRA

(in MHz)

OLd2-ortho-

#d,-orthoFluorotoluene

Fluorotoluene

D-out-of-plane

H-out-cf-plane

b

A+ B+ C+

3 203.18

+ 0.02

3 090.48

+ 0.02

2 118.645

+ 0.002

2 088.775

+ 0.005

1 290.07

+ 0.02

1 260.81

+ 0.07

A

3 202.72

+ 0.02

3 090.17

+ 0.02

B

2 118.31

+ 0.03

2 088.808

+ O.OOE

C

1 290.08

+ 0.03

1 260.81

+ 0.02

l 018.8

+ 2.0

AVtors % Zb

a

b

ac

Calculated twice

fitting

1.6

+ 0.1

3.98

+ 0.06

10.6

+ 1.2

1.5

+ 0.7

(5.68)a

(5.OO)a (16.18)"

from

+

15.05

(16.74)a

'bc H

111.8

structure,

errors

not fitted

SCHWOCH AND RUDOLPH

68

MHz have been employed although the range could have been extended easily by a suitably constructed RF-circuit. The lower limit was given by the “high-frequency” Stark effect which appeared superimposed on the double resonance signal. The energy level arrangement in Fig. 4 is particularly favorable for the application of double resonance. The energy K-doublet immediately above the one in which the strong coupling occurs has a separation of only a few MHz (greatly exaggerated in the figure) and the u-type transition matrix element is large. It is hence well suited for being pumped. Since the K-doublet separations in the +asy and -asy level systems are almost identical, both K-doublet transitions in Fig. 4, 1496-+ 149s, (+) and (-), will be simultaneously pumped and all six transitions which are shown connected to the two doublet levels will be pump-modulated and detectable. The eminent usefulness of double resonance measurements is demonstrated by the sample recording (Fig. 5) for TABLE

INERTIAL (in

amu

XI

A=

DEFECTS

Ic-Ia-Ib

X2)

Calculated

l'rom Rotational Constants Tables

~(d

Fitted,

V

and

From

Assumed

Structure,

X

Table

-ortho-

Fluorotoluene b D

in-plane

D

out-of-plane

a

wd

3.17

3.19

4.46

4.79

6.16

6.38

4.57

4.79

-ortho-

Fluorotoluene c

H

in-plane

Ii out-of-plane

a

b

c!

.;ithin accuracy

given or

no (-)

difference torsional

between

rotational

constants

from

(+)

substate,

Identical

with

moment

of

inertia

of

a CH3-group

Identical

with

moment

of

inertia

of

a CD,-group

Table

X.

I

MICROWAVE

SPECTRA

OF O-FLUOROTOLUENE

69

K_+l,K+l K_+l,K+

K-K+

b, FIG. 3. Possible perturbations due to near-degeneracies systems when R-doublet spacing 6 is of the order Arti,.. of transition J, IL_ K+ + -I, (K- + 1) (K+ - 1).

6 ;L AVtora

(. . .) of rotational Large

levels of +asy and -asy shift of perturbed line doublet member

14,‘-’ ud-’

14&d 14..

Tdr

WP __,,......... .”

142’

14&’

w,*

rIYYl7

u\-l i 142’

1471

14%’

WJ

FIG. 4. Appearance of “forbidden” (i.e., intersystem) transitions by a strong perturbation illustrated in Fig. 3, here between levels 14&+) and 14,w(-_) of cudi-ortho-fluorotoluene.

of the type

SCHWOCH

AND

RUDOLPH

FIG. 5. Same section of spectrum of adz-ortho-fluorotoluene recorded. Above: Stark-spectrometer; below: with a double resonance spectrometer, K-doublet + 1812,8, (f)] = ~[18~~,7 -+ 1812,6, (-)] = 9.2 MHz being pumped.

a group of six transitions &-ortho-fluorotoluene.

ending

ROTATIONAL

on the K-doublets

CONSTANTS

with a conventional transitions $1812.7

1812,r, 1812,6, (+)

and

(-),

of

OF ASY-ROTAMERS

The Hamiltonian operators, Eq. (7), and hence the spectra of the asy-rotamers of a&- and c&-ortho-fluorotoluene depend on 11 rotational parameters, A*, B*, C*, & from a least-squares fit & K,, Rbc, and AvtO,,, which should in turn be determinable of the experimental frequencies to those generated by the Hamiltonian Eq. (7). As has been explained before (3), the R-constants are expected to be very much less important than, though highly correlated with, the constants A, B, C. It is therefore advisable to assume fixed values for R,, and Rbc calculated from a reasonable structure and barrier. The fitting process turned out to be very tedious ; whenever a variation of the parameters to be determined (particularly AQ& tended to produce a near degeneracy in the (+) and (-) level systems of Eq. (7), the transition frequencies involved changed very rapidly. This strongly nonlinear behavior was further complicated by frequent alternations of level arrangements (cf. Figs. 3a and b). We found it useful to set out with a limited collection of “normal” doublet transitions and repeat the fitting procedure including the progressively more perturbed and the “forbidden” transitions in a stepwise fashion. The rotational constants of the final fit which reproduce the experimental spectra very well are presented in Table X for both isotopes. These constants are not appreciably different when only low-J or high-J transitions are included in the fit, only the errors are larger. METHYL

TOP

BARRIER

In order to obtain the barrier potential Tr, the rotational quantities A.4 = A+ - A-, AB = B, - B_, Q, 8 b, and Avtors were calculated as functions of k’s with the first

MICROWAVE

SPECTRA

71

OF 0-FLUOROTOLUENE

part of our program and compared with the rotational parameters just determined from the spectrum. The differences AA and AB were chosen instead of the constants A* and B* because they are less affected by uncertainties in the structure assumed. AC (~0) shows no significant dependence on V3. Since it is the structural uncertainty of the methyl top almost alone that influences the parameters API, AB, Q, 0 b, and Avto, as functions of V3 we have established crude error margins on these calculated functions by computing each of them for two limiting methyl top angles QCCH = 107.5” and 111.5”. These functions are displayed versus Va in Figs. 6a and b. Entering into the diagrams with experimental values of the rotational constants, we obtain from each curve one value of Tia. The weighted mean is k’s = 567 f 48 Cal/mole For the for c&-ortho-fluorotoluene, and k’s 5 711 f 44 Cal/mole for the &-isotope. considerable scatter of 1”s observed within each of the two figures we offer the following explanation. The present treatment is different from the one conventionally employed in the case of symmetric internal rotors, where the barrier potential Va (or the reduced potential s) is explicitly among the (few) parameters to be determined by an optimum reproduction of the spectrum. Following Hirota (3) we have instead taken the rotational quantities of the Hamiltonian (7) to be independently variable parameters in the fit although they are really functions of ‘VS.While this affords added flexibility and permits the excellent reproduction of the complicated spectra, one must realize that any shortcomings of the semirigid model will now become evident when one compares the experimentally determined values of the rotational parameters (which might be contaminated by contributions due to the nonrigidity of top and frame) with the calculated ones (which are based on the semirigid model). Any effect not accounted for by the semirigid model will tend to slightly shift the true curves for the rotational parameters versus Vs away from those depicted in Figs. 6a and b, probably by different amounts and in different directions for the individual parameters present in the figure. When k’s is to be determined from these curves the replacement of the true but unknown curves by those calculated for the semirigid model, as we have done above in Figs. 6a and b, will then necessarily lead to a scatter of the V3 values obtained and probably also to an error of the weighted mean. When an individual parameter depends only slightly on Va the curve is shallow and any small shift of the curve may then easily result in a particularly large deviation

of the V3 determined

& of the c&t-isotope Technical

where a reasonable

reasons of computer

ment where the individual the spectra.

from it. This appears point of intersection

to be the case, e.g., for could not be obtained.

storage and time required us to follow the present

rotational

parameters

We also wished to gain more insight

(instead

of directly

into the manner

treat-

V,) are fitted to

in which structural

changes influence the barrier evaluation. The mean values of Va for the &l-isotope (567 Cal/mole) and the a&-isotope (711 Cal/mole) deviate appreciably and in opposite directions from that of the normal molecule (649 Cal/mole). Even though few reliable data are available regarding the barrier trend when a CHDz-methyl group is substituted for a CHBD-group, it is hard to imagine that the erratic behavior found above is a true reflection of the isotope effect on the barrier. Neither the scatter in VI for each of the two isotopes nor the discrepancy

72

SCHWOCH AND RUDOLPH

I

?!k!L_o.o

A6(Vd

__,

-a1 t

L

10.

6

6

h4

k

2. ---+

270

:< j :

230 190

,’

Athan (v,) ,.I ‘.G ,, i ,,::

150 110

..***e--

70 A%m.,

Wiohted

I,‘:-----:,.

6lo

630

650

670

800

mem

7lo

-

Wd

720

7.50 77oV,(4

FIG. 6a. a&-ortho-Fluorotoluene. “Rotational constants” of Eq. (7) shown calculated from assumed structure, Table I, and dependent on 113.Shaded : due to estimated uncertainty of structure. Evaluation of V( by entering (from the left) with rotational constants determined from fit to spectrum (Table X).

between the two mean values of Va could be significantly reduced by tilting the internal rotation axis with respect to the molecular frame. We believe that the scatter of Va as well as the barrier difference between the two isotopes is a consequence of the inherent shortcomings of the semirigid model in the present case and not merely due to the two simplifications [l] and [2] adopted in the present treatment. [l] The torsional ground state sy-sublevel has been treated as nondegenerate with the asy- sublevel pair because the magnitude of matrix elements which connect sy- with asy-states is less than l/1000 of the difference of the corresponding diagonal elements. If there ha.d been any close interaction between rotational levels of the asy- and the sp-level systems this should have shown up in both spectra as conspicuous deviations of certain experimental transition frequencies from those calculated. This was not the case. [2] The effective rotational operator, Eq. (7), has been limited to terms of at most second order in the Pia However, the inclusion of higher powers would only slightly change the experimental value of Avbra which is derived from a multitude of

MICROWAVE

FIG.

SPECTRA

OF 0-FLUOROTOLUENE

73

6b. Same as Fig. 6a, for a&-ortho-fluorotoluene.

anomalous doublets and forbidden lines; and even Avtirs alone would point to appreciably different barriers for the two isotopes. The two new barrier values for the a&- and c&isotopes straddle the value found earlier for the normal isotope. It appears reasonable to explain the differences as being caused by the effects of nonrigidity (relaxation and vibrational interactions) and of insufficiently known structural changes, all of them not accounted for by the present state of the art. This would require giving a common average value for ortho-fluorotoluene, V3 = 647 f 78 Cal/mole, with a possibly more realistic error margin than could be obtained from an investigation of the normal isotope alone. CONCLUSION

The “two-dimensional” Hamiltonian of the type given in Eq. (7) is evidently well suited for the faithful reproduction of the rotational spectra of the asy-rotamers of the isotopes CY& and cY&-ortho-fluorotoluene when the rotational parameters contained in this equation are independently fitted to the spectra. However, the functional depen-

74

SCHWOCH

AND

RUDOLPH

dence of these parameters on the molecular geometry and the internal rotation barrier 1’3 as derived by the semirigid model appears to be only approximately correct. This is indicated by the considerable scattering when different rotational parameters are used for the evaluation of 1/‘3for each of the isotopes. The considerable difference between the mean values of Va determined for the two isotopes strengthens the argument that it is the neglect of internal motions other than the methyl group torsion in the semirigid model which is primarily responsible for this observation. The investigation of rotational spectra in excited torsional states would be a useful extension of this work and possibly help to clarify the applicability of the present model. ACKNOWLEDGMENTS The authors gratefully acknowledge the support of the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie. The computations have been carried out at the Computing Center of the University of Freiburg, Germany. RECEIVED:

November

21, 1974 REFERENCES

C. R. QUADE AND C. C. LIN, J. Chem. Phys. 38,,540 (1963). P. MEAKIN, D. 0. HARRIS,AND E. HIROTA,J. Chem. Phys. 51,3775 (1969). E. HIROTA,J. Mol. Spectrosc. 34, 516 (1970). J. SUSSKIND,J. Chew Phys. 53, 2492 (1970). J. V. KNOPP AND C. R. QUADE, J. Chew Phys. 48,3317 (1968). H. SCHLESER AND H. D. RU~LPH, to appear. 7. P. DIEHL, P. M. HENRICHS,AND W. NIEDERBERGER, Mol. Phys. 20, 139 (1971).

1. 2. 3. 4. 5. 6.