The ring-puckering vibration and potential function of 3-methylthietan: a reexamination of the microwave and far-infrared data

Volume 168, number 6

CHEMICAL PHYSICS LETTERS

18 May 1990

THE RING-PUCKERING VIBRATION AND POTENTIAL FUNCTION OF 3-METHYLTHIETAN: A REEXAMINATION OF THE MICROWAVE AND FAR-INFRARED DATA D.G. LISTER Dipartimento di Chimica Industriaie, Casella Postale 29, 98166 Sant’Agata di Messina, Italy

J.C. LOPEZ, A.G. LESSARI and J.L. ALONSO Departemento de Quimica Fisica, Facultad de Ciencias, Universidadde Valladolid, 47005 Valladolid, Spain -i. Received 5 February 1990; in final form 5 March 1990

An attempt has been made to account for%e ring-puckering vibrational dependence of the quartic centrifugal distortion constants of 3-methylthietan. The calculations!ndicate revised assignments for the excited vibrational states in the microwave spectrum and for some of the tran’sitions in the f%infrared spectrum of the ring-puckering vibration. The resulting potential function has a slightly higher barrier to ring inversi& for the more stable equatorial conformer and a larger energy difference between the equatorial and axial conformers than thatqroposedpreviously.

The vibrational dependence of the rotational and centrifugal distortion constants df four-membered ring molecules with an asymmetric ring-puckering potential function has not received the attention devoted to molecules with a symmetric potential function. It is not clear to what extent the treatment of the rotational constants developed by Gwinn and coworkers [ 1,2 ] and that of Creswell and Mills [ 3 ] for the centrifugal distortion constants is applicable to molecules with an asymmetrio ring-puckering potential function. Recently we have observed changes in the centrifugal distortion constants on excitation of the ring-puckering vibration in 3-methyloxetan [ 41 almost an order of magnitude larger than those in oxetan [ 3,5]. These changes can be accounted for satisfactorily using the theory developed by Creswell and Mills [ 3 ] incorporating the extensions introduced by Kubota et al. [ 61. Very large changes in the centrifugal distortion constants of 3-methylthietan have been reported by Caminati et al. [ 7 ] and it is of some interest to see whether these can also be accounted for using the same type of approach. Caminati et al. [ 71 observed the microwave spectra of the ground and five excited ring-puckering states (a-f of table 1) of 3-methylthietan. They 564

derived rotational and quartic centrifugal distortion constants using an A-reduced semirigid rotor Hamiltonian and an IQ&s representation [ 81. Their assignment of the ring-puckering states is given as assignment 1 in table 1. The experimental rotational constants (to the nearest MHz) are also given in this table and the experimental centrifugal distortion constants are given in table 2. They derived the ringpuckering potential function from combined micro: wave and far-infrared data using a flexible model approach [ 9 ] and from the far-infrared data alone using a reduced potential function. Both approaches gave essentially the same ring-puckering potential function and this is shown in fig. la. The calculations to be described below have been made using a different form of the reduced potential function and a different definition of the reduced coordinate. The reduced potential used here is V(X) =v&Y4-~tlx2+~3)

)

(1)

where X is the reduced coordinate of Chan and Stelman [ lo] appropriate to a quartic oscillator. Calculations have been made using basis sets of 70 harmonic-oscillator wave functions. Caminati et al. [ 7 1 give two slightly different reduced potential func-

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CHEMICAL PHYSICS LETTERS

Volume 168, number 6

l8May 1990

Table 1 Rotational constants and the assignments of the ring-puckering vibrational states for Zmethylthietan. Assignment 1 is that of ref. [ 71 and corresponds to the reduced potential function of eq. (2), and assignment 2 is that proposed here and corresponds to the reduced potential function of eq. ( 15) Vibrational state a

b

d

C

f

e

0 0

I 2

2

3 4

4 3

6 5

A (MHz) observed assignment 1 assignment 2

9208 9189 9200

7292 7312 7299

9077 9084 9082

7609 7519

7600

8780 8800 8787

8262 8264 8259

B (MHz) observed assignment 1 assignment 2

2872 2874 2872

3217 3214 3216

2887 2885 2887

3150 3151 3151

2931 2926 2930

3022 3030 3022

C (MHz) observed assignment 1 assignment 2

2386 2388 2386

2816 2811 2815

2399 2395 2400

2723 2722 2726

2445 2439 2444

2558 2573 2557

assignment 1 assignment 2

Table 2 Quartic centrifugal distortion constants for 3-methylthietan. Assignment 1 gives the centrifugal distortion constants calculated from the reduced potential function of eq. (2), and assignment 2 those calculated from eq. ( 15) Vibrational state a

b

d

C

e

f

A (kHz) observed assignment I assignment 2

0.44 0.02 0.07

&K (kHz) observed assignment 1 assignment 2

-0.83 -0.11 - 1.71

dK

1.98 2.06 1.50 -11.4 - 15.7 -11.2

0.41 0.04 0.17 -2.79 -1.15 -3.61

-4.5 13.9 -6.3 83.1 -138 89.6

11.3” -9.2 11.1 -131 90.4 -139

6.1 -3.0 6.5 -71.5 31.9 - 79.9

&Hz) observed assignment I assignment 2

8.~(kHz) observed assignment I assignment 2 & (kHz) observed assignment 1 assignment 2

24.5 30.2 20.8 0.077

-0.000 0.018

-330 351 -304

-0.261 -0.406 -0.302 3.6 3.4 2.5

7 17 -3

‘) In ref. [ 71 there is a misprint in table III and d_,for state e is given as 1.13 kHz.

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Volume 168, number 6

CHEMICAL PHYSICS LETTERS

E/cd

18 May 1990

EIcm’

200.

200.

0.

0.

-200 -

-200. I I 4

,

I

I I :)

I I

I 4

I 1 1 I I I I I I 4 0 x 4 (b)

x

Fig. 1. Reduced potential functions for the ring-puckering vibration of 3-methylthietan; (a) the potential function eq. C&inati et al. [i ] and (b) that of eq. ( 15) proposed here

tions. These have been transformed to the form of eq, 11) and also, as a check, the potential functions have been rederived from tits to the same far-infrared transitions. Since both potential functions give s fin the centrifugul distortion con43x+0.51

1X3 ) )

(&P=a,b,e)

3

**. (3)

where &=l (u’=v) and a,.=0 (v’#u) represent the normalization and orthogonality conditions on the vibrational wave functions and XX”} vySis the v, U’matrix element of X”. In terms of the Taylor-series expansion the “baa coefficients are (4)

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It is convenient to work in frequency units and then the ( ~oIoI)vycan be closely identified with the rotational constants. Following Kubota et al. [ 61, one can write the Kivelson-Wilson centrifugal distortion constants [ll] as

(2)

p the rotational constants, 2) corresponds to potential II of table Virrrbf ref. [ 7 1. Both the treatment of the rotational constants developed by Gwinn and coworkers [ 1,2] and that of Cresswell and -Mills [ 31 and Kubota et al. [ 61 for the centrifugal distortion constants depend on the expansion of the inverse inertial tensor (p) as a Taylor series in the reduced coordinate. The vibrational matrix elements of _Umay be written as

(PC@>,*= o~SSvv’$‘rUha{X)w,+2~~(~(L),,+

(2) proposed by

and r&s = rLXc#3 + 2rc#,,

((X,B=a,b,c).

(8)

In eqs. ( 5)-( 7) the 7”s represent the contributions of the other molecular vibrations to the centrifugal distortion constants. The 3-methylthietan molecule maintains its UCsymmetry plane during the ringpuckering vibration and therefore the “pas and “Pi are zero. The additional approximation has been made that the npL,care also zero. For 3-methyloxetan it has been estimated that the “pa may be approximately 10% of the “fib* [ 41. The experimentally determined Watson centrifugal distortion constants [ 121 for the A-reduced semirigid rotor Hamiltonian and an Y-axis representation are

AJ=-Qt7L5bb+5Lc,), AJK

(9)

(10)

=%(7~~b,bbh+5~~~=)--tr~b+7&aec+7bhcc),

&=-a(L,, -

(7bbbb-7~mc)

8 6 K -1 -

+7bbbb+7Lcc)

$(7inzbb+fiwc+756kc)

&=-ii

‘PW “A o~bb-“ka

18 May 1990

CHEMICAL PHYSICS LETTERS

Volume 168, number 6

(11)

,

(12)

,

7hbbb+

0 ok-“P*, pbb-

0 kc

2°k-o~bb-o~u,

*,

cc@2 >

, =bbcc

o&b-oficc

. >

(13)

The first step in calculating the centrifugal distortion constants is to determine the “,uu,,coefficients. This has been done by fitting the experimental rotational constants by least-squares to the equations (14) Inclusion of terms higher than n =2 did not give sig nificantly better fits and gave very heavy correlation between the “pu,,. The calculated rotational constants for the potential function of eq. (2) are given as assignment 1 in table 1 and the ‘paU,,are given in table 3. The calculated centrifugal distortion constants are given as assignment 1 in table 2. For states b and c the differences in the centrifugal distortion constants relative to state a are relatively well reproduced. For states d and e the computed values ap-

pear to be inverted compared to the experimental values. For state f the computed values (in kHz) for v= 5 of A,= 8.1 and AJK= - 89 are closer to the ei-:’ perimental values than those appropriate to v’$‘&” given in table 2. This apparent invei%iW of the’$$~ trifugal distortion constants suggests t&t-the asslgW ment of vibrational quantum numbers+& states & e,andfisv=4ford,v 3foreandv=5foffwith ,,=17cm-‘andA&= the energy separations cm-’ being approxim’f tely cor$F. At this point, it was decided to retu to the assignment of the farinfrared spectrum. far-infrared transitions a diagonal weighed least-squares fitting procedure [ 131 was adopted. vhe weighting scheme used was to give each transitiob an estimated error and then a.&@ equqto the r&iprocal of the square of this sch&e has &n adopted for two rea Can$nati et iI. [ 71 have noticed that t tiod$ quantum number far-infrared tra not @Ied very well. They attribute this tivelf: large differences in the rotational tween the initial and final states of these tran so that the peak of the far-infrared absorption & be somewhat different from the pure vibratio&l transition. Secondly, the centrifugal distortion constants for the u= 3 and v=4 states are very sensitive to A&, and by introducing this as an additional transition with small error it is possible to make fits with essentially fixed values of A.& At the end of each tit the rotational and centrifugal distortion con-

Table 3 The expansion coefficients “&& obtained by fitting the rotational constants of 3-methylthietan using (a) assignment I and the reduced , potential function eq. (2) and (b) assignment 2 and the reduced potential function of eq. ( 15) Assignment 2 (b )

Assignment 1 (a)

‘.uam(MHz) ‘k, (MHz) *k‘z (MHz) ua) (MHz) equatorial barrier (cm-‘) axial barrier (cm-‘) axial-equatorial energy difference (cm- ’ )

ff=a

cu=b

(YEC

a=a

a=b

ff=C-

8250.25 -398.21 - 13.74 27

2988.60 15.96 11.86 6 285 190

2487.38 97.67 22.14 11

8088.87 -395.11 7.20 9

3026.57 76.24 6.74 2 305 169

2541.49 98.68 14.79 2

95

‘{ :)+ h

I_

I36

a1Standard deviation of the least-squares tit.

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Volume 168,number6

CHEMICAL PHYSICSLETTERS

stants were predicted using the “p,, given as assignment 1 in table 3. As a starting point we returned to the assignment of the V= 1 sequence between 50 and 80 cm- * originally considered by Shaw et al. [ 141. These transitions were given an error of 1 cm-’ and AE4) was added to these with an error of 0.5 cm-‘. For AEQ3 in the range 5-25 cm-’ the calculated rotational constants were sufficiently close to the experimental values to indicate that the assignment V= 2 for b and U= 1 for c. The fits also predicted the values of the Av= 2 transitions for v> 6 given in ref. [ 7 ] and these were added to the fits with an error of 2.0 cm-‘. It was also noted that reasonable values for the centrifugal distortion constants for the v=3 and v=4 states required A& to be 15 cm-‘. With this value, good candidates for the low-v far-infrared transitions were indicated. These were included in the final fit with an error of 3.0 cm-‘. The final fit to the farinfrared spectrum is given in table 4 and the reduced Table4 Assigned far-infrared

transitions,

estimated

errors, and residuals

for the ring-puckeringvibration of 3-methylthietan lf’

V’

1

3 4 3 4 4 5 6 5 6 6 7 a 9 10 11 12 14 8 9 10 11 12 13

w& (cm)

17’) (cm)

d b, (cm)

110.3

3.0 3.0 3.0 3.0 0.5 3.0 3.0 3.0 1.0 1.0

1.1 1.3 0.6 3.4 -0.1 3.3 -0.8 1.7 0.8 - 1.6 1.3 0.4 0.3 0.2 0.2 0.1 0.2 -0.4 0.0 -0.1 -0.2 -0.4 0.3 0.0

0 1 1 2 3 2 3 3 4 4 5 6 7 8 9 10 11 13 6 7 8 9 10 11

I) Estimated error.

568

96.0 110.3 81.0 15.0 96.0 66.1 108.0 52.6 89.6 40.6 53.0 51.6 62.5 66.7 70.5 74.1 80.0 110.3 119.5 128.7 136.6 144.7 151.3 bJ w,,-o,,,.

1.0 1.0 1.0 1.0 1.0 I.0 1.0 1.0 3.0 2.0 2.0 2.0 2.0 2.0

18May 1990

potential function obtained from this assignment is V(X) =5.774(X-

12.514X+0.736X),

(15)

which is shown in fig. lb. The rotational constants were refitted using this potential function and the calculated rotational constants are given as assignment 2 in table 1. The “P~~ coefficients are given along with some details of the potential function as assignment 2 in table 3, and the calculated centrifugal distortion constants are given as assignment 2 in table 2. Although the potential function eq. (15) gives a better tit than eq. (2) to the rotational and centrifugal constants, some problems remain. There is still the problem of the large residuals for the low-v farinfrared transitions. A second problem is the disagreement between some of the calculated vibrational energy separations and those obtained from microwave relative intensity measurements. A third problem regards the relative intensities in the far-infrared spectrum. Some progress has been made in rationalizing these using a dipole-moment function obtained from the ,K~electric-dipole-moment components of states a and b but it is necessary to measure p(cfor more vibrational states. The present work shows that quartic centrifugal distortion constants can provide useful information about the relative energies of vibrational states when they are close in energy and there is a reasonably sized matrix element of X connecting them. This is the case here for v=3 and v=4 which are close to the top of the barrier. Although A&, is predicted to be 17 cm- ’ the v= 1 and v=2 states are localized in the equatorial and axial potential energy wells and the matrix element of X connecting them is vanishingly small. We would like to thank W. Caminati for clarifying some points about the microwave spectrum of 3methylthietan for us. We would like to thank the Rector and the University of Messina for the acquisition of an IBM PS/2 computer. We also thank

the Direcci6n General de Investigation Cientifica y TCcnica (DGICYT Grant PB87-0898), the Iberduero Company and the Italian Ministry of Education for financial support.

Volume 168, number 6

CHEMICAL PHYSICS LETTERS

References [ 1 ] S.I.Chan, J. Zinn, J. Fernandez and W.D. Gwinn, I. Chem. Phys. 33 (1960) 1643. [2] D.O. Harris, H.W. Harrington,A.C. Luntz and W.D. Gwinn, J. Chem. Phys. 44 (1966) 3457. [ 31 R.A. &swell and I.M. Mills, J. Mol. Spectry. 52 (1974) 392. [4] J.C. Lopez,A.G. Lessari, D.G. Lister, J.L Alonso, R.A. Shaw and H. Wieser, J. Chem. Phys., submitted for publication. [5] P.D. Mallinson and A.G. Robiette, 3. Mol. Spectry. 52 (1974) 413. [ 61 T. Kubota, K. Ueda, T. Tanaka and J. Laane, J. Mol. Spectry. 128 (1988) 250. [7] W. Caminati, A.C. Fantoni, R. Meyer, R.A. Shaw, T.L. Smithson and H. Wieser, J. Mol. Spectry. 127 ( 1988) 450.

18May 1990

[8] J.K.G. Watson, in: Vibrational spectra and structure, Vol. 6, ed. J.R. Durig (Elsevier, Amsterdam, 1977) ch. 1. [ 9 ] R. Meyer, J. Mol. Spectry. 76 ( 1979) 266. [lo] S.I. Chan and D. Stelman, J. Mol. Spectry. 10 ( 1963) 278. [ 111 D. Kivelson and E.B. Wilson Jr., J. Chem. Phys. 20 ( 1952) 1575. [ 121 W. Gordy and R.L. Cook, Microwave molecular spectra ( Wiley-Interscience, New York, 1985) ch. 8. [ 131 D.L. Albritton, A.L. Schmeltekopf and R.N. Zare, in: Molecular spectroscopy, modem research, Vol. 2, ed. K.N. Rao (Academic Press, New York, 1976) ch. 1. [ 141 R.A Shaw, T.L. Smithson and H. Wieser, J. Mol. Struct. 102 (1983) 199.

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