Determination of the electric dipole moment by microwave spectroscopy in complicated cases using different methods

JOURNAL OF MOLECULAR SPECTROSCOPY 120,

101-109

(1986)

Determination of the Electric Dipole Moment by Microwave Spectroscopy in Complicated Cases Using Different Methods FLAVIO SCAPPINI AND ADOLFO C. FANTONI’ Istitutodi SpettroscopiaMolecolare del CNR, Via De’ Castagnoli1. 40126 Bologna, Italy AND WALTHER CAMINATI Istitutodi Chimica Fisica e Spettroscopia,Universitddi Bologna, Viale Risorgimento4, 40136 Bologna, ItaIy Three methods are discussed to determine the electric dipole moment of asymmetric top molecules in those cases where the conventional second order Stark pattern is difficult to identify, because of spectral complexity. The methods are applied to a test molecule and to a number of mOleah whose dipole moments were not previousIy determined. Q 1986 ~cadnnic Pms, Inc. 1. INTRODUCTION

The determination of the electric dipole moment of asymmetric top molecules by microwave spectroscopy is usually done by measuring the second order Stark shifts of selected rotational transitions lines. The “selection” of the lines is based on the following requirements, (i) the line corresponds to a low or rather low J transition, (ii) there are no other neighbouring lines of comparable intensity, (iii) the intensity of the line is such that the M-components give rise to a measurable pattern, and (iv) the M-components patterns can be resolved into its component lines. When these conditions are met, measurements of the Stark shifts of the M-components with respect to the unperturbed line at a given electric field provide determinations of the dipole moments accurate to a few parts per thousand. It may happen, however, that some or all of these requirements are not fulfilled. This is sometimes the case for medium size asymmetric rotor molecules exhibiting low energy vibrations, such as methyl top torsion, ring puckering, skeletal torsions, etc. The microwave spectrum then looks very dense of lines arising from the ground state but also from the lowest vibrational states with almost equal intensity (the energy of these vibrational states is typically ~100 cm-‘). Moreover, the low J transitions may fall into a too low frequency region to be accessible with standard microwave instrumentation or, even if the region is accessible, they may have small intensities. Under the above circumstances dipole moment determinations are not feasible. On i Permanent address: Departamento de Fisica, Universidad National de La Plata, cc. 67 1900 La Plats, Argentina. 101

0022-2852186 $3.00 Copyright 0 I986 by Academic Ress Inc. All rightsof nproduction in any form mered.

102

SCAPPINI, FANTONI, AND CAMINATI

the other hand, such determinations are often of importance as, for instance, when the energies of different molecular conformations are to be calculated from line intensity measurements (2). The present study was motivated in the course of recent microwave investigations on a number of molecules with large amplitude vibrations (2-5). In fact, the conventional Stark method based on the second order shifts of individual M-components (from now on the method will be referred to as “conventional”) failed because of the above mentioned unfavorable circumstances. Thus, three different methods were thought of as alternatives to the conventional Stark method. The first is the radiofrequency-microwave double resonance (RFMWDR) method in the presence of a dc electric field to split the M-degeneracy of K-doublets and to produce the coherent effect only in the microwave Stark transition involved in the three-level system. The second consists of using such a low Stark field that only transitions connecting A4 sublevels from K-doublets are modulated. The third method consists of applying the Stark field to transitions whose M-components are almost equally sensitive to the electric modulation and therefore tend to pile up. This last method was already applied in preceding cases (6-8). The discussion of the methods and their application to determine electric dipole moments of molecules in cases where they could not be otherwise obtained will form the argument of the present work. 2. THEORETICAL CONSIDERATIONS

The particular methods used in this work to obtain the electric dipole moment will be briefly reviewed in the following. A. Radiofrequency-Microwave Double Resonance Since the first experiment by Autler and Townes (9) and the successive one by Shimoda (10) on OCS, radiofrequency-microwave double resonance was definitely established as a spectroscopic technique in the analysis of microwave spectra by Wodarczyk and Wilson (1 I). In the last experimental configuration a radiofrequency field is applied to the septum of a Stark cell, where a microwave field propagates as well. In the case of asymmetric rotors the radiofrequency pumps transitions between Kdoublets, thus producing a coherent splitting in the microwave signal transitions. In fact, assuming a pressure broadening parameter of 20 MHz/Torr and a typical rotational transition moment of 1 D, saturation at the working pressure of -20 mTorr is achieved already at a radiofrequency power density of a few tens of mW/cm’, which is easily obtainable. The high selectivity of the double resonance technique clears the spectrum of all but the lines arising from transitions within the three level scheme where the K-doublet is pumped. If a dc electric field is applied to the molecule then the microwave transitions connecting M-split levels can be individually monitored as double resonance signals. Due to the “dynamic Stark effect” the other off-resonance M-components still produce “first derivative” signals, but they are the weaker the further the pump is from resonance.

ELECTRIC DIPOLE MOMENT DETERMINATIONS

103

With reference to Fig. 1 and making use of the theory of the “two nearby levels” (12) the Stark components of the rotational transitions J + 1 + J have frequencies: 1

V24 = k [(VL

+

$4)

-

(v?,’

+

4p122f2)“2

+

(Vi:

+

4p34*~*)“*]

(1)

where t is the applied electric field, $s are the unperturbed transition frequencies, ~12and 1134are the transition moments of the 2 + 1 and 4 + 3 transition, respectively. For slightly asymmetric rotors the direct K-doubling transition moments are quite accurately given by those for symmetric rotors:

kMK

(2)

“= J(J+ 1)

where K is the quantum number for the limiting symmetric top, that is, K, or Kc depending on whether the limit is prolate or oblate, and pg is the electric dipole moment component along the principal axis a or c, respectively. Again with reference to Fig. 1, the pumping frequencies corresponding to the J + J transitions in the presence of the electric field t are V12= (Z@+ 4&2*C*)“* ~34 =

(I&?

+

(3)

+.LQ*E~)“*.

The case of an accidentally degenerate pair of levels falls also in this working scheme, provided they are connected by a nonvanishing matrix element, which has to be calculated according to &=&2J(J+

1)

l(J, d%&

+I

(4)

where g = a, b, c.

K-doubling

K-doubling

FIG. 1. Typical four level system formed by two, J and J + 1, K-doublets. For the sake of simplicity the levels are labeled by numbers, which are not quantum numbers. v13and vz4are signal transitions, while viz and vx are pump transitions. The levels spacing is not to scale.

104

SCAPPINI, FANTONI,

AND CAMINATI

Thus the RFMWDR method provides the determination of the pn and pc dipole moment components by using K-doublets of a- or c-type. The pb component can only be determined in favorable cases of accidental b-type degeneracies. In principle the RFMWDR technique can be extended to microwave-microwave double resonance by using as pump a microwave transition and changing the expressions (1) and (3) into the proper second order perturbation expressions for an asymmetric rotor. On the other hand the RFMWDR technique is very simple from the experimental point of view and in most cases the necessary instrumentation is already part of the existing microwave spectrometer facilities.

B. Stark E#ect of K-Doublets By the application of a low square wave modulated electric field (lo-200 V/cm) to an asymmetric top molecule, with typical values of p. or pclc1: 1 D, the most likely transitions to be modulated are those connecting M-sublevels of different K-doublets as those shown in Fig. 1. Other transitions not connecting such nearly degenerate levels are not modulated and the resulting Stark pattern is very simplified. The frequencies of the M-component lines can be accounted for by expressions (1). Accidentally degenerate levels produce a low field modulated Stark pattern as well and can be included in the above scheme. As already discussed in the case of the RFMWDR method, the Stark effect of Kdoublets provides the determination of the pa and pclccomponents, while the &, component can only be determined using b-type accidental degeneracies.

C. Stark EfSectof Piling-Up M-Components After Golden and Wilson (23) the Stark shift of an M-component of a rotational transition in an asymmetric rotor when no degeneracies are present is given by Au,,,= c (AA, + AB,M2)&2 g

(5)

where g = a, b, c, and A and B are coefficients which depend on the molecular geometry and on the rotational quantum numbers, pg are the electric dipole moment components and Eis the applied electric field. If it happens that for a transition 1AB, 14 1AA, 1then the Stark shift is the same or almost the same for all the M-components. This means that the M-components pile up to form one single Stark lobe which moves with the electric field according to expression (5). Particularly when the identification of the Stark pattern in a crowded spectrum presents problems, the piling up of the M-components is a lucky event which produces in general a measurable signal, making the dipole moment determination still possible. 3. EXPERIMENTAL

DETAILS

2-Methoxyethanol was purchased from Aldrich Germany, N-methyl ethylendiamine from Aldrich, pyrrolidine from Carlo Erba, Italy, chlorocyclohexane from FIuka, Switzerland, and carbonyl sulfide from Matheson. All compounds were used without further purification.

ELECTRIC DIPOLE MOMENT DETERMINATIONS

105

Microwave spectra were obtained at about -20°C and at about 20 mTorr (=2.66 Pa), with a computercontrolled Hewlett-Packard Stark modulation spectrometer using frequency stabilized BWO’s as radiation sources in the range 8-40 GHz. Stark measurements on K-doublets (KS-method) were performed superimposing into the cell a square wave voltage to a dc voltage in order to split the Mdegeneracy and at the same time to eliminate the zero field line. The electric field was calibrated using the 2 + 1 transition of OCS with CL(OCS) taken as 0.71521 D (14). For the transition frequencies other than those of OCS the accuracy of the measurements is on the order of 100 kHz. Stark measurements on lines with piling up M-components (PS-method) were done using the same experimental technique as above. Radiofrequency-microwave double resonance experiments (DR-method) were done by application of a radiofrequency field to the cell and at the same time a dc field. Care was taken to prevent the dc voltage from the dc power supply going into the RF generator (O-100 MHz) by interposing in between a capacitance of 0.003 pF. Both the dc field and the 100% amplitude modulated radiofrequency field were stepwise varied in the search of the pump resonance while sweeping over the microwave signal frequency. The maximum applied radiofrequency power density was about 200 mW/ cm’. The poor design of the Stark cell, as the radiofrequency propagation is concerned, resulted in an unmatched system and in a rather nonuniform radiofrequency field in the absorption cell. The frequency measurements are believed to be accurate to 100 kHz. 4. RESULTS AND DISCUSSION

The methods described in Section 2 were applied to the following asymmetric-top molecules: 2-methoxyethanol as a test molecule, N-methyl ethylendiamine, pyrrolidine, and chlorocyclohexane. The results are shown in Table I, where for each molecule the methods which were successfully used are indicated and the obtained dipole moment components values shown. The reported experimental Stark shifts are the largest measured and the calculated ones are according to the expressions (1) in the case of DR- or KS-method, while in the case of the PS-method they follow from the second order perturbation expression (5). The derived values of the dipole moment components were least-squares fitted to all the observed Stark shifts. In the following the different molecules studied will be considered and individually discussed.

A. 2-Methoxyethanol (Test Molecule) This molecule was studied in 1972 by Buckley and Brochu (15) and the three dipole moment components were evaluated by measuring the second order Stark effect of a few rotational lines in the ground state of the gauche-gauche isomer. This same molecule was taken in the present work as a test for the accuracy of the proposed methods to reproduce the values of the dipole moment components. From the DR-method a value of FL,= 2.015(27) D is obtained, which is in good agreement with the previously obtained one, pa = 2.03(2) D. Furthermore the P&method was applied to three transitions having lAB,I 6 lAA,I, as shown in Table II, and, by fixing pa = 2.015 D, the

106

SCAPPINI, FANTONI, AND CAMINATI TABLE I Stark Effect and Dipole Moment Components for the Different Molecules Taken into Consideration in the Present Work

MOLECULE

TRANSITION

METHOD

INla)

DR

Z-Methoxyethanol

1

DIP. MOM.

Avcalc(MH~)

3.07

pa=

3.19

(D)

2.015(27)

-7.02

-7.43

ua = 2.015 b,

1309

-5.19

-5.18

935

-7.42

-7.73

= 1.014(144) 'b uc = 0.511(285)

1

119.4

-3.66

-3.96

uc = 0.643(7)

2

95.7

-8.31

-8.03

1

119.4

3.91

3.96

2

73.7

5.87

5.55

1

113.0

-3.70

-3.79

1

113.0

3.96

3.96

KS

1

285.1

3.41

3.31

DR

1

181.0

1.79

1.63

2

151.0

3.63

3.68

3

74.0

2.20

2.31

1

133.5

-5.83

-5.88

KS

DR

Chlorocyclohexane

31.2

AY~~.(MHz)

1289

PS

Pyrrolidine

&W/cm)

UC=

0.661(8)

UC-

1.082(14)

Axial

KS

Chlorocyclohexane

2945

-3.36

-3.67

Equatorial

2003

-2.24

-2.12

1

N-Methylethylendiamine

2945

6.96

6.98

3887

-4.10

-4.04

2.49

2.50

2966

-15.51

-15.88

1336

13.15

12.67

893

6.44

6.36

1601

-10.36

-10.52

70.5

PC

- 1.094(32)

“a = 1.570(16) = 2.411(37) ;: = 0.37(28)

%=

1.670(14)

(T2g

conformer)

ua 'lb UC

= 1.670 ') = 0.751(78) = 0.596(90)

Note. The methods used, indicated by their initials, are discussed in the text. The Stark shift reported in column VI is the maximum observed. “The value of [MI is not indicated in the case of the PS method as the various Stark lobes almost superimpose. The quoted errorsin the dipole moment values take into consideration their spread. b,Fixed value.

TABLE II Stark Coefficients (Hz - V-’ - cm2 - De2) for the Transitions Used in the PS-Method Applied to 2-Methoxyethanol Transition

6

5 0,s

A%

ABa

**b

ABh

A%

ABc

-0.1315

-0.0042

-3.6047

0.3754

-3.9049

1.0730

71.6 + 61,s

-0.0638

-0.0060

-2.1080

0.0107

-2.2820

0.0846

8 0.8 f 71,7

-0.0817

0.0157

-6.8958

0.0895

-5.4426

-0.5800

1.1

+

*)The fact that IA&l is not much larger than IA&I is immaterial since pc N 0 D.

a)

ELECTRIC DIPOLE MOMENT DETERMINATIONS

107

values of pb and pe were reproduced within the experimental errors. In Fig. 2 a typical piling up of the Stark components is shown for the 71,6 + 61,5transition at different electric fields. In this case the broadening of the Stark lobe due to the M-components distribution is almost negligible up to the measured field, giving clear evidence for their superposition. B. Pyrrolidine The microwave spectrum of pyrrolidine has been recently investigated by Caminati et al. (2), who reported that the bent axial conformation is the most stable. However no dipole moment determination was done because of spectral complexity. We selected the 313+ 2i2 and 303* 202transitions, involving two c-type K-doublets. Both the KS- and the DR-method were applied. In the latter method the 2,~ + 202 transition was pumped starting from the zero field frequency u” = 6.4 MHz. The measurements yielded the pc component of the dipole moment, as reported in Table I. The values obtained by the two methods agree within two standard errors. C. Chlorocyclohexane Chlorocyclohexane was studied by Damiani and Ferretti (3) and by Caminati et al. (4). The first microwave investigation brought to the assignment of the spectrum of the equatorial conformer, while the second to that of the axial conformer and to the analysis of the conformational equilibrium. Since no dipole moment determination could be done, line relative intensity measurements had to be combined with assumed values of the dipole moment components to calculate the conformational energy.

;il--_M 0

2

4

6

8

0 MHz

2

4

6

8

10

nG. 2. Stark effect of the 71,6+ 61,5transition of 2-methoxyethanol (v” = 37356.82 MHz) showing the piling up of the M-components. In order to have a comparison between the FWHM of the unperturbed line (6 = 0) and the M-components Stark lobe (c Z 0) only a zero based square wave voltage was used (without any superimposed dc voltage), which made it possible the observation of both the unperturbed line (upward) and the Stark lobe (downward). (a) T = -2O”C, p = 10 mTorr, RC = 0.1 set, c = 624 V/cm; (b) same as (a), with c = 835 V/cm; (c) same as (a), with c = 1037 V/cm; (d) same as (a), with t = 1433 V/cm.

108

SCAPPINI, FANTONI, AND CAMINATI

Thus, the equatorial form resulted to be more stable than the axial one by 0.51 + 0.15 kcal/mole. In the present investigation we succeeded in determining the pa and pc components for both the axial and the equatorial isomers, as shown in Table I. Using the presently determined values of pCLa (axial) = 1.570( 16) D and pa (equatorial) = 2.41 l(37) D the corrected conformational energy results A,!& = EQO(axial) - EO,O (equatorial) = 0.42 f 0.10 kcal/mole, which still is in agreement with the previously obtained value within the quoted uncertainty. D. N-Methyl Ethylendiamine N-Methyl ethylendiamine has been recently investigated by Caminati et al. (5) and the microwave spectra of two conformers assigned (they are called T 1 and T2g conformers). However, the dipole moment of the T2g could not be determined using the conventional Stark method. In the present work use was made of the double resonance technique, where the IMI = 1 component of the 52.4+ 4*,s transition was monitored at different electric fields while the IMI = 1 transition of the 42,s * 42,~or 5~,~+ 52.3 K-doublet was pumped. The piling up method was also applied to four transitions and by fixing pa, otherwise undetermined, to the value obtained by the DR-method, the values of ,.&b and pc were calculated. The results are shown in Table I. 5. CONCLUSIONS

To overcome the difficulties which sometimes prevent the determination of the electric dipole moment of an asymmetric rotor by using the conventional Stark technique three alternative methods have been proposed. They have been successfully applied to a number of molecules, whose dipole moment could not be previously determined. Whenever possible more than one method has been used for each molecule in order to check the consistency of the results and/or to obtain additional pieces of information. In fact, the values for the same dipole moment component obtained from different methods applied on the same molecule are always consistent within one or two quoted standard errors. Furthermore, the combination of different methods made it possible for all the molecules, except pyrrolidine, to determine the values of all the dipole moment components. The present work shows that the proposed methods lend themselves to complement the conventional Stark determinations of dipole moment in asymmetric rotors, providing both accuracy and ease of application. ACKNOWLEDGMENTS We like to thank Dr. R. Danieli and Mr. R. Pezzoli for instrumental assistance. One of us (A.C.F.) wants to acknowledge the CONICET of Argentina for a fellowship. RECEIVED:

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ELECTRIC DIPOLE MOMENT DETERMINATIONS

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