Journal of Molecular Structure (Theo&em), 257 (1992) 157-166 Elsevier Science Publishers B.V., Amsterdam

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Comparative ab initio study of ( CH3) &HX (X = F, Cl) and (CH&CX,-type molecules (X = H, F, Cl)

Michael Meyer

Abteilung Chemische Physik, Institut fiir Physikulische Chemie, Uniuersitit Kiel, Olshausenstr. 40-60, D-2300 Kiel (Germany)

(Received 24 July 1991)

Abstract

Geometry optimizations by self-consistent field (SCF) computations are presented for (CH3)&Hz, (CH&CHF, (CH3)&F2, (CH1)$HC1 and (CH&CC12. The dipole and molecular quadrupole moments have been calculated for propane and the fluorine species and the barrier to methyl internal rotation has been investigated.

INTRODUCTION

Various spectroscopic studies of molecular structures and barriers to methyl internal rotation of propane [l-3], 2-fluoropropane [ 4-71, 2,2difluoropro- pane [8] and 2-chloropropane [9,10] have been reported. Ab initio studies have been carried out for propane [ 11,121 and 2-fluoropropane [ 7,121.

In the present work comparative ab initio calculations were performed to investigate the effect of fluorine and chlorine substitution of the hydrogen at the secondary carbon atom of propane. The optimized structural parameters are discussed in relation to the corresponding experimental values obtained by microwave (MW) spectroscopy and to those of related molecules.

The dipole moments, molecular quadrupole moments and methyl internal rotation parameters of propane, %fluoropropane and 2,%difluoropropane were computed, since these calculations provide information in addition to the re- sults obtained by MW studies.

METHOD

The calculations were carried out with the GAUSSIAN 66 program [ 131. The split valence basis sets with polarization functions 4-31G* [ 141 and 6-31G**

Correspondence to: Dr. M. Meyer, Abteilung Chemische Physik, Institut fir Physikalische Chemie, Universitit Kiel, Olshausenstr. 40-60, D-2300 Kiel, Germany.

0166-1260/92/$05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.

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[ 151 were used for structure optimizations throughout. The single point cal- culations were carried out using the 6-311G** basis set [ 161 and a multiple polarization basis set [ 171 at the 6-31G** optimized structure. In order to com- pare the calculated properties with MW spectroscopic data the calculated properties refer to the principal axis system of inertia of the corresponding molecules. In Figs. 1 and 2 the orientation of this coordinate system is depicted for propane and 2-fluoropropane. In the case of molecules with C,, symmetry, (CH,),CX,, these coordinate systems coincide with the principal axis systems of the molecular quadrupole moment tensors.

Fig. 1. Projection of the structure of propane on the ac plane of the principal axis system of inertia.

Fig. 2. Projection of the structure of 2-fluoropropane on the ac plane. The hydrogen atom located at the trans position with respect to the fluorine atom is called He The atom H, is located at the trans position with respect to the other methyl group.

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RESULTS AND DISCUSSION

Molecular structures

The optimized structural parameters are listed in Tables 1 and 2. The des- ignation of the hydrogen atoms is explained in Figs. 1 and 2 for propane and 2-fluoropropane respectively. The corresponding Hartree-Fock energies are listed in Table 3. The differences in the structural parameters obtained with the 4-31G* and 6-31G** basis sets are generally small. Thus the 4-31G* param- eters are given for the (CH,),CX, type molecules only. This basis set leads to a slight reduction in the bond lengths compared to those obtained with the 6- 31G** basis set. The calculated structure of 2fluoropropane is close to the one obtained by Durig and co-workers [ 71 with the 6-31G* basis set.

The ab initio calculations predict an increase in the CCC bond angle with halide substitution at the secondary carbon atom of propane. The effect of fluorine substitution is stronger than that of chlorine substitution. The de- crease in the CC bond length caused by substitution is also apparent in the case of ethane and the ethyl halides (see Table 4). The substitution affects the methyl groups via a shortening of the C-H bond lengths. A small tilt of the methyl groups is predicted since the angle ( L i,i’ ) of the normal vectors i and i’ perpendicular to the planes of the three hydrogen atoms of each methyl group differs from the CCC angle. For propane and the chlorine species, L i,i’

TABLE I

Structural parameters of propane, 2,2_difluoropropane and 2,2_dichloropropane

Parameter” (CH,LCH, (CH&CFz (CH&CClz

4-31G* 6-31G** 4-31G* 6-31G** 4-31G* 6-31G**

c-c 1.526 1.528 1.507 1.508 1.518 1.521 c-x 1.086 1.088 1.353 1.355 1.794 1.799 C-H? 1.085 1.086 1.082 1.083 1.080 1.081 C-Hob 1.086 1.087 1.082 1.083 1.083 1.084 LCCC 112.8 112.9 116.0 116.2 113.2 113.1 L XCX’ 106.3 106.3 106.0 105.9 108.5 108.3 L CCHb 111.3 111.3 109.0 109.1 110.6 110.8 L CCHob 111.1 111.1 110.3 110.2 109.5 109.4 r(H,CCC)” 59.9 59.9 60.3 60.3 59.8 59.8 L i,i’ d 112.5 112.6 117.7 117.4 111.8 111.3

“Bond lengths in Zngstrbns and angles in degrees. bSee Fig. 1 for designation of the hydrogen atoms. ‘Dihedral angle. dAngle between the normal vectors perpendicular to the planes of the three hydrogen atoms of each methyl group.

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TABLE 2

Structural parameters of Muoropropane and 2-chloropropat&

Paramete? SH& CHF (CH,), CHCf

C-C c-x C-H,’ C-HZ c-w C-Hi” LCCC LXCH L CCH, LCCH, L CCHi m&CC) T(H,CCC) ?(HiCCC) Li,i’

1,615 1.381 1.085 1.084 1.085 1.085

114.0 106.5 110.3 110.7 110.4

- 177.3 62.7

-57.5 114.3

I.520 1.816 1,081 1.083 1.086 1.084

113.4 104.2 111.2 lXO.3 110.9

- 179.8 60.6

-59.0 111.9

%31G** basis set. bBond lengths in &q&r&m and angles in degrees. ‘See Fig. 2 for the designation of the hydrogen atam.

TABLE 3

Energies of (CH,)&HX and (CH,),CXZ molecules

E (hartres)

6-31G** 4-31iT

(CJW&H~ - 118.27610 - 118.14817 (‘X,)&HP - 217.13027 -216.91%2 (CH,),C% -315.99903 - 315.69047 (CH&CHCI -577.18032 -576.59734 fCH,)@.% - f036*07324 - 1035.677~3

is smaller than L CCC, whereas for the fluorine species the opposite behaviour is predicted. The smaller angles L i,i’ compared to L CCC of propane [l) and ~-~hloropropane f IS] are in agreement with the corresponding s~b~~~tion structures and an analysis of the torsional fine structure in the MW spectrum of propane ]2]. Nowever, exact theoretical and experimental determinations of these tilt angles seem difficult since the deviations from the corresponding CCC bond angles are small.

Although theory attempts to predict the equilibrium geometry, and compar- isons with known equilibrium structures are desirable, the lack of experimental

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TABLE 4

Structural parameters from ab initio calculations and microwave spectroscopy

6-31G** r,

C-F bond length {A) CH3F 1.365 1.383a CH&&F 1.381 1.387(3)b (CH&CHF 1.381 1.403(20)b

C-Cl bond ~~~~ (A) CH,Cl 1.764 1.78131C CH,CH,Cl 1.809 1.789( l)b (CH&CHCl 1.816 1.7973 ( 18)d

C-C bond length (A) WM&H, 1.528 1.526(2)’ CH&H, 1.527 1.52613(8)f (CH&CHCI 1.520 1.5231(21)d CH&H&l 1.520 1.520( l)b (CWJ&HF 1.515 1.5153b*g CH,CH2F 1.511 1.512(2)b

CCC bond angle fdeg) (CHi3MX 112.9 112.4(2)‘_ OXs)sCHF 114.0 113.55(33)b (CH&CHCl 113.4 112.62(26)d

*Ref. 20. bRef. 21. ‘Ref. 22. dR.ef. 18, column (e) of Table XIV. “Ref. 1. %f. 23. ksumed.

structures for these molecules forces one to use effective or substi~tion struc- tures from MY spectroscopy. In Table 4 a compilation of structural parame- ters from ab initio calculations and of available substitution structures ( rS) is given. The differences between both types of structure are systematic rather than random. The optimized bond lengths of CC single bonds agree with the experimental ones, within the errors given in parentheses, whereas the calcu- lated CF bonds are shorter and CC1 bonds are longer than the experimental ones. The discrepancies may arise from deficiencies in the basis sets and ne- glect of electron correlation in the theoretical structure determination and an incomplete compensation of vibrational effects in the substitution structure treatment. The systematic differences offer the possibili~ of scaling the com- puted structural parameters [ 191.

The ab initio calculations may be used to support the experimental deter- mination of structures, For example, the structure of 2-fluoropropane is diffi- cult to evaluate by the substitution method since no stable isotope of fluorine exists and several atoms are close to the .principal axes. The experimental

162

structure is based on an assumed CC bond length of 1.5153 A [6]. This as- sumption has now been confirmed by the ab initio result of 1.515 A.

The calculated dipole moments listed in Table 5 are close to the experimen- tal values from Stark-effect measurements. Usually these experiments yield only the absolute value of the dipole moment and its components and provide no information on the orientation and direction of the dipole moment vector.

In the case of propane the negative pole is directed towards the methyl groups. Single point calculations of the dipole moment with larger basis sets improve the calculated dipole moment. The 6-311G** basis leads to 0.075 D and a com- putation with the 6-311G (3d,2p) basis gives 0.080 D.

For 2fluoropropane, the components 1 pb I= 1.850 D and 1 pc I=O.558 D re- sult from the ab initio cessations with the 6-31G** basis. The experimental valuesare fp*tb/ =1.880(l) Dand ]JJ~] =0.547(l) D [4].

Second moments and molecular quudrupole moments

The results of the lactations of the second electronic moments and the molecular quadrupole moments are listed in Table 6. The anisotropies in the second moments of the electronic coordinates of 2fluoropropane are in good agreement with the experimental values given in Table 7. The agreement of the molecular quadrupole moments is not perfect for this molecule. A 6-311G** single point calculation based on the structure listed in Table 2 yields no fur- ther ~p~vement. It should be pointed out that two sets of quadrupole mo- ments were compatible with the measured spectra and the calculations confirm the choice of B&tcher et al. [ 51. Contrary to experiment it is possible to com- pute the elements of the molecular quadrupole moment tensor in its principal axis system since the off-diagonal element Qbc in the principal axis system of inertia can be determined. The components of the quadrupole moment tensor

TABLE 5

Dipole moments

Y(D)

4-31G* 6-31G** Mw

(C&)&Hz 0.062 0.060 0.083( 1)’ UXWsCHF 1.905 1.932 1.958(1P (C&)&F, 2.272 2.331 2.40(2)’

“Ref. 1. Qef. 4. “Ref. 8.

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TABLE 6

Second momenta of the electronic coordinates and molecular quadrupole momenta

( lo21 > (AZ) <lb21> (AZ) < lc21 > G2”, Q, ( 1O-26 esu cm2) Qbb (10-2sesucm2) Q,, ( 1O-26 esu cm2) Qbc ( 1O-26 esu cm2)

(CH,MW

4-31G* 6-31G**

40.3 40.4 14.0 14.0 9.0 9.1

-0.55 -0.53 -0.01 -0.03

0.56 0.56 - -

(CHd&HF (CHAP,

4-31G* 6-31G** 4-31G* 6-31G**

40.9 40.6 41.4 41.4 33.2 33.3 34.2 34.2 11.4 11.4 30.7 30.7 1.22 1.32 3.20 3.38

-2.76 - 2.64 -0.19 -0.26 1.55 1.52 -3.10 -3.12

-0.32 -0.35 -

TABLE 7

Aniaotropies of the second momenta of the electronic coordinates and molecular quadrupole mo- menta from Zeeman-effect studies and ab initio calculations

( la2-b21) (k) ( IV-C21 ) (At, ( Ic2-a21) (P) Q,, ( 1O-26 esu cm2) Qab ( 10vz6 esu cm2) Q,, (1O-26 esu cm2) Qbe ( 1O-26 esu cm2)

“Ref. 24. bRef. 5.

6-31G** MW” 6-31G** MWb

26.4 7.3 6.2(11) 4.9 21.9 22.3(11)

-31.3 -29.2 -28.5(11) -0.53 -0.32(44) 1.32 2.20(28) -0.03 -0.25(50) -2.64 -2.83(24)

0.56 0.56(36) 1.52 0.63(47) -0.35

in its principal axis system are Q,= - 2.87 X 1O-26 esu cm2, Qw= 1.55 X lo-26

esu cm2 and Q LZ = Q,, = 1.32 x 1O-26 esu cm2. The angle of the x and b axis is 4.5”.

Internal rotation

The barrier height to internal rotation of one methyl group was calculated by a method similar to that of Aljibury et al. [ 121. The torsional potential function defined in eqn. (1) corresponds to the one that is commonly used in MW studies of molecules with two methyl groups:

164

Vt(y1,cc2j = (l/2) V, (1-cos3ai) + (l/2) V, (1-cos6cr,)

+ (l/2) V, (l-cos3az)+ (l/2) V, (l-cosfio+f 0)

+ V,, (cos3a, cos3tu, - 1) + Vi, sin3tu, sin3lr, + __.

The torsional angle cxl referring to one methyl group of the (CHB)&X2 type molecules was monitored by the dihedral angle of the planes HiCC and CCC. Hi is the in-plane hydrogen atom of the equilibrium structure with a1 = rr, = 0 ‘. First, this structure was optimixed employing the 4-31G* basis set. The cor- responding energies E(O”,O” ) are given in Table 3. Then the o~t~~tio~ were repeated at different fixed values of ty,. The torsional angle ozz of the second methyl group was fixed at zero. In this case the interaction terms VIZ and Vl,, of the torsional potential function do not contribute to the potential. Fmahy the barrier parameters V, and Ve were fitted to the energy increments ~~=~~~~*6O~-~~O*,O~~ lis~d~Table6. The~o~side~tionoft~rsion~~- gles in an interval of 120 * is sufficient, provided that the internal rotors possess a threefold symmetry. In consequence of the C,, symmetry of the ( CH3)&X, molecules, the interval is limited to 60” because V( lxl,Oo ) = V( 120’ - cyl,Oo ) .

The results are listed in Table 9, The errors given in parentheses represent only the standard errors of the least-squares fit. V, is increased by the fluorine substitutions and V, is of the expected order of ma~tude* The ex~rimen~ results are slightly smaller than the calculated parameters in Table 9. The torsional fine structure in the MW spectrum of 2,2difluoropropane [8] has not been resolved to date. Comparing experimental and theoretical parameters of the torsional potential function one should consider that the ab initio and the spectroscopic models are different. The analysis of the experimental data is usually based on a model with a rigid frame and two rigidly rotating tops of threefold symmetry. In the quantum chemical calculations a flexible model

TABLE8

Energy incrementr

a1

(deg)

-15 -30 -45 -60 -75 -90

- 105

CL!? (kcal mol-L)

(CH,), CHz

0.467 lx30 2.643 3.368

(C& MXF (CHd&Fz

0.491 0.488 1.727 1.706 3.015 2.981 3.556 3.513 2.996 1.709 0.480

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TABLE 9

Parameters of the torsional potential function

Basis set/ V, method (kcal mol-‘)

V, (keel mol-‘)

(CW,CHz 4-31G* 3.366(2) -0.054(3) MW 3.166(27)”

(CW,CHF 4-31G* 3.558(7) -0.063(7) 3.325 (27)b

(CHd&Fz 4-31G* 3.516(4) -0.050(5)

“Ref. 2. Qef. 4.

was used. The methyl groups do not show an exact threefold symmetry, and an arbitrarily selected hydrogen atom was used to monitor the torsional angles. Furthermore, the barrier parameter V, of two-top molecules is correlated with the potential coupling term VI,. Since it is not possible to determine VI, from the MW spectra of low torsional states, V, should be regarded as an effective value. In principle it is possible to derive VI, and Vi, from ab initio calcula- tions. These parameters are expected to be one order of magnitude smaller than the leading term. They have been neglected in this computational study in order to be consistent with the MW study. Furthermore, the calculation of the smaller parameters is expected to be less accurate. V, was included in the fit because the standard deviations of the fits are reduced significantly.

CONCLUSION

The ab initio calculations are of great value for MW spectroscopic studies. Amongst structural aspects they may be used to support Zeeman-effect studies of molecules possessing small quadrupole moments if an accurate experimen- tal determination is difficult and if it is impossible to derive the elements in the principal axis system from the experiment. The calculation of internal rotation barriers facilitates the torsional fine structure analysis since the mag- nitude of the splittings can be estimated if V, has been calculated.

ACKNOWLEDGEMENTS

Financial support by the Deutsche Forschungsgemeinschaft is gratefully ac- knowledged. The calculations were carried out at the computer centre of the University of Kiel. I should like to thank Professor Dr. H. Dreizler for critically

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reading the manuscript and members of the Institut fiir Physikalische Chemie for interesting discussions.

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