Microwave spectrum, r0 structure, barriers to internal rotation and ab initio calculations of gauche-1,1-difluoropropane

Journal of Molecular Structure 742 (2005) 191–198 www.elsevier.com/locate/molstruc

Microwave spectrum, r0 structure, barriers to internal rotation and ab initio calculations of gauche-1,1-difluoropropane James R. Duriga,*, Chao Zhenga, Gamil A. Guirgisb, Hossein Nanaiec a

Department of Chemistry, University of Missouri-Kansas City, Kansas City, MO 64110-2499, USA b Department of Chemistry and Biochemistry, College of Charleston, Charleston, SC 29424, USA c Department of Chemistry and Biochemistry, Claflin University, Orangeburg, SC 29115, USA Received 2 December 2004; revised 2 December 2004; accepted 3 December 2004 Available online 19 February 2005

Dedicated to Walter J. Lafferty, an excellent scientist and wonderful human being who was my mentor on arrival at M.I.T. in 1958 and the scientist who introduced me to microwave spectroscopy during my first sabbatical at the Bureau of Standards (NIST) in 1968

Abstract 13 12 12 The microwave spectra of four isotopomers, CH3CH12 2 CHF2, CH3CH2 CHF2, CD3CH2 CHF2 and CD3CD2 CHF2, of gauche-1,1difluoropropane, in the ground vibrational state were recorded and assigned. From the measured frequencies for the R and Q branches of the a-, b- and c-type transitions, accurate values for the rotational constants were obtained along with values for DJ, DJK, dJ and DK. The dipole moment components were evaluated from the measurements of the Stark effects of the ground state rotational transitions and the determined values are: jmajZ2.044(3), jmbjZ0.851(5), jmcjZ0.711(35) and jmtotjZ2.326(3) D. Ab initio molecular orbital calculations have been carried out with valence electron correlation by the perturbation method to second-order with various basis sets up to MP2(full)/6-311C G(d,p) from which structural parameters, barriers to internal rotation, and distortion constants have been obtained. The C–H distance of ˚ for the CHF2 moiety has been determined from the isolated stretching frequency from the CD3CD12 1.095G0.002 A 2 CHF2 molecule. The r0 parameters have been obtained by combining the ab initio predicted values with the microwave rotational constants and these parameters for ˚ , :C1C2C3Z112.2(5), :C2C1F5Z the heavy atoms are: rC1–F5Z1.370(5), rC1–F6Z1.372(5), rC1–C2Z1.505(3), rC2–C3Z1.522(3) A 109.8(5), :C2C1F6Z110.9(5)8. The adjusted r0 parameters have also been obtained for 2,2-difluoropropane, CH3CF2CH3. The results are compared to those of some similar molecules. q 2005 Elsevier B.V. All rights reserved.

Keywords: Microwave spectrum; Structure; Barrier to rotation; Gauche-1,1-difluoropropane

1. Introduction The XCH2CH2X molecules have been of interest to chemists since their conformational stability depends on the nature of the substituent. For example, when X is a fluorine atom, the gauche conformer is more stable than the trans form by 280G30 cmK1 (801G86 cal/mol) [1]. When X is a chlorine atom or a methyl group, the trans conformer is the more stable form by 323G8 cmK1 (924G23 cal/mol) [2] and 243G8 cmK1 (695G23 cal/mol) [3], respectively. However, when one of the substituents is a fluorine or

* Corresponding author. Tel.: C1 816 235 6038; fax: C1 816 235 2290. E-mail address: [email protected] (J.R. Durig). 0022-2860/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2004.12.057

chlorine atom and the other one is a methyl group, the gauche conformer is the more stable rotamer by 104G 6 cmK1 (297G17 cal/mol) [4] and 52G3 cmK1 (149G 9 cal/mol) [5], respectively, as determined from variable temperature infrared spectra of rare gas solutions. Since the methyl group and the chlorine atom are of similar size, it is not clear what factors are the most important in governing the conformational stability of these molecules, particularly when the X substituents are different. Nevertheless it is expected that the C–C bond distance is one of the important factors determining the conformational stability of the XCH2CH2X 0 molecules. There is only limited information on the structural parameters for the CHF2 group, since the fluorine atom has only one stable isotope [6–9]. However, the microwave

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spectrum has rather recently been reported for the two different 13C isotopomers of 1,1-difluoroethane and structural parameters determined utilizing additional information from ab initio calculations [9]. Since there is only limited structural and conformational stability data for the 1,1dihalo-substituted propanes, CH3CH2CHX2, we have carried out a microwave study of 1,1-difluoropropane to determine its structural parameters. In order to provide additional structural data, we have also carried out ab initio calculations with valence electron correlation by the perturbation method to second-order with various basis sets up to MP2(full)/6-311CG(d,p). These calculations have been used to predict the potential function governing the conformational interchange between the more stable gauche conformer and the higher energy trans form [10]. Additionally, by combining the ab initio MP2(full)/6-311C G(d,p) predicted parameters with the experimentally determined rotational constants, the adjusted r0 structural parameters have been determined. The results of this spectroscopic and theoretical study are reported herein.

2. Experimental The 1,1-difluoropropane sample and its isotopomers were prepared from the corresponding propionaldehyde by its reaction with diethylaminosulfur trifluoride, as previously described [11]. The samples were purified by using a low-temperature low-pressure fractionating column. The purity of the samples was checked by recording the midinfrared and Raman spectra of the gaseous samples. The microwave spectra of each isotopomer of 1,1difluoropropane was recorded in the frequency region 26.5– 40.0 GHz with a Hewlett Packard Model 8460A MRR spectrometer with a Stark modulation frequency of 33.33 kHz. The spectra were recorded at low temperature provided by Dry Ice covering the Stark cells. The transition frequencies were accurately measured by scanning the peaks in both forward and reverse directions. The accuracy of the measurements is estimated to be better than 50 kHz.

3. Microwave spectra There are two possible conformations of CH3CH2CHF2 where the methyl group is in the trans position relative to the lone hydrogen atom on carbon-1 (Fig. 1) and the second one has the methyl group in the gauche position which results in two equivalent forms. Initially, preliminary rotational constants were calculated for both conformers from ab initio MP2/6-31G(d) calculations. The values for A, B, C (MHz) and k were 6879, 4160, 3433 and K0.57 for the trans rotamer and 8696, 3508, 2779 and K0.62 for the gauche conformer, respectively. At this level of calculation the trans conformer was predicted to be more stable by 75 cmK1 than the gauche form. However, the jmaj was

Fig. 1. Atom numbering for 1,1-difluoropropane.

predicted to be 1.29 D for the trans conformer, but 2.01 D for the gauche form which indicates that the two equivalent gauche rotamers should have the stronger spectrum. We, therefore, began to search the normal species for the individual a-type R-branch transitions with KK1Z0, 1 and 2 for the 5)4 J transitions of the gauche conformer. Eventually these lines were assigned and the determined A and C rotational constants were reasonably close to the predicted values, but the B constants differed by w70 MHz. Once these transitions were assigned, some additional atype R-branch 6)5 J transitions were assigned and it was clear from the values of the rotational constants that the microwave spectrum of the gauche conformer was assigned. Based upon the ab initio predicted dipole moment components of the gauche conformer, a search was made for the b-type Q-branch transitions of this conformer. A significant number of such transitions beginning with JZ9 up to JZ18 were assigned for the normal species for a total of 52 assigned transitions. Similar a-type R-branch and b-type Q-branch transitions were assigned for the three isotopomers, i.e. CH3CH13 2 CHF2, CH3CD2CHF2 and CD3CD2CHF2 and eventually 50, 46 and 44 such transitions were assigned for these isotopomers, respectively. The assigned transitions for all four molecules are listed in Table 1. The three rotational constants and the DJ, DJK, dJ and dK centrifugal distortion constants as defined by Watson’s [12] A-reduction for Ir representation were obtained by a leastsquares-fit of the data listed in Table 1. The values obtained for these quantities for all four molecules with their standard deviations are listed in Table 2. As can be seen from these data, very accurate values were obtained for all three rotational constants for all four isotopomers. Additionally the following dipole moment components (debye) along with the uncertainties in parentheses were obtained from selected transitions of the normal species: jmajZ2.0441(26), jm cjZ0.711(35) and jm totjZ jm bjZ0.8509(48), 2.3256(24) D. Since the trans conformer has a plane of symmetry, these data confirm the assignment of the indicated transitions to the gauche conformer.

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193

Table 1 Rotational transitional frequencies (MHz) for gauche-1,1-difluoropropane isotopomers in the ground vibrational states Transition

41,3)31,2 41,4)30,3 51,5)41,4 50,5)40,4 52,4)42,3 52,3)42,2 51,4)41,3 53,3)43,2 53,2)43,1 51,5)40,4 50,5)41,4 60,6)51,5 60,6)50,5 61,5)51,4 61,5)52,4 61,6)50,5 61,6)51,5 62,5)52,4 62,4)52,3 63,3)53,2 63,4)53,3 63,4)62,5 70,7)60,6 71,7)61,6 71,7)60,6 70,7)61,6 71,6)62,5 73,5)72,6 82,6)73,5 84,4)83,5 84,5)83,5 91,8)90,9 93,7)92,8 94,5)93,6 94,6)93,6 103,7)94,6 103,8)102,9 104,6)103,7 104,7)103,7 111,10)112,9 113,9)112,10 114,8)113,9 114,7)113,8 114,8)113,9 114,8)113,8 122,10)121,11 123,10)122,11 124,8)123,9 124,9)123,10 132,11)131,12 133,10)132,11 134,10)133,11 134,9)133,10 135,8)134,9 135,9)134,9 142,12)141,13 143,11)142,12 144,10)143,11 145,9)144,10 145,10)144,10

CH3CH12 2 CHF2

CH3CH13 2 CHF2 a

CH3CD12 2 CHF2 a

CD3CD2CHF2 a

n(obs)

Dn

n(obs)

Dn

n(obs)

26,814.35 27,139.65 29,395.02 30,232.66 31,546.23 33,051.77 33,312.06

K0.02 K0.04 0.08 0.00 0.00 K0.03 K0.01

0.00

0.01 K0.01 0.06 0.00

K0.01 0.08 0.06 0.01 0.03 K0.01 K0.01 0.09 K0.02 0.04 K0.07 K0.04 K0.01

33,942.04

31,962.24 27,665.53 34,022.39 35,751.89

26,773.30 27,113.48 30,201.88 29,366.06 31,505.34 32,999.17 33,262.64 31,939.40 32,060.39 31,934.36 27,633.48 33,985.30 35,717.83

2867.49 29,410.52 30,822.11 32,446.77 32,533.62 31,303.15 31,455.82 30,725.57 27,363.36 33,454.76 34,769.81

0.03 0.00 0.02 K0.07 K0.02 0.11 K0.09 0.04 K0.09 K0.03 0.01

36,841.92 35,112.35 37,697.66

0.04 0.01 0.00

29,447.81 35,557.70 34,242.62 36,811.42

K0.03 0.09 0.02 0.01

38,737.54 38,420.98 29,268.35

K0.06 0.04 K0.02

37,991.17 37,599.80

K0.07 0.08

35,078.60

29,196.62

K0.07

0.09 K0.03 K0.06 0.04

33,739.57 35,182.84

K0.01 0.03

31,875.20 36,099.79 33,359.40 32,450.74 29,554.40 38,889.99

0.03 K0.02 0.01 K0.04 K0.03 K0.02

31,368.02

0.02

31,337.45

0.03

29,527.47 34,851.45

K0.01 0.00

29,522.33 34,667.19

0.01 0.02

29,529.17

0.00

29,499.28

0.05

27,110.55

K0.04

26,973.90

0.01

28,202.54

0.03

28,163.63

0.03

0.03 0.02

n(obs)

Dna

26,642.25 27,609.32 28,714.18 29,030.58

0.00 0.05 K0.04 0.01

28,337.73

K0.01

31,558.12 34,604.46

0.00 0.00

30,975.03 33,017.64 34,750.86 33,752.59 33,545.40

0.03 K0.03 K0.02 K0.06 0.06

36,414.77 35,995.91 37,108.33 35,302.38

K0.04 0.02 0.08 K0.06

K0.04

36,626.08 30,344.05 31,674.54 36,630.76

31,312.25 27,712.45

Dn

36,563.87 30,263.37

K0.05 K0.06

37,179.60

K0.03

36,568.71 36,410.75 32,004.47 33,634.72 35,132.46 34,733.04 31,875.52 35,978.84 33,320.73 32,424.96 29,396.71

0.02 K0.04 0.10 K0.02 0.03 K0.03 0.03 0.00 0.07 K0.07 0.00

31,689.48

K0.04

30,881.55 30,130.10

0.02 0.03

28,716.72

K0.07

33,340.80

K0.04

30,499.14

K0.06

27,053.85

0.05

36,208.40 36,560.38

0.02 K0.01

32,628.95

K0.04

35,113.81

K0.04

27,655.76 35,087.39 26,795.85 36,001.34 32,140.71

0.04 0.02 0.05 0.00 0.02

37,217.14

0.08

36,699.18

K0.01

31,137.50 27,653.89

K0.01 0.00

26,800.17

K0.08

37,267.16 36,260.95

0.03 K0.08

31,429.87

0.05

34,940.20 32,959.02

0.03 K0.06

37,316.62 K0.06 (continued on next page)

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Table 1 (continued) Transition

153,12)152,13 154,11)153,12 155,11)144,11 155,10)154,11 163,13)162,14 164,12)163,13 165,11)164,12 165,12)164,12 174,13)173,14 175,12)174,13 175,13)174,13 184,14)183,15 185,13)184,14 195,14)194,15 194,15)193,16 196,14)195,14 205,15)204,16 206,15)205,15 215,16)214,17 216,15)215,16 216,16)215,16 226,16)225,17 a

CH3CH12 2 CHF2

CH3CH13 2 CHF2

n(obs)

Dn

36,379.20 28,301.51 36,849.91 39,313.51

a

CH3CD12 2 CHF2 a

CD3CD2CHF2 a

n(obs)

Dn

n(obs)

0.01 0.00 K0.02 0.02

36,167.78 28,213.01 36,867.87

K0.01 0.00 K0.04

36,663.09

0.01

28,476.53

0.02

29,088.52 32,702.80

0.00 0.02

34,684.44 36,059.83 32,820.49

0.00 0.06 0.05

30,118.08 36,958.69 32,655.29 33,208.57 35,138.00 28,093.10 37,496.15 34,214.54 34,466.05

0.00 0.00 K0.01 0.00 K0.02 0.01 0.00 0.00 0.01

29,990.53 36,936.92 32,700.91 33,035.35 35,103.76 28,163.02 37,274.77 34,153.91 34,366.08

0.00 0.01 K0.01 0.00 0.00 0.04 K0.02 0.00 0.01

29,185.71 30,963.83

0.01 0.02

33,211.55 30,107.52

0.02 0.01

30,424.73 32,087.13

K0.01 0.00

33,983.53 31,533.25 26,745.92 32,083.65 27,971.48 29,457.29 30,655.93 29,967.02 33,102.49

0.01 K0.03 0.01 0.00 0.04 K0.02 0.07 K0.01 K0.04

36,063.39

0.02

35,913.23

0.01

33,842.10 35,136.67 28,811.61

0.00 K0.02 K0.01

30,219.76

0.04

39,062.21

K0.02

31,539.20

K0.06

35,633.39

K0.02 34,488.17

K0.04

35,929.74

0.01

33,999.23

Dn

Dna

n(obs)

K0.02

Calculated from the rotational constants listed in Table 2.

4. Structural parameters Since there are only twelve rotational constants, it is not possible to obtain all of the independent structural parameters of gauche-1,1-difluoropropane. However, we [13] have recently shown that ab initio MP2(full)/6-311C G(d,p) calculations predict the r0 structural parameters for more than 50 carbon–hydrogen distances to better than ˚ compared to the experimentally determined [14] 0.002 A values from ‘isolated’ CH stretching frequencies. We have also found [15] that we can obtain good structural parameters by systematically adjusting the structural parameters obtained from the ab initio calculations to fit the rotational constants (computer program A&M, Ab initio and Microwave, developed in our laboratory) obtained from the microwave experimental data. In order to reduce the number of independent variables, the structural parameters are separated into several sets according to their type. Each set uses only one independent

parameter in the optimization and all structural parameters in one set will be changed by the same adjustment factor. The information about the difference between similar structural parameters from ab initio calculations will be retained in the final results in the following way: bond lengths in the same set will keep their relative ratio and bond angles (including torsional angles) in the same set will keep their difference in degrees. This assumption is based on the fact that the errors from ab initio calculations are systematic which is commonly acknowledged. To avoid the possibility of falling into a local minimum instead of the global minimum, a simplex algorithm instead of a gradient method was used. The A&M program adds ab initio structural parameters, although with much smaller weights, to the rotational constants, so that the number of observable is always larger than the number of unknown parameters. As a consequence, unique results can be obtained without any arbitrary assumptions on the values of structural parameters.

Table 2 Rotational and centrifugal distortion constantsa for isotopomers of gauche-1,1-difluoropropane in the ground vibrational state Isotopomers

A (MHz)

B (MHz)

C (MHz)

DJ (kHz)

DJK (kHz)

dJ (kHz)

dK (kHz)

nb

s (MHz)c

CH3CH2CHF2 CH3CH13 2 CHF2 CH3CD2CHF2 CD3CD2CHF2 Ab initiod

8739.9541(30) 8723.6913(35) 8011.9678(59) 7645.2294(58)

3578.1135(22) 3571.6715(18) 3504.7747(44) 3094.6690(41)

2770.1584(21) 2768.0750(18) 2703.1099(45) 2455.1444(42)

0.862(28) 0.762(17) 0.705(67) 0.580(53) 0.753

6.567(19) 6.513(26) 4.269(31) 3.609(22) 5.390

0.1856(15) 0.1827(22) 0.1948(26) 0.1425(17) 0.1753

3.539(36) 3.529(48) 2.461(50) 1.674(37) 3.132

52 50 46 44

0.032 0.042 0.049 0.045

a b c d

Quadratic centrifugal distortion constants are defined according to Watson’s A-reduction for Ir representation. Number of transitions included in the least-squares fit. Standard deviation. Centrifugal distortion constants obtained from the MP2(full)/6-31G(d) calculations for the normal species.

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195

Table 3 ˚ and degree), rotational constants (MHz) and dipole moments (debye) for trans and gauche rotamers of 1,1-difluoropropane Structural parameters (A Parameter ˚) r(C1C2) (A ˚) r(C2C3) (A ˚) r(C1F5) (A ˚) r(C1F6) (A ˚) r(C1H4) (A ˚) r(C2H7) (A ˚) r(C2H8) (A ˚) r(C3H9) (A ˚) r(C3H10) (A ˚) r(C3H11) (A :C1C2C3 (8) :C2C1F5 (8) :C2C1F6 (8) :F5C1F6 (8) :C2C1H4 (8) :C1C2H7 (8) :C1C2H8 (8) :H7C2H8 (8) :C2C3H9 (8) :C2C3H10 (8) :C2C3H11 (8) :H10C3H11 (8) tH4C1C2C3 (8) tF5C1C2C3 (8) tF6C1C2C3 (8) tH9C3C2C1 (8) A (MHz) B (MHz) C (MHz) jmaj (D) jmbj (D) jmcj (D) jmtotj (D)

MP2(full)/6-311CG(d,p)

Adjusted r0

Trans

Gauche

Trans

Gauche

1.506 1.526 1.369 1.369 1.092 1.094 1.094 1.092 1.092 1.092 112.8 110.4 110.4 106.8 114.0 107.3 107.3 107.4 110.1 110.9 110.9 108.4 180 K58.9 58.9 180 6945.6 4112.2 3407.2 1.544 2.087 2.596

1.504 1.526 1.369 1.368 1.093 1.094 1.094 1.092 1.092 1.094 112.1 110.2 110.3 107.0 114.0 107.4 107.4 107.8 110.4 110.9 111.0 108.3 K58.2 62.6 K179.4 178.4 8736.9 3588.4 2774.4 2.364 1.046 0.983 2.765

1.506(3) 1.522(3) 1.371(3) 1.371(3) 1.092(2) 1.094(2) 1.094(2) 1.092(2) 1.092(2) 1.092(2) 112.9(5) 110.5(5) 110.5(5) 107.2(5) 114.0(5) 107.3(5) 107.3(5) 107.4(5) 110.1(5) 110.9(5) 110.9(5) 108.4(5) 180 K58.7(5) 58.7(5) 180 6969.3 4108.3 3411.8

1.505(3) 1.522(3) 1.370(5) 1.372(5) 1.093(2) 1.094(2) 1.094(2) 1.092(2) 1.092(2) 1.094(2) 112.2(5) 109.8(5) 110.9(5) 107.3(5) 114.0(5) 107.4(5) 107.4(5) 107.8(5) 110.4(5) 110.9(5) 111.0(5) 108.3(5) K58.2(5) 63.1(5) K178.5(5) 178.4(5) 8740.4 3578.3 2770.4 2.044(3) 0.851(5) 0.711(35) 2.326(3)

The adjusted r0 parameters for gauche-1,1-difluoropropane are listed in Table 3 along with ab initio MP2(full)/ 6-311CG(d,p) predicted values. The fit of the microwave rotational constants is given in Table 4 and the differences with the observed A, B and C values for the four isotopomers ranges form a high value of 0.7 to a low value of 0.1 with the average of 0.3 MHz. It is believed that the determined values for the CH distances should not be in error by more ˚ , the heavy atom distances by 0.003 A ˚ and the than 0.002 A angles by 0.58.

For the angles the differences are somewhat larger where the :C1C2C3 is 0.78 larger for the trans conformer than the corresponding angle for the gauche form. Most of the corresponding angle differences are 0.38 or less. It is probable that these very small differences are the reason that Table 4 Comparison of rotational constants (MHz) obtained from modified ab initio, MP2/6-311CG(d,p) structural parameters and those from microwave spectra for gauche-1,1-difluoropropane Isotopomer

Rotational constants

Observed

Calculated

D

CH3CH12 2 CHF2

A B C A B C A B C A B C

8739.95 3578.11 2770.16 8723.69 3571.67 2768.08 8011.97 3504.77 2703.11 7645.23 3094.67 2455.14

8740.39 3578.34 2770.41 8723.66 3571.71 2768.08 8011.77 3504.94 2703.08 7645.01 3094.30 2454.94

0.44 0.23 0.25 K0.03 0.04 0.00 K0.20 0.17 K0.03 K0.22 K0.37 K0.20

5. Discussion In Table 3 the predicted structural parameters from ab initio MP2(full)/6-311CG(d,p) calculations are listed for both the trans and gauche conformers of 1,1-difluoropropane. As can be seen from these data, there are only minor differences between the corresponding parameters for the two rotamers. For the most part these differences are only ˚ or less for the distances except for the C1C2 0.001 A ˚ shorter for the gauche conformer. bond which is 0.002 A

CH3CH13 2 CHF2

CD3CH12 2 CHF2

CD3CD12 2 CHF2

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J.R. Durig et al. / Journal of Molecular Structure 742 (2005) 191–198

Fig. 2. Mid-infrared spectrum from 2900 to 3000 cmK1 of CD3CD2CHF2.

the enthalpy difference has been determined [10] to be only 65G5 cmK1 (0.78G0.06 kJ/mol) from variable temperature infrared studies from krypton solutions with the gauche form the more stable conformer. This experimental value is consistent with the smaller CCC angle and shorter C1C2 distance for the gauche conformer. We have estimated the r0 parameters for the trans conformer by adjusting the predicted values from the ab initio MP2(full)/6-311CG(d,p) calculation by the approximate small changes made to the corresponding parameters by adjusting them to fit the experimental rotational constants. It is believed that the predicted A, B and C rotational constants will be within a few megahertz of those 1800

gauche’(TS)

that would be obtained experimentally. Thus, it should be relatively easy to assign the microwave spectrum of the trans conformer from these predicted values. Unfortunately, we do not have a source for our microwave instrument to check this prediction. With the availability of the CD3CD2CHF2 isotopomer, it is possible to obtain the C1–H4 distance for both the trans and gauche conformers from the isolated CH stretching frequencies [14]. The infrared spectrum from 2900 to 3000 cmK1 is shown in Fig. 2 and the observed frequencies for the trans and gauche conformer are 2974 and 2958 cmK1, respectively. Utilizing the previously reported equation of r0 (C–H)Z ˚ for the 1.3982–0.0001023 nCH gives distances of 1.0940 A ˚ trans form and 1.0956 A for the gauche rotamer. This difference is only slightly larger than the ab initio predicted ˚ longer than difference. However, both distances are 0.002 A the adjusted r0 values which is the difference we found for some of the C–H distances in our earlier study [13]. A very limited number of carbon compounds with two fluorine atoms on the same carbon have reliable structural determinations in the gas phase for comparison to the ab initio predicted parameters or to the values for the corresponding bonds in 1,1-difluoropropane. One of these molecules is methylene fluoride, CH2F2, where a rather detailed microwave investigation was carried out and the C–H and C–F distances were determined [7] to be 1.084(3) ˚ , respectively. The ab initio MP2(full)/6and 1.3508(5) A 311CG(d,p) predicted value for the C–F distance is ˚ , which is 0.010 A ˚ longer than the experimental 1.3605 A value. However, when one of the hydrogen atoms of methylene fluoride is replaced by a methyl group, i.e. 1,1difluoroethane, CH3CHF2, the experimental r0 C–F distance ˚ . There are also some data on both the [9] is 1.365(6) A OaCF2 and CH2aCF2 molecules [8,16] and the C–F ˚ (both rz values), distances of 1.311(5) and 1.314(3) A gauche’(TS)

cis (TS)

1600

V(φ), cm-1

1400 1200 1000 800 600 400 gauche

gauche

200 0 -180

trans

trans

-120

-60

0

60

120

180

DIHEDRAL ANGLE, (φ) Fig. 3. Potential function governing the internal rotation of 1,1-difluropropane as determined at the MP2(full)/6-31G(d) (dashed line) and the MP2(full)/6-31C G(d) (solid curve) levels.

J.R. Durig et al. / Journal of Molecular Structure 742 (2005) 191–198

197

1800 gauche’(TS)

gauche’(TS)

1600

cis (TS)

1400

V(φ), cm-1

1200 1000 800 600 400 200 0 -180

gauche

gauche trans

trans

-120

-60

0

60

120

180

DIHEDRAL ANGLE, (φ) Fig. 4. Potential function governing the internal rotation of 1,1-difluropropane as determined at the MP2(full)/6-311G(d,p) (dashed line) and the MP2(full)/6311CG(d,p) (solid curve) levels.

respectively, are in good agreement with the values of 1.317 ˚ , respectively, from MP2(full)/6-311CG(d,p) and 1.319 A ab initio calculations. If anything, these results indicated that the ab initio predicted value of the C–F distance at this level with the 6-311CG(d,p) basis sets may predict the value a little too long. In the earlier vibrational study [10] of 1,1-difluoropropane, the potential governing the conformational interchange was determined from the frequencies of the asymmetric torsional modes of the trans and gauche conformer which included the fundamentals and two excited states along with the enthalpy difference which was determined from variable temperature infrared

spectrum of krypton solutions which was experimentally determined to be 75G7 cmK1 [10]. This experimentally determined potential function was compared [10] to the one predicted from ab initio MP2(full)/6-31G(d) calculations which was nearly a simple three-fold potential function (barriers varied from 1566 to 1672 cmK1) whereas the experimental gauche-to-gauche barrier was determined to be only 1076 cmK1 compared to the predicted value of 1566 cmK1. To see if a better prediction of the gauche-to-gauche barrier could be obtained we carried out the calculations with full electron correlation with diffused functions, i.e. MP2(full)/6-31CG(d) (Fig. 3) as well as with the larger

Table 5 Calculated potential barriers and Fourier potential coefficients of 1,1-difluoropropane Coefficients (cmK1)

MP2(full)/ 6-31G(d)

MP2(full)/ 6-31CG(d)

MP2(full)/ 6-311G(d,p)

MP2(full)/ 6-311CG(d,p)

Experimental [10]

V1 V2 V3 V4 V5 V6 Conformational energy/ enthalpy difference DE (cmK1) DH (cmK1) Potential barriers (cmK1) Trans/gauche Gauche/gauche Gauche/trans Dihedral angles Gauche (min) Gauche 0 (max)

K33 56 K1613 16 4 K44

184 184 K1515 33 0 K37

73 114 K1554 12 K6 K55

208 181 K1515 42 K1 K54

353G9 256G10 K1523G7 100G3 93G4 K49G2

76

22

43

10 65G26

1675 1567 1600

1633 1310 1612

1634 1446 1591

1630 1299 1617

1678 1076 1743

59.978 119.648

58.198 119.838

58.818 119.738

58.228 120.128

60.08 (fixed)

198

J.R. Durig et al. / Journal of Molecular Structure 742 (2005) 191–198

Table 6 ˚ and degree), rotational constants (MHz) and Structural parameters (A dipole moment (debye) of 2,2-difluoropropane Parameter

MP2(full)/ 6-311CG(d,p)

Microwavea values

Adjustedb r0

r(CC) r(CF) r(CHs) r(CHa) :CCC :FCF :CCF :CCHs :CCHa tHsCCC A B C jmbjZjmtotj

1.506 1.378 1.0909 1.0912 116.2 105.7 108.6 109.1 109.8 60.1 5147.2 4840.0 4832.6 2.830

1.532(13) 1.552(13) 1.090* 1.090* 112.5(8) 106.1(14) 109.5(11) 110.0* 110.0* 60.0* 5149.79(4) 4840.11(2) 4805.62(2) 2.40(2)

1.507(5) 1.379(5) 1.091(2) 1.091(2) 116.0(5) 105.7(5) 108.6(5) 109.1(2) 109.8(2) 60.1(3) 5150.0 4840.2 4806.4

a

Ref. [17]; parameters with asterisks were fixed and other parameters obtained from diagnostic least-squares adjustments. b This study; estimated uncertainties in parentheses.

basis set 6-311CG(d,p) (Fig. 4). As can be seen in these figures as well as with the data listed in Table 5 the gaucheto-gauche barrier is reduced by about 300 cmK1, but it is about 200 cmK1 larger than the experimental value. The only way one could obtain a larger barrier from the experimental data is to re-assign the far infrared spectrum so the torsional fundamental and the two associated ‘hot bands’ had higher frequencies. However, an inspection of the spectral data indicates a re-assignment is not possible. Thus, it appears that the ab initio predicted transition state barrier is too large by about 200 cmK1. Also it should be noted that the barrier prediction is not significantly improved with the larger basis set, but the diffuse functions are necessary. We have obtained the values of the centrifugal distortion constants from ab initio MP2(full)/6-31G(d) calculations for the CH3CH2CHF2 molecule and the results are listed in Table 2. The agreement of the predicted values with the experimentally determined ones is quite good even with this small basis set. We also obtained the dipole moment components from MP2(full)/6-311CG(d,p) calculations and they are listed in Table 3. The predicted values are significantly larger than the experimentally determined values as is usually found. Nevertheless the results support the relative determined value of the three different components of the dipole moment. The values of the adjusted r0 parameters have been obtained for 2,2-difluoropropane, CH3CF2CH3, by combining the ab initio MP2(full)/6-311CG(d,p) predicted values with the previously reported [17] rotational constants. The determined values are listed in Table 6 along with the values previously reported. The carbon–hydrogen bond distances and angles were kept to the values predicted from the ab initio ˚ and 0.28. The calculations which should be good to 0.002 A ˚ for the CC other uncertainties are estimated to be G0.005 A

and CF distances based on the earlier calculations on the predicted distances of these parameters from the MP2(full)/ 6-311CG(d,p) calculations for hydrocarbons [13] and fluorine substituted hydrocarbons [9]. However, it should be noted that the CF and CC distances are strongly correlated so an increase in the CC distances results in a corresponding decrease in the CF distance. Nevertheless these adjusted r0 parameters are clearly more accurate than the values previously reported [17]. These new r0 values are consistent with the values obtained for the corresponding parameters for 1,1-difluoropropane and show how structural parameters can be obtained from limited number of rotational constants when coupled with the appropriate ab initio predictions for the hydrocarbons with some fluorine atoms as substituents. Since the fluorine atom has no naturally occurring isotopes there are many structural determinations, which include this atom where the determined distance has very large uncertainty. Therefore, a systematic study of additional carbon–carbon distances of many of the molecules previously investigated for CF predicted distances [9] could aid in obtaining better overall parameters for these type of molecules.

Acknowledgements J.R.D. acknowledges the University of Missouri— Kansas City for a Faculty Research Grant for partial financial support of this research.

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