Gas Phase Structures, Energetics, and Potential Energy Surfaces of

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Gas Phase Structures, Energetics, and Potential Energy Surfaces of Disilacyclohexanes† Ingvar Arnason,*,‡ Palmar I. Gudnason,‡,§ Ragnar Bj€ornsson,|| and Heinz Oberhammer^ ‡

)

Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland School of Chemistry, North Haugh, University of St. Andrews, St. Andrews, Fife, UK KY16 9ST, United Kingdom ^ Institut f€ur Physikalische und Theoretische Chemie, Universit€at T€ubingen, Auf der Morgenstelle 8, 72076 T€ubingen, Germany

bS Supporting Information ABSTRACT: The molecular structures of 1,4-, 1,3-, and 1,2-disilacyclohexanes (denoted as 14, 13, and 12, respectively) were investigated by means of gas electron diffraction (GED). Each molecule was found to possess a chair as the most stable conformation in the gas phase, the point group being C2h, Cs, and C2, respectively. Experimental GED structures are in good agreement with theoretical calculations (MP2/cc-pVTZ and B3LYP/cc-pVTZ). A qualitative ring strain analysis suggests 14 to be the most stable and 12 the least stable of the parent disilacyclohexanes. Relative energy calculations with the G4 model chemistry protocol, on the other hand, predict 13 to be the most stable isomer, 5.9 and 14.2 kcal/mol more stable than 14 and 12, respectively. The enhanced stability of 13 compared to 14 is in agreement with an analysis on endocyclic bond lengths and bond polarities. The heats of formation (G4 calculations) are predicted to be 12.3, 18.1, and 3.9 kcal/mol for 14, 13, and 12, respectively. The potential energy surface (PES) and the lowest energy path for the chair-to-chair inversion have been calculated for each isomer. In addition to the two chair forms in each case and some half-chair or sofalike transition states (four in the case of 14, and two in the case of 13), there are two twist forms found as stationary points on the PES of 14, six twist and six boat forms on the PES of 13, and four twist and six boat forms on the PES of 12.

1. INTRODUCTION The structure and conformational properties of saturated sixmembered rings depends predominantly on angle strain (Baeyer strain) and torsional strain (Pitzer strain). In the chair conformation of cyclohexane, with all bonds being of equal length, the bond angles are close to tetrahedral (111.3(2)) and the torsional angles around the CC bonds of 55.1(7) lead to almost exactly staggered orientation of adjacent CH2 groups.2 This minimizes both strain energies. The twist conformer of cyclohexane possesses almost unchanged bond angles, but four CCCC dihedral angles decrease to about 30 according to B3LYP/6-31G(d) calculation and two angles remain near 60 (63.5).3 This calculation predicts an energy difference of 6.5 kcal/mol between chair and twist conformation, which is slightly higher than experimental results of 4.85.9 kcal/mol.46 In saturated six-membered rings with equal but longer bond lengths, such as 1,3,5-trisilacyclohexane or cyclohexasilane, the energy difference between chair and twist conformers is much smaller (2.17 and 1.89 kcal/mol, respectively, according to DFT calculations).3 Likewise, the Gibbs free energy of activation for the chair-to-chair inversion is generally accepted to be 10.110.5 kcal/mol in cyclohexane but only about half that value in 1,3, 5-trisilacyclohexane and cyclohexasilane.7,8 Silacyclohexane is an example of a ring with unequal bond lengths. The SiC bonds are considerably longer than the CC bonds, and this causes the CSiC bond angle to decrease from the ideal value to 104.2(1.4).9 The Gibbs free energy of activation for the chair-to-chair inversion r 2011 American Chemical Society

in the case of silacyclohexane is similar to that found for 1,3, 5-trisilacyclohexane and cyclohexasilane, however.10,11 Between cyclohexane on one end and cyclohexasilane on the other end, silacyclohexane and 1,3,5-trisilacyclohexane were for many years the only known examples of six-membered rings containing only carbon, silicon, and hydrogen atoms. We have recently published the first successful synthesis of the three isomeric parent disilacyclohexanes.12 In these compounds CC, SiC, and, in one case, SiSi bonds of different lengths alter in different ways within the six-membered ring systems. This may cause deviations from ideal values for bond angles and torsional angles, which may influence the relative stability and conformational properties of the isomeric rings. In the present study, we report on gas phase structures, calculated relative stability, and potential energy surfaces (PES) of these new compounds.

2. EXPERIMENTAL SECTION General. The preparation and spectroscopic characterization of the three parent disilacyclohexanes have been described elsewhere.12 In the following we will use the abbreviations 14, 13, and 12 for the 1,4-, 1,3-, and 1,2-disilacyclohexanes, respectively. After final distillation, and prior to the gas electron diffraction (GED) Received: March 23, 2011 Revised: July 20, 2011 Published: July 24, 2011 10000

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Figure 1. Experimental (dots) and calculated (full line) molecular intensities of long (above) and short (below) nozzle-to-plate distances and differences for 1,4-disilacyclohexane.

experiments, the purity of the products was estimated by their 13C NMR spectra (14 and 12 99%; 13 96%).12 GED Experiments. Electron diffraction intensities were recorded with a Gasdiffraktograph KD-G213 at 25 and 50 cm nozzle-to-plate distances and with an accelerating voltage of about 60 kV. The electron wavelength was determined from ZnO powder diffraction patterns. All samples were kept at 20 C during the experiment and the inlet system and nozzle were at room temperature. The photographic plates (Kodak Electron Image Plates, 18 13 cm) were analyzed with an Agfa Duoscan HiD scanner and total scattering intensity curves were obtained using the program SCAN3.14 Averaged experimental molecular intensities for 14 in the ranges s = 218 Å1 and 835 Å1 in steps of Δs = 0.2 Å1 (s = (4π/λ) sin θ/2, where λ is the electron wavelength and θ is the scattering angle) are shown in Figure 1. Molecular intensities for 13 and 12 are presented in Figures S1 and S2, respectively, in the Supporting Information.

3. RESULTS AND DISCUSSIONS 3.1. Structure Analysis. Gas-phase geometries of the three

disilacyclohexanes were optimized with MP2 and B3LYP methods and cc-pVTZ basis sets for comparison with the experimental structures. Calculated geometric parameters are included in the tables for the experimental structures. Vibrational amplitudes and corrections, Δr = rh1 ra, were derived from theoretical force fields (B3LYP/cc-pVTZ) with the method of Sipachev, using the program SHRINK.15 Calculated amplitudes and corrections are listed together with experimental amplitudes in the Supporting Information. Radial distribution curves were derived by Fourier transformation of the modified molecular intensities applying an artificial damping function exp(γs2 ) with γ = 0.0019 Å2 . Calculated intensities were used in the range s = 02 Å1. For all three compounds, geometric parameters describing the ring structure and mean SiH and CH distances and HCH angles were refined. Other assumptions are based on parameters derived by the MP2/cc-pVTZ method. HSiH angles were constrained to calculated values. The exact orientation of all SiH2 and CH2 groups was described by twisting, rocking, and wagging angles, which were set to the calculated values. Calculated amplitudes were used for all nonbonded distances involving hydrogen atoms. Furthermore, amplitudes that are poorly determined in the GED experiment or which cause high correlations between geometric parameters are set to calculated values. Additional assumptions are described in the analyses for the individual compounds. 1,4-Disilacyclohexane. The experimental radial distribution curve (Figure 2) is reproduced very well with a chair structure

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Figure 2. Experimental radial distribution function and difference curve for 1,4-disilacyclohexane. Important interatomic distances are indicated by vertical bars.

Figure 3. Molecular model and atom numbering for 1,4-disilacyclohexane.

possessing C2h symmetry. A molecular model with atom numbering is shown in Figure 3. Seven geometric parameters (SiC, CC, CH, and SiH distances, CSiC and HCH bond angles, and flap(Si) angle between CSiC and CCCC planes) were refined simultaneously with six vibrational amplitudes in the least-squares analysis. Only a single correlation coefficient (CSiC/flap(Si) = 0.78) had a value larger than 0.70. The results are summarized in Table 1 (geometric parameters) and Table S1 (vibrational amplitudes). 1,3-Disilacyclohexane. The experimental radial distribution function shown in Figure 4 is fitted very well with a chair structure possessing Cs symmetry and with the two opposite carbon atoms out-of-plane. A structural model and atom numbering are shown in Figure 5. The geometric structure was described by the Si1C2, CC, CH, and SiH bond lengths, the SiCSi, CCC, and HCH bond angles, and the flap angles between the SiC2Si and CC5C planes and the SiSiCC plane. The difference between the Si1C2 and Si1C6 bond distances was fixed to the calculated (MP2) value. The nine geometric parameters p1p9 were refined simultaneously with six vibrational amplitudes l1 to l6. Only the correlation CCC/flap(C5) = 0.87 had an absolute value larger than 0.7. Results of the least-squares refinement are listed in Table 2 (geometric parameters) and Table S2 (vibrational amplitudes). 1,2-Disilacyclohexane. The radial distribution function for this molecule is shown in Figure 6. A distorted chair structure (see Figure 7) with the two opposite carbon atoms C3 and C6 bent upward and downward, respectively, reproduces the experimental radial distribution function very well. The structure possesses C2 symmetry with the symmetry axis through the midpoints of the SiSi and opposite CC bonds. In the least-squares 10001

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Table 1. Experimental and Calculated Geometric Parameters of 1,4-Disilacyclohexanea GED (rh1)

MP2/cc-pVTZ

B3LYP/cc-pVTZ


SiC

1.877(1)

p1

1.889

1.896

Si1C2

1.870(1)

CC

1.559(4)

p2

1.544

1.549

Si1C6

1.877(1)d

p1

MP2/cc-pVTZ

B3LYP/cc-pVTZ

1.881

1.888

1.888

1.895

(SiH)mean

1.467(8)

p3

1.486

1.490

CC

1.552(4)

p2

1.537

1.542

(CH)mean

1.103(5)

p4

1.093

1.094

(SiH)mean

1.465(10) p3

1.485

1.490

CSiC

109.4(6)

p5

108.2

108.6

(CH)mean

1.101(5)

p4

1.093

1.094

SiCC HSiH

112.4(5)c 108.6d

112.1 108.6

112.9 108.3

Si1C2Si3 C2Si3C4

110.5(3) p5 109.0(16)e

108.9 108.2

110.0 108.8

HCH

106.8(24)

p6

106.1

105.8

Si3C4C5

113.6(10)e

113.7

114.6

flap(Si)

48.7(8)

p7

50.2

48.8

C4C5C6

112.5(11) p6

113.1

114.0

58.2

56.2

HSiH

108.2f

108.2

107.8

- 56.0

- 53.9

(HCH)mean

105.5(23) p7

106.5

106.0

flap(C2)b

40.0(23)

p8

43.4

40.5

flap(C5)c

58.1(12)

p9

b

τ(SiCCSi) 56.0(6)c τ(CSiCC) 54.4(9)

c

a

Parameters in Å and degrees. Error limits are 3σ values and refer to the last digit. b Flap angle between CSiC plane and CCCC plane. c Dependent parameter. d Not refined.

57.7

55.7

τ(Si1C2Si3C4) 42.4(22)e τ(C2Si3C4C5) 53.8(19)e

45.8 55.4

42.8 52.8

τ(Si3C4C5C6) 66.7(17)e

66.2

64.2

a

Parameters in Å and degrees. Error limits are 3σ values and refer to the last digit. For atom numbering, see Figure 5. b Flap angle between SiC2Si plane and SiSiCC plane. c Flap angle between CC5C plane and SiSiCC plane. d Difference between SiC bond lengths fixed to MP2 value. e Dependent parameter. f Not refined.




refinement five bond lengths (SiSi, SiC, C3C4, CH, and SiH), two bond angles (SiSiC and HCH), and two dihedral angles (CSiSiC and CCCC) were refined simultaneously together with eight vibrational amplitudes. The difference between the two CC distances, (C3C4) (C4C5), was fixed to the calculated value. The following three correlation coefficients had absolute values larger than 0.7: SiSiC/CSiSiC = 0.94; SiSiC/CCCC = 0.80; and CSiSiC/CCCC = 0.93. The results of the least-squares analysis are summarized in Table 3 (geometric parameters) and Table S3 (vibrational amplitudes). 3.2. Structure and Stability. General. Considering the systematic differences between experimental rh1 and calculated re

equilibrium structures and the experimental uncertainties, almost all experimental parameters are reproduced very well by the MP2 and DFT calculations. Only calculated SiC and SiH bond lengths are systematically too long. Experimental vibrational amplitudes (Tables S1S3) are very close to calculated values. Ring Strain. As mentioned in the Introduction, saturated sixmembered ring compounds with equal bond lengths, such as cyclohexane or cyclohexasilane, favor the chair conformation with bond angles and dihedral angles close to the ideal values of 109.5 and 60, respectively. This leads to minimum Baeyer and Pitzer strain. In compounds with heteroatoms in the ring and unequal bond lengths, some bond angles and dihedral angles deviate from the ideal values, leading to increased ring strain in the chair conformation. The GED analyses and quantum chemical calculations demonstrate that the gas phase structures of all three disilacyclohexanes possess chair or near-chair conformation. The 10002



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Table 4. Endocyclic Bond Skeletion in the Disilacyclohexanes



MP2/cc-pVTZ

CC bonds

SiC bonds

SiSi bonds

12

3

2

1

13 14

2 2

4 4

0 0

Table 5. Relative Energies, ΔH at 298 K (in kcal/mol), of the Disilacyclohexanes Using Different Model Chemistry Methods isomer

G4

12

14.24

14.38

14.31

14.98

13

0

0

0

0

14

5.87

5.82

5.90

5.88

B3LYP/cc-pVTZ

SiSi

2.324(4)

p1

2.337

2.345

SiC

1.884(3)

p2

1.896

1.904

C3C4

1.548(3)

p3

1.538

1.543

C4C5

1.544(3)b

(SiH)mean

1.468(10)

(CH)mean Si1Si2C3

1.105(5) 101.5(11)

1.534

1.539

p4

1.485

1.489

p5 p6

1.093 101.5

1.094 102.3

Si2C3C4

113.8(13)c

113.4

114.6

C3C4C5

115.8(18)c

115.2

116.0

HSiH

108.2d

108.2

107.7

(HCH)mean

106.3(36)

106.2

105.8

p7

isomer

τ(C6Si1Si2C3) 40.5(46) p8

38.6

334.9

τ(Si1Si2C3C4) 49.5(28) c

48.8

45.5

τ(Si2C3C4C5) 66.2(22) c τ(C3C4C5C6) 73.0(42) p9

68.0 76.6

65.6 75.2

a

Parameters in Å and degree. Error limits are 3σ values and refer to the last digit. For atom numbering see Figure 7. b Difference between CC bond lengths fixed to MP2 value. c Dependent parameter. d Not refined.

geometric parameters allow a qualitative estimate of the relative ring strain in these six-membered rings. In 14, both bond angles (CSiC = 109.4(6) and SiCC = 112.4(5)) and torsional angles (SiCCSi = 56.0(6) and CSiCC = 54.4(9)), are close to the ideal values, and therefore, ring strain is very small. In 13 all bond angles (109.0(16)113.6(10)) are close to the tetrahedral value, but one torsional angle (SiCSiC = 42.4(22)) deviates appreciably from the ideal value of 60. Thus, increased Pitzer strain is present in this ring. In 12 most bond angles (SiSiC = 101.5(11) and CCC = 115.8(18)), as well as dihedral angles (CSiSiC = 41(5) and CCCC = 73(4)), deviate strongly from the ideal values, causing high Baeyer and Pitzer strain in this ring. Hence, according to qualitative ring strain analysis, the relative stability of the disilacyclohexanes is predicted to be in the order 14 > 13 > 12. Bond Energies. The three disilacyclohexanes are configurational isomers and differ in the positions of the two silicon atoms within the ring system. Compound 12 also differs from the other isomers by the number of different bonds (Table 4). There is, at present, no convenient, self-consistent source of all bond energies.16 However, values of 83, 76, and 53 kcal/mol may be considered as accepted average bond energies for CC, SiC, and SiSi bonds, respectively.16 The weak SiSi bond makes 12 likely to be the least stable isomer, whereas 13 and 14 should possess similar bond energies.

G4MP2

G3B3

CBS-QB3

Relative Stabilities and Heats of Formation. The relative energies of the three disilacyclohexanes were calculated using several quantum chemistry composite methods: CBS-QB3,1720 G3B3,21 G4MP2,22 and G4,23 as implemented in Gaussian 09.24 These methods are designed for highly accurate thermochemistry and involve doing several single-point calculations with different correlation methods (MP2, MP4, QCISD(T), CCSD(T)), which are combined into a single electronic energy at a highly correlated/ complete basis set level. Thermal corrections are calculated from harmonic vibrational frequencies using DFT methods. The methods differ mainly in basis set extrapolation and the different use of correlation methods, with G4 being the most recently developed method and the most expensive. The results, shown in Table 5, reveal unsurprisingly 12 to be the least stable isomer on the disilacyclohexane potential energy surface. Compound 13 is, however, considerably more stable than 14 in contrast to what one would expect, based on the previous ring strain and bond energy analysis. All four methods are in good agreement with each other, showing little sensitivity to the protocol used. The G4 protocol was, hence, used for all subsequent calculations. To compare the stability of the disilacyclohexanes with other carbonsilicon rings, we now turn to heat of formation calculations. The heat (enthalpy) of formation at 298 K, ΔHf,298 is a common measure of stability of organic compounds, which is the relative energy of the molecule with respect to its constituent elements in their standard states. ΔHf,298 is typically derived by calculating a reaction energy, using compounds with known experimental enthalpies of formation. One approach would involve calculating the reaction enthalpy of reaction 1 Six Cy Hz f xSi þ yC þ zH

ð1Þ

which is the atomization enthalpy. The ΔHf,298 of SixCyHz is then obtained by adding to the atomization enthalpy the atomic heats of formation (stoichiometrically). The atomic heats of formation for H (52.103 ( 0.000 kcal/mol) and C (171.336 ( 0.014 kcal/mol) have been taken from current ATcT estimates (active thermochemical tables, version 1.110),2527 while the Si heat of formation (108.19 ( 0.15 kcal/mol) has been taken from a recent high-accuracy theoretical study.28 As the atomization reaction involves a dramatic change in electronic structure, atomization enthalpies are notoriously difficult to calculate accurately. 10003



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Table 6. Heats of Formation, ΔHf,298, (in kcal/mol) of Several CarbonSilicon Rings, Calculated Using Three Different Reactions with G4 Theory

a

reaction 1

reaction 2

reaction 3

1,2-disila

0.42

4.02

3.76

1,3disila

14.67

18.26

18.00

1,4-disila

8.79

12.39

12.13

cyclohexane

28.64

30.89

30.5

monosila 1,3,5-trisila

17.97 17.54

20.89 21.81

20.56 21.61

1,2,3-trisila

12.60

8.33

8.53

1,2,4-trisila

1.84

2.43

2.23

1,2,3,4-tetrasila

25.13

20.19

20.32

1,2,3,5-tetrasila

9.21

4.27

4.40

1,2,4,5-tetrasila

12.10

7.16

7.29

pentasila

32.26

26.66

hexasila

52.44

46.16a

Table 7. Charge Distribution in 1,4-Disilacyclohexane [Electrons] method

Si

C

Mulliken

0.59

0.51

NBO ESP

1.16 0.57

0.84 0.15

Table 8. Charge Distribution in 1,3-Disilacyclohexane [Electrons]a method

a

26.72

C(2)

Si(3)

C(4)

C(5)

Mulliken

0.73

0.56

0.52

0.17

NBO

1.34

1.17

0.84

0.38

ESP

0.52

0.73

0.37

0.27

For atom numbering, see Figure 5.

a

Here, only the Si6H12 + 6 H2 f 6 SiH4 reaction is used.

Simple DFT calculations using popular exchange-correlation approximations, for example, typically give poor heats of formation through the atomization approach (typical errors of several kcal/mol).29 Instead, it is preferable to choose reactions with small molecules having known enthalpies of formation and with the same types of bonds as this involves a much smaller change in electronic structure. Only few silicon compounds have well determined heats of formation, SiH4 being one with an experimental ΔHf,298 of 7.3 ( 0.3 kcal/mol.30 The heats of formation were, hence, also calculated using balanced reactions 2 and 3 using SiH4, CH4, C2H6, and H2 as reactants and products. The ΔHf,298 of CH4 (17.81 ( 0.01), C2H6 (20.03 ( 0.05), and H2 (0 kcal/mol, reference state of element) have been obtained from AtcT estimates made available in the AETDD/Thermodynamics database.31 aSix Cy Hz þ bH2 f cSiH4 þ dCH4

ð2Þ

eSix Cy Hz þ f H2 f gSiH4 þ hC2 H6

ð3Þ

As ΔHf,298 is the stabilization energy of a molecule with respect to its elements, the ΔHf,298 of a molecule can be straightforwardly compared with ΔHf,298 of other molecules. To gain further insight into the stabilizing or destabilization effects of carbonsilicon exchange of the cyclohexane ring, we calculated at the G4 level of theory, ΔHf,298 of several compounds with an increasing number of silicon atoms: cyclohexane, monosilacyclohexane, 1,2-disilacyclohexane, 1,3-disilacyclohexane, 1,4-disilacyclohexane, 1,3,5-trisilacyclohexane, 1,2,3-trisilacyclohexane, 1,2,4-trisilacyclohexane, 1,2,4,5-tetrasilacyclohexane, 1,2,3,4-tetrasilacyclohexane, 1,2,3,5-tetrasilacyclohexane, pentasilacyclohexane, and finally, cyclohexasilane. The G4 heats of formation for all these compounds are shown in Table 6 using the different reactions of eqs 13. Of these compounds, only the ΔHf,298 of cyclohexane is known experimentally, 29.25 ( 0.16 kcal/mol (ATcT estimate31), which is in good (∼1 kcal/mol) agreement with the G4 values. We do note that, in the original G4 theory paper,23 the heats of formation of silicon compounds are noted to be difficult to calculate accurately by the atomization approach and we thus presume that the values

using reactions 2 and 3 are more trustworthy, as cancellations of systematic errors are likely to occur. It must also be noted, however, that the SiH4 ΔHf,298 value is controversial.32 Nonetheless, the relative heats of formation are in good agreement for the three approaches. ΔHf,298 is predicted to be 3.9, 18.1, and 12.3 kcal/mol for 12, 13, and 14, respectively (averaged values from reactions 2 and 3, Table 6). By comparing ΔHf,298 of all compounds, we see that generally there is a trend for decreasing thermodynamic stability with increasing silicon substitution, from 30.7 kcal/mol for cyclohexane to +46.2 kcal/mol for cyclohexasilane. Nevertheless, several molecules break the trend and show considerable variability compared to their isomers, revealing the importance of silicon position in the ring. The symmetric 1,3, 5-trisilacyclohexane shows a remarkable stability; it is predicted to be more stable than any of the disilacyclohexanes and even more stable than monosilacyclohexane. Returning to the disilacyclohexanes, the important question is why is 13 more stable than 14? An intuitive guess arises form a closer inspection of the bond lengths. In 13, all endocyclic bonds should have a polar character; in 14, the CC bonds are clearly nonpolar. A closer look at the bond lengths in Tables 2 and 1, respectively, reveals that the CC bonds are shorter in 13 (1.552(4) Å) than the CC bonds in 14 (1.559(4) Å). In addition, we further note that the two SiC bonds in the SiCSi unit in 13 are significantly shorter (1.870(1) Å) than the SiC bonds in the SiCC units (two in 13 (1.879(1) Å) and four in 14 (1.877(1) Å)). For further verification, we also carried out charge distribution calculations on the isomeric disilacyclohexanes at the B3LYP/ 6-311+G(3df,2p) level of theory using three different charge models: Mulliken, NBO, and ESP atomic charges. Important values are given for 14 (Table 7) and 13 (Table 8). A close relation between bond lengths and bond polarity is nicely demonstrated by the calculations. A complete set of the calculated atomic charges is available in the Supporting Information. As a result, the ring strain in 13 is more than compensated by extra bond energy due to polarized bonds when 13 is compared with 14. 3.3. Potential Energy Surfaces (PES). The conformational surface of cyclohexane is well-known, it has been described as a conformational globe by Cremer and Pople in which the chair and the inverted chair forms sit at the two poles of the globe and the six boat and six twisted boats form a belt of pseudorotation along the meridian.33,34 It must be noted, however, that the 10004



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Table 9. Relative Energies, ΔE at 0 K (in kcal/mol), of Conformers of 1,4-Disilacyclohexane

Figure 8. 3-D presentation of a part of the potential energy surface of 1,4-disilacyclohexane. Relative energy in kcal/mol (B3LYP/STO-3G single point calculations) shown as a function of two endocyclic dihedral angles. See text for further discussion.

Figure 9. Chair-to-chair inversion of 1,4-disilacylohexane. B3LYP/ 6-311+G(d,p) calculated lowest-energy path using the STQN method. Stationary points A (chair), B (half-chair TS), and C (twist) are marked on the graph, and their molecular structures are shown below.

conformational globe only shows how the different conformations are related as described by puckering coordinates. The relative energy for each conformer then has to be calculated separately. In a different approach, the conformational surface of a six-membered ring can be constructed by varying two dihedral angles in steps of a few degrees and calculating the energy at each point of the grid. In this case, the energy is added as the third dimension onto a two-dimensional grid. The PES of a six-membered puckered heterocycle is not easily predicted. If one or more carbon atoms in cyclohexane are substituted by heteroatom(s), then the PES will be changed according to a lowering of the symmetry and the properties of the heteroatom(s).7,10,11 In such cases, it is possible that the number of stationary points, which are located on the PES as twist and boat forms, respectively, will be lower than six. Furthermore, the twist and boat forms, respectively, may not all have the same energy because they may have different geometries. In such cases it is advantageous to use the approach of varying two dihedral angles because this approach can be started from the two chair

B3LYP/6-311+G(d,p)

M06-2X/pc-3

chair

0.00

0.00

TS twist

5.98 1.65

6.70 1.72

forms and it does not rely on any presumptions about existing or nonexisting conformers. It may be sufficient to use inexpensive methods for calculating the grid, and then the lowest energy pathway for the chair-to-chair inversion can be performed using more expensive methods. For silacyclohexane, we have previously encountered six twist forms and four boat forms in addition to the two chairs on two enantiomeric pathways.10,11 The same situation is true for 1-substituted-1-silacyclohexanes.1,3538 We have used the B3LYP functional and the simple STO-3G basis set to map the PES of the three disilacyclohexanes by varying two dihedral angles in steps of 5 from 90 to 90. The minimum energy pathways for the chair-to-chair inversion in each case were calculated in redundant internal coordinates with the STQN method39 as implemented in Gaussian 03.40 The path was calculated in 2, 4, and 3 slices for 14, 13, and 12, respectively, using the keyword OPT(QST3, PATH = 11). We used the B3LYP functional with the 6-311+G(d,p) basis set for these calculations. The number of imaginary frequencies was used to verify the character of each stationary point (minimum or transition state). Further single-point calculations were then carried out on the B3LYP/6-311+G(d,p) geometries for all stationary points using the M06-2X method41,42 and the pc-3 basis set.4345 A special case is described for a part of the path for 13 below. 1,4-Disilacyclohexane. The PES resulting from B3LYP/STO3G calculations and varying the two dihedral angles Si1C2C3Si4 (ω23) and Si4C5C6Si1(ω56) is shown in Figure 8. In the figure, all energy values higher than 7.0 kcal/mol (relative to the chair) are cut off for better clarity. The PES of 14 is a very simple one. Only four local minima are found on the PES; two chair forms and two twisted forms. Four symmetry-related transition states (TS) connect the local minima. In Figure 9, the lowest-energy profile is shown. The TS from the chair to the twisted form corresponds, in this case, approximately to a half-chair or sofa in which a carbon atom has been flipped to be approximately coplanar with the four atoms next to it in the ring. The carbon atom involved can be to the left or to the right of the adjacent silicon atom corresponding to two enantiomeric pathways in Figure 8. The two most pronounced characters of the PES for 14 are its simplicity and the unusual low energy of the twist form, just about 1.7 kcal/mol higher than the chair (Table 9). A puckered six-membered ring is expected to have, in addition to two chair forms, six boat and six twist forms. Therefore, more conformers might be expected for 14; a boat with all C atoms in a gunwale position is one obvious possibility and it should be connected to twist forms that differ from the ones described above. Applying the semiempirical method PM3, such a boat form was found. However, according to B3LYP and MP2 calculations, this conformation was found to have two imaginary frequencies and a geometry optimization to the nearest stable minimum resulted in the low-energy twist already described. Hence, we conclude that only four local minima and four transition states are found as stationary points on the PES for this ring system. 10005




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Figure 12. B3LYP/6-311+G(d,p) calculated path between the two equivalent twist forms (Twists 1a and 1b). Stationary points C (Twist 1a), D (Boat 1), and C0 (Twist 1b), and E are marked on the graph, and their molecular structures are shown below.

Table 10. Relative Energies, ΔE at 0 K (in kcal/mol), of Conformers of 1,3-Disilacyclohexane B3LYP/6-311+G(d,p)

Figure 11. Chair-to-chair inversion of 1,3-disilacylohexane. B3LYP/6311+G(d,p) calculated lowest-energy path using the STQN method. Stationary points A (chair), B (sofa-like TS), C (Twist 1), D (Boat 1), E (Boat 2), and F (Twist 2) are marked on the graph and their molecular structures are shown below.

1,3-Disilacyclohexane. The PES for 13 (Figure 10, Figure 11) is considerably more complicated than that for 14. The first step, starting from a chair form, involves a sofa-like transition state of relatively low energy. In this TS, C2, the carbon atom between the two Si atoms, is almost coplanar with Si3, C4, C6, and Si1. The molecule then relaxes by forming a twist form (Twist 1). For symmetry reasons, there are two equivalent Twist 1 forms (Twist 1a and Twist 1b). Between them, there is a boat form on the PES (Boat 1) in which C5 and C2 may be regarded as taking the stern and prow position, respectively. The region of Twist 1a, Boat 1, and Twist 1b corresponds to a very flat area on the PES, so flat that Boat 1 was encountered as a shallow local minimum by the simple B3LYP/STO-3G calculations. It was even hard to characterize Boat 1 as a saddle point using B3LYP/6-311+G(d,p) calculations.

M06-2X/pc-3

chair

0.00

0.00

TS

3.15

3.76

Twist 1

2.59

2.67

Boat 1 Boat 2

2.62 4.63

2.87 4.73

Twist 2

4.20

3.99

By doing tight geometry optimizations (keyword: opt=vtight) and using a large grid (keyword: int=ultrafine), we were able to locate both conformers unambiguously and relate them to each other by a QST3 calculation. A pseudorotation connects Twist 1a with Twist 1b through Boat 1; however, the activation barrier is unusually low. B3LYP/6-311+G(d,p) and M06-2X/pc-3//B3LYP/ 6-311+G(d,p) calculations predict the energy difference as 0.04 and 0.20 kcal/mol, respectively (Figure 12 and Table 10). Besides all this, there is more to take note of regarding the PES for 13. The PES (Figure 10) is symmetric toward the diagonal 90(ω34), 90(ω16) to 90(ω34),90(ω16) according to the Cs symmetry of 13. It looks that the PES also is symmetric toward the diagonal 90(ω34), 90(ω16) to 90(ω34),90 (ω16) and one could just “jump” from one TwistBoatTwist region to a corresponding one that is related to the inverted chair. This is, however, not possible because the real PES has more dimensions than can be shown in the three-dimensional graph in Figure 10. The landscape, when moving further along the diagonal 90(ω34), 90(ω16) to 90(ω34), 90(ω16) in small steps toward the inverted chair, is a steep upward slope, and the lowest possible paths are to the left or equally to the right passing through a boat form (Boat 2) in which one Si atom takes the prow position. Boat 2 presents the highest energy point on the inversion pathway, and it relaxes, forming a Twist 2 conformer, which marks the midpoint of the pathway. If one starts the inversion from the other (“inverted”) chair, all the same characteristics are found, including a steep upward slope when moving across the diagonal 90(ω34), 90(ω16) to 90 (ω34), 90(ω16). In Figure 10, these slopes are only shown until they meet with equal energy at the 90(ω34), 90(ω16) to 90(ω34), 90(ω16) diagonal. It should be noted that a 10006



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Table 11. Relative Energies, ΔE at 0 K (in kcal/mol), of Conformers of 1,2-Disilacyclohexane


B3LYP/6-311+G(d,p)

M06-2X/pc-3

chair

0.00

0.00

Boat 1 Twist

4.54 3.45

4.71 2.96

Boat 2

5.10

5.00

state between a pair of two twist forms on the inversion path (Figure 14) corresponds to a Boat 2 at the midpoint of the inversion path. Boat 2, in which both Si atoms are in a gunwale position, is somewhat higher in energy than Boat 1 (Table 11). The central point on the PES, that is, 0(ω16), 0(ω34), has a vertical C2 axis and the same arguments as were described for the 13 PES apply here against a seemingly possible transfer from a twist form into the inverted chair without passing first through the Boat 2. In conclusion, we find for 12 six boat forms and four twist forms in addition to the two chairs on the PES.

4. CONCLUSIONS In summary, we have determined the molecular structure of the three parent disilacyclohexanes in the gas phase by gas electron diffraction. In general, there is a good agreement between experimental GED parameters and predictions by quantum chemical calculations. The isomeric compounds differ by the positions of the silicon atoms in the ring, which together with different bond lengths may give rise to ring strain. According to a qualitative analysis on bond angles and torsional angles, the order of relative stability is predicted to be 14 > 13 > 12. In addition, 12 contains one weak SiSi bond, which also predicts it to be the least stable isomer. G4 energy calculations, however, predict 13 to be more stable than 14 by 5.9 kcal/mol. The enhanced stability of 13 was shown to be caused by bond polarization, which can be deduced from bond shortening (GED results, compared to 14), and charge distribution (calculated values). A systematic variation of two endocyclic torsional angles followed by a single point energy calculation at each step is an efficient way to construct the PES of six-membered ring systems. Each disilacyclohexane has a characteristic PES that is not at all easily predicted. Figure 14. Chair-to-chair inversion of 1,2-disilacylohexane. B3LYP/6311+G(d,p) calculated lowest-energy path using the STQN method. Stationary points A (chair), B (Boat 1), C (twist), and D (Boat 2) are marked on the graph and their molecular structures are shown below.

pseudorotation involving six twist and six boat forms is possible in 13 analogous to the pseudorotation along the meridian of the conformational globe of cyclohexane. In contrast to cyclohexane, where all twist forms are equal and likewise all boat forms have the same energy, 13 has two boat forms of low energy (Boat 1) and four Boat 2 of high energy, but four Twist 1 of low energy and two Twist 2 of high energy. 1,2-Disilacyclohexane. All transition states on the PES for 12 (Figure 13) possess a boat character. Starting from a chair, the lowest transition state is a boat (Boat 1) in which one Si atom takes the prow position. Because of symmetry reasons, there are four Boat 1 forms on the PES; two of them are related to each chair form. Each Boat 1 relaxes into a twist form. The transition

’ ASSOCIATED CONTENT

bS

Supporting Information. Molecular intensities for 13 and 12 and vibrational amplitudes for 14, 13, and 12. Calculated charge distribution for the three isomers. Optimized geometries for all stationary points on the minimum energy pathways of the disilacyclohexanes. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Present Addresses §

Ossur hf, Grjothalsi 5, IS-110, Reykjavik, Iceland.

Notes †

Conformations of Silicon-Containing Rings. 10. For Part 9, see ref 1.

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’ ACKNOWLEDGMENT This work was supported by the University of Iceland Research Fund and by the Icelandic Centre for Research (RANNIS). The computing resources made available by the EaStChem Research Computing facility and the University of Iceland Computer Services are gratefully acknowledged. ’ REFERENCES

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Gas Phase Structures, Energetics, and Potential Energy Surfaces of

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