Journal of Molecular Structure 978 (2010) 14–19

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Journal of Molecular Structure

journal homepage: www.elsevier .com/locate /molstruc

A phenomenological relationship between molecular geometry changeand conformational energy change

Andras Bodi a,b,*, Ragnar Bjornsson a,1, Ingvar Arnason a

a Science Institute, University of Iceland, 107 Reykjavik, Icelandb Molecular Dynamics Group, Paul Scherrer Institut, 5232 Villigen, Switzerland

a r t i c l e i n f o

Article history:Received 19 August 2009Received in revised form 1 December 2009Accepted 1 December 2009Available online 6 December 2009

This work is dedicated to Prof. HeinzOberhammer on the occasion of his 70thbirthday.

Keywords:Nuclear repulsion energyConformational energyDensity functional theorySilacyclohexane

0022-2860/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.molstruc.2009.12.002

* Corresponding author. Address: Molecular DynInstitut, 107 Reykjavik, 5232 Villigen, Switzerland. Te

E-mail address: andras.boedi@psi.ch (A. Bodi).1 Present address: University of St. Andrews, Schoo

UK.

a b s t r a c t

A linear correlation is established between the change in the axial/equatorial conformational energy dif-ference and the change in the molecular geometry transformation during conformational inversion insubstituted six-membered ring systems, namely in the 1-substituted cyclohexane/silacyclohexane, cyclo-hexane/N-substituted piperidine and 1-substituted silacyclohexane/P-substituted phosphorinane com-pound families, and for the analogous gauche/anti conformational isomerism in 1-substitutedpropanes/1-silapropanes. The nuclear repulsion energy parameterizes the molecular geometry, andchanges in the conformational energy between the related compound families are linearly correlatedwith the changes in the nuclear repulsion energy difference based on DFT (B3LYP, M06-2X), G3B3, andCBS-QB3 calculations. This correlation reproduces the sometimes remarkable contrast between the con-formational behavior of analogous compounds, e.g., the lack of a general equatorial preference insilacyclohexanes.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction

Understanding the driving forces of conformational behavior,especially those in substituted cyclohexanes and analogous com-pounds is not only important from a practical point of view, span-ning from reaction kinetics to drug design [1], but conformers ofsubstituted cyclohexanes are also one of the archetypical schoolbook examples, by which chemistry students are initiated toconformational isomerism [2,3]. The proposed models invoke ste-ric effects, especially 1,3-synaxial interactions, dipole–dipole inter-actions, and, more often recently, hyperconjugation to describe theexperimentally observed behavior [4–6]. Winstein and Holness de-fined A-values as the thermodynamic preference for the equatorialconformation over the axial one in the chair conformation of mon-osubstituted cyclohexanes (A = Go

ax � Goeq) [7]. A-values are still

considered as a measure for the relative steric size of a substituent,though other models have also been proposed [8]. However, exper-imental A-values for silacyclohexanes often seem to be at oddswith what is expected based on analogies with cyclohexanes andalkanes as well as with expectations based primarily on steric ef-

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amics Group, Paul Scherrerl.: +41 56 310 4471.

l of Chemistry, KY16 9ST Fife,

fects [9–11]. A number of recent experimental results and calcula-tions are summarized in Table 1, including the anti ? gaucheinternal rotational energy in butane and 2-silabutane, a compara-ble process to the equatorial ? axial pseudorotation in six-mem-bered ring compounds [12]. The most evident difference betweenthe cycloalkane and silacycloalkane compound families is the lackof general equatorial preference in the latter. Steric effects as themajor argument for this feature in substituted cyclohexanes andthe corresponding preference for the anti conformer in butane, 1-and 2-silabutane has been questioned recently [6,12,13]. In con-trast, hyperconjugation has been proposed to play a decisive rolein making the eclipsed conformation a transition state and thestaggered one the minimum in ethane [14], although steric repul-sion has since been reestablished as the major factor [15]. In thepresent work, we describe a phenomenological correlation be-tween two physical quantities, the molecular geometry changeand the conformational energy change between six compoundfamilies: 1-substituted cyclohexanes and silacyclohexanes, 1-substituted propanes and 1-silapropanes, as well as 1-substitutedcyclohexanes and piperidines, and 1-substituted silacyclohexanesand phosphorinanes. The close relationship between the geometrychange and the conformational energetics suggests that the con-formational behavior is governed by the same forces in all speciesfamilies. As steric effects play a minor role in determining the ax-ial/equatorial equilibrium in silacyclohexanes (compare, e.g., CF3

and CH3 in Table 1), the steric need of a substituent cannot alone

Table 1Selected experimental and calculated equatorial ? axial free energies of conforma-tional inversion (DG = Go

ax � Goeq) in six-membered ring compounds for substituted

cyclohexanes and silacyclohexanes as well as for butane (methyl-propane) and 2-silabutane (1-methyl-1-silapropane).

L DG (kcal mol�1)

Substituted cycloalkane Substituted silacycloalkane

CH3 1.74 CFCl3 300 K [32,33] 0.45 Gas phase, 298 K [34]1.96 G3B3, 298 Ka 0.38 G3B3, 298 Ka

CF3 2.5 CFCl3, 300 K [35] �0.19 Gas phase, 293 K [9]2.51 G3B3, 298 Ka �0.23 G3B3, 298 Ka

F 0.25 Gas phase, 243 K [36] �0.31 Gas phase, 293 K [10]0.13 G3B3, 298 Ka �0.25 G3B3, 298 Ka

HgH �0.25 CDCl3, 183 K [31]CH3

b 0.71 Gas phase [37] 0.14 Gas phase, 298 K [12]0.63 G3B3, 298 Ka 0.08 G3B3, 298 Ka

Experimental values are given in italics with the temperature and the solvent or gasphase specified.

a This work.b Anti ? gauche internal rotational enthalpies (DH = Hgauche � Hanti) for butane

and 2-silabutane.

A. Bodi et al. / Journal of Molecular Structure 978 (2010) 14–19 15

establish the equatorial preference generally observed in cyclohex-anes. Thus, A-values reflect steric effects less than often assumed.

When two analogous compound families are compared, thechange in the nuclear repulsion energy difference (NRED) and thechange in the total energy difference between the conformers inthe corresponding compound pairs are found to be well correlated.Here, the NRED refers to the change in the nuclear repulsion en-ergy between two conformers of the same molecule (axial/equato-rial or gauche/anti). Due to the relatively limited amount ofexperimental data (accurate gas phase molecular geometries andconformational energies), several methods of calculation withvarying basis sets have been called into play, in order to show thatthe correlation is indeed real, and is no computational artifact.

The total nuclear repulsion is a global parameter describing thecompactness, i.e., the molecular geometry of a given conformer of amolecule. Apeloig et al. have studied the role of the nuclear repul-sion energy term in discussing the stability of methylene and silyl-ene singlet vs. triplet states [16]. Kar and Scheiner [17] as well asMineva, Sicilia and Russo [18] examined the potential energy sur-face, the chemical hardness, the chemical potential and the elec-tronic and nuclear energy terms along isomerization pathways in

Scheme 1. Overview of the studied compound families. The substituent indices corre1-silapropane set.

small molecules. Csizmadia et al. studied the balance betweenthe nuclear and the electronic components of the total energyalong coordinates of internal motion and discussed their relativecontributions [19]. Goddard and Csizmadia also published a parti-tioning of one-electron properties into electronic and nuclear com-ponents [20]. In view of the latter, the current results may be alsoviewed as indication that changes in the studied conformationalequilibria between different compound families are dominatedby the nuclear contribution.

2. Computational approach

Density functional theory (DFT) and composite (G3B3 and CBS-QB3) calculations were carried out with the Gaussian 03 [21] andNWChem 5.1 [22] program suites at the Scientific Modeling andSimulation Laboratory, Memorial University of Newfoundlandand at the Computing Service of the University of Iceland. Six com-pound families have been investigated as illustrated in Scheme 1:1-substituted propanes and 1-silapropanes (anti-gauche confor-mational isomerism), 1-substituted cyclohexanes, silacyclohex-anes, piperidines and phosphorinanes (equatorial–axialisomerism). The anti and gauche conformers of the substitutedpropane and 1-silapropane chains are analogous to the equatorialand axial chair conformers of the discussed six-membered ringcompounds [12].

The substituents show great diversity. Some of them are extre-mely electronegative, some are rather electron donating. They alsocover a large range in terms of steric need or cone angle. At thesame time, they are unbranched, so that the intrasubstituent inter-actions are negligible, and the orientation of the substituent rela-tive to the frame of the molecule is as well defined as possible.Not all of these substituted molecules may exist in the condensedphase, yet they are predicted to have stable anti/gauche or equato-rial/axial conformers in the gas phase that are minima on the po-tential energy surface. The wide selection of substituents isbeneficial in obtaining sufficient statistics on the correlation andis also interesting in testing its limits. The benefits of studyingpartly fictional species or molecules unfeasible to synthesize thusoutweigh the drawback of not being able to reproduce this studycompletely by means of experimental methods.

G3B3 calculations [23], which start with a B3LYP/6-31G(d)geometry optimization step, have been carried out on all species.

spond to those in Table 3 and Figs. 1–3. aLigands only studied in the propane/

16 A. Bodi et al. / Journal of Molecular Structure 978 (2010) 14–19

For the propane and 1-silapropane compounds, CBS-QB3 [24] anddensity functional theory calculations with the B3LYP [25] andM06-2X [26] exchange–correlation functionals and the 6-311++G(d,p) basis set, as well as semi-empirical AM1 [27] calcula-tions have also been carried out to check the stability of the ob-served correlation with respect to the computational approach.Additionally, the calculated energy differences for F, Cl, OH, CH3

and OCH3 substituted silacyclohexanes are in good agreement withthe CCSD(T) results of Weldon and Tschumper [28]. The CBS-QB3model chemistry has a B3LYP geometry optimization step at thestart with the triple-zeta CBSB7 basis set of the form 6-311G(2d,d,p) [29].

Selected G3B3 calculated A-values are compared withexperimental ones in Table 1. The agreement between calculationsand experiment is generally good, partly because the conformershave a similar electronic structure, so that the energy differencecan be reproduced unusually accurately even with routine computa-tional methods. Experimental data for piperidines and phosphorin-anes are few and far between, but, e.g., the G3B3 calculated3.53 kcal mol�1 equatorial ? axial free energy change in N-methyl-piperidine is in good agreement with the experimental3.16 kcal mol�1 [30].

The molecular geometry of each conformer was characterizedby the nuclear repulsion energy, obtained as

VNN ¼X

A;BA<B

ZAZB

RABð1Þ

where A and B index the constituent nuclei, ZA denotes their chargeand RAB their distance. The nuclear repulsion energy can be parti-tioned among the substituent–substituent (A and B both belong inthe substituent group), ring–substituent (only one of A or B belongsin the substituent group) and ring–ring (neither A nor B belong inthe substituent group) terms. As expected, it is the mixed ring–sub-stituent term that changes most during conformational inversion.According to Eq. (1), the ring–ring term accounts for only 15 ± 8%of the total change in nuclear repulsion during the axial ? equato-rial inversion n the substituted (sila)cyclohexanes, and the changein the intrasubstituent term is generally negligible. The lineardependence of the two data sets is characterized by the square ofthe correlation coefficient:

R2 ¼ ðhDDE � DDVNNi � hDDEihDDVNNiÞ2

ðhDDEi2 � hDDE2iÞðhDDVNNi2 � hDDV2NNiÞ

ð2Þ

where <X> stands for the expectation value of X, DDE refers to thechange in the conformational energy when e.g., the carbon atom to

Fig. 1. DDanti ? gaucheE vs. DDanti ? gaucheVNN calculated with the G3B3 compositemethod for the substituted propane/1-silapropane compound families. The linear fitis based on data from the Y = C ? Si columns of Table 3. Ligands omitted from the fitare labelled explicitly and plotted as diamonds (�).

which the substituent is attached is exchanged for silicon andDDVNN stands for the change in NRED, cf. Eqs. 3a, 3b.

The NRED and the conformational energy are not correlatedwithin a single compound set, e.g., R2 = 0.014 and 0.217 for substi-tuted cyclohexanes and propanes, respectively.

It has also been checked whether the change in frame–substitu-ent NRED term can be used to predict the conformational energychanges without an accurate and optimized frame geometry. Theaverage G3B3 anti and gauche propyl radical geometry (optimizedat the B3LYP/6-31G(d) level as in the first step of a G3B3 calcula-tion) were obtained by averaging the internal coordinates in thesame 15 compounds as used in the fit in Fig. 1. The substituentswere then attached to these fixed geometries with their G3B3-opti-mized set of bond lengths, angles and dihedral angles. The result-ing fit has a moderate correlation coefficient of R2 = 0.729, but ithinges on Mg+ and breaks down (R2 = 0.212) if Mg+ is removedfrom the fit. This suggests that partitioning Eq. (1) among ring–ring, ring–substituent and substituent–substituent terms is, albeitintuitive, not beneficial.

3. Results and discussion

A linear dependence of the change in the conformational energyon the change in the nuclear repulsion difference can be parame-terized by a and b:

DC!Si or C!N or Si!PDeq!axE � aDC!Si or C!N or Si!PDeq!axVNN þ b ð3aÞ

for ring compounds with axial/equatorial conformational isomer-ism, and

DC!SiDanti!gaucheE � aDC!SiDanti!gaucheVNN þ b ð3bÞ

for open chain compounds with gauche/anti conformational isom-erism. Note that the conformational energy changes and changesin NRED are different in magnitude, which is also reflected in theirunits, kcal mol�1 and hartree (Eh), respectively. The nuclear repul-sion energy and the electronic energy are, thus, in a delicate equilib-rium, in which nuclear repulsion energy changes in e.g.,conformational inversion are almost quantitatively counteractedby changes in the electronic energy. The nuclear repulsion energyitself is only used to characterize the different conformers and theircompactness and not as a measure of the energy content of a con-formation by itself. For a molecular geometry with 3N � 6 degreesof freedom, there exists a 3N � 7 dimensional isosurface with a con-stant value of the nuclear repulsion energy and very different totalenergy. However, changes in the nuclear repulsion energy betweenconformers (NRED) are uniquely defined, and are characteristic oftheir different molecular compactness change.

Several methods and basis sets were employed for the gauche/anti conformational isomerism in substituted (sila)propanesaccording to Eq. (3b). Table 2 summarizes the correlation coeffi-cients for conformational energy changes with respect to changesin the NRED obtained with different methods and basis sets. TheM06-2X functional was used to calculate the electronic energy atboth the M06-2X and the B3LYP optimized geometry. A standardsemi-empirical method, AM1 was also used to study how impor-tant accurate geometries are. The AM1 fit results (R2 = 0.196, with-out the Mg-substituted (sila)propanes for which the geometryoptimization failed) show that without reliable equilibrium geom-etries, the fit breaks down. The tabulated results for every speciesas well as the complete set of linear regression parameters areavailable as electronic Supplementary material.

Electronegative substituents are generally found to have anequatorial preference in cyclohexane and an anti preference in pro-pane, for example CF3 (2.31, 1.09 kcal mol�1), SiF3 (1.01,0.57 kcal mol�1, respectively). This behavior changes significantly

Table 2Correlation coefficients (R2) for linear fits to changes in NRED vs. conformational energy changes (DDanti ? gaucheE and DDanti ? gaucheG vs. DDVNN) calculated with differentmethods and basis sets for 1-substituted (sila)propanes.

DDanti ? gaucheE (kcal mol�1) calculated at DDanti ? gaucheG (kcal mol�1) calculated at

G3B3 CBS-QB3 Using the 6-311++G(d,p) basis set with

B3LYP M06-2X G3B3

//M06-2X //B3LYP

Change in NRED, DDVNN (Eh) calculated atG3B3 0.928 0.917 0.920 0.930 0.926 0.934CBS-QB3 0.880 0.887 0.889 0.898 0.893 0.874B3LYP 0.869 0.869 0.877 0.892 0.892 0.849M06-2X 0.885 0.853 0.853 0.880 0.886 0.867Average 0.892 0.883 0.885 0.900 0.899 0.883

DDanti ? gaucheE = a DDVNN + b. For a and b values see Supplementary material. G3B3 geometry is optimized at B3LYP/6-31G(d), CBS-QB3 geometry is optimized at B3LYP/CBSB7. M06-2X//M06-2X and M06-2X//B3LYP stand for energies calculated with the M06-2X functional at geometries optimized using the M06-2X and the B3LYP exchange–correlation functional, respectively. DDanti ? gaucheG vs. DDVNN regression analysis is carried out at T = 298 K. Zero-point energy corrections for B3LYP/6-311++G(d,p) andM06-2X/6-311++G(d,p) energies are taken from B3LYP/CBSB7 (CBS-QB3) frequency analysis.

A. Bodi et al. / Journal of Molecular Structure 978 (2010) 14–19 17

in silacyclohexane, because the axial conformer is preferred by0.61 kcal mol�1 for CF3 and by 0.45 kcal mol�1 for SiF3, and in 1-sil-apropane, in which the gauche conformer becomes marginallymore stable than the anti one (by 0.08 and 0.16 kcal mol�1, respec-tively). Electropositive substituents, such as alkali and alkalineearth metals are prone to have an axial preference in cyclohexane,and a less pronounced axial preference for the silicon-containingcompound. For example, the axial conformer of the Mg-substitutedcyclohexane cation is preferred by 3.23 kcal mol�1, whereas theaxial conformer is only preferred by 0.38 kcal mol�1 in the analo-gous silacyclohexane. Despite the lack of a generally valid trendin the conformational energies when carbon is exchanged for sili-con, changes in the energy difference correlate well with thechanges in the NRED.

In the correlation analysis in Table 2, all ligands in Scheme 1were considered, except for Li, NCH3

� and OCF3, appearing as dia-monds in Fig. 1. The average R2 is 0.747 and 0.890 including everyligand, and without Li, NCH3

� and OCF3, respectively. The Mg+ sub-stituent appears to play a disproportionately large role in estab-lishing the correlation in Fig. 1. Still, even without the Mg+

substituent, R2 only decreases from 0.928 to 0.827 for the G3B3 en-ergy/geometry fit with the other regression parameters hardlychanging, so the role of Mg+ is in fact moderate. Correlation coeffi-

Table 3Changes in the conformational energy and the NRED for 1-substituted propanes and 1-si(equatorial/axial conformers, X) as in Scheme 1, calculated with the G3B3 method.

L Y = C ? Si X = C ? Si

DDanti ? gaucheE(kcal mol�1)

DDanti ? gaucheVNN (Eh) DDax ? eqE(kcal mol�1)

DDax ? e

(1) CH3 �0.61 �0.105 �1.62 �0.446(2) CF3 �1.17 0.794 �2.92 1.443(3) SiH3 �0.75 �0.100 �1.29 �0.570(4) SiF3 �0.73 0.838 �1.46 2.948(5) F 0.12 �0.679 �0.27 �2.404(6) Cl �0.20 �0.358 �0.83 �1.522(7) OH 0.04 �0.356 �0.28 �1.557(8) OCl �0.17 �0.349 �0.56 �1.107(9) SH �0.43 �0.190 �1.23 �0.871

SHa �0.45 �1.385(10) OCH3 �0.08 �0.258 �0.25 �1.473(11) Li 0.40 �0.404 1.95 �1.066(12) Na 0.58 �1.222 2.28 �3.224(13) Mg+ 2.02 �3.562 2.85 �7.991(14) MgCH3 0.25 �1.215 1.36 �3.563(15) OCF3 �0.10 �0.708(16) NH3

+ �0.26 0.038(17) NF3

+ �1.23 0.663(18) NCH3

� 0.27 �0.359

a Both the extraannular and the intraannular conformations of the SH group are stud

cients with G3B3 calculated conformational free energy changes(T = 298 K) are also reported in Table 2. The thermal effects playonly a minor role because of the structural similarity of the con-formers, but the entropic effects are large for the open chain com-pounds, as the multiplicity of the gauche and anti conformers aredifferent, thus Danti ? gaucheG = Danti ? gaucheH � TDanti ? gau-

cheS � RT ln 2, where Danti ? gaucheS is the rovibrational contributionto the entropy change. However, the RT ln 2 term cancels out whenthe changes between two compound families are considered, and,therefore, only conformational energy changes are consideredhereafter. G3B3 conformational energy changes between com-pound families (T = 0 K) and the corresponding changes in theNRED are listed in Table 3 and plotted for propanes/1-silapropanesin Fig. 1, and for the ring systems in Figs. 2 and 3.

The fit to the conformational energy change vs. the change inNRED for substituted cyclohexanes and silacyclohexanes is shownin Fig. 2. The fit is considered without the outlier substituents Li,SiF3 and Na that appear to establish a slightly offset linear trendthemselves. Here again, Mg+ seems to have an overwhelming influ-ence in ensuring the linear correlation. However, when Mg+ is re-moved from the set, the correlation coefficient actually improvesslightly from R2 = 0.927 to R2 = 0.937. Out of the three substituentsnot included in the fit, the penalty for including SiF3 and Na is in

lapropanes (anti/gauche conformers Y), and substituted six-membered ring systems

X = C ? N X = Si ? P

qVNN (Eh) DDax?eqE(kcal mol�1)

DDax?eqVNN (Eh) DDax ? eqE(kcal mol�1)

DDax ? eqVNN (Eh)

�1.64 0.801 �0.42 0.1190.54 2.484 �1.58 2.2141.03 4.131 �0.11 0.206No ax/eq isomers found No ax/eq isomers found�1.27 0.535 0.66 �2.657�1.30 0.868 0.51 �1.306�1.17 0.649 0.77 �1.599No ax/eq isomers found 0.58 �3.131�0.77 1.336 0.06 �0.497�0.61 1.691 0.73 �1.233�1.24 1.009 0.72 �2.780No ax/eq isomers found 1.76 0.213No ax/eq isomers found 2.11 �2.792�2.12 7.523 1.35 �2.221No ax/eq isomers found 1.72 �2.555

ied in the ring compounds due to the small energy difference between them.

Fig. 2. DDax ? eqE vs. DDax ? eqVNN based on G3B3 results for the substitutedcyclohexane/silacyclohexane compound families. The fit is based on data from theX = C ? Si columns of Table 3. Ligands omitted from the fit are labelled explicitlyand plotted as diamonds (�).

Fig. 3. G3B3 computed DDax ? eqE vs. DDax ? eqVNN for the 1-substituted cyclo-hexane/piperidine (N, fit – continuous line) and silacyclohexane/phosphorinane (�,fit – dashed line) compound families.

18 A. Bodi et al. / Journal of Molecular Structure 978 (2010) 14–19

fact moderate, with ‘‘the all but Li” linear regression havingR2 = 0.766. In short, the changes in NRED span a wide range, andso do changes in the conformational energy, in good correlationwith the former. The linear approximation predicts the calculatedchange in the axial ? equatorial energy change quantitativelymost of the time, and the prediction breaks down only for few li-gands, possibly because of significant electronic structure changesbetween the conformers.

In order to put these results in context, substituted piperidinesand phosphorinanes have also been examined (Fig. 3, substituentMg+ values for X = C ? N and substituent Li values for X = Si ? Pfrom Table 3 are not plotted or used in the regression analysis).Equatorial and axial conformers have not been found when the li-gand was SiF3 in phosphorinane, and SiF3, Li, Na, OCl, or MgMe inpiperidine. This may indicate either a very low barrier to confor-mational inversion or a potential energy surface with different fea-tures from the ones in the silacyclohexane and cyclohexaneanalogues. In the phosphorinane set, Li is again the exception,but the rest of the species exhibit a linear regression withR2 = 0.746. The number of ligands for the substituted piperidinesis smaller, but, plotted without the outlier Mg+, a quite good linearfit is possible to the remaining nine ligands (R2 = 0.913).

4. Conclusions

The conformational properties of similarly substituted 6-mem-bered ring and 3-membered open chain compounds have been

studied. When pairs of likewise substituted compounds from twocompound families are compared, the difference in NRED and thedifference in the conformational inversion energy are found to becorrelated. The correlation is linear for 1-substituted cyclohexanesand silacyclohexanes, propanes and 1-silapropanes, and, althoughslightly worse, also linear for 1-substituted cyclohexanes andpiperidines, as well as for 1-substituted silacyclohexanes and phos-phorinanes. To the best of our knowledge, this is the first time sucha correlation is described between geometry change and energychange between different molecules.

Electropositive substituents, such as alkali metals and alkalineearth metal ions appear to have strong axial preference in cyclo-hexane, in agreement with the experimentally observed axial pref-erence for mercury substituted cyclohexane molecules [31].Conversely, the strong axial preference for electropositive substit-uents in cyclohexane is well-nigh inverted in silacyclohexane. Onthe other hand, the strong equatorial preference for relatively largeelectronegative or electroneutral substituents in cyclohexane, suchas CF3, Cl or SiF3, becomes diminished or inverted in substitutedsilacyclohexanes. The changes in the NRED seem to reflect both ef-fects in a quantitative way in the cyclohexane/silacyclohexanecompound family as well as in the propane/1-silapropane, cyclo-hexane/piperidine and silacyclohexane/phosphorinane families.Hence, a strong correlation between the conformational energychange and the conformational geometry change suggests thatthe same factors determine the conformational behavior in allcompound families. As the importance of the 1,3-synaxial repulsionis expected to have a secondary role in the conformational equilib-rium of substituted silacyclohexanes, this observation lends weightto arguments about the lesser role of steric factors in substitutedcyclohexanes than had been previously assumed.

A causative relationship between the molecular geometrychange and the conformational energy change between differentcompound families is unlikely. It should, thus, be inferred thatthese two observable parameters are driven both by a third fea-ture. The recent increase in invoking hyperconjugation to describesome of the better-known conformational equilibria suggests thatit may also prove useful in explaining the conformational behaviorof species containing third-row atoms, which is sometimes mark-edly different from that of the analogous second-row molecules.

Acknowledgements

We would like to acknowledge the computational facilitiesmade available by Prof. Paul Mezey, Director, Scientific Modelingand Simulation Laboratory (SMSL), Memorial University ofNewfoundland.

Appendix A. Supplementary data

Supplementary Information available: G3B3, CBS-QB3, B3LYP/6-311++G(d,p), M06-2X/6-311++G(d,p), AM1 single point energies,B3LYP zero-point energy corrections and room temperature G3B3free energies for the substituted propane/1-silapropane com-pounds, G3B3 energies for the other compounds, and their correla-tion analysis with NRED.

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.molstruc.2009.12.002.

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