The Nature of the Silicon–Oxygen Bond - Organometallics (ACS

ARTICLE pubs.acs.org/Organometallics

The Nature of the Silicon
Oxygen Bond Frank Weinhold and Robert West* Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706, United States

bS Supporting Information ABSTRACT: Even though siloxanes form the basis for the entire worldwide silicone industry, the nature of silicon
oxygen bonding has not been well understood. In the present work we employ correlated and highly polarized basis levels and natural bond orbital techniques to analyze the anomalous structural and basicity properties of inorganic Si
O
Si linkages compared to organic C
O
C congeners. We find that vicinal hyperconjugative interactions of nO f σ*XH type are primarily responsible for promoting the increased torsional flexibility and reduced basicity that strongly distinguish disiloxanes from ethers. Paradoxically, the key to enhanced siloxane hyperconjugation lies in the inherently larger X
O
X bond angle for X = Si (consistent with electronegativity and hybridization variations predicted by Bent’s rule), even though such resonance-type corrections are generally stronger in ethers (X = C) at any particular X
O
X angle. These findings have important implications for many aspects of silicone chemistry as well as for improved general understanding of basicity and H-bonding phenomena in terms of resonance-type donor
acceptor (rather than “electrostatic”) concepts.

’ INTRODUCTION Siloxanes and
(R2SiO)n
polymers exhibit outstanding suppleness and inertness properties that underlie the worldwide industry of silicone-based polymeric materials. These properties are in puzzling contrast to those of corresponding organic ethers and alcohols, calling into question our understanding of unique electronic features that distinguish Si from other members of its periodic family. Numerous theoretical1
5 and experimental6
13 studies have addressed the anomalous character of Si
O vs C
O bonding, but the fundamental origin of these differences remains uncertain. Particularly paradoxical is the weak basicity of Si
O vs C
O linkages, despite the expected higher anionic character of O bonded to more electropositive Si. The depressed basicity (and resulting chemical inertness) was originally attributed to p
d dative π-bonding,6,14 but this view was superseded by a model involving hyperconjugative interaction between p-rich Si bonding hybrids and antibonding CH or SiH σ* orbitals.1
3,8
11 The nature of Si
O bonding might have been considered solved at this time. However the question has been decisively reopened in recent papers by Gillespie and Johnson4 and by Grabowski and co-workers,5 based on calculations of the electron localization function. In this view the Si
O bond is regarded as essentially ionic. The latter authors repeatedly describe the hyperconjugative model as “obsolete”.5 These diverse pictures argue the need for further clarification of the nature of Si
O bonding. The unique features of Si
O bonding profoundly affect the physical and chemical properties of diverse natural and synthetic materials ranging from clay minerals15 to the ubiquitous siliconebased ingredients of personal care products.16 The anomalous rheological and inertness properties of cyclic methylsiloxanes and other silicone-based materials are also linked to dispersement and persistence problems of increasing ecological concern.17
19 r 2011 American Chemical Society

In the broader conceptual domain, the surprising structural and acid
base properties of Si
O bonds are highly relevant to ongoing controversies20 concerning the theoretical understanding (and proper computational modeling) of torsional barriers, H-bonding, and other “noncovalent” phenomena of broad chemical and biochemical interest. Thus, improved understanding of the electronic origins of anomalous Si
O bonding properties is of considerable practical and conceptual importance. The present work aims to theoretically clarify fundamental electronic differences between Si
O and C
O linkages that affect molecular structure, vibrational stiffness, and chemical basicity in inorganic silicones vs organic ethers. For this purpose we employ ab initio and density functional computational methods21 in conjunction with natural bond orbital (NBO) analysis techniques.22 Our aim is to gain a coherent conceptual picture of siloxane vs ether linkages (consistent with best available modern wave function technology) that rationalizes fundamental structural, vibrational, and basicity properties and provides practical guidance to their chemical modification and control.

’ NBO-BASED QUANTITATION OF HYPERCONJUGATION NBO theory23 permits general dissection of the molecular wave function Ψ into an idealized localized Lewis (L) wave function ΨL and its non-Lewis (NL) perturbative correction ΨNL, viz., Ψ ¼ ΨL þ ΨNL

ð1Þ

Received: July 23, 2011 Published: October 03, 2011 5815

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The starting ΨL is the natural Lewis structure (NLS) determinantal wave function of doubly occupied Lewis-type NBOs corresponding to the idealized Lewis dot diagram of freshman chemistry. We seek the origins of siloxane structural and basicity anomalies in details of such NBO-based L/NL decomposition. The perturbative correction ΨNL includes all configurational contributions from residual NL orbitals such as valence antibonds and extravalent Rydberg-type NBOs. Each L-type NBO is optimally chosen to maximize its contribution to total electron density F, so the latter can be expressed as the sum of the dominant NLS contribution FL and its resonance-type corrections FNL, viz., F ¼ FL þ FNL

Table 1. Geometrical and Selected Spectroscopic Parameters (for seven lowest IR frequencies) of Disilyl Ether (DSE) and Dimethyl Ether (DME), Comparing Present Work with Best Available Experimental and Theoretical Estimates.(H0 , H00 denote in-plane vs out-of-plane H atoms in the C2v skeletal framework) X = Si parameter

where εi, εj* are the respective σi, σ*j orbital energies (diagonal matrix elements of the Fock or Kohn
Sham one-electron effective Hamiltonian h), and qi is the occupancy of σi (∼2 for closed-shell, ∼1 for open-shell NBOs). Alternatively, ΔEi,j* can be estimated from the variational energy raising when σi
σ*j interaction is deleted from the calculation (by the $DEL keylist option28), viz., ΔEi, j = ΔEi, j ð$DELÞ ¼
½Eij ð$DELÞ
E

ð3bÞ

The $DEL-type estimates can also be extended to multiple donor
acceptor interactions, including contributions from all possible NL-type NBOs (NOSTAR deletion), which corresponds to the idealized localized NLS limit, EL: EL  Eð$DELÞ ðNOSTARÞ

ð4aÞ

Similar perturbative estimates can be obtained by adding the individual second-order ΔEi,j*(2) estimates of eq 3a, but the composite E($DEL) estimate takes partial account of higher-order coupling effects. Moreover, in Hartree
Fock theory the NOSTAR evaluation (eq 4a) corresponds to the rigorous variational expectation value for the idealized ΨL, viz., EL ¼ ÆΨL jHjΨL æ

ð4bÞ

HF-based evaluations of E($DEL) therefore have a more secure ab initio foundation than analogous DFT-based evaluations and will be employed in the present work.

b

CCSD(T)

X=C c

this work

expt

d

this workc

Angles (deg)

ð2Þ

ð3aÞ

expt

X
O
X

For primary covalent bonding effects in unsaturated species, the dominant FL contribution commonly exceeds 99.9% of total F and the residual small FNL contribution can be safely ignored. However, the resonance-type FNL terms often dominate the description of “noncovalent” phenomena such as torsional barriers24 or H-bonding25 that have no obvious origin in the NLS framework. The FNL contributions corresponding to hyperconjugative σ-delocalization effects26 are therefore of primary importance in the present study. In NBO theory, “delocalization effects” correspond to interactions between L-type (σi “donor”) and NL-type (σ*j “acceptor”) NBOs that represent departures (“resonance”) from the idealized NLS picture. The resonance-type stabilization ΔEi,j* due to a chosen σi
σ*j donor
acceptor interaction can be estimated by simple second-order perturbation theory as27 ΔEi, j = ΔEi, j ð2Þ ¼
qi Æσi jhjσ j æ2 =ðεj 
εi Þ

a

151.2

145.3

150.2

111.2

112.7

H0
X
H00

109.6

109.6

109.2

109.0

H00
X
H00

108.9

109.5

108.0

108.5

1.645 1.480

1.411 1.085

1.412 1.088

1.484

1.099

1.097

Bond Lengths (Å) X
O X
H0

1.631

X
H00

1.645 1.479 1.484


1

IR Frequencies (cm ) XH3 torsion(sym)

25

19

XH3 torsion(asym)

48

43

242

207 240

XOX bend

68

97

87

418

409

XO stretch (sym)

599

605

580

928

935

XH3 rock

717 717

716 726

710 720

1046 1179

1115 1161

760

755

745

1244

1190

Linearization Barrier (kcal/mol) ΔElin

0.3

0.48

0.21

33.4

a

J. Koput and A. Wierzbicki, J. Mol. Spectrosc. 1983, 99, 116; J. R. Durig, M. J. Flanagan, and V. F. Kalasinsky, J. Chem. Phys. 1977, 66, 2775; see Bartlett et al. for other experimental values and references. b CCSD(T)/ cc-pVTZ: A. R. Al Derzi, A. Gregusova, K. Runge, and R. J. Bartlett, Int. J. Quantum Chem. 2008, 108, 2088. c B3LYP/aug-cc-pVTZ, this work. d R. C. Taylor and G. L Vidale, J. Chem. Phys. 1957, 26, 122; A. A. Chalmers and D. C. McKean, Spectrochim. Acta 1965, 21, 1387; Y. Nilde and M. Hayashi, J. Mol. Spectrosc. 2003, 220, 65; http://cccbdb.nist.gov/expgeom2.asp?casno=115106&charge=0.

’ THEORETICAL MODEL OF SILOXANE ANGULAR AND H-BONDING PROPERTIES Although organic ethers and alcohols are rather well described by routine ab initio and density functional computational levels, accurate computational modeling of silyl ethers is far from routine. The parent disilyl ether (DSE) compound disiloxane (SiH3OSiH3) exhibits unusual bending and torsional properties that have been shown to require both extended f-type basis functions and inclusion of dynamical correlation effects for accurate description.29 Particularly challenging is the anharmonic angular potential, which features an unusually large Si
O
Si bending angle (ΘSiOSi ≈ 151) and small barrier to linearization (ΔElin ≈ 0.3 kcal/mol).30 In the present work we adopt the B3LYP hybrid density functional method with augmented Dunning-type tripleζ (aug-cc-pVTZ) basis set31 that incorporates both extended diffuse and d/f polarization functions in a correlation-consistent manner, as implemented in the Gaussian 09 program.32 Table 1 compares our B3LYP/aug-cc-pVTZ geometrical and bending parameters for DSE with experimental and highest available [CCSD(T)/cc-pVTZ] theoretical values of Bartlett and co-workers.33 The overall agreement appears quite satisfactory, 5816

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Table 2. Selected B3LYP/aug-cc-pVTZ Energetic (kcal/mol) and Geometrical (Å, deg) Parameters of H-Bonded Me3XOXMe3
Phenol (HMDSE
phenol, HMDME
phenol) and H3XOXH3
Water (DSE
H2O, DME
H2O) Complexes (X = Si or C), with Available Experimental Comparisons in Brackets (Note that neglected anharmonicity and vibrationalaveraging corrections strongly affect the accuracy of T-dependent ΔHHB, ΔGHB values) X = Si

X=C

Me3XOXMe3
Phenol
3.67
1.93


6.45b
4.87

[
3.82]a

[
7.31]a

+9.24

+4.87

[+0.85]a

[
0.75]a

RXO

1.677

1.462b

ROO

2.905

2.842b

ΔEHB ΔHHB ΔGHB

ΘXOX

139.8

127.0b

jXXOO

150.5

139.4b

Figure 1. Calculated X
O
X bending potentials ΔEbend(ΘXOX) for DSE (X = Si, crosses) and DME (X = C, circles), showing full B3LYP (solid line), uncorrelated HF (dotted line), and H-bonded (XH3)2O 3 3 3 HOH complex (dashed line) angular behavior for each species. A heavy dotted line marks the linear limit taken as the “zero” for each plotted potential curve (whereas the actual potential curves are widely separated in energy for each species and theory level).

H3XOXH3
Water

a

ΔEHB


2.01


4.85

ΔHHB


0.58


3.16

ΔGHB

+7.35

+4.06

RXO

1.662

ROO

3.024

1.418 2.869

ΘXOX

139.3

113.0

jXXOO

161.9

138.6

Ref 8. b cc-pVTZ basis; ref 34.

including subtleties of stretch
bend coupling and silyl-tilt distortions not detailed in Table 1. Although the qualitative aspects of hyperconjugation and basicity variation (discussed below) are adequately represented even at lower levels that lack the weak angular bending feature (e.g., B3LYP/6-311++G**, B3LYP6-31 +G*, which were also examined as theoretical models), the more accurate (but numerically challenging34) B3LYP/aug-cc-pVTZ treatment gives reasonable assurance that no significant features of Si
O
Si bending energetics are being overlooked. The final two columns of Table 1 display analogous calculated vs experimental properties of dimethyl ether (DME) for comparison. To compare with available experimental measurements of siloxane vs ether basicity,8 we also carried out corresponding calculations on equilibrium H-bonded complexes of phenol (C6H5OH) with hexamethyldisiloxane [HMDSE, Si(CH3)3OSi(CH3)3] and di-tert-butyl ether [HMDME, C(CH3)3OC(CH3)3, B3LYP/cc-pVTZ level only35], as shown in Table 2. Comparison B3LYP/aug-cc-pVTZ calculations for model DSE
water and DME
water complexes are also shown in the table, exhibiting the rather consistent 2
3 kcal/mol basicity difference that is also found in many other H-bonded complexes of siloxanes vs ethers.8 As noted in the table caption, it is evident that quantitative treatment of HMDSE
phenol H-bonding energetics would require careful vibrational averaging and anharmonicity corrections over the soft Si
O
Si bending potential, beyond the scope of present treatment. Nevertheless, the calculated equilibrium ΔEHB and standard-state ΔH and ΔG values seem to agree qualitatively with experiment in reflecting the measured 2
3 kcal/mol

Figure 2. Comparison potentials for idealized
XH3 torsions (rigidrotor twisting with respect to equilibrium B3LYP/aug-cc-pVTZ subtrate geometry) in DME (circles) and DSE (crosses), showing the virtually vanishing rotation barrier in the latter case.

reduction in phenol H-bonding to siloxanes vs ethers, consistent with other measures of Si
O
Si inertness. As a simple model of DSE and DME angular properties (similar to that of ref 5), we calculated the B3LYP/aug-cc-pVTZ adiabatic bending potential E(ΘXOX) for ΘXOX (X = Si, C) bending angles in the range 90
180 at 10 increments, with all other geometrical variables optimized at each point. We also calculated the adiabatic bending potential for the hydrogen-bonded DSE
H2O and DME
H2O complexes to obtain the strength of H-bonding, ΔEHB(ΘXOX), at each bending angle. This basic angular-bending model forms the starting reference point for theoretical dissection of hyperconjugative effects to be discussed below. Bending and Torsional Potentials. Figure 1 displays the calculated angular potential (relative to the linear ΘXOX = 180 limit, taken as “zero”) for each species, showing the qualitatively different bending behavior of DSE vs DME at correlated or uncorrelated theory levels as well as in their H-bonded complexes. DME exhibits a deep angular well centered near 110, as expected for “sp3-hybridized” organic species, whereas DSE exhibits only a shallow bending minimum centered near 150, 5817

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Table 3. Calculated Angular Dependence of H-Bonding Properties in DME
Water and DSE
Water Complexes, Showing Net Binding Energy ΔEHB (kcal/mol), ROO Separation, and Nonplanarity Φnp (dihedral X
X
O 3 3 3 O angle) at Each Bending Anglea X = Si

X=C

ΘXOX

ΔEHB

ROO (Å)

Φnp (deg)

ΔEHB

ROO (Å)

Φnp (deg)

90


3.52

2.943

133.5


4.78

2.876

109.4

100 110


3.39
3.20

2.949 2.960

147.1 118.8


4.73
4.81

2.881 2.873

121.4 154.7

120


2.95

2.973

160.4


4.96

2.857

148.6

130


2.61

2.995

156.6


5.11

2.837

165.4

140


2.21

3.027

161.6


5.16

2.820

171.9

150


1.68

3.081

167.8


4.95

2.822

174.5

160


1.03

3.150

166.8


4.31

2.851

183.0

170


0.42

3.518

164.3


3.28

2.936

176.2

180


0.38

4.599a

140.8a


2.06

3.081

198.9

Figure 3. Angular dependence of H-bond strength in DME
water (circles) and DSE
water (crosses) complexes; cf. Table 3. The vertical dotted lines mark the equilibrium bending angle for each monomer.

Boldface entries mark the approximate ΘXOX equilibrium bending angles for each monomer. a

barely perceptible on the scale of the diagram. In each case, H-bonding (dashed line) is seen to slightly deepen the well and shift the equilibrium bending angle to slightly smaller value, but the sharp contrast between DME and DSE bending characteristics remains conspicuous. Furthermore, this contrast is essentially unaffected by electron correlation,35 as demonstrated by comparison of the corresponding uncorrelated HF-level values (dotted lines) with full B3LYP values (solid lines) at the same bending geometries. The qualitative differences between DSE and DME vibrational behavior also extend to torsional properties. As a simple model of conformational dependence, we carried out rigid-rotor dihedral twisting of a single
XH3 group with idealized Pople
Gordon geometry (all other geometrical variables being held fixed at equilibrium B3LYP/aug-cc-pVTZ values), as shown in Figure 2. The figure shows that DME exhibits a rather typical ethane-like rotation barrier (ΔERB = 2.40 kcal/mol), whereas that for DSE is 1
2 orders of magnitude weaker (ΔERB = 0.12 kcal/mol), far below the ambient thermal energy theshold (kT ≈ 0.6 kcal/mol) for essential free-rotor behavior. The usual “rotational isomeric states” picture36 of DME torsional dynamics must therefore be replaced by a picture of extreme “rope-like” torsional flexibility for DSE. The sharp difference between DME vs DSE torsional properties (Figure 2) follows directly from the distinct C
O
C vs Si
O
Si bending behavior (Figure 1). In the near-linear Si
O
Si bending limit, the distinction between vicinal syn (jSiOSiH = 0, “eclipsed”) vs anti (jSiOSiH = 60, “staggered”) becomes increasingly blurred, and ethane-like barrier contributions therefore vanish by symmetry in this limit no matter what type of electronic interaction is responsible. (The dominant role of hyperconjugative interactions in ether-type rotation barriers has been carefully documented by Goodman and co-workers,37 and the corresponding dominance for silyl ethers could be exhibited by similar analysis.38) The extreme torsional suppleness of DSE and other silicones can therefore be attributed to the surprisingly different C
O
C vs Si
O
Si angular dependence depicted in Figure 1, which virtually dictates the near-vanishing of torsional forces in the near-linear Si
O
Si geometry. How

Figure 4. Calculated NPA oxygen atomic charge of DME (circles) vs DSE (crosses), showing the significantly higher anionicity in siloxanes compared to ethers at all bending angles.

can we understand the electronic origins of the pronounced differences in DSE vs DME bending behavior? Chemical Basicity. A common conceptual error is that “basicity” of an atomic binding site is primarily dictated by atomic charge at the site, as though classical Coulombic electrostatic forces are primarily responsible for AH 3 3 3 B acid
base interaction. This misconception underlies popular empirical forcefield models of “simple point charge” type,39 which attempt to model AH 3 3 3 B interactions with empirically chosen point charges and Coulombic potential functions of classical electrostatic form. Table 3 shows calculated B3LYP/aug-cc-pVTZ H-bond energetics and selected geometrical parameters for DME
water and DSE
water complexes at each ΘXOX bending angle, and Figure 3 presents the comparisons of H-bond strength in graphical form. As the table and figure show, the ΔEHB binding energies for DME tend to be 1
2 kcal/mol stronger than those for DSE at each bending angle. However, the gradual diminution of ΔEHB at larger ΘXOX together with the intrinsically larger ΘSiOSi equilibrium angle further amplifies this difference to about 3 kcal/mol for the respective equilibrium geometries. The calculations reflect the inherently weaker basicity of DSE vs DME at each bending angle as well as the overall ΘXOX dependence of H-bonding in each species. Contrary to what might be the expected relationship between basicity (or H-bond strength) and anionicity in a simple electrostatic 5818

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picture, the oxygen atomic charge (QO) of DME is found to be markedly less anionic than that of DSE. Figure 4 displays calculated NPA-based40 QO values for DME vs DSE over the entire angular range, showing the significantly higher oxygen anionicity in siloxanes compared to ethers. (Qualitatively similar anionicity patterns are obtained with alternative atomic charge measures or theory levels.) Of course, the relative QO values of Figure 4 are fully consistent with the expected lower electronegativity of Si compared to C, viz., ΞC ¼ 2:60

ð5aÞ

ΞSi ¼ 1:78

ð5bÞ 41

on the natural electronegativity scale. How can we understand the counterintuitive anti-correlation between H-bonding propensity and anionic charge on oxygen?

’ HYPERCONJUGATIVE EFFECTS ON ANGULAR BENDING PROPERTIES From the foregoing computational results we can see the contrasting X
O
X bending behavior in DSE vs DME (Figure 1) and the associated effects on both torsional (Figure 2) and basicity (Figure 3) properties of the two species. How can we understand the underlying electronic origins of these phenomena? A primary factor distinguishing the bending behavior of Si
O
Si vs C
O
C linkages can be inferred from Bent’s rule42 and the electronegativity differences (eqs 5a, 5b). As Bent’s rule predicts, bonding spλ hybrids to atoms of higher electronegativity are expected to employ higher λ (higher %-p character) λ ¼ ð%-p characterÞ=ð%-s characterÞ

ð6Þ

In equilibrium DME, for example, the oxygen bonding hybrid hO of the σCO bond NBO is found to be of the form hO ¼ sp2:57 ð71:72% p-characterÞ, for bond to X ¼ C

ð7aÞ

whereas the corresponding hybrid in the σSiO bond of DSE is hO ¼ sp1:22 ð54:79% p-characterÞ, for bond to X ¼ Si

According to Coulson’s hybrid directionality theorem cos ΘXOX ¼
1=λ

ð7bÞ

43

ð8Þ

the idealized ΘXOX bonding angle is therefore expected to increase for smaller λ, viz., ΘXOX ¼ cos
1 ð
1=2:57Þ ¼ 112:9 for X ¼ C
1



ΘXOX ¼ cos ð
1=1:22Þ ¼ 145:1 for X ¼ Si

ð9aÞ ð9bÞ

in reasonable agreement with the calculated equilibrium structures (Table 1). Thus, the qualitative (ca. 35) increase in bending angle for DSE vs DME can be seen as an elementary consequence of Bent’s rule and the general hybridization picture of Lewis-structural bonding. [In contrast, the hybridizations at Si or C are rather similar (viz,, hSi = sp3.35 in the Si
O bond of H3SiOSiH3 vs hC = sp3.34 in the C
O bond of H3COCH3), because each involves similar competition for p-character between the O and three H ligands.] However, the Lewis-structural model is further modified by significant hyperconjugative interactions involving formal nonLewis (NL, acceptor) NBOs interacting with Lewis (L, donor) NBOs of the parent NLS representation, as described in eqs 1
4.

Figure 5. nO f σ*XH orbital overlap diagrams (contour, surface) for DME (upper) and DSE (lower), with E(2) estimates (kcal/mol) in parentheses.

The resonance-type NL corrections involve many types of delocalization into valence antibonds (σ*XO, σ*XH) as well as extravalent Rydberg-type orbitals of the complete NBO basis. However, for our purposes principal attention focuses on the non-Lewis “O-delocalizations” (ONL) from oxygen lone pairs (nO) into vicinal hydride antibonds (σ*XH), ONL : nO f XH ðX ¼ C or Si; nO ¼ nO ðsÞ or nO ðpÞ Þ ð10Þ where nO(s) or nO(p) respectively distinguish the inequivalent (not “rabbit ears”!44) s-rich or p-rich lone pair NBOs. Figure 5 5819

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Figure 6. Angular dependence of “full” (solid line: HF/aug-cc-pVTZ), OL (dashed line: delete vicinal nO f σ*XH delocalizations), and L (dotted line: delete all delocalizations) computational models for DME (left) and DSE (right), showing magnitudes of deletion energies (in atomic units: 1 au = 627.51 kcal/mol) on the absolute scale of total energy for each species.

Figure 7. Bending potentials for (a) DME (left) and (b) DSE (right) in full HF/aug-cc-pVTZ (solid line) and partially (OL, dashed line) or fully (L, dotted line) localized $DEL-type computational models (see text), shown relative to a common asymptote “zero” at the linear ΘXOX = 180 limit.

Figure 8. Angular dependence of stabilization energy EONL (= EOL
Efull) for hyperconjugative nO f σ*XH delocalizations in DME (circles) and DSE (crosses), with vertical dotted lines marking the equilibrium bending angle in each species.

depicts the principal ONL-type delocalizations for DME and DSE in NBO orbital overlap diagrams,45 with associated secondorder perturbative estimates (eq 3a) of stabilization energy. Note that the net hyperconjugative stabilization energy is greater for DSE than for DME by about 2 kcal/mol, despite the significantly

longer nO f σ*XH distance in the silicon compound. Generalizing to more complex molecules, we locate here the proximate reason for the decreased basicity of siloxanes, by about 2 kcal/mol compared to ethers.8 It arises because of the greater hyperconjugative nO f σ*XH electron release in siloxanes than in ethers, in spite of the longer Si
O bond. Alternatively, we can evaluate individual or total ONL-type delocalizations with selective $DEL deletions (eq 3b) to obtain EOL($DEL) for the “O-localized” (OL) structure with delocalizations (eq 10) absent. Such $DEL calculations allow us to see the explicit structural consequences of complete (L) or partial (OL) removal of hyperconjugative interactions, allowing us to isolate the “smoking gun” most directly responsible for a particular departure from elementary Lewis-structural expectations. As discussed above, we employ HF/aug-cc-pVTZ as the “full” method for variational control of $DEL-type L, OL evaluations to follow. Figure 6 displays the calculated bending potentials for full, OL, and L computational models of DME (left) and DSE (right) on the absolute scale of total energy. These plots show the potential curves in proper variational relationship and facilitate comparison of the absolute magnitudes of ONL and NL deletion energies at each angle. However, comparative details of the angular dependence are somewhat obscured in such absolute energy 5820

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Figure 9. Similar to Figure 7, for binary H-bonded complexes (a) DME
water (left) and (b) DSE
water (right).

plots by the large vertical separations between potential curves, particularly in DSE. We can focus more directly on hyperconjugative details of the angular behavior by shifting each potential curve to a common fixed asymptote “zero” at the linear ΘXOX = 180 limit (cf. Figure 1). Figure 7 shows the corresponding relative ΔE(ΘXOX) plots (on a more convenient kcal/mol energy scale) that allows such angular comparisons. For DME the L/OL bending potentials are seen to be significantly deeper and more harmonic than the hyperconjugatively broadened full potential, but the shift in C
O
C bending angle (∼3) is relatively modest. For DSE, however, the equilibrium OL bond angle is evidently shifted dramatically (∼50) and broadened to extreme anharmonic form by vicinal delocalizations (eq 10) of the oxygen lone pairs. From comparison of Figure 7a,b one can see that the DME and DSE bending potentials would exhibit the expected Lewis-structural similarities at the OL level, but for DSE such similarities are essentially obliterated by hyperconjugative delocalizations (eq 10) of the full calculation. Figure 8 displays the angular dependence of $DEL estimates for ONL-type hyperconjugative stabilization (EONL = EOL
Efull) in each species. The equilibrium bending angles (vertical dotted lines) mark the relevant range of ONL values in each case, allowing one to clarify the somewhat paradoxical relationships between ONL delocalizations in DME vs DSE. From the numerical ONL values plotted in Figure 8, one can judge that: • The slope of EONL with respect to ΘXOX is always positive, so ONL delocalization is always a “driving force” to larger X
O
X angles. • In the relevant region of the potential minimum (vertical dotted lines; cf. Figures 7a,b), the near-equilibrium hyperconjugative ONL stabilization is stronger for DSE than for DME (despite the fact that ONL delocalizations at any particular X
O
X bending angle are usually stronger for DME than for DSE!). One can thereby see that hyperconjugative angle-opening further amplifies the intrinsic ΘSiOSi > ΘCOC relationship imposed by Bent’s rule, driving the X
O
X bending angle to still larger increase for X = Si than for X = C. The hyperconjugative ONL delocalizations make important contributions to the potential energy of both DME and DSE, but their effect on the X
O
X bending potential is significantly greater for DSE due to the intrinsic difference in idealized hybrid angles that is dictated

by electronegativity differences, Bent’s rule, and Coulson-type relationships (eqs 8, 9) to hybrid p-character. The angular behavior shown in Figure 7a,b for DME vs DSE monomers is qualitatively mirrored in the corresponding behavior of H-bonded DME
H2O vs DSE
H2O complexes. Figures 9a,b show the full/OL/L angular behavior of these complexes for direct comparison with Figure 7a,b. The hyperconjugative differences between DSE and DME complexes appear weakened compared to those of the corresponding monomers, indicating important coupling effects between intramolecular bending and intermolecular H-bond formation that will be described in the following section. Note that the $DEL-type ΔEL and ΔEOL values of Figures 6
9 are all calculated for the optimized “full” geometry (including effects of hyperconjugation) at each bending angle. Geometry reoptimization on the localized EL or EOL potential surface can therefore be expected to further amplify the conspicuous differences due to hyperconjugation as depicted in Figures 6
9.

’ HYPERCONJUGATIVE EFFECTS ON INTERMOLECULAR H-BOND FORMATION The fact that ONL-type delocalizations of oxygen lone pairs are intrinsically coupled to intermolecular H-bond formation could be immediately inferred from the nO f σ*OH charge transfer picture of O---HO hydrogen bonding.25 Indeed, it is apparent that intramolecular nO f σ*XH and intermolecular nO f σ*OH delocalizations must compete for the same nO oxygen lone pairs of the H3XOXH3 monomer, leading to anti-cooperative coupling between intramolecular hyperconjugation and intermolecular H-bonding. The enhanced ONL delocalizations of DSE (Figure 8) thereby virtually dictate its reduced propensity for H-bonding compared to DME, as observed. Figure 10 displays numerical occupancies of nO(s), nO(p) lone pairs in DME and DSE that exhibit significantly higher “availability” for intermolecular nO f σ*OH H-bonding interaction in DME. The differences are most apparent for the s-rich (in-plane) nO(s) lone pair, because the p-rich (out-of-plane) nO(p) occupancy is hyperconjugatively depleted to a comparable degree (∼1.92e) in the two species, forcing the H-bond to an unusual degree of in-plane character (cf. Table 2). Indeed, if we compare nO(s) occupancies at the respective near-equilibrium bond angles (∼112 vs ∼150), we see that lone pair availability in 5821

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Table 4. Optimized $DEL-ONL Structures (or partially optimized for H3SiOSiH3 3 3 3 H2O; see ref 34), Showing H-Bond Energetic (kcal/mol) and Geometrical (Å, deg) Parameters for DSE/DME Species Lacking ONL-Type Hyperconjugative nO f σ*XH Delocalization (with corresponding shifts from equilibrium values of Tables 1 and 2 in parentheses) X = Si

Figure 10. NBO occupancies of in-plane σ-type (nO , light lines) and out-of-plane π-type (nO(p), heavy lines) oxygen lone pairs in DME (circles) and DSE (crosses), showing significantly higher availability for intermolecular nO f σ*OH H-bonding interaction in DME. (s)

DME (∼1.97e) far exceeds that of DSE (∼1.93e), corresponding to significantly higher propensity for H-bond formation in DME despite its much weaker anionic charge at oxygen (Figure 4). The anticooperative role of ONL-type delocalizations in reducing H-bond strength can be assessed more directly by $DEL-type reoptimizations with hyperconjugative interactions (eq 10) deleted. Table 4 summarizes the results of such $DELONL reoptimizations (incomplete for DSE
H2O; see ref 34), which lead to pronounced structural and energetic shifts (shown in parentheses for each entry of the table) with respect to the equilibrium values of Tables 1 and 2. Given the extremely weak force constant for Si
O
Si bending and the anticooperative competition between intramolecular and intermolecular hyperconjugation, one can anticipate that practically any solvation or crystalline environment will lead to more strongly bent Si
O
Si geometry than that of the gas-phase species. As expected, deletion of nO f σ*XH interactions tends to affect both species in a similar direction, but with disproportionately larger magnitude for DSE vs DME (e.g., 2.91 vs 1.01 kcal/mol for H-bond strengthening or 11.9 vs 2.6 for ΘXOX bending). Indeed, Table 4 indicates that DSE and DME would be of much more similar basicity in the $DEL-ONL limit, although residual geminal nO f σ*XO hyperconjugation still diminishes the relative basicity of DSE somewhat. The $DEL calculations thereby establish rather directly that the anomalous bending and inertness properties of siloxanes can be primarily attributed to the enhanced strength of intramolecular nO f σ*SiH hyperconjugation and resultant “silencing” of oxygen lone pair availability for intermolecular H-bond formation, as the NBO donor
acceptor picture of H-bonding suggests.

’ SUMMARY AND CONCLUSIONS We have employed NBO-based deletion ($DEL keylist) techniques to isolate, quantify, and compare the effect of total or specific “O-delocalizing” hyperconjugative interactions on the bending, torsional, and H-bonding properties of X
O
X linkages in siloxanes (X = Si) vs ethers (X = C), based on augmented Dunning-type correlation-consistent basis sets of triple-ζ quality (aug-cc-pVTZ) and uncorrelated (HF) or dynamically correlated (B3LYP) computational methods. Our results clarify the important role of hyperconjugation, which acts to open the

X=C

ΔEHB

H3XOXH3 3 3 3 H2O
4.92 (
2.91)

RXO

1.71 (+0.05)

1.48 (+0.07)

ROO

2.87 (
0.15)

2.84 (
0.03)

ΘXOX jXXOO

127.4 (
11.9) 150.0 (
11.9)

110.4 (
2.6) 122.0 (
16.6)

RXO

1.703 (+0.058)

1.482 (+0.070)

ΘXOX

129.2 (
21.0)

110.0 (
2.7)


5.86 (
1.01)

H3XOXH3

X
O
X bond angle and reduce oygen basicity in both siloxanes and ethers, but with significantly greater “leverage” in the siloxane case due to the inherently greater angle between oxygen-bonding hybrids that is dictated by increased electropositivity of Si vs C, in accordance with Bent’s rule. Hyperconjugative Si
O
Si angle opening in turn leads to the near-vanishing of torsional barriers and suppressed basicity (lone pair availability) of siloxanes, despite the much higher anionic character of oxygen bonded to silicon. This seems to resolve many of the puzzling contrasts in structure and reactivity of inorganic siloxanes vs organic ethers that underlie their diverse applications. Although we have focused primarily on angular rather than dissociative properties, it is evident from Figure 6 and other total energy plots that hyperconjugative interactions have profound effects on bond dissociation energies and related thermochemical properties as well. Indeed, from $DEL-ONL optimizations for H3XOXH3 and their dissociation products (analogous to those of Table 4), we can estimate that ONL delocalizations (eq 10) enhance Si
O and C
O bond strength by about 19 kcal/mol (15%) and 23 kcal/mol (28%), respectively. Such large σ-delocalization effects remind us that even “saturated” species often exhibit significant deviations from simple bond additivity and transferability assumptions that require resonance-type corrections to the elementary Lewis-structural picture. The present study supports evolving recognition46 of the profound role of hyperconjugation in a broad range of intraand intermolecular “noncovalent” phenomena, including hydrogen bonding. In the latter context, the paradoxical lowered basicity of siloxanes vs ethers presents a clear challenge to the electrostatics-based “dipole
dipole” picture that pervades current textbook presentations47 as well as empirical modeling of H-bonding. Evidence from many theoretical and experimental lines provides support for the general conclusion48 that resonance-type nO f σ*XH “charge transfer” interactions are the ubiquitous characteristic of H-bonding. Clarification of differences in Si
O
Si vs C
O
C bonding may thus assist in improving broad conceptual understanding of H-bonding and related intermolecular phenomena, as well as guiding chemical modification of polymeric (
SiR2-O
)n or (
CR2-O
)n materials for desired rheological, electro-optical, or reactivity properties. 5822

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’ ASSOCIATED CONTENT

bS

Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

’ ACKNOWLEDGMENT We thank UW-Biochemistry NMRFAM (NIH P41RR02301) and UW-Chemistry Computational Chemistry Facility (NSF CHE-0840494) for partial computational support. R. West thanks the WCU program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (R33-10082) for support. We thank Professors Josef Michl and Yitzhak Apeloig for valuable discussions. ’ REFERENCES (1) Shambayati, S.; Schreiber, S. L.; Blake, J. F.; Wierschke, S. G.; Jorgenson, W. L. J. Am. Chem. Soc. 1990, 112, 697–703. (2) Pitt, C. G. J. Organomet. Chem. 1973, 61, 49–70. (3) Cypryk, M.; Apeloig, Y. Organometallics 1997, 16, 5938–5949. (4) Gillespie, R. J.; Johnson, S. A. Inorg. Chem. 1997, 36, 3031–3039. (5) Grabowski, S. J.; Hesse, M. F.; Paulmann, C.; Luger, P.; Beckmann, J. Inorg. Chem. 2009, 48, 4384–4393. These authors characterize the hyperconjugative model for Si
O bonding as “obsolete”. They also rediscovered the fact that the disiloxane bond becomes more basic upon bending, first pointed out in 1979.8 (6) Baney, R. H.; Lake, K. J.; West, R.; Whatley, L. A. Chem. Ind. 1959, 1129–1130. (7) West, R.; Whatley, L. S.; Lake, K. J. J. Am. Chem. Soc. 1961, 83, 761–764. (8) West, R.; Wilson, L. S.; Powell, D. L. J. Organomet. Chem. 1979, 178, 5–9. (9) Pitt, C. G.; Bursey, M. M.; Chatfield, D. A. J. Chem. Soc., Perkin Trans. 1976, 2, 434–438. (10) Shepherd, B. D. J. Am. Chem. Soc. 1991, 113, 5581–5583. (11) Bock, H.; Mollere, P.; Becker, G.; Fritz, G. J. Organomet. Chem. 1973, 61, 113. (12) Pola, J.; Jakoubovka, M.; Chvalovsky, V. Collect. Czech. Chem. Commun. 1978, 43, 3373–3370. (13) Borisov, S. N.; Timofeeva, N. P.; Yuzhelevskii, Yu. A.; Kagan, E. G.; Kozlova, N. V. Zh. Obshch. Khim. 1972, 43, 873–878. (14) Craig, D. P.; Maccoll, A.; Nyholm, R. S.; Orgel, L. E.; Sutton, L. E. J. Chem. Soc. 1954, 332
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1811. Glendening, E. D.; Badenhoop, J. K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; Weinhold, F. NBO 5.0 Program; Theoretical Chemistry Institute, University of Wisconsin: Madison, WI, 2001); http:// www.chem.wisc.edu/∼nbo5.

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(23) For a comprehensive overview of NBO theory and applications, see: Weinhold, F.; Landis, C. R. Valency and Bonding: A Natural Bond Orbital Donor-Acceptor Perspective; Cambridge Univ. Press: Cambridge, UK, 2005. (24) Brunck, T. K.; Weinhold, F. J. Am. Chem. Soc. 1979, 101, 1700–1709. Pophristic, V.; Goodman, L. Nature 2001, 411, 565–568. Schreiner, P. R. Angew. Chem., Int. Ed. 2002, 114, 3579–3582. Ref 23, pp 220ff. (25) Reed, A. E.; Weinhold, F.; Curtiss, L. A.; Pichatko, D. J. Chem. Phys. 1986, 84, 5687–5705. Weinhold, F. Adv. Protein Chem. 2006, 72, 121–155. Ref 23, pp 593ff. (26) Mulliken, R. S. J. Chem. Phys. 1939, 7, 339–352. Salzner, U.; Schleyer, P. v. R. J. Am. Chem. Soc. 1993, 115, 10231–10236. Ref 23, pp 215ff. (27) Ref 23, pp 16ff. (28) Weinhold, F. NBO 5.0 Program Manual; Theoretical Chemistry Institute, University of Wisconsin: Madison, WI, 2001; pp B-16ff; http://www.chem.wisc.edu/∼nbo5/tut_del.htm. (29) Koput, J. J. Chem. Phys. 1990, 148, 299–308. Koput, J. J. Phys. Chem. 1995, 99, 15874–15880. (30) Durig, J. R.; Flanagan, M. J.; Kalasinsky, V. F. J. Chem. Phys. 1977, 66, 2775–2785. Koput, J.; Wierzbicki, A. J. Mol. Spectrosc. 1983, 99, 116–132. (31) For standard method and basis set designations used herein, see: Foresman, J. B.; Frisch, A.E., Exploring Chemistry with Electronic Structure Methods: A Guide to Using Gaussian, 2nd ed.; Gaussian Inc.: Pittsburgh, PA, 1996. (32) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, € Farkas, Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; S.; Daniels, A. D.; O. Fox, D. J. Gaussian 09; Gaussian, Inc.: Wallingford, CT, 2009. (33) Al Derzi, A. R.; Gregusova, A.; Runge, K.; Bartlett, R. J. Int. J. Quantum Chem. 2008, 108, 2088–2096. (34) Severe numerical difficulties were encountered with the highly extended aug-cc-pVTZ basis set when incipient linear-dependence instabilities sometimes forced unpredictable removal of diffuse functions and/or convergence failures in the Gaussian program. As a consequence, consistent ΔH/ΔG calculations could be completed only at the unaugmented cc-pVTZ level for Me3COCMe3
phenol, as shown in Table 2. Numerical difficulties in the Gaussian NEF numerical derivatives algorithm also allowed only partial $DEL-ONL optimizations for H3SiOSiH3
water (Table 4). (35) It should be noted that electron correlation has a powerful effect on the potential curve for Si
O bond dissociation (as described in the final section), but this occurs along a different coordinate than the angular potential depicted in Figure 1. (36) Flory, P. J. Macromolecules 1974, 7, 381–392. (37) Goodman, L.; Pophristic, V. Chem. Phys. Lett. 1996, 259, 287–295. Pophristic, V.; Goodman, L.; Guchhait, N. J. Phys. Chem. A 1997, 101, 4290–4297. (38) With regard to ethane-type barrier analysis, a referee has called our attention to a recent article [Mo, Y. Nat. Chem. 2011, 469, 76–79. cf. Mo, Y.; Peyerimhof, S. D. J. Chem. Phys. 1998, 109, 1687–1697 for original exposition of this viewpoint] with the remark that “...the NBO technique...is known for its overestimation of hyperconjugation energies, as the derivation of the Lewis wavefunction from the molecular wavefunction is non-optimal.” To this we would reply that Mo’s 5823

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preferred BLW assessment is intrinsically based on the ambiguities of nonorthogonal orbitals, in which significant “overlap density” (not uniquely assignable to one center or another) makes the assessment of hyperconjugative charge “transfer” essentially subjective and arbitrary. In contrast, overlap-free NBO estimates of hyperconjugation energy, whether evaluated by complementary perturbative or $DEL-deletion techniques, have been demonstrated to correlate accurately with one another as well as with NBO-based weightings of the associated resonance structures [see, for example,.Glendening, E. D.; Landis, C. R.; Weinhold, F. Wiley Interdisciplinary Reviews: Computational Molecular Science (in press; DOI 1002/wcms.51); ref 46; ref 23, pp 622ff]. These resonance weightings in turn exhibit close agreement with experimentally inferred values [see, for example., Kemnitz, C. R.; Loewen, M. J. J. Am. Chem. Soc. 2007, 129, 2521–2528], which precludes any significant “overestimation” of hyperconjugation energy or related structural effects. It should also be emphasized that the sum of all hyperconjugation energies, as defined with respect to the idealized NLS limit of eq 4b, is obtained from a rigorous variational expectation value (not a “nonoptimal” estimate), so any purported tendency to overestimate successive hyperconjugation energies must necessarily lead to (unobserved) violations of the variational theorem. (39) Berendsen, H. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269–6271. (40) Reed, A. E.; Weinstock, R. B.; Weinhold, F. J. Chem. Phys. 1985, 83, 735–746. (41) Ref 23, pp 131ff. For all three atoms (C, Si, O) under consideration, the estimates from Pauling (P), Allred-Rochow (AR), or natural (N) electronegativity scales could be used rather interchangeably [viz., C (2.5P, 2.50AR, 2.60N), Si (1.8P, 1.78AR, 1.78N), O (3.5P, 3.50AR, 3.48N)]. (42) Bent, H. A. Chem. Rev. 1961, 61, 275–311. Ref 23, pp 138ff; for early computational evidence of the strong dependence of XOH bending angle on electronegativity, see Schleyer, P. v. R. Pure Appl. Chem. 1987, 59, 1647. (43) Coulson, C. A. Valence, 2nd ed.; Oxford Univ. Press: London, 1952; Chapter 8. (44) Laing, M. J. Chem. Educ. 1987, 64, 124–128. Bartlett, G. J.; Choudhary, A.; Raines, R. T.; Woolfson, D. N. Nat. Chem. Biol. 2010, 6, 615–620. (45) These employ pre-NBO “visualization orbitals” that exhibit interatomic overlap; ref 23, pp 30ff. (46) Alabugin, I. V.; Gilmore, K. M.; Peterson, P. W. Wiley Interdisciplinary Reviews: Computational Molecular Science 2011, 1, 109–141. (47) Current textbook definitions of H-bonding (or, indeed, those of the past half-century) employ near-identical verbiage to express concurrence with the classical electrostatic “dipole
dipole” viewpoint, viz., “a special type of dipole
dipole force” [Silverberg, M. S. Chemistry: The Molecular Nature of Matter and Change, 5th ed.; McGraw-Hill: Boston, 2009; p 452]; “particularly strong dipole
dipole forces” [Zumdahl, S. S. Chemical Principles, 6th ed.; Houghton-Mifflin: Boston, 2009; p 779]; “an extreme form of dipole
dipole interaction” [ Kotz, J. C.; Treichel, P. M.; Townsend, J. R. Chemistry and Chemical Reactivity, 7th ed.; Brooks-Cole: Belmont, CA, 2009; p 562]; “unique dipole
dipole attractions” [ Brown, T. L.; LeMay, H. E., Jr.; Bursten, B. E.; Burdge, J. R. Chemistry: The Central Science, 9th ed.; Prentice-Hall: Upper Saddle River, NJ, 2003; p 413]; “a sort of super dipole
dipole force” [ Tro, N. J., Chemistry: A Molecular Approach, 2nd ed.; Prentice-Hall: Boston, 2011; p 464], and the like. (48) Grabowski, S. J. Chem. Rev. 2011, 111, 2597–2625.

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