Why Do Cumulene Ketones Kink?

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Why Do Cumulene Ketones Kink? Frank Weinhold J. Org. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.joc.7b02089 • Publication Date (Web): 09 Oct 2017 Downloaded from http://pubs.acs.org on October 10, 2017

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The Journal of Organic Chemistry

Why Do Cumulene Ketones Kink? Frank Weinhold* Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706 ([email protected]) ABSTRACT

We employ ab initio and density functional methods to investigate the equilibrium structure and vibrational frequencies of extended cumulene monoketones [CH2=(C=)mO] and diketones [O=(C=)mO], in order to elucidate the electronic origin of the curious “kinked'” spine geometries that are common in such species. The dominant role of symmetry-breaking nO(π)-σ*CC interactions between the p-type lone pair of the terminal oxygen and adjacent unfilled CC antibonding orbital is demonstrated by NBO 2nd-order delocalization energies, Fock matrix deletions, and natural resonance theory (NRT) descriptors, showing the general connection between cumulene kinking and CC bond-breaking reactions that split off CO. Our results provide simple rationalizations for (i) pronounced even/odd alternation patterns in the magnitude or direction of kinking, (ii) the non-existence of O=C=C=O, (iii) the clear preference for trans-like over cis-like kinks, and (iv) the extreme sensitivity of kinking with respect to weak perturbations such as cage or solvent effects, remote chemical substituents, improved treatments of electron correlation, and the like.

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Introduction: Kinking in Cumulene Ketones Cumulenes [=(C=C)m=] are a highly conjugated 1-dimensional form of pure carbon with novel electronic properties. Interesting species of this type include the highly reactive cumulene carbenes that are candidate carriers of diffuse interstellar bands,1 as well as diradical ylids (e.g., propynylidene,2 HC=C=CH) and stable species with divalent closed-shell caps such as cumulene homologs of allene (H2C=C=CH2) or carbon suboxide (O=C=C=C=O). The oxygen-capped ketene derivatives2 are of particular interest and importance as likely reaction intermediates3 in a variety of proposed photochemical mechanistic sequences.4 As remarked by Leffler5 (and quoted by Allen and Tidwell3), “The physical reality of such intermediates depends…on their relation to similar substances that do happen to be stable enough to study directly.” Quantum chemical calculations therefore play a particularly important role in characterizing such experimentally elusive species. Unlike planar conjugated networks such as graphenes, each carbon atom of a cumulene chain offers two pπ-type AOs for pi-bonding. This leads to extended πconjugation in two mutually perpendicular planes whose orientation about the chain axis is indeterminate in idealized C∞h geometry. However, the apparent axial symmetry of pi-interactions can be broken by remote influences of terminal capping groups or other perturbations. In the present work, we investigate such symmetrybreaking interactions in cumulene chains capped by carbonyl groups (which preserve the nominal axial symmetry) or by methylene groups (which do not). Simple hybridization concepts suggest that allene and analogous sp-hybridized H2C=(C=)mCH2 cumulene chains (m > 1) should adopt linear backbone geometry. In this case, the two conjugated pi-bond systems alternate along the carbon-carbon spine in mutually orthogonal planes, with the terminal methylene groups in parallel or perpendicular alignment for even or odd m, respectively. Linear geometry is also expected for the alternative triple-single-bond resonance structures of a cumulene chain, viz., ···C=C=C=C··· ↔ ···C≡C−C≡C···

A similar linear spine geometry might be anticipated if one or both terminal methylene groups are replaced by carbonyl groups. While the latter expectation is confirmed for the leading members of these families [ketene (CH2=C=O) and carbon dioxide (O=C=O)], it is found that cumulene derivatives H2C=(C=)mO or O=(C=)mO of higher pi-bond multiplicity (m > 1) often adopt surprising non-linear geometries, with pronounced kinks along the conjugated spine. The object of the present work is to characterize the prevalence and electronic origin of such symmetry-breaking


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deviations, which seem to violate some of the deepest tenets of elementary pi-bonding theory. The initial suggestion of possible ketene kinking was apparently offered by Radziszewski, Hess, and Zahradnik6 in a graphical “Scheme II” mechanism for production of cyclopentadienylideneketene. Shortly thereafter, Scheiner and Schaefer7 provided strong theoretical evidence for such bending (in close agreement with results presented below), and Radziszewski et al.8 later presented extensive IR experimental evidence “which leaves no doubt about the bent ketene structure.” Other kinked ketene moieties have been also noted in x-ray structures of more complex derivatives.9 While experimental geometries for ketene derivatives are still sparse, they generally provide support for predicted ab initio ketene kinking where comparisons are possible. Figure 1 exhibits ab initio MP2/aug-cc-pVTZ computational evidence for spine kinking in a variety of simple cumulene ketones [H2C=(C=)mO] and diketones [O=(C=)mO], m > 1. The figure illustrates cumulene species with deviations from linearity as large as 30-40 degrees. For example, methylene ketene (H2C=C=C=O, Fig. 1b) exhibits pronounced bending of both the CCO (139º) and CCC (168º) bond angles to give a conspicuous trans-like kink in the CCCO spine geometry. Still more conspicuously, the expected linear diketone O=C=C=O (Fig. 1f) dissociates spontaneously to the weakly bound (CO)2 dimer, apparently oblivious to the strong C=C linkage of a cumulene-type bonding pattern.


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Figure 1. Optimized geometries (MP2/aug-cc-pVTZ level) for cumulene monoketones (a-d) and diketones (e-h) considered in this work.

Table 1 exhibits the optimized kink angles calculated at a variety of theoretical levels, including ab initio uncorrelated (RHF/aug-cc-pVTZ), and correlated (MP2/aug-cc-pVTZ) and density functional (B3LYP/aug-cc-pVTZ) levels. Although kinking is sometimes absent in DFT-level description, appreciable equilibrium nonlinearity is predicted to be a general feature of ab initio-level description in O=(C=)mO monoketone species for m > 1.


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Table 1. Optimized kink angles (α= OC1C2, β= C1C2C3,..., successively along the chain from the terminal carbonyl) for cumulene ketones H2C=(C=)mO and diketones O=(C=)mO, calculated with uncorrelated (RHF), correlated (MP2), and density functional (B3LYP) methods, all at aug-ccpVTZ basis level.

species

RHF

MP2

B3LYP

CH2CO

α

180.00 180.00 180.00

CH2CCO

α β

173.87 167.96 170.64 159.33 139.40 150.61

CH2CCCO

α β γ

174.61 173.69 180.00 155.78 156.11 180.00 178.41 177.41 180.00

CH2CCCCO

α β γ δ [OCCO]a α OCCCO α β OCCCCO α β γ δ a

176.76 167.61 179.02 178.68

172.59 153.72 175.85 176.78

180.00 180.00 180.00 180.00

91.61

28.42

36.14

176.10 180.00 180.00 138.23 180.00 180.00 172.32 160.13 160.13 172.32

164.58 142.76 145.05 164.54

168.12 154.27 154.31 168.15

(CO)2

Inspection of Fig. 1 and Table 1 reveals that kinking is invariably in the trans sense (as in the methylene ketene example cited above). The kinking occurs in a plane which includes, or perpendicularly bisects, the terminal methylene group, so that a plane of overall symmetry is preserved despite the rather conspicuous breakdown of local σ-π symmetry about each backbone bond. It is also noteworthy that the kinking tendency in O=(C=)mO diketones exhibits a pronounced even-odd alternation, with strong kinking for even m (except m = 2, where the species is nonexistent) and linear


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geometries for odd m. Our present aim is to elucidate the electronic origin of each of these propensities. The strong tendency toward kinking in longer cumulene ketones and even-n diketones is further demonstrated by the anomalously low IR frequencies for such deformations. Table 2 presents calculated RHF, MP2, and DFT harmonic frequencies (aug-cc-pVTZ basis level) of spine bending modes for all species studied in this work. Whereas the parent m = 1 species, ketene (CH2CO) and carbon dioxide (CO2), exhibit typical, reasonably stiff bending modes in the region ~400-800 cm−1, the higher-m species reveal extremely soft spine deformation modes ranging below 100 cm−1. These low frequencies suggest that kink-like deformations are readily accessible even in species whose equilibrium geometry is nominally linear. Thus, small energetic changes, such as those associated with electron correlation, cage effects, or other intermolecular influences, may suffice to shift the equilibrium geometry from linear to kinked. Table 2. Lowest frequency bending mode (cm−1) associated with kinking for each species and theory level considered in this work (cf. Fig. 1)

species

RHF MP2 B3LYP CH2CO 495 433 445 CH2CCO 69 196 149 CH2CCCO 50 82 59 CH2CCCCO 16 72 41 OCO 775 674 659 a [OCCO] 13 28 11 OCCCO 101 49 50 OCCCCO 65 102 93 a

(CO)2

Correspondingly low energies are required to deform a kinked species through a linear transition state, as shown by the calculated barrier heights in Table 3 (MP2/augcc-pVTZ level). Such low-barrier, large-amplitude kinking vibrations may render it difficult to distinguish the vibrationally averaged structures for equilibrium linear and nonlinear species. Low-frequency C=C=O bending is also expected to couple strongly with the CC stretching coordinate for CO dissociation. Thus, the kinking deformations of cumulene ketones and diketones can play an important role in the structure, spectroscopy, and reactive dynamics of species that lead to production of carbon monoxide.


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Table 3. Transition state energy and free energy barriers (∆E‡inv, ∆G(0)‡inv; MP2/aug-cc-pVTZ level) for inversion (interconversion of equivalent kinked equilibrium geometries through a linear transition state) of the kinked cumulene monoketones considered in this work (cf. Fig. 1).

Species ∆E inv (kcal/mol) ∆G(0)‡inv (kcal/mol) ‡

CH2CCO

CH2CCCO

CH2CCCCO

1.87 1.69

0.19 0.53

0.31 0.64

As mentioned above, a remarkable consequence of the strong kinking propensity in even-m cumulene diketones is the non-existence14 of the m = 2 member of the sequence (O=C=C=O, 1,2-ethenedione). Such a species possesses a valid Lewis structure that seems to suggest robust double-bonding between carbon atoms. However, geometry relaxation from starting linear or near-linear geometry leads to severe kinking for initial deviations in the trans sense and barrierless dissociation to two CO molecules (at all levels of theory). The non-existence of O=C=C=O can thereby be recognized as a particularly dramatic consequence of the strong kinking propensity of cumulene diketones: the molecule kinks so severely as to rip itself apart. Natural Bond Orbital Picture of Cumulene Ketones The distinctive electronic features of ketene-like compounds are intimately related to the unique features of their Lewis-structural representations. The latter can be quantitatively described in terms of the associated natural bond orbitals (NBOs),10 which furnish an optimal localized orbital representation of the 1-center lone pairs and 2-center bonds of an idealized natural Lewis structure (NLS) picture. However, the elementary NLS picture is subject to the perturbations of other resonance-type conjugative or hyperconjugative interactions that involve participation of non-Lewis NBOs (particularly, valence antibonds) that are ignored at simple Lewis-structural level. More specifically, such departures from idealized NLS form can be estimated with 2nd-order perturbative analysis of donor-acceptor interactions between Lewistype (bond, lone pair) and non-Lewis-type (antibond, Rydberg) NBOs to elucidate specific features of the potential energy surface in terms of familiar Lewis-like bonding concepts. Furthermore, NBO-based natural resonance theory (NRT)11 allows quantification of resonance weightings and non-integer bond orders that underlie a more general resonance-type description of the complex conjugation patterns in cumulenic species. An important distinguishing feature of cumulene ketones is schematically depicted in Figure 2 for ketene in its calculated equilibrium linear geometry. As Fig. 2 indicates, each terminal carbonyl oxygen has two distinct lone pairs, the sigma-type nO(σ) (~ sp-hybridized), oriented along the bond axis, and the pi-type nO(π) (pure p), oriented perpendicular to the bond axis and lying in the nodal plane of the πCO bond.12


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These oxo lone pairs are qualitatively similar to those of formaldehyde, well known in the nπ* photochemistry of carbonyl compounds,4b,c as shown in the (P)NBO depictions of Figure 2. Each nO(π) (Fig. 2b) can evidently conjugate strongly as a powerful π-donor with the coplanar π*CC NBO (Fig. 2c) of the adjacent CC bond, leading to the strong nO(π) -π*CC overlap (Fig. 2d) associated with resonance delocalization of the form

In contrast, the on-axis nO(σ) (Fig. 2a) is oriented to remain essentially inert to piconjugation in linear CCO geometry.


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Figure 2. NBOView depiction of characteristic cumulene ketone NBOs: (a) low-energy (sigmatype) oxygen lone pair nO(σ) ; (b) high-energy (pi-type) oxygen lone pair nO(π) (principal donor); (c) carbon-carbon valence antibond π*CC (principal acceptor); and (d) PNBO overlap diagram for leading nO(π)-π*CC donor-acceptor interaction.

In cumulene diketones for which the multiplicity m of carbon atoms is odd (even number of π bonds), the two terminal nO(π) lone pairs lie in orthogonal planes and conjugate with distinct manifolds of mutually perpendicular pi bonds. However, if m is even, the two nO(π) lone pairs are coplanar and conjugate with a common π-manifold, leaving the perpendicular π-manifold essentially unperturbed. This parallel vs. perpendicular aspect of terminal nO(π) lone pairs appears to strongly distinguish the properties of O=(C=)mO diketones for even vs. odd m. A second distinguishing feature of cumulene diketones, compared to cumulenes or cumulene monoketones, lies in the existence of two distinct Lewis structures of comparable weighting, analogous to the two allene-like structures of carbon dioxide.13 These structures differ in a 90 rotation of each localized π bond (e.g., reformation from px rather than py orbitals), with each terminal nO(π) also lying perpendicular to its orientation in the other structure. The two representations are equivalent in D∞h linear geometry, but any breakdown of linear symmetry leads to enhanced weighting of one or the other Lewis structure in kinked geometry. As remarked above, the relative weightings of resonance structures can be assessed by means of natural resonance theory. Calculated NRT weights for the diketones O(C)mO, m = 2-4, are displayed in Table 4. As seen in the table, “OCCO” has exclusively the triple-bond structures expected in a weak carbon monoxide dimer. OCCCO and OCCCCO are more complex resonance hybrids with expected


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cumulene-type double-bonding in the leading structure, but significant triple-bond secondary contributions, particularly at terminal CO moieties.. Table 4. Leading NRT resonance structures and weightings for cumulene diketones considered in this work ((MP2/aug-cc-pVTZ level; cf. Fig. 1). The parenthesized pre-superscript on an atom denotes the number of lone pairs. Parenthesized numbers following %-weightings denote number of symmetry-equivalent structures of the given weighting.

species OCCO

I

II

III

12.5%

12.0%(2)

11.7%

23.2%

9.1%

4.7%(2)

100% OCCCO OCCCCO

Figure 3 shows the NRT bond order-bond length correlations for all CO and CC bonds of species considered in this work. Whereas reasonable correlation of RCX with NRT bond order bCX(NRT) is seen for terminal CO bonds (Fig. 3a; Pearson r2 = 0.90), no such correlation is evident for interior CC bonds (Fig. 3b; r2 = 0.00). This indicates that the hybridization shifts (and bond elongation) associated with cumulene bending from linear sp-type (50% p-character) to bent [sp2 -type (67%-p) or higher prich hybrids] is the more important determinant of bond length than the donoracceptor occupancy shifts and associated resonance weightings described by bCX(NRT).


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(a)

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(b)

Figure 3. NRT bond order-bond length ( bCX(NRT)-RCX) correlations for (a) CO bonds (left), and (b) CC bonds (right) of species considered in this work, with best least-squares fit (dashed line) and Pearson r2 correlation coefficient (inset). The negligible correlation with bond order in (b) indicates the greater dependence of CC bond length on hybridization shifts from compact s-rich hybrids to p-rich hybrids of greater root-mean-square radius in bent geometry.

Kinking in a Simple Model OCCO Compound To see how the kinking propensity is related to the foregoing features of the NBO Lewis structure, we first examine the (unstable14) species O=C=C=O as a simple symmetric model of spine kinking. We choose fixed idealized Pople-Gordon geometry15 with C=C (1.28 Å) and C=O (1.16 Å) bond lengths, so that the kinked geometry is described in terms of the single OCC bending angle θ, for either translike or cis-like deformations. Figure 4 displays the calculated RHF/aug-cc-pVTZ energy dependence ∆E(θ) for kinks of cis and trans sense. Whereas cis kinking is strongly forbidden, trans kinking leads to an energy minimum near θ = 25 (for the chosen fixed bond lengths). This is consistent with the observation that trans kinking is favored in all known cases of nonlinear spine geometry.


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Figure 4. Calculated energy changes ∆E (RHF/aug-cc-pVTZ level) for symmetric trans-like (solid line) or cis-like (dashed line) kinking deformations of hypothetical OCCO with fixed idealized bond lengths (RCC = 1.28Å, RCO = 1.16Å).

NBO energetic analysis of the interactions favoring trans kinking is presented in Figure 5. Fig. 5a shows leading θ-dependent changes in diagonal Fock matrix elements (orbital energies) of Lewis-type lone pair (nO(π)) and bond (σCC, πCC) NBOs.16 As expected, both σCC and πCC bonds are slightly weakened by kinking (due to weakened overlap of the interacting hybrids), whereas the pi-type nO(π) lone pair is slightly lowered in energy and other NBOs are scarcely affected. Fig. 5b shows corresponding off-diagonal donor-acceptor interactions between Lewis-type (n, σ, π) and non-Lewis-type (σ*, π*) NBOs, as estimated by 2nd-order perturbation theory. As expected, both nO(π)-πCC* and πCO-πCC* interactions are weakened (less stabilizing) from their θ = 0 value. However, Fig. 5b shows the more important gain in stabilization from interactions of nO(π)-σ*CC and nO(σ)-π*CC type, which are strictly absent at θ = 0 but “turn on” in broken-symmetry kinked geometry, θ ≠ 0.


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(a) Lewis-type

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(b) Non-Lewis-type

Figure 5. θ-dependence for (a) leading Lewis-type variations in orbital energy εNBO = 〈NBO|F|NBO〉 for nO(π) (circles), σCC (triangles), and πCC (squares) NBOs; (b) leading nonLewis-type EDA(2) donor-acceptor variations for increased [nO(π)-σ*CC (circles), nO(σ)-π*CC (x’s)] and decreased [nO(π)-π*CC (+’s), (triangles)] stabilization (idealized RHF/aug-cc-pVTZ).

The most important driving forces for kinking are seen to be (i) the nO(π)-σ*CC interaction between the filled p-type oxygen lone pair and the vicinal sigma-type CC antibond σ*CC, and (ii) the nO(σ)-π*CC interaction between the filled s-rich oxygen lone pair and the vicinal pi-type CC antibond π*CC, both depicted in the orbital overlap diagrams of Figure 6. At θ = 0 the individual orbital lobes occupy strongly overlapping regions, but with positive and negative contributions in perfect cancellation (Fig. 6, left). However, non-linearities break the cancellation symmetry and lead to rapidly increasing nO(π)-σ*CC , nO(σ)-π*CC stabilizations for θ ≠ 0 (Fig. 6, right). Both interactions are particularly strong, because a donor lone pair can provide about twice the electron density of a 2-center bond NBO to an adjacent acceptor antibond. Each nO(π)-σ*CC or nO(σ)-π*CC interaction weakens the central CC bond by transferring electron density to the antibonding σ*CC or π*CC orbital, signaling incipient dissociation to CO fragments if geometry relaxation is allowed.


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θ = 0°°

θ = 40°°

Figure 6. Overlap diagrams for NBO donor-acceptor interactions nO(π)-σ*CC (upper panels) and nO(π)→σ*CC (lower panels), showing perfect cancellation at θ = 0° (left) but significant net stabilizing interaction at θ = 40° (right).

The bond-rupturing effect of the nO(π)-σ*CC hyperconjugative interaction is also evident in the corresponding resonance diagrams (1a-d),

(1a)

(1b)

(1c)


(1d) 15


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Figure 7 shows the θ-dependent variation of CC bond order bCC(NRT), as calculated by natural resonance theory. In accordance with resonance mnemonic (1), this figure confirms that the CC bond is significantly weakened by kinking (particularly at larger θ values), foreshadowing the breakup into CO fragments if the CC bond length is allowed to optimize. Figs. 6, 7 and resonance mnemonic (1a-d) suggest the general importance of kink-stretch coupling in transition state dynamics of chemical reactions leading to carbon monoxide production.

Figure 7. Variation of NRT bond order bCC(NRT) of central CC bond with CCO kink angle θ in the frozen-bond idealized RHF/aug-ss-pVTZ model, showing rapid decrease of bCC(NRT) beyond 70°. (For the 8-reference NRT calculations, we included as reference structures any structure contributing 1% or more at any angle.)

The essential role of the symmetry-breaking nO(π)→σ*CC interaction in the kinking phenomenon can also be assessed by deleting the specific 〈nO(π)|F|σ*CC〉 Fock matrix element, then recalculating the variational energy and re-optimizing the structure as though this interaction were absent, using the standard $DEL option of the NBO program. In each case, the kinking that was present in the full calculation is eliminated in the absence of this interaction. The same result is obtained if the nO(σ)-π*CC interaction is deleted. The connection is particularly obvious for the hypothetical O=C=C=O species, which avoids dissociation to two CO molecules and is restored to linear geometry (with rather ordinary equilibrium bond lengths, RCC = 1.2785Å, RCO = 1.1575Å) when either of the 〈nO(π)|F|σ*CC〉 or 〈nO(σ)|F|π*CC〉 interactions is removed.


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Although the nO(π)-σ*CC and nO(σ)-π*CC delocalizations from the terminal oxygen into the adjacent CC antibond appear to be the most important factors responsible for kinking, other π→σ* or σ→π* interactions play a role in propagating the kink deformation along the cumulene spine. When the tendency toward kinking is sufficiently weak, deletion of any one of these interactions may be sufficient to overcome the kinking tendency and restore equilibrium linear geometry. These qualitative characteristics of cumulene ketenes indicate that unusually high levels of ab initio theory will be required to determine quantitative details of their structure and spectroscopy. Trans. vs. Cis Kinking in Even and Odd Diketones Based on the preceding considerations for OCCO, we can now understand why O=(C=)mO diketones should exhibit the strong even vs. odd alternation of kinked vs. unkinked equilibrium structures. As mentioned above, in even-m species, both nO(π) lone pairs interact strongly (from opposite ends) in a common plane, each reinforcing the other through conjugation in a common pi system to induce a non-linear kink lying in the common plane. However, in odd-m species, the two nO(π) orbitals could only stabilize opposing kinks in mutually perpendicular planes (a geometric impossibility). Thus, each nO(π) effectively opposes (rather than reinforces) the kinking propensity of the other, resulting in linear equilibrium geometry for odd-m. For even-m, the strong intrinsic preference for trans-like rather than cis-like kinking was noted in the case of OCCO (Fig. 4). This preference is also recognizable in ethylene, where the two methylene groups can be symmetrically tilted out of the plane more readily in trans- than cis-like fashion, a tendency that might be rationalized in terms of expected overlap strain of sigma and pi hybrids in cis-like vs. trans-like deformations.17 For a single Lewis structure, the intrinsic preference for trans-like deformations is therefore as expected. However, in even-m cumulene diketones, the greater resistance to cis-like kinking has a more unusual electronic origin. As mentioned above, such molecules possess two resonance structures that are equivalent in D∞h geometry, but can be distinguished by whether the central πCC bond lies in-plane or out-of-plane with respect to a bending distortion. Specifically, for a cis-like distortion, the pπ orbitals of the out-of-plane Lewis structure retain their parallel orientation (i.e., the bend is perpendicular to the plane of the π bond and π overlap is preserved), whereas the strained in-plane Lewis structure corresponds to that described in the preceding paragraph. The out-of-plane Lewis structure is therefore favored over the in-plane in any cis-like distortion. In effect, it is impossible to make a cis-like kink “in the plane of the two nO(π) orbitals,” because the preferred Lewis structure will always reorient the two nO(π) lone pairs to remain coparallel during bending. But this circumstance also renders the crucial nO(π)ACS Paragon Plus Environment

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σ*CC interactions completely ineffective in stabilizing cis-like distortions, because the σ*CC orbital is necessarily constrained to remain in the nodal plane of the nO(π) orbital. Consistent with this picture, only trans-like equilibrium structures are calculated (Fig. 1, Table 1) for all even-m cumulene diketones. From the familiar resonance mnemonic associated with nO(π)-σ*CC (or nO(σ)-π*CC) interaction, viz., ..

(+)

:Ö=Cα=Cβ=... ↔ :O ≡Cα−Cβ(−)=... (2a)

(2b)

one recognizes that Cα retains linear sp-type hybridization, whereas Cβ must adopt sp2-like hybridization to accommodate formal carbanion character. Thus, in extended cumulene diketones the principal kinking effects should occur at Cβ and diminish with distance from the terminal O-cap “driving force” for symmetry-breaking, as illustrated, e.g., in Fig. 1h. Trans Kinking in Cumulene Monoketone Derivatives In cumulene ketones, CH2=(C=)mO, only a single Lewis structure is feasible, fixed by the unique orientation of the CH2 plane. The carbonyl nO(π) orbital is therefore oriented parallel to the CH2 plane for even m, or perpendicular for odd m. The driving role of the nO(π) orbital, as discussed in Sec. IV, therefore leads to the expectation that: (1) the kink is most pronounced at Cβ adjacent to the carbonyl terminus, diminishing toward the methylene terminus; (2) the kink is always of trans-like form; (3) the kinking plane lies parallel to the CH2 plane for even m, or perpendicular for odd m. Each of these expectations is well satisfied by the available data in Table 1. It is also noteworthy that there are no conspicuous differences in the magnitudes of bending angles or other aspects of the kinking patterns for even and odd m (other than orientation with respect to the CH2 plane). This again suggests that kinking is primarily driven by the oxygen lone-pair orbitals at the carbonyl terminus, relatively uninfluenced by chemical differences at the opposite end.


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It may seem surprising that the parent species, ketene (m = 1), fails to exhibit an equilibrium kink (Table 1), and indeed shows notably higher stiffness toward the kinking deformation (Table 2). This is presumably due to the fact that “Cβ” of (2a) is now the methylene carbon which already has sp2-like hybrid character, contrary to other cases considered above. In addition, nO(π)-σ*CC delocalization is somewhat weakened by the slightly higher electronegativity of an interior carbon (~sphybridized) compared to a terminal methylene carbon (~sp2-hybridized), resulting in a σ*CC antibond with decreased polarization toward the carbonyl terminus. Finally, it is evident that the simple picture of ketene kinking sketched herein should apply to more complex derivatives, including the cyclopentadienylideneketene species in which such kinking was first established.7,8 Figure 8 shows calculated structures of (a) fulvenone (fulvene ketene, C2v) and (b) cyclopentadienylideneketene (Cs) which may be directly compared with the acyclic species in Fig. 1a, 1b, respectively, and would be analyzed similarly.

(a)

(b)

Figure 8. Optimized MP2/aug-cc-pVTZ structures for (a) fulvenone (C2v) and (b) cyclopentadienylideneketene (Cs; ∠C1-C6-C11 = 137.7°). Summary and Conclusions We have examined the equilibrium geometry and low-frequency bending vibrations of a variety of cumulene ketones and diketones using correlated and uncorrelated ab initio and density functional methods with natural bond orbital (NBO) and natural resonance theory (NRT) analysis. Nonlinear spine-kinking deformations are found to be fairly ubiquitous in these species, with interesting even/odd dependences on cumulene chain length and number of terminal carbonyl groups. We have found a simple orbital picture based on NBO Lewis structure concepts that is able to to ACS Paragon Plus Environment

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satisfactorily rationalize the main kinking trends of available theoretical and (limited) experimental data for these systems. The close connection between kinking and symmetry-breaking interactions of n(π)σ* (or π-σ*) type that promote σ-bond breakage implies that nonlinear kinking deformations will generally play an important role in the dynamics of dissociation reactions leading to rupture of the cumulene chain, particularly loss of CO. The nonexistence of O=C=C=O illustrates the facility of such dissociative kinking in a particularly dramatic way. This circumstance also explains why experimental examples of kinked cumulene ketones and diketones are quite rare: such kinking lies literally on the path to self-destruction. The simple picture we have drawn suggests the general instability of O=C=C... moieties that appear to have robust double-bonded Lewis structures. However, it also suggests how the self-destructive nO(π)-σ*CC tendency might be modified (e.g., by competing nO(π)-σ* interactions with H-bonding solvents) to alter the stability with respect to CO dissociation. The kinking proclivities of cumulene ketones therefore provide further illustration of the importance of resonance-type corrections to simple Lewis-structural concepts in a broad variety of chemical phenomena. Finally, we comment briefly on how the present NBO/NRT description is related to other possible theoretical approaches to analyzing the origin of symmetry-breaking distortions. A well-known example is the Jahn-Teller theorem for degenerate radical species,18 which guarantees that symmetry-breaking must occur but cannot predict the magnitude or relative probability of various distortions that might be considered. NBO/NRT vs. Jahn-Teller descriptions of symmetry-breaking in radical species were recently compared19 to demonstrate how the former can provide additional structural and vibrational detail as well as a clear chemical rationale for the specific distortion adopted by a radical species. For more general non-degenerate molecular species, NBO/NRT analysis can also be compared with pseudo Jahn-Teller (PJT) theory,20 which attributes symmetry-breaking distortions to vibronic coupling with excited electronic states. PJT rationalizations therefore require multi-configurational (CAS, CI, TD-DFT,...) identification of an excited state that overlaps the ground-state electronic wavefunction when shifted along a vibrational mode of proper symmetry, usually employing a perturbative 2-state model of vibronic coupling.21 The present results illustrate how NBO/NRT analysis achieves a chemically enriched rationalization of symmetry-breaking distortions based only on the 1st-order density matrix for ground-state electronic wavefunctions of arbitrary single- or multiconfigurational form, with no direct reference to molecular vibrations.


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Acknowledgments: Computational resources for this research were supported in part by National Science Foundation Grant CHE-0840494. Mr. Scott Tobias provided computational assistance in initial phases of this study. Supporting Information. Gaussian input files containing optimized coordinates, vibrational frequencies, ZPE corrections, and other details for all stationary-state species employed in this work, including NBO keyword input and results for $DELoptimization jobs. REFERENCES 1. (a) Thaddeus, P.; Gottlieb, C. A.; Mollaaghababa, R.; Vrtilek, J. M. (1993) Free carbenes in the interstellar gas, J. Chem. Soc., Faraday Trans. 89, 2125-2129; (b) Thaddeus, P. Carbon chains and the diffuse interstellar band. In, The Diffuse Interstellar Bands; Tielens, A. G. G. M.; Snow, T. P., Eds.; Springer, New York, 2012, p. 369-378. 2. Tidwell, T. T. (2006) Ketenes, 2nd ed.; Wiley, New York. 3. Allen, A. D.; Tidwell, T. T. (2013) Ketenes and other cumulenes as reactive intermediates, Chem. Revs. 113, 7287-7342. 4. See, e.g., (a) Kasha, M. (1960) Paths of molecular excitation, Bioenergetics, Radiation Res. Suppl. 2, 243-275; (b) Zimmerman, H. E.; Schuster, D. J. (1961) The photochemical rearrangement of 4,4-diphenylcyclohexadienone. I. On a general theory of photochemical reactions, J. Am. Chem. Soc. 83, 4486-4488; (c) Zimmerman, H. E. (1976) Mechanistic and exploratory organic photochemistry, Science 191, 523528; (d) Seburg, R. A.; McMahon, R. J. (1995) Automerization in propynylidene (HCCCH), propadienylidene (H2CCC) and cyclopropenylidene (c-C3H12), Angew. Chem. Int. Ed. 107, 2198-2201; (e) Kaiser, R. I.; Ochsenfeld, C.; Head-Gordon, M.; Lee, Y. T.; Suits, A. G. (1996) A combined experimental and theoretical study on the formation of interstellar C3H isomers, Science 274, 1508-1511; (f) Ref. 3 and refs. therein. 5. Leffler, J. E. (1956) The Reactive Intermediates of Organic Chemistry; Interscience, New York. 6. Radziszewski, J. G.; Hess, B. A.; Zahradnik, R. (1992) Infrared spectrum of obenzyne: experiment and theory, J. Am. Chem. Soc. 114, 52-57, Scheme II;


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7. Scheiner, A. C.; Schaefer, H. F. (1992) Cyclopentadienylideneketene: Theoretical consideration of an infrared spectrum frequently mistaken for benzyne, J. Am. Chem. Soc. 114, 4758-4762. 8. Radziszewski, J. G.; Kaszynski, P.; Friderichsen, A.; Abildgaard, J. (1998) Bent cyclopenta-2,4-dienylideneketene: Spectroscopic and ab initio study of reactive intermediate, Collect. Czech. Chem. Commun. 63, 1094-1106. 9. Ortega-Alfaro, M. C.; Rosas-Sanchez, A.; Zarate-Picazo, B. E.; Lopez-Cortes, J. G.; Cortes-Guzman, F.; Toscano, R. A. (2011) Iron(0) promotes aza cyclization of an elusive ferrocenylketene, Organometallics 30, 4830-4837. 10. Weinhold, F.; Landis, C. R. (2012) Discovering Chemistry with Natural Bond Orbitals, Wiley-VCH, Hoboken NJ. 11. (a) Glendening, E. D.; Weinhold, F. (1998) Natural resonance theory. I. General formulation, J. Comput. Chem. 19, 593-609; (b) Glendening, E. D.; Weinhold, F. (1998) Natural resonance theory. II. Natural bond order and valency, J. Comput. Chem. 19, 610-627; (c) Glendening, E. D.; Badenhoop, J. K.; Weinhold, F. (1998) Natural resonance theory. III. Chemical applications, J. Comput. Chem. 91, 628-646. 12. Clauss, A. D.; Nelsen, S. F.; Ayoub, M.; Moore, J. W.; Landis, C. R.; Weinhold, F. (2014) Rabbit ears hybrids, VSEPR sterics, and other orbital anachronisms, Chem. Educ. Res. Pract. 15, 417-434. 13. Pauling, L. (1960) The Nature of the Chemical Bond, 4th ed., Cornell U. Press, Ithaca, NY, p. 267ff. 14. The transient (sub-nanosecond) lifetime of this species nevertheless allows characterization when “synthesized” by photoelectron detachment from a linear precursor anion: Dixon, A. R.; Xue, T.; Sanov, A. (2015) Spectroscopy of ethylenedione, Angew. Chem. Int. Ed. 54, 8764-8767. 15. Pople, J. A.; Gordon, M. (1967) Molecular orbital theory of the electronic structure of molecules. I. Substituent effects and dipole moments, J. Am. Chem. Soc. 87, 4253-4261. 16. The labels “σ,” “π” for the NBOs are not intended to represent strict symmetry designations, nor to imply that the NBOs are numerically constrained to these forms (as opposed to general “banana bonds,” etc.). However, the optimal NBOs are generally found to conform well to the qualitative picture associated with these localsymmetry labels, reflecting their high degree of transferability from isolated diatomic


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molecules where such symmetries are exact. One can therefore conveniently use these labels even in systems of lower symmetry. 17. If each methylene of an idealized ethylene molecule is tilted out of the molecular plane, the natural hybrid orbitals (NHOs) can easily rehybridize to maintain high overlap in a trans-like deformation, but the corresponding flexibility for a cis-like deformation would require directing all four valence hybrids to one side of a plane. For example, if the methylenes are tilted by 20º, the NHO overlaps (RHF/aug-ccpVTZ level) are altered by less than 1% in trans-like deformation (from 0.8256 to 0.8228 for σ-type and from 0.4783 to 0.4715 for π-type) but by 15-20% in cis-like deformation (down to 0.7062 for σ-type and 0.5837 for π-type.) 18. Jahn, H.; Teller, E. (1937) Stability of polyatomic molecules in degenerate electronic states. I. Orbital degeneracy, Proc. R. Soc. London A 161, 220-235. 19. F. Weinhold, C. R. Landis, and E. D. Glendening (2016) What is NBO analysis and how is it useful? Int. Rev. Phys. Chem. 35, 399-440. 20. I. B. Bersuker (2013) Pseudo-Jahn-Teller effect – A two-state paradigm in formation, deformation, and transformation of molecular systems and solids, Chem. Rev. 113, 1351-1390. 21. See, e.g., (a) Jose, D.; Datta, A. (2012) Understating the buckling distortions in silicene, J. Phys. Chem. C 116, 24639-24648; (b) Pratik, S.M.; Datta, A. (2015) 1,4dithiine – puckered in the gas phase but planar in crystals: Role of cooperativity, J. Phys. Chem. C 119, 15770-15776; (c) Pratik, S. M.; Chowdhury, C.; Bhattacharjee, R.; Jahiruddin, S.; Datta, A. (2016) Pseudo Jahn-Teller distortion for a tricyclic carbon sulfide (C6S8) and its suppression in S-oxygenated dithiine (C4H4(SO2)2), Chem. Phys. 460, 101-105.


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