Proposed Symmetric Systems with Six-Coordinate Carbon

molecules

Review Bonding Analysis of Compounds with Unusual Coordination of Carbon: Proposed Symmetric Systems with Six-Coordinate Carbon

Carl Trindle 1,* , Zikri Altun 2 and Erdi Ata Bleda 2

1 Chemistry Department, University of Virginia, Charlottesville, VA 22904, USA 2 Physics Department, Marmara University, Istanbul 34724, Turkey; [email protected] (Z.A.); [email protected] (E.A.B.) * Correspondence: [email protected]; Tel.: +1-434-770-9197

Academic Editor: Steve Scheiner Received: 21 July 2020; Accepted: 26 August 2020; Published: 28 August 2020

Abstract: The possibility of carbon tetravalence in geometries other than tetrahedral and of carbon hypervalence has been taken seriously since the 1970s. Computational modeling and subsequent experimental validation have established the existence of molecules with carbon atoms with planar tetravalence and as many as six objects in carbon’s coordination sphere. In this work, we develop insight into the nature of bonding to carbon in these unusual environs as provided by Bader’s Atoms in Molecules (AIM) analysis of the electron density, along with the electron localization function (ELF) and the non-covalent index (NCI). We review several well-established systems (spiropentadiene dication, hexamethyl benzene dication, dimethanospiro[2.2]octaplane dication, and 1,8-dimethoxy-9-dimethoxyanthracene cation) and propose new D2d–symmetric variants of a hexacoordinated species.

Keywords: AIM modeling; electron localization function; non-covalent interaction; carbon hypercoordination

1. Introduction One of the basic insights of organic chemistry is that saturated carbon atoms arrange four partners in tetrahedral coordination. [1–4] Lewis electron pairing and the Valence Shell Electron Repulsion model [5,6] reinforce the insight, allow easy applications, and shape our intuition. Minor departures from the ideal form can be interpreted as a consequence of the lower symmetry of the arrangement of the four objects in the coordination sphere. But major departures from tetrahedral tetracoordination—that is to say, either serious change as from (a) tetrahedral to planar four-coordination or (b) hyper-coordination with five or more neighbors—are rare, and require special explanation. The instability of planarized tetracoordinate carbon as in planar methane (called tpC,) is attributed to its nonbonding pi lone pair [7,8]; in the tetrahedral form all four valence pairs participate in bonds. Planarity can be enforced by two kinds of influence: (1) Removal of the pair of electrons that destabilize the planar form, first exemplified in the discussion of planar methane [7]; (2) ring strain; and/or (3) suitable substitution and associated electronic effects. For example, the closed-shell ground state dication of CH4 is planar (qualitatively, a C2v complex of H2 with CH2 dication) [9]; the double ionization removes charge from the p-pi AO of the Carbon. We discuss structures for other dications with unusual coordination of a central carbon atom, notably 1–4 (Figure1). The dication of spiropentadiene (1) is D2h in symmetry, as modeled computationally by Lammertsma and Schleyer [10]. The pentagonal-pyramidal structure of hexamethylbenzene 2 is achieved only in the dication, established experimentally by Hogeveen et al. [11–13].

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Molecules[10].2020 The, 25 pentagonal-pyramidal, 3937 structure of hexamethylbenzene 2 is achieved only in the dication,2 of 23 established experimentally by Hogeveen et al. [11–13].

FigureFigure 1. Notable1. Notable structures structures withwith unusual coordination coordination of ofcarbon. carbon.

Radom’sRadom’s alkaplane alkaplane systems systems [14 [1]4] rely rely entirely entirely onon strain to to force force the the central central CC CC4 fragment4 fragment toward toward planarplanar tetracoordination tetracoordination of Carbon. of Carbon. The tpC The with tpC its immediate with its Cimmediate neighbors inC Dneighbors2h dimethanospiro[2.2] in D2h octaplanedimethanospiro[2.2]3 is shown in Figure octaplane1. However, 3 is shown the stabilityin Figure of 1. the However, neutral Dthe2h -symmetricstability of the form neutral is questionable. D2h- RadomMoleculessymmetric and2020, Rasmussen25, xform FOR isPEER questionable. [14 REVIEW] report thatRadom a MP2 and /Rasmussen6-31G(d) calculation [13] report (bythat Marka MP2/6-31G(d) S. Gordon, calculation unpublished)3 of 24 (by Mark S. Gordon, unpublished) produces all-real vibrational frequencies, suggesting the D2h produces all-real vibrational frequencies, suggesting the D2h structure occupies a relative minimum on structure occupies a relative minimum on the potential surface. B3LYP/6-31G(d) calculation and our thereverse potential this motif, surface. calling B3LYP for/6-31G(d) strong pi-donor calculation and and sigma-acceptors our ωB97XD/cc-pVTZ on a periphery. calculation A central both produce example a ωB97XD/cc-pVTZ calculation both produce a substantial imaginary frequency (ca. 300i) suggesting substantialis CAl4 anion imaginary [16]. Structures frequency with (ca. many 300i) suggesting other metals the have symmetric been evaluated form is a transition computationally state between [18–21]. two the symmetric form is a transition state between two twisted forms of the CC4 fragment in the twistedThedimethanospiro[2.2]octaplane. forms same of stratagem the CC4 fragment has prompted Figure in the computational dimethanospiro[2.2]octaplane2 displays the isosurface studies of planarthe .HOMO Figure penta- for2 displays andneutral hexa-coordinated 3 the, which isosurface is ofCarbon. thedominated HOMO For example, forby neutralthe troublesomeExner3, and which Schleyer C islone dominated pair. [22] This used byform B3LYP the of troublesomethe and HOMO CCSD(T)/6-311+G(d,p) is Cin lonegeneral pair. agreement This to form describe with of the a HOMOplanarresults CB is6 in2 −of system general calculations as agreement well at loweras isoelectronic with levels results of theory and of calculations[14,15]. neutral C3B at4 and lower other levels variants. of theory [14,15]. The planarity can be established by ionization; the monocation radical has a planar tpC [15]. We have confirmed that complete removal of two electrons from the HOMO more firmly establishes stability of the D2h symmetry of Radom’s dimethanospiro[2.2]octaplane dication. Substitution of two Carbon atoms by Boron atoms, forming systems isoelectronic with the hydrocarbon dications, accomplishes planarization. This formation of neutral analogs to hydrocarbon cations is called the charge compensation principle by its inventors [13] and is applied to this issue by Wang and Schleyer [16]. A tactic recommended by Hoffmann [7,8] is to surround the central carbon by species which are strong sigma donors and pi acceptors, which then may effect redistribute the troublesome planar-Carbon lone pair toward its surroundings. A series of molecules incorporating Copper and Nickel substituents on the tpC investigated by Schleyer and Boldyrev [17]

Figure 2. HOMO for neutral dimethanospiro[2.2]octaplane. Figure 2. HOMO for neutral dimethanospiro[2.2]octaplane.

In this report we confine our attention to metal-free systems and examine hypercoordinated Carbon atoms with O and S members in the coordination sphere. The coordination sets in our systems are often nonplanar. Our purpose is to characterize the interactions of the hypercoordinated carbon with its neighbors. To assist intuition we employ diagnostics and visualization aids from Bader’s Atoms-in-Molecules theory [23], and related quantities such as the electron localization function [24] and the non-covalent index [25].

2. Computational Methods and Software

2.1. Software We use Gaussian 09 [26] and 16 [27] for electronic structure calculations including geometry optimization and vibrational analysis. The density functional model is ωB97XD [28] and the basis is cc-pVTZ [29] except as otherwise noted. With one exception (5) in which the experimental (X-ray) structure is used, all reported structures are local minima according to ωB97XD/cc-pVTZ, with no imaginary vibrational frequencies. Bader AIM analysis is conducted by AIMALL [30] and Multiwfn software [31]. Construction of the electron localization function (ELF) and the non-covalent index (NCI) is accomplished with Multiwfn and NCIplot [32]. In the following sections we describe AIM, ELF, and NCI methods of characterizing the electron density. Those familiar with these analyses may wish to pass directly to Section 3, in which we describe applications.

2.2. AIM and Bader Terminology The Atoms-in-Molecules (AIM) analysis characterizes bonding with reference to the electron density, an observable of a molecular system. The review by Kumar et al. is a useful introduction, with many examples [33]. At critical points where ∇ρ = 0 we can evaluate the charge density ρ, its Laplacian L = ∇2ρ, and the eigenvalues {λk} of the matrix {Hij} = {∂2ρ/∂xi∂xj} along with various energy densities. Diagonalization of H yields three eigenvalues. There can be three negative eigenvalues, defining NCP nuclear critical points (attractors) coded (3, −3); two negative and one positive value defining BCP bond critical points, coded (3, −1), one negative and two positive values defining RCP ring critical points coded (3, +1), or three positive values defining CCP cage critical points coded (3, +3). The number of critical points of all kinds should obey the Poincare-Hopf rule, which in this case requires that NCP − BCP + RCP − CCP = 1. This is the case for all systems described here.

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The planarity can be established by ionization; the monocation radical has a planar tpC [15]. We have confirmed that complete removal of two electrons from the HOMO more firmly establishes stability of the D2h symmetry of Radom’s dimethanospiro[2.2]octaplane dication. Substitution of two Carbon atoms by Boron atoms, forming systems isoelectronic with the hydrocarbon dications, accomplishes planarization. This formation of neutral analogs to hydrocarbon cations is called the charge compensation principle by its inventors [13] and is applied to this issue by Wang and Schleyer [16]. A tactic recommended by Hoffmann [7,8] is to surround the central carbon by species which are strong sigma donors and pi acceptors, which then may effect redistribute the troublesome planar-Carbon lone pair toward its surroundings. A series of molecules incorporating Copper and Nickel substituents on the tpC investigated by Schleyer and Boldyrev [17] reverse this motif, calling for strong pi-donor and sigma-acceptors on a periphery. A central example is CAl4 anion [16]. Structures with many other metals have been evaluated computationally [18–21]. The same stratagem has prompted computational studies of planar penta- and hexa-coordinated Carbon. For example, Exner and Schleyer [22] used B3LYP and CCSD(T)/6-311+G(d,p) to describe a 2 planar CB6 − system as well as isoelectronic and neutral C3B4 and other variants. In this report we confine our attention to metal-free systems and examine hypercoordinated Carbon atoms with O and S members in the coordination sphere. The coordination sets in our systems are often nonplanar. Our purpose is to characterize the interactions of the hypercoordinated carbon with its neighbors. To assist intuition we employ diagnostics and visualization aids from Bader’s Atoms-in-Molecules theory [23], and related quantities such as the electron localization function [24] and the non-covalent index [25].

2. Computational Methods and Software

2.2. AIM and Bader Terminology The Atoms-in-Molecules (AIM) analysis characterizes bonding with reference to the electron density, an observable of a molecular system. The review by Kumar et al. is a useful introduction, with many examples [33]. At critical points where ρ = 0 we can evaluate the charge density ρ, its ∇ Laplacian L = 2ρ, and the eigenvalues {λ } of the matrix {H } = {∂2ρ/∂x ∂x } along with various energy ∇ k ij i j densities. Diagonalization of H yields three eigenvalues. There can be three negative eigenvalues, defining NCP nuclear critical points (attractors) coded (3, 3); two negative and one positive value − defining BCP bond critical points, coded (3, 1), one negative and two positive values defining RCP − ring critical points coded (3, +1), or three positive values defining CCP cage critical points coded (3, +3). The number of critical points of all kinds should obey the Poincare-Hopf rule, which in this case requires that NCP BCP + RCP CCP = 1. This is the case for all systems described here. − − AIM divides Cartesian space into basins, each containing an attractor—most often a nucleus. The boundaries of the basins are defined by a zero-flux ( ρ = 0) surface. Integration of electronic ∇ charge within a basin including a nucleus produces an AIM atomic charge. Molecules 2020, 25, 3937 4 of 23

For familiar covalent chemical bonds, the electron density ρ at a BCP would be on the order of tenths of density units, electrons per cubic bohr. For weak mainly electrostatic interactions such as H bonds, the density at the BCP would be much smaller (at best, hundredths of atomic units) and the Laplacian would be positive. In all the examples to follow, we find the usual array of nuclear attractors with very large densities and large negative Laplacian values; BCPs for covalent sigma bonds; nonpolar aromatic CC bonds in the anthryl rings; and polar bonds with smaller densities. In AIM analysis the kinetic and potential energy densities G and V at the bond critical points offer insight into the nature of bonding. A useful diagnostic of covalent bonding is the ratio |2G(rbcp)/V(rbcp)|; if this ratio is less than unity then the interaction is covalent [34]. While AIM provides a well-defined methodology for processing molecular electron density (obtained either by theoretical methods or by processing experimental data) its link to intuitive chemical constructs—especially bonds and atomic charges—has been the subject of considerable debate. We refer to only a very small sample, which will convey the flavor [35–38]. We judge that reductio ad absurdum does not undermine the practical value of QTAIM.

2.3. ELF The electronic localization function (ELF) was deﬁned by Becke and Edgecombe [24]. The probability density that a second like-spin electron is found near a “localized” electron is presumably small. This density arising from Fermions in the molecular system is written as:

σ 2 2 D = Σ ψi ρ(r) /4ρ(r) (1) i ∇ − ∇

The sum is over all the occupied molecular spinorbitals; ρσ(r) is the electron density of electrons 2 ( ) = σ ψ with σ spin which in the Kohn–Sham approximation is given by ρσ r Σi i . The smaller the quantity D, the more highly localized is the reference electron. A dimensionless index χ is deﬁned as the ratio of the density D to the corresponding value for the uniform electron gas:

3 2/3 D = (6π2) ρ5/3. (2) 0 5

ELF is conﬁned to the range [0, 1] by the transform ELF = 1/(1 + χ2). The limit of maximum localization is χ = 1.

2.4. NCI A useful description of the non-covalent index, its graphical characterization, and its interpretation is given by Contreras-Garcia, et al. [39]. The reduced (dimensionless) density gradient s (also called RDG) is defined as ρ(r) s(r) = ∇ (3) 2(3π2)1/3ρ(r)r4/3 Two NCI graphic realizations are useful. A two-dimensional plot of s vs. the density ρ (given the sign of the second eigenvalue of H) will produce a broad sweep from one extreme at small density but large s to large density and small s. This is characteristic of an exponentially-decaying density. Superimposed on this sweep may be spikes in s extending to values near zero at modest values of density. In Figure3, plots derived from ωB97XD/cc-pVTZ computations for water dimer and formic acid dimer are shown. The high-density (but low s) regions near nuclei are far to the right or left of the range of densities shown. The low-density region is located primarily in Cartesian space close to the density tails for which s is large. However, s can be small precisely where the density is disturbed by non-covalent interactions, such as van der Waals/dispersion and electrostatic forces. Figure3 shows the plot for water dimer and formic acid dimer. For water dimer, we find one such case at signed density about 0.025, and for formic acid dimer we find two, at +0.01 and 0.05. − − Molecules 2020, 25, x FOR PEER REVIEW 5 of 24 Molecules 2020, 25, 3937 5 of 23 Molecules 2020, 25, x FOR PEER REVIEW 5 of 24

Figure 3. Two-dimensional representation of non-covalent interactions for water dimer and formic Figure 3. Two-dimensional representation of non-covalent interactions for water dimer and formic Figureacid dimer. 3. Two-dimensional representation of non-covalent interactions for water dimer and formic acid dimer. acid dimer. Mapping thosethose zoneszones ofof smallsmall density density and and small smalls (RDG)s (RDG) into into three-dimensional three-dimensional space space (Figure (Figure4), Mapping those zones of small density and small s (RDG) into three-dimensional space (Figure we4), we isolate isolate regions regions of signiﬁcant of significant NCI NCI in isosurfaces in isosurfa ofces value of value 0.05. 0.05. For waterFor water dimer dimer there there is a single is a single zone 4), we isolate regions of significant NCI in isosurfaces of value 0.05. For water dimer there is a single ofzone non-covalent of non-covalent interaction, interaction, which which we must we must associate associate with with H-bonding. H-bonding. One One spike spike from from Figure Figure3 can 3 zone of non-covalent interaction, which we must associate with H-bonding. One spike from Figure 3 refercan refer to more to more than than one zone.one zone. In the In formicthe formic acid acid dimer dimer (Figure (Figure4), we 4), ﬁnd we twofind attractivetwo attractive H-bonding H-bonding NCI can refer to more than one zone. In the formic acid dimer (Figure 4), we find two attractive H-bonding regionsNCI regions and alsoand aalso destabilizing a destabilizing zone zone corresponding corresponding to a ring to a criticalring critical point. point. NCI regions and also a destabilizing zone corresponding to a ring critical point.

Figure 4. Zones for which both reduced density gradient (RDG) and density are small for water dimer (L)Figure and 4. formic Zones acid for which dimer both (R). reduced density gradient (RDG) and density are small for water dimer Figure(L) and 4. formicZones foracid which dimer both (R). reduced density gradient (RDG) and density are small for water dimer 3. Density(L) and formic Analysis acid for dimer Known (R). Examples of Unusual Coordination of Carbon 3. Density Analysis for Known Examples of Unusual Coordination of Carbon 3.3.1. Density Example Analysis 1: Spiropentadiene for Known Dication Examples of Unusual Coordination of Carbon 3.1. Example 1: Spiropentadiene Dication Our ωB97XD/cc-pVTZ calculations and earlier reports [10] verify that D2h-symmetric 3.1. Example 1: Spiropentadiene Dication spiropentadieneOur ωB97XD/cc-pVTZ dication 1 occupies calculations a relative and minimum earlier energy reports point. [9] (The verify unsubstituted that D2h monocation-symmetric andspiropentadieneOur neutral ωB97XD/cc-pVTZ counterparts dication however 1 calculationsoccupies are nonplanar.) a relativeand earlier The minimum neutral reports system energy [9] can verify bepoint. constrained that(The D unsubstituted2h to-symmetric coplanarity spiropentadieneofmonocation the three-membered and neutraldication rings counterparts 1 byoccupies enclosing however a therelative spiropentadiene are nominimumnplanar.) coreTheenergy neutral within point. aromaticsyst em(The can seven-membered unsubstitutedbe constrained monocationringsto coplanarity [40]. Inand thisof neutral the case three-membered counterparts the troublesome however rings electron by are en no pairclosingnplanar.) is exported the Thespiropentadiene neutral from the syst p-piem core can AO within be of constrained tpC aromatic into the toaromaticseven-membered coplanarity region. of the rings three-membered [40]. In this case rings the bytroublesome enclosing theelectron spiropentadiene pair is exported core fromwithin the aromatic p-pi AO seven-memberedof tpC into the aromatic rings [40]. region. In this case the troublesome electron pair is exported from the p-pi AO of3.1.1. tpC AIMinto the Analysis aromatic region. 3.1.1.Firme AIM Analysis et al. [41, 42] presented an AIM analysis of the planar dication of spiropentadiene. Critical 3.1.1. AIM Analysis ω pointsFirme and bondet al. [41,42] paths from presented our AIM2000 an AIM analysisanalysis of of the the density planar dication obtained of with spiropentadiene.B97XD/cc-pVTZ Critical are pointsFirme and et bond al. [41,42] paths presentedfrom our AIM2000 an AIM analysisanalysis ofof the planardensity dication obtained of with spiropentadiene. ωB97XD/cc-pVTZ Critical are points and bond paths from our AIM2000 analysis of the density obtained with ωB97XD/cc-pVTZ are

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shown in Figure 55.. ValuesValues ofof density,density, thethe Laplacian,Laplacian, GG andand VV atat selectedselected BCPsBCPs areare shownshown in Table1 1.. Entries in red are fromfrom Firme,Firme, et al.al. [[41]41] andand agreeagree prettypretty nearlynearly withwith ourour ωωB97XDB97XD/cc-pVTZ/cc-pVTZ values. WeWe seesee thatthat thethe BCPsBCPs alongalong thethe pathspaths fromfrom aa peripheralperipheral CarbonCarbon toto the tetracoordinate planar Carbon have muchmuch smallersmaller valuesvalues of of the the Laplacian Laplacian of of the the density density compared compared with with the the values values at BCPsat BCPs along along the twothe two bond bond paths paths connecting connecting peripheral peripheral C-Cs. C-Cs. We infer We thatinfer the that tpC-Cx the tpC-Cx bond isbond weaker is weaker than the than Cx-Cx the bond.Cx-Cx Itbond. is remarkable It is remarkable that the tpCthat is the has tpC a net is negative has a negative AIM basin AIM charge basin ( charge0.193 absolute (−0.193 electronsabsolute − orelectrons|e|); the or positive |e|); the charge positive in this charge dication in this is disperseddication is to dispersed the surrounding to the surrounding C and H atoms C and (+0.169 H atoms and +(+0.1690.379 | eand| respectively.) +0.379 |e| respectively.)

Figure 5.5. Topological (Bader)(Bader) analysisanalysis ofof spiropentadienespiropentadiene dicationdication 11.. LargeLarge light-graylight-gray spheresspheres == H atoms; largelarge dark dark gray gray spheres spheres= C= atoms;C atoms; small small white white spheres spheres= BCPs; = BCPs; small small red spheres red spheres= RCPs; = RCPs; black lines = bond paths. black lines = bond paths. Table 1. Selected AIM parameters for spiropentadiene dication. Cx is a peripheral Carbon, tetra-coordinateTable 1. Selected carbon AIM asparameters in planar for methane spiropentadiene (tpC) is the dication. tetracoordinate Cx is a planar peripheral Carbon. Carbon, Red: Fromtetra- Firmecoordinate et al. carbon [41]. as in planar methane (tpC) is the tetracoordinate planar Carbon. Red: From Firme et al. [41]. Critical Point Density ρ Laplacian G V |2G/V| Critical Point Density ρ Laplacian G V |2G/V| tpC-Cx: 0.2323 0.1184 − +0.1685 0.3506 0.961 (3,tpC-Cx:1) 0.2300.2323 0.113−0.1184 − − − +0.1685 −0.3506 0.961 Cx-Cx(3, −1) 0.37080.230 1.1167−0.113 − +0.1872 0.6535 0.573 (3, 1) 0.369 1.109 − −Cx-Cx 0.3708 − −1.1167 Cx-H 0.2716 1.0302 +0.1872 −0.6535 0.573 (3, −1) 0.369 − −1.109 +0.0134 0.2844 0.094 (3, 1) 0.275 1.050 − −Cx-H 0.2716 − −1.0302 Basin Charges +0.0134 −0.2844 0.094 (3, −1) 0.275 −1.050 Charge (|e|) H = +0.3794 Cx = +0.1691 tpC = 0.1932 Basin Charges − Charge (|e|) H = +0.3794 Cx = +0.1691 tpC = −0.1932 3.1.2. ELF Analysis 3.1.2.The ELF electron Analysis localization function shown in Figure6 displays the four bonding regions C to H and theThe two electron single localization CC bonds, function top and shown bottom. in TheFigure pi character6 displays of the the four C=C bonding bonds isregions visible C at to the H bottom.and the Thetwo ELFsingle zones CC forbonds, the CH top bonds and bottom. are extensive, The pi compared character with of the CC C=C bonds. bonds From is thevisible AIM at basin the charges,bottom. (TableThe ELF1) it zones appears for thatthe uponCH bonds double are ionization extensive, electron compared density with from CC the bonds. HC = FromCH fragments the AIM hasbasin migrated charges, so (Table that tcC 1) obtainsit appears a net that negative upon double charge. ionization electron density from the HC=CH fragments has migrated so that tcC obtains a net negative charge.

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Figure 6. Electron localization function (ELF) for spiropentadiene (view perpendicular to D plane). Figure 6. Electron localization function (ELF) for spiropentadiene (view perpendicular to2h D2h plane). 3.1.3. NCI Analysis 3.1.3. NCI Analysis The plot of the reduced density gradient s(ρ) against the density as signed by the second eigenvalue The plot of the reduced density gradient s(ρ) against the density as signed by the second of the Laplacian of the density shows no departures from monotone decline in s(ρ) at left and right eigenvalue of the Laplacian of the density shows no departures from monotone decline in s(ρ) at left (See Figure S1, Supplementary Materials). That is, there are no zones of non-covalent interaction in and right (See Figure S1, Supplementary Materials). That is, there are no zones of non-covalent this dication. interaction in this dication. 3.2. Example 2: Hexamethylbenzene Dication 3.2. Example 2: Hexamethylbenzene Dication The structure of hexamethylbenzene dication 2 found by ωB97XD/cc-pVTZ is a pentagonal pyramid,The in structure which a of -CMe hexamethylbenzene cap subtends a five-membereddication 2 found ring. by ω TheB97XD/cc-pVTZ carbon of the is cap a pentagonal could be consideredpyramid, hexacoordinate,in which a -CMe and cap termed subtends hcC. a The five-m crystalembered structure ring. has The been carbon reported of the [43 ]cap along could with be protonconsidered and C-13 hexacoordinate, NMR. Bonding and is termed characterized hcC. The by crys NICStal [ 44structure] the system has been displays reported three-dimensional [43] along with aromaticity.proton and Apical C-13 NMR. to basal Bonding CC bond is orderscharacterized are small by (ca. NICS 0.5), [44] and the the system apical displays (hexa-coordinate) three-dimensional Carbon employsaromaticity. only fourApical electrons to basal in bonding.CC bond Thatorders is, theare octetsmall rule (ca. is 0.5), not violated.and the apical (hexa-coordinate) Carbon employs only four electrons in bonding. That is, the octet rule is not violated. 3.2.1. AIM Analysis 3.2.1. AIM Analysis Figure7 shows bond critical points and bond paths reinforcing the concept that the cap -CCH 3 interactsFigure with 7 all shows five of bond the carbonscritical points in the pentagonaland bond paths base. reinforcing Similarly, CC the bond concept paths that define the cap bonding -CCH3 betweeninteracts neighboring with all five C of atoms the carbons in the pentagonalin the pentagonal base and base. their Similarly, attachment CC bond to methyl paths groups.define bonding Each facebetween of the pentagonalneighboring pyramid C atoms contains in the pentagonal a ring critical base point and (RCP). their attachment to methyl groups. Each face of the pentagonal pyramid contains a ring critical point (RCP). The values of the Laplacian at AIM bond critical points (shown in Table 2) suggest that the C (ring or apex) to C (methyl) bonds are conventional single bonds (the Laplacian is about −0.5, density about 0.27) while the CC bonds within the ring are appreciably stronger, (the Laplacian is about -0.8, density about 0.28). The BCPs for the bonds from apical C to ring Cs are distinct; density is about half that of the single covalent bonds just mentioned and the Laplacian > 0, suggesting that charge is expelled from that region, covalency is weak, and there is some electrostatic component to the interaction. Klein, Havenith, and Knizia [45] consider the compound to be best characterized as a donor-acceptor complex of anionic cyclopentadiene and a “highly Lewis-acidic Carbon atom… capable of acting as an electron-pair donor to a formal CH3+ group.” This is an appealing way to describe the bonding partly because it lends itself so well to interpretation of bonding by means of an interaction diagram. The result of charge migration, as expressed in the basin charges of AIM, is to produce the base ring of five C atoms with associated basin charges near 6.02 electrons (|e|) on

Molecules 2020, 25, x FOR PEER REVIEW 8 of 24 average, with an outer ring of five methyl C atoms with basin charges near 6.037 on average. The basin charge corresponding to the apical six-coordinate C atom is 6.088, and its methyl C basin charge Moleculesis 6.016 2020(|e|)., 25 That, 3937 is, even in this dication the C frame is net negative in charge. The positive charge8 of 23 making up the net +2 is borne by H atoms.

Figure 7. Topological (Bader) analysis of hexamethylbenzene 2.. Large light-gray spheres = HH atoms; large dark dark gray gray spheres spheres == CC atoms; atoms; small small white white spheres spheres = BCPs;= BCPs; small small red redspheres spheres = RCPs;= RCPs; blackblack lines lines= bond= bondpaths. paths.

The valuesTable 2. of Selected the Laplacian Atoms in at Molecules AIM bond (AIM) critical parameters points for (shown hexamethylbenzene in Table2) suggest dication. that the C (ring or apex) to C (methyl) bonds are conventional single bonds (the Laplacian is about 0.5, density Critical Point Density Laplacian G V |2G/V|− about 0.27) while the CC bonds within the ring are appreciably stronger, (the Laplacian is about C ring-C apex: 0.8, density about 0.28). The0.1551 BCPs for+0.0205 the bonds from +0.0913 apical C to ring−0.1765 Cs are 1.0346 distinct; density is − (3, −1) about half that of the single covalent bonds just mentioned and the Laplacian >0, suggesting that C ring-C ring charge is expelled from that region,0.2823 covalency−0.7869 is weak, and+0.0894 there is some−0.3766 electrostatic 0.4748 component to (3, −1) the interaction. Klein, Havenith, and Knizia [45] consider the compound to be best characterized as C apex-Me a donor-acceptor complex of0.2705 anionic cyclopentadiene−0.5607 and+0.0962 a “highly Lewis-acidic−0.3254 0.5913 Carbon atom ... (3, −1) capable of acting as an electron-pair donor to a formal CH + group.” This is an appealing way to C ring-Me 3 describe the bonding partly because0.2722 it lends−0.6231 itself so well+0.0819 to interpretation −0.3194 of bonding 0.5128 by means of an (3, −1) interaction diagram. The result of charge migration, as expressed in the basin charges of AIM, is to Basin Charges produce the base ring of ﬁve C atoms with associated basin charges near 6.02 electrons (|e|) on average, hcC Ring C Apical methyl C Ring methyl C with an outerCharge ring of (|e|) ﬁve methyl C atoms with basin charges near 6.037 on average. The basin charge −0.088 −0.019 −0.016 −0.037 corresponding to the apical six-coordinate C atom is 6.088, and its methyl C basin charge is 6.016 (|e|). That is, even in this dication the C frame is net negative in charge. The positive charge making up the 3.2.2. ELF Analysis net +2 is borne by H atoms. Figure 8 displays the electron localization function (ELF) surface from an elevation toward a face of the pentagonal pyramid (top left) and a view from the pentagonal base (top right). The former view reveals a bond connecting the apical carbon to the carbon of its methyl, and the region of the bonding around the carbon five membered ring. The latter view shows base CC bonds, bonds from those base-plane Carbons to their methyl carbons, and the visible portions of the associated CH bonds. The apical C atom is visible in the center.

Molecules 2020, 25, 3937 9 of 23

Table 2. Selected Atoms in Molecules (AIM) parameters for hexamethylbenzene dication.

Critical Point Density Laplacian G V |2G/V| C ring-C apex: 0.1551 +0.0205 +0.0913 0.1765 1.0346 (3, 1) − − C ring-C ring 0.2823 0.7869 +0.0894 0.3766 0.4748 (3, 1) − − − C apex-Me 0.2705 0.5607 +0.0962 0.3254 0.5913 (3, 1) − − − C ring-Me 0.2722 0.6231 +0.0819 0.3194 0.5128 (3, 1) − − − Basin Charges hcC Ring C Apical methyl C Ring methyl C Charge (|e|) 0.088 0.019 0.016 0.037 − − − −

3.2.2. ELF Analysis Figure8 displays the electron localization function (ELF) surface from an elevation toward a face of the pentagonal pyramid (top left) and a view from the pentagonal base (top right). The former view reveals a bond connecting the apical carbon to the carbon of its methyl, and the region of the bonding around the carbon ﬁve membered ring. The latter view shows base CC bonds, bonds from those base-planeMolecules 2020, 25 Carbons, x FOR PEER to REVIEW their methyl carbons, and the visible portions of the associated9 of 24 CH bonds. The apical C atom is visible in the center.

Figure 8. Views of the electron localization function isosurfaces (top) and the non-covalent interaction Figure 8. Views of the electron localization function isosurfaces (top) and the non-covalent interaction zones (zonesbottom (bottom);); views views from from an elevationan elevation toward toward a facea face of of the the pentagonal pentagonal pyramid (left) (left and) and from from below the basebelow (right the). base (right).

3.2.3. NCI3.2.3. AnalysisNCI Analysis FigureFigure8 (bottom) 8 (bottom) displays displays non-covalent non-covalent inte interactionraction zones zones for forhexamethyl hexamethyl benzene benzene dication. dication. TheseThese include include repulsions repulsions between between adjacent adjacent methyl groups groups in the in the(CH (CH3C)5 base3C)5 ring,base and ring, a feature and a at feature at the center of that ring. The plot of the reduced density gradient (RDG) s(ρ) vs. the signed density (Supplemental information) suggests that the NCI zones identify two kinds of weak van der Waals interactions, which we can see are the ring methyl-methyl interactions and the NCI zone at the center of the five-carbon ring.

3.3. Example 3: Dimethanospiro[2.2]octaplane

Molecules 2020, 25, 3937 10 of 23 the center of that ring. The plot of the reduced density gradient (RDG) s(ρ) vs. the signed density (Supplementary Materials) suggests that the NCI zones identify two kinds of weak van der Waals interactions, which we can see are the ring methyl-methyl interactions and the NCI zone at the center of the ﬁve-carbon ring.

3.3. Example 3: Dimethanospiro[2.2]octaplane

To our knowledge there is no experimental realization of the C5H4 dication 1 itself, but Radom’s ways of stabilizing this structure by steric constraint and charge delocalization might point the way toward a synthesis. The dimethanospiro[2.2]octaplane dication 3 discussed above contains a tetracoordinate planar Carbon (tpC) similar in structure to the spiropentadiene dication. The central CC4 fragment is forced toward planarity primarily by the surrounding rigid cage structure. The constraint is most eﬀective for the dication, and the stable minimum has D2h symmetry Molecules 2020, 25, x FOR PEER REVIEW 10 of 24 3.3.1. AIM Analysis 3.3.1. AIM Analysis Figure9Figure displays 9 displays bond bond critical critical points, points, (white), (white), ringring critical critical points points (red) (red) and andcage cagecritical critical points points (blue). The(blue). Bader The Bader parameters parameters for for cage cage CC CC and and CHCH bond critical critical points points (Table (Table 3) are3) characteristic are characteristic of of saturatedsaturated hydrocarbons. hydrocarbons. Note Note that that there there are are bond bond critical points points and and bond bond paths paths between between two pairs two pairs of C atomsof C coordinatedatoms coordinated to the to tpC,the tpC, consistent consistent with with thethe rectangular arrangement arrangement and the and overall the overall D2h D2h symmetry,symmetry, as in spiropentadieneas in spiropentadiene dication dication1 .1.As As inin the the case case for for 1, 1the, the tpC tpC has hasa negative a negative AIM basin AIM basin charge (−0.165 |e|); the positive charge in this dication is dispersed not substantially to the charge ( 0.165 |e|); the positive charge in this dication is dispersed not substantially to the surrounding surrounding− C atoms in the C5 plane (+0.028 |e| each) but rather mainly to the constraining cage C atomsatoms. in the C5 plane (+0.028 |e| each) but rather mainly to the constraining cage atoms.

Figure 9.FigureTopological 9. Topological analysis analysis of Radom’s of Radom’ dimethanospiro[2.2]octaplanes dimethanospiro[2.2]octaplane 33.. Large Large light-gray light-gray spheres spheres = H atoms; large= H atoms; dark large gray dark spheres gray =spheresC atoms; = C atoms; small sm whiteall white spheres spheres= Bond = Bond CPs; CPs;small small red spheres spheres = = Ring CPs; smallRing blue CPs; spheressmall blue= spheresCage CPs; = Cage black CPs; linesblack =linesbond = bond paths. paths.

Table 3. selected Bader parameters for Radom’s dimethanospiro[2.2]octaplane dication 3.

Critical Point Density Laplacian G V |−2G/V| rC–tcC: 0.2286 −0.2823 +0.1435 −0.3576 0.8026 (3, −1) rC–rC 0.2981 −0.8509 +0.1084 −0.4295 0.5048 (3, −1) sC–sC 0.2493 −0.6234 +0.0729 −0.3016 0.4834 (3, −1)

Molecules 2020, 25, 3937 11 of 23

Table 3. Selected Bader parameters for Radom’s dimethanospiro[2.2]octaplane dication 3.

Critical Point Density Laplacian G V | 2G/V| − rC–tcC: 0.2286 0.2823 +0.1435 0.3576 0.8026 (3, 1) − − − rC–rC 0.2981 0.8509 +0.1084 0.4295 0.5048 (3, 1) − − Molecules 2020, 25, x FOR− PEER REVIEW 11 of 24 sC–sC 0.2493 0.6234 +0.0729 0.3016 0.4834 (3, 1) − − 3.3.2. ELF Analysis −

3.3.2. ELFThe Analysis ELF isosurface diagram shown in Figure 10 (left) reveals the essentially covalent character of the bonds of tpC to its neighbors and the absence of localized charge perpendicular to the plane The ELF isosurface diagram shown in Figure 10 (left) reveals the essentially covalent character containing the tpC and its four bonded C atoms. The lack of localized pi charge at tpC is the of the bonds of tpC to its neighbors and the absence of localized charge perpendicular to the plane consequence of double ionization to the dication. containing the tpC and its four bonded C atoms. The lack of localized pi charge at tpC is the consequence of double ionization to the dication.

Figure 10. ELF for Radom’s D2h dimethanospiro[2.2]octaplane 3, (left) showing central tpC and its bonds to its neighbors. The NCI zones (right) reveal the non-covalent interactions within the rings. Figure 10. ELF for Radom’s D2h dimethanospiro[2.2]octaplane 3, (left) showing central tpC and its 3.3.3. NCIbonds Analysis to its neighbors. The NCI zones (right) reveal the non-covalent interactions within the rings.

3.3.3.The NCI plot Analysis of the reduced density gradient (RDG) s(ρ) vs. the signed density (Supplementary Materials) shows van der Waals features and also strongly repulsive interaction. The NCI zones The plot of the reduced density gradient (RDG) s(ρ) vs. the signed density (Supplementary shown in Figure 10 (right) lie at cage critical points and between the >CH2 bridges of the cyclooctane Materials) shows van der Waals features and also strongly repulsive interaction. The NCI zones fragments at top and bottom of the structure. Curious NCI zones appear above and below the CC4 shown in Figure 10 (right) lie at cage critical points and between the >CH2 bridges of the cyclooctane central plane. fragments at top and bottom of the structure. Curious NCI zones appear above and below the CC4 3.4.central Example plane. 4: 1,8-Dimethoxy-9-Dimethoxymethylanthracene Cation

3.4.Akiba Example and 4: co-workers1,8-Dimethoxy-9-Dimethoxymethylanthracene [46–48] have reported synthesis Cation and isolation of a compound with roughly trigonal bipyramidal ﬁve-coordinated carbon (tbpC). The C2v-symmetric structure from ωB97XDAkiba/cc-pVTZ and isco-workers shown in [46–48] Figure1 haveas species reported4. Thesynthesis X-ray and analysis isolation shows of thata compound the distance with betweenroughly the trigonal Anthryl bipyramidal methoxy Oxygen five-coordinated and the cationic carbon 5-coordinated (tbpC). The tbpC C2v-symmetric (2.44 0.01 A)structure is smaller from ± thanωB97XD/cc-pVTZ the distance between is shown the ipsoin Figure carbons 1 ofas anthracenespecies 4. The to which X-ray they analysis are attached shows that (2.50 the0.02 distance A). ± Computationalbetween the Anthryl characterization methoxy Oxygen [40] of theand system the cationic also 5-coordinated reﬂects a shortening, tbpC (2.44 which ± 0.01 suggests A) is smaller an attractivethan the MeO distance... tbpC between electrostatic the ipso interaction. carbons of anthracene to which they are attached (2.50 ± 0.02 A). Computational characterization [40] of the system also reflects a shortening, which suggests an 3.4.1.attractive AIM Analysis MeO…tbpC electrostatic interaction. Figure 11 shows BCPs and RCPs for 1,8-dimethoxy-9-dimethoxymethylanthracene cation (species 4 3.4.1. AIM Analysis in Figure1). The broken lines representing bond paths connecting anthryl-methoxy oxygens and the Figure 11 shows BCPs and RCPs for 1,8-dimethoxy-9-dimethoxymethylanthracene cation (species 4 in Figure 1). The broken lines representing bond paths connecting anthryl-methoxy oxygens and the tbpC indicate a weak interaction. The Bader parameters for BCPs (Table 4) bear out the expectation that the tbpC…OMe interaction is ionic. The Lapacian’s positive sign shows that charge is exported from the BCP, and the |2G/V| ratio indicates that the interaction is not covalent. We have already suspected from the short Methoxy O…tbpC distance that the tbC cationic center exerts an electrostatic attraction on the methoxy oxygens. The basin charges for the tbpC (+1.539) and methoxy oxygens (−0.140) are consistent with this inference.

Molecules 2020, 25, 3937 12 of 23 tbpC indicate a weak interaction. The Bader parameters for BCPs (Table4) bear out the expectation that the interaction between MeO and tbpC is ionic. The Lapacian’s positive sign shows that charge is exported from the BCP, and the |2G/V| ratio indicates that the interaction is not covalent. We have already suspected from the short distance between methoxy O and tbpC that the tbC cationic center exerts an electrostatic attraction on the methoxy oxygens. The basin charges for the tbpC (+1.539) and methoxy oxygens ( 0.140) are consistent with this inference. Molecules 2020, 25, x FOR− PEER REVIEW 12 of 24

Figure 11. Topological analysis of Akiba’s ﬁve-coordinate Carbon compound 4. Large light-gray spheres = H atoms; large dark gray spheres = C atoms; small white spheres = Bond CPs; small red Figure 11. Topological analysis of Akiba’s five-coordinate Carbon compound 4. Large light-gray spheres = Ring CPs; solid black lines = bond paths; broken black lines = bond paths for weak interactions. spheres = H atoms; large dark gray spheres = C atoms; small white spheres = Bond CPs; small red Tablespheres 4. AIM= Ring features CPs; forsolid 5C carbon;black lines red entries = bond from pa Akibaths; broken et al. obtained black withlines the = B3LYPbond /paths6-31G(d) for model. weak interactions. Critical Point Density Laplacian G V |2G/V| Table 4. AIM featurestbpC-OMe: for 5C carbon; red entries from Akiba et al. obtained with the B3LYP/6-31G(d) 0.3537 0.3326 +0.4764 1.0359 0.9198 model. (3, 1) − − − tbpC ... OMe 0.0235 +0.0898 +0.0209 0.0193 2.1658 Critical(3, 1)Point Density0.022 Laplacian+0.078 G − V |2G/V| − C-O tbpC-OMe: 0.2400 0.6625 +0.2650 0.5445 0.9734 (3, 1) 0.3537 −−0.3326 +0.4764 − −1.0359 0.9198 (3, −1) C=C tbpC…OMe 0.02350.2618 +0.0891.0337 8 +0.0708 0.3073 0.4608 (3, 1) − +0.0209 − −0.0193 2.1658 (3, −1) 0.022 +0.078 C-O 3.4.2. ELF Analysis 0.2400 −0.6625 +0.2650 −0.5445 0.9734 (3, −1) The view of the ELFC=C isosurfaces for Akiba’s ﬁve-coordinated C species (Figure 12, left) shows the 0.2618 −1.0337 +0.0708 −0.3073 0.4608 tbpC-OMe (the clearest(3, view−1) is at lower left) and the OMe connected to the anthryl ring; there is no ELF between that OMe’s O atom and the tbpC. This argues for an interaction dominated by electrostatics. 3.4.2. ELF Analysis The view of the ELF isosurfaces for Akiba’s five-coordinated C species (Figure 12, left) shows the tbpC-OMe (the clearest view is at lower left) and the OMe connected to the anthryl ring; there is no ELF between that OMe’s O atom and the tbpC. This argues for an interaction dominated by electrostatics. Molecules 2020, 25, x FOR PEER REVIEW 13 of 24 Molecules 2020, 25, 3937 13 of 23

Figure 12. ELF isosurfaces and non-covalent index (NCI) zones for Akiba’s five-coordinated carbon Figurespecies 12.4. ELF isosurfaces and non-covalent index (NCI) zones for Akiba’s five-coordinated carbon species 4. 3.4.3. NCI Analysis 3.4.3. TheNCI NCIAnalysis regions displayed in Figure 12 (right) include the interiors of aromatic rings and the interactionThe NCI zone regions between displayed the anthryl in Figure methoxy 12 (right) fragment include and a the nearby interiors CH bond. of aromatic There isrings an NCI and zone the interactionbetween the zone OMe between attached the to anthryl the tbpC methoxy and the fragme anthrylnt and Carbon a nearby to which CH bond. the tbpC There is attached.is an NCI zone Most betweensignificant, the weOMe see attached an NCI betweento the tbpC each and anthryl the anth methoxyryl Carbon O atom to which and the the tbpC. tbpC There is attached. is important Most significant,interaction, we but see suggests an NCI there between is no each covalent anthryl bonding methoxy between O atom the and anthryl the tbpC. methoxy There Ois atomsimportant and interaction,the tbpC. but suggests there is no covalent bonding between the anthryl methoxy O atoms and the tbpC. 4. Proposed Symmetric Variants on a Known Example of Approximately Octahedral Coordination of Carbon 4. Proposed Symmetric Variants on a Known Example of Approximately Octahedral CoordinationYamaguchi of etCarbon al. reported the synthesis of a system with six entities in the coordination sphere of a carbon atom [49]. Yamaguchi et al. reported the synthesis of a system with six entities in the coordination sphere The design principle is shown in Figure 13. In Figure 14 showing the X-ray structure of the of a carbon atom [49]. dication with -SMe(+) bridges, (5) the golden rectangle encloses the central six-coordinate carbon (6cC) The design principle is shown in Figure 13. In Figure 14 showing the X-ray structure of the and its two allenic C neighbors, while the green arrow points to one of the four methoxy oxygen atoms dication with -SMe(+) bridges, (5) the golden rectangle encloses the central six-coordinate carbon in the coordination sphere of 6cC. The system is far from symmetrical, probably a consequence of (6cC) and its two allenic C neighbors, while the green arrow points to one of the four methoxy oxygen packing requirements of the counterions. A variety of related hexacoordinated-C compounds have atoms in the coordination sphere of 6cC. The system is far from symmetrical, probably a consequence been explored computationally; for example, in the coordination sphere -OPh can replace -OMe as R of packing requirements of the counterions. A variety of related hexacoordinated-C compounds have and the bridging >SMe (+) can be replaced by >SO , >CH, and >S as B (Figure 13). Substituents can been explored computationally; for example, in the 2coordination sphere -OPh can replace -OMe as R also beMolecules chosen 2020 which, 25, x FOR influence PEER REVIEW the strength of interactions in the coordination sphere [50–1452 of]. 24 and the bridging >SMe (+) can be replaced by >SO2, >CH, and >S as B (Figure 13). Substituents can also be chosen which influence the strength of interactions in the coordination sphere [50–52]. Since the behavior of this structure is complex, we address only a few details of its topology. Figure 15 displays the results of topological analysis of Yamaguchi’s system, in its crystal geometry. As seen in earlier examples, bond critical points appear on bond paths (heavy black lines) corresponding to links in the molecular drawing. Ring critical points (in red) are found within each of the aromatic rings of the anthryl fragments. Fine white lines connect RCPs and BCPs. Heavy broken lines represent weaker interactions. The four methoxy oxygens are linked by such lines to the central hexacoordinate C. We also observe heavy broken lines connecting the methoxy oxygen atoms with H atoms of the thiomethyl bridging groups, among other surprising connections.

FigureFigure 13. Design 13. Design for for hexacoordinate hexacoordinate Carbon Carbon (hcC). B B is is a abridging bridging group, group, and and R is Ran is electron an electron donor. donor.

Figure 14. View of Yamaguchi’s allene system with hexacoordinate carbon (species 5).

We may expect that the Bader parameters for the X-ray structure, obtained by analysis of a charge distribution that does not correspond to an energy minimum within that computational method, might be called into question. We should judge the results by their consistency with more rigorous calculations on similar systems, as described below. The density and Laplacian values at the BCPs for the allene fragment are conventional for double bonds, and the interaction between methoxy O atoms and the hcC is similar to that found in Akiba’s system for its methoxy O atoms and the pcC. (Tables 4 and 5). That is, the BCPs for the bond path between MeO and the hcC have small positive ∇2ρ values and |2G/V| ratios > 1. This indicates charge depletion at the BCP and predominantly e electrostatic interactions. Since the AIM charges of these O atoms and the hcC are both negative, we can confirm that the electrostatic interaction is repulsive contrary to the suggestion that the

Molecules 2020, 25, x FOR PEER REVIEW 14 of 24

Molecules 2020Figure, 25, 3937 13. Design for hexacoordinate Carbon (hcC). B is a bridging group, and R is an electron donor. 14 of 23

Figure 14. View of Yamaguchi’s allene system with hexacoordinate carbon (species 5).

Since the behaviorFigure 14. ofView this of Yamaguchi’s structure is allene complex, system wewith addresshexacoordinate only carbon a few (species details 5). of its topology. Figure 15 displays the results of topological analysis of Yamaguchi’s system, in its crystal geometry. As seen in earlierWe may examples, expect that bond the criticalBader parameters points appear for onthe bond X-ray paths structure, (heavy obtained black lines) by analysis corresponding of a to linkscharge in the distribution molecular that drawing. does not Ring correspond critical points to an (inenergy red) minimum are found within within that each computational of the aromatic rings ofmethod, the anthryl might fragments.be called into Fine question. white linesWe should connect judge RCPs the andresults BCPs. by their Heavy consistency broken lineswith representmore Molecules 2020, 25, x FOR PEER REVIEW 15 of 24 weakerrigorous interactions. calculations The fouron similar methoxy systems, oxygens as described are linked below. by The such density lines toand the Laplacian central values hexacoordinate at the BCPs for the allene fragment are conventional for double bonds, and the interaction between methoxy C. Weinteraction also observe is stabilizing heavy broken by mixing lines of connectingthe methoxy theO lone methoxy pair with oxygen the allyl atoms π* MO with and H the atoms -OMe of the O atoms and the hcC is similar to that found in Akiba’s system for its methoxy O atoms and the pcC. fragments are forced into the hcC coordination sphere solely by steric constraint. thiomethyl(Tables bridging 4 and 5). groups,That is, the among BCPs other for the surprising bond pathconnections. between MeO and the hcC have small positive ∇2ρ values and |2G/V| ratios > 1. This indicates charge depletion at the BCP and predominantly e electrostatic interactions. Since the AIM charges of these O atoms and the hcC are both negative, we can confirm that the electrostatic interaction is repulsive contrary to the suggestion that the

FigureFigure 15. Bader15. Bader analysis analysis of of Yamaguchi’sYamaguchi’s allene. allene. Large Large light-gray light-gray spheres spheres = H atoms;= H large atoms; dark large gray dark grayspheres == C Catoms; atoms; small small white white spheres spheres = Bond= BondCPs; small CPs; red small spheres red = spheres Ring CPs;= Ringsolid CPs;black solidlines = black lines bond= bond paths; paths; broken broken black black lines lines= bond= pathsbond for paths weak for interactions. weak interactions.

Table 5. Bader parameters for the experimental structure of Yamaguchi’s hexacoordinate (hcC) system.

Kinetic Laplacian Potential Energy Critical Point Density ρ Energy |2G/V| ∇2ρ Density V Density G Allenic hcC=Ca +0.3444 −1.0187 +0.1551 −0.5648 0.5492 Allenic hcC=Cb +0.3385 −0.9761 +0.1515 −0.5470 0.5539 CH3Oa…hcC +0.0182 +0.0584 +0.0128 −0.0105 2.4381 CH3Ob…hcC +0.0192 +0.0739 +0.0165 −0.0146 2.2603 CH3Oc…hcC +0.0140 +0.0593 +0.0155 −0.0136 2.2794 CH3Od…hcC +0.0133 +0.0602 +0.0123 −0.0099 2.4848 Basin Charges Atom hcC Allene Ca Allene Cb CH3Oa CH3Ob CH3Oc CH3Od AIM Q −0.1943 +0.0926 +0.0898 −1.0736 −1.0884 −1.0753 −1.0720

Owing to the difficulty of visualization in this asymmetric system, we do not discuss the ELF and NCI figures. Instead we turn to discussion of our proposed symmetric variants.

4.1. A Neutral Symmetric System with Six-Coordinate Carbon In the example 6 shown in Figure 16 the bridge is >C=O, replacing the >SMe(+) of the first experimental compound 5. High symmetry allows a clearer view of the geometry of our variants. We wish to encourage synthesis of this neutral system and its -SCH3 analog described below. A neutral

Molecules 2020, 25, 3937 15 of 23

We may expect that the Bader parameters for the X-ray structure, obtained by analysis of a charge distribution that does not correspond to an energy minimum within that computational method, might be called into question. We should judge the results by their consistency with more rigorous calculations on similar systems, as described below. The density and Laplacian values at the BCPs for the allene fragment are conventional for double bonds, and the interaction between methoxy O atoms and the hcC is similar to that found in Akiba’s system for its methoxy O atoms and the pcC. (Tables4 and5). That is, the BCPs for the bond path between MeO and the hcC have small positive 2ρ values ∇ and |2G/V| ratios > 1. This indicates charge depletion at the BCP and predominantly e electrostatic interactions. Since the AIM charges of these O atoms and the hcC are both negative, we can conﬁrm that the electrostatic interaction is repulsive contrary to the suggestion that the interaction is stabilizing by mixing of the methoxy O lone pair with the allyl π* MO and the -OMe fragments are forced into the hcC coordination sphere solely by steric constraint.

Table 5. Bader parameters for the experimental structure of Yamaguchi’s hexacoordinate (hcC) system.

Kinetic Laplacian Potential Energy Critical Point Density ρ Energy |2G/V| 2ρ Density V ∇ Density G Allenic hcC=Ca +0.3444 1.0187 +0.1551 0.5648 0.5492 − − Allenic hcC=Cb +0.3385 0.9761 +0.1515 0.5470 0.5539 − − CH3Oa ... hcC +0.0182 +0.0584 +0.0128 0.0105 2.4381 − CH3Ob ... hcC +0.0192 +0.0739 +0.0165 0.0146 2.2603 − CH3Oc ... hcC +0.0140 +0.0593 +0.0155 0.0136 2.2794 − CH3Od ... hcC +0.0133 +0.0602 +0.0123 0.0099 2.4848 − Basin Charges Atom hcC Allene Ca Allene Cb CH3Oa CH3Ob CH3Oc CH3Od AIM Q 0.1943 +0.0926 +0.0898 1.0736 1.0884 1.0753 1.0720 − − − − −

Owing to the diﬃculty of visualization in this asymmetric system, we do not discuss the ELF and NCI ﬁgures. Instead we turn to discussion of our proposed symmetric variants.

4.1. A Neutral Symmetric System with Six-Coordinate Carbon In the example 6 shown in Figure 16 the bridge is >C=O, replacing the >SMe(+) of the ﬁrst Molecules 2020, 25, x FOR PEER REVIEW 16 of 24 experimental compound 5. High symmetry allows a clearer view of the geometry of our variants. We wishcharge to encourageallows for the synthesis possibility of thisof high neutral symmetry system in andthe solid its -SCH phase,3 analog thereby described simplifying below. the X-ray A neutral chargeanalysis. allows for the possibility of high symmetry in the solid phase, thereby simplifying the X-ray analysis.

Figure 16. D2d neutral symmetric variant with >C=O bridge, species 6.

4.1.1. AIM Analysis Symmetry equivalence also allows a compact presentation of AIM results, shown in Figure 17 for the >C=O system 6. Some key numerical values for density, the Laplacian, and energy densities along with the ratio |2G/V| are collected in Table 6. The parameters reflect the double bond character of the allenic core containing the hcC and the polar nature of the H3C-O and C=O bonds. The small values of density and the Laplacian L, and the positive sign of L as well, attest to the weak and predominantly electrostatic nature of the interaction.

Figure 17. AIM analysis of CO system 6.

Molecules 2020, 25, x FOR PEER REVIEW 16 of 24 charge allows for the possibility of high symmetry in the solid phase, thereby simplifying the X-ray analysis.

Molecules 2020, 25, 3937 16 of 23 Figure 16. D2d neutral symmetric variant with >C=O bridge, species 6.

4.1.1. AIM Analysis Symmetry equivalenceequivalence alsoalso allows allows a a compact compact presentation presentation of of AIM AIM results, results, shown shown in Figurein Figure 17 for17 thefor the>C= >C=OO system system6. Some 6. Some key key numerical numerical values values for density, for density, the Laplacian, the Laplacian, and energy and energy densities densities along withalong the with ratio the| 2Gratio/V ||2G/V|are collected are collected in Table in6. Table The parameters 6. The parameters reﬂect thereflect double the double bond character bond character of the of the allenic core containing the hcC and the polar nature of the H3C-O and C=O bonds. The small allenic core containing the hcC and the polar nature of the H3C-O and C=O bonds. The small values of densityvalues of and density the Laplacian and the LLaplacian, and the positiveL, and the sign positive of L as well,sign attestof L as to thewell, weak attest and to predominantlythe weak and electrostaticpredominantly nature electrostatic of the interaction. nature of the interaction.

Figure 17. AIM analysis of CO system 6. Figure 17. AIM analysis of CO system 6.

Table 6. Selected Bader parameters for D2d variant (6) with >C=O bridging.

Critical Point ρ Laplacian G V |2G/V| C=O bond 0.3976 +0.1874 +0.7174 1.3880 1.0337 (3, 1) − − C=C bond 0.3455 1.0337 +0.1576 0.5736 0.5495 (3, 1) − − − H C-O bond 3 0.2523 0.2481 +0.3985 0.6692 1.1910 (3, 1) − − − MeO ... C 0.0203 +0.0755 0.0171 0.0154 2.2207 (3, 1) − −

4.1.2. ELF Analysis The electron localization function (Figure 18) shows the central allene system, with the anthryl methoxy oxygens in the coordination sphere of the hexacoordinated C. There is no indication of ELF amplitude in the bonding region between CH3O and the hcC, but rather an accumulation of charge on the methoxy oxygen and depletion of charge near the hcC. This is entirely consistent with the description of the interaction between MeO and hcC as weak and electrostatic, inferred from the AIM analysis. Molecules 2020, 25, x FOR PEER REVIEW 17 of 24

Table 6. Selected Bader parameters for D2d variant (6) with >C=O bridging.

Critical Point ρ Laplacian G V |2G/V| C=O bond 0.3976 +0.1874 +0.7174 −1.3880 1.0337 (3, −1) C=C bond 0.3455 −1.0337 +0.1576 −0.5736 0.5495 (3, −1) H3C-O bond 0.2523 −0.2481 +0.3985 −0.6692 1.1910 (3, −1) MeO … C 0.0203 +0.0755 0.0171 −0.0154 2.2207 (3, −1)

4.1.2. ELF Analysis The electron localization function (Figure 18) shows the central allene system, with the anthryl methoxy oxygens in the coordination sphere of the hexacoordinated C. There is no indication of ELF amplitude in the bonding region between CH3O and the hcC, but rather an accumulation of charge Molecules 2020on, the25, 3937methoxy oxygen and depletion of charge near the hcC. This is entirely consistent with the 17 of 23 description of the interaction between MeO and hcC as weak and electrostatic, inferred from the AIM analysis.

Figure 18. ELF for the D2d (>CO bridge) variant of Yamaguchi’s system. Figure 18. ELF for the D2d (>CO bridge) variant of Yamaguchi’s system. 4.1.3. NCI Analysis 4.1.3. NCI Analysis The NCIThe zones NCI displayedzones displayed in Figure in Figure 19 19 include include in interactionsteractions between between the bridging the bridging >C=O groups>C= O groups and ipsoand CH ipso groups CH groups of the of the anthryl anthryl fragments, destabilized destabilized regions regionswithin six-membered within six-membered rings, and rings, interactions between -OCH3 methyl groups and nearby CH groups of the anthryl frame. Most and interactions between -OCH3 methyl groups and nearby CH groups of the anthryl frame. Most signiﬁcantsignificant for for our our purpose purpose are noncovalent noncovalent interactions interactions between between -OCH3 -OCHand the allenyland the group’s allenyl group’s central hexacoordinated carbon. 3 central hexacoordinatedMolecules 2020, 25, x carbon.FOR PEER REVIEW 18 of 24

FigureFigure 19. NCI 19. NCI for for CO CO neutral neutral variant. variant.

4.2. A Neutral4.2. SystemA Neutral with System Attractive with Attractive Interactions Interactions in in the the Coordination Coordination Sphere Sphere To enhanceTo possible enhance possible soft–soft soft–soft interaction interaction between between thethe six-coordinate Carbon Carbon and members and members of its of its coordination set we replace the methoxy O atoms by Sulfur atom, retaining D2d symmetry. The coordinationstructure set we 7 replace is shown the in Figure methoxy 20. O atoms by Sulfur atom, retaining D2d symmetry. The structure 7 is shown in Figure 20.

Figure 20. Structure of carbonyl-bridged system with -SCH3 (7).

Molecules 2020, 25, x FOR PEER REVIEW 18 of 24

Figure 19. NCI for CO neutral variant.

4.2. A Neutral System with Attractive Interactions in the Coordination Sphere

Molecules 2020, 25To, 3937 enhance possible soft–soft interaction between the six-coordinate Carbon and members of its 18 of 23 coordination set we replace the methoxy O atoms by Sulfur atom, retaining D2d symmetry. The structure 7 is shown in Figure 20.

Figure 20. Structure of carbonyl-bridged system with -SCH (7). Figure 20. Structure of carbonyl-bridged system with -SCH3 (7). 3 Molecules 2020, 25, x FOR PEER REVIEW 19 of 24 4.2.1. AIM Analysis 4.2.1. AIM Analysis Figure 21 displays the familiar array of bond critical points (CH, CC, C=O, CS, including ring CPs Figure 21 displays the familiar array of bond critical points (CH, CC, C=O, CS, including ring for each six-membered ring. The S ... hcC bond paths are curved oddly in the neighborhood of the CPs for each six-membered ring. The S…hcC bond paths are curved oddly in the neighborhood of hcC, and therethe hcC, is and an unexpectedthere is an unexpected weak bond weak bond from from anthryl anthryl CH CH hydrogen hydrogen to to S-CH S-CH3 methyl3 methyl carbon. carbon.

Figure 21. D2d carbonyl bridge thiamethyl variant. Figure 21. D2d carbonyl bridge thiamethyl variant. According to the AIM data (Table7), the strength of the CH 3S ... C (central) interaction is almost According to the AIM data (Table 7), the strength of the CH3S…C (central) interaction is almost as strong as the CH O ... C (central) interaction. Compare the Laplacian value of 0.0619 for 7 with as strong as3 the CH3O…C (central) interaction. Compare the Laplacian value of 0.0619 for 7 with +0.0755 for+0.07556. for 6. Molecules 2020, 25, 3937 19 of 23

Table 7. Selected Bader parameters for D2d thia methyl variant (7) with >C=O bridging.

Critical Point ρ Laplacian G V |2G/V| C=O bond 0.4045 0.0281 +0.6700 1.3470 0.9948 (3, 1) − − − C=C bond 0.3448 1.0315 +0.1624 0.5826 0.5575 (3, 1) − − − H C-S bond 3 0.1845 0.2965 +0.0497 0.1736 0.5726 (3, 1) − − − MeS ... C 0.0201 +0.0619 +0.0141 0.0128 2.3125 (3, 1) − −

As was the case for the methoxy system’s O ... hcC BCP,the S ... hcC BCP has a positive Laplacian, indicating charge depletion at that point, and predominantly electrostatic interaction. But in this case the interaction is attractive; hcC is negatively charged in each case, but the CH3S sulfur atom has a positive AIM charge whereas the CH3O oxygen atom has a strongly negative AIM charge. (Table8) This qualitative diﬀerence is unaﬀected by enhancing the basis from cc-pVTZ to aug-cc-pVTZ, though the charges in the thia system are appreciably altered.

Table 8. AIM Charges for atoms in the hcC coordination zone for species 6 and 7.

Basis cc-pVTZ Charges (O) C(allyl) hcC O atom Species 6 +0.2193 0.3279 1.1729 − − Charges (S) C(allyl) hcC S atom Species 7 +0.1552 0.3484 +0.1130 − Basis aug-cc-pVTZ Charges (O) C(allyl) hcC O atom Species 6 +0.2213 0.3256 1.1815 − − Charges (S) C(allyl) hcC S atom Species 7 +0.2077 0.4591 +0.1087 −

4.2.2. ELF Analysis In Figure 22, the ELF is again shown as a set of isosurfaces enclosing regions of high charge localization. Along the axis linking the carbonyl oxygens and passing through the allenyl carbons we see features corresponding to the carbonyl oxygen lone pairs (top and bottom) and also the orthogonal pi bonds between the central hcC and its C neighbors in the allene. Two of the four S atoms (from anthryl -SMe substituents) are in view, at right and left. Lone pairs on S atoms are prominent, but there is no evident localization between S atoms and the hcC. This is consistent with the low value of electron density at the BCP on the path fromS to hcC, and conﬁrms the essentially electrostatic nature of the interaction. Molecules 2020, 25, 3937 20 of 23 Molecules 2020, 25, x FOR PEER REVIEW 21 of 24

Molecules 2020, 25, x FOR PEER REVIEW 21 of 24

Figure 22. ELF visualization for thia variant. Oxygen atoms are shown in red, sulfur atoms in brown, and carbonFigure 22. atoms ELF invisualization gray. for thia variant. Oxygen atoms are shown in red, sulfur atoms in brown, and carbon atoms in gray. 4.2.3. NCI Analysis In Figure 23, we ﬁnd regions of non-covalent interaction (a) between anthryl carbonyl groups and nearby anthryl CH hydrogen atoms; (b) between -SCH methyls and nearby anthryl CH hydrogens; Figure 22. ELF visualization for thia variant. Oxygen atoms3 are shown in red, sulfur atoms in brown, and (c) withinand carbon anthryl atoms rings. in gray. Most prominent are the NCI regions between S atoms and the central hcC.

Figure 23. NCI for the thia variant.

Figure 23. NCI for the thia variant. Figure 23. NCI for the thia variant.

Molecules 2020, 25, 3937 21 of 23

5. Conclusions We examined some well-established examples of unusual coordination of carbon atom. Systems 1 and 3 containing tetracoordinate planar carbon (tpC) are stabilized by removal of two electrons; 2+ in Radom’s octaplanes the tpCC4 fragment is further constrained by surrounding hydrocarbon rings. To our knowledge no X-ray structures are known for these systems, though many analogs with metal substituents have been characterized. [17–21] We recommend that the synthesis and spectroscopic characterization of hydrocarbon octaplanes be re-visited. A signal experimental success is the structural study of hexamethyl benzene dication containing hexacoordinated carbon at the apex of a pentagonal pyramid. Bond paths confirm hexacoordination, but need not correspond to electron pair bonds. This electron-deficient species, like many carbocations with unusual carbon coordination, does not threaten the octet rule. Building on a theme first illustrated in a cationic 1,8-dimethoxy-9-dimethoxymethylanthracene, a series of five- and six-coordinated species have been synthesized [46–50]. In the pentacoordinate system two of the O atoms in the coordination sphere are bound weakly. AIM, ELF, and NCI analysis all confirm that for an experimental system possessing six entities in a C atom’s coordination sphere, and for symmetrized variations proposed here, there is evidence for six significant interactions between the allenyl central C and neighbors. The four interactions with O (6) or S (7) are electrostatic, not covalent, in view of the low level of charge sharing and density at the bond critical points. The C is hexacoordinate but not hexavalent. Again, no violation of the octet rule model is claimed. Replacing the oxygen in the methoxy group with sulfur alters the electrostatic interaction from repulsive to attractive. We encourage synthesis of species 6 and 7, and a thorough structural characterization including X-ray, vibrational, and NMR spectra. This should distinguish the repulsive character in 6 from the attractive character of 7.

Supplementary Materials: The following are available online. Analysis of the D2d > CF(+) bridged hcC species, Plots of RDG vs λ2-signed density for Structures 1–4. Analysis of the D2d > SO2 bridged species. Cartesian coordinates for species 1–4, 6, and 7. Author Contributions: Conceptualization, C.T. and Z.A.; methodology, C.T. and Z.A.; resources, C.T. and Z.A.; writing—original draft preparation, C.T.; writing—review and editing, C.T. and Z.A.; visualization, C.T. and Z.A. Software and computations, C.T., Z.A. and E.A.B. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: We thank BAPKO, the research support office of Marmara University, for financial support which allowed purchase of computing equipment. Thanks as well to the Body Foundation which made possible the acquisition of software and supported travel. Conflicts of Interest: The authors declare no conflict of interest.

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