and Polyatomic Donor Ligand Coordination to Perchlorinated

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A: Molecular Structure, Quantum Chemistry, and General Theory

The Mechanism of Charged, Neutral, Mono- and Polyatomic Donor Ligand Coordination to Perchlorinated Cyclohexasilane (SiCl ) 6

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Konstantin Pokhodnya, Kenneth J. Anderson, Svetlana V Kilina, Naveen Kumar Dandu, and Philip Boudjouk J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b11052 • Publication Date (Web): 28 Mar 2018 Downloaded from http://pubs.acs.org on March 28, 2018

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The Journal of Physical Chemistry

The Mechanism of Charged, Neutral, Mono- and Polyatomic Donor Ligand Coordination to Perchlorinated Cyclohexasilane (Si6Cl12) Konstantin Pokhodnya*, Kenneth Anderson, Svetlana Kilina, Naveen Dandu and Philip Boudjouk* Department of Chemistry and Biochemistry, North Dakota State University, Fargo, ND 58108 Abstract We report the detailed computational study of several perchlorinated cyclohexasilane (Si6Cl12) based inverse sandwich compounds. It was found that, regardless of the donor ligand size and charge, e.g., Cl− and CN− anions or neutral HCN and NCPh nitriles, their coordination to the puckered Si6Cl12 ring results in its flattening. The NBO and CDA studies of the complexes showed that coordination occurs due to hybridization of low lying antibonding σ*(Si-Cl) and σ*(Si-Si) unoccupied molecular orbitals (UMOs) of Si6Cl12 and occupied molecular orbitals (OMOs) of donor molecules (predominantly lone pair related) resulting in donor-to-ring charge transfer accompanied by complex stabilization and ring flattening. It is known that the Si6 ring distortion results from vibronic coupling of OMOs and UMOs pairs (pseudo-Jahn−Teller effect, PJT). Consequently, the Si6 ring flattening most probably occurs due to suppression of the PJT effect in all of the studied compounds. In this paper, the stabilization energy E(2) associated with donor-acceptor charge transfer (delocalization) was estimated using NBO analysis for [Si6Cl12⋅2Cl]2−, [Si6Cl12⋅2(NC)]2−, Si6Cl12⋅2(NCH), and Si6Cl12⋅2(NCPh). It was found that the polarizability of the donor might significantly affect the stabilization energy value (Cl− > CN− > HCN). For the neutral complexes, the E(2) value is correlated with the charge on the nitrogen atoms. All these factors, i.e., specific donor E(2) value, charge transfer, complex MO energy

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diagrams, etc., should be taken into account when choosing the ligands suitable for forming Sibased one-dimensional compounds and other nanoscale materials.


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Introduction Liquid oligosilanes, e.g., cyclopenta- (Si5H10, CPS) and cyclohexasilane (Si6H12, CHS), are valuable precursors for fabrication of Si-based microelectronic and optoelectronic devices including solar cells, thin film transistors, nanostructures, and lightweight batteries.1-12 In addition, the halogenated CHS precursor was used for the synthesis of one-dimensional chain structures when 1,4-dicyanobenzene was used to link Si6Cl12 rings. It was shown that, upon halogenation of CHS, a strong Lewis acid site develops in the middle of Si ring that enables coordination of different halogen ions forming the apical vertices of hexagonal bipyramids, i.e., inverse sandwich compounds,13-16 as well as similar complexes with neutral electron donors, such as nitriles.17-18 Another common property characteristic of both halogenated cyclosilanes is Si6 (or Si5) ring flattening upon donors’ coordination that was also observed in charged complexes as well as in the neutral ones. The suppression of ring puckering effect as well as the origin of Si hypercoordination in chlorinated cyclic silanes has been extensively studied.19-24 Using density functional theory (DFT) methodology it was shown that for both chlorinated CPS and CHS the Si ring distortion is presumably a consequence of pseudo-Jahn–Teller (PJT) effect that occurs due to a vibronic coupling between pairs of occupied (OMOs) and unoccupied molecular orbitals (UMOs). The PJT effect which is also known as second-order Jahn–Teller effect (JTE), reveals itself as spontaneous symmetry breaking in molecules and solids that occurs even for nondegenerate electronic states under the influence of vibronic effects leading to mixing between the ground and low-lying excited states of appropriate symmetry. As the result, the geometry of the system at equilibrium does not coincide with the highest possible or even with any high symmetry expected from general symmetry considerations. For instance, linear molecules are bent at equilibrium, planar molecules are puckered, octahedral complexes are elongated, or compressed, or tilted, cubic crystals are tetragonally polarized (or have several structural phases), etc.25 Thus, the investigation of JTE manifestations and possible mechanisms of its suppression



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in the polyatomic systems of different dimensionalities remains one of the actual subjects of modern chemistry. One of the strongest arguments in favor of PJT effect driven Si-ring puckering in halogenated cyclosilanes is a possibility of its suppressing by coordination of two donor ions (e.g., F, Cl, Br, and I anions) below and above the mid-ring. Thus, the DFT modeling has also shown that filling the Si5Cl10 and Si6Cl12 UMOs engaged in vibronic coupling with electron pairs of Cl- donors upon coordination enables complete suppression of the PJT effect (experimentally observed flattening of Si6 ring) and formation of inverse sandwich compounds.19,

23

It was

presumed that the formation of the Lewis acid site in the middle of Si6 ring, on which the apical donors’ electrons are partially accommodated, occurs due to withdrawal of a significant portion of electron density from the Si atoms of the ring by 12 halogens.19, 26 Here we provide rigorous calculations of the natural bond orbitals (NBO) and Charge Decomposition Analysis (CDA) of the (Si6Cl12)-based inverse sandwich compounds with the donor ligands varying in their size and charge, e.g., Cl− vs. CN− anions or neutral HCN and NCPh nitriles. For all complexes, we found that independently of the ligand charge and size, coordination occurs due to hybridization of low lying antibonding σ*(Si-Cl) and σ*(Si-Si) UMOs of Si6Cl12 and OMOs of donor molecules (predominantly lone pair related) resulting in donor-to-ring charge transfer accompanied by complex stabilization and ring flattening. Such a charge transfer character is responsible for suppression of PJT effect in inverse sandwich compounds due to preventing participation of frontier UMOs in vibronic couplings with OMOs. As such, the rigorous understanding of electron density donation and donor-acceptor orbital hybridization is of great importance, especially for neutral donors like NCH and NCPh, where the mechanism of PJT effect involvement has not been proven yet. For getting further insights into mechanisms of PJT suppression in inverse sandwich compounds, we calculate the


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stabilization energy E(2) which is associated with noncovalent energy lowering due to overlap between bonding and antibonding NBO orbitals or donor-acceptor (Si6-ring) charge transfer. It should be noted that antibonding self-consistent field molecular orbitals (SFC-MOs) calculated via ab initio or DFT methods (vide infra) are strictly unoccupied. In contrast, antibonding NBOs generally exhibit nonzero occupancies and their overlap with bonding NBOs may result in substantial energy lowering and shape change of the corresponding hybrid SFC-MO.27 In this work we show that the polarizability (related to the orbital shape) of the donor might significantly affect the stabilization energy value (Cl− > CN− > HCN). For the neutral complexes, the E(2) value is correlated with the charge on the nitrogen atoms. All these factors, i.e., specific donor E(2) value, charge transfer, complex MO energy diagrams, etc., should be taken into account when choosing the ligands suitable for forming Si-based one-dimensional compounds and other nanoscale materials.18 Computational Method The ab initio calculation using second-order Møller–Plesset perturbation level of theory (MP2) allowed an almost exact reproduction of the experimental X-ray structure parameters for both the neutral Si6Cl12 and the dianion [Si6Cl12⋅2Cl]2−.20 However, it is known that ab initio is one of the most resource-consuming calculations, especially for large molecules. In contrast, DFT methods can be very accurate with relatively small computational cost. In earlier studies, the implementation of the hybrid B3LYP level with 6-311++G(d,p)19 and 6-311+G(3df)28 basis sets for geometry optimization of neutral Si6Cl12 and [Si6Cl12⋅2Cl]2− dianion also allowed to quite accurately reproduce the experimental structures, albeit slightly overestimating (~2%) both Si-Si and Si-Cl bond lengths. Previously, we systematically investigated the effect of HF inclusion and long range corrections in the density functionals on Si5X10 (X=H, Cl) geometries by performing



DFT calculations using representative generalized gradient approximation, GGA (PBE)29, GGA/HF hybrid (PBE1)30, and long-range corrected functions, i.e., wB97XD31 and LC-wPBE32. It was shown that the long range corrected LC-wPBE functional provides geometries well agreeing with experimental data if the large basis set is used, regardless whether dispersion corrections were explicitly included.23 The geometries of the studied perchlorinated cyclohexasilane and above mentioned complexes on its basis were optimized within the given symmetry point group with the Gaussian-09 DFT software package.33 To gain insights into PJT effect mechanism, the analysis of the second order perturbation of Fock matrix, LCNBO-MO (LCNBO Linear Combination of NBO orbitals) expansion, and natural population analysis (NPA) was performed with the NBO 6.0 program.34-35

Charge Decomposition Analysis (CDA)36 can also provide information

about charges transfer between fragments in a complex to achieve charge equilibrium. In CDA it was postulated that the molecular orbital (MO) of the complex can be linearly expanded by the sum of basis functions of the fragments NA+NB resulting in (NA+NB) complex MOs. Assigning NA as MOs of the Si6Cl12 ring and NB as MOs of two donor molecules (e.g., two Cl−) and using the same DFT functional/basis set as in the case of the complex, NA MOs of the ring and NB MOs of the donor fragment can be calculated. It should be emphasized that the geometry of the fragment must be kept the same as in the complex. These new fragment MOs can be taken as the new basis functions to linearly expand the MOs of the complex. Once the fragment MOs are obtained, the orbital interaction diagram can be directly plotted, allowing visualization and direct understanding of how the orbitals of the fragments are mixed to form the orbitals of the complex. Since the diffuse functions cannot be used for CDA, all DFT calculations of the inverse sandwich compounds and their fragments’ MOs were performed at the LC-wPBE/6-311G* level,


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which reasonably well describes the halogenated cyclosilanes23 CDA was performed using Multiwfn software.37

Results and Discussion To justify our choice of DFT method, several well-behaving density functionals have been used for structural optimization of the neutral Si6Cl12 molecule as well as charged [Si6Cl12⋅2Cl]2− and neutral Si6Cl12⋅2(NCPh) (Ph=C6H5) inverse sandwich compounds for which crystallographic data are available. The structural data which were obtained using LC-wPBE hybrid functional and 6-311G++(3df,3pd) basis set are shown in Table 1. The available experimental structural parameters14, 38 and the data reported for Si6Cl12 as well Si as the CHS based inverse sandwich compounds using MP2/6-311++G(3d,p) ab-initio approach,20 are presented for comparison. Long range dispersion corrections added to hybrid functionals such as in wB97XD have been shown to be important for accurate modeling of some cyclohexasilane geometries.20 Therefore, the optimized structure parameters of Si6Cl12 and [Si6Cl12⋅2Cl]2− obtained using wB97XD functional containing the dispersion corrections within 6-311G++(3df,3pd) basis set are also shown in Table 1. It should be noted that in the optimized structures of the inverse sandwich compounds obtained at the DFT LC-wPBE/6-311G++(3df,3pd) level with all orbital symmetry constraints lifted, the total energy minimum was achieved for the structure in which the flat Si6Cl12 ring is slightly distorted (e.g., the [Si6Cl12⋅2Cl]2− dianion symmetry is reduced to Cs). A similar problem was also observed for wB97XD functional. However, the total energy difference between compounds with Cs and D6h symmetries is insignificant (~2 meV). For the sake of NBO analysis simplification, the studied inverse sandwich compound structures were optimized with the D6h symmetry constraint.



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Table 1. Experimental and calculated average structural parameters of the studied compounds, i.e., Si-Si, Si-Cl, ∠Si-Si-Si, X⋅⋅⋅Cl, and X⋅⋅⋅Si (X=Cl, N). ∠Si-Si-Si (o) 112.9

Si6Cl12 (exp)

Si-Cl (Å) 2.029

Si-Si (Å) 2.34

Si6Cl12 (MP2)

2.05

2.36

111.4

Si6Cl12 (LC-wPBE)

2.030

2.339

112.4

Si6Cl12 (wB97XD)

2.044

2.352

[Si6Cl12·2Cl] (exp) [Si6Cl12·2Cl] (MP2)

2.076 2.10

2.322 2.33

2.996 2.99

3.616 3.65

120.0 119.9

[Si6Cl12·2Cl] (LC-wPBE)

2.081

2.323

2.986

3.643

120.0

[Si6Cl12·2Cl] (wB97XD)

2.092

2.344

3.047

2.356 2.349

3.059 3.045

3.594 3.590

120.0 120.0

Si6Cl12·2(NCPh) (exp) 2.056 Si6Cl12·2(NCPh) (DFT)* 2.054 * calculated using LC-wPBE/6-311G* level.

Si⋅⋅⋅⋅X (Å)

X⋅⋅⋅⋅Cl (Å)

The performed analysis confirms that the structural parameters of both [Si6Cl12⋅2Cl]2− dianion and Si6Cl12 are in the best agreement with experimental data when LC-wPBE/6311G++(3df,3pd) functional/basis is used. Inclusion of the dispersion corrections in wB97XD functional results in the slight overestimation of all bonds lengths, while the overall energy splitting between electronic states and the orbital nature are negligibly different between these functionals. Therefore, we perform further NBO calculations using LC-wPBE functional. However, modeling Si6Cl12⋅2NCPh with a basis set containing diffuse functions proved to be problematic due to the weakly bound large neutral ligands. To avoid convergence issues, the smaller basis set, 6-311G*, was applied for optimizing this inverse sandwich compound, which provided structural parameters very close to those experimentally observed. Thus, we believe that this DFT functional/basis set combination could be implemented for modeling a large variety of oligosilanes, their halogenated analogs, as well as neutral and ionic compounds on their basis.


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It was pointed out that the donor − Si ring interaction is predominantly of donor-acceptor type between the Lewis acid sites and lone pairs of donors with very weak covalent and ionic components.19, 23, 28 Since the Lewis acid sites are formed by the Si − exocyclic halide atoms antibonding sigma orbitals, their size and acidity strength together with the donor polarizability define the magnitude of inverse sandwich compound stabilization energy gained due to the donor coordination. To elucidate the effect of the donor molecule chemical composition and its charge on the adduct stabilization energy, we studied Cl− and CN− anions as well as neutral NCPh as donors coordinated to the Si6Cl12 ring. The essential information about the Lewis and non-Lewis occupancies (close to 2 and close to 0, respectively) of core, valence, and Rydberg shell contributions as well as the stabilization energy E(2) due to donor coordination can be gained via NBO analysis. In the case of [Si6Cl12·2Cl]2- we calculated the stabilization energy related to the four donor lone pairs LP(1)-LP(4) interaction with acceptor non-Lewis BD*(Si-Si) and BD*(Si-Cl) NBOs. The LP(2) and (3) are of pure p-character oriented parallel to the Si6 ring, while LP(1) and (4) are sphybrids with predominantly sp0.44 and sp2.22 character, respectively. The LP(4) is oriented perpendicular to the ring. Interestingly, despite the larger number of Si atoms in the ring and the similarity of lone pair orientations, the total E(2) value for [Si6Cl12·2Cl]2- is substantially (~11%) smaller than that for [Si5Cl10·2Cl]2- adduct. It is reasonable to assume that the Lewis site size is smaller and acidity is larger in the more compact Si5Cl10·ring than that in Si6Cl12. Table 2. The optimized bond lengths (in Å), NPA atomic charges (in a.u.), and E(2) stabilization energy values (in kcal/mol) of [Si6Cl12·2Cl]2-, [Si6Cl12·2(NC)]2-, and Si6Cl12·2(NCH) inverse sandwich compounds, i.e., Si-Si, Si-Cl, X⋅⋅⋅Cl, and X⋅⋅⋅Si (X=Cl, N), calculated at DFT LCwPBE /6-311G++(3df,3pd) level. For the neutral Si6Cl12·2(NCH) and Si6Cl12·2(NCPh) the 6311G* basis set was used (see text). The data for [Si5Cl10·2Cl]2- are given for comparison.23 [Si5Cl10·2Cl]2-

Si-Si 2.335

Si-Cl 2.089

Sich 0.689

Clch -0.410

Xch -0.608


Si⋅⋅⋅⋅X 2.986

X⋅⋅⋅⋅X’ 4.215

ΣE(2) 122.9


[Si6Cl12·2Cl]2[Si6Cl12 2(NC)]2Si6Cl12 2(NCPh) Si6Cl12 2(NCH)

2.323 2.323 2.349 2.355

2.081 2.074 2.054 2.049

0.622 0.731 0.641 0.624

-0.367 -0.399 -0.332 -0.321

-0.665 -0.916* -0.507* -0.461*

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2.986 2.861 3.587 3.604

3.752 3.178 3.853 4.203

112.5 92.5 53.9 41.0

*the charge on N atom Indeed, by comparing the structural parameters and NPA atomic charges of these two inverse sandwich compounds (Table 2) it is evident that Si-Cl bonds in [Si6Cl12·2Cl]2- are less polarized resulting in a smaller charge transfer from Cl− donor into the Si6 ring. Interestingly, the Si⋅⋅⋅Cl distance is practically the same for both complexes implying that the Cl donor ion in [Si6Cl12·2Cl]2- should go deeper into the ring to secure the comparable stabilization energy for this compound. The observed substantial (~12%) shortening of Cl⋅⋅⋅Cl’ inter-donor distance in [Si6Cl12·2Cl]2- with respect to that in the Si5 analog (Table 2) supports this hypothesis. The cyanide anion (:N≡C:)− possesses a lone pair from both sides suggesting that it can be coordinated to the Lewis acidity site of Si6Cl12 in two ways. Preliminary optimization of both structures using a smaller 6-311G* basis set with D6h symmetry constraint followed by vibrational spectra has shown that the structure with carbon lone pairs coordinating to the ring [Si6Cl12·2(CN)]2- has a total energy about 3.8 kcal/mol higher than that for a nitrogen coordinated [Si6Cl12·2(NC)]2- dianion. In addition, the vibrational spectrum of the former compound possesses two pairs of vibrations with imaginary frequencies of E1g and E1u symmetry corresponding to in-phase and out-of-phase rotations of two CN anions around two mutually perpendicular axes parallel to the Si6Cl12 plane. It suggests the presence of saddle points in the potential energy surface resulting in system instability toward anion rotations. Indeed, it was shown that the optimization process without the symmetry constraint consists of gradual rotations of the CN anions resulting in their octahedral coordination to the same Si atom of the ring via carbon located lone pairs (Fig, S1).


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In contrast, the optimization of the [Si6Cl12·2(NC)]2- dianion without symmetry constraint results in practically identical Si6Cl12 flat ring structures (~1.5 meV difference in total energy) with no modes with imaginary frequencies in their vibrational spectra. The absolute value of calculated NPA charge on CN− donor -0.801 a.u. (-0.904 a.u. on N and 0.103 on C a.u.) implies about 0.2 a.u. charge transfer from CN donor to acceptor (Figure 1A). It is considerably smaller than that in the case of Cl− (see Table 2) despite the shorter Si⋅⋅⋅donor distance. Recently it was shown that donor polarization is a key factor that governs the degree of charge transfer and the stabilization energy E(2) values in inverse sandwich compounds.23

Figure 1. The atomic charges in the optimized D6h conformation of [Si6Cl12·2(NC)]2- (A) and in the optimized [Si6Cl12·2(NCPh)] (B) inverse sandwich compounds. Since the polarizability of nitrogen is approximately half that of chlorine,39 the reduced polarizability could be one of the reasons of charge transfer suppression. To elucidate the influence of other structural factors on donor-acceptor bonding in [Si6Cl12·2(NC)]2- dianion, the NBO analysis was performed. It showed that three BD (n) (N-C) (n = 1, 2, 3) representing the Lewis single, double and triple bond NBOs, in addition to two N and C atom centered lone pairs,



interact with non-Lewis BD*(Si-Cl) and BD*(Si-Si) antibonding moieties. The results are summarized in Table S1 in relation to the atom labels given in Figure S2. The representative NBO#19 BD (1) N19 - C22 with (1.996) occupancy is composed of the natural atomic sp hybrids σCN = 0.784(sp1.06)N + 0.621(sp1.46)C, whereas NBO#19 BD (2) and BD(3) N19 - C22 NBOs with (2.00) occupancies are purely πCN = 0.844 (p1.00)N + 0.536(p1.00)C hybrids. Conversely, nitrogen #155 LP(1) N19 and carbon #157 LP(1) C22 located lone pair NBOs of (1.840) and (1.968) occupancies, consist of sp0.87- and sp0.63 -character hybrids, respectively, similarly to LP(4) Cl- located NBOs in [Si5Cl10·2Cl]2- compound, albeit with weaker pcomponent. In contrast, the antibonding BD*(Si-Si) and BD*(Si-Cl) NBOs, e.g., #979 and #981, of (0.121) and (0.104) occupancies consist of σSiSi* = 0.707(sp2.23)Si - 0.707(sp2.23)Si and σSiCl* = 0.869(sp4.06)Si - 0.495(sp2.25)Cl, respectively, with significantly enhanced p-components. The NBO analysis showed that the natural Lewis structure description for [Si6Cl12·2(NC)]2- covers about 99.13% of the total electron density; therefore, the donor-acceptor (σ→σ*) interactions can be treated as a second-order perturbation in the NBO basis. Thus, the stabilization energy E(2) associated with delocalization of donor bonding NBO (i) into acceptor antibonding NBO (j) can be estimated as 2 = ∆ =

, , −

where qi is the donor orbital occupancy, εi and εj are diagonal elements (in our case CN− bonding and Si6Cl12 antibonding NBO orbital energies), and F(i,j) is the off-diagonal NBO Fock matrix element.27 From the analysis of Table S1 it is clear that BD*(Si-Si) NBOs do not interact with σtype BD(1)N-C bonds as well as both N- and C-centered LP(1) NBOs. Conversely, both π-type BD(2) and BD(3) N-C NBOs do interact with six BD*(Si-Si) NBOs. However, the coupling is


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very weak and the corresponding E(2) value does not exceed 0.22 kcal/mol and varies substantially (factor of 4) due to an anisotropy of p-type hybrids. In contrast, the interaction of all above mentioned NBOs with BD*(Si-Cl) NBOs is significantly higher, especially for the nitrogen-centered LP(1) NBO, which is responsible for 65% of total E(2) value equal to 112.5 kcal/mol per CN− donor. It should be noted that this value is about 10% lower than that for Cl− donor in [Si6Cl12·2Cl]2- (see Table 2). NBO analysis of the planar Si6Cl12 molecule revealed two groups of antibonding BD*(1) type non-Lewis NBOs, i.e., six orbitals originating from the single bonds between adjacent Si atoms, as well as twelve degenerate orbitals originating from the single bonds between Si and the exocyclic Cl atoms.

Figure 2. The shape of close to the HOMO orbitals of [Si6Cl12·2(NC)]2− reveals a hybridization of close to LUMO orbitals of Si6Cl12·(top row) and close to HOMO orbitals of the donor, i.e., πcomponent of N≡C bonds as well as N- and C-centered lone pairs. The LCNBO-MO expansion provides more details regarding the nature of the canonical UMOs and OMOs of Si6Cl12 (D6h) as well as [Si6Cl12·2(NC)]2− dianion in terms of corresponding NBOs. The orbitals ##145, 146, 149 and 150 (LUMO, LUMO+1 and LUMO+4/5) have zero contributions from BD*(Si-Si) antibonding NBOs and consist primarily of BD*(Si-Cl) NBOs. Conversely, the orbitals ## 147 and 148 (LUMO+2/+3) have contributions from both BD*(Si-Si) (~33%) and BD*(Si-Cl) (~64%) NBO, respectively, (Figure 2, top row).



From the shape of the OMOs of [Si6Cl12·2(NC)]2− dianion (Figure 2, bottom) it is evident that both the π-type component of N≡C bond as well as N- and C-centered lone pairs perpendicular to the Si6 ring plane interact with the σ*(Si−Cl) orbitals (former LUMO, LUMO+1 and LUMO+4/5) of planar Si6Cl12 causing stabilization of the dianion. It is known that for donor-acceptor complexes the bonding is defined by the delicate balance between electron pair donation and back-donation. Recently, the results of CDA for the set of inverse sandwich compounds of [Si6X12·2X’ ]2− (X, X’ = F−, Cl−, Br−, I−) were reported.28 It was shown that in these inverse sandwich compounds a significant back-donation charge component from the Si6 ring to donor is present. However, this observation conflicts with our NBO results (Table 2) suggesting that ~0.3 of electron charge is transferred from each Cl− to the S6 ring. To reveal how electronic density is transferred between Si6Cl12 and CN− donors within the [Si6Cl12·2(NC)]2− complex, the CDA was performed. The neutral Si6Cl12 was defined as fragment one (F1), and the two CN− anions positions at the same places as they are in the complex were defined as fragment two (F2). The terms di and bi describe the amount of electron donated from fragment F1 to F2 via MO i of the complex, and the electron back donated from F2 to F1, respectively. Conversely, the term ri indicates the change in the repulsive polarization, i.e., the amount of electron density which is removed from the spatial overlap of the occupied MOs into the nonoverlapping regions. It should be emphasized that both polarization effects and exchange repulsion are included in this scheme.36 A positive value of ri means that two fragments of the -ith MO are accumulated in their overlap region implying mutual attraction, while a negative value indicates that the electrons are depleted from the overlap region, thus


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reflecting electron repulsive effect. The sum of all ri terms is, at large, negative, because overall interaction between filled orbitals is, in general, repulsive.37 The results of CDA for [Si6Cl12·2(NC)]2− dianion are shown in Figure 3. Considering the above described definition of fragments, the negative sign of the di – bi term implies that the back donation, i.e., charge transfer from CN− ions to the Si6Cl12 ring is prevalent. The net electron density donated from both ions to the ring equals 0.46 a.u. which is in a reasonably good agreement with NBO results (0.45 a.u.) obtained using the same DFT basis set.

Figure 3. The effective donor-to-ring charge transfer (A) and occupied orbital repulsion (B) in [Si6Cl12·2(NC)]2− dianion (lines are the guide for the eye). The shape of the HOMO in the flat Si6Cl12, which consists of predominantly Si-Si bonding and Cl-located lone pair orbitals, remains practically unchanged upon complexation (see Figure 2). It implies that the HOMO of the complex is not involved in any electron density exchange with donors, which is confirmed by CDA (Figure 3A). In contrast, the shape of all low lying UMOs of flat Si6Cl12 (Figure 2, top) undergoes significant changes indicating the hybridization of these empty antibonding Si-Cl and Si-Si orbitals with occupied orbitals of the donor (both σ lone pairs and π C-N orbitals) (Figure. 1 bottom). These orbitals (enumerated in



Figure 3A) are responsible for 87% of all donor to ring charge transfer. Moreover, deconvolution of these complex MOs into fragment orbital contributions (Table S2) reveals the hybridization of filled donor fragment orbitals with UMO of the Si6 ring (predominantly of antibonding Si-Cl and Si-Si character) (see Figure 2, bottom). The CDA has shown that contributions from the ring F1 fragment UMOs are relatively small ranging from 2.3 to 6.2 % compared to the contributions from the donor F2 fragment MOs which are significantly larger, reaching 81% for the complex MO #156 (Table S2). The coordination of charged donor molecules with the polarized Si6Cl12 ring creates a substantial repulsion between filled orbitals of these two fragments that is revealed as negative values of ri for the complex MOs demonstrating the largest charge transfer (Figure 3B). The only exceptions are #135 and #136 orbitals for which ri is positive implying the expansion of the fragment MOs within the Si6 ring. It should be noted that according to CDA the main contributors to the complex OMOs of the first two pairs in Table S2 are LP(1) N and LP(1) C NBOs of the donors, while the main contribution in the last three OMOs arises from the BD(2) and BD(3) (C-N) donor NBOs. Moreover, the contributions (%) from the donor and ring NBOs are comparable for the last two MO pairs. For these MOs (150, 151 and 135, 136) the LP(1) lone pairs NBOs of exocyclic Cls atoms (132, 133 and 136, 137) provide 69 and 47% contribution, respectively, to the corresponding MOs. The occupied molecular orbitals ##150, 151 and ##135, 136 of the [Si6Cl12·2(NC)]2− complex are shown in Figure S3. Interestingly, the #150 and #151 pair of complex MOs demonstrate anti-phase arrangement of the BD(C-N) donor and exocyclic LP(Cl) ring NBOs thus facilitating the negative ri factor. In contrast, the #135 and #136 pair of MOs have the in-phase combination of these NBOs enabling the positive ri factor that implies expansion of these orbitals into interatomic space despite having very similar fragment


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composition with ##150,151 MOs. Interestingly, several low-lying orbitals (E < -9 eV, orbital with ## < 120) also demonstrated a substantial positive ri factor. For instance, the degenerate #120 and #121 [Si6Cl12·2(NC)]2− complex MOs are decomposed into contributions of F1 ring orbitals #114 and #115 (~85%), both consisting of σ-BD(Si-Si) NBOs that are hybridized with F2 donor orbitals #9 and #10 (~15%) comprising of π-BD(2) and BD(3) C-N NBOs, respectively. The orbital interaction diagram (Figure 4A) was devised using the CDA MO deconvolution results to aid visual understanding of how orbitals of fragments are mixed to form the complex orbitals, as well as realize their energetic structures. New molecular orbitals that occur due to coordination can be seen as resulting from electron density donation from valence orbitals of the donor fragment (two LP(1) N and three BD(1-3) NBOs) in different phase configurations, i.e., donor orbitals #7-14, to the virtual BD*(1) Si-Cl and Si-Si based LCNBOs (orbitals # 145-150) of the ring fragment (Figure 3A). The resulting [Si6Cl12·2(NC)]2− complex OMOs (marked in red) in the bonding configuration have substantially lower energy (up to ~8 eV) with respect to that of the fragments, thus contributing to overall complex stabilization energy E(2). In contrast, the UMOs that occur in the anti-bonding configuration of fragment MOs have energies ~7 eV higher than those of the fragments. However, they are not contributing to the total energy due to their zero occupancy.



Figure 4. The orbital interaction diagrams of the [Si6Cl12·2(NC)]2− (A) and Si6Cl12·2(NCH) (B) complexes. Occupied and virtual orbitals are represented as solid and dashed bars, respectively; the vertical positions of MOs are determined by their energies. The bars at left and right sides correspond to the fragment orbitals (FOs), respectively; the bars in the middle (in red) correspond to complex orbitals. If composition of a FO in a complex orbital is larger than specific criterion (in our case > 1%), the corresponding two bars (FO and complex MO) are connected by red lines. Small icons represent the F1 and F2 orbitals involved in the charge transfer. It should be emphasized that the interacting fragment OMOs of donor and UMOs of acceptor in [Si6Cl12·2(NC)]2− complex (as well as in other Si5 and Si6 based inverse sandwich compound dianions) are close in energy, which together with their good overlap enables a significant stabilization energy E(2) associated with delocalization. In contrast, in the neutral Si6Cl12 based inverse sandwich compounds the UMOs of the Si6Cl12 ring are much higher in energy compared to the OMOs of nitrile donors. To elucidate the mechanism of charge transfer in the neutral inverse sandwich compounds, we performed the NBO and CDA calculation of the model Si6Cl12·2(NCH) complex constrained to D6h symmetry. Similar to the inverse sandwich


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compound dianions, the NBO analysis showed that the natural Lewis structures description for Si6Cl12·2(NCH) covers about 99.29% of the total electron density. Therefore, the donor-acceptor (σ→σ*) interactions can be treated as a second-order perturbation in the NBO basis. From analysis of the Fock matrix in the NBO basis for Si6Cl12·2(NCH) (Table S3; the atom labels are given in Figure S4,) it is clear that BD*(Si-Si) NBO does not interact with BD(1, 2, 3) N-C bonds as well as both BD(1) C-H bonds and N- centered LP(1) NBOs. In contrast, all above mentioned NBOs couple with BD*(Si-Cl) NBOs, among which the nitrogen-centered LP(1) NBO is responsible for ~74% of total E(2) value equal to 41.0 kcal/mol per two HCN donors. Interestingly, this value is only ~33% of that for Cl− donors in [Si6Cl12·2Cl]2- (see Table 2). To perform CDA for Si6Cl12·2(NCH), the neutral Si6Cl12 was defined as fragment F1, and two HCN molecules positioned at the same places as they are in the complex were defined as fragment F2. The results of CDA for Si6Cl12·2(NCH) are shown in Figures 5A and 5B. The negative sign of the di – bi term implies that the transfer from HCN to the Si6Cl12·ring overcomes the back-donation effect, i.e., charge transfer from Si6Cl12·ring to the HCN molecule. The net charge donated from fragment F2 (both HCN molecules) to the ring equals 0.13 a.u. The absolute value of calculated NPA charges on both HCN donors is 0.11 a.u., which is in reasonable agreement with CDA results.



Figure 5. The effective donor-to-ring charge transfer (A) and occupied orbital repulsion (B) in Si6Cl12·2(NCH) compound (lines are the guide for the eye). It was mentioned above that the MOs of the complex that contain both the UMO of the ring and the OMO of the donor enable significant contributions to the donor-ring charge transfer. The CDA allows identification of the fragment orbital (FO) contributions into the particular MO of the complex. It was found that the Si6Cl12 unoccupied FOs ## 145, 146 and 147/148 contribute to the following complex OMOs: #124 (1.2%), #118 (1.7%); #143(0.6%), #132 (1.5%), #117 (0.5%); and #128/127, (0.5%), respectively, which are shown in Figure 6. These bonding complex MOs also contain the OMOs of 2HCN fragment (nitrogen-centered LP(1) NBOs of different symmetry, i.e., ## 9 and 10, as well as BD(3) N-C NBOs, i.e., ##13 and 14). The contributions from these OMOs range from 21 to 75% suggesting electron density delocalization. Thus, the hybridization of UMO and OMO of F1 and F2 fragments accompanied by substantial donor-to-ring charge transfer (Figure 5A) causes significant lowering of the corresponding Si6Cl12·2(NCH) complex hybrid orbitals (e.g., ##132, 124, 118, Figure 6) with respect to those of the fragments contributing to overall complex stabilization energy. In


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addition, the complex MOs have components from OMOs of the Si6Cl12·fragment (both LP(1) Cl and BD(1) Si-Cl) that may contribute to the repulsion (Figure 5B).

Figure 6. The OMOs of Si6Cl12·2(NCH) compound containing UMO of the Si6Cl12 fragment. It should be noted that in the experimentally determined structure of neutral inverse sandwich compound Si6Cl12·2(NCPh) the C6 planes of both benzonitrile donors make an angle of ~78.6o with the Si6 ring plane (Fig 1B). Thus, the NC fragments of the donor approach the Si6 at this angle in contrast to the 90o for the hypothetical [Si6Cl12·2(NC)]2-, Si6Cl12·2(NCH), and Si6Cl12·2(NCPh) structures. As mentioned above, DFT modeling provides structural parameters of the Si6Cl12·2(NCPh) complex very close to the experimentally observed ones (Table 1). In the optimized structure of C1 symmetry the long axes of NCPh donor molecules are also inclined from the vertical to the Si6 plane, albeit at a slightly higher angle (~75.1o). The NBO analysis performed on Si6Cl12 also showed that the donor-acceptor (σ→σ*) interactions can be treated as a second-order perturbation in the NBO basis. Similarly to the Si6Cl12·2(NCH) complex, the BD*(Si-Si) NBO does not interact with BD(1, 2, 3) N-C bonds, as well as both BD(1) C-C bonds and N-centered LP(1) NBOs structures. In contrast, all of the above mentioned NBOs couple with BD*(Si-Cl) NBOs, among which the nitrogen-centered LP(1) NBO is responsible for ~72% of the total E(2) value of 53.7 kcal/mol (see Table S3). To elucidate the effects of bending, the Si6Cl12·2(NCPh) structure constrained to D2h symmetry was optimized using the same DFT level of theory. The total electronic energy of this



structure is slightly higher (~0.2 kcal/mol). However, the bond lengths and angles, as well as NPA atomic charges, are practically the same as for the structure optimized without any symmetry constraints. The NBO analysis also reveals practically the same E(2) stabilization energies for both structures. As expected, the values of E(2) major components related to the different LP(1) N and BD*(Si-Cl) pairs for C1 structure range between 2.88 to 3.6 kcal/mol reflecting the difference in angle at which the lone pair π-orbital sees the corresponding component of the Lewis acid site. However, the average E(2) value of these components as well as their sum are practically the same as for the D2h structure (Table S4, the atom labels are given in Figure S5 ) suggesting that the effect of inclination from the vertical of donor molecule long axis is insignificant (at least for angles less than 15o). The CDA for C1 structure shows that the net charge donated from fragment F2 (both PhCN molecules) to the Si6 ring (fragment F1) equals -0.192 a.u. suggesting that charge transfer from benzonitrile donors to the Si6Cl12·ring overcomes the donation in opposite direction. It should be noted that the larger amount of charge transfer compared to Si6Cl12·2(NCH) complex is consistent with a larger E(2) value for Si6Cl12·2(NCPh) compound derived by NBO analysis. The results of CDA for Si6Cl12·2(NCPh) compound are shown in Figure S6. The absolute value of calculated NPA charge on the Si6Cl12 is -0.140 a.u., which is in a reasonable agreement with CDA results. Similar to Si6Cl12·2(NCH) compound, it was found that the Si6Cl12·unoccupied FOs ## 145 and 146 contribute (over 1.0%) to the following complex OMOs: #157 (1.0%) as well as #182 (1.3%), and #167 (1.0%), respectively (only OMOs with contribution exceeding 1% were included). The LP(1) N occupied FOs of NCPh donors in bonding (#45) and antibonding (#48) also significantly (over 10%) contribute to these OMOs of the complex implying hybridization of both fragments FOs, which consequently causes


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significant lowering of the corresponding hybrid orbitals energies of Si6Cl12·2(NCPh) complex contributing to overall complex stabilization energy. As in the earlier studies of Si5 and Si6-based inverse sandwich compounds,19, 23 it is assumed that occupation of the orbitals that were involved in vibronic coupling in the Si6 ring (#145 LUMO and #146 LUMO+1) suppresses the PJT effect in both neutral Si6Cl12·2(NCPh) and Si6Cl12·2(NCH) complex making the flat conformation stable.

Conclusion In conclusion, our detailed computational study of the perchlorinated cyclohexasilane (Si6Cl12) based inverse sandwich compounds has shown that regardless of the donor ligand size and charge, e.g., Cl− and CN− anions or neutral HCN and NCPh nitriles, their coordination to Si6Cl12 containing puckered Si6 ring results in its flattening. The NBO and CDA studies of the complexes have confirmed that coordination occurs due to hybridization of low lying antibonding σ*(Si-Cl) and σ*(Si-Si) unoccupied molecular orbitals (UMOs) of Si6Cl12 and occupied molecular orbitals (OMOs) of donor molecules (predominantly lone pair related) resulting in donor-to-ring charge transfer accompanied by complex stabilization and ring flattening. Since the Si6 ring distortion results from vibronic coupling of pairs of OMOs and UMOs (pseudo-Jahn−Teller effect), the Si6 ring flattening most probably occurs due to the PJT effect suppression in all studied compounds. The stabilization energy E(2) associated with donor-acceptor charge transfer (delocalization) was estimated using NBO analysis for all studied inverse sandwich compounds. It was found that the polarizability of the donor might significantly affect the stabilization energy value (Cl− > CN− > HCN). For the neutral complexes the E(2) value correlates with the charge on the nitrogen atoms.



However, the E(2) is only one of the factors that govern synthetic stability together with donor polarizability, possible reaction with the ring, stability vs. conformations, etc. All these factors should be considered when choosing the ligands suitable for forming Si-based one-dimensional compounds and other nanoscale materials. Supporting Information Supporting information contains computational details including atom labeling, intramolecular conformations, second order perturbation theory analysis of Fock matrix in NBO basis, and total contribution to stabilization energy associated with reported BD*(Si-Cl) and BD*(Si-Si) acceptor NBO orbital interactions and CDA orbital interaction diagram. Corresponding Authors [email protected]; [email protected] Acknowledgment Financial support from the Department of Energy (grant DE-FC36-08GO88160), the Office of Naval Research (grant ONR N00014-15-0065), Coretec Industries LLC (Fargo, ND) and the North Dakota Department of Commerce is gratefully acknowledged. S.K. acknowledges financial support of the Alfred P. Sloan Research Fellowship BR2014-073. The authors gratefully acknowledge the use of computational resources at the Center for Computationally Assisted Science and Technology (CCAST) at North Dakota State University.


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15. Dai, X.; Schulz, D. L.; Braun, C. W.; Ugrinov, A.; Boudjouk, P., "Inverse Sandwich" Complexes of Perhalogenated Cyclohexasilane. Organometallics 2010, 29, 2203-2205. 16. Tillmann, J.; Moxter, M.; Bolte, M.; Lerner, H.-W.; Wagner, M., Lewis Acidity of Si6Cl12 and Its Role as Convenient SiCl2 Source. Inorg. Chem. 2015, 54, 9611-9618. 17. Dai, X.; Anderson, K. J.; Schulz, D. L.; Boudjouk, P., Coordination Chemistry of Si5Cl10 with Organocyanides. Dalton Trans. 2010, 39, 11188-11192. 18. Boudjouk, P., Silicon-Based Coordination Polymers as Supramolecular Assembly Templates. In 46th Silicon Symposium Devis, California, USA, June 21-25, 2015. 19. Pokhodnya, K.; Olson, C.; Dai, X.; Schulz, D. L.; Boudjouk, P.; Sergeeva, A. P.; Boldyrev, A. I., Flattening a Puckered Cyclohexasilane Ring by Suppression of the Pseudo-JahnTeller Effect. J. Chem. Phys. 2011, 134, 014105/1-014105/5. 20. Robertazzi, A.; Platts, J. A.; Gamez, P., Anion···Si Interactions in an Inverse Sandwich Complex: A Computational Study. ChemPhysChem 2014, 15, 912-917. 21. Vedha, S. A.; Solomon, R. V.; Venuvanalingam, P., On the Nature of Hypercoordination in Dihalogenated Perhalocyclohexasilanes. J. Phys. Chem. A 2013, 117, 3529-3538. 22. Sergeeva, A. P.; Boldyrev, A. I., Flattening a Puckered Pentasilacyclopentadienide Ring by Suppression of the Pseudo Jahn-Teller Effect. Organometallics 2010, 29, 3951-3954. 23. Pokhodnya, K.; Anderson, K.; Kilina, S.; Boudjouk, P., Toward the Mechanism of Perchlorinated Cyclopentasilane (Si5cl10) Ring Flattening in the [Si5Cl10·2Cl]2- Dianion. J. Phys. Chem. A 2017, 121, 3494-3500. 24. Bersuker, I. B., Manipulation of Structure and Properties of Two-Dimensional Systems Employing the Pseudo Jahn-Teller Effect. FlatChem 2017, 6, 11-27. 25. Bersuker, I. B., Pseudo-Jahn-Teller Effect - a Two-State Paradigm in Formation, Deformation, and Transformation of Molecular Systems and Solids. Chem. Rev. (Washington, DC, U. S.) 2013, 113, 1351-1390. 26. Dai, X.; Choi, S. B.; Braun, C. W.; Vaidya, P.; Kilina, S.; Ugrinov, A.; Schulz, D. L.; Boudjouk, P., Halide Coordination of Perhalocyclohexasilane Si6Cl12 (X=Cl or Br). Inorg. Chem. 2011, 50, 4047-4053. 27. Reed, A. E.; Curtiss, L. A.; Weinhold, F., Intermolecular Interactions from a Natural Bond Orbital, Donor-Acceptor Viewpoint. Chem. Rev. 1988, 88, 899-926. 28. Vedha, S. A.; Solomon, R. V.; Venuvanalingam, P., On the Nature of Hypercoordination in Dihalogenated Perhalocyclohexasilanes. J. Phys. Chem. A 2013, 117, 3529-3538. 29. Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865-3868. 30. Adamo, C.; Barone, V., Toward Reliable Density Functional Methods without Adjustable Parameters: The Pbe0 Model. J. Chem. Phys. 1999, 110, 6158-6169. 31. Chai, J. D.; Head-Gordon, M., Long-Range Corrected Hybrid Density Functionals with Damped Atom-Atom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615-6620. 32. Vydrov, O. A.; Scuseria, G. E.; Perdew, J. P., Tests of Functionals for Systems with Fractional Electron Number. J. Chem. Phys. 2007, 126, 154109/1-154109/8. 33. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H.; et al. Gaussian 09, Version D.01; Gaussian, Inc.: Wallingford, CT, USA, 2009. 34. Foster, J. P.; Weinhold, F., Natural Hybrid Orbitals. J. Am. Chem. Soc. 1980, 102, 72117218.


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The atomic charges in the optimized D6h conformation of [Si6Cl12·2(NC)]2- (A) and in the optimized [Si6Cl12·2(NCPh)] (B) inverse sandwich compounds. 271x121mm (150 x 150 DPI)

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The shape of close to the HOMO orbitals of [Si6Cl12·2(NC)]2− reveals a hybridization of close to LUMO orbitals of Si6Cl12·(top row) and close to HOMO orbitals of the donor, i.e., π-component of N≡C bonds as well as N- and C-centered lone pairs. 127x50mm (96 x 96 DPI)


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The effective donor-to-ring charge transfer (A) and occupied orbital repulsion (B) in [Si6Cl12·2(NC)]2− dianion (lines are the guide for the eye). 233x95mm (96 x 96 DPI)



The orbital interaction diagrams of the [Si6Cl12·2(NC)]2− (A) and Si6Cl12·2(NCH) (B) complexes. Occupied and virtual orbitals are represented as solid and dashed bars, respectively; the vertical positions of MOs are determined by their energies. The bars at left and right sides correspond to the fragment orbitals (FOs), respectively; the bars in the middle (in red) correspond to complex orbitals. If composition of a FO in a complex orbital is larger than specific criterion (in our case > 1%), the corresponding two bars (FO and complex MO) are connected by red lines. Small icons represent the F1 and F2 orbitals involved in the charge transfer. 234x149mm (96 x 96 DPI)


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The effective donor-to-ring charge transfer (A) and occupied orbital repulsion (B) in Si6Cl12·2(NCH) compound (lines are the guide for the eye). 284x116mm (150 x 150 DPI)



The OMOs of Si6Cl12·2(NCH)] compound containing UMO of the Si6Cl12 fragment. 150x33mm (96 x 96 DPI)


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and Polyatomic Donor Ligand Coordination to Perchlorinated

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