1 Introduction

Silicon-oxygen (siloxane) and silicon-nitrogen (silazane) containing linear and cyclic oligomers and polymers are well-known for their diverse applications as, for example, membranes, high-performance elastomers, electrical insulators, water repellents, adhesives, antifoaming agents, mold-release agents, glasses, and high-temperature protective and ceramic coatings [1,2,3,4,5]. The synthesis, structure, physical and dynamic-mechanical properties of the Si–O oligomers and polymers have been well-studied with a long history of industrial applications [6]. Somewhat less explored are low molecular weight Si–N species; however, Si3N4/SiCN ceramics are well-known for their high-temperature stability and mechanical properties [4].

When the polymer backbone is comprised of only silicon atoms; i.e. polysilanes, extensive σ-electron delocalization occurs due to low ionization energies of Si – Si bonds. The interacting occupied orbitals combine to form a valence (bonding) band, while the unfilled orbitals combine to form an “empty” conducting (i.e., anti-bonding) band [7]. As the length of the polymer chain increases, the energy difference between the σ HOMO and σ* LUMO becomes smaller [8, 9]. This has led to polysilane based molecular wires [10, 11].

In polysiloxanes, the substituted Si atoms and the unsubstituted O atoms have significantly different sizes and electronegativities. In addition, the bond angles around the O atoms are significantly larger than those around Si, which results in distinct conformations [7].

Less information is available for polysilazanes [7, 12, 13]. A polysilazane chain generally adopts conformations that are less looped than a polysiloxane chain because the valence angles of Si and N atoms are smaller than for Si and O atoms decreasing the likelihood of backbiting or redistribution reactions during polymerization. Interestingly, polysilazanes have been shown to be more stable than polysiloxanes, despite the lower bond strength of Si–N relative to Si–O [14, 15]. Polysilazanes are also of interest because the N backbone allows for a substituent (i.e., R group) that could be varied for different polymer functionalities [12]. The simplest polysilazane species is composed of fused four-membered Si- and N-containing rings as shown in 1 below; however, six-, eight- and even larger membered ladders are theoretically possible.

Linear Si–O and Si–N oligomers and polymers can be derived from small ring precursors such as the cyclic oligomer A, cyclotrisiloxane, [R2Si-O]3; e.g. R = H, CH3, and cyclotrisilazane, B, [R2Si-NR’]3; R, R′ = H, CH3 (Scheme 1) [16, 17]. The structure of A has been determined by electron diffraction (gas phase) and crystallography (solid state) and indicates a planar ring that deviates only slightly from D3h symmetry [18]. The planarity of this six-membered ring presumably arises from back bonding of the lone pair of electrons on oxygen to the vacant 3d-orbitals on silicon, which alters bond angles about Si and reduces Si–O bond length; i.e. quasi-resonance in the ring. However, it is not quite clear why D3h symmetry is lost in the larger cyclic rings such as the octamer; the loss of planarity may be associated with increased conformational flexibility of the larger rings; however, bond length data suggest double-bond character in Si–O [19, 20].

Scheme 1
scheme 1

Ring structures for [R2SiO]3 and [R2SiNH]3 where R = H, organic group

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The incorporation of cyclic motifs (such as shown in Scheme 1) into ladder oligomers or polymers should result in more rigid structures with lower entropies. This reduction in disorder increases the temperature at which the polymer transitions to the glassy state, providing more flexibility in the reaction conditions required to synthesize the polymer. [7] A ladder structure with siloxyl, silazanyl or siloxazanyl side-rails in the ladder structure (see Fig. 2) should be resistant to degradative chain scission, since that would require multiple simultaneous bond ruptures, which are unlikely to occur [7]. In addition, linear ladder oligomers/polymers containing cyclic monomers may show lower conformational randomness in the amorphous state. Previous studies reported a dependence of the oligosiloxane conformation on the oligomer size and side group flexibility [21, 22]. However, these studies focused on polymers containing non-cyclic monomers.

If N or O atoms in ladder polymers donate a lone pair of electrons to form a π-bond with the Si empty 3d orbitals, resonance may result, possibly conducting electronic current through low-lying delocalization bands and acting as molecular wires with the potential of creating miniaturized electronic devices [23]. However, it has recently been suggested, based on single-molecule conductance studies, that molecular siloxanes function as molecular insulators, not conductors [24].

In this work, eight Si–O, Si–N, and Si–O–Si–N-containing ladder oligomers (Fig. 1) were designed and their structure, bonding, and flexibility were investigated using the Low Mode–Monte Carlo conformational search method (LM:MC), as well as quantum chemical geometry optimizations Density Functional Theory. We sought answers to the following questions:

  1. (1)

    Recognizing that small ring molecules are rigid, what are the structures and conformations of the smaller and larger oligomeric ladders containing Si–O, Si–N and Si–O–Si–N bonds (Fig. 1)?

  2. (2)

    How does the conformational flexibility of the Si–N, Si–O and Si–O–Si–N rings compare to the conformational behavior of classical six- and eight-membered rings?

  3. (3)

    Is there evidence of π-bonding owing to “back donation” of a lone pair of electron from the donor atom (i.e., N or O) to low lying valence 3d-orbitals on Si; and, does such π-bonding lead to resonance in the ring and/or along the “rails” of the ladder?

  4. (4)

    What role does the geometric and electronic ring structure play in the overall flexibility of the oligomeric ladders?

  5. (5)

    If π-bonding and resonance occurs in the –Si–O–Si–O–, –Si–N–Si–N–Si– and/or –Si–O–Si–N–Si– rails of the ladder oligomers, can these materials serve as electron conductors; i.e., molecular wires?

Fig. 1
figure 1

Silazane, siloxane and siloxazane oligomers explored in this study. Degrees of freedom varied during conformational searches of 1–8 are also shown. Curved arrows represent varied torsions; wavy bonds represent ring openings

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1.1 Methods

1.1.1 Conformational Analysis

The conformational ensembles of eight different siloxane, silazane and siloxazane oligomers of 7 repeat units were calculated using the MacroModel V9.8 suite of software [25]. The potential energy surface (PES) for each system was generated using the OPLS-2005 force field (see Table S1–S8 for parameter quality assessment) [26, 27]. Solvent effects (CHCl3) were included using the GB/SA continuum model [28]. Each surface was studied exhaustively using the Low Mode (LM) [29] search method in a 1:1 combination with the Monte Carlo (MC) [30] search method (LM:MC) [31]. The LM search method starts with a local minimum structure and identifies the low energy direction of motion using normal mode analysis. It then takes a fixed step along one of the low energy eigenvectors (chosen at random) to perturb the starting geometry. The perturbed structure is minimized to a second local minimum. Additional minima are found by repetition of the process. In comparison, the MC search method randomly chooses a starting conformation from the potential energy surface and minimizes it into the nearest local minimum. MC then moves to a different position on the PES by randomly rotating the torsional bonds of the initially minimized structure [31]. In the current study, LM and MC conformational steps were interspersed in a 1:1 fashion to take advantage of the barrier crossing ability of MC dovetailed with the local surface exploration strengths of LM. MC conformational search steps varied a random number of torsional angles, from a minimum of two to the maximum number of allowed torsion angles specific to each compound, as shown in Fig. 1. LM explored the 10 lowest eigenvectors for random steps between 3 and 6 Å from a determined minimum. Interconversion of ring conformers was realized using the ring-opening method of Still [32]. Bonds chosen for breakage with this method are shown in Fig. 1 as wavy lines. Searches were run in 25 blocks of 5000 LM:MC steps in order to assess convergence (Tables S9–S16). Convergence was judged by monitoring the energy of the most stable structure, the number of times this structure was visited, and the number of unique conformations found within 12.5 kJ/mol of the lowest energy minimum. Structures with 0.25 Å or higher root-mean-square (RMS) values relative to the previously identified conformations were saved as unique conformations. During the conformational search process, all structures were minimized using the Truncated Newton Conjugate Gradient method [33] (1000 steps). Converged structures from the resulting ensembles (except for 1) were clustered into geometrically similar families with respect to their heavy atoms using XCluster V1.7 [34]. The ratio of the shortest distance between an atom in each cluster and the corresponding atom in any other cluster (separation ratio) was recorded. It was not possible to obtain an ensemble of energy-converged structures for 1; therefore, the ensemble of unconverged structures was clustered. From that clustering, the leading (lowest-energy) structures were determined. Force-field based conformational analysis did not return any planar structures for any of the oligomeric models.

1.1.2 Quantum Minimization

All minimum energy structures identified using classical force fields and clustering were verified using geometry optimizations with density functional theory (DFT) [35]. For computational efficiency, in all oligomer calculations, methyl groups were replaced with hydrogen atoms to increase the speed of the calculations. Unrestrained geometry optimizations were performed using Jaguar V7.8 [36] with the B3LYP functional [37,38,39,40] and the 6-31G* basis set [41, 42]. Solvent effects (CHCl3) were included in the quantum minimizations using the Poisson-Boltzmann finite element (PBF) self-consistent reaction field (SCRF) solvation model [43]. Structures were confirmed as minima using frequency verification. To avoid any force-field bias in the structural results and to ensure that we did not miss any planar structures, B3LYP/6-31G* geometry optimizations in both the gas phase and PBF-SCRF (CHCl3) were also performed starting from planar input structures. Finally, gas-phase quantum calculations on the monomers and 7-mer oligomers of 1–8, along with cyclotrisiloxane, [R2Si-O]3, were performed using the B3LYP/6-311G** methodological treatment. In this case, a larger basis set was employed to provide the best chance of realizing electron delocalization if it were to occur in these molecules.

2 Results and Discussion

2.1 Characterizing the Oligomeric Dynamics Using Molecular Mechanics Conformational Analysis

The dynamical behavior of each oligomer 1–8 was determined using 125,000 LM:MC conformational search steps on the OPLS2005 force field surface with the GB/SA continuum solvent model for chloroform (Table 1). Except for 1, all molecular mechanics (MM) ensembles displayed good geometric convergence. (Details regarding the conformational search results can be found in the Supporting Information Tables S9–S16.) The lack of MM convergence for 1 suggests that the methodological treatment may be inadequate for describing the strained fused four-membered ring nature of 1. This is confirmed by the successful QM convergence of 1 (vide infra).

Table 1 The number of structures found within a 12.5 kJ/mol energy window of the global minimum on the OPLS2005/GBSA(CHCl3) surface and the results of clustering the MM ensembles for the siloxane, silazane and siloxazane polymers
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During the clustering procedure, the lowest minimum separation ratio was 1.1 for ensemble 2 while ensembles 6–8 displayed separation ratios greater than 2. A separation ratio greater than 2 has been shown to indicate statistically significant clustering [34]; so, while clustering for ensembles 2–5 is not as quantitatively reliable as for 6–8, it should still shed qualitative light on the overall conformational dynamics.

All eleven structures found on the MM surface for 1 cluster into a single family, the representative structure for which is shown in Fig. 2. Each four-membered ring is mostly planar but the oligomer adopts a non-planar pseudo staircase-like structure. Attempts to identify alternative conformational families for 1 on the MM surface were unsuccessful.

Fig. 2
figure 2

MM structure for 1

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The representative MM structure from each conformational family of 2–8 is shown in Fig. S1. All oligomeric structures are non-planar, as are most of the monomers that comprise the oligomers. While electron delocalization from the lone pair electrons on O or N with neighboring Si atoms does not necessitate planar structures (as it would with C), the lack of planarity of the monomers that comprise the oligomers, and the conformational flexibility of the oligomers, suggest that delocalization is not occurring. This, together with a bond length analysis, suggests that there is no π-bonding or back bonding interaction between Si and N or O. The Si–N and Si–O bonds found in the oligomers are slightly longer than the literature values for σ-bonds and are, therefore, unlikely to exhibit π-bonding. The long Si–N bond observed in 1 is not unexpected given the ring strain inherent in that oligomer.

A comparison of the molecular structures, numbers of structures found, numbers of conformational families and the distribution of ensemble structures within each family sheds light on both the flexibility of the molecule and the roughness of the PES surface. For instance, the number of structures found for 1–4 (Table 1) mostly agrees with the expectation that conformational flexibility increases as the ring size increases, thereby resulting in a higher number of structures found. However, even though 5 has the greatest number of conformational families, it has a lower total number of structures compared to its size. Surprisingly, 6 has a very small total number of structures. With the greatest total number of structures found and only two conformational families, 7 must have a significantly rougher potential energy surface. Compared to molecules 2–4, which are smaller in size, 8 has a relatively low total number of structures found and clusters into only two families. A comparison of the distribution of ensemble members also sheds light on the flexibility of the oligomers (Fig. S1). For instance, while oligomers 2, 3 and 8 adopt three, three and two families, respectively, in all of these cases one family dominates the behavior by containing more than 97% of the ensemble. In contrast, the ensembles for the other oligomers cluster into families with a more even distribution of structures. From the analysis of the MM results, we conclude that 5 is the most conformationally flexible ensemble (eight families; well distributed); and, while 7 has a very rough PES surface, overall it is conformationally and relatively rigid (two families with 85% of the ensemble clustering into the lowest energy family).

For systems with six- and eight-membered rings (molecules 2–8), the conformational behavior of each ring, in each oligomer, was analyzed. For oligomers containing six-membered rings (2 and 3), if there is back bonding between the Si and O or N atoms, the individual monomer rings will show reduced conformational diversity along with bond lengths indicative of delocalization. However, if such back bonding does not occur, then based upon the conformational behavior of fully saturated, cyclohexane rings, we would expect that the most stable conformation of the six-membered monomer rings would be the chair, followed by the boat, and perhaps the half-chair might be present. (As a reminder: in isolated rings the half-chair is the transition state between chair and boat conformation [44].) For eight-membered rings, based upon the tub-shaped conformations of anti-aromatic cyclooctatetraene, whether or not back bonding is present, we expect non-planar rings, although the conformational diversity of the resulting rings can be used to probe the electronic structure. If back bonding is occurring we would expect to see a single tub-like conformation whereas, if back bonding is not occurring, we would expect a multitude of conformations. In that case, we should expect at least three different structures (Fig. 3): a symmetrical crown conformation with uniform bond angles (3a), a boat–chair conformation (3b) and a boat-boat (3c) conformation. Twisted versions of each of these conformations may also be possible. In isolated cyclooctane rings, the boat–chair conformation is energetically favored. Flexible conformational mixtures are often observed for these systems [43, 45, 46].

Fig. 3
figure 3

Eight-membered ring conformations: a crown, b. boat–chair and c boat

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In Tables S17–S23, we characterize the conformation flexibility of the six- and eight-membered rings for oligomers 2–8. For 2, structures A, B and C (Fig. 4) differ only in the conformation of the 5th and 6th rings. Whereas structure B is curved or C-shaped, structures A and C are both ribbon-like with a kink in the fifth ring, characterized by a half-chair conformation. Conformation A of 3 is a ribbon-like structure while conformation B is curved and conformation C is significantly kinked. All the conformations of 4 are curved and/or highly twisted with an approximately even mix of boat, boat–chair, crown, and twist-crown ring conformations. With eight conformational families and a wide range of energies associated with these conformations, 5 is the most flexible system studied. 5A and 5B have a relatively similar structure. The main difference between these conformations is the second to last ring, which is a boat–chair in 5A but a boat in 5B. 5F and 5G have similar structures. The main difference between the 5F and 5G conformations is the last ring, which is a boat–chair in 5F but a boat in 5G. All of the conformations of 6 contain mostly boat–chair and crown rings. While 7 has two significantly curved and twisted structures, 8 has a zig-zagged structure B and a relatively planar structure A with a pocket. Structure A of 8 contains mostly crown rings, but structure B contains mostly boat and boat–chair rings. For each molecule, the conformations that had similar energies were superimposed to ensure that the structures were significantly different (Tables S24).

Fig. 4
figure 4

QM structures obtained with B3LYP/6-31G* in SCRF (CHCl3). Relative energies (ΔE) are shown (kcal/mol), along with the RMSD values between the MM structure used to initiate the QM minimization and the geometry optimized QM output structure. For clarity, hydrogen atoms are not shown

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2.2 Quantum Mechanical (QM) Verification of Oligomeric Structures

The representative structures from each MM conformational family were used as starting geometries for quantum mechanical refinement using B3LYP/6-31G*/SCRF(CHCl3). In all cases MM minima used as starting structures produced frequency-confirmed minima on the DFT surface verifying the structures found during the MM analysis. Superposition of the MM and QM structures resulted in root-mean-square deviations (RMSD) ranging from 0.2343 to 1.9279 Å, indicating that the majority of the minima are structurally similar on the two surfaces and further validates the MM conformational results. The QM structures and their relative energies are shown in Fig. 4. For 1, the MM and QM structures are the same with a RMSD of 0.2343 Å (see 1 in Fig. 2).

For molecules 3, 4, and 6, quantum minimization confirmed that the MM structures are minimum energy structures; the RMSD values are small and the energetic ordering is the same on the classical and quantum surfaces. For molecules 2 and 7, the number of MM and QM structures is in agreement, the RMSD values are low, and there is some reordering of the minima. For 5 and 8, the number of minima is the same; however, the larger MM:QM RMSD values suggest that the minima are only slightly different. 5A and 5B minimized to very similar structures on the QM surface. Even though the second to last ring has a boat–chair conformation for MM 5A and a boat conformation for MM 5B (see Fig. S1), it is a boat for both QM 5A and QM 5B. The main difference between these QM structures is the last ring, which flips up in one conformation and down in the other conformation. In all cases, the conformational flexibility of the resulting ensembles suggest that these systems are not suitable molecular wire candidates.

To analyze the QM geometries, we measured the unique bond distances within each monomer, i.e. rails and rungs, and then averaged those distances over all monomers in each oligomeric conformation identified for all systems studied. For instance, using 2 as an example, we identified three low energy minima (A–C; Fig. 4). Within each low energy structure of 2, there are eight rungs and 28 bonds in the rails (14 on each side.) To obtain the average rail and rung distances, we averaged over 24 rail bonds (8 × 3 conformations) and 84 rungs (28 × 3), individually (Table 2). These values can be compared to average Si–O and Si–N bond lengths taken from the literature [47,48,49]. in order to gauge any changes in geometry or electronic structure caused by incorporation into the ladder oligomer. In all cases, except for 1, the rail and/or rung bonds are similar to the literature average values for Si–O and Si–N single bonds. This suggests that the oligomers of 2–8 adopt relatively unstrained geometries and lack the electron delocalization necessary for conduction. For 1, the Si–N rung bonds are longer than the rail bonds and longer than the literature average Si–N bonds, thereby hinting at the strain inherent in four-membered rings.

Table 2 Average bond lengths of QM geometries obtained using B3LYP/6-31G* in SCRF (CHCl3). Literature values for average Si–N and Si–O σ bonds are 1.74 (range 1.58–2.26) and 1.63 (range 1.55–1.72) Å, respectively [47,48,49]
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To ensure that the conformational search process and subsequent QM minimizations did not miss oligomeric structures that would be promising molecular wire candidates, we subjected planar starting structures of 1, 2 and 3 to quantum minimization on the B3LYP/6-31G*/SCRF(CHCl3) surface. These structures were optimized to bent and/or curved structures (Fig. 5) with geometries and molecular orbital manifolds that suggest a lack of delocalization.

Fig. 5
figure 5

QM-minimized conformations resulting from planar input structures of 1–3. For clarity, hydrogen atoms are not shown. The RMSD values were measured between the conformations shown in this figure and each of the MM conformations (A, B, …) in Fig. S1

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2.3 Why is Electron Delocalization Not Occurring in 1–8?

The perceived electron delocalization of the cyclic oligomer A, cyclotrisiloxane, [R2Si-O]3; e.g. R = H, CH3, motivated the exploration of 1–8 as potential molecular wire candidates. Cyclotrisiloxane has previously been shown to be planar in both experimental and theoretical studies. The planarity has been attributed principally to back-bonding between the O lone pair of electrons, and the Si atoms. However, planarity may not be required in such back-bonding as the third-row nature of Si provides opportunities for d-orbital interactions. A further complication with the structures of this study is the incorporation of conformationally flexible 8-membered rings. While it is known that molecular mechanics calculations are generally reliable for predicting the conformational preferences of six- and eight-membered rings [45], to ensure that our methodological models were accurately describing the physical nature of these systems, we performed gas-phase geometry optimizations of the monomers and seven-membered oligomers using a larger basis set (6-311G**) than was used (6-31G*) in the solvent-phase quantum studies described above. We also performed a B3LYP/6-311G** geometry optimization on cyclotrisiloxane (A), for comparison.

As shown in Fig. S2-I, our methods reproduce the known planar structure of A; however, an examination of the canonical molecular orbitals shows the π-like delocalized MO lies deep within the manifold (MO#27; HOMO-9)—too low in energy to serve as a simple model for the electron excitation into a conduction band, behavior that would be necessary for a molecular wire. We also examined the geometries and molecular orbital manifolds for the monomers of 1–8 (Fig. S2). None of these monomers is as planar as A, and excepting the monomer of 8, all of the eight-membered ring monomers show significant conformational flexibility. Interestingly, 8 is the most planar of the all of the monomers, other than A. An examination of the monomer MOs shows electron delocalization only in monomers A, 1, 2 and 8; however, in all these cases the delocalized MOs occur too deeply in the MO manifold to be candidates for conduction band excitation.

We also performed B3LYP/6-311G* geometry optimization on the seven-mers of 1–8 and examined the resulting MOs for oligomer spanning delocalization. Similar to the geometry optimizations in solvent (Fig. 4), the gas-phase geometries are non-planar, and the conformational diversity of the oligomers containing eight-membered rings (3–8) is greater than the oligomers with six- or four-membered rings (Fig. S2). Oligomers 1 and 2 were the only systems that showed some degree of oligomer-spanning delocalization. In both these cases, the MOs were not near the conduction band (1 HOMO-5; 2 HOMO-8). In all cases, the quantum structures optimized in gas-phase are more condensed than in solvent due to hydrogen bonding between lone pairs of electrons on N and O and the Si- H bond on the opposite rail of the ladder.

Our detailed analysis of the canonical molecular orbitals suggests that these oligomers are not good molecular wire candidates because of the mismatch in energy between the Si atomic orbitals and the O or N atomic orbitals. More often than not, especially in the more conformationally flexible oligomers, the Si atoms form a multi-atom MO that does not include the N or O atomic MOs, and/or the N and/or O atoms form a multi-atom MO without Si. A good example of this can be seen in Fig. S4.

3 Conclusions

We explored the multi-dimensional surfaces of eight oligomeric models for ladder polymers of polysiloxane, polysilazane and polysiloxazane. We clustered the resulting low energy structures within each ensemble and subjected the representative structure from each conformational family to geometry optimization using the B3LYP/6-31G* treatment in SCRF (CHCl3). The oligomeric models of this study have complex conformational dynamics, and adopt geometries that suggest a lack of electron delocalization. Species 5 (eight-membered siloxazane) was the most flexible (i.e., eight conformational families were found). For oligomers containing six-membered ring monomers, the boat conformation dominated, whereas for the oligomers containing eight-membered ring monomers, no one conformation dominated and a large mixture of conformations was observed. Most oligomers assumed curved structures while a few adopted ribbon-like motifs. In all models, except 1, the individual monomer units that comprise the oligomers adopted non-planar geometries. The Si–N and Si–O bond lengths of all molecules indicated that electron delocalization is not taking place and this was further confirmed using molecular orbital analysis.