Stereochemistry of Simple Molecules Inside Nanotubes and Fullerenes: Unusual Behavior of Usual Systems

molecules

Review Stereochemistry of Simple Molecules inside Nanotubes and Fullerenes: Unusual Behavior of Usual Systems

Valerij Kuznetsov 1,2

1 Ufa State Aviation Technical University, K. Marksa, 12, Ufa 450008, Russia; [email protected] 2 Ufa State Petroleum Technological University, Kosmonavtov, 1, Ufa 450062, Russia

Academic Editor: Bagrat Shainyan Received: 7 May 2020; Accepted: 21 May 2020; Published: 23 May 2020

Abstract: Over the past three decades, carbon nanotubes and fullerenes have become remarkable objects for starting the implementation of new models and technologies in different branches of science. To a great extent, this is defined by the unique electronic and spatial properties of nanocavities due to the ramified π-electron systems. This provides an opportunity for the formation of endohedral complexes containing non-covalently bonded atoms or molecules inside fullerenes and nanotubes. The guest species are exposed to the force field of the nanocavity, which can be described as a combination of electronic and steric requirements. Its action significantly changes conformational properties of even relatively simple molecules, including ethane and its analogs, as well as compounds with C–O, C–S, B–B, B–O, B–N, N–N, Al–Al, Si–Si and Ge–Ge bonds. Besides that, the cavity of the host molecule dramatically alters the stereochemical characteristics of cyclic and heterocyclic systems, affects the energy of pyramidal nitrogen inversion in amines, changes the relative stability of cis and trans isomers and, in the case of chiral nanotubes, strongly influences the properties of R- and S-enantiomers. The present review aims at primary compilation of such unusual stereochemical effects and initial evaluation of the nature of the force field inside nanotubes and fullerenes.

Keywords: nanotube; fullerene; endocomplex; computer simulation; barrier of internal rotation; enantiomer; cis and trans isomers; conformational equilibrium; nitrogen pyramidal inversion

1. Introduction The history of nanotubes [1,2] and fullerenes [3] spans several decades; the most important stages in understanding of their nature and properties are well represented in recent reviews and books [4–10]. The main directions of practical application of such nanoobjects are connected with creation of new materials [4,7–14], applications in pharmacy and medicine [15–24] and wastewater treatment [25]. These possibilities resulted mainly from the formation of endohedral complexes of fullerenes and nanotubes; the ﬁrst example, synthesis of lanthanum complexes of C60, was described in [26]. Soon after, by using a suitable solvent, supercritical CO2, molecular surgery, and plasma ion irradiation methods, a great number of endohedral fullerenes and nanotubes, with metals, nitrogen, hydrogen, boron, noble gases, halogens, sulfur, radioactive isotopes, metal nitrides, water, ammonia, methane, methanol, aromatic hydrocarbons, cyclohexane, heterocycles, metallocenes and biomolecules in their cavities, were obtained [27–64]. The endohedral fullerene complexes inside nanotubes are another type of such species; a recent example is presented in [65]. The structure and properties of hybrid molecule–nanotube and fullerene systems were investigated with both experimental and theoretical methods. In addition to the practical use (such clusters, with unique magnetic and optical properties, are interesting as conductors and semiconductors, eﬀective transporters of drugs in biological systems, and for hydrogen and methane storage) it is important to note that due to the

Molecules 2020, 25, 2437; doi:10.3390/molecules25102437 www.mdpi.com/journal/molecules Molecules 2020, 25, 2437 2 of 37 extensive charge transfer between the carbon cage and the guest molecule, the latter acquires an electric charge [27,29,35–37,43,52,62,66]. Besides that, weak and van der Waals interactions play an important role in the molecular encapsulation [66]. It was shown that flat molecules (benzene, coronene, perylene) tend to align their molecular planes with the nanotube axis. In this case, the chirality of the tubes does not matter, but the tube has an influence on the intermolecular distances for confined species. It was also established that the encapsulation of hydrocarbons in nanotubes is energetically profitable [66]. In the case of armchair (n,n) single-walled carbon nanotubes (SWCNTs) and encapsulated hydrohalogens, the final orientation of the confined molecule depends on the internal diameter of the SWCNT’s hollow space and the halogen’s nature (F, Cl, Br, I) [67]. Guest species inside nanotubes can move under the action of different forces. This phenomenon is experimentally confirmed for “peapod” systems (fullerenes and endohedral fullerenes in SWCNTs) [27]. Besides that, unique conditions in nanotube cavity make possible numerous chemical reactions. For example, theoretical investigation predicted decreasing of the activation barrier of the Menshutkin SN2 reaction inside nanotubes [68]. On the other hand, the calculated energy barrier for Cl− exchange in the SN2 reaction within nanotubes was higher by 6.6 kcal/mol in comparison with the gas phase [69]. Later, it was shown that SWCNTs may be used as effective nanoreactors for preparative syntheses of inorganic [70] and organic [71–75] products with high yields; it is also possible to achieve enantiomeric excess of the products by using a racemic mixture of P and M enantiomers of (n,m) chiral nanotubes [76]. All of the foregoing clearly shows that the domestic area of fullerenes and nanotubes can be viewed as the action of a solvent with specific properties. If that is true, then the question arises: how does that affect the conformational preference and other stereochemical properties of the encapsulated molecule? As indicated by C. Reichardt, “The interactions between species in solvents (and in solutions) are at once too strong to be treated by the laws of the kinetic theory of gases, yet too weak to be treated by the laws of solid-state physics” [77]. This statement is one of the main components of solute–solvent interaction research strategy. Its further development has resulted in two solvent models: implicit (continuum) and explicit (discrete); their comparative effectiveness has been discussed in recent publications [78–84]. In this connection, the endohedral complexes of fullerenes and nanotubes can be viewed as a variety of explicit models. Various approximations based on DFT are usually used as an appropriate computational technique for simulation of the structural, electronic, and conformational properties of such systems. Some of the most useful among them are the PBE, hybrid PBE [85] and wB97XD methods [86]. The author’s investigations are connected with the approximation PBE/3ζ (PRIRODA program [87]) that correctly describes the structural, thermochemical, and polar characteristics of endohedral complexes of fullerenes [88–91]. The 3ζ triple-split basis set [92] is a full-electron non-relativistic Gauss-type set containing an accelerating aux-part and polarization functions. This allowed to get a comparative analysis of structural change of different compounds in nanocavity using a single proven method of calculation. The first example of conformational investigation of simple molecules in the nanocavity was devoted to the examination of the torsion motion of H2O2 inside (5,5) and (6,6) armchair SWCNTs, using B3LYP/6-31G(d, p) approximation [93]. Two types of orientation of the O–O bond of the guest molecule inside nanotubes—along and perpendicular to the tube axis—were considered. The H–O–O–H torsion angle τ was varied from 0 to 180◦ with 10◦ steps. It was established that, in the case of (5,5) SWCNT, the orientation along the axis corresponds to the more stable endohedral complex compared to the perpendicular one. The main minimum on the potential energy surface (PES) in this case belongs to the conformer with τ = 160◦, while for the free H2O2 molecule it corresponds to the form with τ = 120◦. For the adduct H2O2@(6,6), with a larger diameter of the nanotube, both orientations of the guest molecule remain stable; the main minimum for the complex with an O–O bond oriented along nanotube axis corresponds to the conformer with τ = 70 . The effect of the weak O–H π interaction ◦ ··· on the binding of the guest molecule is discussed. Polarization of the nanotube in such complexes was also shown. Molecules 2020, 25, 2437 3 of 37

In view of the foregoing, the objective of the present work is to discuss the conformational behavior and other stereochemical properties a range of compounds: inorganic species, ethane and its analogs, alcohols, ethers, compounds with double bonds, enantiomers, cyclic and heterocyclic molecules—inside nanotubes and fullerenes in comparison with free state or usual solutions. The main focus is on the inﬂuence of the size and chemical composition of nanoobjects as well as of SWCNTs’ chirality and diameter of fullerenes on the stability of preference conformation and chemical structure of the guest molecule.

2. Conformational Behavior of Ethane and Its Analogs in Nanotubes Ethane is the classic object of conformational investigations. After Orville-Thomas’ fundamental book [94], there was a noticeable increase in the number of papers, which raised the question: why is the staggered form of ethane more stable compared to the eclipsed one? According to the concepts of theory, the nature of the rotational barrier about a simple bond is generally determined by exchange-repulsion, electrostatic, steric and hyperconjugation effects. Their relative contributions have been widely discussed in the literature [95–110]. On the other hand, spectral data indicate that ethane molecules adsorbed on the surfaces of silver, indium, and potassium exist in the eclipsed conformation [111]. Computer simulation shows that this is not the only example of such an unusual conformational behavior of alkanes. For example, nanoscale confinement (protein binding sites or carbon nanotubes) significantly changes conformations of butane, hexane and tetracosane from trans to gauche-rich helical form [112–114]. It is also known that linear alkanes are adsorbed on the surface of zeolites in a highly coiled conformation [115]. On the other hand, direct observation of conformational changes of a single molecule using transmission electron microscopy (TEM) [116] indicates the presence of only 6% of the CF2–CF2 and 20% of CH2–CH2 bonds in gauche conformation in a single perfluoroalkyl fullerene molecule inside SWCNT [117]. This qualitatively meets the known conformational data for alkyl chains of free hydrocarbon molecules [94]. However, it should be stressed that citing data refer to the alkane chain that contains fullerenes. Because of this additional factor, the flexibility of the chain links inside the nanotubes may be considerably restricted.

2.1. Ethane The investigation of adsorption and diffusion properties of ethane within SWCNTs was presented in [118–123]. It has been established that nanotube geometry in some cases plays a definite role in the adsorption activity. The selectivity of adsorption of a binary mixture of ethane and ethylene was also studied. On the other hand, the rotational barriers of methyl-sized groups depend on van der Waals interactions and may vary under the influence of the nanosurface [124]. The first example of conformational transformation of ethane in the nanotube cavity was presented in [125]. Surprisingly, during the calculation (DFT approximation PBE/3ζ), the initial staggered form of ethane inside SWCNT (4,4) spontaneously converted to the eclipsed conformation. Its Hessian, in contrast to the staggered form, did not contain imaginary frequencies (Figure1). , The relative stability of the staggered form of free C2H6 (∆G 298) is 2.5 kcal/mol. It should be noted that this value is slightly underestimated in comparison with data from the literature (2.8–3.04 kcal/mol [94]). In the case of encapsulated ethane, the eclipsed form is more stable than the staggered form at 0.4 kcal/mol. Moreover, both encapsulated forms have a negative electric charge ( 0.53), the shortened C–C bond length (r 1.502–1.505 instead of 1.531–1.544 Å for the free molecule) − C–C and decreased Mulliken’s bond order (OC–C 0.78–0.79 instead of 1.00–1.02). The guest molecule is oriented along the symmetry axis of the nanotube. The distance between hydrogen atoms of ethane and the SWCNT sceleton is 1.7 Å [125]. This relationship was confirmed for other endohedral clusters of ethane with different types of SWCNTs (Table1, Figure2)[126–128]. Molecules 2020, 25, 2437 4 of 37 Molecules 2020, 25, x FOR PEER REVIEW 4 of 39

FigureFigure 1.1. Conformational equilibrium of ethane:ethane: free andand insideinside SWCNTSWCNT (4,4).(4,4). Adapted withwith modiﬁcationmodification [[125].125].

Table 1. Energetical and structural parameters of C2H6@nanotubes (PBE/3ζ)[126–128]. The relative stability of the staggered form of free C2H6 (ΔG≠298) is 2.5 kcal/mol. It should be noted , that this value is slightlyForm underestimated∆G 298 (kcal /inmol) comparisonrC–C (Å) withO dataC–C fromCharge the literature (2.8–3.04 kcal/mol [94]). In the case of encapsulated ethane, the eclipsed form is more stable than the staggered C2H6 form at 0.4 kcal/mol. Moreover, both encapsulated forms have a negative electric charge (−0.53), the Staggered 0 1.531 1.02 0 shortened C-C bondEclipsed length (rC-C 1.502–1.5052.5 instead 1.544of 1.531–1.5441.00 Å for 0the free molecule) and decreased Mulliken’s bond order (OC-C 0.78–0.79 instead of 1.00–1.02). The guest molecule is oriented C2H6@(4,4)-closed along the symmetry axis of the nanotube. The distance between hydrogen atoms of ethane and the Staggered 0.6 1.495 0.80 0.54 SWCNT sceleton is 1.7 Å [125]. − Eclipsed 0 1.499 0.78 0.57 This relationship was confirmed for other endohedral clusters of ethane− with different types of C H @(6,0)-short SWCNTs (Table 1, Figure 2) [126–128]. 2 6 Staggered 2.0 1.431 0.51 0.72 Eclipsed 0 1.429 0.53 0.73 Table 1. Energetical and structural parameters of C2H6@nanotubes (PBE/3ζ) [126–128]. C2H6@(6,0)-long Form ΔG≠298 (kcal/mol) rC-C (Å) OC-C Charge Staggered 1.7 1.434 0.49 0.40 Eclipsed 0 C2H6 1.432 0.50 0.48 Staggered 0 1.531 1.02 0 C2H6@(6,0)-CBN Eclipsed 2.5 1.544 1.00 0 Staggered 0.9 1.449 0.66 1.16 C2H6@(4,4)-closed − Eclipsed 0 1.449 0.66 1.22 Staggered 0.6 1.495 0.80 −0.54− Eclipsed 0 1.499 0.78 −0.57 A general characteristic of all clusters is the decrease in C–C bond length with simultaneous C2H6@(6,0)-short reduction of its Mulliken bond order and appearance of positive or negative electric charge on the Staggered 2.0 1.431 0.51 0.72 guest molecule in accordance with the conclusions of [27,29,35–37,43,52,62,66]. SWCNTs with zig-zag Eclipsed 0 1.429 0.53 0.73 geometry, (6,0)-short and (6,0)-long, differ in length (7.11 and 9.34 Å respectively). All endocomplexes C2H6@(6,0)-long demonstrate an evident preference for the eclipsed (or nearly eclipsed) conformation of ethane, although Staggered 1.7 1.434 0.49 0.40 the last cluster with host tube (6,0) with BN fragments (BN nanotubes have been studied in [129–131]) Eclipsed 0 1.432 0.50 0.48 has shown a tendency to reduce the energy differences between both forms, in comparison with C2H6@(6,0)-CBN carbon-analog: nanotube (6,0)-long [127]. The example of complex C H @(6,0)-CBN also demonstrates Staggered 0.9 1.449 0.662 6 −1.16 that, with regard to the van der Waals spheres, the inner cavity of the nanotube is densely filled with Eclipsed 0 1.449 0.66 −1.22 the guest molecule (Figure2).

MoleculesMolecules2020 ,202025,, 2437 25, x FOR PEER REVIEW 5 of 39 5 of 37

FigureFigure 2. Nanoclusters2. Nanoclusters C C2H2H66@SWCNTs. Adapted Adapted with with modification modiﬁcation [126,127]. [126, 127].

2.2. PropaneA general characteristic of all clusters is the decrease in C−C bond length with simultaneous reduction of its Mulliken bond order and appearance of positive or negative electric charge on the Computer simulation of propane inside two model SWCNTs, (4,4) and (6,0) (PBE/3ζ), shows guest molecule in accordance with the conclusions of [27,29,35–37,43,52,62,66]. SWCNTs with zig-zag that staggered conformation in this case is not realized: during the optimization, the guest molecule geometry, (6,0)-short and (6,0)-long, differ in length (7.11 and 9.34 Å respectively). All endocomplexes convertsdemonstrate into the an fully evident eclipsed preference form thatfor the cannot eclipsed exist (or outside nearly theeclipsed) tube(Figure conformation3)[ 132 of]. Thisethane, form is morealthough stable than the last the cluster partially with eclipsed host tube conformation (6,0) with BN fragments (transition (BN state, nanotube TS) bys have 1.6 andbeen 1.2 studied kcal/ molin for , the endocomplexes[129–131]) has shown with a tendency (4,4) and to (6,0) reduce SWCNTs the energy respectively differences between (∆G 298 both); meanwhile, forms, in comparison the calculated with carbon-analog: nanotube (6,0)-long [127]. The example of complex C2H6@(6,0)-CBN also barrierMolecules of internal 2020, 25, rotationx FOR PEER for REVIEW the free propane is 3.0 kcal/mol in favor of the staggered conformer.6 of 39 demonstrates that, with regard to the van der Waals spheres, the inner cavity of the nanotube is densely filled with the guest molecule (Figure 2).

2.2. Propane Computer simulation of propane inside two model SWCNTs, (4,4) and (6,0) (PBE/3ζ), shows that staggered conformation in this case is not realized: during the optimization, the guest molecule converts into the fully eclipsed form that cannot exist outside the tube (Figure 3) [132]. This form is more stable than the partially eclipsed conformation (transition state, TS) by 1.6 and 1.2 kcal/mol for the endocomplexes with (4,4) and (6,0) SWCNTs respectively (ΔG≠298); meanwhile, the calculated barrier of internal rotation for the free propane is 3.0 kcal/mol in favor of the staggered conformer.

FigureFigure 3. Conformational 3. Conformational equilibrium equilibrium in in cluster cluster C3HH88@(4,4).@(4,4). Adapted Adapted with with modification modiﬁcation [132].[ 132].

The guestThe guest species species are are characterized characterized by by shortenedshortened C C–C−C bonds bonds and and a small a small negative negative electric electric charge charge ( 0.37–(−0.370.39);‒−0.39); the the inner inner cavity cavity of of SWCNT SWCNT isis completely filled ﬁlled with with the the guest guest molecule molecule [132]. [132 ]. − −

2.3. 2,2,3,3-Tetramethylbutane2.3. 2,2,3,3-Tetramethylbutane According to the electron diffraction data, the structure of gaseous 2,2,3,3-tetramethylbutane According to the electron diﬀraction data, the structure of gaseous 2,2,3,3-tetramethylbutane (hexamethylethane, C8H18) corresponds to the staggered form. The central C-C bond length is 1.582 (hexamethylethane, C H ) corresponds to the staggered form. The central C–C bond length is Å [133]; our calculation8 18 gives the value 1.590 Å. In this case, the relative stability of the staggered conformer is 8.6 kcal/mol (PBE/3ζ) [134]. However, in endocomplex C8H18@(5,5), the preferred conformation of the guest molecule is nearly eclipsed (Figure 4).

Figure 4. Conformational equilibrium in cluster C8H18@(5,5). Adapted with modification [134].

The relative stability of the eclipsed form is 0.9 kcal/mol (ΔG≠298); the length of the central C−C bond is 1.522 Å (shorter by 0.068 Å than in the free alkane). The encapsulated molecule acquires a negative electric charge (−0.93) [134].

2.4. 2,2-Dimethylpropane 2,2-Dimethylpropane (neopentane) is a convenient model system for investigation of the interconnection between the rotational barrier and the molecular environment around the rotator [124,135]. The experimental barrier to internal rotation (ΔG298≠) is 4.3 kcal/mol [136,137]. However, the conformational behavior of neopentane inside nanotubes differs significantly from that of ethane and its analogs discussed above. Its main feature is a substantial increase in the internal rotation barrier in the case of endocomplexes with SWCNTs of small diameter; TS corresponds to the eclipsed

Molecules 2020, 25, x FOR PEER REVIEW 6 of 39

Figure 3. Conformational equilibrium in cluster C3H8@(4,4). Adapted with modification [132].

The guest species are characterized by shortened C−C bonds and a small negative electric charge (−0.37‒−0.39); the inner cavity of SWCNT is completely filled with the guest molecule [132].

2.3. 2,2,3,3-Tetramethylbutane MoleculesAccording2020, 25, 2437 to the electron diffraction data, the structure of gaseous 2,2,3,3-tetramethylbutane6 of 37 (hexamethylethane, C8H18) corresponds to the staggered form. The central C-C bond length is 1.582 1.582Å [133]; Å [ 133our]; calculation our calculation gives gives the thevalue value 1.590 1.590 Å. Å.In Inthis this case, case, the the relative relative stability stability of of the the staggered staggered conformer is 8.6 kcal/mol (PBE/3ζ) [134]. However, in endocomplex C8H18@(5,5), the preferred conformer is 8.6 kcal/mol (PBE/3ζ)[134]. However, in endocomplex C8H18@(5,5), the preferred conformation of the guest molecule isis nearlynearly eclipsedeclipsed (Figure(Figure4 4).).

FigureFigure 4.4. ConformationalConformational equilibriumequilibrium inin clustercluster CC88H1818@(5,5).@(5,5). Adapted Adapted with with modification modiﬁcation [134]. [134].

, The relative stability of the eclipsed form is 0.9 kcal/mol (∆G 298); the length of the central C–C The relative stability of the eclipsed form is 0.9 kcal/mol (ΔG≠298); the length of the central C−C bond is 1.522 Å (shorter by 0.068 Å than in the free alkane). The encapsulated molecule acquires a bond is 1.522 Å (shorter by 0.068 Å than in the free alkane). The encapsulated molecule acquires a negative electric charge ( 0.93) [134]. negative electric charge (−0.93) [134]. 2.4. 2,2-Dimethylpropane 2.4. 2,2-Dimethylpropane 2,2-Dimethylpropane (neopentane) is a convenient model system for investigation of the 2,2-Dimethylpropane (neopentane) is a convenient model system for investigation of the interconnection between the rotational barrier and the molecular environment around the interconnection between the rotational barrier and the molecular environment, around the rotator rotator [124,135]. The experimental barrier to internal rotation (∆G298 ) is 4.3 kcal/mol [136,137]. [124,135]. The experimental barrier to internal rotation (ΔG298≠) is 4.3 kcal/mol [136,137]. However, However, the conformational behavior of neopentane inside nanotubes differs significantly from that the conformational behavior of neopentane inside nanotubes differs significantly from that of ethane ofMolecules ethane 2020 and, 25,its x FOR analogs PEER REVIEW discussed above. Its main feature is a substantial increase in the internal7 of 39 and its analogs discussed above. Its main feature is a substantial increase in the internal rotation rotation barrier in the case of endocomplexes with SWCNTs of small diameter; TS corresponds to the barrierform. According in the case ofto endocomplexesthe PBE/3ζ approximation, with SWCNTs the of smallvalue diameter; of ΔG298 ≠TS for co ,rrespondscluster C5 Hto12 the@(5,5) eclipsed with eclipsed form. According to the PBE/3ζ approximation, the value of ∆G298 for cluster C5H12@(5,5) diameter 6.8, Å equals 11.1 kcal/mol, in comparison with 3.8 kcal/mol for the free molecule; the with diameter 6.8, Å equals 11.1 kcal/mol, in comparison with 3.8 kcal/mol for the free molecule; the corresponding value for the barrel-shapedbarrel-shaped SWCNT (7,0) withwith diameterdiameter 9.69.6 ÅÅ is 4.64.6 kcalkcal/mol./mol. In both cases, the guest molecule hashas aa negativenegative chargecharge ((−0.72 and −0.490.49 for for the the ground ground state) state) [138]. [138]. − − 2.5. Fluoroethanes The conformational behavior of fluoroethanes fluoroethanes in the SWCNT cavity is not different different from that observed for ethane itself: in in the case of a smallsmall nanotube diameter, the preferredpreferred conformationconformation corresponds to the eclipsed form. Its relative stability varies from 0.8 to 2.3 kcalkcal/mol/mol (Figure5 5 and and Table2 2).). AnAn increaseincrease inin nanotubenanotube diameterdiameter leadsleads toto thethe preferencepreference forfor aa staggeredstaggered formform that,that, however, remains less stablestable thanthan forfor thethe freefree moleculemolecule [[139–143].139–143].

FigureFigure 5.5. ConformationalConformational equilibriumequilibrium inin clustercluster CC22F66@(5,5). Adapted Adapted with with modification modiﬁcation [143]. [143].

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Table 2. Energetical and structural parameters of ﬂuoroethanes (PBE/3ζ).

, Form ∆G 298 (kcal/mol) rC–C (Å) OC–C Charge Reference

C2H5F Staggered 0 1.514 1.03 0 [94,139,140] Eclipsed 3.1 (exp. 3.31) 1.530 1.01 0

C2H5F@(4,4) Staggered 0.8 1.487 0.68 0.19 − [140] Eclipsed 0 1.485 0.73 0.16 − C2H5F@(5,5) Staggered 0 1.508 0.96 0.41 − [140] Eclipsed 2.4 1.522 0.97 0.40 − CH3–CF3 Staggered 0 1.507 1.01 0 [139,141,142] Eclipsed 2.7 (exp. 3.17) 1.521 1.01 0

CH3 CF3@(4,4) − Staggered 1.2 1.505 0.94 0.22 − [142] Eclipsed 0 1.518 0.92 0.20 − CH3 CF3@(5,5) − Staggered 0 1.501 0.99 0.27 − [142] Eclipsed 2.0 1.513 0.98 0.26 − CF3 CF3 − Staggered 0 1.565 0.88 0 [139,143] Eclipsed 4.5 (exp. 4.30) 1.600 0.88 0

CF3 CF3@(5,5) − Staggered 2.3 1.562 0.88 0.15 − [143] Eclipsed 0 1.587 0.86 0.16 − CF3 CF3@(6,6) − Staggered 0 1.539 0.89 0.13 − [143] Eclipsed 4.2 1.572 0.87 0.13 −

In all cases, the guest molecule has a negative electric charge; besides that, cluster C2H5F@(4,4) is characterized by a reduced value of Mulliken C–C bond order (OC–C).

2.6. Ammonia Borane Ammonia borane (borazane) H B NH has an ethane-like structure; according to microwave 3 ← 3 measurements, the barrier to internal rotation about the B N bond equals 2.008–2.047 kcal/mol [144]. ← The main reasons for the relative stability of staggered form have been discussed in [145]. On the other hand, ammonia borane is a valuable source of hydrogen [146,147]. The creation of eﬀective hydrogen storage is connected with nano-encapsulated H B NH [148,149]. In particular, such systems include 3 ← 3 ammonia borane clusters with polypyrrol nanotubes [150]. In this connection, the investigation of borazane endocomplexes is an important direction in nanochemistry. The conformational properties of ammonia borane in the SWCNT cavity are very close to those of ethane. Clusters H3B NH3@(4,4), H3B NH3@(7,0) and H3B NH3@(8,0) demonstrate the preference ← ← ← , for the eclipsed form; its relative stability reaches 0.4–0.8 kcal/mol (∆G 298). In some cases, both forms are degenerate in energy [151]. A comparison of free and encapsulated molecules of H B NH (Figure6) demonstrates that 3 ← 3 boron atomic charge in the cluster has changed its sign and Mulliken B N bond order increased almost ← twofold; all of this indicates the signiﬁcant redistribution of electron density in the guest molecule. Molecules 2020,, 25,, 2437x FOR PEER REVIEW 98 of of 3739

Figure 6. Parameters of free and encapsulated ammonia borane. Adapted with modification [151]. Figure 6. Parameters of free and encapsulated ammonia borane. Adapted with modification [151]. 2.7. Disilane and Digermane 2.7. Disilane and Digermane Different computational approaches confirmed hindered rotation in disilane, its staggered form , beingDifferent more stable computational than the eclipsed approaches one [100 confirmed,152–154]. hindered The calculated rotation rotational in disilane, barrier its (PBE staggered/3ζ, ∆G form298, 1.3being kcal more/mol [stable155]) isthan very the close eclipsed to the oneone experimentally [100,152–154]. measuredThe calculated (1.26 kcalrotational/mol [156 barrier]). At the(PBE/3 sameζ, ≠ time,ΔG 298 computer, 1.3 kcal/mol simulation [155]) is demonstrates very close to that the theone heightexperimentally of the barrier measured in complex (1.26 Sikcal/mol2H6@(8,0) [156]). is only At 0.4the kcalsame/mol time, in computer favor ofthe simulation staggered demonstrates form. In contrast that the to height ethane of clusters,the barrier the in Si–Si complex bond Si length2H6@(8,0) of encapsulatedis only 0.4 kcal/mol disilane in isfavor increased of the bystaggered 0.071–0.045 form. Å In in contrast comparison to ethane with theclusters, free molecule. the Si–Si bond The growth length , of theencapsulated nanotube diameter disilane inis theincreased case of clusterby 0.071–0.0 Si2H6@(6,6)45 Å in increases comparison the value with of the∆G free298 molecule.to 1.7 kcal /molThe (PBEgrowth/3ζ ,[of155 the]). nanotube diameter in the case of cluster Si2H6@(6,6) increases the value of ΔG≠298 to 1.7 kcal/molThe (PBE/3 experimentalζ, [155]). barrier of rotation about the Ge-Ge bond in digermane corresponds to 1.2 kcalThe/mol experimental [157]. On barrier the other of hand,rotation this about compound the Ge-Ge is widely bond in used digermane in epitaxial corresponds technology to for1.2 thekcal/mol creation [157]. of mono-On the or other polycrystalline hand, this thincompound films on is the widely surfaces used of in silicon epitaxial [158– technology161], tin [162 for], andthe germaniumcreation of mono- [163,164 or], polycrystalline with remarkable thin semiconducting films on the surfaces properties. of silicon In this [158–161], connection, tin endohedral [162], and nanocomplexesgermanium [163,164], containing with Ge remarkable2H6 are interesting semiconducti as anng important properties. component In this connection, in this process. endohedral nanocomplexesThe conformational containing behavior Ge2H6 are of digermane interesting in as cluster an important Ge2H6@(8,0) component demonstrates in this process. a preference for , the eclipsedThe conformational form (∆G 298 behavior0.8 kcal/ mol,of digermane in comparison in cluster with Ge 1.12H kcal6@(8,0)/mol demonstrates in favor of the a staggered preference form for ofthe the eclipsed free molecule, form (ΔG PBE≠298/ 30.8ζ)[ kcal/mol,165]. As inin thecomparison previous with case, 1.1 the kcal/mol encapsulated in favor molecule of the isstaggered characterized form byof athe 2% free growth molecule, in the lengthPBE/3 ofζ) Ge-Ge[165]. bondAs in and the a strongprevious negative case, electricthe encapsulated charge ( 1.37). molecule All other is − examinedcharacterized clusters—Ge by a 2% 2growthH6@(5,5), in Gethe2 Hlength6@(6,6) of and Ge-Ge Ge2 Hbond6@(7,7)—with and a strong a greater negative nanotube electric diameter charge , exhibit(−1.37). aAll preference other examined for the staggeredclusters—Ge conformation2H6@(5,5), Ge (∆2GH6@(6,6)298 1.1–1.5 and kcalGe2/Hmol)6@(7,7)—with and electric a greater charge (nanotube0.12– 0.97) diameter on the exhibit guest moleculea preference [165 for]. the staggered conformation (ΔG≠298 1.1–1.5 kcal/mol) and − − electricThus, charge the action(−0.12‒− of0.97) the force on the field guest inside molecule the nanocavity, [165]. understood as a combination of electronic and stericThus, requirements, the action of shifts the theforce conformational field inside equilibriathe nanocavity, of ethane understood and its analogs as a insidecombination nanotubes of ofelectronic relatively and small steric diameter requirements, (with the exceptionshifts the of conformational neopentane) to theequilibria eclipsed of form. ethane This and is accompanied its analogs byinside a significant nanotubes change of relatively in the centralsmall diameter bond length (with and thethe exception bond order. of neopentane) to the eclipsed form. This is accompanied by a significant change in the central bond length and the bond order. 3. Conformational Behavior of Other Acyclic Molecules in Nanotubes 3. Conformational Behavior of Other Acyclic Molecules in Nanotubes 3.1. Hydroxyborane 3.1. HydroxyboraneIn terms of structural chemistry, acyclic derivatives of boron and boronic acids are interesting becauseIn terms of the of partially structural double chemistry, nature acyclic of the derivatives B–O bond; of as boron a result, and their boronic preferred acids are conformation interesting correspondsbecause of the to thepartially planar double form [ 166nature,167 ].of The the rotation B-O bond; barrier as a lies result, within their 8.5–13.8 preferred kcal/ molconformation [168–170]. Accordingcorresponds to to the the PBEplanar/3ζ formapproximation, [166,167]. The the rota orthogonaltion barrier conformation—TS lies within 8.5–13.8 for kcal/mol the molecule [168–170]. of , hydroxyborane,According to the H2 B–OH—isPBE/3ζ approximation, less stable than the the planarorthogonal form (conformation—TS∆G 298) by 13.9 kcal for/mol the (Figure molecule7)[ 171 of]. , hydroxyborane,However, in H the2B-OH—is case of less cluster stable H2 thanB-OH@(6,0), the planar the form value (ΔG of≠298∆G) by298 13.9becomes kcal/mol only (Figure 3.8 kcal 7) [171]./mol (3.66 times lower); the increase in the SWCNT diameter, as in the case of H2B-OH@(6,6), leads to a higher barrier of rotation close to the free molecule (13.4 kcal/mol). The guest molecule in both cases is characterized by electric charge and—for cluster H2B-OH@(6,0)—by a 1.4% decrease in the length of the B–O bond [171].

Molecules 2020, 25, x FOR PEER REVIEW 9 of 39

Figure 6. Parameters of free and encapsulated ammonia borane. Adapted with modification [151].

2.7. Disilane and Digermane Different computational approaches confirmed hindered rotation in disilane, its staggered form being more stable than the eclipsed one [100,152–154]. The calculated rotational barrier (PBE/3ζ, ΔG≠298, 1.3 kcal/mol [155]) is very close to the one experimentally measured (1.26 kcal/mol [156]). At the same time, computer simulation demonstrates that the height of the barrier in complex Si2H6@(8,0) is only 0.4 kcal/mol in favor of the staggered form. In contrast to ethane clusters, the Si–Si bond length of encapsulated disilane is increased by 0.071–0.045 Å in comparison with the free molecule. The growth of the nanotube diameter in the case of cluster Si2H6@(6,6) increases the value of ΔG≠298 to 1.7 kcal/mol (PBE/3ζ, [155]). The experimental barrier of rotation about the Ge-Ge bond in digermane corresponds to 1.2 kcal/mol [157]. On the other hand, this compound is widely used in epitaxial technology for the creation of mono- or polycrystalline thin films on the surfaces of silicon [158–161], tin [162], and germanium [163,164], with remarkable semiconducting properties. In this connection, endohedral nanocomplexes containing Ge2H6 are interesting as an important component in this process. The conformational behavior of digermane in cluster Ge2H6@(8,0) demonstrates a preference for the eclipsed form (ΔG≠298 0.8 kcal/mol, in comparison with 1.1 kcal/mol in favor of the staggered form of the free molecule, PBE/3ζ) [165]. As in the previous case, the encapsulated molecule is characterized by a 2% growth in the length of Ge-Ge bond and a strong negative electric charge (−1.37). All other examined clusters—Ge2H6@(5,5), Ge2H6@(6,6) and Ge2H6@(7,7)—with a greater nanotube diameter exhibit a preference for the staggered conformation (ΔG≠298 1.1–1.5 kcal/mol) and electric charge (−0.12‒−0.97) on the guest molecule [165]. Thus, the action of the force field inside the nanocavity, understood as a combination of electronic and steric requirements, shifts the conformational equilibria of ethane and its analogs inside nanotubes of relatively small diameter (with the exception of neopentane) to the eclipsed form. This is accompanied by a significant change in the central bond length and the bond order.

3. Conformational Behavior of Other Acyclic Molecules in Nanotubes

3.1. Hydroxyborane In terms of structural chemistry, acyclic derivatives of boron and boronic acids are interesting because of the partially double nature of the B-O bond; as a result, their preferred conformation corresponds to the planar form [166,167]. The rotation barrier lies within 8.5–13.8 kcal/mol [168–170].

MoleculesAccording2020 ,to25 ,the 2437 PBE/3ζ approximation, the orthogonal conformation—TS for the molecule9 of of 37 Moleculeshydroxyborane, 2020, 25, x FOR H PEER2B-OH—is REVIEW less stable than the planar form (ΔG≠298) by 13.9 kcal/mol (Figure 7) [171].10 of 39

However, in the case of cluster H2B-OH@(6,0), the value of ΔG≠298 becomes only 3.8 kcal/mol (3.66 times lower); the increase in the SWCNT diameter, as in the case of H2B-OH@(6,6), leads to a higher barrier of rotation close to the free molecule (13.4 kcal/mol). The guest molecule in both cases is characterized by electric charge and—for cluster H2B-OH@(6,0)—by a 1.4% decrease in the length of the B-O bond [171]. Figure 7. Conformational equilibrium of hydroxybor hydroxyborane.ane. Adapted with modification modiﬁcation [[171].171]. 3.2. Diborane (4) 3.2. Diborane (4) A hypotheticalA hypothetical diborane diborane (4) (4) is thethe boron boron analog analog of ethylene.of ethylene. Due toDue the natureto the ofnature the boron–boron of the boron– boronbond, bond, it representsit represents a model a model system system with with non-classical non-classical multi-centered multi-centered bonds bonds [172,173 [172,173].]. The PES The of PES of thisthis compound contains contains three three stationary stationary points points that correspond that correspond to the structures to theA (C2vstructures symmetry), A (С2v symmetry),B (D2d), B and (D2d),C (D2h) and [ 174C (D2h)] (Figure [174]8). (Figure 8).

FigureFigure 8. Forms 8. Forms (A ()–(A–CC)) of of diborane. Adapted Adapted with with modiﬁcation modification [175 [175].].

The first matches the global minimum; the orthogonal conformer B is less stable than A by The first matches the global minimum; the orthogonal conformer B is less stable than A by 2.9 2.9 kcal/mol [CCSD(T)/6-311++G (d,p)] [174] or by 3.0 kcal/mol (PBE/3ζ [175]). It turns into its inverted kcal/mol [CCSD(T)/6-311++G (d,p)] [174] or by 3.0 kcal/mol (PBE/3ζ [175]). It turns into its inverted form (B*) via the TS—a planar structure C with a barrier of 17.9 kcal/mol [175]. form (B*)All via examined the TS—a SWCNT planar clusters structure demonstrate С with a a barrier significant of 17.9 shortening kcal/mol of the [175]. B–B bond length in all formsAll examined and a relatively SWCNT high clusters negative demonstrate electric charge a on significant the guest molecule. shortening Besides of the that, В form–В bondA belongs length in all formsto the and main a minimumrelatively onhigh the negative PES, but dielectricfferences charge in energy on the between guest Amolecule.and B increase Besides 2–4.5 that, times. form A belongsThe heightto the ofmain the rotationminimum barrier on aboutthe PES, the B-Bbut bond differences in endocomplexes in energy is between lowered comparedA and B withincrease a free 2–4.5 times.molecule; The height for clusters of the rotation B2H4@(4,4) barrier and B about2H4@(7,0), the B-B it lies bond in the in interval endocomplexes 3.1–5.7 kcal is/mol. lowered The growth compared withof a thefree nanotube molecule; diameter for clusters in complexes B2H4@(4,4) B2H4 @(5,5)and B and2H4@(7,0), B2H4@(8,0) it lies leads in the to an interval increase 3.1–5.7 in this valuekcal/mol. (14.1–17.4 kcal mol relative to the form B)[175]. The growth of the/ nanotube diameter in complexes B2H4@(5,5) and B2H4@(8,0) leads to an increase in this value3.3. Dialane (14.1–17.4 (4) kcal/mol relative to the form B) [175].

3.3. DialaneDialane (4) (4), Al2H4, in contrast to diborane, really exists in two forms: salt-like structure A and orthogonal B [176,177]. The ﬁrst corresponds to the global minimum on the PES. The last may be convertedDialane (4), into Al invertomer2H4, in contrastB* via TS—planarto diborane, conformation really existsC (Figure in two9 )[forms:178]. salt-like structure A and orthogonalAccording B [176,177]. to the resultsThe first of computer corresponds simulation, to the the global conformational minimum equilibrium on the PES. between The Blastand mayC be convertedforms ininto clusters invertomer Al2H4@(5,5), B* via Al 2TS—planarH4@(8,0) and conformation Al2H4@(9,0), contrary C (Figure to the 9)free [178]. molecule, is completely , , shifted to the planar form C: the appropriate ∆G298 values lie in the interval 2.3–4.5 kcal/mol; ∆E0 corresponds to 1.4–4.2 kcal/mol (Figure 10). In all cases, the guest molecule has a strong negative electric charge [178]. The authors [107] suggested a decisive role of all seven molecular orbitals in the origin of the rotational barrier in ethane. But the common number of MO’s in nanoclusters is very high. That is why we analyzed only HOMO and LUMO orbitals of dialane (4), as well as SWCNT (8,0) and cluster Al2H4@(8,0), using PBE/3ζ and PBE/cc-pVDZ approximations [178] (Figure 11).

Molecules 2020, 25, 2437 10 of 37 Molecules 2020, 25, x FOR PEER REVIEW 11 of 39

The main diﬀerence between the free molecule and cluster is connected with a notable increase in the HOMO energy in the last case; this is also true for the nanotube itself. Thank to this, the energy gap ∆E for complex Al2H4@(8,0) is decreased by 28–34 times compared to free dialane. According to the molecular diagrams, HOMO is localized on the carbon atoms of nanotubes; the highest-energy MO connected with the guest molecule (the planar form of dialane) corresponds to the HOMO-3 level with the energy of 5.3350 eV (PBE/3ζ). Similar results were obtained using PBE/cc-pVDZ approximation. − All this points to the signiﬁcant transformation of the orbital structure of the endocomplex, which mayMolecules be a2020 possible, 25, x FOR reason PEER forREVIEW the change in conformational behavior of the guest molecule. 11 of 39

Figure 9. Forms of dialane, Al2H4. Adapted with modification [178].

According to the results of computer simulation, the conformational equilibrium between B and C forms in clusters Al2H4@(5,5), Al2H4@(8,0) and Al2H4@(9,0), contrary to the free molecule, is completely shifted to the planar form C: the appropriate ΔG298≠ values lie in the interval 2.3–4.5 kcal/mol; ΔE0≠ corresponds to 1.4–4.2 kcal/mol (Figure 10). In all cases, the guest molecule has a strong negative electric charge [178]. Figure 9. Forms of dialane, Al H . Adapted with modiﬁcation [178]. Figure 9. Forms of dialane, Al22H4. Adapted with modification [178].

Figure 10. Relative energy of dialane Al H as a function of the H–Al–Al–H torsion angle τ (0 K). Figure 10. Relative energy of dialane Al2H42 as4 a function of the H–Al–Al–H torsion angle τ (0 K). (a) (a) free molecule; (b) cluster Al2H4@(5,5). Adapted with modiﬁcation [178]. free molecule; (b) cluster Al2H4@(5,5). Adapted with modification [178].

The authors [107] suggested a decisive role of all seven molecular orbitals in the origin of the rotational barrier in ethane. But the common number of MO’s in nanoclusters is very high. That is Figure 10. Relative energy of dialane Al2H4 as a function of the H–Al–Al–H torsion angle τ (0 K). (a) why we analyzed only HOMO and LUMO orbitals of dialane (4), as well as SWCNT (8,0) and cluster free molecule; (b) cluster Al2H4@(5,5). Adapted with modification [178]. Al2H4@(8,0), using PBE/3ζ and PBE/cc-pVDZ approximations [178] (Figure 11). The mainThe authors difference [107] between suggested the a decisivefree molecule role of andall seven cluster molecular is connected orbitals with in the a notable origin of increase the in therotational HOMO energybarrier in ethane.the last But case; the this common is also number true for of the MO’s nanotube in nanoclusters itself. Thank is very to high.this, theThat energy is gap ΔЕwhy for we complex analyzed Al only2H4 @(8,0)HOMO is and decreased LUMO orbitals by 28–34 of dialane times co(4),mpared as well asto SWCNTfree dialane. (8,0) and According cluster to the molecularAl2H4@(8,0), diagrams, using PBE/3 HOMOζ and PBE/cc-pVDZis localized on approximations the carbon atoms [178] (Figureof nanotubes; 11). the highest-energy MO connectedThe main with difference the guest between molecule the (the free planar molecule fo rmand of cluster dialane) is connected corresponds with to a notablethe HOMO-3 increase level with inthe the energyHOMO energyof –5.3350 in the lasteV case;(PBE/3 thisζ is). alsoSimilar true for results the nanotube were itself.obtained Thank using to this, PBE/cc-pVDZthe energy approximation.gap ΔЕ for complex Al2H4@(8,0) is decreased by 28–34 times compared to free dialane. According to the molecular diagrams, HOMO is localized on the carbon atoms of nanotubes; the highest-energy MO connected with the guest molecule (the planar form of dialane) corresponds to the HOMO-3 level with the energy of –5.3350 eV (PBE/3ζ). Similar results were obtained using PBE/cc-pVDZ approximation.

Molecules 2020, 25, x FOR PEER REVIEW 12 of 39

Molecules 2020, 25, 2437 11 of 37 Molecules 2020, 25, x FOR PEER REVIEW 12 of 39

Figure 11. Differences in the energy of HOMO-LUMO of dialane (PBE/3ζ). Adapted with modification [178].

All this points to the significant transformation of the orbital structure of the endocomplex, which may be a possible reason for the change in conformational behavior of the guest. molecule. Figure 11. Differences in the energy of HOMO-LUMO of dialane (PBE/3ζ). Adapted with modification [178]. 3.4. HydrazineFigure 11. Differences in the energy of HOMO-LUMO of dialane (PBE/3ζ). Adapted with 3.4. Hydrazinemodification [178]. Hydrazine, which is widely used in organic synthesis and in medicine, demonstrates the influenceHydrazine, of unshared which iselectron widely usedpairs inon organic the rotation synthesis barrier andin about medicine, N–Ndemonstrates bond. Its conformational the inﬂuence All this points to the significant transformation of the orbital structure of the endocomplex, ofequilibrium unshared electronincludes pairsgauche-form on the rotation A (global barrier minimum), about N–N staggered bond. Itsform conformational B (local TS) and equilibrium eclipsed which may be a possible reason for the change in conformational behavior of the guest molecule. includesform C (main gauche-form TS); theA torsion(global angle minimum), τ in conformer staggered A form equalsB (local 91.5° TS)[179–182]. and eclipsed The energy form C differences(main TS); the torsion angle τ in conformer A equals 91.5 ≠[179–182]. The energy diﬀerences between conformations between3.4. Hydrazine conformations A-B and A-C (ΔG298◦ ) are 1.8 kcal/mol and 7.9 kcal/mol respectively (PBE/3ζ, , AScheme-B and 1)A -[183].C (∆G 298 ) are 1.8 kcal/mol and 7.9 kcal/mol respectively (PBE/3ζ, Scheme1)[183]. Hydrazine, which is widely used in organic synthesis and in medicine, demonstrates the influence of unshared electron pairs on the rotation barrier about N–N bond. Its conformational equilibrium includes gauche-form A (global minimum), staggered form B (local TS) and eclipsed form C (main TS); the torsion angle τ in conformer A equals 91.5° [179–182]. The energy differences between conformations A-B and A-C (ΔG298≠) are 1.8 kcal/mol and 7.9 kcal/mol respectively (PBE/3ζ, Scheme 1) [183].

SchemeScheme 1. 1. FormsForms ( (AA)–(–CC)) of of hydrazine. hydrazine.

The force ﬁeld of SWCNTs substantively changes the conformational behavior of guest molecule (PBE/3ζ)[183]. Clusters N H @(4,4) demonstrate a signiﬁcant decline (to 4.6 kcal/mol) of ∆G , 2 4 298 (forms A-C). In the case of SWCNTs (4,4) and (6,0), the main minimum of hydrazine belongs to the , conformer B with ∆G298 B-C 1.1–2.2 kcal/mol. The increase in the diameter of the nanotube, as for Scheme 1. Forms (A)–(C) of hydrazine.

Molecules 2020, 25, x FOR PEER REVIEW 13 of 39

The force field of SWCNTs substantively changes the conformational behavior of guest molecule (PBE/3ζ) [183]. Clusters N2H4@(4,4) demonstrate a significant decline (to 4.6 kcal/mol) of ΔG298≠ (forms A-C). In the case of SWCNTs (4,4) and (6,0), the main minimum of hydrazine belongs to the conformer B with ΔG298≠ B-C 1.1–2.2 kcal/mol. The increase in the diameter of the nanotube, as for endocomplex N2H4@(6,6), results in an equilibrium close to the free hydrazine. In all cases, the guest molecule has a positive or negative electric charge [183].

3.5. Methanol and Methanethiol Methanol and methanethiol are characterized by a hindered rotation with the potential barrier betweenMolecules 2020 gauche, 25, 2437 (A, minimum) and eclipsed (B, TS) forms at 1.07 and 1.27 kcal/mol respectively12 of 37 (Figure 12) [94,184]; according to PBE/3ζ approximation, the appropriate ΔG298≠ values are 1.0 and 1.2 kcal/mol [128,185]. However, in the cavity of SWCNT (6,0), their conformational behavior has significantlyendocomplex changed. N2H4@(6,6), results in an equilibrium close to the free hydrazine. In all cases, the guest molecule has a positive or negative electric charge [183]. In the case of cluster CH3OH@(6,0), minimum on the PES belongs not to the form A, which becomes3.5. Methanol the main and Methanethiol TS, but to the conformer C, with a torsion angle of HOCH 26.4° (PBE/3ζ, Figure 12). The main (A) and a local (B) TS are less stable by 0.27 and 0.03 kcal/mol respectively (ΔG298≠) [185].Methanol Endocluster and CH methanethiol3SH@(6,0) is are characterized characterized by bythe a torsion hindered angle rotation HSCH with 22.2° the and potential ΔG298≠ barriervalues forbetween A and gauche B forms (A of, minimum)2.1 and 0.6 andkcal/mol. eclipsed In both (B, TS) cases, forms the atguest 1.07 molecule and 1.27 has kcal a/mol positive respectively electric , charge(Figure (0.3–0.7). 12)[94,184 Again,]; according as in the to previous PBE/3ζ approximation,examples, all this the indicates appropriate the important∆G298 values role of are n-electron 1.0 and pairs1.2 kcal in/ molthe guest [128,185 molecule,]. However, affecting in the changes cavity in of its SWCNT conformational (6,0), their preference conformational outside behavior and inside has nanotubes.signiﬁcantly changed.

Figure 12. ConformationalConformational equilibrium of methan methanol.ol. Adapted Adapted with with modification modiﬁcation [185]. [185].

3.6. DimethylIn the case Ether of cluster CH3OH@(6,0), minimum on the PES belongs not to the form A, which becomes the main TS, but to the conformer C, with a torsion angle of HOCH 26.4◦ (PBE/3ζ, Figure 12). The molecule (CH3)2O belongs to the systems with two internal rotors; the experimental, barrier The main (A) and a local (B) TS are less stable by 0.27 and 0.03 kcal/mol respectively (∆G298 )[185]. −1 of rotation between A and B forms is 2.60 kcal/mol (near 900 cm ) (Figure 13) [186–189]., The origin Endocluster CH3SH@(6,0) is characterized by the torsion angle HSCH 22.2◦ and ∆G298 values for A and nature of the barrier, in particular the role of lone pairs, is widely discussed in the literature [190– and B forms of 2.1 and 0.6 kcal/mol. In both cases, the guest molecule has a positive electric charge 193]. However, in the SWCNT cavity, the conformational behavior of this compound is significantly (0.3–0.7). Again, as in the previous examples, all this indicates the important role of n-electron pairs in changed. In clusters (CH3)2O@(4,4), form A is not realized: during the optimization it converts to the the guest molecule, aﬀecting changes in its conformational preference outside and inside nanotubes. unusual conformer C, which corresponds to the minimum and cannot exist outside the tube, turning back3.6. Dimethyl into form Ether A (Figure 13) [194]. According to the PBE/3ζ, approximation the valence angle COC in the free molecule of dimethyl ether (form A) is 111.2°, which is very close to the experimental value The molecule (CH3)2O belongs to the systems with two internal rotors; the experimental barrier of (111.5° [188]). However, for form C in cluster (CH3)2O@(4,4),1 it rises to 127–130° [194]. Meanwhile, rotation between A and B forms is 2.60 kcal/mol (near 900 cm− ) (Figure 13)[186–189]. The origin and form B in this case also corresponds to the TS; the value of ΔG298≠ B-C (1.3–1.9 kcal/mol) is lower than nature of the barrier, in particular the role of lone pairs, is widely discussed in the literature [190–193]. that for the transition A-B of the free molecule (2.5 kcal/mol). However, in the SWCNT cavity, the conformational behavior of this compound is signiﬁcantly changed. In clusters (CH3)2O@(4,4), form A is not realized: during the optimization it converts to the unusual conformer C, which corresponds to the minimum and cannot exist outside the tube, turning back into form A (Figure 13)[194]. According to the PBE/3ζ, approximation the valence angle COC in the free molecule of dimethyl ether (form A) is 111.2◦, which is very close to the experimental value (111.5◦ [188]). However, for form C in cluster (CH3)2O@(4,4), it rises to 127–130◦ [194]. Meanwhile, , form B in this case also corresponds to the TS; the value of ∆G298 B-C (1.3–1.9 kcal/mol) is lower than that for the transition A-B of the free molecule (2.5 kcal/mol). In the case of endocomplex (CH3)2O@(6,0), the angle COC in conformer C rises to 180◦ and the molecule takes the form of a rod with an eclipsed conformation of methyl groups (Figure 13). The appropriate transition state corresponds to the rod-shaped form, with a staggered conformation of , methyl groups and ∆G298 3.5 kcal/mol. In all cases, the guest molecule has positive or negative charge and shortened C-O bonds [194]. Molecules 2020, 25, x FOR PEER REVIEW 14 of 39

Molecules 2020, 25, 2437 13 of 37 Molecules 2020, 25, x FOR PEER REVIEW 14 of 39

Figure 13. Conformations of dimethyl ether in the free state and in clusters with SWCNTs. Adapted with modification [194].

In the case of endocomplex (CH3)2O@(6,0), the angle COC in conformer C rises to 180° and the molecule takes the form of a rod with an eclipsed conformation of methyl groups (Figure 13). The appropriate transition state corresponds to the rod-shaped form, with a staggered conformation of methyl groups and ΔG298≠ 3.5 kcal/mol. Figure 13.13. Conformations of dimethyl ether in the free state and in clustersclusters withwith SWCNTs.SWCNTs. Adapted In all cases, the guest molecule has positive or negative charge and shortened C-O bonds [194]. with modiﬁcationmodification [[194].194]. 4. Conformational Properties of Simple Molecules in Fullerenes In the case of endocomplex (CH3)2O@(6,0), the angle COC in conformer C rises to 180° and the molecule takes the form of a rod with an eclipsed conformation of methyl groups (Figure 13). The 4.1. Ethane and Its Analogs appropriate transition state corresponds to the rod-shaped form, with a staggered conformation of methylThe groups conformational and ΔG298 ≠ behavior 3.5 kcal/mol. of ethane inside fullerenesfullerenes of small diameter was studied on the exampleIn all ofof cases, clustercluster the CC2 2guestH66@Si molecule20 [195].[195]. PES, PES,has inpositive in this this case, case, or negativecontains contains chargetree tree stationary stationary and shortened points: C-Opartially partially bonds eclipsed [194]. AA (global(global minimum),minimum), eclipsedeclipsed BB (main(main TS)TS) andand staggeredstaggered CC (local(local TS)TS) (Figure(Figure 14 14).). 4. Conformational Properties of Simple Molecules in Fullerenes

4.1. Ethane and Its Analogs The conformational behavior of ethane inside fullerenes of small diameter was studied on the example of cluster C2H6@Si20 [195]. PES, in this case, contains tree stationary points: partially eclipsed A (global minimum), eclipsed B (main TS) and staggered C (local TS) (Figure 14).

Figure 14.14. ConformationalConformational equilibriumequilibrium ofof thethe guestguest moleculemolecule in in cluster cluster C C2H2H6@Si6@Si2020.. Adapted withwith modiﬁcationmodification [[195].195].

, Diﬀerences in energy between these forms (∆G298 , PBE/3ζ) account for 1.2 (A-B) and 0.4 (A-C) kcal/mol. Hence, compared to the free ethane, the internal rotation barrier has become two times lower. The guest molecule possesses a strong positive electric charge (1.3–1.4) and is characterized by shortened C–C bond length and a decline in its Mulliken bond order [195]. Figure 14. Conformational equilibrium of the guest molecule in cluster C2H6@Si20. Adapted with Endoclusters of ethane-like molecules with fullerenes C60,C70,C80 and their heteroanalogs, in contrastmodification to the [195]. previous example, are characterized by only two stationary points on the PES:

Molecules 2020, 25, 2437 14 of 37 staggered and eclipsed forms. The first corresponds to the minimum and the second to the TS [196–202]. Ethane inside the C60 cavity exhibits a higher barrier of internal rotation and shorter C–C bond length in comparison with the free molecule [196]. The same is true of its analogs; in some cases, the height of the barrier grows by more than threefold (Table3). This increase in diameter of fullerenes (C 60, , C70,C80 and Si60) naturally leads to the decrease in ∆G298 . In the case of B-N fullerenes (their peculiarities have been discussed in [131]) this dependence is more mixed. In particular, in a series of , endocomplexes, C2F6@C60,C2F6@C12B24N24 and C2F6@B36N24, the value of ∆G298 initially decreases and then increases, while it is still lower than that of the C60 cluster [198]. This influence of chemical composition is also valid for the H B NH endocomplexes with fullerenes containing both 60 and 3 ← 3 80 atoms in their shells [201]. Meanwhile, in series of C2F6 clusters with 80-atomic fullerenes, the barrier for the (BNC)80 system is, vice versa, higher than those of C80 and (BN)80 complexes (Table3). All guest molecules have electric charge; in the case of C5H12 clusters, it is rather large and changes the sign for different fullerenes [200]. Mulliken bond order for the central bond (O), with the exception of several H B NH endocomplexes, depends little on the size and chemical composition of the fullerenes. 3 ← 3 Table 3. Energetical and structural parameters of ethane and its analogs in fullerenes (PBE/3ζ).

, 1 1 1 Cluster; ∆G 298 (kcal/mol) rC–C (Å) O Charge Reference C H @C ; 3.3 (2,5) 1.465 (1.531) 1.12 (1.00) 0.47 [196] 2 6 60 − C2F6@C60; 15.1 (4,6) 1.374 (1.565) 0.86 (0.88) 0.20 [197,198]

C2F6@C12B24N24; 6.5 1.405 0.83 0.46 [198]

C2F6@B36N24; 8.2 1.464 0.86 0.48 [198] C F @C ; 7.2 1.477 0.89 0.27 [197,198] 2 6 80 − C2F6@C14B33N33; 10.0 1.493 0.90 0.15 [198]

C2F6@B47N33; 7.6 1.507 0.92 0.15 [198] C Cl @C ; 43.5 (13,8) 1.431 (1.590) 0.98 (1.06) 0.22 [199] 2 6 80 − C5H12@C60; 10.7 (3,8) 1.366 (1.539) 0.86 (1.00) 2.07 [200] C H @C ; 8.3 1.459 0.86 1.27 [200] 5 12 80 − H B NH @C ; 4.4 (2,0) 1.522 (1.652) 0.43 (0.65) 0.71 [201] 3 ← 3 60 − H B NH @C B N ; 1.5 1.544 0.54 0.79 [201] 3 ← 3 12 24 24 − H B NH @B N ; 2.3 1.558 0.48 0.22 [201] 3 ← 3 36 24 − H B NH @C ; 2.1 1.595 0.62 0.90 [201] 3 ← 3 70 − H B NH @B N ; 1.8 1.610 0.72 0.11 [201] 3 ← 3 41 29 − H B NH @C ; 1.8 1.601 0.58 0.64 [201] 3 ← 3 80 − H B NH @C B N ; 1.1 1.605 0.57 0.11 [201] 3 ← 3 14 33 33 − H B NH @B N ; 1.6 1.618 0.64 0.06 [201] 3 ← 3 47 33 − Si H @Si ; 1.0 (1,3) 2.351 (3.355) 0.97 (1.00) 0.12 [202] 2 6 60 − Si H @C ; 2.4 2.184 1.52 1.16 [202] 2 6 80 − Si2H6@B47N33; 1.6 2.252 1.08 0.01 [202] 1 Values in round brackets correspond to the parameters for the free molecules (rC–C, O and charge were given for the staggered form).

4.2. Methanethiol The conformational equilibrium of methanethiol in endocomplexes with fullerenes, as for the free molecule, is characterized by gauche (minimum) and eclipsed (TS) forms (see part 3.5). But the height , of the rotational barrier about the C-S bond (∆G298 ), in this case, is increased: 2.0 and 2.7 kcal/mol for Molecules 2020, 25, x FOR PEER REVIEW 16 of 39 Molecules 2020, 25, x FOR PEER REVIEW 16 of 39 height of the rotational barrier about the C-S bond (ΔG298≠), in this case, is increased: 2.0 and 2.7 height of the rotational barrier about the C-S bond (ΔG298≠), in this case, is increased: 2.0 and 2.7 kcal/molMolecules 2020 for, 25the, 2437 clusters CH3SH@C60 and CH3SH@C80, respectively, in comparison with 1.2 kcal/mol15 of 37 kcal/mol for the clusters CH3SH@C60 and CH3SH@C80, respectively, in comparison with 1.2 kcal/mol forfor thethe freefree moleculemolecule (PBE/3(PBE/3ζζ)) [203].[203]. AsAs inin previousprevious cases,cases, thethe guestguest moleculemolecule hashas aa certaincertain electricelectric charge (−0.5). thecharge clusters (−0.5). CH 3SH@C60 and CH3SH@C80, respectively, in comparison with 1.2 kcal/mol for the free molecule (PBE/3ζ)[203]. As in previous cases, the guest molecule has a certain electric charge ( 0.5). 5.5. ConformationalConformational BehaviorBehavior ofof SaturatedSaturated CyclicCyclic MoleculesMolecules insideinside NanotubesNanotubes andand FullerenesFullerenes− 5. Conformational Behavior of Saturated Cyclic Molecules inside Nanotubes and Fullerenes ThereThere areare veryvery fewfew examplesexamples devoteddevoted toto thethe behaviorbehavior ofof saturatedsaturated cycliccyclic molecules,molecules, inin particular,particular, cyclohexanecyclohexaneThere are [33][33] very andand few octasiloxaneoctasiloxane examples devoted[27],[27], insideinside to the SWCNTs.SWCNTs. behavior TheseThese of saturated areare largelylargely cyclic focusedfocused molecules, onon thethe in orientationorientation particular, ofcyclohexaneof thethe guestguest moleculemolecule [33] and octasiloxane asas aa wholewhole inin [27 thethe], inside nanocavity.nanocavity. SWCNTs. ItIt shouldshould These arebebe noted,noted, largely however,however, focused on thatthat the inin orientation viewview ofof thethe of structuralthestructural guest molecule transformationstransformations as a whole ofof in theacyclicacyclic nanocavity. moleculesmolecules It should thatthat be werewere noted, discusseddiscussed however, thatinin previousprevious in view of sections,sections, the structural thethe conformationaltransformationsconformational behaviorbehavior of acyclic ofof molecules cycliccyclic systemssystems that were insideinside discussed nanoobjectsnanoobjects in previous alsoalso hashas sections,aa numbernumber the ofof conformationaldistinguishingdistinguishing features.behaviorfeatures. of cyclic systems inside nanoobjects also has a number of distinguishing features.

5.1.5.1. CyclohexaneCyclohexane inin NanotubesNanotubes ItIt is is well well known known that, that, atat usualusual temperatures,temperatures, moleculesmolecules of of cyclohexanecyclohexane exist exist in in conformationalconformational equilibriumequilibrium betweenbetweenbetween chair chairchair (C, (C,(C, main mainmain minimum) minimum)minimum) and twist anandd (Tw, twisttwist local (Tw,(Tw, minimum) locallocal minimum)minimum) forms; the TSforms;forms; corresponds thethe TSTS correspondstocorresponds the half-chair toto thethe conformation half-chairhalf-chair conformationconformation (Scheme2)[94 (Scheme(Scheme]. 2)2) [94].[94].

C TS C TS TwTw

Scheme 2. Conformational equilibrium of free cyclohexane. Scheme 2. Conformational equilibrium of free cyclohexane.

The conformational behavior of cyclohexanecyclohexane in thethe SWCNTSWCNT clustercluster CC6H 12@(8,0)@(8,0) is is characterized characterized The conformational behavior of cyclohexane in the SWCNT cluster C66H1212@(8,0) is characterized byby the the absence absence of of a a Tw-form: Tw-form: the the C-conformer C-conformer directly directly converts converts into into its its invertomer invertomer C* C* over over TS TS that that correspondscorresponds toto the the conformation conformation closeclose toto the the fla ﬂattenedflattenedttened semi-planar semi-planar form; form; thethe height height of of the the barrier barrier ≠, (Δ∆G298 , ,PBE/3 PBE/3ζζ, ,10.4 10.4 kcal/mol) kcal/mol) isisvery very similar similar to to that that for for the the free free cyclohexane cyclohexane (10.5 (10.5 kcal/ mol).kcal/mol). The guest The (ΔG298298≠, PBE/3ζ, 10.4 kcal/mol) is very similar to that for the free cyclohexane (10.5 kcal/mol). The guestmoleculeguest moleculemolecule has a positivehashas aa positivepositive charge chargecharge (0.62) (0.62) and(0.62) is andand oriented isis orientedoriented in the inin direction thethe directiondirection perpendicular peperpendicularrpendicular to the to axisto thethe of axisaxis the ofnanotubeof thethe nanotubenanotube [204] (Figure [204][204] (Figure(Figure 15). 15).15).

Figure 15. Conformational equilibrium of cyclohexane in cluster C H @(8,0). Adapted with Figure 15. Conformational equilibrium of cyclohexane in cluster C6 6H1212@(8,0). Adapted with modiﬁcationFigure 15. Conformational [204]. equilibrium of cyclohexane in cluster C6H12@(8,0). Adapted with modification [204]. modification [204].

The conformational behavior of cyclohexane in cluster C6H12@(5,5) is the same, except that TS in The conformational behavior of cyclohexane in cluster C6H12@(5,5) is the same, except that TS in this caseThe correspondsconformational to thebehavior Tw-form, of cyclohexane the height of in the cluster barrier C6H is12 6.8@(5,5) kcal is/mol the andsame, the except guest that molecule TS in this case corresponds to the Tw-form, the height of the barrier is 6.8 kcal/mol and the guest molecule hasthis acase negative corresponds charge to ( 0.50)the Tw-for [204].m, the height of the barrier is 6.8 kcal/mol and the guest molecule hashas aa negativenegative chargecharge ((−−0.50)0.50) [204].[204]. 5.2. 1,3-Dioxane in Nanotubes It is known that 1,3-dioxanes—very attractive heteroanalogs of cyclohexane—belong to the classical objects of conformational analysis [94]. Besides that, due to their wide range of pharmacological

Molecules 2020, 25, x FOR PEER REVIEW 17 of 39 Molecules 2020, 25, x FOR PEER REVIEW 17 of 39 5.2. 1,3-Dioxane in Nanotubes 5.2. 1,3-Dioxane in Nanotubes MoleculesIt is2020 known, 25, 2437 that 1,3-dioxanes—very attractive heteroanalogs of cyclohexane—belong to16 ofthe 37 It is known that 1,3-dioxanes—very attractive heteroanalogs of cyclohexane—belong to the classical objects of conformational analysis [94]. Besides that, due to their wide range of classical objects of conformational analysis [94]. Besides that, due to their wide range of pharmacological action, they may be used for the creation of new drugs [205,206] and also as reagents pharmacologicalaction, they may action, be used they for may the creation be used offor new the creation drugs [205 of ,new206] drugs and also [205,206] as reagents and also in ﬁne as reagents organic in fine organic synthesis [207–211]. All this makes it relevant to consider the conformational insynthesis fine organic [207–211 synthesis]. All this [207–211]. makesit All relevant this makes to consider it relevant the conformational to consider the properties conformational of these properties of these compounds inside nanotubes, from the perspectives of nanoreactors [68–75] and propertiescompounds of insidethese compounds nanotubes, inside from thenanotubes, perspectives from the of nanoreactorsperspectives of [68 nanoreactors–75] and drug [68–75] delivery and drug delivery systems [15,19]. drugsystems delivery [15,19 systems]. [15,19]. TheThe PES PES of unsubstituted 1,3-dioxane, C 4HH8OO2, ,contains contains tree tree minima minima (C—the (C—the main, main, 2,5-Tw 2,5-Tw and and The PES of unsubstituted 1,3-dioxane, C44H8O22, contains tree minima (C—the main, 2,5-Tw and 1,4-Tw-forms—the local) (Scheme 3) [94,212]. 1,4-Tw-forms—the local)local) (Scheme(Scheme3 3))[ 94[94,212].,212].

O O O O O O O C O C 2,5-Tw 2,5-Tw

O O O O O O O O 1,4-Tw 1,4-Tw C* C* Scheme 3. Conformational equilibrium of free 1,3-dioxane. Scheme 3. Conformational equilibrium of free 1,3-dioxane.

However,However, in a SWCNT cavity of small diameter (≤8.48.4 Å Å),), the the relative relative population population of of these these forms forms However, in a SWCNT cavity of small diameter (≤≤8.4 Å), the relative population of these forms significantlysignificantly changes. changes. In In the the case case of cluster C4HH88OO22@(6,6),@(6,6), the the 1,4-Tw 1,4-Tw conformer conformer is is not not realized, realized, and and significantly changes. In the case of cluster C4H8O2@(6,6), the 1,4-Tw conformer is not realized, and 0 0 PESPES containscontains only only C (mainC (main minimum) minimum) and 2,5-Tw-formsand 2,5-Tw-forms with ∆G with298 3.1 ΔG kcal298 / mol,3.1 whichkcal/mol, is significantly which is PES contains only C (main minimum) and 2,5-Tw-forms with ΔG2980 3.1 kcal/mol, which is significantlylower than for lower free 1,3-dioxanethan for free (5.0 1,3-dioxane kcal/mol). (5.0 In the kcal/mol). case of clustersIn the case C4H of8O clusters2@(5,5) andC4H C8O4H2@(5,5)8O2@(8,0), and significantly lower than for free 1,3-dioxane (5.0 kcal/mol). In the case of clusters C4H8O2@(5,5) and Cthe4H8 mainO2@(8,0), minima the main correspond minima to correspond the 2,5-Tw-conformer, to the 2,5-Tw-conformer, and are 3.0 and and 0.3 are kcal 3.0 /andmol, 0.3 respectively, kcal/mol, C4H8O2@(8,0), the main minima correspond to the 2,5-Tw-conformer, and are 3.0 and 0.3 kcal/mol, respectively, more stable than the C-form; the last remains only as a local minimum. At the same respectively,more stable than more the stable C-form; than the the last C-form; remains the only last as aremains local minimum. only as a At local the sameminimum. time, theAt the barrier same of , ≠ time,interconversion the barrier (of∆ Ginterconversion298 ) is reduced (Δ byG298 up) is to reduced 5.1 kcal/ molby up in to comparison 5.1 kcal/mol with in comparison 9.7 kcal/mol with for free9.7 time, the barrier of interconversion (ΔG298≠) is reduced by up to 5.1 kcal/mol in comparison with 9.7 kcal/mol1,3-dioxane for (PBEfree /1,3-dioxane3ζ)[213]. Cluster (PBE/3 Cζ4)H [213].8O2@(7,0) Cluster demonstrates C4H8O2@(7,0) the demonstrates presence of only the one presence form—2,5-Tw; of only kcal/mol for free 1,3-dioxane (PBE/3ζ) [213]. Cluster C4H8O2@(7,0) demonstrates the presence of only one form—2,5-Tw; the C-conformer in this case is not realized (Figure 16). The van der Waals spheres onethe C-conformerform—2,5-Tw; in the this C-conformer case is not realized in this (Figurecase is not 16). realized The van (Figure der Waals 16). spheresThe van show der Waals that the spheres inner show that the inner cavity of the nanotube is densely filled with 1,3-dioxane. In all cases, the guest showcavity that of the the nanotube inner cavity is densely of the filled nanotube with 1,3-dioxane.is densely filled In all with cases, 1,3-dioxane. the guest molecule In all cases, has athe negative guest molecule has a negative electric charge. moleculeelectric charge. has a negative electric charge.

Figure 16. Cluster C4H8O2@(7,0). Adapted with modiﬁcation [213]. Figure 16. Cluster C4H8O2@(7,0). Adapted with modification [213]. Figure 16. Cluster C4H8O2@(7,0). Adapted with modification [213]. It should be stressed that the conformational behavior of substituted 1,3-dioxanes in usual solvents It should be stressed that the conformational behavior of substituted 1,3-dioxanes in usual is notIt accompaniedshould be stressed by the inversionthat the conformational of stability between behavior the chairof substituted and any other 1,3-dioxanes form; in allin usual cases, solvents is not accompanied by the inversion of stability between the chair and any other form; in all solventsC-conformer is not remains accompanied the main by minimum,the inversion and of the stability role of between the medium the chair is relegated and any only other to form; the shift in all of cases, C-conformer remains the main minimum, and the role of the medium is relegated only to the cases,the conformational C-conformer equilibriumremains the towardsmain minimum, the chair-form and the with role more of the or medium less polarity, is relegated due to theonly axial to the or equatorial orientation of polar substituents or with lower steric restriction [214,215]. In sharp contrast,

MoleculesMolecules 20202020,, 2525,, xx FORFOR PEERPEER REVIEWREVIEW 1818 ofof 3939 shift of the conformational equilibrium towards the chair-form with more or less polarity, due to the shiftMolecules of the2020 conformational, 25, 2437 equilibrium towards the chair-form with more or less polarity, due 17to ofthe 37 axialaxial oror equatorialequatorial orientationorientation ofof polarpolar substituentssubstituents oror withwith lowerlower stericsteric restrictionrestriction [214,215].[214,215]. InIn sharpsharp contrast,contrast, thethe conformationalconformational properpropertiesties ofof unsubstitutedunsubstituted 1,3-dioxane1,3-dioxane inin thethe SWCNTSWCNT cavitycavity areare causedcaused bytheby thethe conformational actionaction ofof aa newnew properties drivingdriving offorce,force, unsubstituted whichwhich cancan 1,3-dioxanedrdramaticallyamatically in alteralter the SWCNTconformationalconformational cavity are propertiesproperties caused byofof the the guestactionguest cycliccyclic of a new moleculesmolecules driving inin force, comparisoncomparison which withwith can dramatically thosethose inin thethe gasgas alter phasephase conformational oror inin thethe usualusual properties solvents.solvents. of the guest cyclic molecules in comparison with those in the gas phase or in the usual solvents. 5.3.5.3. 1,3-Dioxa-2-Silacyclohexane1,3-Dioxa-2-Silacyclohexane inin NanotubesNanotubes 5.3. 1,3-Dioxa-2-Silacyclohexane in Nanotubes TheThe stereochemistrystereochemistry ofof silicon-containingsilicon-containing satusaturatedrated heterocyclesheterocycles isis anan integralintegral partpart ofof organosiliconorganosiliconThe stereochemistry chemistry;chemistry; of thethe silicon-containing introductionintroduction ofof saturated sisiliconlicon atomsatoms heterocycles changeschanges is an thethe integral geometrygeometry part of andand organosilicon electronicelectronic featureschemistry;features ofof the thethe introduction cycliccyclic systemsystem of silicon[216].[216]. AccordingAccording atoms changes toto thethe the resultsresults geometry ofof gas-phasegas-phase and electronic electronelectron features diffraction,diffraction, of the cyclic thethe molecularsystemmolecular [216 structurestructure]. According ofof 2,2-dimethyl-1,3-dioxa-2-silacyclohexane2,2-dimethyl-1,3-dioxa-2-silacyclohexane to the results of gas-phase electron di correspondscorrespondsﬀraction, the toto molecular thethe flattenedflattened structure chairchair [217].of[217]. 2,2-dimethyl-1,3-dioxa-2-silacyclohexane TheoreticalTheoretical investigationinvestigation usingusing Hartree–FockHartree–Fock corresponds (HF)(HF) to andand the ﬂattenedDFTDFT approximationsapproximations chair [217]. Theoreticalledled toto thethe conclusioninvestigationconclusion ofof using aa ratherrather Hartree–Fock lowlow barrierbarrier (HF) ofof and interconintercon DFT approximationsversionversion betweenbetween led twotwo to the C-forms,C-forms, conclusion includingincluding of a rather aa locallocal low minimumbarrierminimum of interconversion ofof 2,5-Tw,2,5-Tw, whichwhich between isis veryvery twocloseclose C-forms, inin energyenergy including toto thethe TSTS a (Scheme local(Scheme minimum 4)4) [212,217–219].[212,217–219]. of 2,5-Tw, In whichIn thethe casecase is very ofof ≠ freeclosefree 1,3-dioxa-2-silacyclohexane,1,3-dioxa-2-silacyclohexane, in energy to the TS (Scheme CC433HH)[88SiOSiO21222, 217(R=H),(R=H),–219 the].the In correspondingcorresponding the case of free ΔΔGG 1,3-dioxa-2-silacyclohexane,298298≠ isis 4.14.1 kcal/molkcal/mol (PBE/3(PBE/3ζζ)) , [220].C[220].3H8 SiO 2 (R=H), the corresponding ∆G298 is 4.1 kcal/mol (PBE/3ζ)[220].

RR Si OO Si O RR RR O OO SiSi OO O RR == H,H, CHCH OO RR O RR 33 Si CC Si 2,5-Tw2,5-Tw C inv C inv RR SchemeScheme 4. 4. ConformationalConformational equilibrium equilibrium of of free free 1,3-dioxa-2-silacyclohexane. 1,3-dioxa-2-silacyclohexane.

ItIt was was found found thatthat thethe mainmain minimumminimumminimum ofofof thethethe guestguestguest moleculemoleculemolecule in inin cluster clustercluster C CC333HHH888SiOSiO22@(5,5)@(5,5) belongs belongs to to thethe structure structure close close to to the the half-chair half-chair (CH) (CH) conformer, conformer, notnotnot toto thethe C-form.C-form. But But other other than than that, that, the the details details ofof conformational conformational behavior behavior of of en encapsulatedencapsulatedcapsulated molecule molecule remain remain the the same; same; the the barrier barrier of of interconversioninterconversion isis slightly slightly higher higher than than for for the the free free molecule molecule (5.1 (5.1 kcal/mol, kcalkcal/mol,/mol, Scheme Scheme 5 5).5).). FormFormForm 2,5-Tw2,5-Tw2,5-Tw remainsremainsremains the thethe local locallocal minimumminimum on on the the PES PES [220]. [[220].220].

HH OO HH OO SiSi OO SiSi H HH OO H HCHC 2,5-Tw2,5-Tw

SchemeScheme 5. 5. ConformationalConformational equilibrium equilibrium of of 1,3-diox 1,3-dioxa-2-silacyclohexane1,3-dioxa-2-silacyclohexanea-2-silacyclohexane inside inside SWCNT SWCNT (5,5). (5,5).

In the case of cluster C H SiO @(8,0) the main minimum corresponds to the C-conformer. InIn thethe casecase ofof clustercluster CC333HH88SiOSiO22@(8,0)@(8,0) thethe mainmain minimumminimum corrcorrespondsesponds toto thethe C-conformer.C-conformer. Equilibrium C 2,5-Tw in this case is described by the relatively low energy differences between these EquilibriumEquilibrium СС ↔ ↔↔ 2,5-Tw2,5-Tw inin thisthis casecase isis describeddescribed byby ththee relativelyrelatively lowlow energyenergy differencesdifferences betweenbetween theseformsthese formsforms (2.6 kcal (2.6(2.6/mol kcal/molkcal/mol in comparison inin comparisoncomparison with 3.3 withwith kcal 3.33.3/mol kcal/molkcal/mol for the for freefor thethe silicon freefree ester siliconsilicon and esterester previous andand previousprevious cluster). cluster).Thecluster). barrier TheThe of barrierbarrier interconversion ofof interconversioninterconversion is slightly increasedisis slightlyslightly (4.8 increasedincreased kcal/mol). (4.8(4.8 In kcal/mol).kcal/mol). all cases theInIn all guestall casescases molecule thethe guestguest has a negative electric charge ( 0.25– 0.87) [220]. moleculemolecule hashas aa negativenegative electricelectric− chargecharge− ((−−0.250.25‒−‒−0.87)0.87) [220].[220]. Thus,Thus, SWCNTs SWCNTs cavitycavity maymay changechange thethe conformationconformaticonformationon corresponding corresponding to to the the minimum minimum as as well well as as altersalters certaincertaincertain energy energyenergy characteristics characteristicscharacteristics of ofof conformational conformationalconformational equilibrium equilibriumequilibrium of six ofof membered sixsix memberedmembered cyclic cycliccyclic silicon siliconsilicon esters. esters.esters. 5.4. Hexahydropyrimidin-2-One in Nanotubes 5.4.5.4. Hexahydropyrimidin-2-OneHexahydropyrimidin-2-OneSubstituted hexahydropirimidine-2-ones inin NanotubesNanotubes belong to the promising class of cyclic urea derivatives with a well-defined biological activity [221] and as reagents in organic chemistry [222,223]. According SubstitutedSubstituted hexahydropirimidine-2-oneshexahydropirimidine-2-ones belongbelong toto thethe promisingpromising classclass ofof cycliccyclic ureaurea derivativesderivatives to the X-ray investigation their structure corresponds to the semi-planar form, or C-conformer with withwith aa well-definedwell-defined biologicalbiological activityactivity [221][221] andand asas reagentsreagents inin organicorganic chemistrychemistry [222,223].[222,223]. AccordingAccording a strong flattened heteroatomic part [224]. Conformational transformation of the free molecule of toto thethe X-rayX-ray investigationinvestigation theirtheir structurestructure corresponcorrespondsds toto thethe semi-planarsemi-planar form,form, oror C-conformerC-conformer withwith hexahydropyrimidin-2-one, C H N O, established by HF/6-31G(d) and PBE/3ζ methods includes two 4 8 2 Molecules 2020, 25, x FOR PEER REVIEW 19 of 39 Molecules 2020, 25, 2437 18 of 37 a strong flattened heteroatomic part [224]. Conformational transformation of the free molecule of hexahydropyrimidin-2-one, C4H8N2O, established by HF/6-31G(d) and PBE/3ζ methods includes two degenerated inin energyenergy flattenedflattened C-conformers, C-conformers, 2,5-Tw 2,5-Tw as as a a local local minimum minimum and and TS TS that that corresponds corresponds to theto the conformation conformation very very close close in energyin energy to theto the 2,5-Tw 2,5-Tw form form (Scheme (Scheme6)[ 2256) [225,226].,226].

H O N H H N H N N N H TS O TS N N TS O TS N H N H O H C 2,5-Tw C* C* Scheme 6. Conformational equilibrium of free hexahydropirimidine-2-one.

Conformational equilibriumequilibrium ofof hexahydropirimidine-2-onehexahydropirimidine-2-one inin clustercluster C C4H4H88NN22O@(5,5)O@(5,5) exhibitsexhibits thethe absenceabsence ofof 2,5-Tw2,5-Tw formform asas aa locallocal minimum:minimum: itit becomesbecomes aa TS.TS. BesidesBesides thisthis conformationconformation PESPES contains two degenerateddegenerated in energy flattenedflattened C-formsC-forms withwith the increasedincreased barrierbarrier ofof interconversioninterconversion (5.4(5.4 kcalkcal/mol/mol inin comparisoncomparison with 3.33.3 kcalkcal/mol/mol forfor thethe freefree cycliccyclic urea,urea, PBEPBE/3/3ζζ).). TheThe guestguest moleculemolecule acquires aa negativenegative electricelectric chargecharge ((−0.66).0.66). InIn thethe casecase ofof clustercluster CC44HH88N22O@(8,0) PES besides C-form acquires a negative electric charge −(−0.66). In the case of cluster C4H8N2O@(8,0) PES besides C-form 0 and TS includes 2,5-Tw2,5-Tw conformerconformer asas aa locallocal minimum;minimum; thethe valuevalue∆ ΔGG2982980 betweenbetween them them (3.1 (3.1 kcal/mol) kcal/mol) isis higherhigher thanthan forfor thethe freefree moleculemolecule (2.4(2.4 kcalkcal/mol),/mol), but the barrier of interconversion (3.5 kcal/mol) kcal/mol) changes veryvery little.little. The encapsulated moleculemolecule has a positive chargecharge (0.32)(0.32) [[226].226]. Thus, the influenceinfluence of nanotubesnanotubes onon thethe conformationalconformational propertiesproperties ofof unsubstitutedunsubstituted cyclic urea isis downdown mainlymainly toto thethe qualitativequalitative changechange inin thethe naturenature ofof intermediateintermediate formsforms andand toto thethe variationvariation inin energy parametersparameters ofof conformationalconformational equilibriumequilibrium betweenbetween flattenedflattened C-conformers.C-conformers.

5.5. 1,3,2-Dioxaborinane in Fullerenes 5.5. 1,3,2-Dioxaborinane in Fullerenes

It was established recently that preferable conformation of 1,4-dioxane in exo adducts with C60 and It was established recently that preferable conformation of 1,4-dioxane in exo adducts with С60 C70 fullerenes is not a chair but a boat form. Such unusual result is connected with a rigidity of fullerene and C70 fullerenes is not a chair but a boat form. Such unusual result is connected with a rigidity of skeleton [227]. In this connection it would be interesting to assess the conformational properties of the fullerene skeleton [227]. In this connection it would be interesting to assess the conformational guest cyclic molecule inside fullerenes. The ﬁrst example of its kind was the simplest six-membered properties of the guest cyclic molecule inside fullerenes. The first example of its kind was the simplest cyclic boronic ester: 1,3,2-dioxaborinane. It belongs to the valuable class of organoboron compounds six-membered cyclic boronic ester: 1,3,2-dioxaborinane. It belongs to the valuable class of which are widely used in organic syntheses [228–231] and are convenient models to assess the eﬀect organoboron compounds which are widely used in organic syntheses [228–231] and are convenient of heteroatoms in changing of the conformational properties of cyclohexane’s heteroanalogs [212]. models to assess the effect of heteroatoms in changing of the conformational properties of The PES of 1,3,2-dioxaborinane itself (C3H7BO2) contains degenerated in energy conformers of sofa cyclohexane’s heteroanalogs [212]. The PES of 1,3,2-dioxaborinane itself (C3H7BO2) contains (Sf) and TS—2,5-Tw form (Scheme7)[212]. degenerated in energy conformers of sofa (Sf) and TS—2,5-Tw form (Scheme 7) [212].

O O O O BH O B H O BH B H O O O Sf 2,5-Tw Sf* Sf* Scheme 7. Conformational equilibrium of free 1,3,2-dioxaborinane.

ItIt should be noted that stabilization of Sf-formSf-form in the free molecule is due to the p- π conjugation inin thethe heteroatomic part of the cyclic ester because of the partially double double nature nature of of B-O B-O bond bond [212]. [212]. However, endocomplexendocomplex CC33HH77BO2@C@C8080 demonstratesdemonstrates the the conformational conformational equilibrium between two ≠ , unusual for this class class of of compounds compounds boat boat (B) (B) forms forms with with Δ∆GG298298≠ 10.110.1 kcal/mol kcal/mol in comparison in comparison with with 7.2 7.2kcal/mol kcal/mol for forthe thefree free molecule molecule of cyclic of cyclic boronic boronic esters esters (PBE/3 (PBEζ/3, ζScheme, Scheme 8);8 );the the guest guest molecule molecule has has a anegative negative charge charge (− (0.74)0.74) [232]. [232 ]. negative charge (−0.74)− [232]. The decrease in fullerene diameter leads to the more signiﬁcant changes in conformational properties of the guest molecule. In cluster C3H7BO2@C60 the main minimum on the PES of cyclic ester belongs to the 1,4-Tw form that may convert to the C-conformer (local minimum) over TS—envelop (E) form (Scheme9).

Molecules 2020, 25, x FOR PEER REVIEW 20 of 39

H O B O O O B H O O B Molecules 2020, 25, 2437 H 19 of 37 B 2,5-Tw Molecules 2020, 25, x FOR PEER REVIEW B* 20 of 39 Scheme 8. ConformationalH equilibrium of 1,3,2-dioxaborinane in cluster C3H7BO2@C80. O B O O The decreaseO in fullerene diameter leads to theB moreH significant changes in conformational O O B properties of the guest molecule. In cluster C3H7BO2@C60 the main minimum on the PES ofH cyclic ester B 2,5-Tw belongs to the 1,4-Tw form that may convert to the C-conformer (local minimum)B* over TS—envelop (E) form (SchemeScheme 9). 8. Scheme 8.Conformational Conformational equilibrium equilibrium of of 1,3,2-dioxaborinane 1,3,2-dioxaborinane in in cluster cluster C C3H3H77BOBO22@C80.. BH O The Odecrease in fullerene diameter leads to the more significant changes Oin conformational 3 7 2O 60 properties of the guestO molecule. In cluster C H BO @C the main minimum on theO PES of cyclic ester belongs to the 1,4-Tw form that may convert to the C-conformer (local minimum) over TS—envelop BH BH (E) form (Scheme1,4-Tw 9). TS: E C

SchemeScheme 9.9. ConformationalConformational equilibriumequilibrium ofof 1,3,2-dioxaborinane1,3,2-dioxaborinane inin clustercluster CC33HH77BO2@C6060. . BH O O 0 O The value ∆G298 between 1,4-Tw and C-conformers is 8.1 kcal/mol and the height of the barrier The value ΔG2980O between 1,4-Tw and C-conformersO is 8.1 kcal/mol and the height of the barrier is 27.9 kcal/mol (3.9 times higher than calculated for the free ester); the guest moleculeO acquires a large is 27.9 kcal/mol (3.9 times higher than calculated for the free ester); the guest molecule acquires a positive charge1,4-Tw (2.53 for the 1,4-Tw form) [232]. BH BH large positive charge (2.53 for the 1,4-Tw form)TS: [232]. E C Thus, a combination of electronic and steric requirements that may be called as a force field inside Thus, a combination of electronic and steric requirements that may be called as a force field fullerenes significantlyScheme 9. Conformational changes conformational equilibrium of properties 1,3,2-dioxaborinane of even relatively in cluster C simple3H7BO2 cyclic@C60. molecule: inside fullerenes significantly changes conformational properties of even relatively simple cyclic forms like B, 1,4-Tw, E and C are never realized for 1,3,2-dioxaborinanes with sp2 boron atom in any molecule: forms like B, 1,4-Tw, E and C are never realized for 1,3,2-dioxaborinanes with sp2 boron solventThe [212 value]. The ΔG sharp2980 between increase 1,4-Tw in population and C-conformers of twist-form is is8.1 connected kcal/mol primarily and the height with a of considerable the barrier atom in any solvent [212]. The sharp increase in population of twist-form is connected primarily with declineis 27.9 kcal/mol in linear size(3.9 oftimes the moleculehigher than inside calculated fullerenes forunder the free the ester); action the of forceguest field. molecule acquires a a considerable decline in linear size of the molecule inside fullerenes under the action of force field. large positive charge (2.53 for the 1,4-Tw form) [232]. 6. NitrogenThus, a Pyramidal combination Inversion of electronic inside and Nanotubes steric requirements and Fullerenes that may be called as a force field 6. Nitrogen Pyramidal Inversion inside Nanotubes and Fullerenes inside fullerenes significantly changes conformational properties of even relatively simple cyclic Recent years exhibit a significant interest to the investigation of pyramidal inversion in XH3 Recent years exhibit a significant interest to the investigation of pyramidal inversion 2in XH3 compoundsmolecule: forms [233 ].like One B, of1,4-Tw, the main E and challenges C are never facing realized the theoretical for 1,3,2-dioxaborinanes spectroscopy is connectedwith sp boron with compounds [233]. One of the main challenges facing the theoretical spectroscopy is connected with a aatom selection in any of solvent ab initio [212]. and The DFT sharp methods increase that canin population ensure the of accurate twist-form estimate is connected the energy primarily of nitrogen with selection of ab initio and DFT methods that can ensure the accurate estimate the energy of nitrogen inversiona considerable barrier decline [234]. in Authorslinear size of of [235 the] suggestedmolecule inside a benchmark fullerenes set under that comprisesthe action of 24 force high-level field. inversion barrier [234]. Authors of [235] suggested a benchmark set that comprises 24 high-level wave-function inversion barriers in different compounds; it is submitted that at least medium-sized wave-function6. Nitrogen Pyramidal inversion Inversion barriers in in differentside Nanotubes compounds; and Fullerenes it is submitted that at least medium-sized triple-split-valence basis sets with at least one set of polarization functions should be used for the triple-split-valence basis sets with at least one set of polarization functions should be used for the theoreticalRecent study years of exhibit pyramidal a significant inversion. interest Formally, to the method investigation PBE/3ζ [ 87of, 92pyramidal] quite meets inversion those criteria.in XH3 theoretical study of pyramidal inversion. Formally, method PBE/3ζ [87,92] quite meets those criteria. Itcompounds should be stressed[233]. One however of the main that itch isallenges also underestimates facing the theoretical the nitrogen spectroscopy inversion is barrier connected in amines. with a It should be stressed however that it is also underestimates the nitrogen inversion barrier in amines. selectionHow of an ab ordinary initio and solvent DFT a ffmethodsects the barrier that can of nitrogenensure the pyramidal accurate inversion? estimate the It was energy established of nitrogen that How an ordinary solvent affects the barrier of nitrogen pyramidal inversion? It was established ininversion polar medium barrier this [234]. value Authors depends of on[235] the suggested number of solvent’sa benchmark molecules set that in thecomprises close surroundings 24 high-level of that in polar medium this value depends on the number of solvent’s molecules in the close thewave-function dissolved species. inversion In particular, barriers in computer different simulation compounds; of inversion it is submitted in 3-methyltetrahydro-1,3-oxazine that at least medium-sized surroundings of the dissolved species. In particular, computer simulation of inversion in 3- surroundedtriple-split-valence by the molecules basis sets of with difluorodichloromethane at least one set of polarization using PBE /functions3ζ approximation should be (explicit used model)for the methyltetrahydro-1,3-oxazine surrounded by the molecules of difluorodichloromethane using revealedtheoretical that study the bestof pyramidal match with inversion. experimental Formally, barrier method was obtained PBE/3ζ [87,92] for the quite case ofmeets four those molecules criteria. in PBE/3ζ approximation (explicit model) revealed that the best match with experimental barrier was solvationIt should shellbe stressed [236]. however that it is also underestimates the nitrogen inversion barrier in amines. obtained for the case of four molecules in solvation shell [236]. How an ordinary solvent affects the barrier of nitrogen pyramidal inversion? It was established 6.1.that Ammoniain polar andmedium Trimethylamine this value in Nanotubesdepends on the number of solvent’s molecules in the close 6.1. Ammonia and Trimethylamine in Nanotubes surroundingsExperimental of the values dissolved of nitrogen species. pyramidal In partic inversionular, computer barriers in simulation ammonia andof trimethylamineinversion in 3- Experimental, values of nitrogen pyramidal inversion barriers in ammonia and trimethylamine (methyltetrahydro-1,3-oxazine∆G298 ) are 5.8 and 7.5 kcal/ molsurrounded respectively by [th237e ].molecules The appropriate of difluorodichloromethane results of PBE/3ζ has using been ≠ (understatedPBE/3ΔG298 ζ) approximationare 5.8 (4.3 and and 7.5 6.0 (explicit kcalkcal/mol/mol model) [respectively238]). revealed However, [237]. that considering theThe best appropriate match numerous with results challengesexperimental of PBE/3 relating ζbarrier has tobeen was the understatedapplicationobtained for of (4.3the more caseand complex 6.0of four kcal/mol molecules methods [238]). and in However, solvation basis sets consideringshell to the [236]. calculation numerous of nanoobjects, challenges itrelating was possible to the applicationto use the PBE of more/3ζ approach complex for methods the estimation and basis of sets the to inversion the calculation barrier of of nanoobjects, amines in SWCNTs. it was possible In the to6.1. use Ammonia the PBE/3 andζ Trimethylamineapproach for the in Nanotubesestimation, of the inversion barrier of amines in SWCNTs. In the case of cluster NH3@(4,4) the value of ∆G298 was 10,9 kcal/mol (more than 2.5 times higher than for case of cluster NH3@(4,4) the value of ΔG298≠ was 10,9 kcal/mol (more than 2.5 times higher than for the freeExperimental molecule). Invalues contrast, of nitrog the appropriateen pyramidal value inversion for trimethylamine barriers in ammonia in cluster and N(CH trimethylamine3)3@(6,6) was the free molecule). In contrast, the appropriate value for trimethylamine in cluster N(CH3)3@(6,6) was 4.8(ΔG kcal298≠)/ molare (1.255.8 and times 7.5 lower kcal/mol than respectively for the free molecule)[237]. The [ 238appropriate]. It should results be noted of PBE/3 that theζ has distance been betweenunderstated guest (4.3 species and 6.0 and kcal/mol carbon [238]). skeleton However, of SWCNT considering in both numerous cases was cha thellenges same (~2.5 relating Å). to Thus, the theapplication value of of inversion more complex barrier methods in nanotube’s and basis cavity sets as forto the the calculation free molecule of nanoobjects, depends to someit was extent possible on the nature of amine. In both cases the guest molecule acquires a relatively small charge (up to 0.50). to use the PBE/3ζ approach for the estimation of the inversion barrier of amines in SWCNTs.− In the case of cluster NH3@(4,4) the value of ΔG298≠ was 10,9 kcal/mol (more than 2.5 times higher than for the free molecule). In contrast, the appropriate value for trimethylamine in cluster N(CH3)3@(6,6) was

Molecules 2020, 25, x FOR PEER REVIEW 21 of 39

Molecules 2020, 25, x FOR PEER REVIEW 21 of 39 4.8 kcal/mol (1.25 times lower than for the free molecule) [238]. It should be noted that the distance between4.8 kcal/mol guest (1.25 species times and lower carbon than skeleton for the offree SWCNT molecule) in both [238]. cases It should was the be same noted (~2.5 that Å the). Thus, distance the valuebetween of inversion guest species barrier and in carbon nanotube’s skeleton cavity of SWCNTas for the in free both molecule cases was depends the same to some (~2.5 extentÅ). Thus, on thethe nature of amine. In both cases the guest molecule acquires a relatively small charge (up to −0.50). Moleculesvalue of2020 inversion, 25, 2437 barrier in nanotube’s cavity as for the free molecule depends to some extent on20 of the 37 nature of amine. In both cases the guest molecule acquires a relatively small charge (up to −0.50). 6.2. Piperidine inside Nanotube 6.2. Piperidine inside Nanotube 6.2. PiperidineIt is necessary inside toNanotube separate two dynamic processes relatively to piperidine (C5H11N): nitrogen pyramidal inversion and interconversion of the cycle. The first leads to the change in orientation of It isis necessarynecessary toto separateseparate twotwo dynamicdynamic processesprocesses relativelyrelatively toto piperidinepiperidine (C(C55HH1111N): nitrogen N-Hpyramidal proton inversion (axial-equatorial, and interconversion a–e) and the of second the cycle. over The several first ﬁrst steps—toleads to the the change alternate in conformation orientation of (SchemeN-H proton 10) [239]. (axial-equatorial, a–e) and the second over several steps—to the alternate conformation (Scheme 1010))[ [239].239].

N H C-e N N H TS C-a N N H N C-e TS H H HC-a H H N Tw N H N Tw C-e H C-a N C-a Scheme 10.C-e Two ways of conformational transformation C-e ↔ C-a of free piperidine. Scheme 10. TwoTwo ways of conformational transformation C-e ↔ C-a of free piperidine. According to the NMR spectroscopy data the barrier of nitrogen↔ pyramidal inversion (ΔG298≠) is 6.1 kcal/molAccording [240] to and the NMRΔG298 spectroscopy≠ for the second data process—10.4 the barrier of kcal/mol nitrogen [241]. pyramidal So, the inversion nitrogen ( ∆inversionG ,) is According to the NMR spectroscopy data the barrier of nitrogen pyramidal inversion (ΔG298298≠) is in6.1 this kcal case/mol requires [240] and lower∆G energy, for the compared second process—10.4 to the conformational kcal/mol [241equilibrium]. So, the nitrogenof the cycle. inversion Besides in 6.1 kcal/mol [240] and ΔG298298≠ for the second process—10.4 kcal/mol [241]. So, the nitrogen inversion that,thisin this caseconformer case requires requires C-e lower islower more energy energy stable compared compared than C-a to the into the conformationalthe gasconformational phase (0.72 equilibrium equilibriumkcal/mol) of [242] the of cycle. theand cycle. Besidesin nonpolar Besides that, mediumconformerthat, conformer (0.2–0.6 C-e is C-ekcal/mol) more is stablemore [243]. stable than C-a than in theC-a gasin the phase gas (0.72 phase kcal (0.72/mol) kcal/mol) [242] and [242] in nonpolar and in nonpolar medium (0.2–0.6mediumIn cluster kcal (0.2–0.6/mol) C5H kcal/mol) [11243N@(6,6)]. [243]. the barrier of nitrogen inversion rises to 6.8 kcal/mol in comparison with 4.7 kcal/molIn cluster for C theH freeN@(6,6) molecule the barrier (PBE/3 ofζ nitrogen) [244]. At inversion the same rises time to 6.8form kcal C-a/mol becomes in comparison more stable with In cluster C5H11N@(6,6) the barrier of nitrogen inversion rises to 6.8 kcal/mol in comparison with 0 inside4.7 kcalkcal/mol SWCNT;/mol forfor the differencesthe free free molecule molecule with (PBEC-e (PBE/3 conformer/3ζ)[ζ244) [244].]. At(Δ theGAt298 the same) is same 2.6 time kcal/mol time form form C-a compared becomes C-a becomes to more 0.6 stablemorekcal/mol insidestable in 0 favorSWCNT; of form diﬀerences C-e for with the C-e free conformer molecule. (∆ TheG encapsulated) is 2.60 kcal/mol piperidine compared acquires to 0.6 kcal a relatively/mol in favor large of inside SWCNT; differences with C-e conformer298 (ΔG298 ) is 2.6 kcal/mol compared to 0.6 kcal/mol in negativeformfavor C-eof charge forform the C-e ( free−0.89 for molecule. forthe the free C-a The molecule. form) encapsulated [244]. The encapsulated piperidine acquires piperidine a relatively acquires large a negativerelatively charge large (negative0.89 for charge the C-a (− form)0.89 for [244 the]. C-a form) [244]. 6.3.− Perhydro-1,3,2-Dioxazine inside Nanotubes 6.3. Perhydro-1,3,2-Dioxazine inside Nanotubes 6.3. Perhydro-1,3,2-DioxPerhydro-1,3,2-dioxazineazine inside (C3 HNanotubes7NO2) is the heteroanalog of cyclohexane with O–N–O ring fragment.Perhydro-1,3,2-dioxazine It was firstly obtained (C 335H 7yearsNO2 )ago is the[245]. heteroanalog Further study of cyclohexaneshowed that withthis compound O–N–O ring is Perhydro-1,3,2-dioxazine (C3H7NO2) is the heteroanalog of cyclohexane with O–N–O ring fragment. It was ﬁrstly obtained 35 years ago [245]. Further study showed that this compound is conformationallyfragment. It was rigidfirstly due obtained to the relatively 35 years highago [245].barrier Further of nitrogen study inversion showed in that N,N this-dialkoxyamines compound is conformationally rigid due to the relatively high barrier of nitrogen inversion in N,N-dialkoxyamines (21.7–24.6conformationally kcal/mol) rigid [246,247]. due to the Detailed relatively conformational high barrier of analysis nitrogen using inversion MP2-RI/ in N,λN2-dialkoxyamines approximation (21.7–24.6 kcal/mol) [246≠ ,247]. Detailed conformational analysis using MP2-RI/λ2 approximation revealed(21.7–24.6 that kcal/mol) the ΔG [246,247].298 value Detailedfor the direct conformational transformation analysis C-a using↔ C-e MP2-RI/ forms ofλ2 perhydro-1,3,2-approximation , dioxazinerevealed that is 23.3 the ∆kcal/molG298 value (Schem for thee 11). direct Wherein transformation conformer C-a C-e isC-e more forms stable of perhydro-1,3,2-dioxazine at 2.5 kcal/mol (ΔG2980) 298≠ ↔ revealed that the ΔG value for the direct transformation↔ C-a C-e forms of perhydro-1,3,2-0 [248].is 23.3 kcal/mol (Scheme 11). Wherein conformer C-e is more stable at 2.5 kcal/mol (∆G298 )[248]. dioxazine is 23.3 kcal/mol (Scheme 11). Wherein conformer C-e is more stable at 2.5 kcal/mol (ΔG2980) [248]. O O O O O H OO O N N O C-eO N H TSO C-aO N N H C-e TS HN H C-a SchemeScheme 11. 11. ConformationalConformational equilibrium equilibrium of of free free perhydro-1,3,2-dioxazine. perhydro-1,3,2-dioxazine. H Scheme 11. Conformational equilibrium of free perhydro-1,3,2-dioxazine. In contrast to the free molecule cluster C3H7NO2@(6,6) demonstrates the preference of C-a form 0 (∆G298 2.1 kcal/mol, PBE/3ζ). The barrier of the nitrogen inversion is almost unchanged, compared to , the free molecule (∆G298 23.4 and 21.7 kcal/mol respectively). The C-a form in the SWCNT cavity is slightly distorted [249]. The preference of C-a form is also observed in endocomplex C3H7NO2@(5,5); Molecules 2020, 25, 2437 21 of 37

0 , the corresponding ∆G298 is 1.1 kcal/mol and ∆G298 for nitrogen inversion is rather close to the free perhydro-1,3,2-dioxazine (20.2 kcal/mol). In both cases the guest molecule acquires a positive charge (0.60–0.65) [249].

6.4. Ammonia and Trimethylamine in Fullerenes

Cluster NH3@C60 demonstrates almost the same barrier on nitrogen inversion as in the free molecule (4.4 kcal/mol); the N-H bond lengths remain practically unchanged and the guest molecule has a small negative charge ( 0.30) [250]. Thus, the cavity of C is large enough to cause changes in the − 60 energy of inversion. In contrast, the inner space of fullerene in the case of N(CH3)3@C60 becomes rather small: the height of the barrier in this case is 3.4 times higher than for the free molecule (25.7 kcal/mol); the C-N bond lengths became shorter by 0.08 Å and the guest molecule acquires a positive charge (0.65 for the ground state and 1.14 for the TS). The increase of fullerene’s diameter leads to the decrease , of ∆G298 for nitrogen inversion (10.3 kcal/mol for the cluster N(CH3)3@C80); the molecule of amine in this case has a negative charge ( 0.83 for the ground state and 0.36 for the TS) [250]. − − Thus, the pyramidal inversion barrier for acyclic amines inside nanotubes and fullerenes depends on the nature of amine and on the size of nanocavity. In the case of cyclic amines in SWCNTs the inversion of the relative stability of axial and equatorial conformers is observed and, in the case of pyrimidine, the barrier of the nitrogen pyramidal inversion is increased in 1.4 times.

7. Recognition of the R- and S-Isomers by Chiral Nanotubes It is well known that helicity is closely linked to chirality, because left-handed and right-handed helixes are non-superimposable to their mirror images. A distinctive feature of chiral nanotubes is the presence of a helical axis. This class of SWCNTs can be described by (n,m) chirality indexes (n , m; m , 0). A diﬀerent chirality suggests that such objects create the individual enantiomeric pairs, also denoted as P and M nanotubes with a single set of values (n,m) [251]. Depending on the ratio between chirality indexes, they display features of conductors or semiconductors [252] and have valuable optical properties [253]. It was shown that the doping of chiral nanotubes with nitrogen diminishes the stress caused by the small diameter and the corresponding energy strongly depends on the tube helicity [254]. However, the most prominent quality of chiral nanotubes is their ability to form complexes with chiral molecules possessing diﬀerent degrees of stability. In principle, this enable to provide asymmetric synthesis [76] and make possible a separation of left-handed from right-handed isomers by using, for example, chiral SWCNTs as stationary phases in chromatography. It is also possible to induce chirality in the chains of guest molecules [251,255,256]. In this connection, the relative stability of some R- and S-isomers in the cavity of chiral nanotubes was investigated using the PBE/3ζ approximation.

7.1. R- and S-Isomers of 1-Fluoroethanol Inside SWCNTs (4,4) and (4,1)

According to the previous analysis, both enantiomers of free 1-fluoroethanol (C2H5FO) participate 0 in conformational equilibrium between a and b forms with differences in stability (∆G298 ) 0.3 kcal/mol Moleculesin favor 2020 of a, 25(Figure, x FOR 17PEER)[257 REVIEW]. This result is confirmed by [258]. 23 of 39

Figure 17. Conformers of S-1-fluoroethanol. S-1-ﬂuoroethanol. Adapted with modification modiﬁcation [257]. [257].

Molecules of 1-fluoroethanol inside SWCNTs (4,4) and M(4,1) convert into preferable conformation close to the eclipsed (Figure 18).

Figure 18. Preferred conformation of S-1-fluoroethanol inside SWCNTs. Adapted with modification [257].

The energies of clusters R-C2H5FO@(4,4) and S-C2H5FO@(4,4) were predictably the same. However, endocomplex R-C2H5FO@M(4,1) was proven to be more stable than S-C2H5FO@M(4,1) at 4.4 kcal/mol, and in comparison with cluster C2H5FO@(4,4) at 12.8 kcal/mol (ΔG2980). This means that, despite the greater stability of SWCNT (4,4), cluster R-C2H5FO@M(4,1) exhibits a large energy gain which can serve as a theoretical basis to separate both enantiomers. Besides that, the guest molecule in all cases has a slight negative charge (up to −0.12) [257].

7.2. R- and S-Isomers of α-Alanine inside SWCNTs (n,m)

Conformational analysis of free α-alanine (C3H7NO2), carried out for S-isomer by rotating around the bond С(NH2)−C(O), indicates the presence of several stationary points on the PES; the main minimum corresponds to the form A, and the main TS to the conformation B (Scheme 12, Table 4) [259]. These results are quite consistent with the data of [260].

H C 3 NH2 H2N H HO O HO O HO O H3C H NH2 H A CH3 TS-1 (В) C

HO O H2N CH3 TS-2 (D) Scheme 12. Conformational equilibrium of free α-alanine.

SWCNTs (5,5), (5,1) and (5,2), which were used as nanoobjects for the investigation of α-alanine properties in endocomplexes, differ in energy: as in the previous case (Section 7.1), the most stable is nanotube (5,5) (Table 4). The conformational behavior of α-alanine in clusters, for the example of S-C3H7NO2@P(5,2), is presented in Scheme 13. In this case, the main minimum on the PES corresponds to the conformer D.

Molecules 2020, 25, x FOR PEER REVIEW 23 of 39

Molecules 2020, 25, 2437 22 of 37

It should beFigure noted 17. that Conformers both nanotubes—(4,4) of S-1-fluoroethanol. and (4,1)—that Adapted with were modification used as nanoobjects [257]. in clusters with 1-ﬂuoroethanolFigure have 17. Conformers the same grossof S-1-fluoroethanol. formula (C80H Adapted16), but SWCNTwith modification (4,4) is more [257]. stable than (4,1) 0 at 0.6Molecules kcal/mol ( ∆ofG 2981-fluoroethanol). Hence, these inside nanotubes SWCNTs can be viewed(4,4) and as structuralM(4,1) convert isomers. into preferable conformationMolecules close ofof 1-ﬂuoroethanol to1-fluoroethanol the eclipsed inside (Figure inside SWCNTs 18). SWCNTs (4,4) and (4,4) M(4,1) and convert M(4,1) into convert preferable into conformation preferable closeconformation to the eclipsed close to (Figure the eclipsed 18). (Figure 18).

Figure 18. Preferred conformation of S-1-fluoroethanol inside SWCNTs. Adapted with modification Figure[257]. 18. Preferred conformationconformation of of S-1-fluoroethanol S-1-fluoroethanol inside inside SWCNTs. SWCNTs. Adapted Adapted with with modification modification [257]. [257]. TheThe energiesenergies ofof clustersclusters R-CR-C22HH55FO@(4,4) and S-CS-C22H5FO@(4,4)FO@(4,4) were were predictably predictably the same. However, endocomplex R-C H FO@M(4,1) was proven to be more stable than S-C H FO@M(4,1) at However,The energies endocomplex of clusters R-C22H 55R-CFO@M(4,1)2H5FO@(4,4) was provenand S-C to2H be5FO@(4,4) more stable were than predictably S-C22H55FO@M(4,1) the same. at 4.4 kcal/mol, and in comparison with cluster C H FO@(4,4) at 12.8 kcal/mol (∆G 00). This means that, However,4.4 kcal/mol, endocomplex and in comparison R-C2H5FO@M(4,1) with cluster was C2 2H 5proven5FO@(4,4) to beat 12.8more kcal/mol stable than (ΔG298 298S-C).2 HThis5FO@M(4,1) means that, at despite the greater stability of SWCNT (4,4), cluster R-C H FO@M(4,1) exhibits a large energy gain 4.4despite kcal/mol, the greater and in stabilitycomparison of SWCNT with cluster (4,4), C cluster2H5FO@(4,4) R-C22H at55FO@M(4,1) 12.8 kcal/mol exhibits (ΔG298 a0). large This energymeans that,gain which can serve as a theoretical basis to separate both enantiomers. Besides that, the guest molecule in despitewhich can the serve greater as stabilitya theoretical of SWCNT basis to (4,4),separate cluster both R-C enantiomers.2H5FO@M(4,1) Besides exhibits that, a the large guest energy molecule gain allin all cases cases has has a slight a slight negative negative charge charge (up (up to to0.12) −0.12) [257 [257].]. which can serve as a theoretical basis to separate− both enantiomers. Besides that, the guest molecule in all cases has a slight negative charge (up to −0.12) [257]. 7.2.7.2. R- and S-Isomers of α-Alanine insideinside SWCNTsSWCNTs (n,m)(n,m) α 7.2. R-ConformationalConformational and S-Isomers of analysis analysisα-Alanine of of free inside free-alanine SWCNTsα-alanine (C (n,m)3 H(C7NO3H 72NO), carried2), carried out forout S-isomer for S-isomer by rotating by rotating around the bond C(NH2)–C(O), indicates the presence of several stationary points on the PES; the main aroundConformational the bond С(NH analysis2)−C(O), of indicatesfree α-alanine the presence (C3H7NO of 2several), carried stationary out for pointsS-isomer on theby PES;rotating the minimum corresponds to the form A, and the main TS to the conformation B (Scheme 12, Table4)[ 259]. aroundmain minimum the bond corresponds С(NH2)−C(O), to the indicates form A the, and presence the main of TS several to the conformationstationary points B (Scheme on the 12,PES; Table the These results are quite consistent with the data of [260]. main4) [259]. minimum These results corresponds are quite to theconsistent form A ,with and the datamain of TS [260]. to the conformation B (Scheme 12, Table 4) [259]. These results are quite consistent with the data of [260]. H C 3 NH2 H C H2N H HO 3 O HO NH2 O HO O H3C H2N H HO NHO2 HO H O O H HO CH A H3C 3 H NH2 TS-1 (ВH) C A CH3 TS-1 (В) C H

HO H O H N CH HO 2 3O H2NTS-2 (DCH) 3 SchemeScheme 12.12. ConformationalTS-2 equilibrium (D) ofof freefree αα-alanine.-alanine. SWCNTs (5,5), (5,1) and (5,2), which were used as nanoobjects for the investigation of α-alanine Scheme 12. Conformational equilibrium of free α-alanine. propertiesSWCNTs in endocomplexes, (5,5), (5,1) and (5,2), diﬀer which in energy: were asused in the as nanoobjects previous case for (Section the investigation 7.1), the most of α stable-alanine is nanotubepropertiesSWCNTs (5,5) in endocomplexes, (5,5), (Table (5,1)4). and (5,2), differ which in energy: were asused in theas nanoobjects previous case for (Section the investigation 7.1), the most of α -alaninestable is propertiesnanotubeThe conformational (5,5)in endocomplexes, (Table 4). behavior differ ofin αenergy:-alanine as inin clusters,the previous for the case example (Section of 7.1), S-C the3H most7NO2 stable@P(5,2), is isnanotube presentedThe conformational(5,5) in Scheme(Table 4). 13 .behavior In this case, of α the-alanine main minimumin clusters, on for the the PES example corresponds of S-C to3H the7NO conformer2@P(5,2), Dis. Comparison of clusters’ energy (Table4) indicates that in a series of clusters with SWCNTs: (5,5), presentedThe conformational in Scheme 13. Inbehavior this case, of the α-alanine main minimum in clusters, on forthe thePES example corresponds of S-C to3 Hthe7NO conformer2@P(5,2), Dis. (5,1)presented and (5,2)in Scheme their relative 13. In this stability case, the grows; main theminimum most stable on the are PES practically corresponds degenerated to the conformer in energy D. endocomplexes S-C3H7NO2@P(5,2) and R-C3H7NO2@M(5,2) (Figure 19). Thus, the increase in chirality index m leads to a rise in the relative stability of the appropriate chiral clusters.

Molecules 2020, 25, 2437 23 of 37

Table 4. Relative energies of SWCNTs, α-alanine and clusters of α-alanine together with the electric charge of the guest molecule (PBE/3ζ)[259].

0 Object ∆G298 (∆G298,), kcal/mol Electric Charge (5,5) 0 0 P,M(5,1) 1 5.9 0 P,M(5,2) 1 16.1 0

S-C3H7NO2 (A) 0 0 2 S-C3H7NO2 (B) (3.1) 0 2 S-C3H7NO2 (D) (2.7) 0 R,S-C H NO @(5,5) 3 13.9 0.69 3 7 2 − S-C H NO @M(5,1) 3 12.3 0.69 3 7 2 − S-C H NO @P(5,1) 3 12.1 0.67 3 7 2 − R-C H NO @M(5,1) 3 12.1 0.67 3 7 2 − R-C H NO @P(5,1) 3 12.3 0.69 3 7 2 − Molecules 2020, 25, x FORS-C PEERH NO REVIEW@M(5,2) 3 4.6 0.64 24 of 39 3 7 2 − S-C H NO @P(5,2) 0 0.67 3 7 2 CH3 − H H3C NH2 R-C H NO @M(5,2) 3 HO 0.1 0.67 HO 3 7 2O H O HO − O R-C H NO @P(5,2) 3 4.7 H N 0.65 CH 3 7 2 NH2 2 − 3 1 H 2 3 Molecules 2020Relative, 25, x FOR to(5,5). PEERE REVIEWRelative to form A. RelativeTS-3 to(F S-C) 3H7NO2@P(5,2) (conformer DDfor α-alanine). 24 of 39

CH3 H H3C NH2 HO O H O HO NH2 HO O H N CH NH2 2 3 H O E HO TS-3 (F) D H3C H TS-4 (G)

Scheme 13. Conformational equilibriumNH2 of S-C3H7NO2@P(5,2). HO O Comparison of clusters’ energy (Table 4) indicates that in a series of clusters with SWCNTs: (5,5), H C H (5,1) and (5,2) their relative stability grows;3 the most stable are practically degenerated in energy TS-4 (G) endocomplexes S-C3H7NO2@P(5,2) and R-C3H7NO2@M(5,2) (Figure 19). Thus, the increase in chirality index m leads to a rise in the relative stability of the appropriate chiral clusters. SchemeScheme 13.13. Conformational equilibrium of S-CS-C33H7NONO22@P(5,2).@P(5,2).

Comparison of clusters’ energy (Table 4) indicates that in a series of clusters with SWCNTs: (5,5), (5,1) and (5,2) their relative stability grows; the most stable are practically degenerated in energy endocomplexes S-C3H7NO2@P(5,2) and R-C3H7NO2@M(5,2) (Figure 19). Thus, the increase in chirality index m leads to a rise in the relative stability of the appropriate chiral clusters.

Figure 19. The most stable endocomplex, S-C3H7NO2@P(5,2). Adapted with modiﬁcation [259]. Figure 19. The most stable endocomplex, S-C3H7NO2@P(5,2). Adapted with modification [259].

Table 4. Relative energies of SWCNTs, α-alanine and clusters of α-alanine together with the electric charge of the guest molecule (PBE/3ζ) [259].

Object ΔG2980 (ΔG298≠), kcal/mol Electric Charge Figure 19. The most (5,5)stable endocomplex, S-C3H7NO0 2@P(5,2). Adapted with0 modification [259]. P,M(5,1) 1 5.9 0 Table 4. Relative energies of SWCNTs, α-alanine and clusters of α-alanine together with the electric P,M(5,2) 1 16.1 0 charge of the guest molecule (PBE/3ζ) [259]. S-C3H7NO2 (A) 0 0 0 ≠ S-C3HObject7NO2 (B) 2 ΔG298 (ΔG(3.1)298 ), kcal/mol Electric0 Charge S-C3H(5,5)7NO 2 (D) 2 (2.7)0 00 1 R,S-CP3H,M7NO(5,1)2@(5,5) 3 13.95.9 −0.690 1 S-C3HP7,NOM(5,2)2@M (5,1) 3 16.112.3 −0.690 S-CS-C3H37HNO7NO2@2P ((5,1)A) 3 12.10 −0.67 0 2 R-CS-C3H3H7NO7NO2@2M (B(5,1)) 3 (3.1)12.1 −0.670 2 R-CS-C3H3H7NO7NO2@2 P(D(5,1)) 3 (2.7)12.3 −0.690 3 RS-C,S-C3H3H7NO7NO2@2M@(5,5)(5,2) 3 13.94.6 −0.690.64 3 SS-C-C3H3H7NO7NO2@2@MP(5,1)(5,2) 12.30 −0.690.67 3 RS-C3H7NO2@MP(5,1)(5,2) 3 12.10.1 −0.67 3 RR-C-C33HH77NONO22@@MP(5,2)(5,1) 3 12.14.7 −0.670.65 3 1 Relative to (5,5).R-C3 2H Relative7NO2@ Pto(5,1) form A. 3 Relative to12.3 S-C 3H7NO2@P(5,2) (conformer−0.69 D for α-alanine). S-C3H7NO2@M(5,2) 3 4.6 −0.64 S-C3H7NO2@P(5,2) 0 −0.67 R-C3H7NO2@M(5,2) 3 0.1 −0.67 R-C3H7NO2@P(5,2) 3 4.7 −0.65

1 Relative to (5,5). 2 Relative to form A. 3 Relative to S-C3H7NO2@P(5,2) (conformer D for α-alanine).

Molecules 2020, 25, 2437 24 of 37

All results conﬁrm the earlier conclusion [257] that the combination of S-enantiomer with P-SWCNT and R-enantiomer with M-SWCNT leads to the formation of most stable endocomplexes and creates a theoretical foundation for the recognition and eﬀective separation of optical isomers.

8. Relative Stability of Cis and Trans Isomers inside Nanotubes. The “Trans-Effect” It is well known that, in some cases, the cis isomer of compounds with a double bond is more stable than its trans form. This applies, for example, to 1,2-difluoroethene and difluorodiazene [261,262]. Such phenomenon is called the “cis effect”, and its probable causes have been discussed in the literature [263–266]. In particular, according to [266], the cis effect in the case of difluorodiazene is caused for a number of reasons. One of them is connected with a destabilization of the trans form because of the increased ionic character of the bonds linking the central to the peripheral atoms. This leads to the destabilizing reduction of the valence angles in both isomers, but in cis form this change is relaxed by Coulombic repulsion between two terminal atoms. Using the PBE/3ζ approximation, it has been shown that free 1,2-difluoroethene and difluorodiazene demonstrate an advantage in energy in their cis form. However, investigation of the relative stability of both isomers in the cavity of SWCNT (4,4) demonstrates the action of the “trans-effect”: the predominance of the trans-configuration. The energy differences from the cis form reach two-digit numbers (Table5) [ 267,268]. The same pattern is valid also for the cluster CHF=CHF@(6,6), although with less distinction in energy between both isomers.

Table 5. Relative energies of geometric isomers of 1,2-diﬂuoroethene and diﬂuorodiazene, their

endocomplexes with SWCNTs, the bond order of the double bond, OX=X and the electric charge on the guest molecule (PBE/3ζ)[267,268].

0 Object ∆G298 , kcal/mol OX=X Charge CHF=CHF, cis- 0 1.78 0 trans- 0.6 1.77 0 FN=NF, cis- 0 1.76 0 trans- 3.4 1.66 0 CHF=CHF@(4,4), cis- 26.2 1.32 0.46 trans- 0 1.44 0.52 CHF=CHF@(6,6), cis- 0.9 1.72 0.16 − trans- 0 1.73 0.17 − FN=NF@(4,4), cis- 27.4 1.46 0.36 − trans- 0 1.73 0.36 − FN=NF@(6,6), cis- 0 1.71 0.03 − trans- 3.8 1.69 0.004 −

The observed effect depends on the diameter of the nanotubes (Figure 20). It should be noted that there are several reasons for this complex phenomenon. On the one hand, the force field inside the nanotube significantly changes the structure of the guest species. In particular, the distance between fluorine atoms in cis-N2F2@(4,4) (2.402 Å) is shorter than for the free cis-difluorodiazene (2.452 Å), which enhances additional internal stress and leads to the destabilization of cis-configuration. On the other hand, in the case of cis-CHF=CHF@(4,4), the observed distance (3.084 Å) becomes greater than for the free cis-1,2-difluoroethene (2.793 Å). However, the cis isomer still remains unstable. Hence, it is also necessary to take into account the role of electronic factors: the noticeable change in Mulliken bond order (OX=X, Table5) inside SWCNT (4,4) demonstrates a significant redistribution of electron density in the guest molecule, probably because of orbital interactions with the π-system of the nanotube. Thus, SWCNTs are able to drastically change the relative stability of cis and trans isomers in their cavity for several reasons. Molecules 2020, 25, x FOR PEER REVIEW 25 of 39

All results confirm the earlier conclusion [257] that the combination of S-enantiomer with P- SWCNT and R-enantiomer with M-SWCNT leads to the formation of most stable endocomplexes and creates a theoretical foundation for the recognition and effective separation of optical isomers.

8. Relative Stability of Cis and Trans Isomers inside Nanotubes. The “Trans-Effect” It is well known that, in some cases, the cis isomer of compounds with a double bond is more stable than its trans form. This applies, for example, to 1,2-difluoroethene and difluorodiazene [261,262]. Such phenomenon is called the “cis effect”, and its probable causes have been discussed in the literature [263–266]. In particular, according to [266], the cis effect in the case of difluorodiazene is caused for a number of reasons. One of them is connected with a destabilization of the trans form because of the increased ionic character of the bonds linking the central to the peripheral atoms. This leads to the destabilizing reduction of the valence angles in both isomers, but in cis form this change is relaxed by Coulombic repulsion between two terminal atoms. Using the PBE/3ζ approximation, it has been shown that free 1,2-difluoroethene and difluorodiazene demonstrate an advantage in energy in their cis form. However, investigation of the relative stability of both isomers in the cavity of SWCNT (4,4) demonstrates the action of the “trans- effect”: the predominance of the trans-configuration. The energy differences from the cis form reach two-digit numbers (Table 5) [267,268]. The same pattern is valid also for the cluster CHF=CHF@(6,6), although with less distinction in energy between both isomers. The observed effect depends on the diameter of the nanotubes (Figure 20). It should be noted that there are several reasons for this complex phenomenon. On the one hand, the force field inside the nanotube significantly changes the structure of the guest species. In particular, the distance between fluorine atoms in cis-N2F2@(4,4) (2.402 Å) is shorter than for the free cis-difluorodiazene (2.452 Å), which enhances additional internal stress and leads to the destabilization of cis- configuration. On the other hand, in the case of cis-CHF=CHF@(4,4), the observed distance (3.084 Å) becomes greater than for the free cis-1,2-difluoroethene (2.793 Å). However, the cis isomer still remains unstable. Hence, it is also necessary to take into account the role of electronic factors: the noticeable change in Mulliken bond order (OX=X, Table 5) inside SWCNT (4,4) demonstrates a

Moleculessignificant2020 ,redistribution25, 2437 of electron density in the guest molecule, probably because of orbital25 of 37 interactions with the π-system of the nanotube.

FigureFigure 20.20. Clusters ofof cis-Ncis-N22F2 inin the the light light of of van der Waals spheres.spheres. The distances betweenbetween thethe guestguest moleculemolecule andand thethe SWCNTSWCNT wallwall areare 2.42.4 ÅÅ and 3.7 ÅÅ for (4,4) and (6,6) endocomplexes, respectively. AdaptedAdapted withwith modiﬁcationmodification [[267].267]. 9. Conclusions

Promising opportunities of different nanostructured objects are largely connected with the formation of endohedral complexes of fullerenes and nanotubes. Unique conditions in their cavities can be viewed as the action of a solvent with specific properties. As a result, a combination of electronic and steric requirements, that may be called a force field, inside fullerenes and nanotubes significantly changes the stereochemical properties of even relatively simple molecules in comparison with their free state or with the action of usual solvents. Principal differences are mainly the following:

The preferred conformation of ethane and its analogs inside nanotubes of small diameter is not • the staggered, but the eclipsed form. The conformational behavior of ethane-like molecules inside fullerenes is less clear and depends on the size and chemical composition of the nanoobject. Hydroxyborane and diborane in endohedral clusters of nanotubes are characterized by reducing • the barriers of internal rotation about the B-O and B-B bonds; in the case of dialane, the planar form—the transition state for the free molecule—becomes the minimum on the potential energy surface. A similar change in the nature of the preferred conformation is observed for hydrazine, methanol, methanethiol and dimethyl ether, together with cyclic molecules: cyclohexane, 1,3-dioxa-2-silacyclohexane and hexahydropirimidine-2-one inside nanotubes. In the case of 1,3-dioxane inside SWCNT and 1,3,2-dioxaborinane inside fullerene C60 conformational equilibrium is shifted to forms that can never be realized as a ground state for neither free molecule, nor for these species in any solvent. The barrier to pyramidal inversion of amines in endocomplexes varies depending on the nature of • the amine and the size of the nanocavity. Chiral nanotubes are able to recognize molecules of enantiomers owing to increased aﬃnity of • P-SWCNT for the S-isomer and M-SWCNT for the R-form. SWCNTs of small diameter are able to drastically change the relative stability of cis and trans • isomers in their cavity.

Everything mentioned above indicates fundamental changes in the structural properties of the guest species, and constitutes the ground for an in-depth systematic stereochemical investigation of a large variety of compounds inside nanotubes and fullerenes. Molecules 2020, 25, 2437 26 of 37

Funding: This research received no external funding Conﬂicts of Interest: The authors declare no conﬂict of interest

Abbreviations

SWCNTs single-walled carbon nanotubes PES potential energy surface TS transition state DFT density functional theory HF Hartree–Fock PBE Perdew–Burke–Ernzerhof O Mulliken bond order HOMO high occupied molecular orbital LUMO low unoccupied molecular orbital C conformation of chair form Tw conformation of twist form

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