Analysis of a bicyclic, triple disulphide molecular nanopropeller

Abstract

The bicyclic, triple disulphide molecule, HC(S₂)₃CH called propellerdisulphide (PS), has been quantum chemically shown in this work to be a stable, isolated molecule with potential applications to nanoparticle transportation for biomedical uses. The desire of hydrogen disulphide to twist in its lowest energy conformation is exploited to create a bicyclic compound that has non-zero τ(C–S–S–C) dihedral angles and is, consequently, also optically active. This angle creates an inclined plane or screw-like pattern within the molecule that can direct particles in a way similar to that of a macroscopic screw. The barrier to rotation for directly linking PS to a model fullerene surface is 6.00 kcal mol⁻¹ while linking it through a pyrrolidine bridging group is nearly double this. It is suggested herein that pulsed THz energy could excite the low-lying PS twisting vibrational frequency relative to the nanoparticle surface over several quanta. This action could overcome the barrier to rotation such that the PS ligand will spin and give propeller-like properties for enhancing the movement of fullerene nanoparticles. Applications of this behavior stretch into medicine since endohedral fullerene nanoparticle cages can encapsulate imaging or therapeutic compounds, and directing the nanoparticles to the desired site more efficiently could make a significant impact on treatment.

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1 Introduction

A bicyclic, disulphide molecule (HC(S₂)₃CH) is explored through ab initio quantum chemical computations for its propeller- or screw-like properties in order to direct the passage of nanoparticles such as endohedral metallofullerenes with application to drug delivery and nanorobotics. Since the discovery of fullerenes in the 1980s, it has been speculated that these molecular species could serve as chemical transportation cages¹ for applications ranging from medicine to small-scale robotics and energy harnessing.² In fact, this discovery with its roots in astrochemistry ushered in the “nanotechnology” revolution.² Extrusion of fullerenes anisotropically creates carbon nanotubes. Flattening these structures gives graphene sheets. These carbon structures have garnered two Nobel Prizes (Chemistry 1996 for the discovery of fullerenes and Physics 2010 for applications of graphene) and continue to have significant application promise across the science and technology disciplines. Fullerenes have even now been detected in the interstellar medium^3–5 confirming earlier hypotheses that they should be common thermodynamic products of long-term hydrocarbon chemistry.⁶

Within a decade of the discovery of fullerenes, encapsulation of other atomic and chemical species, initially Sc₂, within the carbon allotrope nanoparticle cages was clearly shown.⁷ Modern synthesis and application of these endohedral metallofullerenes promises to be a vital tool in the imaging and treatment for various types of tumors.^8,9 The chemical agent for either function is encapsulated in a fullerene cage through established but not fully understood means. The cage and its cargo can be injected into the body and carried through the bloodstream to the treatment site as is typical for most pharmaceuticals. The cages can be treated with certain functional groups to make them attractive to the desired malignancy⁸ such that they will bind to the tumor once they are carried through the body's natural channels. Ring-opening techniques can be employed to release the anti-cancer agent encased in the cage,¹⁰ or the imaging compound is simply retained for visualization. In either case, the cage and its remaining contents are flushed from the body.

While utilizing the body's natural pathways is essential for any drug delivery, allowing the nanoparticle merely to go at the pace of the bloodstream can lead to relatively long timeframes for delivery of enough material to the active site. Providing a further means of propelling the material could significantly enhance treatment where minutes or even seconds may make the difference. Taking a cue from bacteria flagella, Schamel and coworkers¹¹ have recently synthesized a polymer chain that functions as a propeller on the 300 nanometer scale. This revolutionary development promises to behave as a controlled nanorobot within various liquid media including biological fluids. These “micropropellers” or “nanoscrews” will allow for delivery of nanocargo materials with unprecedented control. However, fullerenes, specifically C₆₀, are on the order of 1% the size of these nanoscrews. While several could fit within the delivery head of such nanorobots, it would be beneficial to have enhanced control over these smaller species. Brownian forces must not be neglected for nanoscale and even microscale particles, but giving some directional control to the nanoparticles will enhance their ability to traverse distances.

A simple approach for fullerene locomotion would be to put paddles on the side of the cage. Such paddles have been shown as viable structures,¹² but they can be larger than the fullerene itself. This creates issues with counter-rotation about the “axle” or chemical bond and torque energies that may break such a bond. Smaller triptycene gears have been created,¹³ but it would require at least two of these gears or paddles, in this case, to be placed on opposite sides of the fullerene. Such an involved synthetic step would only increase the production cost of such a system. In the macroscopic world, the need for co-rotating paddles is overcome by creating a screw-like propeller. Some directionality or screw-like construction in the panels for the flat portion radiating from the axis of rotation ensures that only one propeller-like ligand would have to be added to serve as the propulsion source.

Bicyclo[2,2,2]octene (or “barrelene”) is a known D_3h molecule¹⁴ and serves as the base for the aforementioned triptycene gears. However, its external butadiene, τ(C–C–C–C) dihedral angle is 0.0° and, hence, can not produce any screw-like behavior. Hydrogen peroxide, on the other hand, is neither cis nor trans in its lowest energy confirmation. As such, creating a bicyclic, triple peroxide structure by replacing the three C₂H₂ groups on the outside of the barrelene ring with O₂ groups would likely create a D₃ structure where the τ(C–O–O–C) dihedral angle is greater than 0.0°. However, peroxides are notoriously unstable. Differently, sulphur is analogous to oxygen but is known to make strong bonds to other sulphur atoms in addition to relatively strong bonds with carbon. Hydrogen disulphide (HSSH) is also known not to be cis nor trans in its lowest energy conformation. Consequently, this work will explore the bicyclic compound that arises when the ethylene groups on the exterior of the barrelene ring are replaced with three disulphide groups. Work has shown that bicyclic structures are stable and can be synthesized even when replacing the carbons with other atoms including sulphur.^15,16 As such, it is not beyond the realm of possibility for disulphide groups to be present in non-planar, bicyclic compounds. The molecule of study here (HC(S₂)₃CH) will be called propellerdisulphide, or PS, for the remainder of the discussion.

Attaching an external ligand to a fullerene requires two additions since the aromaticity is broken. Consequently, exterior fullerene ligands often come in pairs to attach twice in para positions on one of the benzene rings.¹⁷ In the case of such large groups as PS, double addition would likely interfere with the rotation for each of the propeller-like functional groups. Consequently, a hydrogen atom will be added on the ring para to the PS ligand. However, most studies have shown that a linking group on the fullerene surface is more effective for the addition of exterior ligands. A common linker is a pyrrolidine structure where a H₂CN(H)CH₂ moiety adds above a C=C bond in between two of the six-membered rings on the surface of the fullerene.^17,18 Functional groups are then added to the nitrogen thereby replacing the amide hydrogen when in the axial position. Several other linkers including epoxides¹⁹ are also possible, but the present work will be limited to appending PS to model fullerene surfaces (acenaphthylene and pyracyclene, specifically) through direct means and through the pyrrolidine linker. Such analysis will provide insight into the structure and rotational properties of PS as a potential propeller for enhancing fullerene and molecular-scale free movement.

2 Computational details

This work utilizes Møller–Plesset second-order perturbation theory (MP2)²⁰ for all quantum chemical computations unless otherwise noted. However, the density-fitted form of MP2 (DF-MP2)²¹ is very efficient in the free and open-source PSI4 program,²² which is the quantum chemical program employed here. DF-MP2 is even faster than density-functional theory within PSI4 in some cases, and will be used as a result. MP2 is known to create a Pauling point of exceptional accuracy when utilizing double-zeta basis sets.²³ Consequently, the 6-31+G* basis set²⁴ is a natural fit for molecules with as many electrons and subsequent basis functions as will be considered in the present computations. The largest molecule analyzed here is PS appended to pyracyclene via the pyrrolidine linker for a total of 525 basis functions. Furthermore MP2/6-31+G* has been rated as one of the most accurate methods for the least amount of computational cost.²⁵ All geometry optimizations are followed by vibrational frequency analysis to ensure that the optimized structures are minima. All computations are also done without solvation models, but the estimates of the potential energy surfaces should not be significantly changed by the solvent for the types of analyses undertaken as has been shown previously for rotational conformational analysis.²⁶

The WebMO graphical user interface²⁷ has been employed for visualizing the molecular structures in all figures and for the construction of the potential energy surfaces (PESs). In the latter case, full group response to a change of a local coordinate value is essential. For example the τ(S–C–N–C) dihedral in the PS–pyrrolidine–pyracyclene is varied to produce the conformational PES of the full PS group rotating about the linking C–N bond.

Additionally, PS is optically active due to its D₃ yet rigid structure discussed below. Coupled cluster singles and doubles (CCSD)^28,29 linear response theory³⁰ aug-cc-pVDZ computations available within PSI4 are known to be useful for computing such values even of related bicyclic compounds.^31,32 Standard wavelengths of 355 nm and 589 nm are utilized for the computation of PS optical rotation from the MP2/6-31+G* optimized geometry. Finally, vertical electronic excitations are also determined from equation of motion^33,34 CCSD/aug-cc-pVDZ computations again from the MP2/6-31+G* optimized geometry.

3 Results

3.1 Propellerdisulphide

The structure of PS is given in Fig. 1. Numerical values for the internal coordinate parameters are provided in Table 1 as well as comparison to MP2 results with the larger aug-cc-pVTZ basis set.^35,36 PS has D₃ symmetry since it lacks mirror planes, and the 6-31+G* and aug-cc-pVTZ geometrical parameters differ by what is expected. The bond lengths are slightly longer for the smaller basis set. The differences in the bond angles and dihedrals are smaller than 3.0°. Regardless, the smaller 6-31+G* basis appears to be adequate for describing this molecule.

Fig. 1 HC(S₂)₃CH or propellerdisulphide (PS).

Table 1 The structure, rotational constants, and harmonic frequencies of HC(S₂)₃CH in Å, degrees, and cm⁻¹

	D3 MP2/6-31+G*	D3 MP2/aug-cc-pVTZ	D3h MP2/6-31+G*
C–H	1.095	1.085	1.098
C–S	1.831	1.822	1.817
S–S	2.079	2.052	2.124
∠H–C–S	106.78	107.77	101.92
∠C–S–S	98.87	98.52	101.92
∠S–C–S	112.03	111.12	115.85
τ(C–S–S–C)	41.00	44.44	0.00
τ(H–C–S–S)	154.99	153.10	180.00
τ(S–C–H–S)	120.00	120.00	120.00
A/B	0.031925	0.032970	0.028950
C	0.028599	0.029202	0.027790
ω1 (a1, S2 twist)	185.3	194.7	128.2i
ω2 (e)	203.1	209.7	145.0
ω3 (e)	266.3	263.2	265.1
ω4 (e)	305.8	305.9	284.5
ω5 (a1)	411.6	398.6	424.3
ω6 (a2)	485.7	481.7	490.8
ω7 (a1)	510.8	535.5	465.0
ω8 (e)	512.7	529.8	478.9
ω9 (a1)	646.0	628.1	661.4
ω10 (a2)	677.9	666.9	682.3
ω11 (e)	715.7	704.3	735.7
ω12 (e)	740.0	732.3	778.0
ω13 (e)	1188.1	1129.5	1197.8
ω14 (e)	1190.9	1135.5	1199.2
ω15 (a2)	3140.7	3133.9	3104.2
ω16 (a1)	3142.1	3134.1	3108.6
Hrel.			14.94 kcal mol^−1

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None of the bond lengths or angles vary from the expected values of R–S–S–R systems. The 2.079 Å S–S bond is in line with the ∼2.05 Å expected in most disulphide bonds. The ∠C–S–S bond angle of 98.87° with a sulphur atom at the center is closer to 90° than 109.5° since third-row atoms do not engage in the typical hybridization patterns as their second-row analogues do.^37–39 The τ(C–S–S–C) dihedral angle clearly demonstrates a twist in the molecule creating the desired propeller or screw pattern necessary. This is also clearly shown in the side-on view of PS in Fig. 1. Hydrogen disulphide itself has a MP2/6-31+G* τ(H–S–S–H) dihedral angle of 90.63°. However, the ∠H–S–S value in H₂S₂ is 98.90°, and S–S is 2.072 Å. These values are quite close to the same values as that in PS. As a result, PS is not highly strained and has almost no Baeyer strain. Most of the estimated 12.2 kcal mol⁻¹ ring strain estimated by WebMO comes from the need to reduce the dihedral angle by more than half in PS compared to hydrogen disulphide.

Homolytic bond cleavage for each S–S bond in PS is estimated to cost 40.21 kcal in line with previous work⁴⁰ and require 51.51 kcal mol⁻¹ for the C–S bonds. These estimates involve breaking the bonds in question and pairing the unpaired electron with a hydrogen atom. After geometry optimizations of these structures, the hydrogens are removed, and single-point energies are computed. The bond energy is then taken to be the difference between the energies of the stable molecule and that with the broken bond.

The optimized D_3h form of PS whose geometrical data are also given in Table 1 shows more signs of strain in addition to the 14.94 kcal mol⁻¹ higher relative enthalpy (H_rel.). The S–S bonds lengthen slightly while the ∠H–S–S and ∠S–C–S values shift by more than 4.0° relative to the lower-energy D₃ structure. The D_3h isomer also possesses one imaginary frequency corresponding to the twist of the S₂ groups orthogonal to the primary C₃ axis.

The MP2/6-31+G* harmonic vibrational frequency for this same mode in the more stable isomer is 185.3 cm⁻¹, and MP2/aug-cc-pVTZ puts this value a little higher at 194.7 cm⁻¹ as given in Table 1. The low-frequency nature of this mode will make the first few quanta of this vibrational state notably populated under thermal conditions. In and of itself, such motion could be enough to provide some buffering behavior to enhance transportation of any attached fullerenes or nanoparticles. All of the other harmonic vibrational frequencies also fall below 1200 cm⁻¹ except for the two C–H stretching modes (antisymmetric and symmetric) which are at 3140.7 cm⁻¹ and 3142.1 cm⁻¹, respectively. The harmonic vibrational frequency agreement between the two basis sets is also excellent, and clear delineations are shown between the D_3h and D₃ isomers from these harmonic vibrational frequencies.

Consideration of rotation in a true propeller motion requires the rotational constants. The equilibrium rotational constants are unsurprisingly low for PS in Table 1 since the longer C–S bonds and heavier masses of sulphur give a larger moment of inertia to the exterior S₂ portions of the molecule that are rotating. While this free rotation should be easily accessible, especially for rotation about the C–C axis, this does not provide a clear picture as to how PS can rotate when attached to a fullerene or similar nanoparticle.

The electrostatic potential map in Fig. 2 shows how the electron probability “surface” of the molecule will create the physically-interacting propeller. Most of the exposed propeller surface is in warmer tones indicating a relatively electron-rich area. It also is somewhat bulbous but does have enough contours to interact with and direct other ambient particles with which it may come into contact.

Fig. 2 The PS electrostatic potential map.

The length-gauge specific rotation optical activity [α] for the 355 nm wavelength tested is −498.4 deg dm⁻¹ (g mL⁻¹)⁻¹, and the 589 nm rotation is 43.5 deg dm⁻¹ (g mL⁻¹)⁻¹. The velocity-gauge [α] values are 2279.7 deg dm⁻¹ (g mL⁻¹)⁻¹ and 340.1 deg dm⁻¹ (g mL⁻¹)⁻¹, respective of 355 nm and 589 nm. The modified velocity-gauge optical rotations are slightly less at 2054.0 deg dm⁻¹ (g mL⁻¹)⁻¹ and 114.4 deg dm⁻¹ (g mL⁻¹)⁻¹, respectively. In any of these cases, the shorter wavelength at 355 nm appears to be more optically active than the longer wavelength explored, and PS is clearly optically active.

The two lowest energy electronic transitions involve promoting electrons out of the highest occupied a₁ orbital, which is the globally highest occupied molecular orbital (HOMO), as well as the highest e orbital (the HOMO−1). The electrons are accepted into the third-lowest unoccupied orbital (LUMO+2) in both cases, which also has e symmetry. The lowest energy electronic excitation creates the 1 ¹E state. The transition takes place in the ultraviolet A (UVA) range at 3.73 eV (332 nm) with an oscillator strength of 8 × 10⁻⁴. The transition is composed primarily of a₁ → e* and mixed portions of e → e* promotions of 0.42 and 0.22/0.22 character, respectively. Another excitation, that creating the 2 ¹A₁ state, also lies within the UVA range at 3.83 eV or 324 nm with an oscillator strength of 1 × 10⁻³. The 2 ¹A₁ state is comprised of e → e* (0.35/0.35) and a₁ → a^*₁ (0.26) character, where the a^*₁ orbital in question is the LUMO−3.

3.2 Directly linked PS

As mentioned above, the conceptually simplest way to attach a functional group to a fullerene is to link the ligand directly to the fullerene cage surface and provide a hydrogen atom in the para position on the same six-membered ring. In order to probe this behavior, the full fullerene is approximated in the present model with acenaphthylene (C₁₂H₈). The MP2/6-31+G* optimized geometry for this linked structure is given in Fig. 3. While the structure of the PS ligand changes upon linkage relative to the isolated compound, these values are not greater than 0.05 Å for the bond lengths and 3.0° for the bond angles and dihedrals. Case in point, the τS–C–H–S dihedral angle increases to 120.29° up from 120.00° for the sulphur closest to the new, axial hydrogen. The other, related dihedrals decrease in response. Consequently, the PS structure changes some, but not significantly. A notable new value, however, is the 1.578 Å C–C bond that connects PS to the acenaphthylene. This is a fairly long C–C bond, but dissociation of PS from the acenaphthylene is computed here to be more than 100 kcal mol⁻¹. Therefore, the C–C bond strength is estimated to be on the order of more than 80 kcal mol⁻¹ after hydrogen bonding and other non-covalent interactions between the two groups are considered.

Fig. 3 The structure of PS–acenaphthylene.

The S₂ twisting vibrational frequency of the PS ligand increases to 196.9 cm⁻¹, 11.6 cm⁻¹ higher than the isolated molecule. However, this increase of 11.6 cm⁻¹ is not a significant jump and will still leave several quanta populated. The lowest frequency harmonic mode for the directly linked PS–acenaphthylene is actually the twisting of PS relative to the acenaphthylene model surface at 28.5 cm⁻¹ for MP2/6-31+G*. This bodes well for the free rotation of the propeller-like properties of PS since several quantum levels will be filled for this motion at ambient conditions. However, the barrier to free rotation will be inhibited by interactions of the lower sulphur atoms with the π clouds of the fullerene surface, as modeled by acenaphthylene in this case, as well as the additional hydrogen atom 2.804 Å away from the closest sulphur.

In order to examine this behavior, the PES for rotation of the τ(S–C–C–C) dihedral angle is produced again with MP2/6-31+G*. The optimized structure τ(S–C–C–C) is 50.77°. The scan begins at 0.0°, steps every 5.0°, and ends after completing slightly more than a full period at 125.0°. The geometries are not optimized at each point, but the variances between the rigid structures used here and the optimized should be fairly small due to little change in the linked versus isolated PS geometries. The results of this scan as well as visual depictions for the top-down view of the PS–acenaphthylene structures at the initial, minimum, and maximum points are given in Fig. 4. The minimum is simply the optimized geometry. The maximum takes place in the 100.0° range and is 6.00 kcal mol⁻¹. The scan is nearly perfectly periodic even without optimizations of the structures at frozen τ(S–C–C–C). Consequently, it is clear that the rotation of PS directly linked to a fullerene surface should not require significant amounts of extra energy in order for the ligand to rotate. The 6.00 kcal mol⁻¹ (or 2100 cm⁻¹) barrier is on the order of that for butane⁴¹ where similar behavior and good performance of the same computational method is also noted. The 6.00 kcal mol⁻¹ rotational barrier is certainly surmountable with the proper allocation of energy. This is discussed in more detail below.

Fig. 4 The PES for the rotation of PS attached to acenaphthylene.

In an attempt to reduce the barrier to free rotation, PS is linked to the acenaphthylene with an additional C₂ group in between. However, the π electrons of the C₂ group are highly drawn to the π cloud on the aromatic surface beneath. As a result, the entire propeller group collapses to the acenaphthylene surface and undergoes several bond breakages. Addition of an acetylene “drive shaft” would not be a practical means of linking PS as a ligand to a fullerene.

3.3 Pyrrolidine-linked PS

As mentioned previously, pyrrolidine linkers are common for adding ligands to fullerenes and related nanoparticles. They bind at two sites on the fullerene cage limiting the amount of additional steps necessary to avoid radical chemistry on the surface. In this case, the fullerene model molecule needs to be more complete than the acenaphthylene utilized for direct linkage since the linker needs to bond to interior carbons in our model molecule. Pyracyclene (PyC, C₁₄H₈) is actually the smallest stand-alone repeating unit within a C₆₀ surface, minus the hydrogens of course. The model system for adding the PS ligand to a fullerene surface via the pyrrolidine linker is shown in Fig. 5. The PyC structure bends in such a manner as is present in fullerenes, and the axial configuration of the pyrrolidine allows for linkage. The equatorial position of the amide hydrogen is the favored position due to interactions with the PyC π cloud, again, but, the axial position is only 3.68 kcal mol⁻¹ higher than the equatorial from optimized geometries computed in this work on the isolated PyC structures.

Fig. 5 The structure of PS–pyrrolidine–pyracyclene from the “front” (a), “side” (b), and “top-down” (c) perspectives.

The optimized structure of PS–pyrrolidine–PyC, again shown in Fig. 5, has a C–N bond between PS and the pyrrolidine of 1.415 Å. The energy of homolytic cleavage between PS and pyrrolidine linker at this C–N bond is 82.6 kcal mol⁻¹. The optimized τ(S–C–N–C) dihedral angle is 74.29° for the sulphur atom whose C–S bond can be viewed as bisecting the pyrrolidine group. This is the sulphur closer (“lower”) to the PyC surface shown at the bottom of Fig. 5c. The τ(C–N–C_p1–C_p2) dihedral angle is 123.79°. The planes for this angle are defined by each of the two pyrrolidine linker carbons: C_p1 is on the left side of Fig. 5a and c with C_p2 on the right. From this, τ(S–C–N–C) could also be given equivalently as 49.50°. The most notable changes in the PS ligand compared to the isolated PS molecule are the three lower C–S bonds. Each lengthen. The largest increase is for the C–S bond where the lower sulphur is, again, the one depicted at the bottom of Fig. 5c. This bond is now 1.883 Å, which is up from 1.831 Å in isolated PS. Fig. 5 clearly shows that the sulphur atoms in the lower portion of PS are in a position to hydrogen bond to the methylene groups present in the pyrrolidine linker. The shortest distance between a lower sulphur and pyrrolidine hydrogen is 2.575 Å and is on the left-hand side of Fig. 5c. Such a value is in line with typical hydrogen bonding. As a result, the barrier to rotation will be affected by these interactions.

Fig. 6 shows the rotational PES for PS–pyrrolidine–PyC about the τ(S–C–N–C_p1) dihedral. Like with PS–acenaphthylene, the optimized geometry is utilized for the rotational scan where only the dihedral is changed. The scan begins with τ(S–C–N–C_p1) = 0.00° and steps by 5.00°, once more, through the minimum at 74.29°, and finishes at 135.00°. The most noteworthy item from the PES is that it is not immediately classified as periodic over the scanned area. A maximum of 12.03 kcal mol⁻¹ is produced at 5.00°, but the corresponding maximum on the other side of the plot is at 8.98 kcal mol⁻¹ for 135.00°. Receding from the C_p1 atom will be different for the sulphur atom than approaching the C_p2 on the other side, but this does not account for the different in peak heights. The inconsistency is a product of the different C–S bond lengths in the utilized PS structure, that from the optimized PS–pyrrolidine–PyC computation. In any case, with MP2/6-31+G* accuracies on the order of 2.00 kcal mol⁻¹,²⁵ the barrier height should be within 9.00–12.0 kcal mol⁻¹, or 3150–4200 cm⁻¹. The hydrogen bonding present between the pyrrolidine linker and the PS ligand creates slightly higher barriers than that for PS directly linked to the model fullerene surface. Other linkers may reduce this barrier and are an exciting avenue for potential future research, but 12.0 kcal mol⁻¹ is, again, not a huge barrier to rotation.

Fig. 6 The PES for the rotation of PS attached to pyracyclene.

4 Discussion

Even though the upper-estimate barriers to rotation are 6.00 kcal mol⁻¹ for PS linked directly to a fullerene nanoparticle and 12.0 kcal mol⁻¹ in the PS–pyrrolidine–fullerene structure, additional energy will be required for the PS ligand in either case to functions as a propeller, screw, or even environmental disrupting agitator for nanoparticle movement enhancement. Collision with a single water molecule, for instance, could reverse the spin of the rotating PS ligand. Thermal conditions could not overcome either barrier since the temperatures would have to rise to over 3000 K and 6000 K in each case. However, directing radiation in such an energy range could effectively make a switch of the PS ligand. Turning on the radiation source could be used to turn the propeller on and off and, thus, direct the nanoparticles through the bloodstream or other medium in a more efficient manner. Unfortunately, 6.00 kcal mol⁻¹ corresponds to 4.77 μm and 12.0 kcal mol⁻¹ is 2.38 μm, which are both toward the blue-end of the mid-infrared (IR) range. These wavelength ranges are optically dark for most tissue studies even though they are non-lethal and relatively safe for in vivo usage. However, recent work has shown that quantum cascade lasers can penetrate to the lower depths of the skin in the mid-IR,⁴² but deeper penetration of the directive light would require prohibitive invasive means.

It could also be possible to electronically excite the PS ligand in the first electronically excited state in the range of 332 nm. A subsequent vibrational cascade through the quanta of the PS spinning vibrational mode could elicit the desired rotations. Unfortunately, the optical window for body tissue is more than 300 nm longer making this electronic transition unlikely to be accessed in vivo. Furthermore, isolating the vibrational energy dissipation for the desired vibrational mode is not trivial.

Another possibility could come from THz-pumping. The THz region of the electromagnetic spectrum is typically considered to lie within the 0.3 to 30 μm range, and it has shown promise recently for non-invasive and deeper tissue penetration for safe biomedical imaging and diagnosis.^43,44 The low-frequency of the PS twisting relative to the fullerene surface will fall in roughly the 1.0 THz range since this harmonic frequency in PS–acenaphthylene is 27 cm⁻¹ or 0.81 THz. Additionally, the harmonic frequency for the twisting of the S₂ groups on the outside of PS is in the 190 cm⁻¹ range or 5.70 THz. Coherent ps pulses of THz energy at either or both of these frequencies (or additional multiples of these energies) could pump and populate the higher vibrational quantum levels. The pumping imparts energy into the system in order to overcome the rotational PES barriers as well as the energy requirements for keeping the propeller spinning even after interactions with ambient particles.

Multiple PS ligands could also be functionalized onto a fullerene surface, as well. If synthetic pathways could orient these on one side of the nanoparticle, multiple propellers would further enhance the fullerene transportation. Multiple PS groups bring about the issue of the propellers counterbalancing each other with some spinning in the “forward” direction and other spinning in the “backward” direction. However, circularly polarized THz beams⁴⁵ can be generated. Consequently, only PS ligands of the proper directionality would be pumped and engaged. Even if the PS ligands could not be anisotropically added to the fullerene, their rotating presence on the surface would disrupt the surrounding environments enough for nanoparticles to traverse their surroundings more efficiently. The need for circularly polarized THz radiation would not be required if the PS groups were to function as rotating “plows” in such a case.

5 Conclusions

The PS molecule is shaped like a propeller. It has directionality in its structure brought about by the conformational properties of disulphides. This creates a screw- or propeller-like shape. Even though the atoms will be in constant vibrational motion, the averaged directionality highlighted by the PS equilibrium geometry can still be conceptualized as a molecular propeller. Adding this ligand to a fullerene nanoparticle would enhance the particle's ability to traverse its environment either as a propeller or an environmental agitator. The barrier to rotation for PS on a fullerene surface either though direct linkage or the common pyrrolidine linker is fairly low, on the order of 6.00 kcal mol⁻¹ to 12.0 kcal mol⁻¹. Direct linkage of the PS to the fullerene gives a lower barrier to rotation than utilizing the pyrrolidine, but other linkers may reduce this energy cost and are left for future study. Future study should also include expanding the size of the propeller “blades” beyond just the disulphide groups in order to increase the surface area and interactions of the propeller with the molecular environment.

Additionally, more energy than is available in thermal conditions would be required for the PS, or any related, group to function as a propeller or screw in order to whisk particles out of the nanoparticle's path. Additionally, the physics for such energy would not keep the propeller spinning in the same direction continuously. This required extra energy must come from outside of the system. Pulsed THz energy is a viable option for powering PS as a propeller. This work shows the energetics of PS linkage, rotation, and harmonic vibration. It also proposes how these properties can be utilized for PS to function as a molecular propeller in order to add further promise for the role of fullerenes in medicine and nanotechnology.

Acknowledgements

RCF would like to thank Georgia Southern University for the provision of startup funds necessary to complete this research.

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