Magnetic Field-Induced Alignment of Molecular Rotor-Shaped

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Magnetic Field-Induced Alignment of Molecular Rotor-Shaped Cyclophanes Stefano Pelloni,*,† Inmaculada García Cuesta,‡ Alfredo S anchez de Mer as,‡ and † Paolo Lazzeretti †

Dipartimento di Chimica dell'Universit a degli Studi di Modena e Reggio Emilia, Via Campi 183, 41100 Modena, Italy, and Institut de Ciencia Molecular, Universitat de Val encia, P.O. Box 22085, E-46071 Val encia, Spain

‡

ABSTRACT Molecular pinwheels consisting of dipolar substituted cyclophanes in solution can function as free microscopic rotors in the presence of a homogeneous static magnetic field B and a circularly polarized electric field E rotating on a plane containing B. Owing to the high magnetic anisotropy of [26](1,2,3,4,5,6)cyclophane and [36](1,2,3,4,5,6)cyclophane biased by strong ring currents, ∼1 in 105 molecules are expected to align with the C6 symmetry axis perpendicular to a magnetic field of 21 T. The magnetic-field-controlled alignment of rotor-shaped cyclophanes is insignificantly affected by nonpolar solvents, for example, toluene. SECTION Molecular Structure, Quantum Chemistry, General Theory

S

everal attempts to design and construct nanomachines capable of operating as mechanical devices on the molecular level are presently being made.1-4 Microscopic engines functioning as switches, gears, rotors,5-7 reversible brakes,8 valves,4 rack-and-pinions,9 wheelbarrows,4 information ratchets,10 and nanocars4 have been described in a number of recent studies. Rotating molecular-sized systems are particularly interesting for theoretical and practical purposes. Nanomotors can rotate microscale objects11 and can be used to measure the viscosity of live cells.12 Propeller-shaped rotors driven by a circularly polarized electric field might act as a loudspeaker in the presence of a gas.6 Rotary motors on surfaces4,13,14 consist of a turning part and a stationary part, referred to as the rotor and the stator, respectively. Submolecular component rotary motion has also been studied.15 On the other hand, nanoengines freely rotating in a medium have seldom been investigated. Intense linearly polarized light induces a dipole force that orients anisotropic molecules, for example, Cl2, along the direction of polarization; then, rotating the polarization makes the molecule spin from near rest up to high angular momentum states.16 Energy can be supplied for a molecular rotor to work by a chemical fuel4 or by physical sources, for example, laser light, heat, and electromagnetic fields.2,3,17 A grid-mounted dipolar rotor can be driven by a circularly polarized electric field, as shown by Vacek and Michl.6 A rotating electric field can also be used to make free dipolar molecules rotate in solution, provided that they are properly oriented and kept in position by a force continuously acting on them. The purpose of this letter is to show that an external magnetic field can induce a statistically relevant alignment of molecules characterized by strong anisotropy of the magnetic susceptibility. These molecules, properly functionalized by attaching chemical moieties which give rise to a big electric

r 2010 American Chemical Society

dipole moment, can function as a collection of free elementary rotors when acted upon by a circularly polarized electric field rotating on a plane normal to the magnetic field. This cooperative work should possibly amplify the phenomenology from the microscopic to macroscopic level, becoming observable by the onset of some ordered rotation in the random and incessant Brownian motion. The second-order energy of a diamagnetic molecule interacting with a magnetic field with strength H and flux density B is 1 1 ð1Þ ΔW ¼ - H 3 χ H 3 B ¼ - B 3 χ 3 B 2 2 The vector B is related to H, and the susceptibility tensor χ to χH, by ð2Þ B ¼ μH; χ H ¼ μχ where μ is the permeability. We will assume that, in the cases studied here, μ differs insignificantly from μ0, the permeability of free space, so that χ H ¼ μ0 χ

ð3Þ

The SI units for the quantities in eqs 1-3 are joule (J) for ΔW, amp ere per meter (A/m) for H, tesla (T) for B, m3 per molecule for χH, J T-2 per molecule for χH, and 4π 10-7 T2 m3 J-1 for μ0. Molecules in the disordered phase in the absence of the magnetic field are characterized by random tumbling motion. In the presence of a field, diamagnetic molecules tend to be oriented in a position of minimum energy (eq 1). The degree of alignment of a molecule-fixed (principal) axis Received Date: March 11, 2010 Accepted Date: April 13, 2010 Published on Web Date: April 21, 2010

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DOI: 10.1021/jz100319r |J. Phys. Chem. Lett. 2010, 1, 1463–1467

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R relative to the applied magnetic field B is specified by the parameter 3 1 ð4Þ SRB ¼ Æcos2 θRB æ 2 2 where θRB is the angle between the R axis and B and the brackets denote the average value of the enclosed expression.18 The SRB parameter is 0 for completely random molecular tumbling and 1 when the R axis is exactly parallel to B. For SRB= -1/2, the R axis is orthogonal to B. The average value in eq 4 is evaluated assuming a Boltzmann distribution in the energies. Therefore R 2π Rπ ΔW 3 1 2 cos sin θRB dθRB dφ exp θ RB 0 0 kT 2 2 SRB ¼ Rπ R 2π ΔW sin θRB dθRB 0 dφ 0 exp - kT ð5Þ For small ΔW, that is, for weak B in eq 1, the exponential can be approximated by 1 - ΔW/kT, so that18 SRB

ΔχHR B2 Δχ B2 ¼ R 15kTμ0 15kT

ð6Þ

)

where ΔχHR and ΔχR indicate the magnetic anisotropy with respect to the R axis, k = 1.3806505 10-23 J K-1 is the Boltzmann constant,19 and T is the absolute temperature in Kelvin. Using the symbol for the principal rotation axis (of three-fold or higher symmetry) and the symbol ^ for axes perpendicular to the principal rotation axis, the anisotropy is given by )

χ χzz

)

Δχ ¼ χ - χ^

χ^ χxx ¼ χyy

ð7Þ

Two rotor-shaped molecules, 1 and 2 in Figure 1, have been studied in the present work, namely, the [26](1,2,3,4,5,6)cyclophane, with D6h symmetry (also named superphane),20-24 and the [36](1,2,3,4,5,6)cyclophane,24,25 with C6h symmetry. For these compounds, the R direction in eqs 4-7 coincides with z, the six-fold molecular symmetry axis C6. Both of the cyclophane pinwheels are characterized by enhanced magnetic anisotropy. The origin-independent values calculated via the DZ2 variant26 of the procedure of continuous translation of the origin of the current density diamagnetic zero (CTOCD-DZ),27 in J T-2 per molecule, are χ = -5.389 10-27 and χ^ = -2.997 10-27 for 1 and χ = -6.428 10-27 and χ^ = -3.655 10-27 for 2. The corresponding anisotropies are Δχ = -2.392 10-27 and Δχ = -2.769 10-27. The near-Hartree-Fock magnetic anisotropy of benzene evaluated by the same procedure and the extended basis set from a previous paper28 is -1.145 10-27 J T-2. These estimates have been obtained by the SYSMO code29 using the complete point group symmetry of the molecules via a (13s8p3d/8s3p) f [11s6p3d/6s3p] Gaussian basis set with 1488 contracted functions for 1 and a (9s5p2d/ 5s2p) basis with 1476 primitive functions for 2. For both 1 and 2, the big values of the χ components and of the anisotropies are determined by strong delocalized electronic currents on planes at right angles to B, sustained by π and σ electrons, as shown in Figures 2 and 3. Ring stacking causes a peculiar

Figure 1. Below, [26](1,2,3,4,5,6)cyclophane (superphane), 1, and above, [36](1,2,3,4,5,6)cyclophane, 2.

)

)

)

)

magnetic response of cyclophanes. An intense diatropic annular current, characterized by a remarkable “leap-frog“ flow about the C nuclei,30 is observed on a plane at 1 bohr above that of a carbon ring in 1. This ring current circulates also around the trimethylene bridges in 2. A paratropic whirlpool rotates about the center of mass in the interior of the rings. The essential difference between compounds 1 and 2 arises from the regime inside of the stacked carbon rings, as shown in Figure 3 for a plane 1 bohr below the carbon rings; the perpendicular χ component of 2 is bigger due to much stronger diatropic currents flowing inside of the cage. The alignment parameters calculated via eq 6 for a field of 14.1 T, at which orientation effects are observable in nuclear magnetic resonance (NMR) spectra,18 are -7.66 10-6 for 1 and -8.86 10-6 for 2. Current superconductor technology allows the operation of 21 T persistent and homogeneous NMR magnets.31 With such a field, the orientation parameters become -1.69 10-5 for 1 and -1.97 10-5 for 2. However, more powerful magnets are presently becoming available,32


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Figure 2. Electron current density induced in [26](1,2,3,4,5,6)cyclophane 1 (below) and [36](1,2,3,4,5,6)cyclophane 2 (above) by a magnetic field B with an intensity of 1 au perpendicular to the plot plane at 1 bohr above the benzenic ring and directed outward. Diatropic currents are clockwise. The size of the arrows is proportional to the intensity of the current. Blue (red) colors denote ascending (descending) behavior.

Figure 3. Electron current density over a plot plane at -1 bohr below the benzenic ring of cyclophanes. The plotting conventions are the same as those in Figure 2.

To drive rotation about a given laboratory axis, say x, the cyclophane windmills studied here should be functionalized by introducing polar substituents to make them acquire a big electric dipole moment. For instance, the calculated electric dipole moment for both 1 and 2 carrying a -NO2 group attached to an external carbon bridge is ∼5 debye. The magnetic anisotropies of -NO2-substituted molecules become -2.165 10-27 and -3.677 10-27 J T-2, respectively, which implies a similar degree of alignment in a magnetic field. Then, a circularly polarized electric field rotating on a

which could align the six-fold symmetry axis of cyclophane pinwheels in disordered phase at right angles to the direction of B to a much higher extent than 1 molecule in ∼105. At any rate, although the C6 symmetry axis of 1 and 2 cyclophanes is forced to orient perpendicularly to the direction of B, say the vertical z axis of the laboratory frame, it may form any angle with a horizontal direction in the laboratory.


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plane containing the magnetic field, for example, yz, would force this dipole to rotate on planes parallel to yz.6,17 The interplay of the two fields may possibly lead to observable effects in solution. To estimate the importance of solvent effects, the magnetic susceptibilty of [36](1,2,3,4,5,6) and [26](1,2,3,4,5,6)cyclophane was evaluated in toluene within the Polarizable Continuum Model (PCM) of Tomasi and co-workers.33,34 Very small changes were found for both calculated properties, the average susceptibility and anisotropy of the susceptibility tensor; see the Supporting Information available. Therefore, solvent effects would not significantly modify the magnetic-field-induced alignment of molecular rotorshaped cyclophanes.

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SUPPORTING INFORMATION AVAILABLE Details of the calculations are reported, specifying large Gaussian basis sets and molecular geometries of [26](1,2,3,4,5,6)cyclophane and [36](1,2,3,4, 5,6) cyclophane. The near-Hartree-Fock quality of calculated magnetic properties is proven via extended comparison of results from different theoretical methods. The solvent effects estimated via the PCM methods for [26](1,2,3,4,5,6) and [36](1,2,3,4,5,6) cyclophane and for the -NO2 derivative of the latter are documented. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION Corresponding Author: *To whom correspondence should be addressed. E-mail: pelloni. [email protected].

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ACKNOWLEDGMENT Financial support to this work from the

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Spanish FEDERþMEC Project CTQ2007-67143-C02-01/BQU, from Generalitat Valenciana through FEDER funds (ACOMP09/292, GV/2007/093, GVAINF 2007-051), from the Fondazione Cassa di Risparmio di Modena, and from the Italian MURST (Ministero dell'Universita e della Ricerca Scientifica e Tecnologica), via FAR funds, is gratefully acknowledged.

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Magnetic Field-Induced Alignment of Molecular Rotor-Shaped

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