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Laser-driven, Surface-mounted Unidirectional Rotor Joshua E. Szekely, Felix K Amankona-Diawuo, and Tamar Seideman J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b05476 • Publication Date (Web): 22 Jul 2016 Downloaded from http://pubs.acs.org on July 28, 2016

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The Journal of Physical Chemistry

Laser-driven, Surface-mounted Unidirectional Rotor Joshua E. Szekely, Felix K. Amankona-Diawuo, and Tamar Seideman∗ Department of Chemistry, Northwestern University, Evanston, IL 60208, USA E-mail: [email protected] Phone: 847-467-4979

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Abstract We propose a design for a class of molecular rotors fixed to a semiconductor surface, induced by a moderately intense, linearly-polarized laser pulse. The rotor consists of an organic molecule possessing a polarizable head group that is attached via a linear component to the surface. The polarization direction in parallel to the surface plane is determined so as to maximize the torque experienced by the molecular head group and hence the duration of the ensuing rotation, while also controlling the sense of rotation. We find that the molecule continues to rotate for many rotational periods after the laser pulse turns off, before multiple scattering by the potential barrier result in dephasing.

Introduction The control of external degrees of freedom of molecular systems by moderately intense laser fields has been a subject of considerable interest over the past two decades. This includes alignment and orientation of molecules, 1–3 control of molecular torsions, 4–6 focusing and deflection of molecules, 7–14 trapping, 15,16 acceleration and angular acceleration. 17–20 Closely related to external control is the development of molecular rotors, pursued by a number of independent research groups, driving motion phase through both chemical mechanisms and external fields. 21–35 Further developments in the field of molecular rotors include both experimental studies on single molecule rotors 36,37 and surface-mounted rotors. 38–40 Binding molecular rotors to a surface introduces, potentially, a number of opportunities, including utilization in nanodevices and nanoelectronics and detection using scanning tunneling microscopy techniques. 41–43 Theoretical work has also explored the design and dynamics of various classes of molecular rotors. 40,44–47 For a more comprehensive review, we refer the reader to references 48, 49, and 50. Here we propose and numerically illustrate a new class of laser-driven molecular rotors that offer potentially several desired features amenable to these STM-type experiments: 1) the molecule design is experimentally realizable; 2) the rotor is ultrafast, and undergoes 2


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persistent rotary motion after the pulse turnoff, free of external forces; 3) the directionality of the rotor is readily controlled by the polarization of the light; and 4) the approach is general, insensitive to the laser parameters and applicable to a host of organic molecules. The molecular rotors we propose consist of organic molecules mounted on a nonmetallic scaffold such as silicon, and subject to a moderately-intense (below damage thresholds), non-resonant laser pulse whose duration is shorter than the natural system time-scales but otherwise flexible. The choice of a nonmetallic surface and a low (sub-bandgap) frequency avoids electron-hole pair excitation and substrate-mediated chemistry, which often complicate the use of metallic substrates. The rotator (the non-stationary molecular component) is a polarizable moiety that would generally be sufficiently large for a scanning tunneling microscope (STM) image to distinguish between a rotating head group, which will generate an averaged image, and a head group that is fixed at its equilibrium configuration. The axle about which the rotator moves is rigid (librations about the axle are not considered) and determines the distance of the head group from the rest of the structure, thereby controlling the rotational barrier height. A convenient choice for this structure is a simple carboncarbon triple bond. The axle is connected to a final molecular component, the purpose of which is to contain a functional group that offers a motive for binding to the surface. For example, with silicon as the scaffold, diketones offer a convenient motive for binding to the silicon surface. 51 An important consideration is a molecular design that would minimize the required the laser intensities. The two most straightforward routes to that end are use of molecules with long axles, hence low torsional barriers, or head moieties with large polarizability anisotropy (where the polarizability anisotropy is the difference between the two components of the space-fixed polarizability tensor parallel to the surface). Figure 1 shows a variety of molecules following these design criteria. Throughout the rest of this manuscript, we will consider molecule 1a, although all the molecules were numerically found to behave qualitatively in the same manner.

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Theory To model the rotors we solve the time-dependent Schrödinger equation (TDSE),

i

i h ∂ Ψ(φ, t) = Tˆ + Vˆtors (φ) + Vînt (φ, t) Ψ(φ, t), ∂t

(1)

where we denoted by φ the rotational angle of the rotor, Tˆ is the kinetic energy operator, d2 ˆ Tˆ = − 2I1 dφ 2 , I is the moment of inertia of the rotator, Vtors (φ) is the field-free potential

and we adopted atomic units, h ¯ = 1. The potential component is primarily composed of steric interactions between the rotator and the stationary base of the molecule, in addition to electrostatic interactions. The rotator is activated by a far off-resonance laser pulse through interaction with the molecular polarizability tensor, producing an induced dipole moment rather than rely on the presence of a permanent dipole (as explored in reference 52). The interaction Hamiltonian is thus 1 1 Vînt (φ, t) = − 4

X

(2)

ερ (t)αρρ′ ε∗ρ′ (t),

ρ,ρ′

where the laser is treated as a classical entity. The electric field pulse envelop, ~ε, and the molecular polarizability tensor elements, αρρ′ in Eq. (2) are defined with respect to the space-fixed Cartesian coordinate system, {ρ, ρ′ } = {x, y, z}, where we follow the standard convention of defining the z-axis to lie along the surface normal and arbitrarily choose the silicon dimer row to define the y-axis. We consider a linearly-polarized laser parallel to the surface plane throughout the rest of this work, ρ, ρ′ = x, y, and hence the interaction Hamiltonian simplifies as, 1 Vînt = − ε2 (t) αxx ε2x + αyy ε2y + 2αxy εx εy 4

(3)

with a polarization angle φ0 = tan−1 (εy /εx ). The intensity envelop, ε2 (t), is modeled as a Gaussian function of frequency and time. 5




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technique, Ψ(φ, t + dt) = Uˆ (dt)Ψ(φ, t) ˆ

= e−iHdt/¯h Ψ(φ, t) i i ˆ i ˆ ˆ ˆ 3 ) Ψ(φ, t), = e− 2¯h T dt e− h¯ V dt e− 2¯h T dt + O(dt

(4)

ˆ is the total Hamiltonian. The initial wavewhere Uˆ is the time-evolution operator and H function (shown in figure 2) is taken to be the ground eigenstate of the torsional Hamiltonian and calculated using the imaginary time propagation technique of Refs. 57 and 58.

Results & Discussion

Probability Density

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Figure 3: Time evolution of the rotational wavepacket during and after a laser pulse (5.0 ps FWHM, 5.5 TW) at a polarization angle of 28◦ (left) and a cut along the plot showing the wavefunction amplitude at φ = 5π/4 (right). The polarizability tensors and torsional potentials are very similar for the different molecules shown in figure 1. The induced dynamics depends primarily on the field polarization direction in the surface (x, y) plane, the pulse duration and the laser intensity. Thus, the rotator dynamics are general and largely controllable. In practice, the rotator axle need be sufficiently long and/or the head group have a sufficiently large polarizability 7



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anisotropy (∆α) that the barrier to rotation would be smaller than the field induced energy 1 ∆αε2max 4

while εmax , the peak field, does not exceed the damage threshold. For molecule

1a, the barrier to rotation is approximately 40 meV. The potential curve is nearly π-periodic (that is, nearly symmetric with respect to φ → φ + π), except for a notable difference in minima, due to the asymmetric nature of the bonding motif between the rotor and the shaft molecule. The polarizability components have the expected structure, with the same periodicity and maxima corresponding to the directions parallel to the ring structures. For the system considered, the polarizability diagonal components vary by nearly 200 au over a rotational period and hence the polarizability anisotropy is large. To optimally drive the molecular rotor, a polarization angle is needed that maximizes d Vint . The gradient of equation 3 is provided as, the gradient of the interaction potential, dφ

d 1 2 ∂αxx ∂α ∂α yy xy 2 2 Vint = εmax + 2α cos(2φ) cos φ + sin φ + sin(2φ) α − α + xy yy xx dφ 4 ∂φ ∂φ ∂φ (5)

with εx = cos φ and εy = sin φ. For Molecule 1a the optimal polarization angles are φ0 = 28.3◦ (for the anti clockwise sense) and π − φ0 (for the clockwise sense). Figure 3 shows the rotational wavepacket evolving over 45 ps after turn-off of a 5 ps laser pulse at the optimal polarization angle. Upon turn-off of the laser pulse, the head group begins to rotate counterclockwise about the axle moiety. Rotation continues while the wavepacket undergoes multiple scattering from the torsional potential barrier. Due to the π periodic nature of the interaction potential, counterclockwise motion occurs regardless of which potential minimum the rotor moiety initially occupies (π/2 or 3π/2). Figure 3 also shows a slice of the wavefunction at a fixed rotational angle, illustrating the persistence of the rotations for many rotational periods and the multiple scattering effect. Applying a pulse from the complementary polarization angle induces identical dynamics, but in a clockwise direction, illustrated in the supporting information. Additional insights are provided by analyzing the expectation values of the kinetic and

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nature of this rather massive system is evident in the observation of Figures 3 and 4 that the potential barrier scatters the wavepacket even for kinetic energies significantly exceeding the barrier height. Figure 5 quantifies the conclusions of 4 by showing the angular frequency of the rotator as a function of laser intensity for a 5 ps long pulse. Varying the laser intensity between approximately 3 TW and 12 TW produces angular frequencies that vary nonlinearly between 4 and 13 ps. Interestingly, the rotational frequency reaches a plateau, illustrating that the degree of kinetic energy that the pulse can transfer to the system is upper bounded. The plateau is expected for a sufficiently short pulse (with respect to the natural rotational period of the molecule). In the short pulse case, the degree of rotational excitation is upper-bounded by the pulse duration rather than by the intensity, and is qualitatively given by the number of rotational eigenstates that can be excited during the pulse.

Induced Rotational Frequency 1400

1100

t (GHz)

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840

600 470 3.3 4

5

8

12 2

Ipeak (TW/cm )

Figure 5: Frequency of the molecular rotation over the range of intensities capable of inducing complete rotation. A frequency upper bound is observed around 1400 GHz (4.5 ps).

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Conclusion Summarizing, we have proposed a new design for a class of molecular rotors induced by a moderately intense laser pulse of duration below the natural system time-scale. The rotor motion is unidirectional and its sense and speed may be controlled through choice of the polarization angle and peak intensity. It is based on a few, rather general design principles. The use of a semiconductor surface and sub-bandgap frequencies circumvents competing processes, such as substrate-mediated chemistry. The length of the axle moiety controls the barrier height and hence the intensity required to observe complete rotations. The size of the headgroup would be usually taken sufficiently large for an STM image to readily distinguish between a head group that undergoes rotation and generates an averaged image and a head group that is stationary at the equilibrium configuration. The larger the peak intensity the higher the kinetic energy stored in the system and the higher the rotation frequency. Given, however, that the interaction Hamiltonian scales as the product of the intensity by the polarizability anisotropy, the design of a highly polarizable head group allows minimizing the peak intensity for a given outcome. Importantly, the polarization angle of the linearly-polarized field in the surface plane determines the sense of rotation and the duration of motion before dephasing ensues. In general the rotation angle would be fixed so as to maximize the torque experienced by the molecule. We find that under realizable conditions rotation about the central axle continues for many rotation periods before multiple scattering results in dephasing.

Supporting Information Available For plots showing control over the direction of rotational motion, wavefunction evolution for various laser intensities, and a rotational period as a function of laser intensity, please see the supporting information. This material is available free of charge via the Internet at http://pubs.acs.org/. 11



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Acknowledgement The authors thank the Department of Energy (Award No. DEFG02-04ER15612/0011) and the National Science Foundation (Award No. DMR-1121262) to the Northwestern Materials Research Center for support of this research.

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