Chirality-induced spin polarization places symmetry constraints on biomolecular interactions Anup Kumara, Eyal Capuaa, Manoj K. Kesharwanib, Jan M. L. Martinb, Einat Sitbonc, David H. Waldeckd, and Ron Naamana,1 a Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel; bDepartment of Organic Chemistry, Weizmann Institute of Science, Rehovot 76100, Israel; cEvogene Ltd., Rehovot 76121, Israel; and dDepartment of Chemistry, University of Pittsburgh, Pittsburgh, PA 15260

Edited by R. Stephen Berry, The University of Chicago, Chicago, IL, and approved January 17, 2017 (received for review July 13, 2016)

Noncovalent interactions between molecules are key for many biological processes. Necessarily, when molecules interact, the electronic charge in each of them is redistributed. Here, we show experimentally that, in chiral molecules, charge redistribution is accompanied by spin polarization. We describe how this spin polarization adds an enantioselective term to the forces, so that homochiral interaction energies differ from heterochiral ones. The spin polarization was measured by using a modified Hall effect device. An electric field that is applied along the molecules causes charge redistribution, and for chiral molecules, a Hall voltage is measured that indicates the spin polarization. Based on this observation, we conjecture that the spin polarization enforces symmetry constraints on the biorecognition process between two chiral molecules, and we describe how these constraints can lead to selectivity in the interaction between enantiomers based on their handedness. Model quantum chemistry calculations that rigorously enforce these constraints show that the interaction energy for methyl groups on homochiral molecules differs significantly from that found for heterochiral molecules at van der Waals contact and shorter (i.e., ∼0.5 kcal/mol at 0.26 nm). spin

| chirality | enantioselectivity | biorecognition | exchange interaction

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he wealth of information on protein structure has led to a much better understanding of the relation between structure and function in biomolecular processes and biological machines (1); however, basic phenomena remain unexplained in terms of structure–function relationships. Biorecognition, which is based on noncovalent interactions between molecules, retains mysteries, and its calculation evades first principles theory (2, 3). This failure suggests that some essential features are not included in our current description of these interactions (4, 5). In this study, we show that charge polarization, which occurs in any biorecognition event, is accompanied by spin polarization for chiral molecules, an effect that is missing in most treatments. The subsequent magnetic interaction energies are small and therefore, play no significant role in the interactions; however, the spin polarization constrains the symmetry of the wave function(s) involved with the intermolecular interaction, so that significant differences in energy emerge for interactions between molecules of the same chirality and those of opposite chirality. Thus, this phenomenon may impact quantitative modeling of biorecognition events and contribute to our understanding of enantiorecognition in nature (6). Nucleotides, amino acids, and sugars are chiral; namely, they do not possess mirror plane symmetry but have symmetry like a “hand” (cheir in Greek). Force field models for the interaction between biomolecules do not account for spin polarization or include terms with chiral symmetry. Noncovalent interactions between biomolecules are commonly described classically by way of force fields, which are constructed from their geometries and charge distributions. Although quantum mechanics must be used to calculate the charge distributions and polarizabilities of the molecules, the force fields themselves are commonly constructed in a classical form (i.e., ion–ion forces, charge–dipole forces, etc.), and the exchange interactions (Pauli exclusion) are manifest as sharply 2474–2478 | PNAS | March 7, 2017 | vol. 114 | no. 10

repulsive forces at short range about individual atoms (or functional groups). Thus, they present chirality effects in terms of the 3D arrangement of the atoms and do not include spin effects or exchange effects at short range, which may arise from the more global chiral symmetry of the molecule (7). Although recent developments of quantum mechanical force fields (8) and reactive force fields (9) represent significant improvements, they do not yet include the spin polarization effects described here. The spin polarization observed in this work is consistent with the chiral-induced spin selectivity (CISS) effect (10), because it arises from the transient current associated with the charge displacement that is generated as two chiral molecules interact. The CISS effect implies that the electrons traverse a chiral molecule more easily in one direction than in the other depending on their spin orientation and the chirality (left vs. right) of the molecule. The effect arises because of the molecule’s chiral electrostatic field acting on the electrons. In the rest frame of the electrons, this force can be expressed as an effective magnetic field acting along the axis of the chiral system. This effective field stabilizes one spin orientation of the electrons over the other and gives rise to a spin-dependent transmission (11). Since its discovery, the effect has been observed experimentally and verified in different systems (12–18). In the first part of this manuscript, we describe how the spin polarization in monolayers of chiral molecules was measured, and in the second part, we present calculations on model systems and discuss how this phenomenon introduces considerations for describing the interaction between chiral molecules. Significance Chiral molecules are the building blocks of life. Although artificially, it is difficult to separate two different enantiomers of the same molecules; in nature, this process is efficient. This work proposes a mechanism for understanding this efficiency. In many bioprocesses, the interactions between molecules result from electron reorganization in the molecules, like that which occurs when an external electric field is applied. We show that the charge reorganization in chiral molecules is accompanied by a polarization of the spins associated with the displaced charge. The symmetry constraints imposed by the spin polarization may help account for the enantioselectivity. Calculations indicate that this contribution to the interaction energy for two molecules of the same handedness can be comparable with the available thermal energy. Author contributions: E.C., E.S., D.H.W., and R.N. designed research; A.K. and E.C. performed research; M.K.K., J.M.L.M., and E.S. contributed new reagents/analytic tools; A.K., D.H.W., and R.N. analyzed data; and E.C., J.M.L.M., E.S., D.H.W., and R.N. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. Freely available online through the PNAS open access option. 1

To whom correspondence should be addressed. Email: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1611467114/-/DCSupplemental.

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Spin Polarization and Enantioselectivity Although the magnetic interaction energies are too small to affect the intermolecular interactions significantly at room temperature, the spin polarization imposes a symmetry constraint that affects the electron cloud overlap (Pauli exclusion). Although it is well-known (21, 22) that electron exchange and charge penetration contribute

Fig. 1. (A) The experimental setup in which a Hall device, coated with a self-assembled organic monolayer, is placed in solution with a G electrode and an inert electrolyte. When an electric potential VG is applied between the G electrode and the device, the ionic solution is polarized, so that an electric field acts on the adsorbed molecules. As a result, the molecules are polarized because of charge reorganization (partial charges q+ and q−), inducing a charge displacement in the surface region of the device. Because the charge polarization is accompanied by spin polarization (red balls with black arrows in C), a magnetic field that acts on the electrons flowing between the S and D electrodes is also created. The Hall potential VH, which is formed as a result of the spin magnetization, can be measured as a function of VG. (B) A schematic diagram illustrating the electrical operation of the device, where ISD indicates the applied S–D current, VG is the gate voltage, and VH is the differential Hall potential across the conductive channel. (C) A scheme describing the spin polarization. When an electric field is applied on a chiral molecule (via VG), it induces charge reorganization in the molecule, resulting in spin polarization.

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{Ala-2-aminoisobutyric acid or 2-methylalanine (Aib)}5-COOH and the longer L-SHCH2CH2CO-{Ala-Aib}7-COOH. The L and D refer to the different handedness of the amino acid units making up the oligopeptide. Measurements were conducted on three devices for each molecule type; the error bars are calculated from the variation in the signal for three trials (SI Appendix). The Hall voltage observed with the chiral molecules shows a roughly linear dependence on the applied gate voltage, and its sign depends on the chirality of the molecule. Fig. 2C presents examples of the Hall potential VH data measured when a gate voltage of −10 V is applied on a device coated with the chiral L-oligopeptide [SHCH2CH2CO-{Ala-Aib}7-COOH]. Because of the molecular chirality, the polarized charge distribution is spin polarized (possesses a magnetization), and a magnetic field is created, which is responsible for the Hall voltage. Although the intrinsic spin depolarization in GaN (which makes up the Hall device) occurs on a submicrosecond timescale, the high capacitance of the measurement leads to a signal that decays with the time constant of the system (1/RC, where R is the resistance, and C is the capacitance). After the decay of the Hall voltage, the device is still charged (because the gate voltage is still applied), but no spin polarization exists. When the gate voltage is removed, the charge decays, and a charge displacement flows through the molecules in the opposite direction. This charge displacement is accompanied by a spin polarization with a magnetic field that generates a Hall voltage of the opposite sign, because the spin polarization in the device is in the opposite direction. The Hall signal decays as the spin polarization decays. With the D-oligopeptide, an opposite signal was obtained, indicating an opposite spin polarization. The experimental data show that charge polarization in chiral molecules results in a spin polarization. The device was calibrated using an external magnetic field as described in Methods. For an external voltage of 10 V, the Hall signal corresponds to about a 50Oersted or 5-mT field for the case of the SHCH2CH2CO-{AlaAib}7-COOH chiral oligopeptide. It is important to appreciate that, because of the high capacitance of the device, the measured signal is broadened in time, and therefore, the actual signal peak could be much larger.

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Measurement of Charge-Induced Spin Polarization To measure the spin polarization that accompanies the charge polarization in chiral molecules, we developed a type of Hall effect device (Fig. 1A and Fig. S1). The Hall effect is a longknown phenomenon (19), and it is used as a standard way to characterize electrical properties of semiconductors. Briefly, when current is flowing in a substrate between two electrodes and a magnetic field is applied perpendicular to the current flow, it induces an electric potential perpendicular to both the current and the magnetic field direction (20). For the modified device illustrated in Fig. 1, a constant current/voltage is driven between the source (S) and drain (D) electrodes through the device, and the Hall voltage is measured between the electrodes H1 and H2 along the direction perpendicular to the current flow. To study the chiral molecules’ spin polarization, a monolayer of the molecules is placed on the surface of the device over the area between the S and D electrodes. In our measurements, the Hall device was placed into a buffered electrolyte solution, and a voltage was applied between the substrate on which the device is patterned and a counter- or gate (G) electrode, which is insulated from the solution by a glass coverslip that is 100-μm thick. The applied electrical voltage generates an electrostatic field that acts across the molecular film, the inner part of an electrical double layer, and induces a charge polarization. If this charge polarization is accompanied by spin polarization, then a Hall voltage develops. It is important to realize that the ability to observe a significant Hall potential results, in part, from the proximity of the polarized spin distribution to the conductive channel. More experimental details are given in SI Appendix. The electric field-induced spin polarization was studied for two chiral L-oligopeptides of different length, a chiral D-oligopeptide, and an achiral molecule as a control. The molecules were selfassembled as monolayers (SAM) on top of the conduction channel of the Hall device (details are in Methods). The monolayers were characterized by IR spectroscopy and X-ray photoelectron spectroscopy (XPS) (Figs. S2 and S3 and Table S1). The SAM-coated Hall devices were placed in an electrochemical cell and positioned 5 mm from a G electrode that was insulated from the electrolyte by glass, which allowed voltage biases as high as 10 V to be applied without generating any significant leakage current between the G electrode and the Hall device. Fig. 2 A and B plots the Hall voltages as a function of the gate potential for the achiral monolayer (11-mercapto-undecanoic acid) and the chiral oligopeptides: L- and D-SHCH2CH2CO-

Fig. 2. Gate voltage (VG)-dependent Hall measurements conducted on devices coated with different oligopeptides. (A) Hall potential measured when the adsorbed layer is either L-SHCH2CH2CO-{Ala-Aib}5-COOH (red) or D-SHCH2CH2CO-{Ala-Aib}5-COOH (blue). The Hall potential was calculated as the difference between the peak responses for each applied gate voltage; ΔVH+ and ΔVH− correspond to positive and negative values of ISD, respectively. More details are in Fig. S4. (B) The dependence of the Hall voltage on VG is shown for monolayer films of achiral 11-mercapto-undecanoic acid (black), chiral L-SHCH2CH2CO-{Ala-Aib}5-COOH (red), and chiral L-SHCH2CH2CO-{Ala-Aib}7-COOH (green). (C) The time-dependent Hall potential measured with L-SHCH2CH2CO-{Ala-Aib}7-COOH when a voltage of −10 V is applied (indicated in blue) between the gate and the Hall device. On switching the potential off (indicated in green), an opposite signal appears for the chiral molecules as a result of charge flowing back the other way through the monolayer film (in the text). Note that the timescale of the response is controlled by the large capacitance of the measurement method. (D) The time-dependent Hall measurements are shown for various gate voltages. The on and off switching of the gate is marked with blue and green arrows, respectively.

significantly to intermolecular forces at short range, they are not described rigorously in the generation of force fields for simulating biomolecular interactions. Notably, the indistinguishability of electrons results in an exchange interaction that can act to stabilize the energy of two electrons with charge distributions that share a region of space (or orbital overlap) as long as they have opposite “spins”(23, 24). Thus, a key difference between classical electrostatics and quantum mechanics is the electron spin. Whereas the spin is typically neglected for two interacting closed shell molecules, the fact that spin polarization accompanies charge polarization for chiral molecules implies that it must be considered in describing the interaction strength between chiral molecules. As an example, consider the interaction between two helical molecules (Fig. 3). It is important to appreciate that helices are an example of secondary structure that is chiral, whereas amino acids and sugars are chiral because of the existence of asymmetric carbon atoms; namely, their primary structure is chiral. Because it relies on the helicity of the electron cloud, the considerations presented here are valid for those molecules as well. The relative orientation of the two interacting molecules in Fig. 3 is only for illustration purposes. Because chirality (handedness) does not depend on the direction from which the molecule is viewed, the arguments presented below are valid for all relative orientations. It is, of course, true that the extent of charge polarization depends on the relative orientation of the two interacting species, and hence, the magnitude of the interaction energy will depend on the relative orientation. The schematic image in Fig. 3B shows a polarized charge separation along one helix that induces a charge separation (dipole moment) in a nearby helix. When two chiral molecules of the same handedness 2476 | www.pnas.org/cgi/doi/10.1073/pnas.1611467114

interact, the charge polarization is accompanied by a spin polarization acting in the same direction (e.g., pointing outward along the helical axis) (Fig. 3C). In this case, the exchange interaction between the molecules is characterized by two opposite spin polarization directions, analogous to a singlet state (the region of Fig. 3C enclosed in the dashed oval). In contrast, for two interacting molecules of opposite chirality, their spin polarizations have opposite directions (Fig. 3D); in this case, the exchange interaction between the molecules corresponds to two parallel spins, analogous to a triplet state (as noted in Fig. 3D). Hence, the interaction between the spins results in an enantioselective interaction. Because the spin polarization is generated by the motion of the electronic charge, it is a dynamic phenomenon. Therefore, the spin polarization will happen simultaneously with the charge polarization, but after the flow of charge stops, the spin direction is expected to randomize. In typical organic molecules, biomolecules included, the spin randomization time is quite long: microseconds or even longer (25). However, after the two molecules interact via the exchange interaction, the spins involved in the interaction can be “locked” relative to each other (aligned antiparallel to each other as in Fig. 3C), and the spin randomization could be slowed. The physical argument can be presented more quantitatively by considering the interaction between two methyl groups. Fig. 4 summarizes the results for two model systems derived from the methane dimer (which is purely dispersion-bound): (i) R— CH3. . .CH3—R, in which R is a chiral–CFClBr group that can be either R- or S-handed (Fig. 4 A and B) and (ii) •CH3. . .CH3•, two methyl radicals at the equilibrium geometry of the methane dimer (Fig. 4C). This specific configuration was chosen, because the chirality of the molecules does not affect directly their electrostatic interaction at this orientation. Hence, the difference in interaction energy arises from the symmetry constraints introduced by the spin polarization that accompanies the charge polarization. The closed shell calculations were performed by symmetry-adapted perturbation theory as described in ref. 26 and using the aug-cc-pVTZ basis set (27); additional details are in Figs. S5 and S6 (28).

Fig. 3. (A) The schematic diagram illustrates the electron distribution (blue cloud) in a molecule that does not have a dipole moment before it interacts with another molecule. In this case, the distribution is symmetric. (B) This diagram illustrates the electron distribution where two molecules interact via dispersive forces. The interaction induces an asymmetry in the electrons’ distribution, resulting in an “induced dipole” in each molecule. This charge polarization causes an “induced dipole–induced dipole” interaction. (C) The diagram illustrates the induced dipole interaction of two molecules with the same handedness. As charge q transfers from one side of the molecule to the other, it generates a spin polarization (represented by a red ball and black arrow) of the same spin in the two molecules. The electron density left behind has, therefore, the opposite spin polarization; hence, the interaction between the molecules is characterized by two opposite spins as illustrated by the dotted circle singlet region. (D) When the two interacting molecules are of opposite chirality, the interaction between the molecules is characterized by two spins parallel to each other (in the dotted circle triplet region). Reproduced from ref. 11.

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i) Even when the interacting groups are not chiral, chiral recognition may exist because of the spin polarization, which reflects the chirality of the molecule as whole. Kumar et al.

ii) The interaction is of short range and therefore, plays an important role only when the two interacting molecules are in contact. This requirement arises because the electrons’ correlation energy is of importance only when the electronic wave functions have significant overlap. This situation is relevant in biosystems, where electrostatic forces push the molecules toward one another, whereas it is less important when the molecules are at the van der Waals distance. This effect may explain the efficient enantiorecognition in biological systems vs. the less efficient process occurring in solutions or separating columns. iii) Because the “surface of interaction” between two biomolecules can be large, many functional groups may contribute to the enantioselectivity, and the difference in interaction between R-R and R-S enantiomers can be many times the magnitude of the interaction calculated here for a single methyl– methyl interaction. These considerations indicate that spin polarization effects should be included to properly describe enantiospecific biorecognition. Summary Based on the experimental finding that charge polarization in chiral molecules is accompanied by spin polarization, we propose a mechanism for the interaction between chiral molecules. This interaction is less repulsive for molecules of alike chirality (homochiral) than for molecules of different chirality (enantiomers), so that the overall interaction between two molecules has an enantiospecific term. While assessing the importance of this type of interaction, several issues must be considered. The effect occurs only between chiral molecules, but the point of contact between the two interacting molecules could be distant from the chiral center. Although the induced dipole–induced dipole interactions resemble dispersive forces, like those first discussed by London (33), this interaction is important at short range, where orbital overlap is significant. This mechanism is based on exchange interaction and a pure quantum mechanical effect. It must be emphasized that the interaction presented here does not replace the known interactions or alter them. Rather, it is an additional contribution to the forces acting at short distance that can enhance the affinity and are intrinsically enantioselective. It has long been known that the current physical models used to describe the interaction between biological molecules do not PNAS | March 7, 2017 | vol. 114 | no. 10 | 2477

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Fig. 4A shows the geometry considered in calculating the interaction energy between two methyl groups on different chirality molecules, and Fig. 4B shows how the spin-dependent interaction energy between the two molecules changes as a function of the distance between the carbons of the methyl group. The red curve in Fig. 4B shows the interaction energy for the case in which the two molecules have opposite handedness (RS), and the less repulsive (namely, the blue curve in Fig. 4B) shows the case in which the two molecules have the same handedness (SS). Based on our experimental results and the discussion above, we assumed that the spins are polarized antiparallel for the SS case, whereas they are polarized parallel in the RS case. The calculations show that the interaction is less repulsive by about 0.5 kcal/mol at 0.26 nm for the case in which the spins are antiparallel-aligned (paired) than in the case in which the two spins are parallel. By design, the system calculated does not show any “enantiospecific interaction” in any other terms of the interaction potential, and only the spin-dependent term is enantiospecific. The calculations were repeated for the two interacting •CH3. . .CH3• systems (Fig. 4C), and the results again show the less repulsive force for the two opposite spins. Interestingly, the same order of magnitude for the difference in the interaction energy is found in experiments on the wetting of leucinol grafted surfaces by leucinol [C3H7CH(NH2)CH2OH] liquid droplets, for which the Gibbs energy change of the chiral interaction (or chiral discrimination) per molecule was found to be about 0.25 kBT at room temperature (29). Although the effect of the “spin-related terms” is significant only at C-C distances of 0.3 nm or less, which is typical for van der Waals contact (30), short distances are relevant in biology, and the effects are cumulative. In many biological systems, the distances associated with the substrate–protein interactions are below 0.3 nm. For example, in the most common globular protein fold, the triosephosphate isomerase (TIM) barrel, a ligand is typically at ∼0.25 nm from the closest amino acid residue (Fig. S7) (31, 32). Hence, the interactions that are associated with the chiral-induced spin polarization ought to be relevant. The analysis of Fig. 4 leads to several important implications.

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Fig. 4. (A) A scheme of two chiral molecules interacting through achiral methyl groups. (B) Plot of the second-order dispersion energy for aligned spins (blue) and antiparallel spins (red) for the model system R–CH3. . .CH3–R as a function of the carbon–carbon distance, d, for the case of RS interaction (the same spins; red curve) and when the spins are aligned antiparallel in the case of SS interaction (blue curves). (C) Plot of the difference in spin correlation energies, for the same spin and the opposite spin, as a function of intermonomer distance for •CH3. . .CH3• in open shell singlet (blue) and triplet (red) couplings.

properly account for the enantioselectivity and binding energies in biorecognition (2–5). In the past, this gap was filled using empirically based methods (34). The enantioselective interactions proposed here may fill (or partly fill) this gap and provide a theoretical basis to explain and predict biological phenomena that could not be explained or predicted before. We suggest that this mechanism for the intermolecular interaction of chiral molecules may be a missing component in explaining enantioselectivity [e.g., biorecognition events or chemical reactions that take place with a preference for one enantiomer over the other (for one hand over the other)] and may also explain why chirality has been preserved through evolution. Methods Device Fabrication. The device was fabricated from an AlGaN/GaN wafer on a sapphire substrate. It consisted of the following layers: first, the nucleation layer; second, i-GaN (1,800 nm); third, i-AlGaN (20 nm); and a capping layer of i-GaN (2 nm). The chip layout contained two sets of Hall probes. A schematic representation of the AlGaN/GaN Hall devices and the setup that were used in this work is given in Fig. S1. The AlGaN/GaN Hall devices were fabricated by photolithography. The width of the conducting channel is 40 μm, and the length is 500 μm. The electrodes on the GaN device are all coated with alumina to avoid contact with the solution.

sample with a clean GaN surface as a reference and mounting the GaN sample at a Brewster angle of incidence of 67.4°. In the aliphatic region, the spectrum of the 11-mercaptoundecanoic acid monolayer exhibited two large peaks at 2,849 and 2,917 cm−1 that are attributed to the symmetric and asymmetric CH2 stretching vibrations, respectively (Fig. S2A). The spectra of two of the oligopeptides SHCH2CH2CO-{Ala-Aib}5-COOH and SHCH2CH2CO{Ala-Aib}7-COOH exhibit characteristic stretching frequency peaks at 1,664 and 1,668 cm−1 corresponding to the amide I band and peaks at 1,539 and 1,540 cm−1 corresponding to the amide II band (Fig. S2 B and C). Hall Measurements. The device reported here is similar to the one reported before (35), and it is based on a 2D electron gas structure, onto which two sets of Hall probe electrodes were evaporated. This device differs from the earlier one by not having nanoparticles and by operating in solution. A GaN substrate was used for the device, because it has a long spin lifetime and can function for several hours in an aqueous solution without serious corrosion. The device was attached to a sample holder and electrically connected (Fig. 1B) to a constant current source by way of the S and D electrodes, and the Hall voltage VSD was measured between electrodes H1 and H2 (Fig. 1). Chiral molecules were absorbed directly on the GaN over the channel region. Typically, a constant voltage of 100 mV was applied between the S and D contacts using a Keithley 2636 source measure unit. The voltage drop across electrodes H1 and H2 was measured using a Keithley Nanovoltmeter 2182A device. To avoid a contribution to the Hall potential from the device asymmetry, the Hall signal was obtained by adding the signal measured when the S–D current flows in one direction to the signal obtained with the current flowing in the opposite direction. Because the Hall electrodes are not symmetric relative to the S and D, the Hall voltage resulting from this addition is almost the full potential induced by the spins.

Formation of Monolayers. The molecular monolayers (11-mercaptoundecanoic acid, SHCH2CH2CO-{Ala-Aib}5-COOH, and SHCH2CH2CO-{Ala-Aib}7-COOH) were adsorbed on GaN according to the procedure detailed below. Before the molecular adsorption, the GaN devices were cleaned by sonication in hot acetone and ethanol, and then, they were etched for 30 s in 6 M HCl, rinsed in water, and dried under an N2 stream. After the samples were treated with UV/ ozone oxidation for 30 min, they were placed immediately in the incubation solution (1 mM in toluene) for 72 h. The monolayer films were characterized by FTIR spectroscopy and XPS. The FTIR spectra were collected by accumulating a minimum of 500 scans per

ACKNOWLEDGMENTS. We thank Profs. Meir Wilchek, Naama Barkay, Amnon Horovitz, and Catalina Achim for insightful discussions. D.H.W. acknowledges support from United States National Science Foundation Grant CHE-1464701. R.N. acknowledges funding from the European Research Council (ERC) under European Union’s Seventh Framework Program FP7/2007-2013/ERC Grant 338720 CISS (chiral-induced spin selectivity).

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Kumar et al.

Chirality-induced spin polarization places symmetry constraints on biomolecular interactions.

Noncovalent interactions between molecules are key for many biological processes. Necessarily, when molecules interact, the electronic charge in each ...
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