Direct observation of long-range chirality transfer in a self-assembled supramolecular monolayer at interface in situ

Due to the interest in the origin of life and the need to synthesize new functional materials, the study of the origin of chirality has been given significant attention. The mechanism of chirality transfer at molecular and supramolecular levels remains underexplored. Herein, we study the mechanism of chirality transfer of N, N’-bis (octadecyl)-L-/D-(anthracene-9-carboxamide)-glutamic diamide (L-/D-GAn) supramolecular chiral self-assembled at the air/water interface by chiral sum-frequency generation vibrational spectroscopy (chiral SFG) and molecular dynamics (MD) simulations. We observe long-range chirality transfer in the systems. The chirality of Cα-H is transferred first to amide groups and then transferred to the anthracene unit, through intermolecular hydrogen bonds and π-π stacking to produce an antiparallel β-sheet-like structure, and finally it is transferred to the end of hydrophobic alkyl chains at the interface. These results are relevant for understanding the chirality origin in supramolecular systems and the rational design of supramolecular chiral materials.


Vibrational sum-frequency generation
Sum-frequency vibration (SFG) spectroscopy is a second-order nonlinear optical technique, which principle has been widely reported in the literature. [1][2][3][4][5] spectroscopy has two pulsed laser sources, infrared (IR) and visible (Vis) beams, that can generate SFG signals when the two beams achieve spatial and temporal overlap at the interface. For a certain polarization setting, the SFG intensity can be described by effective second-order susceptibility, The second-order susceptibility ( (2) ) of an interface consists of a non-resonant term and resonant terms, as follows, (2) = (2) + ∑ (2) = (2) + ∑ − + (2) in which (2) is the nonresonant susceptibility, which is typically very small in the air/water interface experiments. , , and Γ are the amplitude, resonant frequency, and Lorentzian width of the th vibrational mode respectively. To reveal the vibrational signatures of the interfacial molecules, SFG spectra are commonly plotted as a function of the incident IR wavenumber (in cm -1 ). In this paper, we used eq. 2 to perform global fitting of spectral peaks.
As shown in Supplementary Figs. 1a-b, we performed sss polarization measurement of the D-GAn monolayer in the amide and C-H regions in the rotation sample cell. The results showed that the sss signal was zero ( is zero), which confirmed that the L-/D-GAn monolayer was an isotropic interface with ∞ symmetry 6,7 . In addition, we also measured the ssp and sss polarization spectra of the D-GAn monolayer at high surface pressure ( Supplementary Fig. 1c) to further check the anisotropy of the interface.
The results confirmed that no sss signal was detected neither due to experimental error nor low signal-to-noise ratio. Therefore, the L-/D-GAn self-assemblies are isotropic at the interface and the self-assembly did not form the microcrystal.
It must be pointed out that we used a broadband SFG (resolution ~8 cm -1 ) to do the S3 additional sss polarization measurement to avoid the high laser intensity damage to the samples in the high-resolution sum-frequency generation (HR-SFG, resolution 0.4 cm -1 ) we used.

SFG-VS polarization combinations
In vibrational SFG, the sample interacts with a tunable IR beam with frequency and polarization K , and with a non-resonant visible beam with frequency and polarization Ĵ. The SFG signal is emitted with frequency = + and polarization Î. Typically, we define the Z-axis as the surface normal, and the X-Z plane as the scattering plane. The beams are polarized either in the X-Z plane (p-polarization) or in the Y-direction (s-polarization). The angles of the input and sum-frequency wavevectors with respect to the surface normal are , , and (the is between 0 and 90° for all three beams). All these definitions apply to the laboratory frame, symbolized here using capital letters (X/Y/Z and I/J/K).
We focused our derivation on the lab-frame ssp (s-polarized SFG, s-polarized visible beam, and p-polarized IR beam), sps, ppp and psp, spp, pps signals, which consist of three types of factors: elements of the (second-rank) Fresnel tensor L, which describe effects caused by the different refractive indices of the media under study; factors arising from the angles of the input and sum-frequency beams; and elements of the complex third-rank tensor (individual elements are symbolized as (2) ), which describe the intrinsic response of the sample. We symbolize the full lab-frame response (including all three effects) as (2) , the "effective" response. (2) is related to χ by the equation S3: To write the final expressions for the effective ssp, sps, ppp and psp, spp, pps signals, , , , , , and , , , , , note that s-polarization corresponds to Ŷ-polarization in the lab frame, whereas p-polarization corresponds to polarization in the direction + for the IR beam, + for the visible beam, or − + for the sum-frequency beam. Substituting these polarization vectors into eq. 3, the nonzero (2) elements of an interface can be measured by manipulating the polarization of incident beams and S5 SFG signals: , , , , For an chiral surface with ∞ symmetry, there are thirteen nonzero (2) elements, of which seven achiral elements ( ) and six chiral elements ( , (2) , (2) , (2) , (2) ), so effective secondorder susceptibility tensor elements, , , , , , and , , , , , in eq. 4-9 can be simplified: , , , , , ,

Molecular hyperpolarizability and calculation of group orientation
In order to calculate the molecular orientation information, we introduced the molecular hyperpolarizability (β), which determines the SFG response of a molecule.
The (2) tensor elements can be expressed in terms of the (2) tensor elements using the Euler transformation: , where I, J, K are the laboratory coordinates (X, Y, Z) and i, j, k are molecular coordinates (a, b, c); N is the number density of the molecular moiety under study; , and are elements of the rotational transformation matrix connecting the molecular coordinates to the laboratory coordinates. In this work, the effective secondorder susceptibility correlates to the hyperpolarizability (β) tensor of molecules at interfaces by using the z-y-z Euler transformation. The z-y-z transformation is achieved by the clockwise rotation of the molecular c axis by ψ, b axis by θ, and c axis by ϕ to overlap with the laboratory coordinates. For a monolayer with a random orientation distribution within the surface plane, the Euler transformation introduces the molecular S8 orientation (θ, ψ), while the in-plane rotation angle (ϕ) is averaged by the integration over 0 to 2π for the isotropic interface, with 2 = 2 = 1 2 and = 0. 8

Chiral SFG-VS spectroscopy of amide modes
The hydrogen bond formed between different amide groups usually gives four different bands, i.e. amide I (primarily CO stretch), amide II (CN stretch and NH inplane bend), amide III (CN stretch, NH bend, and CO in-plane bend), and amide A (NH stretch). 9 Previous studies have shown the amide I band is sensitive to the structures and amount of secondary structures and the local environments which are not strongly influenced by side chains. 10 The α-helical, parallel, and antiparallel β-sheet structures are the most widely encountered secondary structures in peptides and proteins, and different types of secondary structures show different peak centers. In order to deduce the type and orientation of secondary structure from SFG signals obtained using various polarization combinations, we need to know the second-order surface susceptibility of interfacial peptides in the lab coordinate system and the hyperpolarizability in the molecular coordinate system associated with it. In this work, we used two chiral polarization combinations of psp and spp to detect chiral amide Ⅰ stretch. The intensity of the chiral SFG signal measured by the psp polarization is related to , and consequently (2) , and (2) in the chiral interface with ∞ symmetry, as shown in eq. 13. Similarly, the intensity of the chiral SFG signal measured using the spp polarization is related to , and consequently (2) , and (2) , eq. 14.

ɑ-helical structure and symmetry
The work of the Chen group has shown that both the A mode and E1 mode of ɑhelix amide I stretching can contribute to SFG signals, and the repeating unit of ɑ-helix follow 18 5 symmetry. 11,12 The nonzero hyperpolarizability tensor elements for the A mode are , = . We can deduce the susceptibility tensor elements for the A mode of ɑ-helices: The nonzero hyperpolarizability tensor elements for the E1 mode of ɑ-helices are , and the susceptibility tensor elements for the E1 mode: Where is the surface density of ɑ-helical repeat units. From the above derivation, it can be seen that , = 0 for the A mode and , for E1 mode of the ɑ-helical structure.

Parallel β-sheet structure and symmetry
A parallel β-sheet is characterized by two peptide strands running in the same direction held together by hydrogen bonding between the strands. The repeat unit has 2 symmetry, thus two modes of amides I are expected: A and B modes. 13 Since the signal derived from the contribution of the B mode of the amide Ⅰ band of parallel βsheet usually appears at a lower frequency (about 1620 cm -1 ), it does not match the signal peak position of the amide Ⅰ band we observed in our experiment, so here we only discussed the A mode of parallel β-sheet structure.
The nonzero hyperpolarizability tensor elements for the A mode of parallel β-sheet are , , , = , and the susceptibility tensor elements for the A mode: Where is the surface density of parallel β-sheet repeat units. From the above derivation, it can be seen that , for the A mode of the parallel βsheet structure. S10

Antiparallel β-sheet structure and symmetry
The antiparallel β-sheet structure follows 2 symmetry, in which the susceptibility tensor elements of different modes and orientation analysis are discussed in detail in Supplementary Section 7 (Orientation determination of antiparallel β-sheet). For B2 mode of antiparallel β-sheet structure, , ) .

Interference chiral polarization combinations
In this work, we monitored the SFG spectra in the C-H and amide region of L-GAn and D-GAn monolayers in different surface pressure at the air/water interface using the ssp, sps, ppp achiral polarization combinations and psp, spp, s(+m)p-s(-m)p, p(+m)pp(-m)p chiral polarization combinations to investigate the supramolecular chiral information transfer during fabricating the self-assembled supramolecular monolayer.
We can use the psp polarization combination to measure the interface chirality in the amide region, but in the C-H region, the chiral signal is weak, and it is difficult to use the chiral polarization combination of psp, spp, and pps to detect. We measured the weaker chiral SFG spectra in the C-H region by using the interference method of s(+m)p-s(-m)p polarization. Where the m (usually 45°) denotes the mixed s and p polarization, + denotes clockwise rotation from the p polarization in the incident plane facing the incoming beam, and -denotes counterclockwise rotation from the p polarization. By exploiting the s(+m)p-s(-m)p polarization, the achiral SFG field will be introduced to interfere with the chiral SFG signals, so that the chiral part could be enhanced in comparison to the direct measurement of the much smaller | The interference crossing term for s(+m)p-s(-m)p is, Similarly, the interference crossing term for p(+m)p-p(-m)p is, As stated in the equation above, the s(+m)p-s(-m)p spectra measure the actual value S11 of the product of achiral ssp and chiral spp magnetic susceptibility terms, and the p(+m)p-p(-m)p spectra measure the actual value of the product of achiral ppp and chiral psp magnetic susceptibility terms. And because L-GAn, D-GAn, and racemic mixtures (50/50 equivalent mixtures) show the same ssp and ppp SFG spectra at the air/water interface, that is, L-GAn and D-GAn actually have the same effective achiral susceptibility. 14 Therefore, the p(+m)p-p(-m)p spectrum is a direct measurement of the relationship between the intensity and the sign of the chiral psp term.

Air/water interfacial assembly of L-/D-GAn
The phase behavior of L-GAn at the air/water interface was investigated by surface pressure measurements (isotherm experiments) and Brewster angle microscopy. The The illustration on the right shows Brewster angle microscopy images of D-GAn monolayers in three surface pressures.

Distinguish the peaks of three amide groups of glutamate
The amide I vibrational mode arises mainly from the C=O stretching vibration, with minor contributions from the out-of-phase CN stretching vibration, CN deformation, and NH in-plane bending and is known to be intrinsically sensitive to the peptide or protein backbone and secondary structures at or above approximately 1600 cm -1 . 17 The amide II mode is the out-of-phase combination of the NH in-plane bending and CN stretching vibrations, with smaller contributions from the CO in-plane bending and the CC and NC stretching vibrations. However, the correlation between the secondary structure and the frequency of the amide II band is less straightforward than that for the amide I vibration 18 .
As shown in Supplementary Fig. 4a, the molecular structure of the Fmoc-Glu-C18 and Fmoc-Asp-C17 is very similar, and the main difference is that the number of methylene groups that are connected between the amide 2 and the chiral carbon.
Because the molecular structure of the two molecules is highly similar, we believe that the two molecules are spread as monolayers on the interface in a similar assembly structure. By comparing the signal peaks of the two monolayers in the amide band Using a similar analysis method as above, we selected two molecules of D-GAn and Fmoc-Glu-C18 as a control group to distinguish the amide Ⅰ and amide Ⅱ band of amide 1. As shown in Supplementary Fig. 5a, for the molecular structure of Fmoc-Glu-C18, the steric hindrance between the aromatic ring and amide 1 was diminished by the spacer than D-GAn. In addition, the carbon-carbon stretching vibration of the fluorenylmethoxycarbonyl protecting group (Fmoc group) and anthracene group is  Supplementary Fig. 5b, the spectrum measured under the chiral polarization combination used the left-hand coordinate system, and the spectra measured under achiral polarization combinations used the right-hand coordinate system.) S17

L-GAn molecules form an antiparallel β-sheet-like structure at the air-water interface
In the above analysis (Figs. 1d and f, Table 1, and Supplementary Section 4), we have clearly assigned three amide groups of L-/D-GAn separately, which allows us to continue to explore the intermolecular hydrogen bonds structures of amide bands.
Usually, amide I signal contributed from different secondary motifs in a protein can be separated in the frequency domain using vibrational spectroscopy 19,20 . For example, an α-helix has its characteristic amide I frequency in the range of 1650-1660 cm -1 .
However, sometimes disordered structure and β-turn may also contribute to amide I signal in this spectral range. Therefore, the assignment of the amide I signal needs to be carefully examined. In this work, we carefully identify the structure of the formed supramolecular assembly not only based on the frequency domain of the chiral peak but also on the relative intensity of the chiral signal and then infer the molecular packing of the molecules self-assemble on the interface.
The symmetry of the repeating unit of an antiparallel β-sheet can be assumed as D2 symmetry, and theoretically, the B1, B2, and B3 modes are SFG active 21 . The peak at 1637 cm -1 (amide I band of amide 3) is attributed to the B2 mode of the antiparallel βsheet-like structure, and the B1 and B3 modes are not visible in our spectra (Table 1) 22 , and the other at 1646 (amide I band of amide 2) and 1657 cm -1 (amide I band of amide 1) are attributed to disordered structure and β-turn-like 23 . In order to confirm our inference on the structure, we further explored the polarization-dependent spectroscopy ( Supplementary Fig. 6). In which, the achiral and the pure chiral SFG spectra and the chiral spectra obtained by the interference of the two can help us identify the chirality that originates from the specific functional groups (Supplementary Figs. 6a, b, and d).
Besides, the intensity of the chiral SFG signal measured by the psp and spp polarization combinations are related to , and , , respectively, and different secondary structures have different strengths ratios of , , (Supplementary Section 1). Therefore, we can deduce the structure formed by three amide groups of L-/D-GAn S18 by comparing the strength of the signal in the amide Ⅰ band under psp and spp chiral polarization combinations with combining the frequency of the signal peak.
In Supplementary Fig. 6c, the chiral signal of amide Ⅰ of amide 3 (center peak at 1637 cm -1 ) can be observed under two chiral and two interference chiral polarization combinations, and the chiral SFG vibrational signal are strong. As shown in previous work, antiparallel β-sheet structures can easily pack with twist angles at the interface, therefore generating strong chiral signals for B1 (1680-1690 cm -1 ) and B2 (1630-1640 cm -1 ) vibrational modes. 24,25 In addition, under the chiral polarization combination of psp and spp, the amide I of amide 3 showed the same intensity, that is , (Supplementary Table 5), which is consistent with the derived equation = −  Fig. 6c).
These results indicated that the chiral signals of amide 1 and 2 in the amide Ⅰ and Ⅱ regions are very weak and , in amide Ⅰ region. According to the derived equations (17)(18)(19)(20)(21) in Supplementary Section 1.4, there are , in amide Ⅰ region for α-helix and β-sheet structures, so we believed amide 1 and 2 forming the disordered structures or non-hydrogen bonded amide group by selfassembly. These disordered structures may have varied symmetry and orientations and contribute to chiral SFG signals that can also behave differently under different polarization combinations.
We also probed the amide III region as an addition to unambiguously identify the supramolecular structure of D-GAn because the characteristic spectral features of α-S19 helix-like, β-sheet-like, β-turn-like, and random coils are well separated in this spectral region. However, the SFG signal intensity in the amide-III region is so weak, and we did not obtain SFG signals with a reasonable signal-to-noise ratio.

SFG spectra of L-/D-GAn monolayers in different surface pressures
According to the SFG theory in eq.16 ( ,

Orientation determination of antiparallel β-sheet-like
SFG spectra collected from amide I modes of peptides and proteins using different polarization combinations can be used to determine membrane orientations of peptides and proteins, as shown in a previous publication. 27 We used polarization-dependent achiral SFG to determine the tilt angle ( , ∈ [0 − 90°] ) and twist angle ( , ∈ [0 − 180°]) of the β-sheet-like segments of L-/D-GAn molecules. The symmetry of the repeating unit of an antiparallel β-sheet can be treated as D2 symmetry, and theoretically, the B1, B2, and B3 modes are SFG active. 28 The peak at 1637 cm -1 belongs to the B2 mode of antiparallel β-sheet-like structure, the B1 and B3 modes are not observed in our spectral results (Fig. 1d). The nonzero hyperpolarizability tensor elements for B2 mode we have = . 23 Euler transformations from the molecular coordinates (a, b, c) to laboratory coordinates (X, Y, Z) for an antiparallel β-sheet-like unit were shown in Supplementary Fig. 9. The relationship between the laboratory-fixed axis system and the molecule-fixed coordinate system can be specified by the Euler angles (θ (tilt angle), ψ (twist angle), and φ (in-plane rotation angle)). Euler transformation matrices can be applied to project the microscopic hyperpolarizability from the molecular coordinates to the laboratory coordinates to yield macroscopic second-order susceptibility. In the following discussion, the z-y-z transformation as depicted in the work of the Simpson group is used. 8 The SFG signals for the ssp, sps, ppp, and psp combinations of the polarization directions are related to χ (2) tensor elements. For example, the intensity of the ssp achiral SFG signal is related to χ (2) , and consequently χ (2) . Similarly, the intensity of the chiral SFG signal measured by the psp polarization is related to χ (2) and consequently χ (2) in the absence of electronic resonance, details are written in SI.
The spectra fitting results are given in Supplementary Tables 1-3. The expressions for these macroscopic susceptibility elements (χ (2) ) can be obtained using eq. 4-7. The Euler transformation introduces the molecular orientation (θ, ψ), while the in-plane rotation angle (ϕ) is averaged by the integration over 0 to 2π for an isotropic interface S23 on the x-y plane to yield. By assuming that the L-/D-GAn monolayers are azimuthally symmetric, we have the following nonzero susceptibility tensor elements for the B2 modes as follows: 8,23,29 (2) = (2) = 0 (28) In the above equations, is the surface density of the repeating unit of the β-sheet.
Assume that the value of hyperpolarizability quantities is -34.5 29 , which can be calculated from the Raman tensors and IR transition dipoles. We assumed that both θ and ψ have δ distributions, we can calculate the magnitude of second-order nonlinear susceptibility tensor elements as a function of θ and ψ according to eq. 24-28. From (2) ≈ -5.9) and 60 ± 0.3˚ and 58 ± 0.9˚ (with the ratio (2) (2) ≈ 0.7 and

Chiral SFG spectra in the region corresponding to C-H stretching vibrations
As shown in the infrared spectrum of the anthracene molecule, we have observed the =C-H stretching vibration peak of the anthracene ring at 3046 cm -1 (Supplementary Fig.   10a). However, in the SFG measurement at 2750-3150 cm -1 , both the chiral SFG signal and achiral SFG signal of the =C-H stretching vibrations of the anthracene groups of L-GAn and D-GAn molecules (center peak at 3046 cm -1 ) cannot be observed (Supplementary Figs. 10c and e) even the IR laser intensity at 3000-3100 cm -1 is high enough (Supplementary Fig. 10b). Supplementary Fig. 10b shows the non-resonant SFG signal from z-cut quartz, from which we conclude that the IR laser intensity is high enough to get reasonable SFG spectra for =C-H stretching vibrations of the anthracene groups. The absence of the =C-H SFG signal might have two reasons. One is that the anthracene ring has a centrosymmetric structure that the dipole moment of the =C-H has been canceled out. The second reason is the anthracene rings parallel to S25 the interface; which can be confirmed by MD simulation (about 70° with an orientation contribution of 0-160° (Fig. 3f).) Moreover, the weak resonant SHG signal on the D-GAn monolayer which indicated the anthracene ring should lie on the interface because the typical absorption of anthracene is in the 330-400 nm when the incident laser beam is 780 nm (Supplementary Fig. 10d).
It should be noted that although the chiral SFG response of aromatic =C-H stretches is not present, we can still conclude that the chirality transfer from the chiral-center carbon to the anthracene group from CD spectra and SHG spectra. The CD spectra of

Orientation determination of methyl groups
The macroscopic chirality response on surfaces detected by SFG spectra comes from both the intrinsic chirality of chiral molecules and the orientational or structural chirality. The contribution of the achiral or chiral CH3 groups to the chiral SFG spectra is orientational or structural chirality, as the result of averaging over the orientational distributions of the surface molecular groups. 31 Here, we measure the orientations of the methyl group and amide group separately and then deduce the conformation and overall orientation of the molecules. The chiral information on the carbon atom in the chiral center is already very weak when it passes through the 18-carbon alkyl chains to the terminal methyl groups and cannot be detected with the independent chiral polarization. Therefore, we assumed that the end methyl groups of the alkyl chain obey symmetry, and used the ratio method widely reported in the literature to determine molecular group orientation angles at the interface. [32][33][34] Experimentally, the CH3 vibrational peaks in the SFG-VS ssp and ppp spectra well obey the polarization selection rules for the end methyl groups as shown in the ssp and ppp SFG spectra, as in Fig. 2. The effective SFG susceptibility (2) can be simplified to the following expression: 35

S28
Where is the surface density of the probed interfacial species; is the susceptibility strength factor, which is a constant in a specific experimental configuration for a given molecular system; and ( ) is the orientational field functional, which contains all orientational information at a given SFG experimental configuration. 28,36 The equation shows that (2) ( ) is a function of interfacial molecular density and orientation angle (θ). The sps intensity in the whole orientation angle (θ) range was close to zero at C-H bands, therefore using the ratio , − , − , − , − (2) ≈ −9.7) for the methyl group of the interfacial L-GAn and D-GAn molecules with the surface pressure rising. That means with the increase of surface pressure, the alkyl chains stand straighter and molecules self-assembly forming a more orderly assembly structure, which is consistent with the changes of morphology and SFG intensity in the C-H stretch region.
As discussed above, for the L-GAn monolayer constructed at the air-water interface, we used the ssp and ppp polarization intensity ratio to calculate the orientation angles of the CH3 groups at different surface pressure and we found the tilt angle was changed from 44° to 37° which is very close to the magic angle ( Supplementary Fig. 12). But The illustration on the right shows a methyl group unit of the alkyl chain and the orientation angle of the methyl group in the given molecular frame. Axis c is the principal axis of the methyl group, axis z represents the surface normal, orientation angle (θ) is defined as the angle between axis z and axis c.

Molecular snapshots of self-assembly
The initial state of the simulated system (L-GAn monolayer spread at the air/water interface) is presented by t = 0 s. Under 1 bar of lateral pressure, and limiting the orientation of the anthracene ring to remain unchanged, after 5 ns, L-GAn forms a dense monolayer on the interface with a monomolecular area of 53 Å 2 (the surface pressure is about 20 mN/m, as shown in Supplementary Fig. 2). After 55 ns, it is observed that the anthracene ring of the molecule has undergone a larger twist, and the lateral S31 interaction between the molecules has been strengthened, as shown in Supplementary   Fig. 13a.
The top-view and side-view system snapshots of the last frame as shown in Supplementary Figs. 13b-c. The simulation system consists of 100 L-GAn molecules (10×10 molecules) and many water molecules. In order to ascertain the assembly structure of the molecules, we selected 9 molecules (red box) and 4 molecules (purple box) from the central area of the box for coloring in the VMD, as shown in the main text of Figs. 3b-c.
As mentioned above, under the orientation restriction of the molecular head group was released and the lateral pressure was no longer applied, a 50 ns simulation was performed again. The total number of hydrogen bonds formed between L-GAn molecules was counted as a function of the simulation time in Supplementary Fig. 13d.
The probability statistics of the height of a single-molecule after 55 ns dynamics simulation are shown in Supplementary Fig. 13e. The result showed that the height of the single-molecule is between 33-41 Å 2 and deduced that the thickness of the monolayer is about 36 Å 2 .
Supplementary Fig. 13 The results of MD simulations. a, Side-view system snapshots for the S32 self-assembly process of L-GAn molecules at the air/water interface. The (b) top-view and (c) sideview system snapshots of the last frame after 55 ns MD simulation. The red and purple boxes indicated the molecular positions shown in Figs. 3b-c of the main text, respectively. d, The number of hydrogen bonds between L-GAn molecules changes with the simulation time. The solid line is the result of the linear fitting. e, After performing a 55 ns simulation, the probability statistics of the height of a single molecule.

Number of molecules assembled into nanorods
The monolayers were transferred onto the freshly cleaved mica surface and their atomic force microscopy (AFM) was measured. As reported in published references, for the L-GAn Langmuir-Blodgett films at 15 mN/m, nanorods with a height of 29-43 Å 2 were observed (Supplementary Figs. 14a and b), and when the surface pressure was increased to 30 mN/m, the nanorods were packed closer 30 .
We calculated the distance between the alkyl chain end methyl and the anthracene rings of the 100 L-GAn molecules that reached equilibrium after 55 ns MD simulation; the highest probability is located at 36 Å ( Supplementary Fig. 13e). We deduced that We now attempt to characterize the Fmoc-Glu-C18 supramolecular self-assembly from AFM imagines using the same method as the L-GAn supramolecular self-assembly.
We assume that L-GAn and Fmoc-Glu-C18 assemblies have similar three-dimension S34 single-molecule sizes at the interface because the molecular structures of Fmoc-Glu-C18 molecules and L-GAn molecules are similar (Fig. 1a), which of both self-assembly form nanorod structures with similar shapes (Supplementary Figs. 14a-b and Supplementary Fig. 15). Using the AFM results in Supplementary Fig. 15 and MD simulation of the L-GAn assemblies, we can roughly estimate the number of Fmoc-Glu-C18 molecules constructed a single nanorod. The Fmoc-Glu-C18 molecules at the interface are driven by π-π interaction to build the length of the nanorods along the ydirection of the coordinate axis and driven by the hydrogen bond to build the width of the nanorods along the x-direction of the coordinate axis. The length, width, and height of the nanorods can be estimated to be 400 molecules (2187Å/5.0Å, y-axis), 40 molecules (375Å/9.2Å, x-axis), and a single molecule (z-axis), respectively ( Supplementary Fig. 15d). It must be pointed out that the number of Fmoc-Glu-C18 molecules assembled to form nanorods in the xyz direction above is just a rough estimate. In the future, we will calculate the length, width, and height of a single Fmoc-Glu-C18 molecule to form supramolecular assemblies at the interface by MD simulation to gain the exact number of molecules of the nanorods.

Global fitting of SFG spectra in amide region
Supplementary Table 1 The Global-Fitting parameters and vibrational mode assignments for the spectra of L-GAn monolayer in the amide region. The spectra are fitted with Lorentzian line shape function as Eq. 2. The peak position of the vibrational modes , the peak width Γ , and the oscillator strength factor χeff,q,ijk ( , , ) of the vibrational modes and assignment of the characteristic peaks are listed.