Figure 1

Schematic view of the unit cells relevant to alkanethiols on Au(111). The large open circles are the gold atoms. The Au(111) and the $\left(\surd 3\times \surd 3\right)R30°$ unit cells are shown in dotted and solid lines, respectively. Methyl groups, which are lifted and shifted above the Au plane at the end of the alkyl chains, are still located on a $\left(\surd 3\times \surd 3\right)R30°$ lattice (small circles). However the black and gray circles correspond to different heights, implying that the unit cell is $c\left(4\times 2\right)$ (broken lines). The methyl surface structure can be alternatively described using the $\left(3a\times 2a\surd 3\right)$ [or $p\left(3\times 2\surd 3\right)$] rectangular unit cell [with a the Au(111) lattice constant] (rectangle in solid lines). According to Ref. 10 S atoms are not arranged on the same lattice (see Fig. 2).Reuse & Permissions

Figure 2

Top-view sketch of the surface structure proposed in Ref. 10. Two types of conformations (black and gray) coexist. Each of them exhibits a gauche defect near the surface, resulting in an L shape to account for the pairing of S atoms at a distance of $2.2\text{Å}$ while the C backbones must remain at a much larger distance to optimize attractive van der Waals interactions. The $\left(3a\times 2a\surd 3\right)$ unit cell is recalled in dotted lines, together with the hexagons formed by the methyl groups. For clarity the patterns of ${\text{CH}}_3$ groups and S atoms in the unit cell are shown as insets. A second quantitative information provided by Ref. 10 is the angle of the tilt planes (containing the C backbones) with respect to the raw of Au atoms. Also displayed around the adsorption site of the molecule located down and on the right are the nearest threefold hollow (gray) and bridge sites (black), and the six bridge sites ${\text{B}}_1-{\text{B}}_6$ (black) located $2.2\text{Å}$ away.Reuse & Permissions

Figure 3

Experimental SFG spectrum of ODT, showing that the ${\text{CH}}_2$ symmetric stretching mode and its Fermi resonance are indeed present although very weak (see text). The ${\text{CH}}_2$ asymmetric stretching mode is not detectable. Also shown are the reference SFG spectrum recorded on GaAs which gives the spectral shape of the IR laser, the fit of the spectrum to formula (1), and the deconvolution of the spectrum into four Lorentzians.Reuse & Permissions

Figure 4

Definition of the angles that characterize the molecular conformation. $\Theta$ and $\Phi$ are the molecular tilt and twist angles. Note the arbitrary choices of the C plane $\left(XZ\right)$ and of the orientation of the ${\text{CH}}_2{\text{-CH}}_3$ bond. The directions of the dipole moments of ${\text{CH}}_3$ (symmetric ${\mu }_{s3}$, asymmetric in-plane ${\mu }_{\text{as}3\text{ip}}$ and out-of-plane ${\mu }_{\text{as}3\text{op}}$) and ${\text{CH}}_2$ (symmetric ${\mu }_{s2}$ and antisymmetric ${\mu }_{\text{as}2}$) are also indicated. Left inset: angles defining the geometry at the bottom of the alkyl chain. Right inset: local frames. $z_i$ is along ${\text{C}}_{\left(i\right)}{\text{C}}_{\left(i+1\right)}$, $y_i{z}_i$ is a mirror plane for ${\text{C}}_{\left(i\right)}{\text{H}}_2$ and $x_i$ is parallel to HH. Euler angles relating $x_{i-1}{y}_{i-1}{z}_{i-1}$ and $x_i{y}_i{z}_i$ (about $z_{i-1}$, the rotated $x_{i-1}$, and $z_i$, successively) are $\left(0,\pi \text{−}\alpha ,\pi \right)$ in the all-trans conformation, with $\alpha$ as the tetrahedron angle. Near the substrate Euler angles are successively $\left({\alpha }_{\text{SC}},\pi \text{−}{\alpha }_{\text{S}},\pi \right)$, $\left({\psi }_0,\pi \text{−}\alpha ,\pi \right)$, and $\left({\psi }_1,\pi \text{−}\alpha ,\pi \right)$. The symmetry axis of ${\text{C}}_{\left(17\right)}{\text{H}}_3$ is $z_{16}$.Reuse & Permissions

Figure 5

Calculated ratio of the asymmetric to symmetric SFG intensities $\text{as}3/s3$ as a function of the tilt angle ${\text{tilt}}_{\text{CH}3}$ of the ${\text{CH}}_3$ symmetry axis with respect to the surface normal. The molecular tilt angle is $\Theta =30°$. To allow direct comparison between ODT and PDT, the ratios are actually $A_{\text{as}3}/A_{s3}$ which are independent of the linewidth variations from one spectrum to the other. Labels at the crossing of horizontal and vertical lines indicate the points corresponding to experiment: ODT and PDT in the case where the spectrum is attributed to a single molecule, ${\text{ODT}}_{\text{A}/\text{B}}$ and ${\text{PDT}}_{\text{A}/\text{B}}$ in the case of two types of molecules. Inset: relationship between the tilt of the methyl group and the molecular twist angle for a molecular tilt angle between 25 and $40°$.Reuse & Permissions

Figure 6

Variation in the ${\text{Au-S-C}}_{\left(0\right)}$ angle ${\alpha }_{\text{S}}$ as a function of the angle ${\psi }_1$ about the ${\text{C}}_{\left(0\right)}{\text{-C}}_{\left(1\right)}$ bond for molecules A and B. The straight horizontal line recalls that steric hindrance implies that ${\alpha }_{\text{S}}>100°$.Reuse & Permissions

Figure 7

Variation in the ${\text{tilt}}_{\text{CH}2}^0$ angle, characterizing the orientation of the IR dipole moment of the unpaired ${\text{CH}}_2$ group with respect to surface normal, as a function of the dihedral angle about the ${\text{C}}_{\left(0\right)}{\text{-C}}_{\left(1\right)}$ bond, for A and B molecules. The line at ${\text{tilt}}_{\text{CH}2}^0=90°$ indicates the angle for which the SFG signal is zero for the ${\text{CH}}_2$ symmetric stretch. The dots correspond to the best values of ${\psi }_1$.Reuse & Permissions

Figure 8

(Color online) Example of calculated molecules and their SFG spectra, where the contributions of the two molecules to the ${\text{CH}}_2$ symmetric stretch cancel. Molecule A: tilt $\Theta =30°$, twist ${\Phi }^{\text{A}}=245°$, ${\psi }_1^{\text{A}}=30°$ (conformation intermediate between trans and eclipsed), and ${\text{tilt}}_{\text{CH}2}^0\left(\text{A}\right)=71°$. Molecule B: tilt $\Theta =30°$, twist ${\Phi }^{\text{B}}=335°$, ${\psi }_1^{\text{B}}=100°$ (nearly gauche), and ${\text{tilt}}_{\text{CH}2}^0\left(\text{B}\right)=114°$. The IR dipole moment of the unpaired ${\text{CH}}_2$ point by $29°$ above and $24°$ below; the surface plane in molecules A and B, respectively. Their contributions to the SFG spectrum cancel. Note that for clarity the length of the molecules is 12 instead of 18.Reuse & Permissions

Figure 9

(Color online) Example of calculated molecules and their SFG spectra, where the contributions of the two molecules to the ${\text{CH}}_2$ symmetric stretch add up. Molecule A: tilt $\Theta =30°$, twist ${\Phi }^{\text{A}}=245°$, ${\psi }_1^{\text{A}}=-60°$ (eclipsed conformation), and ${\text{tilt}}_{\text{CH}2}^0\left(\text{A}\right)=113°$. Molecule B as in Fig. 10: tilt $\Theta =30°$, twist ${\Phi }^{\text{B}}=335°$, ${\psi }_1^{\text{B}}=100°$ (nearly gauche), and ${\text{tilt}}_{\text{CH}2}^0\left(\text{B}\right)=114°$. The unpaired ${\text{CH}}_2$ have almost the same orientations in the two molecules, and their contributions to the SFG spectrum add up. Note that for clarity the length of the molecules is 12 instead of 18.Reuse & Permissions

Figure 10

Case of two molecules with perpendicular C planes ($\Theta =30°$, ${\Phi }^{\text{A}}=245°$, and ${\Phi }^{\text{B}}=335°$): calculated intensity ratio $s2/s3$ of the ${\text{CH}}_2$ symmetric stretch to ${\text{CH}}_3$ symmetric stretch modes as a function of the dihedral angle ${\psi }_1^{\text{A}}$ about the ${\text{C}}_{\left(0\right)}{\text{C}}_{\left(1\right)}$ bond of molecule A for ${\psi }_1^{\text{B}}=100°$. The variation in $s2/s3$ as a function of ${\psi }_1^{\text{B}}$ assuming ${\psi }_1^{\text{A}}=90°$ is similar.Reuse & Permissions

Figure 11

Calculated spectra of A and B molecules for the appropriate angles characterizing the L shape: $\Theta =30°$, ${\Phi }^{\text{A}}=245°$, ${\Phi }^{\text{B}}=335°$, ${\psi }_1^{\text{A}}=90°$, and ${\psi }_1^{\text{B}}=100°$. Three spectra are shown, corresponding to molecular conformations A alone, B alone, and A and B together. The angle of incidence is $60°$.Reuse & Permissions

Figure 12

Sketch of molecules A and B for two orientations of the tilt plane (the plane that contains the average tilted C backbone). Atoms ${\text{S}}^{\text{A}}$ and ${\text{S}}^{\text{B}}$ are adsorbed on well defined sites of Au(111) (bridge for A and threefold hollow for B). The positions of the methyl groups depend on the molecular conformations and on the orientation of the tilt plane. They must fall on the hexagon in dashed lines [the size of which is given by the Au(111) structure, but the position of which with respect to Au(111) depends on the molecular conformations]. The degree of freedom to accommodate the molecule simultaneously on the Au(111) sites and on the hexagon is the rotation of the tilt plane.Reuse & Permissions

Figure 13

Top view of the conformations and arrangement of A (black) and B (gray) molecules in the $\left(3a\times 2a\surd 3\right)$ unit cell. The $YZ$ plane is the tilt plane. The rectangle in dotted lines is the unit cell in the plane of the ${\text{CH}}_3$ groups. The rectangle in bold lines is the unit cell in the plane of the S atoms. To keep the figure as simple as possible, H atoms are not shown, and the number of C atoms is 12 instead of 18.Reuse & Permissions

Figure 14

Perspective view of the molecules. The perspective is chosen to show that the C planes of molecules A and B are perpendicular. Other details are like in Fig. 13.Reuse & Permissions

Figure 15

View of the molecules along the average chain axis. Other details are as in Fig. 13. A hexagon formed by the ${\text{CH}}_3$ groups is also shown in bold gray lines, and the planes formed by the C backbones are materialized by a bold black line.Reuse & Permissions