Research ArticleCONDENSED MATTER PHYSICS

Automated structure discovery in atomic force microscopy

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Science Advances  26 Feb 2020:
Vol. 6, no. 9, eaay6913
DOI: 10.1126/sciadv.aay6913
  • Fig. 1 Schematic illustration of the CO-tip AFM imaging process and the proposed solution for the inverse imaging problem.

    (A to D) The imaging process Φ : XY of molecular geometry X (A) originates predominantly from probe particle (PP) displacement due to interactions with sample atoms (B). The resulting PP displacement Δr is plotted in (C). The fibers show deflection of the PP as it approaches the surface, with the red-blue gradient representing the tip-sample distance (red, far; blue, close). (D) The resulting AFM frequency shift [Δf(r)] images Y obtained by integrating the forces felt by the relaxed PP over its path. (E to G) The inverse imaging process (i.e., reconstruction of geometry) Φ−1 : YX approximated by a convolutional NN (F) transforming a 3D stack of AFM images Y (E) to a description of the molecular geometry X [represented by, e.g., van der Waals spheres (G)].

  • Fig. 2 Examples of CNN prediction from simulated and experimental data.

    (A to F) A molecule from the validation set with formula C7H10O2. (G to L) A dibenzo[a,h]thianthrene molecule (49). (M to U) A fullerene C60 [experimental data in (S) to (U)]. (V to X) Comparison of image descriptors, vdW-Spheres, height map, and atomic disk representation (see the SM for explanation) predicted from experimental images of C60. Columns 1 to 3 show simulated AFM signal (Δf) at different heights. Column 4 shows the vdW-Spheres representation predicted by the trained CNN (naturally, the reference is not available for experiment). Column 5 shows the reference vdW-Spheres representation calculated directly from geometry. Column 6 depicts a 3D render of the molecule.

  • Fig. 3 Discrimination of functional groups.

    Here, we compare three hypothetical anthraquinone derivatives that have differing numbers of chlorine atoms: one chlorine (A-F), two chlorines (G-L) and four chlorines (M-R). The first three columns show simulated AFM images at far, middle, and close tip-sample distances. The fourth column shows the associated NN prediction for the vdW-Spheres representation. The fifth column shows atom-type prediction from another NN that discriminates three different types of atoms: hydrogens (red), nonhydrogen peripheral (green), and carbon backbone (blue). The final column shows the molecular geometry. Note that the molecule is tilted so that the bottom edge is higher than the upper edge.

  • Fig. 4 Identification of the 1S-camphor adsorption configurations on Cu(111) with ASD-AFM.

    1 to 5 refer to distinct molecular configurations with experiments in columns (A) to (D) and simulations in columns (E) to (I). Selected experimental AFM images (out of 10 slices used for input): at (A), far; (B), middle; (C), close tip-sample distances; and NN prediction (D) for the vdW-Spheres representation. The vdW-Spheres representation shown in (E) corresponds to the full molecular configuration (F) resulting from the best match to the experiment. The corresponding simulated AFM images are given in (G) to (I) (far, middle, and close).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/9/eaay6913/DC1

    Section S1. Image representations of output molecular structure

    Section S2. Matching experiment to relaxed on-surface simulated configurations

    Section S3. Effect of small perturbations on AFM imaging and matching

    Section S4. Neural network architecture

    Section S5. PP simulations

    Fig. S1. Different 2D image representations of the output geometry X for simulated AFM images of a C7H10O2 molecule from the training set.

    Fig. S2. Different 2D image representations of the output geometry X for simulated AFM images of a C60 molecule.

    Fig. S3. Different 2D image representations of the output geometry X for simulated AFM images of dibenzo[a,h]thianthrene molecule (71).

    Fig. S4. Molecules from the validation data set together with the vdW-Spheres representation predicted by the CNN.

    Fig. S5. Matching between simulated relaxed configurations of 1S-camphor and experiment.

    Fig. S6. Effect of tilt of molecules on simulated AFM images 1 to 5.

    Fig. S7. Adjustment of simulated configuration by –CH3 group rotations.

    Fig. S8. Matching experimental configuration 2 of 1S-camphor with the closest simulated configurations.

    Fig. S9. Illustration of the layers of the CNN model.

    Fig. S10. The mean squared loss for height maps, vdW-Spheres, and atomic disks.

    Table S1. Losses on the training and test sets for the trained models.

    Table S2. Model architecture.

    Table S3. Lennard-Jones parameters in PP simulation and rigid body relaxation of surface.

    References (6776)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Image representations of output molecular structure
    • Section S2. Matching experiment to relaxed on-surface simulated configurations
    • Section S3. Effect of small perturbations on AFM imaging and matching
    • Section S4. Neural network architecture
    • Section S5. PP simulations
    • Fig. S1. Different 2D image representations of the output geometry X for simulated AFM images of a C7H10O2 molecule from the training set.
    • Fig. S2. Different 2D image representations of the output geometry X for simulated AFM images of a C60 molecule.
    • Fig. S3. Different 2D image representations of the output geometry X for simulated AFM images of dibenzoa,hthianthrene molecule (71).
    • Fig. S4. Molecules from the validation data set together with the vdW-Spheres representation predicted by the CNN.
    • Fig. S5. Matching between simulated relaxed configurations of 1S-camphor and experiment.
    • Fig. S6. Effect of tilt of molecules on simulated AFM images 1 to 5.
    • Fig. S7. Adjustment of simulated configuration by –CH3 group rotations.
    • Fig. S8. Matching experimental configuration 2 of 1S-camphor with the closest simulated configurations.
    • Fig. S9. Illustration of the layers of the CNN model.
    • Fig. S10. The mean squared loss for height maps, vdW-Spheres, and atomic disks.
    • Table S1. Losses on the training and test sets for the trained models.
    • Table S2. Model architecture.
    • Table S3. Lennard-Jones parameters in PP simulation and rigid body relaxation of surface.
    • References (6776)

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