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Non-additivity of molecule-surface van der Waals potentials from force measurements.

Wagner C, Fournier N, Ruiz VG, Li C, Müllen K, Rohlfing M, Tkatchenko A, Temirov R, Tautz FS - Nat Commun (2014)

Bottom Line: The experiment allows testing the asymptotic vdW force law and its validity range.We find a superlinear growth of the vdW attraction with molecular size, originating from the increased deconfinement of electrons in the molecules.Because such non-additive vdW contributions are not accounted for in most first-principles or empirical calculations, we suggest further development in that direction.

View Article: PubMed Central - PubMed

Affiliation: 1] Peter Grünberg Institut (PGI-3), Forschungszentrum Jülich, 52425 Jülich, Germany [2] Jülich Aachen Research Alliance (JARA)-Fundamentals of Future Information Technology, 52425 Jülich, Germany.

ABSTRACT
Van der Waals (vdW) forces act ubiquitously in condensed matter. Despite being weak on an atomic level, they substantially influence molecular and biological systems due to their long range and system-size scaling. The difficulty to isolate and measure vdW forces on a single-molecule level causes our present understanding to be strongly theory based. Here we show measurements of the attractive potential between differently sized organic molecules and a metal surface using an atomic force microscope. Our choice of molecules and the large molecule-surface separation cause this attraction to be purely of vdW type. The experiment allows testing the asymptotic vdW force law and its validity range. We find a superlinear growth of the vdW attraction with molecular size, originating from the increased deconfinement of electrons in the molecules. Because such non-additive vdW contributions are not accounted for in most first-principles or empirical calculations, we suggest further development in that direction.

No MeSH data available.


Related in: MedlinePlus

Experimental results and comparison with theory.(a) Summary of the experimentally obtained C3 values. The experimental error bars indicate the uncertainty in the C3 coefficients due to the influence of the experimental noise on the fitting routine. Calculated values from the semi-empirical dispersion correction scheme vdWsurf and from DFT+RPA are also shown. (b) Dynamic per-atom polarizabilities of carbon for NTCDA, PTCDA and TTCDA as resulting from RPA calculations. The coordinates x, y and z refer to the directions along the long axis, short axis and perpendicular to the plane of each molecule. (c) The true vdW potential of PTCDA (coplanar to the surface) deviates from the asymptotic form (green) at small molecule-surface separations (compare Fig. 3b). The potential close to the adsorption height is estimated by the orange curve calculated on the basis of ref. 24, while the true vdW potential is an interpolation between the two branches. The invalid parts of both potentials are dashed.
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f4: Experimental results and comparison with theory.(a) Summary of the experimentally obtained C3 values. The experimental error bars indicate the uncertainty in the C3 coefficients due to the influence of the experimental noise on the fitting routine. Calculated values from the semi-empirical dispersion correction scheme vdWsurf and from DFT+RPA are also shown. (b) Dynamic per-atom polarizabilities of carbon for NTCDA, PTCDA and TTCDA as resulting from RPA calculations. The coordinates x, y and z refer to the directions along the long axis, short axis and perpendicular to the plane of each molecule. (c) The true vdW potential of PTCDA (coplanar to the surface) deviates from the asymptotic form (green) at small molecule-surface separations (compare Fig. 3b). The potential close to the adsorption height is estimated by the orange curve calculated on the basis of ref. 24, while the true vdW potential is an interpolation between the two branches. The invalid parts of both potentials are dashed.

Mentions: We now turn to the determination of precise C3 coefficients within the theoretical model given by equation (2). For a correct recovery of the (by definition asymptotic) C3 values, it is crucial to exclude the ztip-interval where the height zmol of the lower end of the molecule above the surface (Fig. 1) is small and deviations from equation (3) are expected, due to Pauli repulsion, higher-order terms of the vdW multipole expansion, and the invalid point dipole approximation. To identify the minimal allowed zmol, we fit the experiments in intervals that start between zmol=3.5 and 7.0 Å (yellow regions in Fig. 3a) and end at the largest ztip values reached. We find that all fit parameters (Fig. 3b) and the fit quality s (inset of Fig. 3a) converge to a plateau for zmol≥4.8 Å. Below this threshold, the fitted parameters depend strongly on the starting value of the fit region, with z0 becoming unphysically small. The value of the threshold is consistent with calculations in the random phase approximation (RPA)33 (see Supplementary Methods). Fits for a starting value of zmol=5.3 Å are displayed in Fig. 3a, while Fig. 3c shows how the fit quality depends on the individual C3,X values. For all three molecules, we find a clear minimum in s, for NTCDA at C3,N=24.9 kcal mol−1 Å3, for PTCDA C3,P=25.9 kcal mol−1 Å3 and for TTCDA C3,T=28.0 kcal mol−1 Å3. The respective data points are plotted in Fig. 4a.


Non-additivity of molecule-surface van der Waals potentials from force measurements.

Wagner C, Fournier N, Ruiz VG, Li C, Müllen K, Rohlfing M, Tkatchenko A, Temirov R, Tautz FS - Nat Commun (2014)

Experimental results and comparison with theory.(a) Summary of the experimentally obtained C3 values. The experimental error bars indicate the uncertainty in the C3 coefficients due to the influence of the experimental noise on the fitting routine. Calculated values from the semi-empirical dispersion correction scheme vdWsurf and from DFT+RPA are also shown. (b) Dynamic per-atom polarizabilities of carbon for NTCDA, PTCDA and TTCDA as resulting from RPA calculations. The coordinates x, y and z refer to the directions along the long axis, short axis and perpendicular to the plane of each molecule. (c) The true vdW potential of PTCDA (coplanar to the surface) deviates from the asymptotic form (green) at small molecule-surface separations (compare Fig. 3b). The potential close to the adsorption height is estimated by the orange curve calculated on the basis of ref. 24, while the true vdW potential is an interpolation between the two branches. The invalid parts of both potentials are dashed.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4263323&req=5

f4: Experimental results and comparison with theory.(a) Summary of the experimentally obtained C3 values. The experimental error bars indicate the uncertainty in the C3 coefficients due to the influence of the experimental noise on the fitting routine. Calculated values from the semi-empirical dispersion correction scheme vdWsurf and from DFT+RPA are also shown. (b) Dynamic per-atom polarizabilities of carbon for NTCDA, PTCDA and TTCDA as resulting from RPA calculations. The coordinates x, y and z refer to the directions along the long axis, short axis and perpendicular to the plane of each molecule. (c) The true vdW potential of PTCDA (coplanar to the surface) deviates from the asymptotic form (green) at small molecule-surface separations (compare Fig. 3b). The potential close to the adsorption height is estimated by the orange curve calculated on the basis of ref. 24, while the true vdW potential is an interpolation between the two branches. The invalid parts of both potentials are dashed.
Mentions: We now turn to the determination of precise C3 coefficients within the theoretical model given by equation (2). For a correct recovery of the (by definition asymptotic) C3 values, it is crucial to exclude the ztip-interval where the height zmol of the lower end of the molecule above the surface (Fig. 1) is small and deviations from equation (3) are expected, due to Pauli repulsion, higher-order terms of the vdW multipole expansion, and the invalid point dipole approximation. To identify the minimal allowed zmol, we fit the experiments in intervals that start between zmol=3.5 and 7.0 Å (yellow regions in Fig. 3a) and end at the largest ztip values reached. We find that all fit parameters (Fig. 3b) and the fit quality s (inset of Fig. 3a) converge to a plateau for zmol≥4.8 Å. Below this threshold, the fitted parameters depend strongly on the starting value of the fit region, with z0 becoming unphysically small. The value of the threshold is consistent with calculations in the random phase approximation (RPA)33 (see Supplementary Methods). Fits for a starting value of zmol=5.3 Å are displayed in Fig. 3a, while Fig. 3c shows how the fit quality depends on the individual C3,X values. For all three molecules, we find a clear minimum in s, for NTCDA at C3,N=24.9 kcal mol−1 Å3, for PTCDA C3,P=25.9 kcal mol−1 Å3 and for TTCDA C3,T=28.0 kcal mol−1 Å3. The respective data points are plotted in Fig. 4a.

Bottom Line: The experiment allows testing the asymptotic vdW force law and its validity range.We find a superlinear growth of the vdW attraction with molecular size, originating from the increased deconfinement of electrons in the molecules.Because such non-additive vdW contributions are not accounted for in most first-principles or empirical calculations, we suggest further development in that direction.

View Article: PubMed Central - PubMed

Affiliation: 1] Peter Grünberg Institut (PGI-3), Forschungszentrum Jülich, 52425 Jülich, Germany [2] Jülich Aachen Research Alliance (JARA)-Fundamentals of Future Information Technology, 52425 Jülich, Germany.

ABSTRACT
Van der Waals (vdW) forces act ubiquitously in condensed matter. Despite being weak on an atomic level, they substantially influence molecular and biological systems due to their long range and system-size scaling. The difficulty to isolate and measure vdW forces on a single-molecule level causes our present understanding to be strongly theory based. Here we show measurements of the attractive potential between differently sized organic molecules and a metal surface using an atomic force microscope. Our choice of molecules and the large molecule-surface separation cause this attraction to be purely of vdW type. The experiment allows testing the asymptotic vdW force law and its validity range. We find a superlinear growth of the vdW attraction with molecular size, originating from the increased deconfinement of electrons in the molecules. Because such non-additive vdW contributions are not accounted for in most first-principles or empirical calculations, we suggest further development in that direction.

No MeSH data available.


Related in: MedlinePlus