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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

Determination of the asymptotic vdW coefficients.(a) Plot of the experimental Δf data for the detached molecules (on a (−Δf)−1/5 scale). The starting point of the fit intervals was varied within the yellow-marked regions that correspond to molecular heights 3.5 Å<zmol<7.0 Å. The displayed fits to the experimental data (solid lines) have been obtained for a starting point of zmol=5.3 Å. The inset shows how the fit quality s depends on the starting point of the fit interval. We show the residuals of each fit and compare them with the residuals (marked by an asterisk) obtained in a fit where all C3,X are constrained to be identical, that is, without superlinearity. (b) Best-fit parameter values z0, C3,N, C3,P and C3,T as a function of the fit interval starting point. We obtain unphysical values if the asymptotic force law of equation (3) is used too close to the surface. (c) Dependency of the fit quality s on the change of a single C3,X parameter. The three other fit parameters remain at their optimal values from b. The start of the fit interval was set to zmol=5.3 Å.
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f3: Determination of the asymptotic vdW coefficients.(a) Plot of the experimental Δf data for the detached molecules (on a (−Δf)−1/5 scale). The starting point of the fit intervals was varied within the yellow-marked regions that correspond to molecular heights 3.5 Å<zmol<7.0 Å. The displayed fits to the experimental data (solid lines) have been obtained for a starting point of zmol=5.3 Å. The inset shows how the fit quality s depends on the starting point of the fit interval. We show the residuals of each fit and compare them with the residuals (marked by an asterisk) obtained in a fit where all C3,X are constrained to be identical, that is, without superlinearity. (b) Best-fit parameter values z0, C3,N, C3,P and C3,T as a function of the fit interval starting point. We obtain unphysical values if the asymptotic force law of equation (3) is used too close to the surface. (c) Dependency of the fit quality s on the change of a single C3,X parameter. The three other fit parameters remain at their optimal values from b. The start of the fit interval was set to zmol=5.3 Å.

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)

Determination of the asymptotic vdW coefficients.(a) Plot of the experimental Δf data for the detached molecules (on a (−Δf)−1/5 scale). The starting point of the fit intervals was varied within the yellow-marked regions that correspond to molecular heights 3.5 Å<zmol<7.0 Å. The displayed fits to the experimental data (solid lines) have been obtained for a starting point of zmol=5.3 Å. The inset shows how the fit quality s depends on the starting point of the fit interval. We show the residuals of each fit and compare them with the residuals (marked by an asterisk) obtained in a fit where all C3,X are constrained to be identical, that is, without superlinearity. (b) Best-fit parameter values z0, C3,N, C3,P and C3,T as a function of the fit interval starting point. We obtain unphysical values if the asymptotic force law of equation (3) is used too close to the surface. (c) Dependency of the fit quality s on the change of a single C3,X parameter. The three other fit parameters remain at their optimal values from b. The start of the fit interval was set to zmol=5.3 Å.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Determination of the asymptotic vdW coefficients.(a) Plot of the experimental Δf data for the detached molecules (on a (−Δf)−1/5 scale). The starting point of the fit intervals was varied within the yellow-marked regions that correspond to molecular heights 3.5 Å<zmol<7.0 Å. The displayed fits to the experimental data (solid lines) have been obtained for a starting point of zmol=5.3 Å. The inset shows how the fit quality s depends on the starting point of the fit interval. We show the residuals of each fit and compare them with the residuals (marked by an asterisk) obtained in a fit where all C3,X are constrained to be identical, that is, without superlinearity. (b) Best-fit parameter values z0, C3,N, C3,P and C3,T as a function of the fit interval starting point. We obtain unphysical values if the asymptotic force law of equation (3) is used too close to the surface. (c) Dependency of the fit quality s on the change of a single C3,X parameter. The three other fit parameters remain at their optimal values from b. The start of the fit interval was set to zmol=5.3 Å.
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