Ab-initio force prediction for single molecule force spectroscopy made simple

Abstract

Bond rupture under the action of external forces is induced by temperature fluctuations. We show that measured forces from single molecule force spectroscopy experiments can be predicted from two quantities describing the bond that are the barrier to break the bond in absence of force as well as the maximal force the bond can withstand. The former can be obtained by a force free transition state calculation and the latter is determined by a simple constrained ge- ometry simulates forces (COGEF) calculation. Considering experimental temperature and force loading rate allows the prediction of measured bond rupture forces from a closed expression with very good accuracy.

Figures (7)

• Figure 1: Force dependent potentials of the AuAg$_2$ model sketched in Fig. \ref{['fig:AuAg2_barrier']}. The barriers for bond rupture without force $\Delta U^\ddagger=\Delta H^\ddagger(0)$ and with force $\Delta H^\ddagger(F)$ are indicated.
• Figure 2: Barriers for breaking of the Ag-Ag bond under the constraint of a given external force $F$. The numerical barrier (determined by an explicit inclusion of the external force) is compared to the analytical expression of Eq. (\ref{['eq:quadratic']}). The setup of the AuAg$_2$ model is sketched.
• Figure 3: $\partial P/\partial F$ of the AuAg$_{2}$ molecule for a) various loading rates at $T$=300 K and b) different temperatures at $\alpha$=100 nN/s. The broken line indicates $F_{\mathrm{max}}$.
• Figure 4: a) Most probable force from Eq. (\ref{['eq:numerical_mpf']}) (Numeric), from Eq. (\ref{['eq:dpdf_peak']}) (Quadratic), and from max($\partial P/\partial f$) depending on loading rate at $T$=500 K. b) The probability derivative distribution scaled by the loading rate $\alpha$ when the peak position goes towards negative values.
• Figure 5: Most probable force for AuAg$_{2}$ molecule at various loading rates (left, for $T$ = 300 K) and temperatures (right, for $\alpha$= 10 nN/s ). Eq. (\ref{['eq:numerical_mpf']}) (Numeric), Eq. (\ref{['eq:bell_mpf']}) (Bell) and Eq. (\ref{['eq:generalbarrier_mpf']}) (Quadratic) are compared.