“…The interactions have also been modeled from van der Waals interactions (Giessibl, 1997;Sasaki & Tsukada, 1999;Xie, Sun, & Ning, 2005). The cantilever dynamics has been approached by the classical perturbation theory (Giessibl, 1997;Stich, Tobik, Perez, Terakura, & Ke, 2000), and by forced vibration equations (Nunes, Zanette, Caride, Prioli, & Rivas, 2003;Sasaki & Tsukada, 1999;Xie, 2005). The firstprincipal electronic state calculations and the DFT theory in plane-wave pseudopotential formalism have the advantage of no empirical constants and surface relaxations are embodied in the interaction simulations, which have been shown to be important for image corrugations (Ke, Uda, & Terakura, 2002).…”