Conjugate gradient filtering of instantaneous normal modes, saddles on the energy landscape, and diffusion in liquids

Instantaneous normal modes (INM’s) are calculated during a conjugate-gradient (CG) descent of the potential energy landscape, starting from an equilibrium configuration of a liquid or crystal. A small number $\left(\sim 4\right)$ of CG steps removes all the $\mathrm{Im}-\omega$ modes in the crystal and leaves the liquid with diffusive $\mathrm{Im}-\omega$ which accurately represent the self-diffusion constant D. Conjugate gradient filtering appears to be a promising method, applicable to any system, of obtaining diffusive modes and facilitating INM theory of D. The relation of the CG-step dependent INM quantities to the landscape and its saddles is discussed.