Efficient exploration of complex free energy landscapes by stepwise multi-subphase space metadynamics

We present an efficient method based on an extension of metadynamics for exploring complex free energy landscapes (FELs). The method employs two-step metadynamics simulations. In the first step, rapid metadynamics simulations using broad and tall Gaussians are performed to identify a free energy pathway (FEP) connecting the two states of interest. The FEP is then divided into a series of independent subphase spaces that comprise selected discrete images of the system. Using appropriate collective variables (CVs) chosen according to the FEP, the accurate FEL of each subphase space is separately calculated in subsequent divide-and-conquer metadynamics simulations with narrow and low Gaussians. Finally, all FELs calculated in each subphase space are merged to obtain the full FEL. We show that the method greatly improves the performance of the metadynamics approach. In particular, we are able to efficiently model chemical systems with complex FELs, such as chemical reactions at the air/water interface. We demonstrate the performance of this method on two model reactions: the hydrolysis of formaldehyde in the gas phase and at the air/water interface.