The astronomical number of accessible discrete chemical structures makes rational molecular design extremely challenging. By using a linear combination of atomic potentials (LCAP) to expand electron-nuclear attraction potentials, a continuous alchemical space can be constructed and explored with respect to specific tailored properties. We show that the optimal structures can be determined without exhausted enumerations of possible structures. To address further challenges arising from the rugged, continuous property surfaces in the LCAP approach, we develop a gradient-directed Monte Carlo (GDMC) strategy as an augmentation to the original LCAP optimization method. The GDMC method retains the power of exploring molecular space by utilizing local gradient information computed from the LCAP approach to jump between discrete molecular structures. It also allows random MC moves to overcome barriers between local optima on property surfaces. The combined GDMC-LCAP approach is demonstrated for optimizing nonlinear optical properties in a class of donor-acceptor substituted benzene and porphyrin frameworks at the quantum mechanical level. Furthermore, as a general global optimization algorithm, GDMC was also applied to protein sequence design and protein folding problems. In summary, the GDMC approach is general and robust for discrete global optimization problems when a continuous treatment (e.g., the LCAP approach) of discrete molecular space can be performed.
This work has been a collaboration with Xiangqian Hu and David Beratan.