The Adaptive Tempering Monte Carlo method (ATMC)

Nanoclusters and nanoparticles are the building blocks in several nanotechnology applications. Physical and chemical properties of nanoclusters are strongly size dependent and their structural stability is a signature of how the nanocluster responds to external fields and temperature changes. Development of efficient global optimization algorithms able to scale up the ladder of sizes from small to large nanoclusters is crucial for the understanding of phenomena at the nanoscale. Computational optimization of a nanocluster structure requires a mathematical minimization in a space of many variables. This is an NP-hard problem because obtaining its solution is harder than solving problems in polynomial time by a nondeterministic turing machine.

The Adaptive Tempering Monte Carlo (ATMC) method was recently developed by Professor Blaisten-Barojas and co-workers in the Computational Materials Science Center for the structural optimization of nanosystem structures. The method is designed for driving a disordered system of many atoms to the most ordered structural arrangement in an efficient, cost effective manner. The most ordered state of a system is usually its ground state. Because experiments to discover the structure of nanoclusters are yet to be developed, the computer experiments carry a strong predictive power. (Xiao Dong and Estela Blaisten-Barojas, Journal of Computational and Theoretical Nanoscience Vol. 3 (2005) 118-127).

This new method belongs to the family of multicanonical / parallel-tempering methodologies that have been proposed in the past five years as promising for predicting the ground state of complex systems. The method differs from the existing ones in the way the multi canonical ensembles are connected. The ATMC bridges the different canonical ensembles through a super-Markov chain based on local fluctuations of the energy. This characteristic ensures that along a simulation, the temperature is changed adaptively depending upon the location of the system in configuration space. This is a dramatic improvement over other multicanonical and parallel tempering methods where a limited set of predetermined temperatures may restrict the sampling of configuration space. The adaptive excursion of the system in configuration space produced by the ATMC allows for a rapid discovery of topological paths on the potential energy surface (PES) that drive the system towards the global minimum.

The ATMC simulations are implemented in both serial and parallel modes. The parallel version of the ATMC, or multi-thread ATMC, is such that a group of tempering threads are thrown simultaneously. All the threads explore the PES simultaneously and if one temperature is repeated, then samplings of the two data segments sharing equal temperature are appended.

The ATMC is a new methodology with predictive capabilities for the multiscale design of functional materials. The ATMC has already been applied to a variety of systems, including the crystallization of thin films and nanoclusters under the Lennard-Jones potential, structural optimization of Morse-potential nanoclusters, characterization of the best folded structure of a prototype polypeptide. More recently we linked this new tempering methodology with a raugh quantum description of the PES at the well known tight-binding approximation (TB) for the electronic structure. The TB-ATMC was further applied for discovering the optimal structure of calcium nanoclusters and sheding light on the liquid-like to solid-like transition in these nanoclusters (Xiao Dong, Silvina Gatica and Estela Blaisten-Barojas, Computing Letters Vol. 1, (2005) 152-157).