Path Optimization in Free Energy Calculations

Free energy calculations are a computational method for determining thermodynamic quantities, such as free energies of binding, via simulation.

Currently, due to computational and algorithmic limitations, free energy calculations are limited in scope.

In this work, we propose two methods for improving the efficiency of free energy calculations.

First, we expand the state space of alchemical intermediates, and show that this expansion enables us to calculate free energies along lower variance paths.

We use Q-learning, a reinforcement learning technique, to discover and optimize paths at low computational cost.

Second, we reduce the cost of sampling along a given path by using sequential Monte Carlo samplers.

We develop a new free energy estimator, pCrooks (pairwise Crooks), a variant on the Crooks fluctuation theorem (CFT), which enables decomposition of the variance of the free energy estimate for discrete paths, while retaining beneficial characteristics of CFT.

Combining these two advancements, we show that for some test models, optimal expanded-space paths have a nearly 80% reduction in variance relative to the standard path.

Additionally, our free energy estimator converges at a more consistent rate and on average 1.8 times faster when we enable path searching, even when the cost of path discovery and refinement is considered.

Phase coexistence of cluster crystals: beyond the Gibbs phase rule

We report a study of the phase behavior of multiple-occupancy crystals through simulation. We argue that in order to reproduce the equilibrium behavior of such crystals it is essential to treat the number of lattice sites as a constraining thermodynamic variable. The resulting free-energy calculations thus differ considerably from schemes used for single-occupancy lattices. Using our approach, we obtain the phase diagram and the bulk modulus for a generalized exponential model that forms cluster crystals at high densities. We compare the simulation results with existing theoretical predictions. We also identify two types of density fluctuations that can lead to two sound modes and evaluate the corresponding elastic constants.

Where does energy R&D come from? Examining crowding out from energy R&D

Recent efforts to endogenize technological change in climate policy models demonstrate the importance of accounting for the opportunity cost of climate R&D investments. Because the social returns to R&D investments are typically higher than the social returns to other types of investment, any new climate mitigation R&D that comes at the expense of other R&D investment may dampen the overall gains from induced technological change. Unfortunately, there has been little empirical work to guide modelers as to the potential magnitude of such crowding out effects. This paper considers both the private and social opportunity costs of climate R&D. Addressing private costs, we ask whether an increase in climate R&D represents new R&D spending, or whether some (or all) of the additional climate R&D comes at the expense of other R&D. Addressing social costs, we use patent citations to compare the social value of alternative energy research to other types of R&D that may be crowded out. Beginning at the industry level, we find no evidence of crowding out across sectors-that is, increases in energy R&D do not draw R&D resources away from sectors that do not perform R&D. Given this, we proceed with a detailed look at alternative energy R&D. Linking patent data and financial data by firm, we ask whether an increase in alternative energy patents leads to a decrease in other types of patenting activity. While we find that increases in alternative energy patents do result in fewer patents of other types, the evidence suggests that this is due to profit-maximizing changes in research effort, rather than financial constraints that limit the total amount of R&D possible. Finally, we use patent citation data to compare the social value of alternative energy patents to other patents by these firms. Alternative energy patents are cited more frequently, and by a wider range of other technologies, than other patents by these firms, suggesting that their social value is higher. © 2011 Elsevier B.V.