Accurate Calculation of the Density of States near the Ground-State Energy of the Peptides Met-Enkephalin and (Alanine)5 with the Wang-Landau Method: Lessons Learned

Abstract

The Wang-Landau method estimates the relative density of states (DOS) by performing random walk in energy space. However, estimation of the DOS near the ground state minimum is highly challenging because of the dearth of states in the low-energy region compared to that at the high-energy region. Ideally the derivative of the logarithm of the DOS with respect to energy, which is proportional to the inverse of temperature, should become steeper with decrease in energy. However, in actual estimation of the DOS for molecular systems, it is nontrivial to achieve this. In the current work, the accuracy of the Wang-Landau method in estimating the DOS near the ground state minimum is investigated for two peptides, Met-enkephalin and (Alanine)5. It has been found that the steepness of the DOS can be achieved if the correct ground state energy is found, the bin used to discretize the energy space is extremely small (0.1 kcal/mol was used in the current case) and the energy range used to estimate the DOS is small. The findings of this work can help in devising new protocols for calculating the DOS with high accuracy near the ground state minimum for molecular systems.