Entropy calculation beyond the harmonic approximation: Application to diffusion by concerted exchange in Si

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Abstract
We present a formulation for calculating entropy based on the application of classical transition-rate theory to quantum-mechanical energy surfaces. Using this approach, which avoids difficulties due to anharmonicity and large energy barriers, we calculate the entropy of concerted exchange (CE) in Si and find it to be 3.3k in the high-temperature regime. The relatively high entropy of CE is traced to multiple equivalent exchange paths and to a a combination of a stiff mode at the equilibrium and a soft mode at the saddle-point configurations. Comparison to harmonic-approximation results shows substantial differences, in both the low- and in the high-temperature limits.