To further characterize the level of overlap between the gold and water VDOS we computed the Bhattacharyya coefficient (BC, Equation ), a measure of overlap between probability distributions which ranges from 0 (no overlap) to 1 (perfect overlap), between the VDOS of each gold structure and water (Figure ). At 300 K, the BC values ranged from 0.28-0.29. At 370 K, the BC values increased to 0.30-0.32, indicating improved overlap between the gold and water VDOS. To further confirm this effect, we computed the cross-temperature BC values (Figure ). Similarly, the BC only increased when the water temperature was 370 K, confirming that shifts in the water VDOS are the primary factor improving the overlap between the gold and water VDOS.