{'fraction_non_alphanumeric': 0.03234624145785877, 'fraction_numerical': 0.007289293849658315, 'mean_word_length': 5.310344827586207, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Energy landscapes of quantum Lennard-Jones solids.

To generalize inherent structure analysis to understand structural changes in quantum liquids and solids, differences between classical (V(x)) and quantum-corrected (U(qeff)(x)) energy landscapes are estimated as a function of the de Boer parameter (Λ). Path integral simulations of quantum Lennard-Jones solids are performed at zero pressure and a dimensionless reduced temperature of 0.123, corresponding to an absolute temperature of 4.2K. At constant temperature and pressure, Λ is increased from the classical limit of zero to Λ = 0.28, corresponding to para-H(2). Increasing quantum delocalization effects result in a continuous decrease in density and local order but without a transition to a disordered, liquid state. The inherent structure landscape of bulk systems is strongly dependent on density with the energy and stability of crystalline minima decreasing relative to that of amorphous packing minima as the system is stretched. For Λ ≈ 0.23, the volume fluctuations in quantum solids are sufficient to result in sampling of disordered minima while for Λ = 0.28, the underlying classical inherent structures are completely disordered, indicating that the topography of U(qeff)(x) and V(x) are qualitatively different for such values of Λ. To assess the nature of the quantum-corrected energy landscape, effective pair potentials are defined by u(qeff)(r) = -kT ln g(r) using the pair correlation function (g(r)) of the quantum system in the neighborhood of the first peak. Our results show that as Λ increases, the pair potentials become increasingly softer, shallower, and of increasing range with a shifting of the potential minimum to larger distances. For example, the reduction of the entropy of fusion and melting temperatures of quantum solids with increasing Λ are analogous to the changes in thermodynamics of melting seen in classical solids with increasing range and softness of interactions. The energy landscapes associated with such coarse-grained potentials should be useful as predictors of structural transformations in quantum systems, analogous to their use in understanding phase diagrams of complex fluids.