{'fraction_non_alphanumeric': 0.0416156670746634, 'fraction_numerical': 0.009791921664626682, 'mean_word_length': 4.8428571428571425, '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}}
Non-locality in the exchange energy density of the inhomogeneous electron liquids in H2O, NH3 and CH4 treated by Hartree–Fock theory

The exchange energy density has been studied by Hartree–Fock (HF) theory in the 10-electron molecules H2O, NH3 and CH4. The local density approximation (LDA) then provides a natural starting point for interpreting the HF data. Though LDA leads to ‘shape similarity’ for the exchange density of these three molecules, there is, (a) no universality and (b) multivalued character at low densities. The low-density regime can, however, be interpreted in terms of a functional , with ρ the ground-state electron density. This functional is here provided with a firm theoretical foundation. Thus, there is a ‘cross-over’ from LDA at high densities to a low-density functional in HF theory.