{'fraction_non_alphanumeric': 0.011049723756906077, 'fraction_numerical': 0.0, 'mean_word_length': 5.252873563218391, '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}}
Kinetic and exchange energy density functionals for finite systems

The authors propose a new model for the Fermi correlation function for a pair of electrons of the same spin in a system with a finite number of electrons. Using this correlation function, they have derived new expressions for the exchange and kinetic energy density functionals, depending explicitly on the number of electrons. The numerical results obtained for several atomic systems show good agreement, thus demonstrating the accuracy of prediction of the proposed model.