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Fractional Paradigms in Quantum Chemistry
  • Mohammad Mostafanejad
Mohammad Mostafanejad
Virginia Polytechnic Institute and State University
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Abstract

The realization of fractional quantum chemistry is presented. Adopting the integro-differential operators of the calculus of arbitrary-order, we develop a general framework for the description of quantum nonlocal effects in the complex electronic environments. After a brief overview of the historical and fundamental aspects of the calculus of arbitrary-order, various classes of fractional Schr\"odinger equations are discussed and pertinent controversies and open problems around their applications to model systems are detailed. We provide a unified approach toward fractional generalization of the quantum chemical models such as Hartree-Fock and Kohn-Sham density functional theory and develop fractional variants of the fundamental molecular integrals and correlation energy . Furthermore, we offer various strategies for modeling static- and dynamic-order quantum nonlocal effects through constant- and variable-order fractional operators, respectively. Possible directions for future developments of fractional quantum chemistry are also outlined..

Peer review status:ACCEPTED

14 Apr 2021Submitted to International Journal of Quantum Chemistry
15 Apr 2021Submission Checks Completed
15 Apr 2021Assigned to Editor
16 Apr 2021Reviewer(s) Assigned
14 May 2021Review(s) Completed, Editorial Evaluation Pending
14 May 2021Editorial Decision: Revise Minor
18 May 20211st Revision Received
19 May 2021Submission Checks Completed
19 May 2021Assigned to Editor
19 May 2021Reviewer(s) Assigned
11 Jun 2021Review(s) Completed, Editorial Evaluation Pending
11 Jun 2021Editorial Decision: Accept