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Title: Analytical derivatives of the individual state energies in ensemble density functional theory method. I. General formalism

The state-averaged (SA) spin restricted ensemble referenced Kohn-Sham (REKS) method and its state interaction (SI) extension, SI-SA-REKS, enable one to describe correctly the shape of the ground and excited potential energy surfaces of molecules undergoing bond breaking/bond formation reactions including features such as conical intersections crucial for theoretical modeling of non-adiabatic reactions. Until recently, application of the SA-REKS and SI-SA-REKS methods to modeling the dynamics of such reactions was obstructed due to the lack of the analytical energy derivatives. Here, the analytical derivatives of the individual SA-REKS and SI-SA-REKS energies are derived. The final analytic gradient expressions are formulated entirely in terms of traces of matrix products and are presented in the form convenient for implementation in the traditional quantum chemical codes employing basis set expansions of the molecular orbitals. Finally, we will describe the implementation and benchmarking of the derived formalism in a subsequent article of this series.
Authors:
 [1] ; ORCiD logo [2] ; ORCiD logo [2]
  1. Ulsan National Inst. of Science and Technology (UNIST), Ulsan (South Korea). Dept. of Chemistry
  2. Stanford Univ., CA (United States). Dept. of Chemistry, PULSE Inst.
Publication Date:
Grant/Contract Number:
AC02-76SF00515
Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 147; Journal Issue: 3; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Research Org:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
OSTI Identifier:
1390315