Analytic gradients for compressed multistate pair-density functional theory

Jie J. Bao, Matthew R Hermes, Thais Scott, Andrew M Sand, Roland Lindh, Laura Gagliardi, Donald G. Truhlar

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5 Scopus citations


Photochemical reactions often involve states that are closely coupled due to near degeneracies, for example by proximity to conical intersections. Therefore, a multistate method is used to accurately describe these states; for example, ordinary perturbation theory is replaced by quasidegenerate perturbation theory. Multiconfiguration pair-density functional theory (MC-PDFT) provides an efficient way to approximate the full dynamical correlation energy of strongly correlated systems, and we recently proposed compressed multistate pair-density functional theory (CMS-PDFT) to treat closely coupled states. In the present paper, we report the implementation of analytic gradients for CMS-PDFT in both OpenMolcas and PySCF, and we illustrate the use of these gradients by applying the method to the excited states of formaldehyde and phenol.

Original languageEnglish (US)
Article numbere2110534
JournalMolecular Physics
Issue number19-20
StatePublished - 2022

Bibliographical note

Funding Information:
The present work is supported by the National Science Foundation under grant CHE-2054723. R.L. acknowledges the Swedish Research Council (VR, Grant 2020-03182) for funding. T.R.S. acknowledges that this material is also based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE 1746045, Project No. 00074041. The authors are grateful to David Yarkony and Christopher Malbon for providing the vertical excitation energy of the S state of phenol from their potential energy surface of Ref. [63]. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Publisher Copyright:
© 2022 Informa UK Limited, trading as Taylor & Francis Group.


  • Analytic gradients
  • electronic structure method
  • excited states
  • molecular geometry
  • pair-density functional theory


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