Journal of Mathematical Chemistry

, Volume 56, Issue 5, pp 1445–1455 | Cite as

Analytic second-order energy derivatives in natural orbital functional theory

  • Ion Mitxelena
  • Mario Piris
Original Paper


The analytic energy gradients in the atomic orbital representation have recently been published (Mitxelena and Piris in J Chem Phys 146:014102, 2017) within the framework of the natural orbital functional theory (NOFT). We provide here an alternative expression for them in terms of natural orbitals, and use it to derive the analytic second-order energy derivatives with respect to nuclear displacements in the NOFT. The computational burden is shifted to the calculation of perturbed natural orbitals and occupancies, since a set of linear coupled-perturbed equations obtained from the variational Euler equations must be solved to attain the analytic Hessian at the perturbed geometry. The linear response of both natural orbitals and occupation numbers to nuclear geometry displacements need only specify the reconstruction of the second-order reduced density matrix in terms of occupation numbers.


Analytic second-order energy derivatives Analytic Hessian Analytic energy gradients Coupled-perturbed equations Natural orbital functional theory 



Financial support comes from Eusko Jaurlaritza (Ref. IT588-13) and Ministerio de Economia y Competitividad (Ref. CTQ2015-67608-P). One of us (I.M.) is grateful to Vice-Rectory for research of the UPV/EHU for the Ph.D. Grant (PIF//15/043). The SGI/IZO–SGIker UPV/EHU is gratefully acknowledged for generous allocation of computational resources.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Kimika FakultateaEuskal Herriko Unibertsitatea (UPV/EHU)DonostiaSpain
  2. 2.Donostia International Physics Center (DIPC)DonostiaSpain
  3. 3.IKERBASQUE, Basque Foundation for ScienceBilbaoSpain

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