Abstract
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.
Similar content being viewed by others
References
I. Papai, A. St-Amant, J. Ushio, D. Salahub, Int. J. Quant. Chem. 38, 29 (1990)
M. Frisch, M. Head-Gordon, J. Pople, Chem. Phys. Lett. 141, 189 (1990)
J. Russel Thomas, J. DeLeeuw Bradley, T. George Vacek, J. Chem. Phys. 99, 403 (1993)
M.W. Wong, Chem. Phys. Lett. 256, 391 (1996)
P. Pulay, WIREs Comput. Mol. Sci. 4, 169 (2014)
Y. Yamaguchi, H.F. Schaefer, Analytic Derivative Methods in Molecular Electronic Structure Theory : A New Dimension to Quantum Chemistry and its Applications to Spectroscopy (John Wiley and Sons, LTD, Hoboken, 2011)
I. Mitxelena, M. Piris, J. Chem. Phys. 144, 204108 (2016)
A.J.S. Valentine, D.A. Mazziotti, Chem. Phys. Lett. 685, 300–304 (2017)
D. A. Mazziotti, in Reduced-Density-Matrix Mechanics: With Applications to Many-Electron Atoms and Molecules, chap. 3, 1st ed. by D. A. Mazziotti (John Wiley and Sons, Hoboken, New Jersey, USA, 2007), pp. 21–59
A.Y. Sokolov, J.J. Wilke, A.C. Simmonett, H.F. Schaefer, J. Chem. Phys. 137, 204110 (2012)
M. Piris, J.M. Ugalde, Int. J. Quant. Chem. 114, 1169 (2014). (and references therein)
David A. Mazziotti, Phys. Rev. Lett. 117, 153001 (2016)
A.W. Schlimgen, C.W. Heaps, D.A. Mazziotti, J. Phys. Chem. Lett. 7(4), 627–631 (2016)
A.R. McIsaac, David A. Mazziotti, Phys. Chem. Chem. Phys. 19, 4656–4660 (2017)
A.J. Coleman, Rev. Mod. Phys. 35, 668 (1963)
M. Piris, in Reduced-Density-Matrix Mechanics: With Applications to Many-Electron Atoms and Molecules, chap. 14, ed. by D. A. Mazziotti (John Wiley and Sons, Hoboken, New Jersey, USA, 2007), pp. 387–427
M. Piris, in Many-Body Approaches at Different Scales: A Tribute to N. H. March on the Ocasion of his 90th Birthday, chap. 22, ed. by G.G.N. Angilella, C. Amovilli (Springer, New York, USA, 2017), pp. 231–247
K. Pernal, K.J.H. Giesbertz, Top Curr Chem. 368, 125 (2016). (and references therein)
I. Mitxelena, M. Piris, J. Chem. Phys. 146, 014102 (2017)
M. Piris, J.M. Ugalde, J. Comput. Chem. 30, 2078 (2009)
K. Pernal, E.J. Baerends, J. Chem. Phys. 124, 014102 (2006)
K.J.H. Giesbertz, Ph.D. thesis, Vrije Universiteit, Amsterdam, The Netherlands (2010)
Acknowledgements
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mitxelena, I., Piris, M. Analytic second-order energy derivatives in natural orbital functional theory. J Math Chem 56, 1445–1455 (2018). https://doi.org/10.1007/s10910-018-0870-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-018-0870-0