49. Piris M, Ugalde JM (2014) Perspective on natural orbital functional theory. Int J Quant Chem
114(18, SI):1169–1175. doi:10.1002/qua.24663
50. Piris M (2013) A natural orbital functional based on an explicit approach of the two-electron
cumulant. Int J Quant Chem 113(5, SI):620–630. doi:10.1002/qua.24020
51. Piris M, Matxain JM, Lopez X, Ugalde JM (2009) Spin conserving natural orbital functional
theory. J Chem Phys 131(2):021102. doi:10.1063/1.3180958
52. Leiva P, Piris M (2006) Calculation of vertical ionization potentials with the Piris natural
orbital functional. J Mol Struct (THEOCHEM) 770(1–3):45–49. doi:10.1016/j.theochem.
2006.05.001
53. Lopez X, Piris M, Matxain JM, Ugalde JM (2010) Performance of PNOF3 for reactivity
studies: X[BO] and X[CN] isomerization reactions (X ¼ H, Li) as a case study. Phys Chem
Chem Phys 12(40):12931–12934. doi:10.1039/c003379k
54. Lopez X, Ruiperez F, Piris M, Matxain JM, Matito E, Ugalde JM (2012) Performance of
PNOF5 natural orbital functional for radical formation reactions: hydrogen atom abstraction
and C-C and O-O homolytic bond cleavage in selected molecules. J Chem Theory Comput 8
(8):2646–2652. doi:10.1021/ct300414t
55. Ruiperez F, Piris M, Ugalde JM, Matxain JM (2013) The natural orbital functional theory of
the bonding in Cr2, Mo2 and W2. Phys Chem Chem Phys 15(6):2055–2062. doi:10.1039/
c2cp43559d
56. Matxain JM, Piris M, Ruiperez F, Lopez X, Ugalde JM (2011) Homolytic molecular
dissociation in natural orbital functional theory. Phys Chem Chem Phys 13
(45):20129–20135. doi:10.1039/c1cp21696a
57. Piris M (2013) Interpair electron correlation by second-order perturbative corrections to
PNOF5. J Chem Phys 139(6):064111. doi:10.1063/1.4817946
58. Piris M, Ruiperez F, Matxain JM (2014) Assessment of the second-order perturbative
corrections to PNOF5. Mol Phys 112(5–6, SI):1–8. doi:10.1080/00268976.2013.854933
59. Szabados A ´ , Rolik Z, T oth G, Surja ´n PR (2005) Multiconfiguration perturbation theory: size
consistency at second order. J Chem Phys 122(11):114104. doi:10.1063/1.1862235
60. Pernal K (2013) The equivalence of the Piris Natural Orbital Functional 5 (PNOF5) and the
antisymmetrized product of strongly orthogonal geminal theory. Comput Theor Chem 1003
(SI):127–129. doi:10.1016/j.comptc.2012.08.022
61. Surja ´n PR (1999) An introduction to the theory of geminals. In: Surja ´n PR (ed) Correlation
and localization, vol 203, Topics in current chemistry. Springer, Berlin/Heidelberg, pp 63–88
62. Rassolov V (2002) A geminal model chemistry. J Chem Phys 117(13):5978–5987.
doi:10.1063/1.1503773
63. Rassolov VA, Xu F (2007) Geminal model chemistry. IV. Variational and size consistent
pure spin states. J Chem Phys 127(4):044104. doi:10.1063/1.2755738
64. Hurley AC, Lennard-Jones J, Pople JA (1953) The molecular orbital theory of chemical
valency. A theory of paired-electrons in polyatomic molecules. Proc R Soc Lond A Math
Phys Sci 220(1143):446–455. doi:10.1098/rspa.1953.0198
65. Kutzelnigg W (1964) Direct determination of natural orbitals and natural expansion coefficients of many-electron wavefunctions. I. Natural orbitals in geminal product approximation.
J Chem Phys 40(12):3640–3647. doi:10.1063/1.1725065
66. Arai T (1960) Theorem on separability of electron pairs. J Chem Phys 33(1):95–98.
doi:10.1063/1.1731142
67. Mehler EL, Reudenberg K, Silver DM (1970) Electron correlation and separated pair
approximation in diatomic molecules. II. Lithium hydride and boron hydride. J Chem Phys
52(3):1181–1205. doi:10.1063/1.1673115
68. Matxain JM, Piris M, Uranga J, Lopez X, Merino G, Ugalde JM (2012) The nature of
chemical bonds from PNOF5 calculations. Chemphyschem 13(9):2297–2303. doi:10.1002/
cphc.201200205
69. Piris M, Matxain JM, Lopez X (2013) The intrapair electron correlation in natural orbital
functional theory. J Chem Phys 139(23):234109. doi:10.1063/1.4844075
178
K. Pernal and K.J.H. Giesbertz
114(18, SI):1169–1175. doi:10.1002/qua.24663
50. Piris M (2013) A natural orbital functional based on an explicit approach of the two-electron
cumulant. Int J Quant Chem 113(5, SI):620–630. doi:10.1002/qua.24020
51. Piris M, Matxain JM, Lopez X, Ugalde JM (2009) Spin conserving natural orbital functional
theory. J Chem Phys 131(2):021102. doi:10.1063/1.3180958
52. Leiva P, Piris M (2006) Calculation of vertical ionization potentials with the Piris natural
orbital functional. J Mol Struct (THEOCHEM) 770(1–3):45–49. doi:10.1016/j.theochem.
2006.05.001
53. Lopez X, Piris M, Matxain JM, Ugalde JM (2010) Performance of PNOF3 for reactivity
studies: X[BO] and X[CN] isomerization reactions (X ¼ H, Li) as a case study. Phys Chem
Chem Phys 12(40):12931–12934. doi:10.1039/c003379k
54. Lopez X, Ruiperez F, Piris M, Matxain JM, Matito E, Ugalde JM (2012) Performance of
PNOF5 natural orbital functional for radical formation reactions: hydrogen atom abstraction
and C-C and O-O homolytic bond cleavage in selected molecules. J Chem Theory Comput 8
(8):2646–2652. doi:10.1021/ct300414t
55. Ruiperez F, Piris M, Ugalde JM, Matxain JM (2013) The natural orbital functional theory of
the bonding in Cr2, Mo2 and W2. Phys Chem Chem Phys 15(6):2055–2062. doi:10.1039/
c2cp43559d
56. Matxain JM, Piris M, Ruiperez F, Lopez X, Ugalde JM (2011) Homolytic molecular
dissociation in natural orbital functional theory. Phys Chem Chem Phys 13
(45):20129–20135. doi:10.1039/c1cp21696a
57. Piris M (2013) Interpair electron correlation by second-order perturbative corrections to
PNOF5. J Chem Phys 139(6):064111. doi:10.1063/1.4817946
58. Piris M, Ruiperez F, Matxain JM (2014) Assessment of the second-order perturbative
corrections to PNOF5. Mol Phys 112(5–6, SI):1–8. doi:10.1080/00268976.2013.854933
59. Szabados A ´ , Rolik Z, T oth G, Surja ´n PR (2005) Multiconfiguration perturbation theory: size
consistency at second order. J Chem Phys 122(11):114104. doi:10.1063/1.1862235
60. Pernal K (2013) The equivalence of the Piris Natural Orbital Functional 5 (PNOF5) and the
antisymmetrized product of strongly orthogonal geminal theory. Comput Theor Chem 1003
(SI):127–129. doi:10.1016/j.comptc.2012.08.022
61. Surja ´n PR (1999) An introduction to the theory of geminals. In: Surja ´n PR (ed) Correlation
and localization, vol 203, Topics in current chemistry. Springer, Berlin/Heidelberg, pp 63–88
62. Rassolov V (2002) A geminal model chemistry. J Chem Phys 117(13):5978–5987.
doi:10.1063/1.1503773
63. Rassolov VA, Xu F (2007) Geminal model chemistry. IV. Variational and size consistent
pure spin states. J Chem Phys 127(4):044104. doi:10.1063/1.2755738
64. Hurley AC, Lennard-Jones J, Pople JA (1953) The molecular orbital theory of chemical
valency. A theory of paired-electrons in polyatomic molecules. Proc R Soc Lond A Math
Phys Sci 220(1143):446–455. doi:10.1098/rspa.1953.0198
65. Kutzelnigg W (1964) Direct determination of natural orbitals and natural expansion coefficients of many-electron wavefunctions. I. Natural orbitals in geminal product approximation.
J Chem Phys 40(12):3640–3647. doi:10.1063/1.1725065
66. Arai T (1960) Theorem on separability of electron pairs. J Chem Phys 33(1):95–98.
doi:10.1063/1.1731142
67. Mehler EL, Reudenberg K, Silver DM (1970) Electron correlation and separated pair
approximation in diatomic molecules. II. Lithium hydride and boron hydride. J Chem Phys
52(3):1181–1205. doi:10.1063/1.1673115
68. Matxain JM, Piris M, Uranga J, Lopez X, Merino G, Ugalde JM (2012) The nature of
chemical bonds from PNOF5 calculations. Chemphyschem 13(9):2297–2303. doi:10.1002/
cphc.201200205
69. Piris M, Matxain JM, Lopez X (2013) The intrapair electron correlation in natural orbital
functional theory. J Chem Phys 139(23):234109. doi:10.1063/1.4844075
178
K. Pernal and K.J.H. Giesbertz