27. Gritsenko O, Pernal K, Baerends E (2005) An improved density matrix functional by
physically motivated repulsive corrections. J Chem Phys 122(20):204102. doi:10.1063/1.
1906203
28. Goedecker S, Umrigar CJ (1998) Natural orbital functional for the many-electron problem.
Phys Rev Lett 81(4):866–869. doi:10.1103/PhysRevLett.81.866
29. Goedecker S, Umrigar CJ (2000) Natural orbital functional theory. In: Cioslowski J (ed) -
Many-electron densities and reduced density matrices. Kluwer, New York, p 165
30. Lathiotakis NN, Marques MAL (2008) Benchmark calculations for reduced density-matrix
functional theory. J Chem Phys 128(18):184103. doi:10.1063/1.2899328
31. Csanyi G, Arias TA (2000) Tensor product expansions for correlation in quantum many-body
systems. Phys Rev B 61(11):7348–7352. doi:10.1103/PhysRevB.61.7348
32. Staroverov VN, Scuseria GE (2002) Optimization of density matrix functionals by the
Hartree-Fock-Bogoliubov method. J Chem Phys 117(24):11107–11112. doi:10.1063/1.
1523060
33. Kutzelnigg W, Mukherjee D (1999) Cumulant expansion of the reduced density matrices.
J Chem Phys 110(6):2800–2809. doi:10.1063/1.478189
34. Kutzelnigg W (1963) Die losung des quantenmechanischen zwei-elektronenproblems durch
unmittelbare bestimmung der naturlichen einelektronenfunktionen. I. Theorie. Theor Chim
Acta 1(4):327–342. doi:10.1007/BF00528764
35. Shull H, L€ owdin PO (1956) Correlation splitting in helium-like ions. J Chem Phys 25
(5):1035–1040. doi:10.1063/1.1743093
36. Cioslowski J, Pernal K (2006) Unoccupied natural orbitals in two-electron Coulombic
systems. Chem Phys Lett 430(1–3):188–190. doi:10.1016/j.cplett.2006.08.011
37. Sheng XW, Mentel LM, Gritsenko OV, Baerends EJ (2013) A natural orbital analysis of the
long range behavior of chemical bonding and van der Waals interaction in singlet H2: the
issue of zero natural orbital occupation numbers. J Chem Phys 138(16):164105. doi:10.1063/
1.4801431
38. Giesbertz KJH, van Leeuwen R (2013) Long-range interactions and the sign of natural
amplitudes in two-electron systems. J Chem Phys 139(10):104110. doi:10.1063/1.4820418
39. Cioslowski J, Pernal K (2000) The ground state of harmonium. J Chem Phys 113
(19):8434–8443. doi:10.1063/1.1318767
40. Rohr DR, Pernal K, Gritsenko OV, Baerends EJ (2008) A density matrix functional with
occupation number driven treatment of dynamical and nondynamical correlation. J Chem
Phys 129(16):164105. doi:10.1063/1.2998201
41. Pernal K, Cioslowski J (2004) Phase dilemma in density matrix functional theory. J Chem
Phys 120(13):5987–5992. doi:10.1063/1.1651059
42. Mentel LM, van Meer R, Gritsenko OV, Baerends EJ (2014) The density matrix functional
approach to electron correlation: dynamic and nondynamic correlation along the full dissociation coordinate. J Chem Phys 140(21):214105. doi:10.1063/1.4879776
43. Piris M (2006) A new approach for the two-electron cumulant in natural orbital functional
theory. Int J Quant Chem 106(5):1093–1104. doi:10.1002/qua.20858
44. Piris M, Lopez X, Ugalde JM (2007) Dispersion interactions within the Piris natural orbital
functional theory: the helium dimer. J Chem Phys 126(21):214103. doi:10.1063/1.2743019
45. Piris M, Matxain JM, Lopez X, Ugalde JM (2010) Communications: accurate description of
atoms and molecules by natural orbital functional theory. J Chem Phys 132(3):031103.
doi:10.1063/1.3298694
46. Piris M, Matxain JM, Lopez X, Ugalde JM (2010) Communication: the role of the positivity
N-representability conditions in natural orbital functional theory. J Chem Phys 133
(11):111101. doi:10.1063/1.3481578
47. Piris M, Lopez X, Ruiperez F, Matxain JM, Ugalde JM (2011) A natural orbital functional for
multiconfigurational states. J Chem Phys 134(16):164102. doi:10.1063/1.3582792
48. Piris M (2014) Interacting pairs in natural orbital functional theory. J Chem Phys 141:044107.
doi:10.1063/1.4890653
Reduced Density Matrix Functional Theory (RDMFT) and Linear Response Time. . .
177
physically motivated repulsive corrections. J Chem Phys 122(20):204102. doi:10.1063/1.
1906203
28. Goedecker S, Umrigar CJ (1998) Natural orbital functional for the many-electron problem.
Phys Rev Lett 81(4):866–869. doi:10.1103/PhysRevLett.81.866
29. Goedecker S, Umrigar CJ (2000) Natural orbital functional theory. In: Cioslowski J (ed) -
Many-electron densities and reduced density matrices. Kluwer, New York, p 165
30. Lathiotakis NN, Marques MAL (2008) Benchmark calculations for reduced density-matrix
functional theory. J Chem Phys 128(18):184103. doi:10.1063/1.2899328
31. Csanyi G, Arias TA (2000) Tensor product expansions for correlation in quantum many-body
systems. Phys Rev B 61(11):7348–7352. doi:10.1103/PhysRevB.61.7348
32. Staroverov VN, Scuseria GE (2002) Optimization of density matrix functionals by the
Hartree-Fock-Bogoliubov method. J Chem Phys 117(24):11107–11112. doi:10.1063/1.
1523060
33. Kutzelnigg W, Mukherjee D (1999) Cumulant expansion of the reduced density matrices.
J Chem Phys 110(6):2800–2809. doi:10.1063/1.478189
34. Kutzelnigg W (1963) Die losung des quantenmechanischen zwei-elektronenproblems durch
unmittelbare bestimmung der naturlichen einelektronenfunktionen. I. Theorie. Theor Chim
Acta 1(4):327–342. doi:10.1007/BF00528764
35. Shull H, L€ owdin PO (1956) Correlation splitting in helium-like ions. J Chem Phys 25
(5):1035–1040. doi:10.1063/1.1743093
36. Cioslowski J, Pernal K (2006) Unoccupied natural orbitals in two-electron Coulombic
systems. Chem Phys Lett 430(1–3):188–190. doi:10.1016/j.cplett.2006.08.011
37. Sheng XW, Mentel LM, Gritsenko OV, Baerends EJ (2013) A natural orbital analysis of the
long range behavior of chemical bonding and van der Waals interaction in singlet H2: the
issue of zero natural orbital occupation numbers. J Chem Phys 138(16):164105. doi:10.1063/
1.4801431
38. Giesbertz KJH, van Leeuwen R (2013) Long-range interactions and the sign of natural
amplitudes in two-electron systems. J Chem Phys 139(10):104110. doi:10.1063/1.4820418
39. Cioslowski J, Pernal K (2000) The ground state of harmonium. J Chem Phys 113
(19):8434–8443. doi:10.1063/1.1318767
40. Rohr DR, Pernal K, Gritsenko OV, Baerends EJ (2008) A density matrix functional with
occupation number driven treatment of dynamical and nondynamical correlation. J Chem
Phys 129(16):164105. doi:10.1063/1.2998201
41. Pernal K, Cioslowski J (2004) Phase dilemma in density matrix functional theory. J Chem
Phys 120(13):5987–5992. doi:10.1063/1.1651059
42. Mentel LM, van Meer R, Gritsenko OV, Baerends EJ (2014) The density matrix functional
approach to electron correlation: dynamic and nondynamic correlation along the full dissociation coordinate. J Chem Phys 140(21):214105. doi:10.1063/1.4879776
43. Piris M (2006) A new approach for the two-electron cumulant in natural orbital functional
theory. Int J Quant Chem 106(5):1093–1104. doi:10.1002/qua.20858
44. Piris M, Lopez X, Ugalde JM (2007) Dispersion interactions within the Piris natural orbital
functional theory: the helium dimer. J Chem Phys 126(21):214103. doi:10.1063/1.2743019
45. Piris M, Matxain JM, Lopez X, Ugalde JM (2010) Communications: accurate description of
atoms and molecules by natural orbital functional theory. J Chem Phys 132(3):031103.
doi:10.1063/1.3298694
46. Piris M, Matxain JM, Lopez X, Ugalde JM (2010) Communication: the role of the positivity
N-representability conditions in natural orbital functional theory. J Chem Phys 133
(11):111101. doi:10.1063/1.3481578
47. Piris M, Lopez X, Ruiperez F, Matxain JM, Ugalde JM (2011) A natural orbital functional for
multiconfigurational states. J Chem Phys 134(16):164102. doi:10.1063/1.3582792
48. Piris M (2014) Interacting pairs in natural orbital functional theory. J Chem Phys 141:044107.
doi:10.1063/1.4890653
Reduced Density Matrix Functional Theory (RDMFT) and Linear Response Time. . .
177