56. Rafat M, Popelier PLA (2007) Topological atom-atom partitioning of molecular exchange
energy and its multipolar convergence. In: Matta CF, Boyd RJ (eds) Quantum theory of atoms
in molecules, vol 5. Wiley, Weinheim, pp 121–140
57. AIMAll: Todd A, Keith TK (2014) Gristmill software, overland Park KS, USA, (aim.
tkgristmill.com)
58. Popelier PLA (2012) Quantum chemical topology: knowledgeable atoms in peptides. AIP
Conf Proc 1456:261–268
59. Popelier P, Rafat M, Devereux M, Liem SY, Leslie M (2005) Towards a force field via
quantum chemical topology. Lect Series Comput Comput Sci 4:1251–1255
60. Popelier PLA (2012) A generic force field based on quantum chemical topology. In: Gatti C,
Macchi P (eds) Modern charge-density analysis, vol 14. Springer, Germany, pp 505–526
61. Cardamone S, Hughes TJ, Popelier PLA (2014) Multipolar electrostatics. Phys Chem Chem
Phys 16:10367–10387
62. Ivanov MV, Talipov MR, Timerghazin QD (2015) Genetic algorithm optimization of point
charges in force field development: challenges and insights. J Phys Chem A 119:1422–1434
63. Rafat M, Popelier PLA (2006) A convergent multipole expansion for 1,3 and 1,4 Coulomb
interactions. J Chem Phys 124(144102):1–7
64. Rafat M, Popelier PLA (2007) Long range behaviour of high-rank topological multipole
moments. J Comput Chem 28:832–838
65. Popelier PLA, Joubert L, Kosov DS (2001) Convergence of the electrostatic interaction based
on topological atoms. J Phys Chem A 105:8254–8261
66. Yuan Y, Mills MJL, Popelier PLA (2014) Multipolar electrostatics for proteins: atom-atom
electrostatic energies in crambin. J Comp Chem 35:343–359
67. Solano CJF, Pendás AM, Francisco E, Blanco MA, Popelier PLA (2010) Convergence of the
multipole expansion for 1,2 Coulomb interactions: the modified multipole shifting algorithm.
J Chem Phys 132:194110
68. Pendas AM, Francisco E, Blanco MA (2006) Binding energies of first row diatomics in the
light of the interacting quantum atoms approach. J Phys Chem A 110:12864–12869
69. Angyan JG, Loos M, Mayer I (1994) Covalent bond orders and atomic valence indices in the
topological theory of atoms in molecules. J Phys Chem 98:5244–5248
70. Garcia-Revilla M, Francisco E, Popelier PLA, Martin-Pendas AM (2013) Domain-averaged
exchange correlation energies as a physical underpinning for chemical graphs. Chem Phys
Chem 14:1211–1218
71. Chávez-Calvillo R, García-Revilla M, Francisco E, Martín Pendás A, Rocha-Rinza T (2015)
Dynamical correlation within the Interacting quantum atoms method through coupled cluster
theory. Comput Theor Chem 1053:90–95
72. Grimme S (2004) Accurate description of van der Waals complexes by density functional
theory including empirical corrections. J Comput Chem 25:1463–1473
73. Fletcher T, Davie SJ, Popelier PLA (2014) Prediction of intramolecular polarization of
aromatic amino acids using kriging machine learning. J Chem Theory Comput 10:3708–3719
74. Grimme S, Antony J, Ehrlich S, Krieg H (2010) A consistent and accurate ab initio
parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu.
J Chem Phys 132:154104–154122
75. Badenhoop JK, Weinhold F (1997) Natural bond orbital analysis of steric interactions. J Chem
Phys 107:5406–5421
76. Verstraelen T, Ayers PW, Van Speybroeck V, Waroquier M (2013) Hirshfeld-E partitioning:
AIM charges with an improved trade-off between robustness and accurate electrostatics.
J Chem Theory Comput 9:2221–2225
77. Hirshfeld FL (1977) Bonded-atom fragments for describing molecular charge densities. Theor
Chem Acta 44:129–138
78. Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. The MIT
Press, Cambridge
79. Krige DG (1951) A statistical approach to some basic mine valuation problems on the
Witwatersran. J Chem Metall Mining Soc South Africa 52:119–139
2 On Quantum Chemical Topology
51
energy and its multipolar convergence. In: Matta CF, Boyd RJ (eds) Quantum theory of atoms
in molecules, vol 5. Wiley, Weinheim, pp 121–140
57. AIMAll: Todd A, Keith TK (2014) Gristmill software, overland Park KS, USA, (aim.
tkgristmill.com)
58. Popelier PLA (2012) Quantum chemical topology: knowledgeable atoms in peptides. AIP
Conf Proc 1456:261–268
59. Popelier P, Rafat M, Devereux M, Liem SY, Leslie M (2005) Towards a force field via
quantum chemical topology. Lect Series Comput Comput Sci 4:1251–1255
60. Popelier PLA (2012) A generic force field based on quantum chemical topology. In: Gatti C,
Macchi P (eds) Modern charge-density analysis, vol 14. Springer, Germany, pp 505–526
61. Cardamone S, Hughes TJ, Popelier PLA (2014) Multipolar electrostatics. Phys Chem Chem
Phys 16:10367–10387
62. Ivanov MV, Talipov MR, Timerghazin QD (2015) Genetic algorithm optimization of point
charges in force field development: challenges and insights. J Phys Chem A 119:1422–1434
63. Rafat M, Popelier PLA (2006) A convergent multipole expansion for 1,3 and 1,4 Coulomb
interactions. J Chem Phys 124(144102):1–7
64. Rafat M, Popelier PLA (2007) Long range behaviour of high-rank topological multipole
moments. J Comput Chem 28:832–838
65. Popelier PLA, Joubert L, Kosov DS (2001) Convergence of the electrostatic interaction based
on topological atoms. J Phys Chem A 105:8254–8261
66. Yuan Y, Mills MJL, Popelier PLA (2014) Multipolar electrostatics for proteins: atom-atom
electrostatic energies in crambin. J Comp Chem 35:343–359
67. Solano CJF, Pendás AM, Francisco E, Blanco MA, Popelier PLA (2010) Convergence of the
multipole expansion for 1,2 Coulomb interactions: the modified multipole shifting algorithm.
J Chem Phys 132:194110
68. Pendas AM, Francisco E, Blanco MA (2006) Binding energies of first row diatomics in the
light of the interacting quantum atoms approach. J Phys Chem A 110:12864–12869
69. Angyan JG, Loos M, Mayer I (1994) Covalent bond orders and atomic valence indices in the
topological theory of atoms in molecules. J Phys Chem 98:5244–5248
70. Garcia-Revilla M, Francisco E, Popelier PLA, Martin-Pendas AM (2013) Domain-averaged
exchange correlation energies as a physical underpinning for chemical graphs. Chem Phys
Chem 14:1211–1218
71. Chávez-Calvillo R, García-Revilla M, Francisco E, Martín Pendás A, Rocha-Rinza T (2015)
Dynamical correlation within the Interacting quantum atoms method through coupled cluster
theory. Comput Theor Chem 1053:90–95
72. Grimme S (2004) Accurate description of van der Waals complexes by density functional
theory including empirical corrections. J Comput Chem 25:1463–1473
73. Fletcher T, Davie SJ, Popelier PLA (2014) Prediction of intramolecular polarization of
aromatic amino acids using kriging machine learning. J Chem Theory Comput 10:3708–3719
74. Grimme S, Antony J, Ehrlich S, Krieg H (2010) A consistent and accurate ab initio
parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu.
J Chem Phys 132:154104–154122
75. Badenhoop JK, Weinhold F (1997) Natural bond orbital analysis of steric interactions. J Chem
Phys 107:5406–5421
76. Verstraelen T, Ayers PW, Van Speybroeck V, Waroquier M (2013) Hirshfeld-E partitioning:
AIM charges with an improved trade-off between robustness and accurate electrostatics.
J Chem Theory Comput 9:2221–2225
77. Hirshfeld FL (1977) Bonded-atom fragments for describing molecular charge densities. Theor
Chem Acta 44:129–138
78. Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. The MIT
Press, Cambridge
79. Krige DG (1951) A statistical approach to some basic mine valuation problems on the
Witwatersran. J Chem Metall Mining Soc South Africa 52:119–139
2 On Quantum Chemical Topology
51