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37. Grimme S, Antony J, Ehrlich S, Krieg H (2010) J Chem Phys 132(15):154104. https://doi.
org/10.1063/1.3382344. https://doi.org/10.1063/1.3382344
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92(24):246401. https://doi.org/10.1103/PhysRevLett.92.246401. https://link.aps.org/doi/10.
1103/PhysRevLett.92.246401
41. Dion M, Rydberg H, Schröder E, Langreth DC, Lundqvist BI (2005) Phys Rev Lett 95(10),
109902. https://link.aps.org/doi/10.1103/PhysRevLett.95.109902
42. Klimes J, Bowler DR, Michaelides A (2011) Phys Rev B Condens Matter Mater
Phys 83(19):195131. https://doi.org/10.1103/PhysRevB.83.195131. https://link.aps.org/doi/
10.1103/PhysRevB.83.195131
43. Santra B, Michaelides A, Fuchs M, Tkatchenko A, Filippi C, Scheffler M (2008) J Chem Phys
129(19):194111 https://doi.org/10.1063/1.3012573. https://doi.org/10.1063/1.3012573
44. Gulans A, Puska M, Nieminen R (2009) Phys Rev B 79(20):201105. https://doi.org/10.1103/
PhysRevB.79.201105. https://link.aps.org/doi/10.1103/PhysRevB.79.201105
45. Senftle TP, Hong S, Islam MM, Kylasa SB, Zheng Y, Shin YK, Junkermeier C, Engel-Herbert
R, Janik MJ, Aktulga HM, Verstraelen T, Grama A, van Duin ACT (2016) NPJ Comput
Mater 2(1):15011. https://doi.org/10.1038/npjcompumats.2015.11. http://www.nature.com/
articles/npjcompumats201511
46. Lid S, Köppen S, Colombi Ciacchi L (2017) Comput Mater Sci 140:307. https://doi.
org/10.1016/j.commatsci.2017.09.003. https://www.sciencedirect.com/science/article/pii/
S0927025617304731
47. Maseras F, Morokuma K (1995) J Comput Chem 16(9):1170. https://doi.org/10.1002/jcc.
540160911. http://doi.wiley.com/10.1002/jcc.540160911
48. Humbel S, Sieber S, Morokuma K (1998) J Chem Phys 105(5):1959. https://doi.org/10.1063/
1.472065. https://aip.scitation.org/doi/abs/10.1063/1.472065
49. Svensson M, Humbel S, Froese RDJ, Matsubara T, Sieber S, Morokuma K (1996) J
Phys Chem 100(50):19357. https://doi.org/10.1021/jp962071j. http://pubs.acs.org/doi/abs/
10.1021/jp962071j
50. Sauer J, Sierka M (2000) J Comput Chem 21(16):1470. https://doi.org/10.1002/1096987X(200012)21:16<1470::AID-JCC5>3.0.CO;2-L. http://doi.wiley.com/10.1002/1096987X%28200012%2921%3A16%3C1470%3A%3AAID-JCC5%3E3.0.CO%3B2-L
51. Boys SF (1950) Proc R Soc Lond Ser A Math Phys Sci 200(1063):542 LP. http://rspa.
royalsocietypublishing.org/content/200/1063/542.abstract
389
30. Pacchioni G (2015) In: Jupille J, Thornton G (eds) Defects at oxide surfaces. Chap 1.3 Proble,
Springer series in surface sciences, vol 58. Springer International Publishing, Cham, p 472.
https://doi.org/10.1007/978-3-319-14367-5. https://link.springer.com/book/10.1007/978-3319-14367-5
31. Runge E, Gross EKU (1984) Phys Rev Lett 52(12):997. https://doi.org/10.1103/PhysRevLett.
52.997. https://link.aps.org/doi/10.1103/PhysRevLett.52.997
32. Marques MAL, Ullrich CA, Nogueira F, Rubio A, Burke K, Gross EKU, (2006) Timedependent density functional theory. Lecture notes in physics, vol 706. Springer, Heidelberg.
https://doi.org/10.1007/b11767107. http://link.springer.com/10.1007/b11767107
33. Casida ME, Huix-Rotllant M (2015) Springer International Publishing, Cham pp 1–60. https://
doi.org/10.1007/128_2015_632. https://link.springer.com/chapter/10.1007/128_2015_632
34. Wu X, Vargas MC, Nayak S (2001) J Chem Phys 115(19):8748. https://doi.org/10.1063/1.
1412004. https://doi.org/10.1063/1.1412004
35. Grimme S (2004) J Computat Chem 25(12):1463. https://doi.org/10.1002/jcc.20078. http://
doi.wiley.com/10.1002/jcc.20078
36. Grimme S (2006) J Computat Chem 27(15):1787. https://doi.org/10.1002/jcc.20495. http://
doi.wiley.com/10.1002/jcc.20495
37. Grimme S, Antony J, Ehrlich S, Krieg H (2010) J Chem Phys 132(15):154104. https://doi.
org/10.1063/1.3382344. https://doi.org/10.1063/1.3382344
38. Smith DGA, Burns LA, Patkowski K, Sherrill CD (2016) J Phys Chem Lett 7(12):2197.
https://doi.org/10.1021/acs.jpclett.6b00780. https://doi.org/10.1021/acs.jpclett.6b00780
39. Reckien W, Janetzko F, Peintinger MF, Bredow T (2012) J Comput Chem 33(25):2023. https://
doi.org/10.1002/jcc.23037. https://onlinelibrary.wiley.com/doi/10.1002/jcc.23037
40. Dion M, Rydberg H, Schröder E, Langreth DC, Lundqvist BI (2004) Phys Rev Lett
92(24):246401. https://doi.org/10.1103/PhysRevLett.92.246401. https://link.aps.org/doi/10.
1103/PhysRevLett.92.246401
41. Dion M, Rydberg H, Schröder E, Langreth DC, Lundqvist BI (2005) Phys Rev Lett 95(10),
109902. https://link.aps.org/doi/10.1103/PhysRevLett.95.109902
42. Klimes J, Bowler DR, Michaelides A (2011) Phys Rev B Condens Matter Mater
Phys 83(19):195131. https://doi.org/10.1103/PhysRevB.83.195131. https://link.aps.org/doi/
10.1103/PhysRevB.83.195131
43. Santra B, Michaelides A, Fuchs M, Tkatchenko A, Filippi C, Scheffler M (2008) J Chem Phys
129(19):194111 https://doi.org/10.1063/1.3012573. https://doi.org/10.1063/1.3012573
44. Gulans A, Puska M, Nieminen R (2009) Phys Rev B 79(20):201105. https://doi.org/10.1103/
PhysRevB.79.201105. https://link.aps.org/doi/10.1103/PhysRevB.79.201105
45. Senftle TP, Hong S, Islam MM, Kylasa SB, Zheng Y, Shin YK, Junkermeier C, Engel-Herbert
R, Janik MJ, Aktulga HM, Verstraelen T, Grama A, van Duin ACT (2016) NPJ Comput
Mater 2(1):15011. https://doi.org/10.1038/npjcompumats.2015.11. http://www.nature.com/
articles/npjcompumats201511
46. Lid S, Köppen S, Colombi Ciacchi L (2017) Comput Mater Sci 140:307. https://doi.
org/10.1016/j.commatsci.2017.09.003. https://www.sciencedirect.com/science/article/pii/
S0927025617304731
47. Maseras F, Morokuma K (1995) J Comput Chem 16(9):1170. https://doi.org/10.1002/jcc.
540160911. http://doi.wiley.com/10.1002/jcc.540160911
48. Humbel S, Sieber S, Morokuma K (1998) J Chem Phys 105(5):1959. https://doi.org/10.1063/
1.472065. https://aip.scitation.org/doi/abs/10.1063/1.472065
49. Svensson M, Humbel S, Froese RDJ, Matsubara T, Sieber S, Morokuma K (1996) J
Phys Chem 100(50):19357. https://doi.org/10.1021/jp962071j. http://pubs.acs.org/doi/abs/
10.1021/jp962071j
50. Sauer J, Sierka M (2000) J Comput Chem 21(16):1470. https://doi.org/10.1002/1096987X(200012)21:16<1470::AID-JCC5>3.0.CO;2-L. http://doi.wiley.com/10.1002/1096987X%28200012%2921%3A16%3C1470%3A%3AAID-JCC5%3E3.0.CO%3B2-L
51. Boys SF (1950) Proc R Soc Lond Ser A Math Phys Sci 200(1063):542 LP. http://rspa.
royalsocietypublishing.org/content/200/1063/542.abstract