Excited states properties of organic molecules: From density functional theory to the GW and Bethe-Salpeter Green's function formalisms

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 372, Issue 2011, 2014, Pages

  Faber, C ^a,b   Boulanger, P ^a   Attaccalite, C ^a   Duchemin, I ^b   Blase, X ^a  

^a CNRS   (France)

^b CEA GRENOBLE   (France)

Author keywords

Ab initio simulations; Density functional theory; Many body perturbation theory; Molecular systems; Optical properties; Theory and modelling

Indexed keywords

EXCITED STATES; GREEN'S FUNCTION; MOLECULES; OPTICAL PROPERTIES; PERTURBATION TECHNIQUES; QUANTUM CHEMISTRY;

AB INITIO SIMULATIONS; BACTERIOCHLOROPHYLLS; BETHE-SALPETER EQUATION; ELECTRONIC EXCITATION; EXCITED STATES PROPERTIES; MANY BODY PERTURBATION THEORY; MOLECULAR SYSTEMS; THEORY AND MODELLING;

DENSITY FUNCTIONAL THEORY;

BACTERIOCHLOROPHYLL; FULLERENE DERIVATIVE; ORGANIC COMPOUND; PORPHYRIN; ZINC;

AB INITIO SIMULATIONS; ALGORITHM; BIOCHEMISTRY; CATALYSIS; CHEMISTRY; DENSITY FUNCTIONAL THEORY; ELECTRON; GAS; MANY-BODY PERTURBATION THEORY; METHODOLOGY; MOLECULAR SYSTEMS; OPTICAL PROPERTIES; OPTICS; PHOTOCHEMISTRY; REVIEW; THEORETICAL MODEL; THEORY AND MODELLING;

AB INITIO SIMULATIONS; DENSITY FUNCTIONAL THEORY; MANY-BODY PERTURBATION THEORY; MOLECULAR SYSTEMS; OPTICAL PROPERTIES; THEORY AND MODELLING;

ALGORITHMS; BACTERIOCHLOROPHYLLS; BIOCHEMISTRY; CATALYSIS; ELECTRONS; FULLERENES; GASES; MODELS, THEORETICAL; OPTICS AND PHOTONICS; ORGANIC CHEMICALS; PHOTOCHEMISTRY; PORPHYRINS; ZINC;

EID: 84894278991     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2013.0271     Document Type: Review

References (124)

1. Bauer GH et al. 2003 Organic photovoltaics: concepts and realization. In Springer Series in Material Science (eds C Brabec, V Dyakonov, J Parisi NS Sariciftci), New York, NY: Springer.
2. Forrest SR. 2004 The path to ubiquitous and low-cost organic electronic appliances on plastic. Nature 428, 911-918. (doi:10.1038/nature02498)
3. TangCW, VanSlyke SA. 1987 Organic electroluminescent diodes. Appl. Phys. Lett. 51, 913-915. (doi:10.1063/1.98799)
4. Forrest SR, Thompson ME. 2007 Introduction: organic electronics and optoelectronics. Chem. Rev. 107, 923-925. (doi:10.1021/cr0501590)
5. Klessinger M, Michl J. (eds) 1994 Excited states and photochemistry of organic molecules. New York, NY:Wiley-VCH.
6. van Amerongen H, Valkünas L, van Grondelle R. (eds.) 2000 Photosynthetic excitons. Singapore:World Scientific.
7. Coropceanu V, Cornil J, da Silva Filho DA, Olivier Y, Silbey R, Brédas J-L. 2007 Charge transport in organic semiconductors. Chem. Rev. 107, 926-952. (doi:10.1021/cr050140x PMid:17378615)
8. Ceperley DM, Alder BJ. 1980 Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566-569. (doi:10.1103/PhysRevLett.45. 566)
9. Perdew JP, Zunger A. 1981 Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23, 5048-5079. (doi:10.1103/PhysRevB.23.5048)
10. Vosko SH, Wilk L, Nusair M. 1980 Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can. J. Phys. 58, 1200-1211. (doi:10.1139/p80-159)
11. Perdew JP, Burke K, Ernzerhof M. 1996 Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865-3868. (doi:10.1103/PhysRevLett.77.3865)
12. Perdew JP, Parr RG, Levy M, Balduz JL. 1982 Density-functional theory for fractional particle number: derivative discontinuities of the energy. Phys. Rev. Lett. 49, 1691-1694. (doi:10.1103/PhysRevLett.49.1691)
13. Godby RM, Schlüter M, Sham LJ. 1986 Accurate exchange-correlation potential for silicon and its discontinuity on addition of an electron. Phys. Rev. Lett. 56, 2415-2418. (doi:10.1103/PhysRevLett.56.2415)
14. Shishkin M, Kresse G. 2007 Self-consistent GW calculations for semiconductors and insulators. Phys. Rev. B 75, 235102. (doi:10.1103/PhysRevB. 75.235102)
15. Orlando R, Dovesi R, Roetti C, Saunders VR. 1990 Ab initio Hartree-Fock calculations for periodic compounds: application to semiconductors. J. Phys. Condensed Matter 2, 7769-7789. (doi:10.1088/0953-8984/2/38/005)
16. Svane A. 1987 Hartree-Fock band-structure calculations with the linear muffin-tin-orbital method: application to C, Si, Ge, and a-Sn. Phys. Rev. B 35, 5496-5502. (doi:10.1103/ PhysRevB.35.5496)
17. Refaely-Abramson S, Baer R, Kronik L. 2011 Fundamental and excitation gaps in molecules of relevance for organic photovoltaics from an optimally tuned range-separated hybrid functional. Phys. Rev. B 84, 075144. (doi:10.1103/PhysRevB.84.075144)
18. Dabo I, Ferretti A, Park C-H, Poilvert N, Li Y, Cococcioni M, Marzari N. 2013 Donor and acceptor levels of organic photovoltaic compounds from first principles. Phys. Chem. Chem. Phys. 15, 685-695. (doi:10.1039/c2cp43491a PMid:23171936)
19. Blase X, Attaccalite C, Olevano V. 2011 First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications. Phys. Rev. B 83, 115103. (doi:10.1103/ PhysRevB.83.115103)
20. Valiev M. et al. 2010 NWChem: a comprehensive and scalable open-source solution for large scale molecular simulations. Comput. Phys. Commun. 181, 1477-1489. (doi:10.1016/ j.cpc.2010.04.018)
21. Becke AD. 1993 Density functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 98, 5648. (doi:10.1063/1.464913)
22. Seidl A, Görling A, Vogl P, Majewski JA, Levy M. 1996 Generalized Kohn-Sham schemes and the band-gap problem. Phys. Rev. B 53, 3764-3774. (doi:10.1103/PhysRevB.53.3764)
23. Kümmel S, Kronik L. 2008 Orbital-dependent density functionals: theory and applications. Rev. Mod. Phys. 80, 3-60. (doi:10.1103/RevModPhys.80.3)
24. Talman JD, ShadwickWF. 1976 Optimized effective atomic central potential. Phys. Rev. A 14, 36-40. (doi:10.1103/PhysRevA.14.36)
25. Sham LJ. 1985 Exchange and correlation in density-functional theory. Phys. Rev. B 32, 3876-3882. (doi:10.1103/PhysRevB.32.3876)
26. White ID, Godby RW, Rieger MM, Needs RJ. 1998 Dynamic image potential at an Al(111) surface. Phys. Rev. Lett. 80, 4265-4268. (doi:10.1103/PhysRevLett.80. 4265)
27. Valsson O, Filippi C. 2012 Gas-phase retinal spectroscopy: temperature effects are but a mirage. J. Phys. Chem. Lett. 3, 908-912. (doi:10.1021/ jz300183g)
28. Zhao Y, Truhlar D. 2008 The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of fourM06-class functionals and 12 other functionals. Theor. Chem. Acc. 120, 215-241. (doi:10.1007/s00214-007-0310-x)
29. Savin A. 1996 On degeneracy, near-degeneracy and density functional theory. In Recent developments and applications of modern density functional theory (ed. JM Seminario), pp. 327-357, Amsterdam: Elsevier.
30. Leininger T, Stoll H, Werner H-J, Savin A. 1997 Combining long-range configuration interaction with short-range density functionals. Chem. Phys. Lett. 275, 151-160. (doi:10.1016/ S0009-2614(97)00758-6)
31. Baer R, Neuhauser D. 2005 Density functional theory with correct long-range asymptotic behavior. Phys. Rev. Lett. 94, 043002. (doi:10.1103/PhysRevLett.94.043002)
32. Livshits E, Baer R. 2007 A well-tempered density functional theory of electrons in molecules. Phys. Chem. Chem. Phys. 9, 2932-2941. (doi:10.1039/b617919c)
33. Stein T, Eisenberg H, Kronik L, Baer R. 2010 Fundamental gaps in finite systems from eigenvalues of a generalized Kohn-Sham method. Phys. Rev. Lett. 105, 266802. (doi:10.1103/ PhysRevLett.105.266802)
34. Kronik L, Stein T, Refaely-Abramson S, Baer R. 2012 Excitation gaps of finite-sized systems from optimally tuned range-separated hybrid functionals. J. Chem. Theory Comput. 8, 1515-1531. (doi:10.1021/ct2009363)
35. Akinaga Y, Seiichiro T-N. 2009 Intramolecular CT excitation energies from range-separated hybrid functionals using the Yukawa potential. Int. J. Quant. Chem. 109, 1905.
36. Yanai T, Tew DP, Handy NC. 2004 A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP). Chem. Phys. Lett. 393, 51-57. (doi:10.1016/ j.cplett.2004.06.011)
37. Refaely-Abramson S, Sharifzadeh S, Govind N, Autschbach J, Neaton JB, Baer R, Kronik L. 2012 Quasiparticle spectra from a nonempirical optimally tuned range-separated hybrid density functional. Phys. Rev. Lett. 109, 226405. (doi:10.1103/PhysRevLett.109.226405)
38. Hedin L. 1965 Newmethod for calculating the one-particle Green's function with application to the electron-gas problem. Phys. Rev. A 139, 796-823. (doi:10.1103/PhysRev.139.A796)
39. Strinati G, Mattausch HJ, Hanke W. 1980 Dynamical correlation effects on the quasiparticle bloch states of a covalent crystal. Phys. Rev. Lett. 45, 290-294. (doi:10.1103/PhysRevLett.45.290)
40. Hybertsen MS, Louie SG. 1986 Electron correlation in semiconductors and insulators: band gaps and quasiparticle energies. Phys. Rev. B 34, 5390-5413. (doi:10.1103/PhysRevB.34.5390)
41. Godby RW, Schlüter M, Sham LJ. 1988 Self-energy operators and exchange-correlation potentials in semiconductors. Phys. Rev. B 37, 10 159-10 175. (doi:10.1103/PhysRevB. 37.10159)
42. Mahan G. 2010 In Many particle physics, 3rd edn. New York, NY: Springer.
43. Martin PC, Schwinger J. 1959 Theory of many-particle systems. I. Phys. Rev. 115, 1342-1373. (doi:10.1103/PhysRev.115.1342)
44. Tiago ML, Northrup JE, Louie SG. 2003 Ab initio calculation of the electronic and optical properties of solid pentacene. Phys. Rev. B 67, 115212. (doi:10.1103/PhysRevB.67.115212)
45. Sharifzadeh S, Biller A, Kronik L, Neaton JB. 2012 Quasiparticle and optical spectroscopy of the organic semiconductors pentacene and PTCDA from first principles. Phys. Rev. B 85, 125307. (doi:10.1103/PhysRevB.85.125307)
46. Berger JA, Reining L, Sottile F. 2012 Efficient GW calculations for SnO2, ZnO, and rubrene: the effective-energy technique. Phys. Rev. B 85, 085126. (doi:10.1103/PhysRevB.85.085126)
47. Ethridge EC, Fry JL, Zaider M. 1996 Quasiparticle spectra of trans-polyacetylene. Phys. Rev. B 53, 3662-3668. (doi:10.1103/PhysRevB.53.3662)
48. Tiago ML, Rohlfing M, Louie SG. 2004 Bound excitons and optical properties of bulk transpolyacetylene. Phys. Rev. B 70, 193204. (doi:10.1103/PhysRevB.70.193204)
49. Ferretti A, Giuseppe M, Martin-Samos L, Bussi G, Ruini A, Montanari B, Harrison NM. 2012 Ab initio complex band structure of conjugated polymers: effects of hybrid density functional theory and GW schemes. Phys. Rev. B 85, 235105. (doi:10.1103/PhysRevB.85.235105)
50. Hogan C, Palumno M, Gierschner J, Rubio A. 2013 Correlation effects in the optical spectra of porphyrin oligomer chains: exciton confinement and length dependence. J. Chem. Phys. 138, 024312. (doi:10.1063/1.4773582 PMid:23320688)
51. Dori N, Menon M, Killian L, Sokolowski M, Kronik L, Umbach E. 2006 Valence electronic structure of gas-phase 3, 4, 9, 10-perylene tetracarboxylic acid dianhydride: experiment and theory. Phys. Rev. B 73, 195208. (doi:10.1103/PhysRevB.73.195208)
52. Palummo M, Hogan C, Sottile F, Bagalá P, Rubio A. 2009 Ab initio electronic and optical spectra of free-base porphyrins: the role of electronic correlation. J. Chem. Phys. 131, 084102. (doi:10.1063/1.3204938 PMid:19725603)
53. Faber C, Attaccalite C, Olevano V, Runge E, Blase X. 2011 First-principles GW calculations for DNA and RNA nucleobases. Phys. Rev. B 83, 115123. (doi:10.1103/PhysRevB.83.115123)
54. Qian X, Umari P, Marzari N. 2011 Photoelectron properties of DNA and RNA bases from many-body perturbation theory. Phys. Rev. B 84, 075103. (doi:10.1103/PhysRevB.84. 075103)
55. Marom N, Ren X, Moussa JE, Chelikowsky JR, Kronik L. 2011 Electronic structure of copper phthalocyanine from G(0)W(0) calculations. Phys. Rev. B 84, 195143. (doi:10.1103/PhysRevB.84.195143)
56. Foerster D, Koval P, Sánchez-Portal D. 2011 An O(N3) implementation of Hedin's GW approximation for molecules. J. Chem. Phys. 135, 074105. (doi:10.1063/1.3624731 PMid:21861554)
57. Sharifzadeh S, Tamblyn I, Doak P, Darancet PT, Neaton JB. 2012 Quantitative molecular orbital energies within a G0W0 approximation. Eur. Phys. J. B 85, 323. (doi:10.1140/ epjb/e2012-30206-0)
58. Umari P, Fabris S. 2012 Importance of semicore states in GW calculations for simulating accurately the photoemission spectra of metal phthalocyanine molecules. J. Chem. Phys. 136, 174310. (doi:10.1063/1.4705360)
59. Marom N, Caruso F, Ren X, Hofmann OT, Körzdörfer T, Chelikowsky JR, Rubio A, Scheffler M & Rinke P 2012 Benchmark of GW methods for azabenzenes. Phys. Rev. B 86, 245127. (doi:10.1103/PhysRevB.86.245127)
60. Körzdörfer T, Marom N. 2012 Strategy for finding a reliable starting point for G0W0 demonstrated for molecules. Phys. Rev. B 86, 041110. (doi:10.1103/PhysRevB.86.041110)
61. Pham TA, Nguyen H-V, Rocca D, Galli G. 2013 GW calculations using the spectral decomposition of the dielectric matrix: verification, validation, and comparison of methods. Phys. Rev. B 87, 155148. (doi:10.1103/PhysRevB.87.155148)
62. RohlfingM, Krüger P, Pollmann P. 1995 Efficient scheme forGW quasiparticle band-structure calculations with applications to bulk Si and to the Si(001)-(2x1) surface. Phys. Rev. B 52, 1905. (doi:10.1103/PhysRevB.52.1905)
63. Ren X, Rinke P, Blum V, Wieferink J, Tkatchenko A, Sanfilippo A, Reuter K, Scheffler M. 2012 Resolution-of-identity approach to Hartree-Fock, hybrid density functionals, RPA, MP2 and GW with numeric atom-centered orbital basis functions. New J. Phys. 14, 053020. (doi:10.1088/1367-2630/14/5/053020)
64. Huebener H, Perez-Osorio MA, Ordejón P, Giustino F. 2012 Dielectric screening in extended systems using the self-consistent Sternheimer equation and localized basis sets. Phys. Rev. B 85, 245125. (doi:10.1103/ PhysRevB.85.245125)
65. van Setten MJ, Weigend F, Evers F. 2013 The GW-method for quantum chemistry applications: theory and implementation. J. Chem. Theory Comput. 9, 232-246. (doi:10.1021/ ct300648t)
66. Bruneval F, Gonze X. 2008 Accurate GW self-energies in a plane-wave basis using only a few empty states: towards large systems. Phys. Rev. B 78, 085125. (doi:10.1103/ PhysRevB.78.085125)
67. Umari P, Stenuit G, Baroni S. 2010 GW quasiparticle spectra from occupied states only. Phys. Rev. B 81, 115104. (doi:10.1103/PhysRevB.81.115104)
68. Giustino F, Cohen ML, Louie SG. 2010 GW method with the selfconsistent Sternheimer equation. Phys. Rev. B 81, 115105. (doi:10.1103/PhysRevB.81.115105)
69. Nguyen H-V, Anh Pham T, Rocca D, Galli G. 2012 Improving accuracy and efficiency of calculations of photoemission spectra within the many-body perturbation theory. Phys. Rev. B 85, 081101. (doi:10.1103/PhysRevB.85.081101)
70. Bruneval F, MarquesMAL. 2013 Benchmarking the starting points of the GW approximation for molecules. J. Chem. Theory Comput. 9, 324-329. (doi:10.1021/ct300835h)
71. Ke S-H. 2011 All-electron GW methods implemented in molecular orbital space: ionization energy and electron affinity of conjugated molecules. Phys. Rev. B 84, 205415. (doi:10.1103/PhysRevB.84.205415)
72. Bruneval F. 2012 Ionization energy of atoms obtained from GW self-energy or from random phase approximation total energies. J. Chem. Phys. 136, 194107. (doi:10.1063/1.4718428)
73. Thygesen KS, Jacobsen KW & Rostgaard C 2010 Fully self-consistent GW calculations for molecules. Phys. Rev. B 81, 085103. (doi:10.1103/PhysRevB.81. 085103)
74. Foster ME, Wong BM. 2012 Nonempirically tuned range-separated DFT accurately predicts both fundamental and excitation gaps in DNA and RNA nucleobases. J. Chem. Theory Comput. 8, 2682-2687. (doi:10.1021/ct300420f)
75. Faber C, Janssen JL, Côté M, Runge E, Blase X. 2011 Electron-phonon coupling in the C-60 fullerene within the many-body GW approach. Phys. Rev. B 84, 155104. (doi:10.1103/ PhysRevB.84.155104)
76. Ciuchi S, Hatch RC, Höchst H, Faber C, Blase X, Fratini S. 2012 Molecular fingerprints in the electronic properties of crystalline organic semiconductors: from experiment to theory. Phys. Rev. Lett. 108, 256401. (doi:10.1103/PhysRevLett.108.256401)
77. Bethe H, Salpeter E. 1951 A relativistic equation for bound-state problems. Phys. Rev. 84, 1232-1242. (doi:10.1103/PhysRev.84.1232)
78. Sham LJ, Rice TM. 1966 Many-particle derivation of the effective-mass equation for the Wannier exciton. Phys. Rev. 144, 708-714. (doi:10.1103/PhysRev. 144.708)
79. Hanke W, Sham LJ. 1979 Many-particle effects in the optical excitations of a semiconductor. Phys. Rev. Lett. 43, 387-390. (doi:10.1103/PhysRevLett.43. 387)
80. Strinati G. 1982 Dynamical shift and broadening of core excitons in semiconductors. Phys. Rev. Lett. 49, 1519-1522. (doi:10.1103/PhysRevLett.49. 1519)
81. Elliott RJ. 1957 Intensity of optical absorption by excitons. Phys. Rev. 108, 1384-1389. (doi:10.1103/PhysRev.108.1384)
82. Rohlfing M, Louie SG. 1998 Excitonic effects and the optical absorption spectrum of hydrogenated Si clusters. Phys. Rev. Lett. 80, 3320-3323. (doi:10.1103/PhysRevLett.80.3320)
83. Albrecht S, Reining L, Del Sole R, Onida G. 1998 Ab initio calculation of excitonic effects in the optical spectra of semiconductors. Phys. Rev. Lett. 80, 4510-4513. (doi:10.1103/ PhysRevLett.80.4510)
84. Benedict LX, Shirley E, Bohn RB. 1998 Optical absorption of insulators and the electron- hole interaction: an Ab initio calculation. Phys. Rev. Lett. 80, 4514-4517. (doi:10.1103/ PhysRevLett.80.4514)
85. Hohenester U. 2001 Ab initio calculation of optical absorption in semiconductors: a densitymatrix description. Phys. Rev. B 64, 205305. (doi:10.1103/PhysRevB.64.205305)
86. Puschnig P, Ambrosch-Draxl C. 2002 Optical absorption spectra of semiconductors and insulators including electron-hole correlations: an ab initio study within the LAPW method. Phys. Rev. B 66, 165105. (doi:10.1103/PhysRevB. 66.165105)
87. Bussi G, Ruini A, Molinari E, Caldas MJ, Puschnig P, Ambrosch-Draxl C. 2002 Interchain interaction and Davydov splitting in polythiophene crystals: an ab initio approach. Appl. Phys. Lett. 80, 4118-4210. (doi:10.1063/1.1483905)
88. Tiago ML, Chelikowsky JR. 2005 First-principles GW-BSE excitations in organic molecules. Solid State Commun. 136, 333-337. (doi:10.1016/j.ssc.2005.08. 012)
89. Tiago ML, Kent PRC, Hood RQ, Reboredo FA. 2008 Neutral and charged excitations in carbon fullerenes from first-principles many-body theories. J. Chem. Phys. 129, 084311. (doi:10.1063/1.2973627)
90. Ma Y, Rohlfing M, Molteni C. 2009 Excited states of biological chromophores studied using many-body perturbation theory: effects of resonant-antiresonant coupling and dynamical screening. Phys. Rev. B 80, 241405. (doi:10.1103/PhysRevB.80.241405)
91. Ma Y, Rohlfing M, Molteni C. 2010 Modeling the excited states of biological chromophores within many-body Green's function theory. J. Chem. Theory Comput. 6, 257-265. (doi:10.1021/ ct900528h)
92. Rocca D, Lu D, Galli G. 2010 Ab initio calculations of optical absorption spectra: solution of the Bethe-Salpeter equation within density matrix perturbation theory. J. Chem. Phys. 133, 164109. (doi:10.1063/1.3494540)
93. Kaczmarski MS, Ma Y, Rohlfing M. 2010 Diabatic states of a photoexcited retinal chromophore from ab initio many-body perturbation theory. Phys. Rev. B 81, 115433. (doi:10.1103/PhysRevB.81.115433)
94. Blase X, Attaccalite C. 2011 CT excitations inmolecular donor-acceptor complexes within the many-body Bethe-Salpeter approach. Appl. Phys. Lett. 99, 171909. (doi:10.1063/1.3655352)
95. Faber C, Duchemin I, Deutsch T, Blase X. 2012 Many-body Green's function study of Coumarins for dye-sensitized solar cells. Phys. Rev. B 86, 155315. (doi:10.1103/ PhysRevB.86.155315)
96. Duchemin I, Deutsch T, Blase X. 2012 Short-range to long-range charge-transfer excitations in the Zincbacteriochlorin-Bacteriochlorin complex: a Bethe-Salpeter study. Phys. Rev. Lett 109, 167801. (doi:10.1103/PhysRevLett. 109.167801)
97. Baumeier B, Andrienko D, Rohlfing M. 2012 Excited states of dicyanovinyl-substituted oligothiophenes from many-body greens functions theory. J. Chem. Theory Comput. 8, 2790-2795. (doi:10.1021/ct300311x)
98. Duchemin I, Blase X. 2013 Resonant hot charge-transfer excitations in fullerene-porphyrin complexes: many-body Bethe-Salpeter study. Phys. Rev. B 87, 245412. (doi:10.1103/ PhysRevB.87.245412)
99. Rohlfing M, Louie SG. 2000 Electron-hole excitations and optical spectra from first principles. Phys. Rev. B 62, 4927-4944. (doi:10.1103/PhysRevB.62. 4927)
100. Hahn PH, Schmidt WG, Bechstedt F. 2005 Molecular electronic excitations calculated from a solid-state approach: methodology and numerics. Phys. Rev. B 24, 245425. (doi:10.1103/ PhysRevB.72.245425)
101. Hummer K, Puschnig P, Ambrosch-Draxl C. 2004 Lowest optical excitations in molecular crystals: bound excitons versus free electron-hole pairs in anthracene. Phys. Rev. Lett. 92, 147402. (doi:10.1103/PhysRevLett.92.147402)
102. Hummer K, Ambrosch-Draxl C. 2005 Oligoacene exciton binding energies: their dependence on molecular size. Phys. Rev. B 71, 081202. (doi:10.1103/PhysRevB.71.081202)
103. Cudazzo P, Gatti M, Rubio A. 2012 Excitons in molecular crystals from first-principles many-body perturbation theory: picene versus pentacene. Phys. Rev. B 86, 195307. (doi:10.1103/PhysRevB.86.195307)
104. Runge E, Gross EKU. 1984 Density-functional theory for time-dependent systems. Phys. Rev. Lett. 52, 997-1000. (doi:10.1103/PhysRevLett.52.997)
105. Marques L, Ullrich CA, Nogueira F, Rubio A, Burke K, Gross EKU. 2006 (eds) Time-dependent density functional theory. New York, NY: Springer.
106. Casida ME. 2009 Time-dependent density-functional theory for molecules and molecular solids. J. Mol. Struct. (Theochem) 914, 3-18. (doi:10.1016/j. theochem.2009.08.018)
107. Leang SS, Zahariev F, Gordon MS. 2012 Benchmarking the performance of timedependent density functional methods. J. Chem. Phys. 136, 104101. (doi:10.1063/1.3689445 PMid:22423822)
108. Dreuw A, Head-Gordon M. 2004 Failure of time-dependent density functional theory for long-range charge-transfer excited states: the Zincbacteriochlorin- Bacteriochlorin and Bacteriochlorophyll-Spheroidene complexes. J. Am. Chem. Soc. 126, 4007-4016. (doi:10.1021/ ja039556n)
109. Yamaguchi Y, Yokoyama S, Mashiko S. 2002 Strong coupling of the single excitations in the Q-like bands of phenylene-linked free-base and zinc bacteriochlorin dimers: a timedependent density functional theory study. J. Chem. Phys. 116, 6541. (doi:10.1063/1.1461815)
110. Wu Q, van Voorhis T. 2005 Direct optimization method to study constrained systems within density-functional theory. Phys. Rev. A 72, 024502. (doi:10.1103/PhysRevA.72.024502)
111. Kobayashi R, Amos RD. 2006 The application of CAM-B3LYP to the charge-transfer band problem of the Zincbacteriochlorin-Bacteriochlorin complex. Chem. Phys. Lett. 420, 106-109. (doi:10.1016/j.cplett.2005.12.040)
112. Rhee Y-M, Head-Gordon M. 2007 Scaled second-order perturbation corrections to configuration interaction singles: efficient and reliable excitation energy methods. J. Phys. Chem. A 111, 5314. The CIS(D) approach is analogous to TD-Hartree-Fock (CIS) plus secondorder perturbation corrections for static and dynamical correlations. (doi:10.1021/jp068409j)
113. Mulliken RS. 1952 Molecular compounds and their spectra. II. J. Am. Chem. Soc. 74, 811-824. (doi:10.1021/ja01123a067)
114. Stein T, Kronik L, Baer R. 2009 Prediction of charge-transfer excitations in coumarin-based dyes using a range-separated functional tuned from first principles. J. Chem. Phys. 131, 244119. (doi:10.1063/1.3269029)
115. Hanazaki I. 1972 Vapor-phase electron donor-acceptor complexes of tetracyanoethylene and of sulfur dioxide. J. Phys. Chem. 76, 1982-1989. (doi:10.1021/j100658a012)
116. Stein T, Kronik L, Baer R. 2009 Reliable prediction of charge transfer excitations in molecular complexes using time-dependent density functional theory. J. Am. Chem. Soc. 131, 2818-2820. (doi:10.1021/ja8087482)
117. Garcia-Lastra JM, Thygesen KS. 2011 Renormalization of optical excitations in molecules near a metal surface. Phys. Rev. Lett. 106, 187402. (doi:10.1103/PhysRevLett.106.187402)
118. Krukau AV, Scuseria GE, Perdew JP, Savin A. 2008 Hybrid functionals with local range separation. J. Chem. Phys. 129, 124103. (doi:10.1063/1.2978377)
119. Scalmani G, Frisch MJ, Mennucci B, Tomasi J, Cammi R, Barone V. 2006 Geometries and properties of excited states in the gas phase and in solution: theory and application of a TDDFT polarizable continuum model. J. Chem. Phys. 124, 094107. (doi:10.1063/1.2173258)
120. Tomasi J, Mennucci B, Cammi R. 2005 Quantum mechanical continuum solvation models. Chem. Rev. 105, 2999-3093. (doi:10.1021/cr9904009)
121. Adamo C, Jacquemin D. 2013 The calculations of excited-state properties with Time-Dependent Density Functional Theory. Chem. Soc. Rev. 42, 845. (doi:10.1039/c2cs35394f)
122. Furche F, Ahlrichs R. 2002 Adiabatic time-dependent density functional methods for excited state properties. J. Chem. Phys. 117, 7433. (doi:10.1063/1.1508368)
123. Van Caillie C, Amos RD. 2000 Geometric derivatives of density functional theory excitation energies using gradient-corrected functionals. Chem. Phys. Lett. 317, 159-164. (doi:10.1016/ S0009-2614(99)01346-9)
124. Ismail-Beigi S, Louie SG. 2003 Excited-state forces within a first-principles Green's function formalism. Phys. Rev. Lett 90, 076401. (doi:10.1103/PhysRevLett.90.076401)