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What makes differences between intra- and inter-molecular charge transfer excitations in conjugated long-chained polyene? EOM-CCSD and LC-BOP study

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Abstract

We performed intra- and inter-molecular charge transfer (CT) excitation calculations of H2N–(CH=CH) n –NO2 (a) and its equidistant H2N–H···H–NO2 (b) using EOM-CCSD (n = 1–9), time-dependent (TD) long-range corrected (LC) density functional theory (DFT) (n = 1–10). It was shown that LC-BOP and LCgau-BOP outperform all the tested DFT functionals on inter- and intra-CT excitation energy and oscillator strength, regardless of CT interaction distance (R). Decomposition of TD-DFT optical excitation energies of (a) and (b) into HOMO–LUMO gap and excitonic binding energy disclosed that HOMO–LUMO gap reduction resulting from delocalization of HOMO and LUMO through bridged polyene conjugation is mainly responsible for the decreasing of intra-molecular CT excitation energy with chain number, while inter-molecular CT increases linearly with −1/R, which is wholly due to the decrease in excitonic energy between HOMO and LUMO. We found that success of exchange correlation functional on long-distanced intra-molecular CT calculations depends on correct descriptions of (1) Koopmans’ energy of donor and acceptor and (2) excitonic energy between donor and acceptor, and (3) correct far-nucleus asymptotic behavior, −1/R. We found that LC scheme can satisfy (3), but needs an appropriate choice of long-range parameter able to satisfy (1) and (2). On the other hand, the pure, conventional hybrid, and screened hybrid functionals show near-zero intra- and inter-molecular excitonic energy regardless of R, which means optical band gap coincide with HOMO–LUMO gap. Therefore, we conclude that 100 % long-range Hartree–Fock exchange inclusion is indispensable for correct descriptions of intra-molecular CT excitations as well as inter-molecular CT.

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References

  1. Jono R, Fujisawa J, Segawa H, Yamashita K (2011) Theoretical study of the surface complex between TiO2 and TCNQ showing interfacial charge-transfer transitions. J Phys Chem Lett 2(10):1167–1170. doi:10.1021/Jz200390g

    Article  CAS  Google Scholar 

  2. Jono R, Yamashita K (2012) Two different lifetimes of charge separated states: a porphyrin–quinone system in artificial photosynthesis. J Phys Chem C 116(1):1445–1449. doi:10.1021/Jp2075034

    Article  CAS  Google Scholar 

  3. Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140(4A):A1133–A1138

    Article  Google Scholar 

  4. Tozer DJ, Handy NC (1998) Improving virtual Kohn–Sham orbitals and eigenvalues: application to excitation energies and static polarizabilities. J Chem Phys 109(23):10180–10189. doi:10.1063/1.477711

    Article  CAS  Google Scholar 

  5. Dreuw A, Weisman JL, Head-Gordon M (2003) Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange. J Chem Phys 119(6):2943. doi:10.1063/1.1590951

    Article  CAS  Google Scholar 

  6. Savin A (1996) In: Seminario JM (ed) Recent developments and applications of modern density functional theory. Elsevier, Amsterdam, p 327

    Chapter  Google Scholar 

  7. Iikura H, Tsuneda T, Yanai T, Hirao K (2001) A long-range correction scheme for generalized-gradient-approximation exchange functionals. J Chem Phys 115(8):3540. doi:10.1063/1.1383587

    Article  CAS  Google Scholar 

  8. Tawada Y, Tsuneda T, Yanagisawa S, Yanai T, Hirao K (2004) A long-range-corrected time-dependent density functional theory. J Chem Phys 120(18):8425. doi:10.1063/1.1688752

    Article  CAS  Google Scholar 

  9. Tretiak S, Igumenshchev K, Chernyak V (2005) Exciton sizes of conducting polymers predicted by time-dependent density functional theory. Phys Rev B 71(3). doi:10.1103/Physrevb.71.033201

  10. Wong BM (2009) Optoelectronic properties of carbon nanorings: excitonic effects from time-dependent density functional theory. J Phys Chem C 113(52):21921–21927. doi:10.1021/Jp9074674

    Article  CAS  Google Scholar 

  11. Wong BM, Hsieh TH (2010) Optoelectronic and excitonic properties of oligoacenes: substantial improvements from range-separated time-dependent density functional theory. J Chem Theory Comput 6(12):3704–3712. doi:10.1021/Ct100529s

    Article  CAS  Google Scholar 

  12. Salzner U, Aydin A (2011) Improved prediction of properties of pi-conjugated oligomers with range-separated hybrid density functionals. J Chem Theory Comput 7(8):2568–2583. doi:10.1021/Ct2003447

    Article  CAS  Google Scholar 

  13. Yanai T, Tew DP, Handy NC (2004) A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP). Chem Phys Lett 393(1–3):51–57. doi:10.1016/j.cplett.2004.06.011

    Article  CAS  Google Scholar 

  14. Peach MJG, Benfield P, Helgaker T, Tozer DJ (2008) Excitation energies in density functional theory: an evaluation and a diagnostic test. J Chem Phys 128(4):044118. doi:10.1063/1.2831900

    Article  Google Scholar 

  15. Plotner J, Tozer DJ, Dreuw A (2010) Dependence of excited state potential energy surfaces on the spatial overlap of the Kohn–Sham orbitals and the amount of nonlocal Hartree–Fock exchange in time-dependent density functional theory. J Chem Theory Comput 6(8):2315–2324. doi:10.1021/Ct1001973

    Article  Google Scholar 

  16. Dev P, Agrawal S, English NJ (2012) Determining the appropriate exchange-correlation functional for time-dependent density functional theory studies of charge-transfer excitations in organic dyes. J Chem Phys 136(22). doi:10.1063/1.4725540

  17. Kuritz N, Stein T, Baer R, Kronik L (2011) Charge-Transfer-Like π → π* excitations in time-dependent density functional theory: a conundrum and its solution. J Chem Theory Comput 7(8):2408–2415. doi:10.1021/Ct2002804

    Article  CAS  Google Scholar 

  18. Rohrdanz MA, Herbert JM (2008) Simultaneous benchmarking of ground- and excited-state properties with long-range-corrected density functional theory. J Chem Phys 129(3):034107. doi:10.1063/1.2954017

    Article  Google Scholar 

  19. Song J-W, Peng DL, Hirao K (2011) A semiempirical long-range corrected exchange correlation functional including a short-range Gaussian attenuation (LCgau-B97). J Comput Chem 32(15):3269–3275. doi:10.1002/Jcc.21912

    Article  CAS  Google Scholar 

  20. Peach MJG, Tellgrent EI, Salek P, Helgaker T, Tozer DJ (2007) Structural and electronic properties of polyacetylene and polyyne from hybrid and coulomb-attenuated density functionals. J Phys Chem A 111(46):11930–11935. doi:10.1021/Jp0754839

    Article  CAS  Google Scholar 

  21. Anne FB, Purpan FD, Jacquemin D (2013) Charge-transfer in quasilinear push–pull polyene chains. Chem Phys Lett 581:52–56. doi:10.1016/j.cplett.2013.07.021

    Article  CAS  Google Scholar 

  22. Koch H, Jorgensen P (1990) Coupled cluster response functions. J Chem Phys 93(5):3333–3344. doi:10.1063/1.458814

    Article  CAS  Google Scholar 

  23. Stanton JF, Bartlett RJ (1993) The equation of motion coupled-cluster method—a systematic biorthogonal approach to molecular-excitation energies, transition-probabilities, and excited-state properties. J Chem Phys 98(9):7029–7039. doi:10.1063/1.464746

    Article  CAS  Google Scholar 

  24. Koch H, Kobayashi R, Demeras AS, Jorgensen P (1994) Calculation of size-intensive transition moments from the coupled cluster singles and doubles linear-response function. J Chem Phys 100(6):4393–4400. doi:10.1063/1.466321

    Article  CAS  Google Scholar 

  25. Kallay M, Gauss J (2004) Calculation of excited-state properties using general coupled-cluster and configuration-interaction models. J Chem Phys 121(19):9257–9269. doi:10.1063/1.1805494

    Article  CAS  Google Scholar 

  26. Krylov AN (2008) A study of the dynamics of contaminants in the own external atmosphere of orbital stations. Russ J Phys Chem B 2(5):827–833. doi:10.1134/S1990793108050266

    Article  Google Scholar 

  27. Bartlett RJ (2012) Coupled-cluster theory and its equation-of-motion extensions. Wiley Interdiscip Rev Comput Mol Sci 2(1):126–138. doi:10.1002/wcms.76

    Article  CAS  Google Scholar 

  28. Schreiber M, Silva-Junior MR, Sauer SPA, Thiel W (2008) Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3. J Chem Phys 128(13):134110. doi:10.1063/1.2889385

    Article  Google Scholar 

  29. Musial M, Bartlett RJ (2011) Charge-transfer separability and size-extensivity in the equation-of-motion coupled cluster method: EOM-CCx. J Chem Phys 134(3):034106. doi:10.1063/1.3511783

    Article  Google Scholar 

  30. 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(5):1515–1531. doi:10.1021/Ct2009363

    Article  CAS  Google Scholar 

  31. Kar R, Song J-W, Hirao K (2013) Long-range corrected functionals satisfy Koopmans’ theorem: calculation of correlation and relaxation energies. J Comput Chem 34(11):958–964. doi:10.1002/Jcc.23222

    Article  CAS  Google Scholar 

  32. Livshits E, Baer R (2007) A well-tempered density functional theory of electrons in molecules. Phys Chem Chem Phys 9(23):2932. doi:10.1039/b617919c

    Article  CAS  Google Scholar 

  33. Tsuneda T, Song J-W, Suzuki S, Hirao K (2010) On Koopmans’ theorem in density functional theory. J Chem Phys 133(17):174101. doi:10.1063/1.3491272

    Article  Google Scholar 

  34. Song J-W, Tokura S, Sato T, Watson MA, Hirao K (2007) An improved long-range corrected hybrid exchange-correlation functional including a short-range Gaussian attenuation (LCgau-BOP). J Chem Phys 127(15):154109. doi:10.1063/1.2790017

    Article  Google Scholar 

  35. Curtiss LA, Raghavachari K, Redfern PC, Pople JA (1997) Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation. J Chem Phys 106(3):1063–1079

    Article  CAS  Google Scholar 

  36. Song J-W, Watson MA, Hirao K (2009) An improved long-range corrected hybrid functional with vanishing Hartree–Fock exchange at zero interelectronic distance (LC2gau-BOP). J Chem Phys 131(14):144108. doi:10.1063/1.3243819

    Article  Google Scholar 

  37. Song J-W, Hirao K (2013) Long-range corrected density functional theory with optimized one-parameter progressive correlation functional (LC-BOP12 and LCgau-BOP12). Chem Phys Lett 563:15–19. doi:10.1016/j.cplett.2013.01.064

    Article  CAS  Google Scholar 

  38. Song J-W, Watson MA, Sekino H, Hirao K (2008) Nonlinear optical property calculations of polyynes with long-range corrected hybrid exchange-correlation functionals. J Chem Phys 129(2):024117. doi:10.1063/1.2936830

    Article  Google Scholar 

  39. Jacquemin D, Adamo C (2011) Bond length alternation of conjugated oligomers: wave function and DFT benchmarks. J Chem Theory Comput 7(2):369–376. doi:10.1021/Ct1006532

    Article  CAS  Google Scholar 

  40. Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic behavior. Phys Rev A 38(6):3098–3100

    Article  CAS  Google Scholar 

  41. Song J-W, Hirosawa T, Tsuneda T, Hirao K (2007) Long-range corrected density functional calculations of chemical reactions: redetermination of parameter. J Chem Phys 126(15):154105. doi:10.1063/1.2721532

    Article  Google Scholar 

  42. Tsuneda T, Hirao K (1997) A new spin-polarized Colle–Salvetti-type correlation energy functional. Chem Phys Lett 268(5–6):510–520

    Article  CAS  Google Scholar 

  43. Vydrov OA, Scuseria GE (2006) Assessment of a long-range corrected hybrid functional. J Chem Phys 125(23):234109. doi:10.1063/1.2409292

    Article  Google Scholar 

  44. Chai J-D, Head-Gordon M (2008) Systematic optimization of long-range corrected hybrid density functionals. J Chem Phys 128(8):084106. doi:10.1063/1.2834918

    Article  Google Scholar 

  45. Becke AD (1993) Density-functional thermochemistry. 3. The role of exact exchange. J Chem Phys 98(7):5648–5652

    Article  CAS  Google Scholar 

  46. Heyd J, Scuseria GE, Ernzerhof M (2003) Hybrid functionals based on a screened Coulomb potential. J Chem Phys 118(18):8207. doi:10.1063/1.1564060

    Article  CAS  Google Scholar 

  47. Song J-W, Yamashita K, Hirao K (2012) Gaussian attenuation hybrid scheme applied to the Ernzerhof–Perdew exchange hole model (Gau-PBEh). J Chem Phys 137(24):244105. doi:10.1063/1.4772401

    Article  Google Scholar 

  48. Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77(18):3865–3868

    Article  CAS  Google Scholar 

  49. Tsuneda T, Suzumura T, Hirao K (1999) A new one-parameter progressive Colle–Salvetti-type correlation functional. J Chem Phys 110(22):10664–10678

    Article  CAS  Google Scholar 

  50. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA Jr, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam NJ, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas O, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian09, Revision A.1. Gaussian, Inc, Wallingford, CT

  51. Izmaylov AF, Scuseria GE (2008) Why are time-dependent density functional theory excitations in solids equal to band structure energy gaps for semilocal functionals, and how does nonlocal Hartree–Fock-type exchange introduce excitonic effects? J Chem Phys 129(3):034101. doi:10.1063/1.2953701

    Article  Google Scholar 

  52. Baer R, Livshits E, Salzner U (2010) Tuned range-separated hybrids in density functional theory. Annu Rev Phys Chem 61:85–109. doi:10.1146/annurev.physchem.012809.103321

    Article  CAS  Google Scholar 

  53. Koch H, Christiansen O, Jorgensen P, deMeras AMS, Helgaker T (1997) The CC3 model: an iterative coupled cluster approach including connected triples. J Chem Phys 106(5):1808–1818. doi:10.1063/1.473322

    Article  CAS  Google Scholar 

  54. Schreiber M, Silva MR, Sauer SPA, Thiel W (2008) Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3. J Chem Phys 128(13):131410. doi:10.1063/1.2889385

    Google Scholar 

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Acknowledgments

We would like to pay honors to Prof. Dunning for his great achievements. This research was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Number 23225001. The numerical calculations were conducted on the RIKEN Cluster of Clusters (RICC).

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  1. Computational Chemistry Unit, RIKEN Advanced Institute for Computational Science, 7-1-26, Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo, 650-0047, Japan

    Jong-Won Song & Kimihiko Hirao

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  1. Jong-Won Song
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  2. Kimihiko Hirao
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Correspondence to Kimihiko Hirao.

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Dedicated to Professor Thom Dunning and published as part of the special collection of articles celebrating his career upon his retirement.

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Song, JW., Hirao, K. What makes differences between intra- and inter-molecular charge transfer excitations in conjugated long-chained polyene? EOM-CCSD and LC-BOP study. Theor Chem Acc 133, 1438 (2014). https://doi.org/10.1007/s00214-013-1438-5

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