Density functional theory studies on the excited-state properties of Bilirubin molecule

Li Yuan-Yuan; Hu Zhu-Bin; Sun Hai-Tao; Sun Zhen-Rong

doi:10.7498/aps.69.20200518

Abstract

Bilirubin is the main pigment in human bile, which is closely related to human health. Bilirubin combining with fluorescent protein represents a new type of fluorescent chromophore and has important applications in the field of biological imaging and biosensor. Due to the lack of efficient and accurate electronic structure methods, the electronic structure and excited-state properties of bilirubin molecule are not characterized quantitatively and accurately. Firstly, the vertical absorption energy, oscillator strength and vertical emission energy of the lowest singlet excited state of bilirubin molecule are calculated by combining the implicit solvent model and the linear response time-dependent density functional theory (TDDFT) method. Compared to the experimental data and high-level RI-ADC(2) calculation, the prediction performance of a series of density functional methods is systematically investigated. The results show that the optimally-tuned range separated density functional method has the best overall performance and the minimum absolute and relative errors. This is obviously due to the fact that the suitable proportion of exact exchange included in density functionals can produce neither delocalized nor localized electronic structures. Based on the produced wavefunction by the optimally-tuned method, the excited-state characteristics of the S₁ state of bilirubin molecule indicate a hybrid local and charge transfer excitation, based on the quantitative characterization using hole-electron analysis and interfragment charge transfer method. This work can provide a theoretical basis for the study of excited-state dynamics and spectral properties of bilirubin molecules and the optimally tuned range-separated DFT method also provide a reliable and efficient theoretical tool to study the excited-state properties of other biomolecular systems in the future.

Keywords:

Authors and contacts

State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200241, China

Corresponding author: Sun Hai-Tao, htsun@phy.ecnu.edu.cn ; Sun Zhen-Rong, zrsun@phy.ecnu.edu.cn

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References

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[9]	Braslavsky S E, Holzwarth A R, Schaffner K 1983 Angew. Chem. Int. Ed. 22 656 Google Scholar
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[12]	Cao X D, Zhang C C, Gao Z H, Liu Y Y, Zhao Y Z, Yang Y, Chen J Q, Jimenez R, Xu J H 2019 Phys. Chem. Chem. Phys. 21 2365 Google Scholar
[13]	Zietz B, Blomgren F 2006 Chem. Phys. Lett. 420 556 Google Scholar
[14]	Fabiano E, Della Sala F, Cingolani R, Weimer M, Görling A 2005 J. Phys. Chem. A 109 3078 Google Scholar
[15]	Hammond J R, Kowalski K 2009 J. Chem. Phys. 130 194108 Google Scholar
[16]	Budzák Š, Scalmani G, Jacquemin D 2017 J. Chem. Theory Comput. 13 6237 Google Scholar
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[18]	Hybertsen M S, Louie S G 1986 Phys. Rev. B 34 5390 Google Scholar
[19]	Kohn W, Sham L J 1965 Phys. Rev. 140 A1133 Google Scholar
[20]	Cohen A J, Mori-Sanchez P, Yang W T 2011 Chem. Rev. 112 289
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[26]	Stein T, Kronik L, Baer R 2009 J. Am. Chem. Soc. 131 2818 Google Scholar
[27]	Sun H T, Zhong C, Brédas J 2015 J. Chem. Theory Comput. 11 3851 Google Scholar
[28]	Penfold T J 2015 J. Phys. Chem. C 119 13535 Google Scholar
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[32]	Baer R, Livshits E, Salzner U 2010 Annu. Rev. Phys. Chem. 61 85 Google Scholar
[33]	Stein T, Kronik L, Baer R 2009 J. Chem. Phys. 131 244119 Google Scholar
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[40]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[41]	Yu H S, He X, Li S L, Truhlar D G 2016 Chem. Sci. 7 5032 Google Scholar
[42]	Zhao Y, Truhlar D G 2008 Theor. Chem. Acc. 120 215 Google Scholar
[43]	Zhao Y, Truhlar D G 2006 J. Phys. Chem. A 110 13126 Google Scholar
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[45]	Vydrov O A, Scuseria G E 2006 J. Chem. Phys. 125 234109 Google Scholar
[46]	Chai J D, Head-Gordon M 2008 Phys. Chem. Chem. Phys. 10 6615 Google Scholar
[47]	Peverati R, Truhlar D G 2011 J. Phys. Chem. Lett. 2 2810 Google Scholar
[48]	Goerigk L, Grimme S 2010 J. Chem. Phys. 132 184103 Google Scholar
[49]	Trofimov A B, Schirmer J 1995 J. Phys. B: At., Mol. Opt. Phys. 28 2299 Google Scholar
[50]	Schäfer A, Horn H, Ahlrichs R 1992 J. Chem. Phys. 97 2571 Google Scholar
[51]	Schäfer A, Huber C, Ahlrichs R 1994 J. Chem. Phys. 100 5829 Google Scholar
[52]	Weigend F, Ahlrichs R 2005 Phys. Chem. Chem. Phys. 7 3297 Google Scholar
[53]	Kumagai A, Ando R, Miyatake H, Greimel P, Kobayashi T, Hirabayashi Y, Shimogori T, Miyawaki A 2013 Cell 153 1602 Google Scholar
[54]	Mennucci B 2012 Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2 386 Google Scholar
[55]	Tomasi J, Mennucci B, Cammi R 2005 Chem. Rev. 105 2999 Google Scholar
[56]	Marenich A V, Cramer C J, Truhlar D G 2009 J. Phys. Chem. B 113 6378 Google Scholar
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[62]	Lu T, Chen F W 2012 J. Comput. Chem. 33 580 Google Scholar
[63]	Humphrey W, Dalke A, Schulten K 1996 J. Mol. Graphics 14 33 Google Scholar

Cited By

图 1 本文研究的胆红素分子结构

Figure 1. The molecular structure of bilirubin studied in this work.

DownLoad: Full-Size Img PowerPoint

图 2 本文中各种密度泛函中所含准确交换项比例(eX%)与电子间距离(r₁₂)关系示意图

Figure 2. Percentages of exact-exchange (eX%) included in various density functionals as a function of intereletronic distance (r₁₂, Bohr).

DownLoad: Full-Size Img PowerPoint

图 3 胆红素分子最低单重激发态的空穴-电子分布示意图

Figure 3. Diagram of hole-electron distribution for the lowest singlet excited state (isovalue=0.001).

DownLoad: Full-Size Img PowerPoint

图 4 胆红素分子的三个片段划分及各片段对最低单重激发态的空穴和电子的贡献

Figure 4. The divided three fragments of bilirubin molecule and contribution of each fragment to the hole and electron for the lowest singlet excited state.

DownLoad: Full-Size Img PowerPoint

图 5 胆红素分子最低单重激发态的各片段电子转移矩阵热图

Figure 5. Diagram of electron transfer matrix for each fragment of lowest singlet excited state of bilirubin molecule.

DownLoad: Full-Size Img PowerPoint

表 1 基组对计算的垂直激发能(E_VA)的影响

Table 1. Influence of basis set on the calculated vertical excitation energy (E_VA).

Basis set	E_VA/eV
	CAM-B3 LYP		RI-ADC(2)
	PCM	GAS	COSMO	GAS
def-SV(P)	2.98	3.11	2.80	2.97
def-TZVP	2.91	3.05	2.69	2.86
def2-TZVP	2.90	3.04	—	2.81
EXP ^a	2.73	—	—	—
^aExperimental values are taken from Refs. [12,53].

DownLoad: CSV

表 2 各种理论方法计算胆红素分子的垂直激发能(E_VA)、振子强度(f )和垂直发射能(E_VE)以及与实验值相比的绝对误差和相对误差

Table 2. Vertical absorption energies (E_VA)_,oscillator strength (f ) and vertical emission energies (E_VE) of bilirubin and the absolute errors and relative errors compared to the available experimental data.

	ω	E_VA/eV	f (S₁)	AE/eV	RE/%	E_VE/eV	AE/eV	RE/%
PBE	—	1.83	0.02	-0.90	33	1.68	-0.71	30
B3LYP	—	2.48	0.12	-0.25	9	2.25	-0.14	6
MN15	—	2.81	1.21	0.08	3	2.40	0.01	0.4
M062X	—	2.91	1.30	0.18	7	2.46	0.07	3
M06HF	—	3.12	1.42	0.39	14	2.52	0.13	6
CAM-B3LYP	0.330	2.91	1.33	0.18	7	2.45	0.06	3
LC-ωPBE	0.400	3.11	1.43	0.38	14	2.54	0.15	6
ω B97XD	0.200	2.94	1.36	0.21	8	2.46	0.07	3
M11	0.250	3.01	1.40	0.28	10	2.49	0.10	4
LC-ω PBE*	0.178	2.76	1.20	0.03	1	2.36	-0.03	1
ω B97XD*	0.137	2.85	1.28	0.12	4	2.43	0.04	2
B2 GPPLYP	—	2.92	1.13	0.19	7	—	—	—
RI-ADC(2)	—	2.69	1.06	-0.04	1	—	—	—
EXP^a	—	2.73	—	—	—	2.39	—	—
^aExperimental values are taken from Refs. [12,53].

DownLoad: CSV

表 3 胆红素分子最低单重激发态的各片段电子净变化量以及片段间电子转移量

Table 3. Net change of each fragment and electron transfer between fragments for lowest singlet excited state of bilirubin molecule.

	Electron transfer between fragments
	1	2	3
1	0.109	0.418	0.002
2	0.095	0.364	0.002
3	0.002	0.008	0.000
Net change of each fragment	–0.323	0.329	–0.006

DownLoad: CSV

[1]	Stocker R, Yamamoto Y, Mcdonagh A F, Glazer A N, Ames B N 1987 Science 235 1043 Google Scholar
[2]	Fevery J 2008 Liver Int. 28 592 Google Scholar
[3]	Hissi E G V, Martinez J C G, Zamarbide G N, Estrada M R, Jensen S J K, Tomas-Vert F, Csizmadia I G 2009 J. Mol. Struc.: THEOCHEM 911 24 Google Scholar
[4]	Carreira-Blanco C, Singer P, Diller R, Lustres J L P 2016 Phys. Chem. Chem. Phys. 18 7148 Google Scholar
[5]	Person R V, Peterson B R, Lightner D A 1994 J. Am. Chem. Soc. 116 42 Google Scholar
[6]	Nogales D, Lightner D A 1995 J. Biol. Chem. 270 73 Google Scholar
[7]	Boiadjiev S E, Watters K, Wolf S, Lai B N, Welch W H, McDonagh A F, Lightner D A 2004 Biochemistry 43 15617 Google Scholar
[8]	Lightner D A, Holmes D L, McDonagh A F 1996 J. Biol. Chem. 271 2397 Google Scholar
[9]	Braslavsky S E, Holzwarth A R, Schaffner K 1983 Angew. Chem. Int. Ed. 22 656 Google Scholar
[10]	Zietz B, Macpherson A N, Gillbro T 2004 Phys. Chem. Chem. Phys. 6 4535 Google Scholar
[11]	Zietz B, Gillbro T 2007 J. Phys. Chem. B 111 11997 Google Scholar
[12]	Cao X D, Zhang C C, Gao Z H, Liu Y Y, Zhao Y Z, Yang Y, Chen J Q, Jimenez R, Xu J H 2019 Phys. Chem. Chem. Phys. 21 2365 Google Scholar
[13]	Zietz B, Blomgren F 2006 Chem. Phys. Lett. 420 556 Google Scholar
[14]	Fabiano E, Della Sala F, Cingolani R, Weimer M, Görling A 2005 J. Phys. Chem. A 109 3078 Google Scholar
[15]	Hammond J R, Kowalski K 2009 J. Chem. Phys. 130 194108 Google Scholar
[16]	Budzák Š, Scalmani G, Jacquemin D 2017 J. Chem. Theory Comput. 13 6237 Google Scholar
[17]	Hedin L 1965 Phys. Rev. 139 A796 Google Scholar
[18]	Hybertsen M S, Louie S G 1986 Phys. Rev. B 34 5390 Google Scholar
[19]	Kohn W, Sham L J 1965 Phys. Rev. 140 A1133 Google Scholar
[20]	Cohen A J, Mori-Sanchez P, Yang W T 2011 Chem. Rev. 112 289
[21]	Jacquemin D, Wathelet V, Perpète E A, Adamo C 2009 J. Chem. Theory Comput. 5 2420 Google Scholar
[22]	Tian X H, Sun H T, Zhang Q S, Adachi C 2016 Chin. Chem. Lett. 27 1445 Google Scholar
[23]	Sun H T, Autschbach J 2013 ChemPhysChem 14 2450 Google Scholar
[24]	Jiang Y R, Hu Z B, Zhou B, Zhong C, Sun Z R, Sun H T 2019 J. Phys. Chem. C 123 5616 Google Scholar
[25]	Sutton C, Sears J S, Coropceanu V, Brédas J 2013 J. Phys. Chem. Lett. 4 919 Google Scholar
[26]	Stein T, Kronik L, Baer R 2009 J. Am. Chem. Soc. 131 2818 Google Scholar
[27]	Sun H T, Zhong C, Brédas J 2015 J. Chem. Theory Comput. 11 3851 Google Scholar
[28]	Penfold T J 2015 J. Phys. Chem. C 119 13535 Google Scholar
[29]	Kronik L, Stein T, Refaely-Abramson S, Baer R 2012 J. Chem. Theory Comput. 8 1515 Google Scholar
[30]	孙海涛, 钟成, 孙真荣 2016 物理化学学报 32 2197 Google Scholar Sun H T, Zhong C, Sun Z R 2016 Acta Phys.-Chim. Sin. 32 2197 Google Scholar
[31]	Körzdörfer T, Sears J S, Sutton C, Brédas J 2011 J. Chem. Phys. 135 204107 Google Scholar
[32]	Baer R, Livshits E, Salzner U 2010 Annu. Rev. Phys. Chem. 61 85 Google Scholar
[33]	Stein T, Kronik L, Baer R 2009 J. Chem. Phys. 131 244119 Google Scholar
[34]	Becke A D 1993 J. Chem. Phys. 98 5648 Google Scholar
[35]	Lee C, Yang W T, Parr R G 1988 Phys. Rev. B 37 785 Google Scholar
[36]	Grimme S, Ehrlich S, Goerigk L 2011 J. Comput. Chem. 32 1456 Google Scholar
[37]	Ditchfield R, Hehre W J, Pople J A 1971 J. Chem. Phys. 54 724 Google Scholar
[38]	Hehre W J, Ditchfield R, Pople J A 1972 J. Chem. Phys. 56 2257 Google Scholar
[39]	Hariharan P C, Pople J A 1973 Theor. Chim. Acta 28 213 Google Scholar
[40]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[41]	Yu H S, He X, Li S L, Truhlar D G 2016 Chem. Sci. 7 5032 Google Scholar
[42]	Zhao Y, Truhlar D G 2008 Theor. Chem. Acc. 120 215 Google Scholar
[43]	Zhao Y, Truhlar D G 2006 J. Phys. Chem. A 110 13126 Google Scholar
[44]	Yanai T, Tew D P, Handy N C 2004 Chem. Phys. Lett. 393 51 Google Scholar
[45]	Vydrov O A, Scuseria G E 2006 J. Chem. Phys. 125 234109 Google Scholar
[46]	Chai J D, Head-Gordon M 2008 Phys. Chem. Chem. Phys. 10 6615 Google Scholar
[47]	Peverati R, Truhlar D G 2011 J. Phys. Chem. Lett. 2 2810 Google Scholar
[48]	Goerigk L, Grimme S 2010 J. Chem. Phys. 132 184103 Google Scholar
[49]	Trofimov A B, Schirmer J 1995 J. Phys. B: At., Mol. Opt. Phys. 28 2299 Google Scholar
[50]	Schäfer A, Horn H, Ahlrichs R 1992 J. Chem. Phys. 97 2571 Google Scholar
[51]	Schäfer A, Huber C, Ahlrichs R 1994 J. Chem. Phys. 100 5829 Google Scholar
[52]	Weigend F, Ahlrichs R 2005 Phys. Chem. Chem. Phys. 7 3297 Google Scholar
[53]	Kumagai A, Ando R, Miyatake H, Greimel P, Kobayashi T, Hirabayashi Y, Shimogori T, Miyawaki A 2013 Cell 153 1602 Google Scholar
[54]	Mennucci B 2012 Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2 386 Google Scholar
[55]	Tomasi J, Mennucci B, Cammi R 2005 Chem. Rev. 105 2999 Google Scholar
[56]	Marenich A V, Cramer C J, Truhlar D G 2009 J. Phys. Chem. B 113 6378 Google Scholar
[57]	Klamt A, Schüürmann G 1993 J. Chem. Soc., Perkin Trans. 2 799
[58]	Frisch M J, Trucks G W, Schlegel H B, Scuseria G E, Robb M A, Cheeseman J R, Scalmani G, Barone V, Petersson G A, Nakatsuji H, Li X, Caricato M, Marenich A V, Bloino J, Janesko B G, Gomperts R, Mennucci B, Hratchian H P, Ortiz J V, Izmaylov A F, Sonnenberg J L, Williams, Ding F, Lipparini F, Egidi F, Goings J, Peng B, Petrone A, Henderson T, Ranasinghe D, Zakrzewski V G, Gao J, Rega N, Zheng G, Liang W, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Throssell K, Montgomery J J A, Peralta J E, Ogliaro F, Bearpark M J, Heyd J J, Brothers E N, Kudin K N, Staroverov V N, Keith T A, Kobayashi R, Normand J, Raghavachari K, Rendell A P, Burant J C, Iyengar S S, Tomasi J, Cossi M, Millam J M, Klene M, Adamo C, Cammi R, Ochterski J W, Martin R L, Morokuma K, Farkas O, Foresman J B, Fox D J 2013 Gaussian 09 Revision E. 01 Wallingford: Gaussian Inc
[59]	Frisch M J, Trucks G W, Schlegel H B, Scuseria G E, Robb M A, Cheeseman J R, Scalmani G, Barone V, Petersson G A, Nakatsuji H, Li X, Caricato M, Marenich A V, Bloino J, Janesko B G, Gomperts R, Mennucci B, Hratchian H P, Ortiz J V, Izmaylov A F, Sonnenberg J L, Williams, Ding F, Lipparini F, Egidi F, Goings J, Peng B, Petrone A, Henderson T, Ranasinghe D, Zakrzewski V G, Gao J, Rega N, Zheng G, Liang W, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Throssell K, Montgomery J J A, Peralta J E, Ogliaro F, Bearpark M J, Heyd J J, Brothers E N, Kudin K N, Staroverov V N, Keith T A, Kobayashi R, Normand J, Raghavachari K, Rendell A P, Burant J C, Iyengar S S, Tomasi J, Cossi M, Millam J M, Klene M, Adamo C, Cammi R, Ochterski J W, Martin R L, Morokuma K, Farkas O, Foresman J B, Fox D J 2016 Gaussian 16 Revision A. 03 Wallingford: Gaussian Inc
[60]	Neese F 2012 Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2 73 Google Scholar
[61]	Ahlrichs R, Bär M, Häser M, Horn H, Kölmel C 1989 Chem. Phys. Lett. 162 165 Google Scholar
[62]	Lu T, Chen F W 2012 J. Comput. Chem. 33 580 Google Scholar
[63]	Humphrey W, Dalke A, Schulten K 1996 J. Mol. Graphics 14 33 Google Scholar

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Vol. 69, Issue 16 - 2020-08-20

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