# Optical Excitations of Chlorophyll a and Chlorophyll b

## Transcript Of Optical Excitations of Chlorophyll a and Chlorophyll b

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Optical Excitations of Chlorophyll a and Chlorophyll b Monomers and Dimers

Journal: Journal of Chemical Theory and Computation

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Preciado-Rivas, María; Yachay Tech University, School of Physical Sciences and Nanotechnology Mowbray, Duncan; Yachay Tech University, School of Physical Sciences and Nanotechnology Larsen, Ask; Universidad del Pais Vasco, Nano-bio spectroscopy group, Departamento de Fisica de Materiales Milne, Bruce; University of Coimbra, Coimbra Chemistry Center, Department of Chemistry

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56 Optical Excitations of Chlorophyll a and Chlorophyll b

78 Monomers and Dimers

910 María Rosa Preciado-Rivas,† Duncan John Mowbray,∗,†,‡ Ask Hjorth Larsen,‡ and Bruce Forbes Milne ,§,‡

11 † School of Physical Sciences and Nanotechnology, Yachay Tech University, Urcuquí 100119, Ecuador

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‡ Nano-Bio Spectroscopy Group and ETSF Scientiﬁc Development Centre, Departamento de Física de Materiales, Universidad del País

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Vasco UPV/EHU, E-20018 San Sebastián, Spain

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Coimbra Chemistry Center, Department of Chemistry, University of Coimbra, Rua Larga, 3004-535 Coimbra, Portugal

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§ CFisUC, Department of Physics, University of Coimbra, Rua Larga, 3004-516 Coimbra, Portugal

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ABSTRACT: A necessary ﬁrst step in the development of technologies such as artiﬁcial photosynthesis is understanding the photoexcitation

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process within the basic building blocks of naturally-occuring light harvesting complexes (LHCs). The most important of these building

blocks in biological LHCs such as LHC II from green plants are the chlorophyll a (Chl a) and chlorophyll b (Chl b) chromophores dispersed

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throughout the protein matrix. Eﬀorts are still hampered by the lack of economical computational methods that are able to describe optical

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absorption in large biomolecules with suﬃcient accuracy. In this work we employ a highly eﬃcient localized basis set representation of

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the Kohn–Sham (KS) wave functions at the density functional theory (DFT) level to perform time dependent density functional theory

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(TDDFT) real time and frequency domain calculations of the optical absorption spectra of Chl a and Chl b monomers and dimers. We ﬁnd

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our TDDFT calculations using linear combinations of atomic orbitals (LCAO) reproduce results obtained with a plane wave (PW) and real

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space (RS) representations of the KS wave functions, but with a signiﬁcant reduction in computational eﬀort. This work opens the path to

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ﬁrst principles calculations of optical excitations in macromolecular systems.

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Keywords: chlorophyll, optical excitations, artiﬁcial photosynthesis, TDDFT, LCAO, RPA

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1. INTRODUCTION

the Bethe–Salpeter equation (BSE), 29 while often achieving quan-

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titative accuracy, are extremely heavy computationally. 30 As a re-

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Chlorophyll a (Chl a or C55H72MgN4O5) and chlorophyll b (Chl b

sult, only recently have even the smallest dye-sensitized solar cells

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or C55H70MgN4O6), 1,2 depicted schematically in Figure 1, are the

(DSSC) been described at the BSE level. 31 Moreover, such meth-

33 fIuI)n4dpamreesenntatlifnungcretieonnapllaunntist.s oAfsthseuclihg,hutnhdaerrvsetsatnindgincgotmheplpexho(tLoHexC- ondosn-apreeriiondtriicnssyicsatellmy si.ll-suited to the description of isolated and/or

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citation process within Chl a and Chl b is of great importance in

Although TDDFT 20,32 real time 33–36 and frequency domain 37–41

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the development of technologies such as those involved in the op-

calculations provide an attractive alternative, implementations

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timization of food crop production 5,6 and conversion of solar radi-

based on real-space (RS) or plane-wave (PW) representations of

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ation into a usable form of energy directly through methods such

the KS orbitals 27 are both computationally expensive, and exhibit

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as conventional solar cells 7,8 or via subsidiary technologies such as

a strong exchange and correlation (xc) functional dependence for

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photosynthetically-driven (bio)reactor systems for hydrogen com-

their accuracy. For RS calculations, time propagation RS-TDDFT

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bustion. 9–12 Moreover, such information is more generally applica-

calculations require time steps much shorter than what is needed to

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ble to the in silico design and optimization of dye-sensitized solar

resolve the features of the spectra in order to ensure the stability of

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cells, 13 organic photovoltaic cells, 14 photocatalytic systems, 15 op-

the calculation. 25 Such instabilities of RS calculations may be re-

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toelectronic devices, 16 and plasmonics. 17

lated to their freedom in representing the KS wavefunctions, which

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Although much progress has been recently made in both the ex-

are only constrained by the grid spacing.

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perimental measurement of individual monomer and dimer Chl a

In this work we employ linear combinations of atomic orbitals

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and Chl b spectra, 3,18,19 and their theoretical description at the time-

(LCAOs) to provide a more eﬃcient representation of the KS or-

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dependent density functional theory (TDDFT) 20 level, 21–24 the lack

bitals, while retaining the accuracy of RS and PW based TDDFT

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of reasonably accurate yet highly eﬃcient computational methods

real time and frequency domain calculations of the optical ab-

49 hcoasnthaainminpgerbedioemﬀoolretcsutoleds.esIcnriitbiaeltahteteomptpitcsaltoabinsovrepsttiiognatoeftlhaergoepCtichal-l ssoenrptatitoionn. oFf utrhteheKr,Sthweavcoefnusntrcatiinotnss immapyosbeed ebxypeacnteLdCtAo Oimrperporvee-

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absorption characteristics of biomacromolecules such as the LHC

the stability of time-propagation TDDFT calculations, allowing

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II using ﬁrst-principles electronic structure methods have helped to

one to use larger time steps. However, the reliability of LCAO-

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clarify several aspects of the functioning of these systems, how-

TDDFT is inherently basis set dependent. 42 This makes an as-

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ever the computational resources required for a complete treatment

sessment and benchmarking for the fundamental functional units

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of systems of this size lie considerably beyond what is generally

with RS-TDDFT or PW-TDDFT essential before applying LCAO-

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available to most researchers. 25,26

TDDFT to the complete macromolecular system. By applying

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On the one hand, methods based on the Kohn–Sham (KS) density

LCAO-TDDFT methods 43,44 to the Chl a and Chl b monomer and

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of states, 27 while being quite eﬃcient, often underestimate energy

dimer systems, we may clearly explain their advantages and disad-

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gaps by more than half. This is because an independent-particle

vantages for describing light-harvesting systems, with the aim of

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picture fails to describe electronic screening of the excited states. 28

applying these methods to macromolecules such as the complete

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On the other hand, quasiparticle-based calculations of spectra from

LHC II. Note that since experimental measurements of the Chl b

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AUTHOR INFORMATION

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Corresponding Author

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E-mail: [email protected] (D.J.M.).

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Notes

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The authors declare no competing ﬁnancial interest.

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A.H.L. acknowledges funding from the European Union’s Hori-

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Project PEst-OE/QUI/UI0313/2014 and POCI-01-0145-FEDER-

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Optical Excitations of Chlorophyll a and Chlorophyll b Monomers and Dimers

Journal: Journal of Chemical Theory and Computation

Manuscript ID Draft

Manuscript Type: Article

Date Submitted by the Author: n/a

Complete List of Authors:

Preciado-Rivas, María; Yachay Tech University, School of Physical Sciences and Nanotechnology Mowbray, Duncan; Yachay Tech University, School of Physical Sciences and Nanotechnology Larsen, Ask; Universidad del Pais Vasco, Nano-bio spectroscopy group, Departamento de Fisica de Materiales Milne, Bruce; University of Coimbra, Coimbra Chemistry Center, Department of Chemistry

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56 Optical Excitations of Chlorophyll a and Chlorophyll b

78 Monomers and Dimers

910 María Rosa Preciado-Rivas,† Duncan John Mowbray,∗,†,‡ Ask Hjorth Larsen,‡ and Bruce Forbes Milne ,§,‡

11 † School of Physical Sciences and Nanotechnology, Yachay Tech University, Urcuquí 100119, Ecuador

12

‡ Nano-Bio Spectroscopy Group and ETSF Scientiﬁc Development Centre, Departamento de Física de Materiales, Universidad del País

13

Vasco UPV/EHU, E-20018 San Sebastián, Spain

14

Coimbra Chemistry Center, Department of Chemistry, University of Coimbra, Rua Larga, 3004-535 Coimbra, Portugal

15

§ CFisUC, Department of Physics, University of Coimbra, Rua Larga, 3004-516 Coimbra, Portugal

16

17

ABSTRACT: A necessary ﬁrst step in the development of technologies such as artiﬁcial photosynthesis is understanding the photoexcitation

18

process within the basic building blocks of naturally-occuring light harvesting complexes (LHCs). The most important of these building

blocks in biological LHCs such as LHC II from green plants are the chlorophyll a (Chl a) and chlorophyll b (Chl b) chromophores dispersed

19

throughout the protein matrix. Eﬀorts are still hampered by the lack of economical computational methods that are able to describe optical

20

absorption in large biomolecules with suﬃcient accuracy. In this work we employ a highly eﬃcient localized basis set representation of

21

the Kohn–Sham (KS) wave functions at the density functional theory (DFT) level to perform time dependent density functional theory

22

(TDDFT) real time and frequency domain calculations of the optical absorption spectra of Chl a and Chl b monomers and dimers. We ﬁnd

23

our TDDFT calculations using linear combinations of atomic orbitals (LCAO) reproduce results obtained with a plane wave (PW) and real

24

space (RS) representations of the KS wave functions, but with a signiﬁcant reduction in computational eﬀort. This work opens the path to

25

ﬁrst principles calculations of optical excitations in macromolecular systems.

26

Keywords: chlorophyll, optical excitations, artiﬁcial photosynthesis, TDDFT, LCAO, RPA

27

28

29

1. INTRODUCTION

the Bethe–Salpeter equation (BSE), 29 while often achieving quan-

30

titative accuracy, are extremely heavy computationally. 30 As a re-

31

Chlorophyll a (Chl a or C55H72MgN4O5) and chlorophyll b (Chl b

sult, only recently have even the smallest dye-sensitized solar cells

32

or C55H70MgN4O6), 1,2 depicted schematically in Figure 1, are the

(DSSC) been described at the BSE level. 31 Moreover, such meth-

33 fIuI)n4dpamreesenntatlifnungcretieonnapllaunntist.s oAfsthseuclihg,hutnhdaerrvsetsatnindgincgotmheplpexho(tLoHexC- ondosn-apreeriiondtriicnssyicsatellmy si.ll-suited to the description of isolated and/or

34

citation process within Chl a and Chl b is of great importance in

Although TDDFT 20,32 real time 33–36 and frequency domain 37–41

35

the development of technologies such as those involved in the op-

calculations provide an attractive alternative, implementations

36

timization of food crop production 5,6 and conversion of solar radi-

based on real-space (RS) or plane-wave (PW) representations of

37

ation into a usable form of energy directly through methods such

the KS orbitals 27 are both computationally expensive, and exhibit

38

as conventional solar cells 7,8 or via subsidiary technologies such as

a strong exchange and correlation (xc) functional dependence for

39

photosynthetically-driven (bio)reactor systems for hydrogen com-

their accuracy. For RS calculations, time propagation RS-TDDFT

40

bustion. 9–12 Moreover, such information is more generally applica-

calculations require time steps much shorter than what is needed to

41

ble to the in silico design and optimization of dye-sensitized solar

resolve the features of the spectra in order to ensure the stability of

42

cells, 13 organic photovoltaic cells, 14 photocatalytic systems, 15 op-

the calculation. 25 Such instabilities of RS calculations may be re-

43

toelectronic devices, 16 and plasmonics. 17

lated to their freedom in representing the KS wavefunctions, which

44

Although much progress has been recently made in both the ex-

are only constrained by the grid spacing.

45

perimental measurement of individual monomer and dimer Chl a

In this work we employ linear combinations of atomic orbitals

46

and Chl b spectra, 3,18,19 and their theoretical description at the time-

(LCAOs) to provide a more eﬃcient representation of the KS or-

47

dependent density functional theory (TDDFT) 20 level, 21–24 the lack

bitals, while retaining the accuracy of RS and PW based TDDFT

48

of reasonably accurate yet highly eﬃcient computational methods

real time and frequency domain calculations of the optical ab-

49 hcoasnthaainminpgerbedioemﬀoolretcsutoleds.esIcnriitbiaeltahteteomptpitcsaltoabinsovrepsttiiognatoeftlhaergoepCtichal-l ssoenrptatitoionn. oFf utrhteheKr,Sthweavcoefnusntrcatiinotnss immapyosbeed ebxypeacnteLdCtAo Oimrperporvee-

50

absorption characteristics of biomacromolecules such as the LHC

the stability of time-propagation TDDFT calculations, allowing

51

II using ﬁrst-principles electronic structure methods have helped to

one to use larger time steps. However, the reliability of LCAO-

52

clarify several aspects of the functioning of these systems, how-

TDDFT is inherently basis set dependent. 42 This makes an as-

53

ever the computational resources required for a complete treatment

sessment and benchmarking for the fundamental functional units

54

of systems of this size lie considerably beyond what is generally

with RS-TDDFT or PW-TDDFT essential before applying LCAO-

55

available to most researchers. 25,26

TDDFT to the complete macromolecular system. By applying

56

On the one hand, methods based on the Kohn–Sham (KS) density

LCAO-TDDFT methods 43,44 to the Chl a and Chl b monomer and

57

of states, 27 while being quite eﬃcient, often underestimate energy

dimer systems, we may clearly explain their advantages and disad-

58

gaps by more than half. This is because an independent-particle

vantages for describing light-harvesting systems, with the aim of

59

picture fails to describe electronic screening of the excited states. 28

applying these methods to macromolecules such as the complete

60

On the other hand, quasiparticle-based calculations of spectra from

LHC II. Note that since experimental measurements of the Chl b

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Corresponding Author

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E-mail: [email protected] (D.J.M.).

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Notes

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The authors declare no competing ﬁnancial interest.

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A.H.L. acknowledges funding from the European Union’s Hori-

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