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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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Optical Excitations of Chlorophyll a and Chlorophyll b

Monomers and Dimers

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

† School of Physical Sciences and Nanotechnology, Yachay Tech University, Urcuquí 100119, Ecuador‡ Nano-Bio Spectroscopy Group and ETSF Scientific Development Centre, Departamento de Física de Materiales, Universidad del PaísVasco UPV/EHU, E-20018 San Sebastián, Spain¶ Coimbra Chemistry Center, Department of Chemistry, University of Coimbra, Rua Larga, 3004-535 Coimbra, Portugal§ CFisUC, Department of Physics, University of Coimbra, Rua Larga, 3004-516 Coimbra, Portugal

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

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

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

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

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

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

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

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

first principles calculations of optical excitations in macromolecular systems.

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

1. INTRODUCTION

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

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

fundamental functional units of the light harvesting complex (LHC

II) 4 present in green plants. As such, understanding the photoex-

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

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

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

ation into a usable form of energy directly through methods such

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

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

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

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

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

toelectronic devices, 16 and plasmonics. 17

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

perimental measurement of individual monomer and dimer Chl a

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

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

of reasonably accurate yet highly efficient computational methods

has hampered efforts to describe the optical absorption of large Chl-

containing biomolecules. Initial attempts to investigate the optical

absorption characteristics of biomacromolecules such as the LHC

II using first-principles electronic structure methods have helped to

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

ever the computational resources required for a complete treatment

of systems of this size lie considerably beyond what is generally

available to most researchers. 25,26

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

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

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

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

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

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

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

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

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

ods are intrinsically ill-suited to the description of isolated and/or

non-periodic systems.

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

calculations provide an attractive alternative, implementations

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

the KS orbitals 27 are both computationally expensive, and exhibit

a strong exchange and correlation (xc) functional dependence for

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

calculations require time steps much shorter than what is needed to

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

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

lated to their freedom in representing the KS wavefunctions, which

are only constrained by the grid spacing.

In this work we employ linear combinations of atomic orbitals

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

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

real time and frequency domain calculations of the optical ab-

sorption. Further, the constraints imposed by an LCAO repre-

sentation of the KS wavefunctions may be expected to improve

the stability of time-propagation TDDFT calculations, allowing

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

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

sessment and benchmarking for the fundamental functional units

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

TDDFT to the complete macromolecular system. By applying

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

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

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

applying these methods to macromolecules such as the complete

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

1

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Altogether, this suggests that for even larger systems, such as the

LHC II, we may reasonably expect LCAO-TDDFT to continue to

perform well.

In Table 1 we provide a direct comparison of the Q-band en-

ergy (transitions (i) and (ii) shown in Figures 4, S1, and S2) for

Chl a, Chl b, and (Chl a)2 obtained from photoinduced dissociation

measurements (PID), TD-CAM-B3LYP/Def2-SVP calculations of

the Casida type 37,38 using the imaginary part of the dynamic po-

larizability α(ω) ( 4πωc

Im[α(ω)]), LCAO-TDDFT-t (F {dm(t)}), and

PW-TDDFT-ω and LCAO-TDDFT-ω (Im[εm(ω)]). Overall, we

find excellent agreement between PID, LCAO-TDDFT-t, and TD-

CAM-B3LYP/Def2-SVP. In fact, our LCAO-TDDFT-t calculations

perform somewhat better than TD-CAM-B3LYP/Def2-SVP for de-

scribing the Q band energies of Chl a, Chl b, and (Chl a)2. These

results, along with its computational speed-up, provide strong mo-

tivation for the future use of LCAO-TDDFT-t to describing larger

systems such as the LHC II.

4. CONCLUSIONS

We have shown that while LCAO-TDDFT calculations in both the

frequency and real time domains are significantly faster 43,44 than

their PW-TDDFT, TD-CAM-B3LYP/Def2-SVP, and RS-TDDFT

counterparts, they also provide a similar level of accuracy to al-

ternative TDDFT methods in the description of the optical absorp-

tion spectrum of the key photosynthetic light-harvesting molecules

Chl a and Chl b and the dimeric system (Chl a)2. Specifically,

our LCAO-TDDFT-t calculations provide both a quantitative and

qualitative description of the spectra of chlorophyll monomers and

dimers, while yielding an order of magnitude speed-up compared

to RS-TDDFT-t calculations due to the increased numerical sta-

bility of LCAO-TDDFT-t. These results pave the way for future

studies applying these highly efficient and accurate LCAO-TDDFT

methods to the characterization of biomacromolecules such as the

LHC II.

ASSOCIATED CONTENT

Supporting Information

Isosurfaces of the first four transitions for charge tagged Chl a and

Chl b, total energies, and atomic coordinates of all structures.

AUTHOR INFORMATION

Corresponding Author

E-mail: duncan.mowbray@gmail.com (D.J.M.).

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS

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

zon 2020 research and innovation program under grant agree-

ment no. 676580 with The Novel Materials Discovery (NO-

MAD) Laboratory, a European Center of Excellence; the Euro-

pean Research Council (ERC-2010-AdG-267374); Spanish grant

(FIS2013-46159-C3-1-P); and Grupos Consolidados (IT578-13).

The Coimbra Chemistry Centre is supported by FCT, through the

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

007630. B.F.M. thanks the Portuguese Foundation for Science and

Technology (project CENTRO-01-0145-FEDER-000014, 2017-

2020) and the Donostia International Physics Centre for financial

support. We acknowledge computational time from the Empresa

Pública Yachay on the “Supercomputador Quinde”.

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