Computational Nanochemistry Study of theMolecular Structure and Properties of Chlorophyll a

e M06 family of density functionals has been assessed for the calculation of the molecular structure and properties of the chlorophyll a molecule. Besides the determination of the molecular structures, the UV-Vis spectra have been computed using TD-DFT in the presence of a solvent, and the results were compared with the experimental data available. e chemical reactivity descriptors have been calculated through conceptual DFT. e active sites for nucleophilic and electrophilic attacks have been chosen by relating them to the Fukui function indices. A comparison between the descriptors calculated through vertical energy values and those arising from the Koopmans’ theorem approximation have been performed in order to check for the validity of the last procedure.


Introduction
e sun has been shining for some four and half a billion years and is expected to do so for as long again.It is the earth's only truly sustainable source of energy.Photosynthesis, the process by which the energy of sunlight absorbed in the chlorophyll pigments of green plants �xes atmospheric carbon dioxide (CO 2 ) to carbohydrates, supplies us directly or indirectly with all our food.e oxygen discarded by plants as part of this process replenishes the atmosphere with the oxygen humans and animals need for survival [1].Photosynthesis is by far the most spectacular physiological process in plant growth and productivity.Due to this fact, the study of photosynthesis has captivated plant physiologists, botanists, plant biologists, horticulturalists, agronomists, agriculturalists, crop growers, and, most recently, plant molecular and cellular biologists around the world [2].
A fundamental principle of photochemistry-photosynthesis is partly a photochemical reaction-is that, for light to drive a reaction, it must �rst be absorbed.is means that there must be a pigment, which is any molecule that absorbs light.Chlorophyll a serves a dual role in oxygenic photosynthesis: in light harvesting as well as in converting energy of absorbed photons to chemical energy [3].e biological importance of chlorophyll a seems obvious because it is necessary for the photochemistry in oxygenic photosynthetic organisms, with the only known exception of A. marinus which utilizes both chlorophyll d and chlorophyll a for the photochemistry [4].e aim of this work is to test the performance of the M06 family of density functionals [5][6][7] for the prediction of the infrared (IR) and ultraviolet-visible (UV-vis) spectra, the dipole moment, polarizability, and the chemical reactivity descriptors that arise from conceptual density functional theory (DFT) [8,9] for the chlorophyll a molecule.A comparison between the descriptors calculated through vertical energy values and those arising from the Koopmans' theorem approximation will be performed in order to check for the validity of the last procedure within DFT. e results will be compared with the empirical evidence available in the literature.

Theory and Computational Details
All computational studies were performed with the Gaussian 09 [10] series of programs with density functional methods as implemented in the computational package.e equilibrium geometries of the molecules were determined by means of the gradient technique.e force constants and vibrational frequencies were determined by computing analytical frequencies on the stationary points obtained aer the optimization to check if there were true minima.e basis sets used in these work were MIDIY, which is the same basis set as MIDI! with a polarization function added to the hydrogen atoms, and the DGDZVP basis set for Mg.e MIDI! basis is a small double-zeta basis with polarization functions on N-F, Si-Cl, Br, and I [11][12][13][14][15][16].
For the calculation of the molecular structure and properties of the studied systems, we have chosen the hybrid meta-GGA density functionals: M06, M06L, M06-2X, and M06HF [5], which consistently provide satisfactory results for several structural and thermodynamic properties.Solvation energies were computed by the integral equation formalism polarizable continuum model (IEF-PCM) [17], including the UAKS model and methanol as a solvent.
e calculation of the ultraviolet (UV-Vis) spectra of the studied systems has been performed by solving the time-dependent DFT (TD-DFT) equations according to the method implemented in Gaussian 09 [13,[18][19][20].e equations have been solved for 10 excited states.
e infrared (IR) and ultraviolet (UV-Vis) spectra were calculated using the SWizard program [21,22] and visualized with Gabedit [23].In all cases the displayed spectra show the calculated frequencies and absorption or emission wavelengths.
e highest-occupied molecular orbital (HOMO) and lowest-occupied molecular Orbital (LUMO) were extracted from the calculations and visualized using the Chemcra Program Revision 1.6 [24].
Within the conceptual framework of DFT [8,9], the chemical potential , which measures the escaping tendency of electron from equilibrium is de�ned as where  is the electronegativity.e global hardness  can be seen as the resistance to charge transfer: Using a �nite di�erence approximation and Koopmans� theorem [13][14][15][16], the above expressions can be written as with   being the LCAO coefficients and   the overlap matrix.e condensed Fukui functions are normalized, thus ∑    =1 and  0   [     −  2.e electrodonating ( − ) and electroaccepting (  ) powers have been de�ned as [25]: It follows that a larger   value corresponds to a better capability of accepting charge, whereas a smaller value of  − value of a system makes it a better electron donor.In order to compare   with − − , the following de�nition of net electrophilicity has been proposed [26]: that is, the electroaccepting power relative to the electrodonating power.Indeed, there exist in the literature many other methods for the computation of the chemical reactivity descriptors considered in this work [27][28][29].

Results and Discussion
e molecular structure of chlorophyll a was preoptimized by starting with the readily available PDB structure, and �nding  predicted by the different functionals for the optimized structure of the chlorophyll a molecule.However, a comparison of the results by superimposing structures reveals that there are not important differences between them.is is not surprising because modern density functionals are able to predict molecular structures with a good degree of accuracy and using low-cost basis sets.ese results are an improvement over those obtained with other low-level older density functionals [30].e situation is quite different for the prediction of the IR and UV-Vis spectra, and this could be ascribed to the different functional form of the density functionals.e infrared spectra of the chlorophyll a molecule calculated with the M06, M06L, M06-2X, and M06-HF density functionals and the MIDIY and DGDZVP basis sets are shown in Figure 2. Indeed, we should note that none of the IR spectra display a frequency value below zero or imaginary, and this means that the structures predicted by all the functionals are a minimum on the potential energy surface.e IR spectrum of chlorophyll a has been measured and elucidated more than 60 years ago [31].A comparison of the results shown in Figure 2 with those reported in Figure 1 of the mentioned article reveals that the overall shape is more or less the same, with signi�cant differences for the M06-2X and M06-HF spectra.It is well known that calculated Hartree-Fock (HF) IR spectra must be scaled to account for the effects of anharmonicity and correlation.With modern density functionals that explicitly include correlation, this scaling factor is close to 1, and this can be an indication of the goodness of a given functional.For the results presented here, it is remarkable that the M06 and the local M06L predict so well the IR spectrum of chlorophyll a. Notwithstanding, these results should be taken with care because the experimental spectrum in that paper (and also in later works) has been taken from the solid, while the present calculations have been done in the presence of methanol simulated through a polarized continuum method.It should be noticed that a recent work on the estimation of scaling factors for a large number of density functionals have shown that functionals with low percentages of HF exchange tend to predict more accurate frequencies [32].
e molecular dipole moment is perhaps the simplest experimental measure of charge distribution in a molecule.e accuracy of the overall distribution of electrons in a molecule is hard to quantify, since it involves all the multipoles.e polarizability  contributes to the understanding of the response of the system when the external �eld is changed, while the number of electrons  is kept �xed.e polarizability is calculated as the average of the polarizability tensor ⟨    +   +   .
e molecular dipole moments  (in Debye) and global polarizabilities  (in Bohr  ) of the chlorophyll a molecule calculated with the M06, M06L, M06-2X and M06-HF density functionals and the MIDIY and DGDZVP basis sets are shown in Table 1.e visible part of the electronic absorption spectrum is one of the more fascinating features of chlorophyll molecules [30].For this reason, there is a great interest in the study of photosynthetic materials for their application in organic solar cells.First, we can refer to a theoretical study of the excited states of chlorophyll a and pheophytin a using a combination of density functional theory and the multireference con�guration interaction method (DFT�M��I) [33].In a second place, there has been several interesting experimental and theoretical studies on photosynthetic materials: (i) chlorophyll a derivatives with various hydrocarbon ester groups for efficient dye-sensitized solar cells [34]; (ii) natural chlorophyll-related porphyrins and chlorins for dyesensitized solar cells [35] and (iii) to a signi�cant enhancement in the power-conversion efficiency of chlorophyll cosensitized solar cells by mimicking the principles of natural photosynthetic light-harvesting complexes.Indeed, this is a very enlightenment work, but in this study we only want to compare our results with the available experimental data for the absorption spectrum of chlorophyll a in methanol.ere is also a recent DFT benchmark calculation on the performance of density-functional-based methods in the description of some biological systems, chlorophyll a among them [36].
e absorption or UV-Vis spectra of the chlorophyll a molecule calculated with the M06, M06L, M06-2X, and M06-HF density functionals and the MIDIY and DGDZVP basis sets are presented in Figure 3. e experimental absorption spectrum of chlorophyll a in methanol has been reported [37] and displays the characteristics bands at 432 and 665 nm.All the calculated spectra have the same shape, and it is the same as for the experimental absorption spectrum.However, there is a shi in each one of the spectrum that can be related to the amount of HF exchange that it is included for every density functional considered in this study.e functional form of the M06, M06-2X and M06-HF functionals is the same, with the only difference given by the aforementioned amount of HF exchange.It is evident from the results in Figure 3 that a larger amount of HF exchange included leads to larger shis of the peaks when compared with the experimental spectrum.Notwithstanding, only the M06L density functional results are able to reproduce the experimental spectrum with a very small error for the blue band (437.4 nm) and of 38 nm for the band belonging to the maximum wavelength (627 nm).e results for the orbital transition assignments for each one of the calculations are given in Tables A3, A4, A5, and A6 of the Supplementary Materials for the interested reader.e HOMO and LUMO orbitals of the chlorophyll a molecule calculated with the M06, M06L, M06-2X, and M06-HF density functionals and the MIDIY and DGDZVP basis sets are shown in Figure 4.
e validity of the Koopmans' theorem within the DFT approximation is controversial.However, it has been shown [38] that although the KS orbitals may differ in shape and energy from the HF orbitals, and the combination of them produces conceptual DFT reactivity descriptors that correlate quite well with the reactivity descriptors obtained through Hartree-Fock calculations.us, it is worth to calculate the electronegativity, global hardness, and global electrophilicity for the studied systems using both approximations in order to verify the quality of the procedures.
e HOMO and LUMO orbital energies (in eV), ionization potentials  and electron affinities  (in eV), and global electronegativity , total hardness , and global electrophilicity  of the chlorophyll a molecule calculated with the M06, M06L, M06-2X, and M06-HF density functionals and the MIDIY and DGDZVP basis sets are presented in Table 2. e upper part of the table shows the results derived assuming the validity of Koopmans' theorem, and the lower part shows the results derived from the calculated vertical  and .
e condensed Fukui functions have been calculated using the AOMix molecular analysis program [22,39] starting from single-point energy calculations.We have presented, discussed, and successfully applied the described procedure in our previous studies on different molecular systems [40][41][42][43].
e condensed dual descriptor has been de�ned as Δ  =  +  −  −  [44,45].From the interpretation given to the Fukui function, one can note that the sign of the dual descriptor is very important to characterize the reactivity of a site within a molecule toward a nucleophilic or an electrophilic attack.at is, if Δ  > 0, then the site is favored for a nucleophilic attack, whereas if Δ  < 0, then the site may be favored for an electrophilic attack [44][45][46].e electrophilic  + and nucleophilic  − condensed Fukui functions and Δ over the atoms of the chlorophyll a molecule calculated with the M06, M06L, M06-2X and M06-HF density functionals and the MIDIY and DGDZVP basis sets are shown in Table 3. e actual values have been multiplied by 100 for an easier comparison.
e electrodonating ( − ) and electroaccepting ( + ) powers and net electrophilicity Δ ± of the chlorophyll a molecule calculated with the M06, M06L, M06-2X and M06-HF density functionals and the MIDIY and DGDZVP basis sets are presented in Table 4. e upper part of the table shows the results derived assuming the validity of Koopmans' theorem and the lower part shows the results derived from the calculated vertical  and .
e results from Table 4 clearly indicate that chlorophyll a is an electrodonating molecule, with the same result predicted by all the four density functionals considered in this study.However, only the results obtained through the calculations with the M06 and M06L density functionals are in fairly agreement between those from vertical calculations of  and  and those coming from the assumption of the validity of the Koopmans' theorem in DFT.

Conclusions
From the whole of the results presented in this contribution it has been clearly demonstrated that the sites of interaction of the chlorophyll a molecule can be predicted by using DFTbased reactivity descriptors such as the hardness, soness, and electrophilicity, as well as Fukui function calculations.ese descriptors were used in the characterization and successfully description of the preferred reactive sites and provide a �rm e�planation for the reactivity of the chlorophyll a molecule.e M06 family of density functionals (M06, M06L, M06-2X, and M06-HF) used in the present work leads to the same qualitatively and quantitatively similar description of the chemistry and reactivity of the chlorophyll a molecule, yielding reasonable results.However, for the case of the M06 and M06L functionals, the agreement between the results obtained through energy calculations and those that assume the validity of the Koopmans' theorem is fairly good.

F 1 :F 2 :
Optimized molecular structure of the chlorophyll a molecule.Infrared spectra of the chlorophyll a molecule calculated with the M06, M06L, M06-2X, and M06-HF density functionals and the MIDIY and DGDZVP basis sets.

F 3 :
Absorption spectra of the chlorophyll a molecule calculated with the M06, M06L, M06-2X, and M06-HF density functionals and the MIDIY and DGDZVP basis sets.

F 4 :
HOMO and LUMO orbitals of the chlorophyll a molecule calculated with the M06, M06L, M06-2X, and M06-HF density functionals and the MIDIY and DGDZVP basis sets.T 2: HOMO and LUMO orbital energies (in eV), ionization potentials  and electron affinities  (in eV), and global electronegativity , total hardness , and global electrophilicity  of chlorophyll a calculated with the M06, M06L, M06-2X, and M06-HF density functionals and the MIDIY and DGDZVP basis sets.e upper part of the T 1: Molecular dipole moments  (in Debye) and global polarizabilities  (in Bohr 3 ) of chlorophyll a calculated with the M06, M06L, M06-2X, and M06-HF density functionals and the MIDIY and DGDZVP basis sets.
table shows the results derived assuming the validity of Koopmans' theorem and the lower part shows the results derived from the calculated vertical  and .
T 3: Electrophilic  + and nucleophilic  − condensed Fukui functions and Δ over the atoms of the chlorophyll a molecule calculated with the M06, M06L, M06-2X, and M06-HF density functionals and the MIDIY and DGDZVP basis set.e actual values have been multiplied by 100 for an easier comparison.Electrodonating ( − ) and electroaccepting ( + ) powers and net electrophilicity Δ ± of chlorophyll a calculated with the M06, M06L, M06-2X, and M06-HF density functionals and the MIDIY and DGDZVP basis sets.e upper part of the table shows the results derived assuming the validity of Koopmans' theorem, and the lower part shows the results derived from the calculated vertical  and .