Chemical Physics Letters 472 (2009) 243–247

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Chemical Physics Letters

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Six-coordination in Chlorophylls: The fundamental role of dispersion energy

A. Ben Fredj a,b, Z. Ben Lakhdar a, M.F. Ruiz-López b,*

a Laboratoire de Spectroscopie Atomique, Moléculaire et Applications, Faculté des Sciences de Tunis, 1060 Tunis, Tunisiab Equipe de Chimie et Biochimie Théoriques, SRSMC, Nancy-University, CNRS, BP 239, 54506 Vandoeuvre-lès-Nancy, France

a r t i c l e i n f o

Article history:Received 24 January 2009In final form 11 March 2009Available online 14 March 2009

0009-2614/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.cplett.2009.03.025

* Corresponding author. Fax: +33 383684371.E-mail address: Manuel.Ruiz@cbt.uhp-nancy.fr (M

a b s t r a c t

Though protein embedded Chlorophylls almost exclusively exhibits five-coordination of the Mg atom,six-coordination has been well established in some solvents. The factors governing the coordinationnumber are uncertain since insufficient thermodynamic data are available. To investigate this biologicallyimportant question, we report calculations on mono and diaxial coordination of pyridine and water toMg-porphyrin using MP2 and density functional (corrected for dispersion) methods. In agreement withexperiments, binding of a second axial ligand is exergonic for pyridine but not for water; the large valueof the dispersion energy in the first case is found to be the key factor.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

Chlorophylls are essential pigments involved in the primarystages of the photosynthesis, i.e. in the conversion of solar energyto chemical energy by green plants, algae and cyanobacteria. All ofthem are characterized by the presence of a modified porphyrinmacrocycle, with a central Mg ion bonded to four pyrrole rings.The determination of Chlorophylls structure within their complexprotein environment is a vast challenge and a field of intenseinvestigation since it represents a key step towards the under-standing of the photosystems machinery.

In Chlorophyll proteins, the Mg atom exhibits almost exclu-sively pentacoordination [1,2]. The fifth axial ligand may be a pro-tein residue (His, Asp/Glu, Asn/Gln, for instance) or a watermolecule. Water would provide an important stabilizing factorin the special Chlorophyll pairs P700 and P680 according to clas-sical models [3–6]. Six-coordination in vivo seems to be prohib-ited, as long as no unambiguous evidence has yet been reported(note however than some recent experiments point towards thepossible existence of such a coordination mode [7]). This is anintriguing question since the hard Mg2+ ion tends to adopt six-coordination, for example in aqueous environments [8–10]. More-over, five- or six-coordination of Chlorophylls (usually Chloro-phyllides) in solution is well documented and has beeninvestigated with a large variety of experimental techniques[11–18]. Thus, in solvents such as diethylether or acetone, Mg ispentacoordinated with a single solvent molecule occupying theaxial position. In other solvents such as pyridine, dioxane orTHF, Mg adopts six-coordination. Concomitant with studies ofChlorophylls in solution, there has been a considerable amountof work devoted to investigate the self-assembly of Chlorophyll

ll rights reserved.

.F. Ruiz-López).

monomers in aqueous media (see [12,19–21] and references citedtherein). Axial coordination plays a key role here since aggrega-tion results from monomer interactions linked by water mole-cules. It is worth mentioning that crystal structures of Mg-porphyrins usually exhibit four- or five-coordination but thestructure of a six-coordinated complex with two axial pyridinehas been solved [22,23].

The reasons for five- or six-coordination of Chlorophyllsdepending on chemical environment remain unclear. In fact,despite its considerable biological relevance, the energetics of axialcoordination to Chlorophylls has deserved little attention in the lit-erature, nonetheless some experimental [17,11,24] and theoretical[25–29] works have been carried out. In a recent experimentalstudy, Kania and Fiedor [11] have obtained thermodynamicparameters for the second axial binding of various types of ligands(acetone, dimethylformamide, imidazole, and pyridine) to diaste-reoisomeric Bacteriochlorophylls from van’t Hoff’s plots. They haveshown that at ambient temperature, spontaneous six-coordinationof Mg occurs for imidazole and pyridine only. The free energy forsecond axial coordination of pyridine in acetonitrile solution isabout �0.9 kcal mol�1. Due to significant entropic terms, DG�becomes positive for second ligation of acetone or dimethylform-amide. The authors have given an interpretation of Mg coordina-tion in prophyrins in terms of the modification of the Mg2+ ionhardness through coordination to tetrapyrrole. There are also anumber of experimental studies on Mg-porphyrin complexes withaxial ligands. Most relevant for the purpose of the present investi-gation are those of Lebedeva et al. [30] and Kadish and Shiue [31]on pyridine complexes.

Quantum mechanical calculations on Chlorophylls and Bacte-riochlorophylls have been reviewed by Linnanto and Korppi-Tom-mola [26]. These authors have also reported results for a 1:2complex with acetone at the B3LYP/6-31G(d) level and a 1:2 com-plex with pyridine at the semiempirical PM5 level. However, no

244 A. Ben Fredj et al. / Chemical Physics Letters 472 (2009) 243–247

details on binding energies and thermodynamic quantities havebeen discussed. Élkin et al. [27] have reported a theoretical studyon first axial coordination of the imidazole molecule to either Mg-porphyrin or Mg-chlorin (B3LYP/6-31G(d) level). The authors re-ported free energies of �3.6 kcal mol�1 and �3.4 kcal mol�1 forMg-porphyrin or Mg-chlorin respectively. Heimdal et al. [25] havestudied axial ligation of Chlorophyll and Bacteriochlorophyll foreleven different ligands (including water and imidazole). Diaxialcoordination was studied for imidazole only. Energy calculationshave been carried out at the B3LYP/6-311+G(2d,2p) level on opti-mized geometries at the BP86/6-31G(d) level. The interactionenergy for the second ligation of imidazole in gas phase waspredicted to be about �3.5 kcal mol�1. This energy is rather smalland incorporation of thermal energies and entropy (estimated bythe authors to 7–17 kcal mol�1) would make second coordinationof imidazole clearly unfavorable. To the best of our knowledge,the only thermodynamically stable diaxial complex has been re-ported in our preceding study [29] for Chlorophyllide–water.However, second axial binding was predicted to be slightly exer-gonic and taking into account the simple theoretical approachused (B3LYP/6-31G(d) calculations without correction for basisset superposition errors) we could not provide a definitive conclu-sion on the thermodynamic stability of the six-coordinatedcomplex.

The objective of the present work has been to get a deeper in-sight on axial ligation thermodynamics to Mg in Chlorophylls.We have carried out quantum chemical calculations at the densityfunctional theory (DFT) and ab initio levels for complexes of Mg-porphyrin (MgP) with pyridine or water (Fig. 1). MgP is the sim-plest Chlorophyll model since electron delocalization associatedto the macrocycle is taken into account. As noted above, it has beenshown than porphyrin and chlorin rings lead to similar axial coor-dination energetics [27]. This point will be further commented be-low on the basis of calculations for a more elaborated Chlorophyllmodel. Pyridine and water ligands have been selected for compar-ison since they are known to present different coordination modeswith Mg-porphyrins: six-coordination for pyridine [22], five-coor-dination for water [32]. Interestingly, these ligands display similarpolarity (l = 2.21 D and 1.85 D for pyridine and water in gas phase,respectively) and therefore electrostatic interactions with MgP arenot expected to differ much.

Fig. 1. Mg-porphyrin (MgP) and schematic axial complexes with one or two pyridine moalso been studied.

2. Calculations

Basically, previous theoretical studies on Chlorophyll modelsand Mg-porphyrins have been carried out at semiempirical andDFT levels. Semiempirical methods do not provide accurate resultswhereas DFT calculations, which usually represents a good com-promise between accuracy and computational cost, suffers fromthe poor description of van der Waals interactions [33]. Some abinitio calculations at the Hartree–Fock (HF) level have been re-ported too (for a review, see [26]) but the neglect of electronic cor-relation cannot be expected to provide good interaction energies.Correlated ab initio calculations are very scarce due to high com-putational cost and have been limited to study some specific prop-erties. We have to mention the MP2 study by Wu et al. [23] on25Mg quadrupole parameters for a bis(pyridine) Mg-porphyrinusing crystallographic data.

In order to reach a sufficiently high accuracy on interactionenergies, methods beyond HF and standard DFT have to be used.In the present study, two main approaches have been envisaged.First, ab initio calculations at the MP2 level have been carriedout. More accurate correlated methods such as CCSD(T) or QCISDwere computationally unaffordable for the systems studied here.We use a composite approach. Geometry optimization is carriedout at the MP2/6-31G(d) level and afterwards single-point energycalculations are done at the MP2/6-311++G(2d,2p) level. For com-parison, HF results are also reported.

Second, DFT calculations have been carried out. In order toincorporate the dispersion contribution to the interaction energy,we have used the recently developed DFT+D computationalscheme [34,35] which is based on the use of a parameterized pair-wise-additive term, following related procedures in Hartree–Fock[36,37] and semiempirical [38–40] methods. As for MP2 calcula-tions, we use a composite approach. Geometries have been opti-mized using the widespread B3LYP hybrid exchange-correlationfunctional [41] and the 6-31G(d) basis set. Afterwards, single-pointenergy calculations are performed using the 6-311++G(2d,2p) basisset. Other exchange-correlation functionals have been used forcomparison and results will be commented briefly. Finally, thecomputed DFT interaction energies are corrected by adding anintermolecular dispersion term (we assume intramolecular termsto neglect in complex formation processes):

lecules. Similar complexes with water molecules (MgP–H2O and MgP–(H2O)2) have

A. Ben Fredj et al. / Chemical Physics Letters 472 (2009) 243–247 245

E ¼ EDFT � s6

Xi2A

Xj2B

Cij6

R6ij

fdmpðRijÞ ð1Þ

with

Cij6 ¼

ffiffiffiffiffiffiffiffiffiffiffiCi

6Cj6

qð2Þ

In these expressions, s6 is a global scaling factor, Cij6 is the dispersion

coefficient for the atom pair i (on molecule A) and j (on molecule B)and fdmp is a damping function

fdmpðRijÞ ¼1

1þ e�dðRij=Rr�1Þ ð3Þ

where Rij is the interatomic distance, d is a parameter and Rr repre-sents the sum of atomic van der Waals radii Ro. Parameters in ourcalculations have been taken from [34] and are summarized inTable 1.

Several conformations can be envisaged in some cases (in par-ticular for six-coordinated complexes); they have been consideredto start the geometry optimizations but we only report the moststable one for each complex. Interaction energies have been cor-rected for Basis Set Superposition Error (BSSE) using the counter-poise method [42]. Vibrational frequencies have been computedat the B3LYP/6-31G(d) level in order to estimate thermodynamicquantities using the ideal gas approximation (zero-point energy,thermal corrections to enthalpy, entropy). Frequency computa-tions at the MP2 level were not possible due to computational lim-itations; hence, MP2 free energies have been obtained using thethermodynamic corrections at the DFT level, which is a commonapproximation. Some calculations at the B3LYP/6-31G(d) levelhave also been done for a complex consisting of a model Chloro-phyll and one or two pyridine molecules. Net atomic charges, bondorders and charge transfer have been obtained using natural pop-ulation analysis [43]. All calculations have been carried out withthe GAUSSIAN 03 program [44].

3. Results and discussion

Main structural parameters for the studied complexes (Fig. 1)are shown in Table 2. Full geometries are provided as Supplemen-tary material (Table S1). Distances are comparable to availablecrystallographic data for bis(pyridine) Mg-porphyrin (dMg–N(pyr) =

Table 1Parameters from Ref. [34] used here to evaluate the dispersion energy correction toB3LYP interaction energies. C6 parameters in J nm6 mol�1, van der Waals radii Ro in Å.The other parameters used in the DFT+D method are s6 = 1.05 and d = 20.

Element C6 Ro

H 0.14 1.001C 1.75 1.452N 1.23 1.397O 0.70 1.342Mg 5.71 1.364

Table 2Structural parameters for optimized complexes of MgP with pyridine and water at the Batomic charge (qMg) and charge transfer (Dq) in atomic units. X represents the N or O atomaverage plane of the four N pyrrole atoms. HF values correspond to calculations using Ha

dMg-plane dMg–X BM

B3LYP MP2 B3LYP MP2 B3

MgP–Pyr 0.346 0.299 2.249 2.201 0.0MgP–(Pyr)2 0.0 0.0 2.444 2.316 0.0MgP–H2O 0.259 0.275 2.161 2.148 0.0MgP–(H2O)2 0.0 0.0 2.243 2.221 0.0

2.389 Å [22] or 2.369 Å [23]) and water Mg-porphyrin complexes(dMg–O = 2.097 Å and dMg-plane = 0.273 Å [32]). The agreement be-tween B3LYP and MP2 results is reasonably good though thereare some significant differences; for example, the Mg–X distancein the MgP–(Pyr)2 complex is 0.12 Å longer in B3LYP calculations,and the Mg net charge is systematically smaller when computedwith this method. The predicted changes in going from five- tosix-coordinated complexes are as expected: the Mg atom comesinto the plane, the Mg–X distances increase and the correspondingbond orders decrease.

Table 3 summarizes energy results at different computationallevels for the following processes (further details on energeticscan be found in Table S2, Supplementary material):

MgPþ Pyr!Mg� Pyr ð1� PyrÞMgP� Pyrþ Pyr!Mg� ðPyrÞ2 ð2� PyrÞMgPþH2O!Mg�H2O ð1�H2OÞMgP�H2OþH2O!Mg� ðH2OÞ2 ð2�H2OÞ

As shown, there are quite large differences between the methods.Especially striking is the disparity between B3LYP and MP2 ener-gies, the latter being significantly larger in absolute value. This sug-gests that dispersion energy represents an important component ofthe interaction energy in these complexes, as confirmed by lookingat the values of dD and dcorr in Table 3. Indeed, when corrected fordispersion, the B3LYP binding energies become quite similar tothose predicted by MP2. Other important remarks need to be made:

– dispersion (or equivalently, correlation) contributions aresignificantly higher for pyridine complexes,

– at the HF or B3LYP levels (dispersion effects neglected), sec-ond coordination processes are predicted to be not muchfavorable, with water more favorable than pyridine,

– conversely, at the B3LYP+D or MP2 levels (dispersion effectsincluded), second coordination processes are predicted to bequite favorable, with pyridine more favorable than water.

We have tested the influence of the exchange-correlation func-tional on the results by carrying out similar calculations for pyri-dine complexes with other methods, namely, PBE1PBE [45] andB97-1 [46,47]. The latter has been shown to be one of the DFTmethods that give the best performances for weak interactions innon-bonded complexes [48]. The computed interaction energiesincrease by 2–3 kcal mol�1 (in absolute value) with respect toB3LYP results but remain far from MP2 predictions (see Supple-mentary material Table S2). One might wonder also whether differ-ences on B3LYP and MP2 optimized geometries could beresponsible for differences in interaction energy. To check thispoint, MP2 calculations using B3LYP geometries, and inversely,B3LYP calculations on MP2 geometries have been carried out forall the complexes. The influence of the geometry on the complexformation energetics is: dDEg = |DE(A,B) � DE(A,A)|, where DE(X,Y)means that the binding energy is computed with method X usingthe geometries optimized with method Y. The average dDEg is

3LYP/6-31G(d) and MP2/6-31G(d) levels. Distances (d) in Å, bond orders (B), Mg netin the axial ligand. The distance dMg-plane represents the distance of the Mg atom to thertree–Fock densities on MP2 optimized geometries.

g–X qMg Dq

LYP HF B3LYP HF B3LYP HF

78 0.064 1.694 1.754 0.035 0.03155 0.054 1.698 1.736 0.053 0.05477 0.062 1.691 1.757 0.035 0.03067 0.055 1.684 1.742 0.061 0.054

Fig. 2. Model of Chlorophyll-a considered in this work.

Table 3Energetics (kcal mol�1) for axial binding processes of pyridine and water to MgP.Energy calculations using the 6-311++G(2d,2p) basis set, corrected for BSSE, ongeometries optimized using the 6-31G(d) basis set. HF values correspond to Hartree–Fock calculations on MP2 optimized geometries. The dispersion and correlationcontributions to the reaction energy are represented by dD and dcorr respectively.

DEDFT DEab initio

B3LYP B3LYP+D dD HF MP2 dcorr

1-Pyr �12.8 �24.7 �11.9 �10.7 �23.5 �12.82-Pyr �2.0 �13.6 �11.6 2.6 �16.7 �19.31-H2O �9.5 �15.8 �6.3 �8.9 �12.9 �4.02-H2O �3.8 �10.4 �6.6 �1.4 �8.3 �6.9

246 A. Ben Fredj et al. / Chemical Physics Letters 472 (2009) 243–247

found to be as small as 0.4 kcal mol�1, and in all casesdDEg < 1 kcal mol�1 (see Supplementary material, Table S2).

Though neither B3LYP+D (which includes parameterized terms)nor MP2 (which lacks a substantial part of correlation contribu-tions) can be considered as benchmark results, the preceding anal-ysis clearly indicates that standard DFT energy calculations onaxial ligation to Mg-porphyrins cannot be regarded with confi-dence. These findings lead to the conclusion that DFT methods,which are widely used to model Chlorophyll systems, have to behandle with special care. In principle, satisfactory results may beexpected for equilibrium geometries, and probably for physicalproperties such as IR and UV spectra. In contrast, substantial errorsshould be present on interaction energies if no explicit correctionfor dispersion forces is introduced.

Let us know discuss free energies. As said, we have consideredin all cases the ideal gas approximation using the contributionsfrom the B3LYP/6-31G(d) calculations gathered in Table 4. Resultsfor free energies are summarized in Table 5 for different methodsand processes. Entropy contributions are significant and opposecomplex formation, as expected. Our values are close to those re-ported by Élkin et al. [27] for imidazole ligation to Mg-porphyrinand Mg-chlorin. Experimentally, large entropy effects have beenreported [11] for the second coordination of ligands to Bacterio-chlorophylls though those experimental values cannot be directlycompared to ours due to the role of solvation, which is importanton Chlorophyll–ligand interactions [25,29].

Table 4Changes in zero-point energy (DZPE), thermal contribution to enthalpy at 298.15 K(DdY298) and entropy (DS) for first and second axial coordination of pyridine andwater to MgP. Calculations at the B3LYP/ 6-31G(d) level. Energies in kcal mol�1,entropy in cal mol�1 K�1.

DZPE DdY298 DS

1-Pyr 0.7 0.6 �37.22-Pyr 0.5 0.6 �35.91-H2O 1.6 �0.2 �29.52-H2O 1.8 �0.5 �33.5

Table 5Free energies at 298.15 K for first and second axial coordination of pyridine and waterto MgP using energies from Table 3 and thermodynamic contributions from Table 4.HF values correspond to Hartree–Fock calculations on MP2 optimized geometries.Values in kcal mol�1.

DGDFT DGab initio

B3LYP B3LYP+D HF MP2

1-Pyr �0.4 �12.3 1.7 �11.12-Pyr 9.8 �1.8 14.4 �4.91-H2O 0.7 �5.6 1.3 �2.72-H2O 7.6 1.0 10.0 3.1

Free energies at 298.15 K in Table 5 are noteworthy. Theyclearly show that the HF method is unable to predict spontaneouscoordination of either pyridine or water to MgP, all free energiesbeing positive. The results are quite similar for the standardB3LYP method though in this case free energy for the first coordi-nation to pyridine is slightly negative. When methods incorporat-ing dispersion (B3LYP+D, MP2) are used, free energies decreasealgebraically, both methods predicting similar trends. First coordi-nation becomes highly exergonic for pyridine and to a less extent,also for water. Second coordination of pyridine is also significantlyexergonic but remains endergonic for water. The experimental freeenergy reported by Kania and Fiedor [11] for second coordinationof pyridine in acetonitrile is about �0.9 kcal mol�1. Consideringthe differences in both, systems (MgP instead of Bacteriochloro-phyll) and conditions (gas phase vs acetonitrile solution), theagreement between our theoretical value and the experimentalone can be considered as satisfactory. In the case of water, our pre-dicted positive free energy for second axial binding is consistentwith experimental facts, since any six-coordinated complex withwater has been observed (existence of a possible biligated Chloro-phyll-a species in n-octane solution has been invoked however[49]).

Finally, in order to test whether or not our results for MgP canbe extrapolated to Chlorophylls we have carried out a calculationfor a Chlorophyll-a model in which all groups are included exceptthe phytyl ester side chain, which is replaced by a methyl group(Fig. 2). We have computed the interaction energy in complexeswith one or two pyridine molecules. First coordination to Mg is as-sumed to occur on the syn periplanar position with respect to theester group, which has been found to be the preferred one in thecase of water coordination [25–29]. For simplicity, and consideringthe large system size, calculations have been only done at theB3LYP+D level using the 6-31G(d) basis set. The energetics is sum-marized in Table 6. All quantities are relatively close to those pre-sented above for the MgP molecule and therefore similarconclusions for pyridine coordination can be derived. In particular,

Table 6Energetics at 298.15 K for first and second axial coordination of pyridine to theChlorophyll-a model in Fig. 2 at the B3LYP+D level using the 6-31G(d) basis set.Energies in kcal mol�1, entropy in cal mol�1 K�1.

DEB3LYP DEB3LYP+D DZPE DdY298 DS DG

1-Pyr �13.8 �27.2 0.8 0.6 �37.2 �14.72-Pyr �1.8 �14.1 0.5 0.7 �37.6 �1.8

A. Ben Fredj et al. / Chemical Physics Letters 472 (2009) 243–247 247

the negative value of free energy for the second coordination pro-cess corroborates the trend of Mg atom to be six-coordinated withtwo axial pyridine molecules.

4. Conclusions

The present study demonstrates that London forces play anessential role in the interaction of MgP with axial ligands. In partic-ular, second ligation of Mg cannot be correctly described if disper-sion energy is neglected. This can explain why previous theoreticalstudies carried out with standard DFT techniques have failed topredict thermodynamically stable diligated systems. The differentcoordination modes experimentally found for pyridine (six-coordi-nation) and water (five-coordination) are attributed to the consid-erably higher dispersion energy in the first case. With these resultson hand, a comprehensive theoretical modeling of the influence ofprotein or solvent environments on axial Mg ligation in Chloro-phylls becomes feasible. Work in this direction is in progress.

Acknowledgements

The authors thank the French CINES for providing computa-tional facilities as well as the DGRSRT and CNRS for financial sup-port. ABF thanks the IDB (Islamic Development Bank) for a one-year grant supporting her stay in Nancy.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.cplett.2009.03.025.

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