A density-functional-theory study of bacteriochlorophyll b

Dage Sundholm

Department of Chemistry, P.O. Box 55, FIN-00014, University of Helsinki, Finland

Received 4th June 2003, Accepted 27th August 2003First published as an Advance Article on the web 5th September 2003

The molecular structure, electronic absorption spectrum, transition-dipole-moment directions, androtatory strengths have been studied at density-functional-theory (DFT) levels for bacteriochlorophyll b ligatedwith an imidazole. In the DFT calculations, pure density functionals, i.e. functionals without Hartree–Fockexchange terms, as well as hybrid functionals were employed. The pure density functionals yielded practicallyidentical excitation energies. However, with pure density functionals spurious states with small oscillatorstrengths were obtained between the Q and B bands, whereas the electronic absorption spectra calculated usingthe popular B3LYP hybrid functional consist of less transitions and agree well with measured excitationenergies and band strengths. At the B3LYP level, the Qy , Qx , and B bands are obtained at 1.80 eV (1.56 eV);2.11 eV (2.09 eV); 3.05 eV (3.03 eV); 3.34 eV, 3.36 eV, and 3.39 eV (3.33 eV), respectively. The experimentalvalues are given in parentheses. Two weak transitions were also obtained between the Q and B bands at 2.93 eVand 3.00 eV. When the oscillator strengths are also taken into account, the B3LYP spectrum shows an almostperfect pattern, matching with the experimental spectrum; the largest discrepancy of 0.24 eV was obtained forthe first excited state. Transition-moment directions and rotatory strengths calculated at the B3LYP levelwere also found to be in close agreement with available experimental data showing that B3LYP DFTcalculations can be used for supporting the interpretation of data obtained using advanced spectroscopy onchlorophylls.

I. Introduction

Bacteriochlorophyll b molecules1,2 (see Fig. 1) play an impor-tant role in the photo-absorption processes of the photosyn-thetic unit of purple bacteria. In purple bacteria, hundreds ofbacteriochlorophylls collect light and transfer the energy tothe reaction center where it is converted into chemical energy.Most of the bacteriochlorophylls serve as light antennae,whereas the rest are involved in the transportation of the elec-tronic excitation energy by means of electron transfer. TheX-ray structure of the photosynthetic bacteria Blastochlorisviridis also called Rhodopseudomonas viridis, first reported byDeisenhofer et al.,3–5 reveals that the light collecting bacterio-chlorophyll b molecules form noncovalently linked dimers

called special pairs; the light absorption of the dimer is a co-operation of both bacteriochlorophyll molecules in the pair.The two bacteriochlorophyll molecules are juxtaposed withhistidine residues binding to the magnesium atoms from theback side of the bacteriochlorophylls. In this work, the histi-dine is modeled by a ligating imidazole. The co-operation ofthe bacteriochlorophylls in the special pair is observed in theabsorption spectrum. The first maximum in the electronicabsorption spectrum measured in vivo6 is red-shifted by ca.200 nm, as compared to the corresponding in vitro spectrum.7

The photo-absorption processes and the energy transfer reac-tions in purple bacteria have been the subject of many experi-mental6–13 and theoretical or computational14–30 studies. Acomprehensive review article with the title Photophysics ofphotosynthesis. Structure and spectroscopy of reaction centersof purple bacteria by Hoff and Deisenhofer31 contains usefulbackground information.The huge size of the photo-absorption complex still to some

extent restricts the application of accurate computationalmethods such as ab initio and density-functional-theory(DFT) methods. However, due to the recent developmentsof efficient algorithms and fast computers, DFT and ab initiocalculations can nowadays be routinely performed on singlechlorophyll molecules.32–42 Extensive ab initio and DFT calcu-lations on the special pair have already been reported43–45 andthanks to the development of new efficient computational algo-rithms also some parts of the protein surrounding the reactioncentre can, in a near future, be considered at quantum mechan-ical level in electronic structure calculations. The calculatedand observed absorption spectra for chlorophylls and chloro-phyll dimers agree qualitatively. However, a general trendhas shown that for chlorophylls significantly more excitedstates have been obtained at the DFT level than in the wave-function-based ab initio calculations.34,35,42–44 The reasonfor the discrepancies between DFT and ab initio spectra might

Fig. 1 The molecular structure of bacteriochlorophylls. For bacterio-chlorophyll b: R3 ¼ –CO–CH3 , R7 ¼ –CH3 , R8 ¼ –CH–CH3 ,R12 ¼ –CH3 , R13 ¼ –CO–O–CH3 , R17 ¼ –C2H4–CO–O–R0 (R0 isphytyl), R20 ¼ –H, and R ¼ –CH3 .

DOI: 10.1039/b306301a Phys. Chem. Chem. Phys., 2003, 5, 4265–4271 4265

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be the known DFT underestimation of the excitation energiesof charge transfer states,46–48 whereas in the ab initio cal-culations, electron correlation effects on the ground state andexcited states might be difficult to obtain accurately enough.The DFT and ab initio approaches thus each suffer from theirown difficulty, and are complementary. In the present study, afew commonly used DFT functionals were therefore employedand the obtained excitation energies were compared to energiescalculated at the coupled-cluster singles level; the more elabo-rate the approximative coupled-cluster singles and doubles(CC2) method49,50 is in principle feasible but computationallyexpensive.In experimental studies of chlorophylls, in addition to ordin-

ary electronic absorption spectroscopy, also more elaboratedspectroscopic techniques are used to obtain information aboutthe excitation process and the electron transport at the reac-tion centre. Linear dichroism (LD) measurements on orientedpigments yield information about the excitation direction, i.e.the direction of the transition dipole moment relative toa molecule-fixed coordinate system. The transition dipolemoment is related to the direction of the initial electron trans-fer. Here, DFT calculations are used for assisting the interpre-tation of the absorption spectrum of bacteriochlorophyll b,including the direction of the electronic transitions. DFT cal-culations of circular dichroism (CD) spectra for chlorophyllsare also presented. Rotatory strengths, which are related tooptical activity and circular dichroism, have been calculatedat the DFT level and they are compared to available experi-mental data. A similar DFT study on the bacteriochlorophylldimer is in progress.

II. Computational methods

The molecular structures were optimized at the density-functional-theory (DFT) level51 with the Becke–Perdew (BP)functional52–54 as implemented in TURBOMOLE.55 The electronicexcitation energies were calculated at the DFT level using thetime-dependent perturbation-theory approach (TDDFT).56,57

In the TDDFT calculations, besides the BP functional, theBHLYP (Becke’s half-and-half functional),58 BLYP,54,59

PBE,60,61 and the B3LYP59,62,63 functionals were employed.For comparison, the Hartree–Fock based linear response64

also called the random-phase approximation (RPA) and thecoupled-cluster singles50 methods were used. In DFT calcula-tions, using the pure density functionals, i.e. functionals with-out Hartree–Fock exchange terms, the resolution of theidentity (RI) approximation of Coulomb type matrix elementswas employed.51,56,57 The molecular structure was optimizedusing split-valence quality basis sets augmented with polariza-tion functions on C, N, O, and Mg (SV(P)),65 whereas in thecalculation of the electronic excitation spectra also triple-zetavalence basis sets augmented with polarization functions(TZVP)66 were used.

III. Molecular structures

The computational methods described in section II wereapplied on bacteriochlorophyll b models. The molecular struc-ture of bacteriochlorophyll b (BChl) with an axially ligatedimidazole (BChl+ I) is shown in Fig. 2 and the Cartesian coor-dinates are available on our Internet page.67 The pyrrole ringsare numbered clockwise starting from the ring with the substi-tuent –CO–CH3 and ending at the ring to which the phytylchain is attached. In the calculations, the phytyl group wasreplaced by a hydrogen. The cyclopentanone is ring V.Due to the repulsion between the imidazole and the chloro-

phyll rings, Mg is pulled ca. 32 pm out from the porphyrinplane yielding N–Mg–N angles across the porphyrin ring of

ca. 160�. The displacement out from the plane also results in3–4 pm longer Mg–N distances for BChl+ I than for BChl.The Mg–N distances are given in Table 1. Bacteriochlorophyllb without a ligating imidazole is practically planar; the twoN–Mg–N bend angles across the porphyrin are 179 and177�, respectively. In Table 1, one can also see that the BChlstructure optimized at the PM3 CI level27 significantly differsfrom the BP DFT structure.The remarkably long and short alternating C–C distances in

the cyclopentanone ring obtained for chlorophyll a34 are alsofound for BChl and BChl+ I. The C–C bond between the car-bonyl carbon (C1) and the b carbon (Cb) of ring III is only146.4 pm, which is indeed a short bond distance for a formalC–C single bond. The C–C bond between C1 and the secondcarbon of the cyclopentanone ring (C2) is 159.6 pm which isca. 6–7 pm longer than a typical C–C single bond (see Fig.2). This bond alternation introduces some double-bond char-acter into the third outer bond of the cyclopentanone ring.The rest of the bond distances, bond angles, and torsion anglesof ring V do not deviate from expected values. By protonatingthe carbonyl oxygen or by allowing a hydrogen-bond inter-action between the carbonyl oxygen and the protein, onewould expect a contraction of the bond between C1 and C2

and changes in the bond angles at C1 causing deformationsin ring V. The protonation of the carbonyl group by H3O

+

indeed affects the bond lengths of ring V. In the protonatedform, the bond lengths of the two outer bonds are 140.2 pmand 156.7 pm, as compared to 146.4 pm and 159.6 pm forthe unprotonated BChl+ I. The torsion angles of ring V werenot much affected by a hydrogen bonded H2O molecule or byprotonation.

Fig. 2 Molecular structure of bacteriochlorophyll b ligated with animidazole optimized at the BP/SV(P) level.

Table 1 Mg–N distances (in pm) obtained at the BP/SV(P) level for

bacteriochlorophyll b with and without a ligating imidazole

Bonda

DFT Structure, this workSemi empirical, PM3 CI

BChl BChl+ I Ref. 27

Mg –N(I) 204.8 208.0 237.2

Mg – N(II) 213.1 216.8 245.4

Mg – N(III) 202.8 205.5 183.2

Mg – N(IV) 217.0 220.7 182.1

Mg – N(imid.) 219.3

a For ring numbering see Fig. 2.

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IV. Electronic absorption spectra

The electronic absorption spectrum for bacteriochlorophyll bwith one ligating imidazole (BChl+ I) was studied by employ-ing a few frequently used density functionals. The results ofthis study are summarized in Table 2. The pure density func-tionals (BP, BLYP, PBE) yield identical excitation energies;the deviations are less than 0.05 eV. The excitation thresholdobtained at the RPA level is 1.07 eV and the splitting betweenthe Qy and B bands is almost 2 eV showing that the Hartree–Fock based RPA method must not be used in chlorophyll stu-dies. The excitation spectra obtained using hybrid functionals(BHLYP and B3LYP) are in rather good agreement withexperiment. As seen in Table 3, especially the B3LYP spectrumshows an almost perfect pattern, matching with experiment.The transitions with very small oscillator strengths are omittedin Table 3 (see also Fig. 3). At the B3LYP level, the strong Qy

band is obtained at 1.80 eV (1.56 eV), the excitation energy ofthe weaker Qx band is 2.11 eV (2.09 eV). The two strong Btransitions appear at 3.05 eV (3.03 eV) and 3.34 eV (3.33eV), respectively. The experimental data are given in parenth-eses. In the B3LYP calculation, two weak transitions areobtained between the Q and B bands at 2.93 eV and 3.00eV. Due to the small oscillator strengths of 0.005 and 0.05,respectively, these states cannot easily be observed in theexperiment. The B3LYP calculation also shows that the Bband indeed consists of more than two strong transitions; fourstrong and two weak transitions are obtained between 3.05 and3.39 eV. Comparison of the excitation spectra obtained at theB3LYP and BP levels shows that spurious states with smallintensities appear in the excitation spectrum when pure densityfunctionals are employed. The spurious states are clearly seenin the simulated BP DFT spectrum for BChl+ I shown inFig. 4. In addition, the B band calculated at the BP level seemsto be down-shifted by 0.3–0.4 eV as compared to the B3LYPand measured spectra. The largest discrepancy is obtainedfor the Qy band whose ground-state transition energy is 0.24eV larger than the experimental value. In Table 3, one cansee that the energies of Qy and Qx calculated using all

functionals are in qualitatively good agreement with experi-ment, whereas at the BHLYP level, the excitation energies ofthe Soret band are ca. 0.5 eV too large.The ligating imidazole has little effect on the excitation ener-

gies. The Qx band and the spurious 3A and 4A states arered-shifted by 0.05–0.10 eV. The largest differences betweenthe BChl and BChl+ I spectra appear at 3.2–3.5 eV (seeTable 4). In the third column of Table 4, excitation energiesfor BChl calculated at the coupled-cluster singles (CCS) levelare reported. At the CCS level, the lowest excitation energyis 1.80 eV which is 0.24 eV larger than experimental valuebut agrees well with the excitation energy calculated at theB3LYP level. As SV(P) is a rather small basis set forcoupled-cluster calculations, a larger basis set would probablygive a CCS excitation energy in better agreement with experi-ment. However, the excitation energies of the higher excitedstates are 0.5–1.5 eV too large indicating that more sophisti-cated coupled-cluster models have to be employed to obtainaccurate absorption spectra of chlorophylls.Solvent effects on the excitation energies of BChl have pre-

viously been studied at the ZINDO/S CIS level. In the semi-empirical calculations, Linnanto and Korppi-Tommola27

obtained solvent shifts of only 4–13 nm for the Q and the Btransitions.

V. Transition-moment directions

Every electronic excitation process is associated with a transi-tion direction. The transition-moment direction relative to themolecular frame indicates the direction of the electron transferat excitation. For oriented chlorophylls, the transition-moment directions of the excitations can be measured bymeans of linear dichroism (LD)10,31,68–70 and luminescenceexperiments.71–73 The main problem in all these measurementsis to find an accurate and well-defined reference direction.Many different experimental techniques have been used to fixthe coordinates of the molecular frame.31 Computationally,the excitation direction (transition-moment direction) relative

Fig. 3 Comparison of the absorption spectrum for bacteriochloro-phyll b calculated at the B3LYP/SV(P) level with experiment.

Table 2 Comparison of excitation energies of bacteriochlorophyll b

(BChl+ I) calculated using some commonly used density functionals.

In the molecular structure optimization and in the TDDFT calcula-

tions the SV(P) basis sets were employed

State BP BPa BLYP PBE BHLYP B3LYP RPA Exp.b

2A 1.72 1.67 1.71 1.72 1.73 1.80 1.07 1.56

3A 1.92 1.90 1.91 1.91 2.23 2.11 1.96 2.09

4A 2.07 2.13 2.10 2.05 3.41 2.93 3.72 3.03

5A 2.09 2.18 2.10 2.06 3.54 3.00 4.35 3.33

6A 2.50 2.48 2.50 2.50 3.84 3.05 4.51

7A 2.67 2.59 2.65 2.66 3.88 3.06 4.58

8A 2.77 2.74 2.76 2.77 3.91 3.25 4.67

9A 2.82 2.79 2.81 2.82 3.95 3.34 4.68

10A 2.87 2.85 2.87 2.87 3.96 3.36 4.70

11A 2.92 2.86 2.90 2.90 4.06 3.39 4.85

12A 2.94 2.94 2.96 2.93 4.20 3.51 5.01

13A 3.00 3.02 2.99 2.99 4.44 3.71 5.22

14A 3.06 3.06 3.02

15A 3.07 3.11 3.07

16A 3.16 3.20 3.17

17A 3.17 3.22 3.19

18A 3.22 3.23 3.23

19A 3.30 3.25 3.26

20A 3.34 3.29 3.29

21A 3.36 3.30 3.39

a In the TDDFT calculation, the TZVP basis sets were employed.b The experimental spectrum was recorded in ethyl ether.83 It is also

reported in ref. 27.

Table 3 Oscillator strengths ( f) of the lowest strong transitions

( f > 0.05) of BChl+ I calculated at DFT levels using the SV(P) basis

sets. The excitation energies (in eV) for BChl are given in parenthesis

f (BP) f (BHLYP) f (B3LYP) f (exp)a

0.24 (2A, 1.72) 0.39 (2A, 1.73) 0.32 (2A, 1.80) 0.35 (2A, 1.56)

0.06 (3A, 1.92) 0.07 (3A, 2.23) 0.07 (3A, 2.11) 0.08 (3A, 2.09)

0.13 (7A, 2.67) 0.78 (4A, 3.41) 0.27 (6A, 3.05) 0.23 (4A, 3.03)

0.11 (11A, 2.92) 0.19 (6A, 3.84) 0.23 (9A, 3.34) 0.25 (5A, 3.33)

0.11 (13A, 3.00) 0.60 (8A, 3.91) 0.10 (10A, 3.36)

0.05 (15A, 3.07) 0.15 (10A, 3.96) 0.23 (11A, 3.39)

0.28 (19A, 3.30) 0.10 (11A, 4.06) 0.06 (12A, 3.51)

0.16 (20A, 3.34) 0.10 (12A, 4.20) 0.05 (13A, 3.71)

a The experimental oscillator strengths are scaled to 0.25 at 360 nm.27

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to the molecular frame can easily be deduced from the threetransition-moment contributions to the oscillator strength.The transition-moment vector is defined as

~mmif ¼DCi

���xx���Cf

E~iiþ

DCi

���yy���Cf

E~jjþ

DCi

���~zz���Cf

E~kk ð1Þ

where~ii,~jj and~kk are the Cartesian unit vectors. The position ofthree atoms can be used to define a direction vector of themolecular frame. The angle between the vector of the molecu-lar reference frame and the transition-moment vector is thedirection of the transition moment. In the present calculations,the molecule-fixed coordinate system is defined as follows: thex axis is defined by the positions of the Cb atom with themethyl substituent in ring II and the Cb atom in ring IV towhich the phytyl chain is attached; the xy plane is defined bythe position of the common Cb atom of ring III and ring V;the z axis is perpendicular to the xy plane. The imidazoleN–Mg bond thus lies approximately along the negative z axis.This reference frame is one of the previously used definitions ofthe molecular coordinate system for chlorophylls.68,70,72

The transition-moment direction has not been measured forBChl, but there is strong experimental evidence that the Qy

transition is directed along the N(I)–N(III) axis.31 This direction

corresponds to an angle of about 90� which agrees well withthe current value of 93�, as obtained at the B3LYP level.The calculated transition-moment directions and the excitationwavelengths for the twelve first transitions of BChl+ I aresummarized in Table 5. The tiny z component of the transi-tion-moment vectors is omitted; all transitions are practicallyin the xy plane. The periodicity of the transition-momentdirections is 180� due to the arbitrary phases of the initialand final states.Whereas excitation directions for BChl have not yet been

verified experimentally, the transition-moment directions ofchlorophyll a have been measured by several researchgroups.68,70,72,74 In Table 6 and Table 7, calculated and mea-sured transition-moment directions are compared. The calcu-lated excitation direction of 78� for the Qy band agrees wellwith the experimental value of 70� obtained by Fragataet al.68 and by Simonetto et al..70 In the angle-resolved fluores-cence depolarization (AFD) measurements by van Zandvoortet al.,72 a somewhat larger angle of 105� was obtained. Thisvalue is also supported by the time-resolved fluorescence aniso-tropy spectroscopy measurements by Kleima et al.74 whoreported an excitation angle of 290� which corresponds to110� when the periodicity of 180� is taken into consideration.For the Qx band, the calculated transition angle is 173� atthe B3LYP level, whereas Fragata et al. reported 90� for thetransition that they assigned as C2. The experimental transi-tion direction of the C3 and C4 bands is 0� which is in agree-ment with the calculated value of 173� (or �7�) for the Qx

band. These results indicate that C2 is probably a vibronic-coupled component of the Qy transition and that C3 prob-ably belongs to the Qx band. A comparison of the calculatedand measured transition directions for the Soret band is lesstrivial. van Zandvoort et al. also reported transition directionsof 176 and 96� for two bands (s1 and s2) in the Soret region.72

The corresponding transition directions obtained in theB3LYP calculations are 126, 164, 160, 157, and 64�. Thus, inthe simulation of the AFD measurements one should considerat least three transition directions in the Soret band. The twolast values (157 and 64) correspond to the strongest transitionsof the Soret band. The calculations show that transition-moment directions calculated at the B3LYP level can assistthe interpretation of data from time-resolved fluorescenceanisotropy measurements.

VI. Rotatory strengths and circular dichroism

Circular dichroism (CD) spectroscopy which detects thedifferential absorption of left and right polarized light is an

Table 4 Comparison of TDDFT and CCS excitation energies calcu-

lated for bacteriochlorophyll b without imidazole. The BP/SV(P)

molecular structure was used. The oscillator strengths are given in

parentheses

State BP B3LYP CCSa BPb

2A 1.71(0.25) 1.79(0.33) 1.80 1.72(0.23)

3A 1.97(0.00) 2.20(0.06) 2.56 1.92(0.06)

4A 1.97(0.02) 2.93(0.00) 4.22 2.07(0.00)

5A 2.04(0.04) 2.95(0.01) 4.39 2.09(0.00)

6A 2.51(0.02) 2.96(0.01) 4.52 2.50(0.02)

7A 2.71(0.16) 3.10(0.46) 4.76 2.67(0.13)

8A 2.78(0.01) 3.26(0.08) 4.77 2.77(0.04)

9A 2.81(0.01) 3.34(0.02) 4.88 2.82(0.05)

10A 2.86(0.01) 3.40(0.24) 4.95 2.87(0.01)

11A 2.91(0.03) 3.48(0.40) 5.03 2.92(0.11)

12A 2.94(0.09) 3.57(0.08) 5.10 2.94(0.00)

13A 3.01(0.15) 3.87(0.36) 5.30 3.00(0.11)

14A 3.05(0.20) 3.06(0.01)

15A 3.07(0.00) 3.07(0.05)

16A 3.09(0.00) 3.16(0.01)

17A 3.39(0.05) 3.17(0.00)

18A 3.39(0.22) 3.22(0.00)

19A 3.47(0.16) 3.30(0.28)

20A 3.47(0.01) 3.34(0.16)

21A 3.54(0.01) 3.36(0.00)

a The oscillator strengths were not calculated at the CCS level. For

comparison, the three first excitation energies calculated by teh SAC-

CI method are: 1.52 eV, 2.34 eV, and 3.53 eV.44 b With an axially ligat-

ing imidazole.

Fig. 4 Comparison of the absorption spectrum for bacteriochloro-phyll b ligated with an imidazole calculated at the BP/SV(P) andB3LYP/SV(P) levels.

Table 5 Excitation wavelength (nm) and transition-moment direc-

tiona (�) for the lowest states of BChl+ I calculated at the BP/TZVP

and B3LYP/SV(P) levels of theory

State l BP/TZVPb l B3LYP/SV(P)b

2 A 742 89 s 690 93 s

3 A 653 158 s 589 169 s

4 A 581 73 s 424 58 s

5 A 570 123 s 413 9 s

6 A 478 106 s 406 5 s

7 A 453 176 s 405 6 s

8 A 444 89 s 381 15 s

9 A 436 76 s 371 91 s

10 A 434 170 s 369 8 s

11 A 421 160 s 366 25 s

12 A 411 16 s 353 164 s

13 A 405 143 s 334 80 s

a The definition of the coordinate system is given in the text. b The

strong transitions are indicated by s.

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important tool for obtaining chiroptical data for chloro-phylls.75–78 The optical activity measured in the circulardichroism experiments is related to the rotatory strength whichcan be calculated at the DFT level.79–82 The rotatory strengthis defined as the imaginary part of the scalar product betweenthe electric and magnetic transition-moment vectors

Rif ¼���~mmif

������~mmfi

��� cos f~mmfi ;~mmfi

� �ð2Þ

where ~mmfi is the magnetic transition moment in the gauge-inde-pendent momentum representation81,82 and ~mmfi is the electrictransition dipole moment. The transition dipole moments aregiven by

~mmfi ¼e�h

2mc

DCf

���~rr�~HH���Ci

E; ~mmfi ¼ e

DCf

���~rr���Ci

E: ð3Þ

f~mmf ;~mmfiis the angle between the transition dipole moments. The

measured intensity difference De (in dm3 mol�1 cm�1) is relatedto the rotatory strength (in cgs units) by

Rexpif ¼ 2:297� 10�39

ZDeudu:

The rotatory strengths for the visible and near-UV part ofthe electronic excitation spectrum of BChl+ I have been calcu-lated at the BP and B3LYP levels using the SV(P) and TZVPbasis sets. The calculated rotatory strengths are listed inTable 8. For the lowest states, the rotatory strengths are ratherbasis-set independent, whereas for the fourth and fifth transi-

tions significant differences in the rotatory strengths appear.For the 6th to 8th excitations the BP SV(P) and BP TZVPcalculations yield similar rotatory strengths, whereas for thehigher excited states, the rotatory strengths obtained usingthe SV(P) and TZVP basis sets significantly differ. The rotatorystrengths thus provide additional information about the inter-pretation of the absorption spectra and they are an additionalcheck of the reliability of the calculations. The simulated CDspectrum for BChl+ I are shown in Figs. 5 and 6. The rotatorystrengths obtained for the Qx and Qy bands are rather indepen-dent of the size of the basis set and of the functional used,whereas the rotatory strengths for the Soret band calculatedusing the BP and B3LYP functionals differ. In the calculatedCD spectra, one can see that the Q bands calculated at theB3LYP are blue-shifted, as compared to the BP spectrumand that the BP spectrum contains extra transitions in the vici-nity of the Soret band. Unfortunately, I have not been able tofind any experimental data for rotatory strengths of BChl+ Itransitions in the literature. However, more than 30 yearsago Houssier and Sauer75 reported circular dichroism spectraof chlorophyll a and pheophytin a. For the Qy band ofchlorophyll a and pheophytin a they obtained rotatory streng-ths of �8.7 � 10�40 cgs, and �5.2 � 10�40 cgs, respectively,as compared to the calculated values of �9.4 � 10�40 cgs

Fig. 5 Circular dichroism spectrum for bacteriochlorophyll b ligatedwith an imidazole calculated at the BP/SV(P) and BP/TZVP levels.The momentum representation has been used.

Table 8 Rotatory strength for BChl+ I (in 10�40 erg*cm3) calculated

at the BP SV(P), BP TZVP, and B3LYP SV(P) levels using the BP

SV(P) molecular structure

BP SV(P) BP TZVP B3LYP SV(P)

State l Rif(p) l Rif(p) l Rif (p)

2A 722 17.5 742 16.6 690 18.81

3A 645 �17.6 653 �11.9 589 �10.64

4A 598 �0.26 581 �0.40 424 �5.08

5A 594 �0.07 570 �3.79 413 �20.14

6A 495 1.24 501 0.58 406 �92.00

7A 465 �13.6 478 �15.0 405 68.84

8A 447 13.8 453 16.5 381 1.51

9A 439 �10.6 444 �7.9 371 9.14

10A 431 0.25 436 �14.1 369 �1.51

11A 425 �11.6 434 5.2 366 �19.14

12A 421 1.3 421 �15.6 353 5.98

13A 413 1.4 411 4.1 334 13.72

14A 405 �6.1 405 4.4

15A 404 2.2 399 �0.17

16A 392 14.9 387 �0.33

17A 391 �3.1 385 39.5

18A 386 �8.0 384 �33.3

19A 376 �25.0 382 �3.2

20A 371 �11.8 377 1.6

21A 369 �4.3 376 �34.2

22A 361 31.4 374 4.4

23A 359 2.1 370 3.9

Table 6 The first excitation energies (in eV) and the corresponding

wavelengths (l, in nm), the oscillator strengths ( f), and the transi-

tion-moment directiona (c, in degrees) for chlorophyll a calculated

at the B3LYP/SV(P) level as compared to experimental data

State Energy

Calculation Experiment 68

l f c l f b c

2 A 2.10 591 0.256 78 670 100 70

3 A 2.25 550 0.031 173 649 14 90

4 A 2.83 439 0.022 126 635 9 0

5 A 3.07 404 0.057 164 557 2 0

6 A 3.09 401 0.021 160 436 73 0

7 A 3.14 395 0.477 157 429 39 50

8 A 3.26 380 0.696 64 389 17 0

9 A 3.44 361 0.157 10 377 28 90

10 A 3.63 341 0.001 21 346 28 0

11 A 3.70 336 0.018 43

a The molecule-fixed coordinate system is defined as for BChl. b The

band strengths are normalized to 100 for the Qy band.

Table 7 Calculated transition-moment directions (in degrees) for

chlorophyll a compared to available experimental data

State Label BP/SV(P) B3LYP/SV(P) Exp. Ref.

2A Qy 76 78 This work

2A Qy 105 72

2A C1 70 68

2A Qy 70 70

2A Qy 290 74

3A Qx 177 173 This work

Q-band C2 90 68

Q-band C3 0 68

7A Bx 157 This work

8A By 64 This work

Soret C5 0 68

Soret C6 50 68

Soret Bs1176 72

Soret Bs296 72

Phys. Chem. Chem. Phys., 2003, 5, 4265–4271 4269

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�4.0 � 10�40 cgs. The good agreement between the calculatedand measured rotatory strengths for the Qy band of chloro-phyll a and pheophytin a shows that DFT calculations canindeed be useful in CD studies. The rotatory strengthsobtained for bacteriochlorophyll b, chlorophyll a, and pheo-phytin a at the B3LYP level are summarized in Table 9. Asseen in Table 9, the ligating imidazole changes the sign ofthe rotatory strength for the Qy band. Even though the ligatingimidazole has small effects on the absorption spectrum, itstrongly affects the CD spectrum. The remarkably large effectof the axial ligand on the CD spectrum might be due to the factthat the planar shape of the bacteriochlorophyll b molecule isdestroyed by the ligating imidazole.

VII. Summary

Bacteriochlorophyll b has been studied at the DFT levelemploying pure density functionals (BP, BLYP, and PBE) aswell as hybrid functionals (BHLYP, B3LYP). The BP, BLYP,and PBE functionals yield excitation energies that differ by lessthan 0.05 eV. The excitation energies of the Qx and Qy transi-tions obtained with pure density functionals agree well withexperiment, but spurious states with small oscillator strengthsappear at higher energies in these calculations.The excitation spectrum calculated at the B3LYP level

agrees well with experiment. The strong Qy , Qx , and B bandsare obtained at 1.80 eV (1.56 eV); 2.11 eV (2.09 eV); 3.05 eV(3.03 eV); 3.34 eV, 3.36 eV, and 3.39 eV (3.33 eV), respectively.The experimental values are given in parentheses. In addition,two weak transitions are obtained between the Q and B bandsat 2.93 eV and 3.00 eV. Due to the small oscillator strengths,

they probably cannot be observed in a measured spectrum.At the B3LYP level, the B band is found to consist of fourstrong and two weak transitions between 3.05 eV and 3.39 eV.Transition-moment directions have been calculated at the

BP and B3LYP level for BChl+ I and for chlorophyll a. ForBChl+ I, the excitation direction of the first transition is calcu-lated to 93�, which supports the previous notion that the Qy

transition is directed along the N(I)–N(III) axis.31 For chloro-phyll a, the calculated transition moments agree with experi-mental results of two measurements, but deviate by about30� from the experimental values obtained in two other inde-pendent measurements. The calculations show that reliableexcitation directions can be obtained at the B3LYP level, atleast for the Q bands.Rotatory strengths have been calculated for BChl, BChl+ I,

chlorophyll a, and pheophytin a. For chlorophyll a and pheo-phytin a, the rotatory strengths for the Qy transition calculatedat the BP and B3LYP levels agree well with experimental data,whereas for BChl and BChl+ I no experimental data for rota-tory strengths seem to be available. Due to the spurious statesobtained in the BP DFT and in other pure DFT calculations,the rotatory strengths calculated at these levels are less reliablethan those obtained at the B3LYP level.

Acknowledgements

We acknowledge the support from the European researchtraining network on ‘‘Molecular Properties and MolecularMaterials ’’ (MOLPROP) contract No. HPRN-2000-00013and the Academy of Finland. I also thank Prof. R. Ahlrichsfor a copy of TURBOMOLE and Dr Henrik Konschin forcomments on the manuscript.

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Fig. 6 Circular dichroism spectrum for bacteriochlorophyll b ligatedwith an imidazole calculated at the BP/SV(P) and B3LYP/SV(P)levels. The momentum representation has been used.

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10A 369 �1.5 364 8.0 341 �0.9 335 6.0

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a The experimental value is�8.7 75 b The experimental value is�5.2. 75

4270 Phys. Chem. Chem. Phys., 2003, 5, 4265–4271

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