The role of high-level calculations in the assignment

The role of high-level calculations in the assignment of the Q-band spectra of chlorophyll Jeffrey R. Reimers, Zheng-Li Cai, Rika Kobayashi, Margus Rätsep, Arvi Freiberg, and Elmars Krausz Citation: AIP Conference Proceedings 1618, 18 (2014); doi: 10.1063/1.4897663 View online: http://dx.doi.org/10.1063/1.4897663 View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1618?ver=pdfcov Published by the AIP Publishing Articles you may be interested in High-sensitivity Q-band electron spin resonance imaging system with submicron resolution Rev. Sci. Instrum. 82, 043708 (2011); 10.1063/1.3581226 Optimized virtual orbital space for highlevel correlated calculations J. Chem. Phys. 86, 6314 (1987); 10.1063/1.452468 ESR dual sample cavities for Qband and for spectrometers with small magnets Rev. Sci. Instrum. 50, 425 (1979); 10.1063/1.1135844 Simple method of modulating Qband microwaves Rev. Sci. Instrum. 50, 383 (1979); 10.1063/1.1135834 Helium cooling units for X and Qband ESR spectrometers Rev. Sci. Instrum. 47, 1172 (1976); 10.1063/1.1134794

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The Role of High-Level Calculations in the Assignment of the Q-Band Spectra of Chlorophyll Jeffrey R. Reimersa, Zheng-Li Caib, Rika Kobayashic, Margus Rätsepd, Arvi Freibergd,e and Elmars Krauszf a School of Physics and Materials Science, The University of Technology, Sydney NSW Australia School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, Brisbane QLD4001, Australia c Australian National University Supercomputer Facility, Mills Rd, Canberra, ACT 0200, Australia. d Institute of Physics, University of Tartu, Riia 142, 51014 Tartu, Estonia. e Institute of Molecular and Cell Biology, University of Tartu, Riia 23, 51010 Tartu, Estonia. f Research School of Chemistry, The Australian National University, Canberra 2601, Australia.

b

Abstract.We recently established a novel assignment of the visible absorption spectrum of chlorophyll-a that sees the two components Qx and Qy of the low-energy Q band as being intrinsically mixed by non-adiabatic coupling. This ended 50 years debate as to the nature of the Q bands, with prior discussion poised only in the language of the BornOppenheimer and Condon approximations. The new assignment presents significant ramifications for exciton transport and quantum coherence effects in photosystems. Results from state of the art electronic structure calculations have always been used to justify assignments, but quantitative inaccuracies and systematic failures have historically limited usefulness. We examine the role of CAM-B3LYP time-dependent density-functional theory (TD-DFT) and Symmetry Adapted Cluster-Configuration Interaction (SAC-CI) calculations in first showing that all previous assignments were untenable, in justifying the new assignment, in making some extraordinary predictions that were vindicated by the new assignment, and in then identifying small but significant anomalies in the extensive experimental data record.

INTRODUCTION Recently, we demonstrated a new assignment of the Q-band spectrum of chlorophyll-a (Chl-a) and many other chlorophyllides.[1-3] Its key features, plus those of the previously competitive “traditional” 1960’s [4-7] and “modern” 1980’s [8-12] proposals are depicted in FIG. 1. Shown for Chl-a in ether are the observed absorption band contour ('A/Q(Q) where A is the absorption coefficient [12] and Q is frequency), reflected emission band contour (E(Q)/Q3(Q) where E(Q)=E(O)/Q2 is the emission strength [13]), and magnetic circular dichroism (MCD) band contour.[12] The Q-band is made up of two independent electronic transitions Qy and Qx, each with a dominant origin band and associated vibrational sideband tail tohigher energy; the lowest-energy band is clearly the intense Qy origin, the debated issue concerns the location of the weak Qx origin somewhere amidst the Qy sideband. As the emission is much weaker at Qy+~2000 cm-1 than is the absorption, the Qx origin is likely to be located here, [7] leading to the “traditional” assignment. MCD spectra are like absorption spectra except that Qyappears with positive signal whilst the Qx appears negative, and the relative intensity ratios (known as the “B/D ratio”) are very different for Qx and Qy.

International Conference of Computational Methods in Sciences and Engineering 2014 (ICCMSE 2014) AIP Conf. Proc. 1618, 18-22 (2014); doi: 10.1063/1.4897663 © 2014 AIP Publishing LLC 978-0-7354-1255-2/$30.00

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. FIGURE E 1. The observved absorption band contour inn Q-band (670--550 nm) regionn for Chl-a in etther is shown as a a function of frequenccy difference 'Q Q from the intennse Qy origin (bblue) where it iss compared to thhe observed em mission band con ntour reflected abouut this origin (ggreen) and the MCD M band conttour (red).

FIG. 1 loocates the moost intense neggative MCD peak p at a similar location, supporting thhe “traditionall” assignment. Howeverr, a second negative MCD peak p at Qy+~1000 cm-1 is also a apparent,, and the “moddern” assignm ment attributess this to Qx instead. IIt was propossed based onn polarized fluorescence-exxcitation specctra in diethy ylether at low w temperatuures, [8-12] and a strongly supported s by both b linear diichroism [11] and careful M MCD analyses.[12] Neitherr assignmeent could expllain the existennce of two neegative bands in the Qx regiion, however. Research prooceeded basedd on the asssumption thatt one of the tw wo options was fundamenttally correct annd that some unknown aux xiliary processs was respponsible for thhe observed anomalies, an nd for 50 years the questt was to meaasure some trruly indicativee property to resolve thee fundamentall assignment question. q In this t vein, we developed higgh-resolution spectroscopicc techniquees in 2009 and 2010 whosee results appeared consistennt with, in one case,only thhe “traditionall” assignment, [14] and in the other case,only c the “modern” asssignment (shoowing here siggnificantly thaat the emissio on spectrum iss also depressed at Qy+~1000 + cm-1). ) [13] All analyses of photosystem p function and coherence have h used thee d h “traditionnal” assignmeent, both for its simplicityy and becausee key informaation such ass the Qx/Qy dipole-strength ratios, reqquired to utilize the “moderrn” assignmennt, had never been b properly determined. Both the “traditionnal” and “moddern” assignm ments are based on the Boorn-Oppenheim mer approxim mation and thee Condon princiiple that portrray electronic spectral bandds as being dominated d by a single struccture centeredd Franck-C about thee vertical exccitation energgy,which for chlorophylls manifests as an intense oorigin plusweaak vibrationall sideband(s).Instead, ouur new assign nment, which is consistent with all know wn experimenntal data, allow ws the Qy andd d by vibronic--coupling effects that makee the electronic wavefunctioons dependentt Qx states to become sttrongly mixed m, in violation of the Born-O Oppenheimer approximation. As a resultt, for Chl-a thhe usual singlee on nucleaar momentum observedd origin+sidebbandstructure becomes b splitt into two equual-intensity origin+sideban o nd systems, with w very littlee absorptioon or emissionn occurring att the band’s acctual vertical excitation eneergy; this assiignment placees the Qx statee at Qy+~1500 cm-1, as ddepicted in FIG. 1. The connsideration off such a scenarrio was first ccontemplated by b Goutermann [5, 15] annd others in thhe 1960’s: whhile it couldacccount for the observed specctra of Chl-a, analogous speectra for otherr chlorophyyllides such asbacteriochlo a orophyll-a (BC Chl-a) and phheophytin-a (P Pheo-a) show wed only one peak whereass two woulld be expectedd. Our recent work has idenntified the misssing peaks foor all chlorophhyllides. [1, 2]] These peakss can be quuite weakand identification i required the development d o a range of new of n data-anallysis methods.. [1, 2] Our primary p intereest herein conccerns the rolee of high-levell electronic-sttructure calcullations in the establishmentt of our neew assignmentt. There are three t ways in which calculaations can reaadily contributte. First, from m a qualitativee perspectiive, calculatioons can potenttially provide alternate expplanations to thhe observatioon of two x-po olarized bandss in the MC CD results, foor example byy showing thatt a third electrronic stateis loocated near Qx. Second, caalculations cann readily predict p the banndgap 'E, a quantity q centrral to the assiggnment optionns. Finally, ccalculations can predict thee Qx/Qy dip pole-strength ratio but this aspect has noot been of greeat historical significance s aas the “modern n” assignmentt was neveer applied to yyieldthis quanttity for compaarison. Theorretical understanding of thee spectra of porphyrins p andd chlorophylls dates back tto Gouterman n’s “4-orbital”” model. [116] This conssiders only thhe two highestt occupied orbbitals and twoo lowest unocccupied ones, depicting d fourr independdent electronicc transitions Qx, Qy, and the t analogouss Soret-band components Bx and By. Higher-energy H y transitionns are known for porphyrins starting at thhe N band, buut the Soret baandshape is coomplex for chllorophylls andd the N baands have nevver been reliaably identifiedd. Early emppirical,semi-em mpirical, and ab initio mollecular-orbitall calculatioons confirmedd Gouterman’s analysis, plaacing the N bands etc. at much m higher ennergy than the Q and Sorett bands. Historically, H itt was firmly believed b that the Q bands w were isolatedd and that no other o electron nic state couldd contributte significantlyy to the two observed x-ppolarized bandds. These callculations alm most invariablygave a largee


energy gaap 'E that wo ould seem to be b consistent only with thee “traditional” assignment, tthough likely shortcomingss in the callculations werre known to ex xceed the diffferences in 'E Eas perceived by b the variouss assignments. Durin ng the 1990’s Time-Depend dent Density-F Functional Thheory (TD-DF FT) provided aan alternate paath to excited-state anaalysis, and calculations c [ [17, 18] depicted a signiificantly diffe ferent excitedd-state manifo old in which h unidentiffied electronicc states sat very close to Qx, explaining the observatio on of two x-ppolarized band ds to vindicatee the “mod dern” assignm ment.As TD-D DFT includes a much betterr description of o electron correlation than n did the olderr Hartree-F Fock-based m methods, the new results were consideered as moree reliable. H However, Mu ulti-Referencee Configurration Interacttion(MRCI)-D DFT results beecame availab ble soon afterw wards [19] wh hich predicted d a state to bee between the Q and So oret bands bu ut close to thee Soret band, more supporrting “traditioonal” analysess. As MRCI-DFTemb bodies an emp pirical enhanccement to norrmal DFT, thaat at the timee was not suppported by a wide w range off successfu ul applicationns, it was thennatural to th hink of thesee results as in nferior. Alsoo at that timee the accuratee moleculaar-orbital Sym mmetric Adaapted Clusteer-Configuration Interactio on (SAC-CI))method wass applied to o chlorophy ylls, again vin ndicating the “traditional” analysis. [20]] Searching for f answers aas to the qualiity of the TD-DFT resu ults, we meassured and analyzed oligopo orphyrin and polyacetylene p e structure andd spectra, [21, 22] pointing g out systeematic failing gs of TD-DFT T when appliied using gen neralized-grad dient approxim mation (GGA A) and hybrid d functionaals, of the typpe used prev viously for Ch hl-a. We theen showed th hat the novel low-energybaand that such h functionaals predict [17 7, 18] is in facct the N band, a band of chaarge-transfer type t that GGA A-type functio onals seriously y underestiimate in enerrgy, and that these method ds incorrectlyy predict thiss state to be the lowest-en nergy state in n PhotosysstemI. [23] Th he newly sugg gested CAM-B B3LYP densitty functional [24] [ containinng corrections for this effectt was then n programmed d [25] and deemonstrated [26] [ to provid de realistic an nswers for poorphyrins and d chlorophyllss whilst otther newly creeated function nals designed to address th he same issuess still gave thhe old failuress. All currentt high-leveel computatioonal methods thus indicatee that only Qx and Qy con ntribute signifficantly to thee spectrum off chlorophy yll in the Q-band region.

FIGURE E 2. Original SA AC-CI and SAC C-B3LYP calcu ulations using continuum solveent models appeear to support th he “traditional”” assignmentt but cannot inteerpret observed d large explicit solvation s effectts.

LYP/6-31G* aand SAC-CI/6 6-31G* to calculate the ban nd gap 'E and d Betweeen 2005 and 2007 we applliedCAM-B3L thus disccriminate bettween the “trraditional” an nd “modern” assignments. Calculationns were perfo ormed for 34 4 chlorophy yllide-solventt combination ns, initially usiing continuum m dielectric solvation modells. Apparently y good resultss were obtaained, as illussrtated in FIG. 2, but these were misleadding as the coo ordinaton of thhe magnesium m atom can bee either fiv ve-coordinate (5CO) or six x-coordinate (6 6CO) [27, 288] and the corrresponding laarge change in n'Ecannot bee accounted for. This leed us to consiider chlorophy yllide-solvent complexes. Unfortunately U y, the extremee truncation off integrals required to make m SAC-CI calculations feasible f introd duced errors th hat were of thhe order of thee effects being g investigaated, leaving only CAM-B B3LYP as a viable comp putational meethod. Resuults for expliccitly solvated d moleculees in addition n to a surroun nding dielectrric continuum m model are shown s in FIG G. 3, though we w found thatt dielectricc solvation had an insignificcant effect on n explicitly sollvated chlorop phyllides and so for simpliccity published d previouslly only resultss for gas-phasse complexes.. [1] Again thhe “traditional””assignment sshows a generral correlation n with CAM M-B3LYP bu ut the data can n be blocked into groups that t behave qu uite differentlly. The insertt in the figuree highlightts this, considdering the chaange in 'Eon lowering the temperature,converting 5C CO species in nto 6CO ones. This is a property thaat the calculattions would be b expected tto describe well, w yet there is no correlaation with thee


“traditional” assignment. These aspects again reoccur for the “modern” assignment. However, good agreement is found with our new vibronic-coupling assignment, although free-basechlorophyllides (e.g., pheophytins) appear displaced by 1000 cm-1 from metal-containing analogues, and the slopes of the lines of best fit are near 0.75 instead of unity. These differences are attributed to unknown shortcomings of CAM-B3LYP.

FIGURE 3. CAM-B3LYP calculated Qx-Qy band gaps 'E are compared to observed values based on the “traditional”, “modern”, and our new vibronic-coupling assignment of chlorophyllide spectra. Red- 6CO species, blue- 5CO species, greenfree-base species. The inserts show the changes in 'E (scale -2000 to 0 cm-1) from 6CO to 5CO species in the same solvent.

When the CAM-B3LYP calculations were completed in 2007,results were difficult to interpret as it was unknown as to whether or not the method had delivered the required quantitative accuracy. In the following years we demonstrated that CAM-B3LYP could predict the exciton couplings and energy dispersion amongst chlorophylls in Photosystem-I using coordinates from a PW91/6-31(+)G* optimization of the 150000-atom photosystem trimer, [29] suggesting that the Qy band is described well. [30] Later we also showed that it could predict and interpret the unexpected large asymmetry between absorption and emission observed for BChl-a, [31] indicating that CAMB3LYP gives a good representationQyas a function of Condon-allowed nuclear coordinates. These results suggested that the CAM-B3LYP results for 'E were reliable, highlightingthe need for a new assignment. While the results shown in FIG. 3 then provided strong theoretical endorsement for the new assignment, even more important results turned out to be the prediction of a 7-fold variability in the relative Qx intensity, a completely unforeseen property that emerged during the spectral fitting to the vibronic-coupling model that was initially interpreted as arising from a flawed assignment. [1] Also, spectroscopic data in ether was initially highly inconsistent with the CAM-B3LYP predictions, leading to the discovery that 30 years of critical data had been compromised (to a small but significant extent) through trace water contamination.[3] In conclusion we see that the availability of high-quality calculated data contributed significantly to the understanding that a new assignment was required, and thenwas essential to the establishment of its legitimacy. The assignment not only explains all available experimental data but is also consistent with basic theory. It was only because a wide range of experimental and theoretical data was available that the assignment could be made.

ACKNOWLEDGMENTS We thank the Australian Research Council, National Computational Infrastructure, Intersect, the Estonian Research Council (grant IUT02-28) for supporting this work.

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