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E = E[ρ]. ��

" QIZTJDBMMZ JOUVJUJWF BSHVNFOU BT UP XIZ UIF FMFDUSPO EFOTJUZ NBQT UP UIF FMFDUSPOJD FOFSHZXBT GPSNVMBUFE CZ &� #� 8JMTPO�� XIP TUBUFE UIBU UIF JOUFHSBM PG UIF EFOTJUZ ZJFMET UIF OVNCFSPG FMFDUSPOT XIJMF DVTQT JO UIF EFOTJUZ EFmOF CPUI UIF QPTJUJPOT BOE DIBSHFT PG UIF OVDMFJ�6OGPSUVOBUFMZ UIF FYBDU GVODUJPOBMf UIBU ZJFMET UIF DPSSFDU FMFDUSPOJD FOFSHZ JT VOLOPXO�

ɧF ,PIO�4IBN GPSNVMBUJPO

*O QSJODJQMF POF DPVME QFSGPSN %'5 DBMDVMBUJPOT GPS XIJDI UIF DPNQVUBUJPOBM FĊPSU JT JOEF�QFOEFOU PG UIF TJ[F PG UIF TZTUFN� *O QSBDUJDF IPXFWFS UIFTF QVSF PS PSCJUBM�GSFF %'5 NFUIPETBSF OPU ZFU BDDVSBUF FOPVHI GPS CJPDIFNJDBM DPNQVUBUJPOT NBJOMZ EVF UP UIF MBSHF VODFSUBJOUZJO DBMDVMBUJOH UIF LJOFUJD FOFSHZ� ɨF LFZ UP VTF %'5 JO DPNQVUBUJPOBM DIFNJTUSZ XBT UIF TVH�HFTUJPO NBEF CZ ,PIO BOE 4IBN�� UP SF�JOUSPEVDF PSCJUBMT BOE UP DBMDVMBUF UIF LJOFUJD FOFSHZGPS B mDUJUJPVT TZTUFN XIFSF UIF FMFDUSPOT BSF OPO�JOUFSBDUJOH CVU XIPTF EFOTJUZ JT UIF TBNF BTUIF FYBDU EFOTJUZ� 6TJOH UIF ,PIO�4IBN ,4 BQQSPBDI UIF FOFSHZ GVODUJPOBM DBO CF XSJUUFOBT

E[ρ] = T4[ρ] + EOF[ρ] + J [ρ] + EYD[ρ], ��

XIFSF T4[ρ] JT UIF FYBDU LJOFUJD FOFSHZ GPS UIF OPO�JOUFSBDUJOH TZTUFN EOF[ρ] JT UIF DPVMPNCJDBUUSBDUJPO CFUXFFO UIF FMFDUSPOT BOE UIF OVDMFJ BOE J [ρ] JT UIF BWFSBHF SFQVMTJPO CFUXFFO FMFD�USPOT� ɨFTF mSTU UISFF UFSNT DBO CF DBMDVMBUFE FYBDUMZ BOE EJSFDUMZ BOBMPHPVTMZ UP )' UIFPSZ XIJMF BMM SFNBJOJOH DPOUSJCVUJPOT J�F� DPSSFDUJPOT UP UIF LJOFUJD FOFSHZ BT XFMM BT FYDIBOHF BOEEZOBNJD DPSSFMBUJPO FĊFDUT BSF MVNQFE JOUP UIF FYDIBOHF�DPSSFMBUJPO GVODUJPOBM EYD[ρ]�

EYD[ρ] = (T [ρ]− T4[ρ]) + (EFF[ρ]− J [ρ]), ��

XIFSF T [ρ] JT UIF LJOFUJD FOFSHZ GPS UIF SFBM JOUFSBDUJOH TZTUFN BOE EFF[ρ] JT UIF FYBDU FMFDUSPOJDSFQVMTJPO�

fɨF UFSN GVODUJPOBM SFGFST UP B GVODUJPO PG BOPUIFS GVODUJPO� *O UIJT DBTF UIF FOFSHZ JT B GVODUJPO PG UIFFMFDUSPO EFOTJUZ XIJDI JT B GVODUJPO PG UIF TQBUJBM DPPSEJOBUFT�

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" IJFSBSDIZ PG GVODUJPOBMT

ɨF NZSJBE EJĊFSFOU GVODUJPOBMT UIBU FYJTU UPEBZ EJĊFS POMZ JO UIF GPSN PG UIF FYDIBOHF�DPSSFMB�UJPO GVODUJPOBM XIJDI JT VTVBMMZ GVSUIFS EJWJEFE JOUP BO FYDIBOHF QBSU BOE B DPSSFMBUJPO QBSU�0OF PG UIF NBJO ESBXCBDLT PG %'5 JT UIBU UIFSF JT OP DMFBS TZTUFNBUJD XBZ UP JNQSPWF UIFBDDVSBDZ PG UIF GVODUJPOBM� ɨFSF JT IPXFWFS B DPNNPOMZ BDDFQUFE IJFSBSDIZ BNPOH EJĊFSFOUGVODUJPOBM UZQFT� ɨJT IJFSBSDIZ JT PGUFO UFSNFE +BDPC�T MBEEFS PG GVODUJPOBMT��

'PS GVODUJPOBMT XPSLJOH VOEFS UIF MPDBM�EFOTJUZ BQQSPYJNBUJPO -%"�� UIF FMFDUSPO EFO�TJUZ JT BQQSPYJNBUFE UP CF VOJGPSN J�F� TMPXMZ WBSZJOH JO TQBDF� ɨJT JT B SBUIFS DSVEF BQQSPYJ�NBUJPO BOE -%" GVODUJPOBMT BSF SBSFMZ VTFE UPEBZ GPS CJPNPMFDVMBS DBMDVMBUJPOT� " TJHOJmDBOUJNQSPWFNFOU JO UIF BDDVSBDZ DBO CF PCUBJOFE JG UIF HSBEJFOU PG UIF FMFDUSPO EFOTJUZ JT UBLFO JOUPBDDPVOU ZJFMEJOH GVODUJPOBMT PG UIF HFOFSBMJ[FE HSBEJFOU BQQSPYJNBUJPO ((" UZQF� (("GVODUJPOBMT BMSFBEZ ZJFME NVDI CFUUFS HFPNFUSJFT BOE FOFSHJFT UIBO -%" GVODUJPOBMT� "O FY�BNQMF PG B QPQVMBS BOE SPCVTU ((" GVODUJPOBM UIBU IBT CFFO FYUFOTJWFMZ VTFE GPS NPEFMJOHCJPNPMFDVMFT JT UIF #1�� GVODUJPOBM� 5P SFBDI UIF OFYU SVOH PO UIF MBEEFS B EFQFOEFODFPO UIF TFDPOE EFSJWBUJWF PG UIF FMFDUSPO EFOTJUZ JT JOUSPEVDFE ZJFMEJOH NFUB�((" GVODUJPOBMT XIJDI JODMVEF F�H� UIF 5144�� GVODUJPOBM� "OPUIFS TVCUZQF PG ((" GVODUJPOBMT BSF UIF TP�DBMMFE IZCSJE ((" GVODUJPOBMT JO XIJDI BEEJUJPOBM JNQSPWFNFOU JT BDIJFWFE CZ JODMVEJOH UIFFYDIBOHF UFSN GSPN )' UIFPSZ� ɨF CZ GBS NPTU QPQVMBS BOE XJEFMZ VTFE IZCSJE GVODUJPOBM JT UIF#�-:1�� GVODUJPOBM XIJDI XF IBWF VTFE JO BMM BSUJDMFT QSFTFOUFE IFSF� -BTUMZ B EFQFOEFODFPO WJSUVBM PSCJUBMT DBO CF JODMVEFE JO UIF GVODUJPOBM� 'PS JOTUBODF EPVCMF�IZCSJE GVODUJPOBMTNJY JO BO .1��MJLF FOFSHZ FYQSFTTJPO BMUIPVHI UIJT BMTP JODSFBTFT UIF DPNQVUBUJPOBM DPTU UPUIF TBNF PSEFS BT .1��

ɨFSF BSF TPNF JTTVFT UIBU BSF DPNNPO UP BMM %'5 NFUIPET� "MNPTU BMM GVODUJPOBMT DPOUBJOUIF VOQIZTJDBM TFMG�JOUFSBDUJPO FSSPS XIJDI TUFNT GSPN UIF GBDU UIBU UIF OPO�MPDBM FYDIBOHF UFSNGSPN )' UIFPSZ JT SFQMBDFE CZ UIF FYDIBOHF�DPSSFMBUJPO GVODUJPOBM MFBEJOH UP B QPPS USFBUNFOUPG F�H� DIBSHF�USBOTGFS QIFOPNFOB� .PSFPWFS UIF NBUIFNBUJDBM GPSN PG BOZ GVODUJPOBM FTTFO�UJBMMZ IBT UP CF HVFTTFE BMUIPVHI UIFPSFUJDBM BSHVNFOUT TVDI BT SFRVJSJOH UIF DPSSFDU DVTQ BOEMPOH�SBOHF CFIBWJPST DBO IFMQ HVJEF UIF GPSNVMBUJPO�� .BOZ GVODUJPOBMT BSF CFODINBSLFEBHBJOTU B QBSUJDVMBS TFU PG FYQFSJNFOUBM EBUB PS NPSF BDDVSBUF XBWFGVODUJPO�CBTFE DBMDVMBUJPOTBOE NPEJmFE BDDPSEJOHMZ� ɨVT DBSF IBT UP CF UBLFO UP EFUFSNJOF XIFUIFS B HJWFO GVODUJPOBM JTTVJUBCMF GPS UIF QSPCMFN BU IBOE XIJDI DBO CF EJĊFSFOU GSPN UIF CFODINBSL EBUB TFU� %FTQJUFUIFTF JTTVFT %'5 NFUIPET BSF IBSE UP CFBU JO UFSNT PG UIFJS BDDVSBDZ�UP�DPNQVUBUJPOBM�DPTUSBUJP FTQFDJBMMZ GPS HSPVOE�TUBUF FOFSHFUJDT BOE HFPNFUSZ PQUJNJ[BUJPOT�

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5SFBUNFOU PG EJTQFSTJPO GPSDFT

%JTQFSTJPO JT B OPO�MPDBM RVBOUVN NFDIBOJDBM DPSSFMBUJPO FĊFDU BOE JT OPU USFBUFE XJUIJO TUBO�EBSE %'5�� %PVCMF�IZCSJE GVODUJPOBMT DBO BDDPVOU GPS B QBSU PG EJTQFSTJPO UISPVHI UIF .1��MJLF FYQSFTTJPO CVU BU JODSFBTFE DPNQVUBUJPOBM DPTU� " TJNQMFS XBZ UP JODMVEF EJTQFSTJPO FĊFDUTUIBU IBT QSPWFO UP CF FYUSFNFMZ FċDJFOU JT UP JODMVEF UIF EJTQFSTJPO FOFSHZ BT BO BEE�PO UP UIFUPUBM FOFSHZ�

E%'5−% = E%'5 + EEJTQ. ��

1FSIBQT UIF NPTU XJEFMZ VTFE NFUIPE GPS DBMDVMBUJOH EEJTQ UPEBZ JT (SJNNF�T %� DPSSFDUJPO�� XIJDI XF BMTP IBWF FNQMPZFE JO UIJT XPSL� *O %'5�%� UIF EJTQFSTJPO DPSSFDUJPO JT DBMDVMBUFEBT B TVN PG UXP�CPEZ BOE UISFF�CPEZ UFSNT�� ɨF UXP�CPEZ UFSN E(2) XIJDI IBT UIF MBSHFTUDPOUSJCVUJPO UP EEJTQ DBO CF XSJUUFO BT

E(2) =∑

AB

∑

n=6,8,10,...

snCAB

n

rnAB

fd,n(rAB), ��

XIFSF UIF TVNNBUJPO AB JT PWFS BMM BUPN QBJST JO UIF TZTUFN CABn BSF UIF n�UI PSEFS EJTQFS�

TJPO DPFċDJFOUT GPS FBDI QBJS rAB JT UIF EJTUBODF CFUXFFO UIF BUPNT JO B QBJS sn JT B TDBMJOHGBDUPS BOE fd,n JT B EBNQJOH GVODUJPO��

6UJMJ[JOH B EJTQFSTJPO DPSSFDUJPO JO DPOKVODUJPO XJUI %'5 DBMDVMBUJPOT IBT CFFO TIPXO UPJNQSPWF NPMFDVMBS HFPNFUSJFT BOE FOFSHJFT BMNPTU XJUIPVU FYDFQUJPO� *U TIPVME CF OPUFE IPX�FWFS UIBU UIF FMFDUSPOJD TUSVDUVSF JT OPU EJSFDUMZ BĊFDUFE CZ UIF EJTQFSTJPO BEE�PO BMUIPVHIJOEJSFDU FĊFDUT DBO CF QBSUMZ DBQUVSFE EVF UP UIF FĊFDU PO UIF NPMFDVMBS HFPNFUSZ�

5JNF�EFQFOEFOU EFOTJUZ GVODUJPOBM UIFPSZ

&YDJUFE TUBUFT XJUIJO %'5 DBO CF DBMDVMBUFE VTJOH MJOFBS�SFTQPOTF UJNF�EFQFOEFOU EFOTJUZ GVOD�UJPOBM UIFPSZ 5%%'5�� %VF UP UIF MPX DPNQVUBUJPOBM DPTUT XJUIM3�M4 TDBMJOH 5%%'5NFUIPET IBWF CFFO JNNFOTFMZ QPQVMBS GPS EFTDSJCJOH FYDJUBUJPO TQFDUSB GPS CJPNPMFDVMFT� ɨF5%%'5 FRVBUJPOT GPS PCUBJOJOH WFSUJDBM FYDJUBUJPO FOFSHJFT ω DBO CF FYQSFTTFE BT�

(" ## "

)(9:

)= ω

(1 00 −1

)(9:

), ��

XIFSF UIF " BOE #�NBUSJDFT UIF FYBDU GPSNT PG XIJDI EFQFOE PO UIF FNQMPZFE GVODUJPOBM EFQFOE PO UIF PDDVQJFE BOE VOPDDVQJFE ,4�%'5 PSCJUBMT�

ɨF NBJO QSPCMFN XJUI 5%%'5 NFUIPET IPXFWFS JT UIBU UIF PCUBJOFE BDDVSBDZ DBO CF VO�QSFEJDUBCMF BOE JT WFSZ NVDI EFQFOEFOU PO UIF FNQMPZFE GVODUJPOBM� *U JT XFMM�LOPXO UIBU TUBO�EBSE 5%%'5 DBMDVMBUJPOT VTJOH ((" PS IZCSJE GVODUJPOBMT GBJM JO EFTDSJCJOH DIBSHF�USBOTGFS

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1

r12=

1− FSG(µr12)r12

+FSG(µr12)

r12, ��

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�� 'VSUIFS BQQSPYJNBUJPOT

3FTPMVUJPO PG UIF JEFOUJUZ

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-BQMBDF�USBOTGPSNFE TDBMFE PQQPTJUF�TQJO

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ɨF "%$� BOE $$� BQQSPBDIFT XIJDI GPSNBMMZ TDBMF BTM5 DBO CF SFEVDFE UPM4 TDBMJOHCZ FNQMPZJOH UIF 3* BOE 404 BQQSPYJNBUJPOT BOE CZ SFGPSNVMBUJOH UIF SBUF�MJNJUJOH TUFQ VTJOHB -BQMBDF USBOTGPSNBUJPO -5 UIF JOUFHSBM PG XIJDI JT DBMDVMBUFE OVNFSJDBMMZ VTJOH RVBESB�UVSF�� ɨF SBUF�MJNJUJOH JOUFSNFEJBUF GPS CPUI 404�"%$� BOE 404�$$� DBMDVMBUJPOT JTUIF JOUFSNFEJBUF

Y Qai = cPT

∑

bj

tabijBQbj, ��

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XIFSF cPT = 1.3 JT UIF 404 DPFċDJFOU BOE BQbj BSF UIF UISFF�JOEFY JOUFSNFEJBUFT PCUBJOFE GSPN

UIF 3* BQQSPYJNBUJPO PG UIF GPVS�JOEFY FMFDUSPO SFQVMTJPO JOUFHSBMT�� ɨF EPVCMFT BNQMJUVEFTtabij BSF HJWFO CZ

tabij = −∑

P BPaiB

Pbj

ϵiajb, ��

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1

ϵiajb=

∫ ∞

0

FYQ(−ϵiajbt)Et ≈nL∑

z

wz FYQ(−ϵiajbtz) =nL∑

z

wz FYQ(−ϵiatz) FYQ(−ϵjbtz),

��XIFSF wz BSF UIF XFJHIUT PG UIF OVNFSJDBM JOUFHSBUJPO TDIFNF tz BSF UIF JOUFHSBUJPO QPJOUT BOEϵia = ϵi − ϵa BOE ϵjb = ϵj − ϵb� ɨF tabij DPOUSJCVUJPOT DBO CF XSJUUFO BT

tabij = −nL∑

z

wz

∑

P

BPai FYQ(−ϵaitz) BP

bj FYQ(−ϵbjtz) ��

BOE UIF SBUF�MJNJUJOH JOUFSNFEJBUF DBO CF FYQSFTTFE BT

Y Qai = −cos

nL∑

z

wz

∑

P

NPQz BP

ai FYQ(−ϵaitz) ��

XJUINPQ

z =∑

bj

BQbjB

Pbj FYQ(−ϵbjtz), ��

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ɨF -5�404 BQQSPBDI IBT CFFO GPVOE UP HJWF TJNJMBS FYDJUBUJPO FOFSHJFT BT VOTDBMFE "%$�PS $$�� %VF UP UIF FNQJSJDBM 404 TDBMJOH GBDUPS IPXFWFS DBSF TIPVME CF UBLFO UP CFODI�NBSL UIFTF NFUIPET PO OFX NPMFDVMBS TZTUFNT�

ɧF GSP[FO�DPSF BQQSPYJNBUJPO

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∑

θ

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∑

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chromophorechromophore

in protein monomer dimer monomer

∆Estrain ∆Eel

GS

ES

B

Ener

gy

GS

ES

C

Molecular geometry

GS

ES

Ener

gy

A

vertical(VEE)

adiabatic(0-0)

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r (eV

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RVS threshold (eV) RVS threshold (eV)

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P700

P870

2.03 eV

2.04 eV

2.00 eV 2.01 eV

2.02 eV 2.04 eV

2.03 eV

2.03 eV

1.61 eV

2.02 eV 2.04 eV

2.05 eV 2.07 eV

1.52 eV 1.56 eV

1.59 eV 1.62 eV

2.03 eV

2.08 eV

1.52 eV

1.61 eV

BChl-L

Chl-L

Chl-L

(Chl-L)2 (Chl-L)4

(Chl-L)2 (Chl-L)4

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10

0 0.2 0.4 0.6 0.8 1 1.2 1.4d(SB

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0) (Å

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Time (µs)

KR2 K/L M

A

A

B C D

E

F

G

B C D

E

F

G

K/L → M

B

D

PSB

L120

D116

N112

PSB

L120D116

N112

SB

L120

D116

N112

KR2 K/L M

KR2 K/L M

A

S64

S60N61

L120

Q123

E11

D116

N112 D251

R109

COpen

Closed

trans-PSB cis-PSB cis-SBE11

R109

D251N112

D116

L120

Q123

S64

S60

E11 E11

R109R109

N112 N112D251

D116

L120

Q123 Q123

D116

L120S64 S64

S60S60

D251Z = 0

−20−15−10−5 0 5

10 15 20

0 0.1 0.2 0.3 0.4 0.5

Z (Å

)

Time (µs)

K/LM

A

B

Site 1

Site 1 Site 2 Site 3

Site 2

Site 3

PSB PSB SB

IN

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Inte

nsity

350 400 450 500 550 600 650

0.00

0.01

0.02

0.03

KR2LMO

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Multiscale computational studies of biological light capture

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