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  • ELECTRONIC SUPPLEMENTARY INFORMATION for

    Excited state characterization of carbonyl containing carotenoids:

    a comparison between single and multireference descriptions

    Riccardo Speziaa, Stefan Knechtb and Benedetta Mennuccic

    aCNRS, Laboratoire Analyse et Modélisation pour la Biologie et l’Environnement, UMR

    8587 CNRS-CEA-UEVE, Université d'Evry-Val-d'Essonne, 91025 Evry Cedex, France. bLaboratorium für Physikalische Chemie, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich,

    Switzerland cDipartimento di Chimica, Università di Pisa, Italy

    1 2

    B3LYP Exp B3LYP Exp

    Astaxanthin (Keto) 1510 (1546) 1524a 1161 (1189) 1157 a

    Astaxanthin (Eno) 1513 (1549) 1156 (1183)

    Fucoxanthin 1532 (1568) 1532b 1173 (1201) 1156b

    Capsanthin 1521 (1557) 1164 (1192)

    Capsorubin 1523 (1559) 1164 (1192)

    Table S1. Vibrational frequencies of Astaxanthin and Fucoxanthin as obtained from B3LYP/6-

    311G(d,p) calculations. Values were scaled with the scaling factor of 0.9769. In parenthesis we report

    the unscaled frequencies. aExperiments from Ref. 1. bExperiments from Ref. 2.

    Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is © the Owner Societies 2017

  • S1 S2 S3 S4 B3LYP 2.2714 (4.1763) 2.6408 (1.1660) 3.0590 (0.0038) 3.1800 (0.0081) TPSS 1.8850 (1.3080) 2.1484 (0.7572) 2.2553 (2.7927) 2.4631 (0.1663) Rev-TPSS 1.9020 (1.3388) 2.1583 (0.6852) 2.2718 (2.8813) 2.4865 (0.1488) VSXC 1.9084 (1.4307) 2.2143 (1.7055) 2.2914 (1.9724) 2.5000 (0.1095) VSXC/6-31+G(d) 1.9137 (1.4321) 2.2294 (1.9850) 2.3063 (1.7180) 2.5085 (0.0990) HCTH 1.8304 (1.1764) 2.0524 (0.3569) 2.1963 (3.0843) 2.3893 (0.2135) TPSSh 2.1315 (2.8506) 2.4400 (2.4712) 2.7738 (0.0469) 2.8037 (0.0157) M06L 1.9627 (1.4958) 2.2852 (2.9377) 2.3911 (0.5880) 2.5628 (0.1133) M11L 1.9176 (1.6170) 2.2057 (3.4969) 2.4936 (0.1928) 2.5157 (0.0105) M11L/6-31+G(d) 1.9328 (1.6817) 2.2191 (3.5070) 2.5221 (0.1602) 2.5750 (0.0056) MN12L 2.0571 (2.0991) 2.3599 (3.3675) 2.6944 (0.1059) 2.8019 (0.0107) PBE 1.8211 (1.1476) 1.9804 (0.2394) 2.1837 (3.2356) 2.3764 (0.2686) BLYP 1.8172 (1.1549) 2.0483 (0.4330) 2.1847 (3.0659) 2.3739 (0.1932) PW91 1.8185 (1.1535) 1.9974 (0.2696) 2.1822 (3.2078) 2.3733 (0.2542) M06 2.3365 (4.6220) 2.8127 (0.5035) 3.2370 (0.0099) 3.3428 (0.0042) BHandH 2.6666 (5.0738) 3.6060 (0.0865) 3.8060 (0.0949) 3.9257 (0.0017) HSEH1PBE 2.2367 (3.5231) 2.5719 (1.8584) 2.9908 (0.0117) 3.1769 (0.0120) PBE0 2.3581 (4.6265) 2.7951 (0.7402) 3.2275 (0.0039) 3.3102 (0.0061) CAM-B3LYP 2.6966 (4.8525) 3.7178 (0.0104) 3.7490 (0.0308) 3.8432 (0.1135) LC-wPBE 3.0539 (4.6116) 3.8836 (0.0041) 4.1309 (0.0793) 4.8083 (0.1199)

    Table S2. S0-Sn (n=1-4) energies (in eV) and oscillator strengths (in parenthesis) for CC-echinenone

    as obtained from TDA/6-311+G(d,p) calculations (when specified 6-31+G(d) basis set was also used).

    S1 S2 S3 S4 B3LYP 2.2065 (4.3614) 2.5571 (1.5817) 3.0136 (0.0167) 3.0896 (0.0001) TPSS 1.8302 (1.2087) 2.1287 (0.0012) 2.1944 (4.1764) 2.4369 (0.4336) VSXC 1.8568 (1.3175) 2.1895 (0.0537) 2.2158 (4.3096) 2.4738 (0.3321) RevTPSS 1.8468 (1.2417) 2.1316 (0.0004) 2.2113 (4.2057) 2.4606 (0.4043) TPSSh 2.0688 (2.7624) 2.3791 (3.2352) 2.7063 (0.0013) 2.7622 (0.0875) HCTC 1.7778 (1.0890) 2.0296 (0.0000) 2.1460 (3.9949) 2.3667 (0.5372) M06L 1.9007 (1.3872) 2.2574 (4.2207) 2.3295 (0.0047) 2.5258 (0.2978) M11L 1.8623 (1.4407) 2.1679 (4.3296) 2.4647 (0.3088) 2.4708 (0.0029) MN12L 1.9956 (1.9322) 2.3094 (4.2282) 2.6557 (0.2101) 2.7460 (0.0013) PBE 1.7702 (1.0719) 1.9564 (0.0000) 2.1380 (3.9966) 2.3534 (0.6191) BLYP 1.7661 (1.0655) 2.0222 (0.0003) 2.1338 (4.0496) 2.3529 (0.5174) PW91 1.7678 (1.0729) 1.9739 (0.0001) 2.1355 (4.0060) 2.3509 (0.6013) M06 2.2682 (4.9567) 2.7165 (0.6954) 3.1870 (0.0013) 3.2508 (0.0001) BHandH 2.5841 (5.4852) 3.4937 (0.1454) 3.7550 (0.0089) 3.8667 (0.0000) HSEH1PBE 2.1664 (3.5229) 2.4928 (2.4847) 2.9399 (0.0426) 3.0855 (0.0006) PBE0 No convergence CAM-B3LYP 2.6144 (5.2444) 3.6422 (0.0849) 3.6852 (0.0001) 3.7633 (0.0170) LC-wPBE 2.9661 (4.9647) 3.8647 (0.0002) 4.0628 (0.0038) 4.6948 (0.0205)

    Table S3. S0-Sn (n=1-4) energies (in eV) and oscillator strengths (in parenthesis) for TC-echinenone

    as obtained from TDA/6-311+G(d,p) calculations.

  • S1 S2 S3 S4 B3LYP 2.2722 (5.4210) 2.5276 (0.0000) 3.1008 (0.0755) 3.1909 (0.0000) TPSS 1.9488 (0.0000) 2.0389 (3.9720) 2.0943 (0.0000) 2.0963 (0.8061) RevTPSS 1.9651 (0.0000) 2.0507 (3.8361) 2.1027 (0.0000) 2.1054 (0.9647) VSXC 1.9770 (0.0000) 2.0588 (4.8103) 2.1673 (0.1045) 2.1693 (0.0000) HCTC 1.8900 (0.0000) 1.9702 (1.2553) 1.9939 (0.0000) 2.0197 (3.3279) TPSSh 2.1915 (5.3523) 2.2687 (0.0000) 2.7305 (0.0002) 2.7343 (0.0000) M06L 2.0366 (0.0000) 2.1073 (4.8805) 2.2927 (0.0427) 2.2959 (0.0000) M11L 1.9891 (0.0000) 2.0471 (5.1852) 2.4279 (0.0009) 2.4313 (0.0000) MN12L 2.1492 (0.0000) 2.1621 (5.4555) 2.7068 (0.0469) 2.7218 (0.0000) PBE 1.8664 (0.0000) 1.9021 (0.2750) 1.9321 (0.0000) 2.0083 (4.3651) BLYP 1.7548 (0.0000) 1.8756 (0.0042) 1.8756 (0.0000) 1.9282 (5.1527) PW91 1.8701 (0.0000) 1.9191 (0.3938) 1.9440 (0.0000) 2.0059 (4.2335) M06 2.3096 (5.2337) 2.7291 (0.0000) 3.3045 (0.0511) 3.3349 (0.0000) BHandH no convergence HSEH1PBE 2.2680 (5.4143) 2.4287 (0.0000) 3.0345 (0.1013) 3.1695 (0.0000) PBE0 2.3420 (5.4765) 2.7002 (0.0000) 3.2903 (0.0489) 3.3324 (0.0000) CAM-B3LYP 2.6392 (5.0468) 3.6905 (0.0000) 3.7304 (0.0000) 3.7750 (0.0017) LC-wPBE 2.9872 (4.7272) 3.9164 (0.0000) 3.9207 (0.0012) 4.0624 (0.0000)

    Table S4. S0-Sn (n=1-4) energies (in eV) and oscillator strengths (in parenthesis) for CC-

    canthaxanthin as obtained from TDA/6-311+G(d,p) calculations.

    S1 S2 S3 S4 B3LYP 2.2234 (5.6707) 2.4542 (0.0908) 3.0422 (0.0478) 3.0544 (0.0129) TPSS 1.8813 (0.1596) 2.0142 (3.8527) 2.0253 (0.0178) 2.0448 (1.0792) RevTPSS 1.8975 (0.1729) 2.0259 (3.2946) 2.0284 (0.2474) 2.0539 (1.4257) VSXC 1.9094 (0.1595) 2.0327 (5.0200) 2.0834 (0.0084) 2.1165 (0.0785) HCTC 1.8264 (0.1283) 1.9253 (0.0000) 1.9335 (0.2740) 1.9830 (4.5024) TPSSh 2.1383 (4.6897) 2.2076 (1.0177) 2.6362 (0.0001) 2.6922 (0.0002) M06L 1.9611 (0.2742) 2.0767 (4.9476) 2.2276 (0.0007) 2.2407 (0.0247) M11L 1.9170 (0.2538) 2.0184 (5.2500) 2.3729 (0.0005) 2.3802 (0.0011) MN12L 2.0648 (0.8391) 2.1327 (4.9724) 2.6473 (0.0016) 2.6597 (0.0213) PBE 1.8094 (0.1348) 1.8524 (0.0000) 1.8679 (0.0169) 1.9775 (4.8076) BLYP 1.8113 (0.1136) 1.9186 (0.0023) 1.9305 (0.4813) 1.9713 (4.3039) PW91 1.8106 (0.1288) 1.8698 (0.0002) 1.8823 (0.0501) 1.9744 (4.7702) M06 2.2603 (5.5106) 2.6528 (0.0326) 3.2255 (0.0026) 3.2433 (0.0399) BHandH 2.5603 (5.6003) 3.4607 (0.0063) 3.7034 (0.0275) 3.8571 (0.0001) HSEH1PBE 2.2141 (5.4649) 2.3532 (0.2788) 2.9742 (0.0711) 3.0387 (0.0021) PBE0 2.2915 (5.7583) 2.6234 (0.0476) 3.1929 (0.0005) 3.2293 (0.0395) CAM-B3LYP 2.5890 (5.3257) 3.6141 (0.0037) 3.6778 (0.0004) 3.6907 (0.0272) LC-wPBE 2.9411 (4.9977) 3.8620 (0.0002) 3.9160 (0.0032) 3.9908 (0.0235)

    Table S5. S0-Sn (n=1-4) energies (in eV) and oscillator strengths (in parenthesis) for TC-canthaxanthin

    as obtained from TDA/6-311+G(d,p) calculations.

  • S1 S2 S3 S4

    Ech-CC 2.1201 (0.16920) 2.3193 (3.57768) 2.5871 (0.04025) 2.9128 (0.00428)

    Ech-TC 1.9646 (0.11007) 2.2380 (3.92380) 2.4357 (0.03813) 2.7410 (0.00001)

    Ech-CT 1.9889 (0.12447) 2.2452 (3.83820) 2.4576 (0.06318) 2.9684 (0.00396)

    Ech-TT 1.8614 (0.11348) 2.1724 (3.99291) 2.3149 (0.10270) 2.8074 (0.00016)

    Canth-CC 2.0735 (0.00000) 2.2623 (3.97160) 2.5121 (0.00194) 2.9696 (0.00000)

    Canth-TC 1.9586 (0.00920) 2.2065 (4.18587) 2.3779 (0.00043) 2.7882 (0.00002)

    Canth-TT 1.8590 (0.00000) 2.1512 (4.40137) 2.2506 (0.01843) 2.7573 (0.00025)

    Table S6. Electronic transition energies to the first 4 excited states (in eV) and oscillator strengths (in

    parenthesis) as obtained by DFT/MRCI calculations.

  • Echinenone Cantaxanthin

    S1 S2 S3 S4 S1 S2 S3 S4

    CC

    B3LYP 2.27 2.64 3.06 3.18 2.27 2.53 3.10 3.19

    TPSS 1.89 2.15 2.26 2.46 1.95 2.04 2.09 2.10

    M06L 1.96 2.29 2.39 2.56 2.04 2.11 2.29 2.30

    M11L 1.92 2.21 2.49 2.52 1.99 2.05 2.43 2.43

    MN12L 2.06 2.36 2.69 2.80 2.15 2.16 2.71 2.72

    MRCI 2.12 2.40 2.54 2.71 2.01 2.34 2.60 2.64

    TC

    B3LYP 2.21 2.56 3.01 3.09 2.22 2.45 3.04 3.05

    TPSS 1.83 2.13 2.19 2.44 1.88 2.01 2.03 2.04

    M06L 1.90 2.26 2.33 2.53 1.96 2.08 2.23 2.24

    M11L 1.86 2.17 2.46 2.47 1.92 2.02 2.37 2.38

    MN12L 2.00 2.31 2.66 2.75 2.06 2.13 2.65 2.66

    MRCI 1.96 2.32 2.50 2.55 1.92 2.29 2.42 2.49

    CT

    B3LYP 2.21 2.56 3.01 3.24

    TPSS 1.84 2.17 2.22 2.44

    M06L 1.91 2.25 2.41 2.54

    M11L 1.87 2.16 2.48 2.55

    MN12L 2.00 2.30 2.67 2.84

    MRCI 1.99 2.25 2.46 2.97

    TT

    B3LYP 2.13 2.50 2.96 3.09 2.18 2.38 2.98 3.04

    TPSS 1.76 2.13 2.15 2.41 1.82 1.98 1.98 1.98

    M06L 1.83 2.21 2.33 2.50 1.90 2.03 2.18 2.18

    M11L 1.80 2.12 2.44 2.47 1.86 1.97 2.33 2.33

    MN12L 1.92 2.26 2.63 2.74 2.00 2.08 2.60 2.61

    MRCI 1.86 2.17 2.31 2.81 1.86 2.15 2.25 2.76

    EXP 2.56-2.44 2.50-2.31

    Table S7. DFT/MRCI and TDA-DFT transition energies (in eV) for the first four excited states of

    Echinenone

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