Citation
Daviso, E. (2008, November 18). The solid state photo-CIDNP effect. Retrieved from https://hdl.handle.net/1887/13264
Version: Corrected Publisher’s Version
License: Licence agreement concerning inclusion of doctoral thesis in the Institutional Repository of the University of Leiden
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APPENDICES
Appendix A
DFT calculations of hyperfine tensors
DFT computations of hf coupling tensors were performed with the ADF 2002.1 package (SCM N.V., Amsterdam, The Netherlands), using the TZP all-electron basis set for all atoms as described before (Prakash et al., 2006). Geometries of ground-state molecules were taken from the crystal structure in the charge-neutral state (PDB identifier 1AIJ) (Stowell et al., 1997) and subjected to geometry optimization within ADF in the cation radical state in vacuo. Such geometry optimization converges to the local minimum of the energy hypersurface that is next to the experimental structure, so that side group conformations and deformations of the macrocycles are preserved. The hf computations were performed considering P
Land P
Mcoordinated with His-L173 and His-M202 to the Mg atom and with the phytyl chain substituted by a methyl group. In the special pair the total electron spin densities on
13C nuclei in the macrocycles are distributed between P
Land P
Min a ratio 0.59 : 0.41. No significant differences in this distribution are found between spin densities in s (0.588 : 0.412) and p (0.591 : 0.409) orbitals. Spin density distributions in monomeric P
L+•/ His-L173 and P
M+•/ His-M202 were computed for comparison. As a further reference the spin density distribution was computed in BChl with an idealized structure (Facelli, 1998) in the absence of histidine coordination.
Changes in spin densities due to histidine coordination, changes in side group
conformation and deformation of the macrocycles do not lead to strong asymmetries in spin
density distribution within each macrocycle (Figure A1). The slight preference for
localization of s spin density on pyrroles II and IV is maintained. However, these changes in
geometric structure do have a profound influence on distribution of the spin density into side
groups. This spin density is mostly localized on carbonyl oxygens O-3
1, O-13
1, and O-17
3(Table A1). The geometric structure of the M moiety favors localization of some spin density
on O-3
1attached to pyrrole I, which is involved in π overlap between the two moieties, while
the geometric structure of the L moiety favors localization of some spin density on O-17
3in
the phytyl chain.
Figure A1: Correlation of spin densities on 13C nuclei between bacteriochlorophyll cation radicals coordinated by histidine and having the geometric structure as in the special pair and an uncoordinated bacteriochlorophyll cation radical BChlideal+•
with idealized structure. (A) s spin density for PM moiety. (B) p spin density for PM moiety. (C) s spin density for PL moiety. (D) p spin density for PL moiety. Dotted lines correspond to unchanged spin densities.
This carbonyl oxygen is close to the accessory chlorophyll in the active L branch.
Formation of the special pair does not lead to significant asymmetries within each of the
moieties either (Table A1). Distribution of spin density to side groups (carbonyl oxygens)
decreases strongly. Again the slight preference for localization of s spin density on pyrroles
II and IV is maintained. All pyrroles in P
Lgain both s and p spin density at the expense of
pyrroles II and IV in the M moiety (Figure A2) and of side groups of both moieties.
SPECIES PYRROLE I
PYRROLE II
PYRROLE III
PYRROLE IV
O- 3
1O- 13
1O- 17
3BCHLIDEAL+•
S ORBITALS
20.7 27.7 23.4 28.2 0.0 0.3 0.0
BCHLIDEAL+•
P ORBITALS
23.1 24.8 27.1 25.0 0.2 1.1 0.1
PM+•
/ HIS M202 S ORBITALS
19.1 28.5 20.8 31.6 0.4 0.4 0.0
PM+•
/ HIS M202 P ORBITALS
24.7 24.7 24.5 26.1 1.3 1.5 0.1
PL+•
/ HIS L173 S ORBITALS
20.6 28.1 21.4 29.9 0.1 0.6 0.3
PL+•
/ HIS L173 P ORBITALS
24.3 24.5 25.0 26.2 0.6 1.7 2.4
SP+• M MOIETY S ORBITALS
23.9 26.9 22.6 26.6 0.0 0.0 0.0
SP+• M MOIETY P ORBITALS
25.5 24.1 26.9 23.5 −0.1 0.0 0.1
SP+• L MOIETY S ORBITALS
22.6 26.6 22.3 28.5 0.2 0.0 0.2
SP+• L MOIETY P ORBITALS
24.6 23.8 26.5 25.1 0.6 0.3 0.0
Table A1: Spin densities in s and p orbitals normalized to the respective total 13C spin densities in the four pyrrole rings of the bacteriochlorophyll macrocycle. Values are given in percent.
Figure A2: Correlation of spin densities on 13C nuclei between BChl cofactors in the special pair coordinated by histidine and monomeric BChl cation radicals with the same geometric structure. (A) s spin density for PM moiety. (B) p spin density for PM moiety. (C) s spin density for PL moiety. (D) p spin density for PL moiety. Dotted lines correspond to equal distribution of spin densities over both moieties.
IUPAC
number Cartesian coordinates Axx
(MHz) Ayy
(MHz) Azz
(MHz) Eigenvectors aiso
(MHz)
∆A (MHz) 1 53.6560 102.7900 41.6350 −1.6392 −1.2091 8.1677 0.7365 0.4303 −0.5219 1.7731 9.5919
0.2829 0.5049 0.8155 0.6144 −0.7482 0.2501
2 53.4830 102.2000 40.3960 −1.5919 −1.2931 7.9541 0.7738 0.6106 −0.1688 1.6897 9.3966 −0.0313 0.3030 0.9525
0.6326 −0.7317 0.2535
3 52.3950 101.3300 40.5290 −2.1442 −1.9851 −1.7874 0.6605 −0.5195 −0.5421 −1.9722 0.2773 0.6120 0.7908 −0.0121
0.4349 −0.3237 0.8402
4 51.9610 101.4600 41.8650 −0.1558 −0.0152 10.9860 0.4673 0.5930 0.6558 3.6050 11.0715 −0.6354 −0.2905 0.7155
0.6147 −0.7509 0.2410
5 50.9500 100.7700 42.5230 −5.1538 −2.9752 −2.3081 0.6498 −0.7416 0.1668 −3.4790 1.7564 0.5664 0.6188 0.5444
−0.5068 −0.2592 0.8221
6 50.5870 100.7700 43.8580 0.3122 0.4103 13.8010 0.6061 0.6632 0.4390 4.8412 13.4397 −0.3893 −0.2340 0.8909
0.6935 −0.7109 0.1163
7 49.5420 99.8310 44.4270 −1.5785 −1.4362 −0.9657 −0.2160 −0.1318 0.9675 −1.3268 0.5416 −0.8199 −0.5136 −0.2530
0.5302 −0.8478 0.0029
8 49.6320 100.0400 45.9110 −1.7941 −1.6749 −1.3497 0.1061 0.2738 0.9559 −1.6062 0.3848 0.7515 0.6075 −0.2574
0.6511 −0.7456 0.1413
9 50.7040 101.1000 46.0700 −0.1280 0.1305 14.6520 0.6053 0.5190 −0.6035 4.8848 14.6508 0.4132 0.4431 0.7955
0.6803 −0.7309 0.0537
10 51.0880 101.6400 47.3010 −3.3068 −2.6936 −2.4436 −0.5658 −0.3992 0.7215 −2.8147 0.5566 0.2536 −0.9168 −0.3084
−0.7845 −0.0084 −0.6199
11 52.0330 102.6300 47.5370 −2.1456 −1.5769 8.7156 0.5956 0.5212 −0.6113 1.6644 10.5769 0.3610 0.5062 0.7833
0.7176 −0.6871 0.1132
12 52.3720 103.1900 48.7630 −2.0639 −1.7670 10.1530 0.6757 0.6754 −0.2954 2.1074 12.0685 0.1357 0.2799 0.9504
0.7245 −0.6822 0.0974
13 53.3430 104.1700 48.5890 −2.4283 −2.1280 −1.6642 −0.1880 −0.0161 0.9820 −2.0735 0.6140 0.5552 0.8231 0.1198
0.8102 −0.5676 0.1457
14 53.5090 104.1200 47.1910 −0.2024 0.0843 10.7840 0.5497 0.6512 0.5232 3.5553 10.8430 −0.4291 −0.3172 0.8457
0.7166 −0.6894 0.1050
15 54.4650 104.9700 46.6370 −5.8135 −3.2468 −2.5880 0.6828 −0.7080 0.1806 −3.8828 1.9422 0.5489 0.6602 0.5127
−0.4821 −0.2508 0.8393
16 54.8700 105.0100 45.2800 0.5740 0.6775 16.2670 0.5134 0.6530 0.5568 5.8395 15.6412 −0.5352 −0.2635 0.8026
0.6707 −0.7100 0.2141
17 56.0130 105.8300 44.6770 −1.8336 −1.6506 −1.3963 −0.2558 0.0179 0.9666 −1.6268 0.3458 0.4972 0.8599 0.1157
0.8291 −0.5101 0.2288
18 56.0540 105.3900 43.2450 −1.6031 −1.4939 −1.2546 −0.0472 0.4250 0.9039 −1.4505 0.2939 0.9526 0.2915 −0.0873
0.3006 −0.8569 0.4186
19 54.9440 104.3600 43.1290 0.0055 0.2365 14.0980 0.6710 0.3099 −0.6736 4.7800 13.9770 0.4327 0.5741 0.6952
0.6020 −0.7579 0.2511
20 54.6440 103.7200 41.9320 −3.9846 −2.9851 −2.2080 0.5990 −0.7375 0.3118 −3.0592 1.2769 −0.6804 −0.2635 0.6839
0.4221 0.6218 0.6596
21 54.3390 102.5000 39.1670 −1.4575 −1.1929 −0.8836 −0.7421 −0.5935 −0.3116 −1.1780 0.4416 −0.3353 −0.0738 0.9392
0.5804 −0.8014 0.1442
31 51.9800 100.4400 39.5070 −0.1610 −0.0399 0.0079 −0.8238 −0.3045 0.4781 −0.0643 0.1084 0.5514 −0.6262 0.5512
0.1315 0.7177 0.6837
32 50.7460 99.5800 39.6690 −0.1180 −0.0006 0.0912 0.9642 −0.1396 −0.2257 −0.0091 0.1505 0.1952 0.9493 0.2466
0.1797 −0.2817 0.9424
71 48.1770 100.2700 43.9270 5.0851 5.1191 6.0948 −0.2762 −0.6365 0.7201 5.4330 0.9927 −0.1556 0.7690 0.6201
0.9484 −0.0592 0.3114
81 50.0760 98.7490 46.5830 5.0322 5.0748 6.1709 0.9318 0.1911 0.3085 5.4260 1.1174 −0.3593 0.3660 0.8585
0.0511 −0.9107 0.4097
82 49.0810 97.5800 46.4280 −0.0190 0.0376 0.2883 0.7153 −0.5945 0.3674 0.1023 0.2790 −0.1547 0.3779 0.9128
−0.6815 −0.7097 0.1782
121 51.8210 102.7800 50.1170 −1.7928 −1.4543 −1.2779 −0.6479 −0.7248 −0.2342 −1.5083 0.3457 −0.2124 −0.1233 0.9694
0.7314 −0.6778 0.0741
131 54.2440 105.1600 48.9830 −0.6910 −0.5018 −0.2436 −0.6361 −0.4954 0.5916 −0.4788 0.3528 0.7154 −0.6658 0.2118
0.2889 0.5579 0.7779
132 54.9970 105.7700 47.8130 −0.0546 0.1083 0.2090 0.6823 −0.6920 0.2359 0.0875 0.1821 −0.5253 −0.2396 0.8165
−0.5085 −0.6809 −0.5269
133 54.5490 107.2200 47.6430 −0.9971 −0.8530 −0.7230 0.3936 −0.7406 0.5446 −0.8577 0.2021 0.9124 0.2425 −0.3296
0.1121 0.6266 0.7712
134 52.7770 108.2100 46.4940 −0.0028 0.0223 0.1219 0.8286 0.0303 0.5590 0.0472 0.1121 −0.4941 −0.4299 0.7557
0.2632 −0.9023 −0.3412
171 57.3700 105.5200 45.3090 4.1858 4.1944 5.3476 −0.1321 −0.8200 0.5570 4.5759 1.1575 −0.2306 0.5719 0.7873
−0.9640 −0.0244 −0.2646
172 58.4590 106.5100 44.9070 −0.1904 −0.1647 0.1483 0.5675 −0.8118 0.1379 −0.0690 0.3259 0.1390 0.2596 0.9557
−0.8115 −0.5231 0.2601
173 59.8950 106.1700 45.3000 0.0055 0.0182 0.1091 −0.1699 0.9804 0.0999 0.0443 0.0973 −0.0202 −0.1048 0.9943
0.9852 0.1668 0.0375
181 55.7660 106.5200 42.2960 4.9702 4.9881 5.9349 0.6609 −0.5466 −0.5142 5.2977 0.9557 0.7257 0.2908 0.6235
−0.1912 −0.7852 0.5888
Table A2: 13C Cartesian coordinates, computed hf tensors for PM and eigenvectors, isotropic (Fermi contact) and anisotropic hfi.
IUPAC
number Cartesian coordinates Axx
(MHz) Ayy
(MHz) Azz
(MHz) Eigenvectors aiso
(MHz)
∆A (MHz) 1 55.4540 99.0470 40.8800 −2.2009 −1.5854 12.4350 0.8432 0.4676 −0.2652 2.8829 14.3282
0.0686 0.3957 0.9158 0.5331 −0.7904 0.3016
2 55.7700 99.7500 42.0390 −2.3971 −2.0288 10.9000 0.7354 0.2801 −0.6170 2.1580 13.1130 0.3708 0.5957 0.7125
0.5671 −0.7527 0.3342
3 54.7730 99.4240 42.9760 −2.9852 −2.9019 −1.2141 0.7707 0.6338 0.0657 −2.3671 1.7295 −0.2077 0.1524 0.9662
0.6023 −0.7583 0.2491
4 53.9130 98.5300 42.3100 −0.1747 0.0848 15.8350 −0.2000 0.2194 0.9549 5.2484 15.8799 0.7934 0.6082 0.0264
0.5749 −0.7628 0.2956
5 52.7660 97.9000 42.8190 −6.8769 −4.1523 −3.2456 0.5349 −0.7835 0.3163 −4.7583 2.2690 −0.2599 0.2036 0.9439
0.8039 0.5870 0.0947
6 51.8740 97.0270 42.1860 0.5535 0.7075 19.7950 −0.3647 0.1584 0.9176 7.0186 19.1645 0.7869 0.5793 0.2127
0.4978 −0.7995 0.3359
7 50.6050 96.4950 42.8340 −2.2580 −2.0514 −1.4714 −0.7432 −0.4750 −0.4712 −1.9269 0.6833 −0.4637 −0.1420 0.8746
0.4823 −0.8684 0.1147
8 49.9170 95.7190 41.7380 −2.4488 −2.2575 −1.9554 0.3409 0.4909 0.8018 −2.2206 0.3978 0.6872 0.4519 −0.5689
0.6415 −0.7448 0.1832
9 50.8540 95.8560 40.5520 0.0311 0.3082 20.3410 0.8640 0.4943 −0.0956 6.8934 20.1713 −0.0161 0.2170 0.9760
0.5032 −0.8417 0.1954
10 50.5270 95.3980 39.2760 −5.6380 −4.5492 −3.4611 0.5637 −0.8045 0.1871 −4.5494 1.6325 0.8228 0.5670 −0.0407
−0.0733 0.1768 0.9814
11 51.2110 95.6150 38.0850 −2.8672 −2.1488 13.0370 0.8445 0.4728 −0.2514 2.6737 15.5450 0.1653 0.2164 0.9622
0.5093 −0.8541 0.1046
12 50.7980 95.2400 36.8180 −2.9087 −2.5142 13.8410 0.7327 0.3962 −0.5533 2.8060 16.5525 0.4471 0.3327 0.8303
0.5130 −0.8557 0.0667
13 51.7060 95.7140 35.8570 −3.2658 −2.8906 −1.7111 0.7120 0.4984 0.4947 −2.6225 1.3671 −0.4997 −0.1353 0.8556
0.4933 −0.8563 0.1527
14 52.6380 96.3530 36.6920 −0.3443 0.0678 14.5950 −0.1349 −0.0183 0.9907 4.7728 14.7333 0.8320 0.5409 0.1233
0.5381 −0.8408 0.0576
15 53.7120 96.9840 36.0640 −7.3831 −4.7665 −3.7807 0.5151 −0.8495 0.1139 −5.3101 2.2941 −0.2150 0.0005 0.9766
0.8297 0.5275 0.1823
16 54.7290 97.7250 36.7000 0.9747 1.1976 25.5230 −0.1776 0.0084 0.9841 9.2318 24.4369 0.8327 0.5342 0.1457
0.5244 −0.8453 0.1018
17 55.9370 98.3850 36.0460 −2.9350 −2.6399 −2.2003 −0.5721 −0.5796 −0.5804 −2.5917 0.5872 −0.5997 −0.1872 0.7781
0.5596 −0.7930 0.2404
18 56.7000 98.9320 37.2140 −2.3794 −2.1852 −1.6710 0.2494 0.5583 0.7913 −2.0785 0.6113 0.5772 0.5704 −0.5843
0.7775 −0.6024 0.1799
19 55.8600 98.6010 38.4220 0.9519 1.2996 21.9620 0.8277 0.5503 −0.1096 8.0712 20.8362 0.0206 0.1655 0.9860
0.5607 −0.8183 0.1256
20 56.1510 99.1330 39.6770 −5.8480 −4.3916 −3.2071 0.5191 −0.8442 0.1333 −4.4822 1.9127 0.8545 0.5163 −0.0578
−0.0200 0.1439 0.9893
21 56.9640 100.7100 42.1180 −1.9408 −1.5709 −1.4489 −0.3698 −0.0602 0.9272 −1.6535 0.3070 −0.8846 −0.2824 −0.3711
0.2841 −0.9574 0.0511
31 54.5890 99.9150 44.2930 −0.7697 −0.5569 −0.3066 0.6050 −0.7487 0.2710 −0.5444 0.3567 0.7928 0.5980 −0.1175
−0.0740 0.2859 0.9553
32 55.5000 100.9500 44.9380 −0.1854 −0.1701 −0.0412 0.4864 −0.7616 0.4283 −0.1322 0.1365 0.8669 0.3596 −0.3452
0.1088 0.5391 0.8351
71 50.9700 95.5660 43.9680 6.4399 6.4605 7.7657 0.9912 −0.0717 −0.1117 6.8887 1.3155 −0.1224 −0.8187 −0.5610
0.0511 −0.5696 0.8202
81 48.5660 96.3410 41.3480 6.9729 6.9876 8.5067 0.1813 0.9814 −0.0631 7.4891 1.5265 −0.0113 0.0662 0.9977
0.9833 −0.1801 0.0231
82 47.5910 96.6800 42.4870 −0.0105 0.0631 0.4668 −0.3198 0.8304 −0.4563 0.1731 0.4405 0.5892 0.5514 0.5906
0.7420 −0.0799 −0.6655
121 49.5400 94.4430 36.4880 −2.4369 −1.9778 −1.7001 −0.4042 −0.1246 0.9062 −2.0383 0.5073 −0.7826 −0.4657 −0.4131
0.4734 −0.8761 0.0907
131 52.1980 95.9430 34.5730 −1.0039 −0.7593 −0.3838 −0.5355 −0.8054 0.2540 −0.7157 0.4978 0.8341 −0.5516 0.0094
0.1325 0.2168 0.9671
132 53.4670 96.7640 34.5770 0.0177 0.2743 0.3579 0.4920 −0.8649 0.0996 0.2166 0.2119 0.8695 0.4939 −0.0071
−0.0430 0.0900 0.9950
133 54.5270 95.9830 33.7820 −1.3500 −1.2320 −1.1168 −0.7847 0.5953 0.1726 −1.2329 0.1742 −0.5429 −0.7945 0.2722
0.2991 0.1199 0.9466
134 55.1560 95.4690 31.5620 −0.0567 −0.0508 0.0084 0.4991 −0.8019 0.3286 −0.0330 0.0622 0.8313 0.5501 0.0798
−0.2447 0.2333 0.9410
171 55.5090 99.5640 35.1900 8.0991 8.1315 9.8765 0.6067 0.5225 0.5991 8.7024 1.7612 0.7892 −0.3051 −0.5331
0.0957 −0.7962 0.5974
172 56.5200 100.2200 34.2600 −0.0797 −0.0344 0.3600 0.6590 −0.7488 −0.0706 0.0819 0.4170
0.3875 0.2576 0.8851 −0.6446 −0.6106 0.4599
173 56.4970 99.6990 32.8330 −0.0869 −0.0720 0.0356 0.8832 −0.4191 0.2105 −0.0411 0.1150 −0.3166 −0.8639 −0.3917
−0.3459 −0.2792 0.8957
181 57.9790 98.1790 37.4020 8.2887 8.3092 9.8827 0.2214 0.4849 0.8461 8.8269 1.5838 0.2009 0.8264 −0.5261
0.9542 −0.2864 −0.0855
Table A3: 13C Cartesian coordinates, computed hf tensors for PL and eigenvectors, isotropic (Fermi contact) and anisotropic hfi.
IUPAC
Number Cartesian coordinates Axx
(MHz) Ayy
(MHz) Azz
(MHz) Eigenvectors aiso
(MHz)
∆A (MHz) 1 55.7380 107.4200 27.3050 −7.3220 −5.8689 0.9214 0.8459 −0.4946 0.1995 −4.0898 7.5168
−0.4232 −0.3950 0.8154 −0.3245 −0.7741 −0.5434
2 54.8760 107.0200 28.3540 −3.0025 −2.5038 30.8260 0.8554 −0.5019 0.1280 8.4399 33.5792 −0.3819 −0.4443 0.8104
−0.3498 −0.7421 −0.5717
3 55.6030 106.0900 29.1900 −5.3016 −4.5060 8.0551 0.9267 −0.1896 −0.3245 −0.5842 12.9589 0.1310 −0.6463 0.7518
−0.3522 −0.7391 −0.5740
4 56.9650 105.9700 28.6190 −4.0973 −3.8258 −3.1494 0.6564 0.7479 −0.0988 −3.6908 0.8122 0.1809 −0.0289 0.9831
0.7324 −0.6631 −0.1542
5 58.0150 105.2000 29.1760 −1.2657 −0.9420 21.0920 0.3833 −0.6360 0.6698 6.2948 22.1958 0.8954 0.0779 −0.4384
−0.2266 −0.7677 −0.5993
6 59.3640 105.0700 28.8490 −8.9149 −5.9587 −4.5688 −0.2291 −0.7877 −0.5719 −6.4808 2.8680 0.5962 −0.5780 0.5572
−0.7694 −0.2133 0.6020
7 60.2990 104.2000 29.7290 −0.0501 0.1074 0.3561 −0.3918 −0.7122 −0.5825 0.1378 0.3274 0.6832 0.1988 −0.7026
0.6161 −0.6732 0.4086
8 61.7100 104.4200 29.0870 −0.0287 0.0918 0.3202 −0.2781 −0.8593 −0.4293 0.1277 0.2887 0.9130 −0.0976 −0.3962
0.2985 −0.5021 0.8116
9 61.3920 105.3100 27.8690 −7.4411 −5.5084 −4.4786 −0.1610 −0.8372 −0.5226 −5.8094 1.9962 0.2558 −0.5468 0.7972
0.9532 0.0053 −0.3021
10 62.3190 105.7600 26.9380 −1.5911 −1.3594 18.3330 0.8011 −0.4503 0.3943 5.1275 19.8083 −0.5711 −0.3780 0.7287
−0.1790 −0.8089 −0.5599
11 61.9740 106.5900 25.8390 −6.0936 −4.8820 −0.2637 0.9034 −0.3731 0.2113 −3.7464 5.2241 −0.3787 −0.4633 0.8012
−0.2010 −0.8038 −0.5598
12 62.7810 107.1100 24.7860 −2.2192 −1.8397 26.5580 0.9144 −0.3602 0.1849 7.4997 28.5875 −0.3471 −0.4620 0.8162
−0.2085 −0.8104 −0.5474
13 61.9100 107.8900 23.9680 −5.3958 −4.3475 3.9777 0.8933 0.0594 −0.4455 −1.9219 8.8494 0.3999 −0.5576 0.7275
−0.2051 −0.8279 −0.5218
14 60.5830 107.8300 24.5260 −4.8739 −3.8142 −3.4253 −0.1878 −0.8504 −0.4915 −4.0378 0.9188 −0.4165 −0.3842 0.8240
0.8895 −0.3593 0.2820
15 59.6110 108.5300 23.7630 −0.7125 −0.2982 25.0810 0.5603 −0.5323 0.6346 8.0234 25.5863 0.8120 0.2017 −0.5477
−0.1635 −0.8221 −0.5452
16 58.2600 108.6800 24.0400 −11.2670 −6.9808 −5.4932 −0.1849 −0.8542 −0.4859 −7.9137 3.6307 0.6421 −0.4793 0.5983
−0.7439 −0.2013 0.6371
17 57.2740 109.4600 23.1420 −0.0298 0.2703 0.4459 −0.0499 −0.8072 −0.5882 0.2288 0.3256 0.8316 0.2926 −0.4720
0.5530 −0.5127 0.6566
18 56.0500 109.6700 24.1020 −0.4376 −0.2276 0.0154 0.0809 −0.7534 −0.6526 −0.2166 0.3480 0.9529 0.2503 −0.1710
0.2921 −0.6080 0.7381
19 58.0150 105.2000 29.1760 −1.2657 −0.9420 21.0920 0.3833 −0.6360 0.6698 6.2948 22.1958 0.8954 0.0779 −0.4384
−0.2266 −0.7677 −0.5993
20 55.4560 108.3100 26.2270 −2.1822 −1.7926 22.4980 0.7822 −0.5403 0.3103 6.1744 24.4854 −0.5368 −0.3316 0.7758
−0.3162 −0.7734 −0.5493
21 53.4720 107.5600 28.5190 −4.6647 −4.5279 −3.9228 −0.0217 −0.7375 0.6750 −4.3718 0.6735 0.3114 0.6366 0.7056
0.9500 −0.2255 −0.2157
31 55.1280 105.3600 30.3890 −2.5495 −1.8984 8.7641 0.9678 −0.1601 −0.1941 1.4387 10.9881 0.0568 −0.6126 0.7884
−0.2451 −0.7740 −0.5837
32 53.6540 105.4900 30.8270 −2.0459 −1.8664 −1.6840 0.5033 −0.7013 0.5049 −1.8654 0.2722 0.5632 0.7094 0.4239
−0.6554 0.0710 0.7519
71 60.2500 104.5700 31.2380 −0.4761 −0.3554 −0.1125 −0.2388 0.6010 0.7627 −0.3147 0.3033 0.5452 0.7330 −0.4069
0.8036 −0.3186 0.5026
81 62.4800 103.1000 28.7490 −0.6792 −0.5703 −0.3918 −0.2552 0.6587 0.7078 −0.5471 0.2329 0.9559 0.2822 0.0820
0.1456 −0.6974 0.7016
82 61.8090 102.2400 27.6470 0.2664 0.3588 0.5637 0.6780 0.3782 0.6303 0.3963 0.2511 0.7318 −0.2659 −0.6276
0.0697 −0.8866 0.4570
121 64.2590 106.8700 24.5740 −3.8522 −3.6950 −3.2908 0.0320 −0.5913 0.8058 −3.6127 0.4828 0.2023 0.7934 0.5741
0.9788 −0.1446 −0.1450
131 61.9010 108.6600 22.7560 −2.5372 −1.6602 8.7329 0.7853 −0.4583 0.4164 1.5118 10.8316 −0.5853 −0.3299 0.7407
−0.2020 −0.8253 −0.5272
132 60.3680 109.1100 22.5400 −4.1259 −4.0574 −3.8887 −0.5242 −0.4872 −0.6984 −4.0240 0.2030 0.6053 −0.7901 0.0968
−0.5989 −0.3720 0.7091
133 60.2700 110.6200 22.3670 0.0819 0.5542 0.7882 0.3501 0.5849 0.7316 0.4748 0.4701 0.0482 −0.7913 0.6096
0.9354 −0.1781 −0.3052
134 60.7400 112.8000 23.4260 −0.1373 −0.0951 0.0644 0.5398 0.1048 0.8352 −0.0560 0.1806 0.8395 −0.1402 −0.5250
−0.0620 −0.9845 0.1636
171 56.9020 108.6800 21.8410 −0.8516 −0.5746 −0.4613 −0.0836 −0.8094 −0.5812 −0.6292 0.2518 −0.5011 −0.4700 0.7267
0.8613 −0.3520 0.3662
172 56.1390 109.6000 20.8490 0.1010 0.1496 0.2771 0.1298 −0.9291 −0.3464 0.1759 0.1519
0.9130 0.2482 −0.3237 0.3866 −0.2742 0.8804
173 55.6020 108.8700 19.6280 −0.0577 −0.0122 0.0451 0.3957 −0.8236 −0.4064 −0.0083 0.0801 0.8656 0.4824 −0.1348
0.3070 −0.2983 0.9037
181 55.9770 111.1200 24.6500 0.6523 0.8493 1.0817 0.0573 0.5948 0.8019 0.8611 0.3309 0.9735 −0.2115 0.0873
−0.2215 −0.7755 0.5911
Table A4: 13C Cartesian coordinates, computed hf tensors for Φ and eigenvectors, isotropic (Fermi contact) and anisotropic hfi.
Electron-electron exchange and dipolar coupling, g tensor
Relevant magnetic parameters expressed in the principal axis system for the occurrence of the solid state photo-CIDNP effect in the radical pair state (P
•+Φ
•−) observed in purified quinone depleted RCs of Rb. sphaeroides. See Chapter 3, 4 and 5.
g tensor
Cartesian coordinates gxx gyy gzz
Eigenvectors Donor 53.4240 97.1880 39.5280 2.0033 2.0024 2.0020 −0.4877 0.0209 −0.8728
0.7517 0.5186 −0.4076 0.4441 −0.8548 −0.2686 Table A5: Cartesian coordinates, computed principal values and eigenvectors of the g tensor for the donor P (Jeschke, personal communication).
g tensor
Cartesian coordinates gxx gyy gzz
Eigenvectors Acceptor 58.8270 106.9170 26.5295 2.0044 2.0034 2.0024 −0.6920 −0.3261 0.6440
0.6942 −0.5454 0.4698 0.1980 0.7721 0.6038 Table A6: Cartesian coordinates, computed principal values and eigenvectors of the g tensor for the acceptor Φ (Jeschke, personal communication).
dipolar coupling
Electron-electron vector Magnitude D (MHz)
5.4030 9.7290 −12.9985 14.0124
Table A7: electron-electron vector and magnitude of the dipolar coupling calculated using the point-dipole approximation as discussed in Till et al. (1997). The sign convention adopted in this thesis is opposite.
J coupling Magnitude (MHz)
19.6
Table A8: Magnitude of the J coupling between the electrons of the donor P and acceptor Φ obtained used to perform photo-CIDNP simulations. The value has been obtained from Till et al. (1997).
Appendix B
Photo-CID P MAS MR simulations
Numerical simulations of the photo-CIDNP effect were based on the theory described in (Matysik and Jeschke, 2003; Prakash et al., 2006) as implemented in a home written Matlab program for density matrix computation using the EasySpin library. The program starts from a pure singlet state and computes time evolution under a Hamiltonian including electron Zeeman, nuclear Zeeman, and hfi as well as dipole-dipole and exchange coupling between the two electron spins. The part of the density matrix that decays to the ground state from either S or T
0is projected out (diamagnetic part) and is further evolved under a Hamiltonian including only the nuclear Zeeman interaction and paramagnetic relaxation for the T. Nuclear polarization of the diamagnetic part of the density matrix from the S is determined and used to simulate transient spectra. This procedure is performed for a full powder average, describing all interactions by tensors. A spherical grid function sphgrid implemented in EasySpin (Stoll and Schweiger, 2006) with 16 knots and C
isymmetry (481 orientations) has been found to be sufficient for powder averaging. Nuclear polarization was normalized to the thermal polarization at the measurement temperature of 233 K.
For very short radical pair life times singlet-triplet mixing due to hfi conforms to the linear regime so that powder-averaged nuclear polarization originating from the S only is proportional to the a
iso. For the
13C nuclei with the largest isotropic hfi this linear approximation is violated. Furthermore, additional contributions to the polarization stemming from the TSM and DD mechanisms are significant for nuclei with large ∆A. Nevertheless, our numerical simulations reveal a satisfying linear correlation between polarization originating from the S state (transient nuclear polarization in time-resolved experiments) and the a
iso(correlation coefficient 0.8779).
Analogous linear-regime arguments suggest that the polarization due to the TSM (Jeschke, 1998) and DD mechanisms (Diller et al., 2007b) is proportional to the square of the anisotropic hfi ∆A
2. ∆A on
13C nuclei is dominated by spin density in the 2p
zorbital on that nucleus and modified by dipole-dipole interaction with spin density on neighboring atoms.
As shown before there exists a satisfying correlation between the TSM and DD polarization derived from both S and T
0states that is observable in the time-resolved experiments after all special pairs have returned from the T to the ground state (400 µs after the light pulse) and the square of spin density in p orbitals ρ
p2(Diller et al., 2007b).
Simpson script (Bak et al., 2000) used to simulate singlet plus triplet spectrum of photo-CIDNP MAS NMR of the donor P in 4–ALA labeled RC of Rb. sphaeroides WT. The spin echo pulse sequence is implemented with CYCLOPS phase cycling of the (π/2) pulse.
spinsys { channels 13C
nuclei 13C 13C 13C 13C 13C 13C 13C 13C shift 1 143.2p 0 0 0 0 0
shift 2 153.3p 0 0 0 0 0 shift 3 159.8p 0 0 0 0 0 shift 4 164.0p 0 0 0 0 0 shift 5 148.2p 0 0 0 0 0 shift 6 150.3p 0 0 0 0 0 shift 7 162.5p 0 0 0 0 0 shift 8 166.8p 0 0 0 0 0 }
par {
proton_frequency 200e6 spin_rate 8000 sw 30000
start_operator -0.08*I1z-0.09*I2z-0.17*I3z-0.17*I4z-0.17*I5z-0.22*I6z- 0.42*I7z-0.34*I8z
detect_operator Inp variable rf 125000 gamma_angles 1 verbose 1101 np 1024
crystal_file alpha0beta0 }
proc pulseq {} { global par maxdt 1
set t90 [expr 0.25e6/$par(rf)]
set t180 [expr 0.5e6/$par(rf)]
set d6 [expr 1e6/$par(spin_rate)-2*$t90]
pulse $t90 $par(rf) [lindex {x x y y -x -x -y -y x x y y -x -x -y -y}
$par(p)]
delay $d6
pulse $t180 $par(rf) [lindex {y y x x y y -x -x -y -y -x -x -y -y x x}
$par(p)]
delay [expr $d6+$t90]
for {set i 1} {$i <= $par(np)} {incr i} {
acq [lindex {-y -y x x y y -x -x -y -y x x y y -x -x} $par(p)]
delay [expr 1e6/$par(sw)]
} }
proc main {} { global par
for {set par(p) 0} {$par(p) <16} {incr par(p)} { set f [fsimpson]
if [info exist g] { fadd $g $f
} else {
set g [fdup $f]
} funload $f }
fsave $g $par(name).fid faddlb $g 50 0
fzerofill $g 4096 fft $g
#fsave $g $par(name).txt -xreim fsave $g $par(name).spe
funload $g }
