Supporting information for: First hyperpolarizability of collagen using the. point dipole approximation

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Supporting information for: First hyperpolarizability of collagen using the point dipole approximation Ignat Harczuk, Olav Vahtras, and Hans Ågren KTH Royal Institute of Technology, School of Biotechnology, Division of Theoretical Chemistry and Biology, SE-106 91 Stockholm, Sweden E-mail: hagren@theochem.kth.se MFCC procedure Three coordinate files presented in order to demonstrate the MFCC procedure. The ready keyword denotes the residue in which the properties will be added to the final collagen location. The concap will denote the structure for which the properties will be subtracted for the equivalent positions. All the heavy atoms in these structures are those taken from the collagen structure. The extra hydrogens are added to fullfil valency, and their properties are transfered to the closest corresponding heavy atom before the properties of that heavy atom are added or subtracted to or from the final collagen model. In total, the property P a of atom or bond a of the collagen in the MFCC structure i is obtained from the formula P a = i c i p a i (1) where c i is 1 for ready, and -1 for concap. p a i denotes the LoProp distributed property of atom a in structure i, where the properties in our case are the molecular charge, dipole-moment, polarizabil- S1

ity, and hyperpolarizability. A-PRO1-ready.xyz 21 N -1.899696-2.939110 41.741882 H -1.466696-2.018110 41.526882 C -3.139696-2.717110 42.551882 H -3.046696-1.798110 43.165882 H -3.243696-3.569110 43.254882 C -4.334696-2.655110 41.576882 H -4.612696-1.606110 41.366882 H -5.227696-3.137110 42.003882 C -3.865696-3.359110 40.292882 H -4.072696-2.738110 39.400882 H -4.399696-4.310110 40.139882 C -2.344696-3.609110 40.478882 H -2.141696-4.702110 40.614882 C -1.566696-3.072110 39.276882 O -0.937696-2.012110 39.321882 N -1.526696-3.831110 38.117882 C -1.002696-3.262110 36.848882 H 0.056304-2.902110 37.024882 H -2.053012-4.779660 37.935554 H -1.048398-4.076181 36.110505 H -1.622916-2.412152 36.528103 S2

A-PRO2-ready.xyz 26 C -2.344696-3.609110 40.478882 H -2.141696-4.702110 40.614882 C -1.566696-3.072110 39.276882 O -0.937696-2.012110 39.321882 N -1.526696-3.831110 38.117882 C -2.239696-5.116110 37.870882 H -3.335696-4.944110 37.800882 H -2.051696-5.822110 38.703882 C -1.667696-5.625110 36.533882 H -2.452696-6.100110 35.921882 H -0.892696-6.393110 36.704882 C -1.066696-4.402110 35.814882 H -1.685696-4.119110 34.940882 H -0.057696-4.610110 35.402882 C -1.002696-3.262110 36.848882 H 0.056304-2.902110 37.024882 C -1.874696-2.067110 36.397882 O -2.989696-1.820110 36.841882 N -1.254696-1.268110 35.455882 H -0.281696-1.431110 35.168882 C -1.882696-0.049110 34.940882 H -1.066696 0.708890 34.728882 H -2.535696 0.415890 35.724882 H -2.017788-3.116911 41.406714 H -3.422314-3.431987 40.347102 H -2.468311-0.222412 34.025993 S3

A-PRO1-concap.xyz 12 C -2.344696-3.609110 40.478882 H -2.141696-4.702110 40.614882 C -1.566696-3.072110 39.276882 O -0.937696-2.012110 39.321882 N -1.526696-3.831110 38.117882 C -1.002696-3.262110 36.848882 H 0.056304-2.902110 37.024882 H -2.017788-3.116911 41.406714 H -3.422314-3.431987 40.347102 H -2.053012-4.779660 37.935554 H -1.048398-4.076181 36.110505 H -1.622916-2.412152 36.528103 S4

β properties of all atoms and bonds For all QM methods, residues types (GLY/PRO), the sum of all the atomic and bond decomposed properties α zz, β xxx, and β yyy, β xxz, β yyz, β zzz, are tabulated. Labels for the residues can be seen in Figure S1. Figure S1: Labels for the various atoms in collagen. N-PRO denotes N-terminal proline residues, which are 3 in total. C-PRO denotes C-terminal prolines, which are 3 in total. Table S1: TD-HF, Proline, atomic N 584.6-20.3-326.9 63.4-372.0-845.0 H1 1.5-1.1-0.8-4.3-0.1-0.9 CD 429.8 6.2-298.1-12.6-311.4-870.0 HD1 44.3-1.0-44.1-31.5-64.2-74.5 HD2 181.4 11.3-156.6-4.2-163.9-675.4 CG 408.3 4.8 183.0 3.9 179.7 309.3 HG1 96.8-13.0 206.4-22.1 209.8 202.8 HG2 44.0 13.7-112.8 6.8-105.6-16.3 CB 410.6 6.2 334.8-29.7 324.5 1446.2 HB1 213.5 2.6 47.6-10.4 67.0 994.0 HB2 58.6 0.2 96.7-9.2 99.7 151.3 CA 587.3 25.4 7.6 44.8-5.4-315.3 HA 51.5 17.9 15.1 19.7 22.6-84.0 C 513.0-38.9-298.0 55.5-315.0-1343.2 O 238.7-8.3-23.1 30.4-29.4-418.5 OC1 25.4-7.4 3.4-11.4 1.8 29.7 HCO 3.7-20.0-2.8-1.2-5.5-7.0 S5

Table S2: TD-HF, Proline, Bond N 299.5-17.1-332.3 52.0-366.2-1007.1 N-H1 1.6-2.4-1.5-5.7-0.1-4.2 N-CD 62.7-5.5-164.7 17.9-169.1-120.1 N-CA 505.9 1.4 177.0 10.5 157.6 448.5 CD 35.9-3.7-130.7 6.8-126.9-320.9 CD-HD1 59.3 4.2-63.7-41.0-89.6-118.3 CD-HD2 263.5 11.1-176.4-11.5-186.3-780.2 CD-CG 402.4 10.2 69.8-4.1 76.1-79.6 HD1 14.7-3.1-12.2-11.0-19.4-15.4 HD2 49.7 5.8-68.5 1.5-70.7-285.3 CG 13.4 2.7 67.5 8.6 64.6 72.7 CG-HG1 135.8-15.9 258.5-28.5 260.5 171.5 CG-HG2 57.1 17.5-140.5 8.4-128.8 63.5 CG-CB 194.4-7.5 43.3 14.8 22.6 317.7 HG1 28.9-5.1 77.2-7.8 79.6 117.1 HG2 15.5 5.0-42.6 2.6-41.2-48.1 CB 37.9 3.6 202.6-22.3 190.6 471.7 CB-HB1 313.3 3.6-1.8-9.9 23.5 1184.6 CB-HB2 87.0-1.6 138.8-13.1 142.2 270.0 CB-CA 150.8 10.9 84.2-6.5 79.5 176.9 HB1 56.9 0.8 48.5-5.5 55.2 401.7 HB2 15.1 1.0 27.3-2.6 28.6 16.3 CA 92.6 4.4-99.1 23.5-101.3-461.0 CA-HA 42.3 25.9-24.0 27.6-8.1-10.1 CA-C 290.4 3.8-23.8 11.0-37.2-323.8 HA 30.4 5.0 27.1 5.9 26.7-78.9 C 311.1-29.8-305.0 44.3-307.0-1161.8 C-O 76.9 10.9 57.2 4.0 49.3 25.8 O 200.2-13.8-51.7 28.4-54.1-431.4 C-OC1 31.8-9.1-17.7 9.4-23.1-62.3 C-HCO 4.7-23.9-1.6-2.1-5.1-2.5 OC1 9.5-2.9 12.3-16.1 13.3 60.9 HCO 1.3-8.1-2.0-0.2-3.0-5.8 S6

Table S3: TD-B3LYP, Proline, atomic N 713.4-16.5-176.1 78.8-230.2-404.4 H1 1.6-2.1-1.5-6.0-1.5-2.2 CD 467.8 14.3-514.9-17.8-536.7-1458.7 HD1 46.5-1.6-16.6-37.0-41.9-71.8 HD2 181.6 13.0-187.4-3.2-192.2-693.3 CG 442.6 18.1 363.7-7.0 352.0 599.6 HG1 99.2-13.3 222.4-23.0 227.7 220.7 HG2 45.8 15.5-105.1 4.3-98.5 1.7 CB 445.6 30.9 713.4-76.8 680.5 2363.6 HB1 215.1 3.9 46.5-14.8 67.5 1020.2 HB2 61.5 1.9 113.5-12.9 115.3 190.6 CA 698.2 51.3 62.5 82.4 34.0-256.1 HA 57.5 17.7 26.6 25.3 33.3-142.1 C 642.4-61.5-300.4 73.9-311.6-1566.1 O 264.4-15.5-73.3 36.6-70.3-594.2 OC1 27.1-13.0 2.5-15.4 3.2 74.4 HCO 3.8-24.7-3.7-1.7-6.6-8.8 S7

Table S4: TD-B3LYP, Proline, Bond N 383.6-14.5-249.7 67.0-281.1-794.5 N-H1 1.5-4.0-2.3-7.7-1.6-2.8 N-CD 67.6-3.0-203.9 21.7-212.5-157.4 N-CA 590.4 3.1 353.4 9.6 315.9 940.4 H1 0.9-0.1-0.3-2.1-0.7-0.8 CD 58.2-3.5-354.4 9.1-354.3-874.9 CD-HD1 60.8 6.1-36.5-48.6-69.4-113.9 CD-HD2 263.7 12.2-220.8-12.8-228.6-799.4 CD-CG 427.1 20.2 140.2-14.2 145.8-96.9 HD1 16.0-4.7 1.6-12.7-7.2-14.9 HD2 49.8 6.9-77.0 3.2-77.9-293.6 CG 25.4 9.2 171.8 3.0 167.7 224.6 CG-HG1 139.1-16.3 289.5-30.1 293.5 185.9 CG-HG2 58.9 20.4-130.3 6.1-118.7 115.2 CG-CB 209.2-6.4 84.4 18.2 47.9 545.7 HG1 29.7-5.1 77.7-8.0 81.0 127.7 HG2 16.4 5.3-40.0 1.3-39.2-55.9 CB 61.7 16.0 505.1-58.8 480.6 1176.0 CB-HB1 316.0 5.3-14.2-15.0 13.2 1230.8 CB-HB2 91.4-0.2 171.6-19.5 172.4 348.4 CB-CA 151.1 31.2 174.8-19.6 166.3 250.1 HB1 57.1 1.3 53.6-7.3 60.9 404.8 HB2 15.8 2.0 27.7-3.1 29.1 16.5 CA 128.2 18.1-174.9 56.6-178.4-701.3 CA-HA 43.6 26.8-42.7 37.6-25.8-25.0 CA-C 354.9 5.5-10.7 24.0-31.7-275.1 HA 35.7 4.3 48.0 6.5 46.2-129.6 C 404.8-44.5-278.5 52.2-276.6-1430.6 C-O 83.2 2.4-9.9 11.5-7.7 30.9 O 222.8-16.7-68.3 30.9-66.5-609.7 C-OC1 32.4-12.7-21.4 10.5-24.9-23.0 C-HCO 4.8-29.4-1.9-2.7-5.7-3.8 OC1 10.9-6.7 13.1-20.7 15.7 85.9 HCO 1.4-10.0-2.8-0.4-3.7-6.9 S8

Table S5: TD-CAMB3LYP, Proline, atom N 676.3-20.2-279.3 74.4-331.8-670.7 H1 1.6-1.7-1.2-5.2-1.1-1.3 CD 456.1 8.9-449.9-14.4-467.6-1272.4 HD1 46.1-1.6-25.4-34.3-48.2-71.2 HD2 180.4 12.1-171.6-3.5-176.7-671.7 CG 431.9 10.1 277.3 1.5 268.7 477.6 HG1 98.6-12.9 206.2-22.1 210.4 206.0 HG2 45.6 14.2-105.4 5.8-98.7-5.8 CB 434.7 21.1 572.7-55.8 548.8 2028.7 HB1 213.8 3.4 45.7-13.3 65.4 990.7 HB2 60.8 1.2 103.6-11.0 106.0 170.8 CA 663.3 39.9 26.6 72.3 3.0-351.3 HA 56.5 17.6 28.4 22.7 35.0-120.7 C 609.0-57.4-341.8 71.2-355.1-1591.8 O 262.6-16.8-79.4 38.1-79.0-579.3 OC1 26.7-11.7 4.3-15.8 4.8 70.8 HCO 3.8-22.5-3.5-1.2-6.2-9.2 S9

Table S6: TD-CAMB3LYP, Proline, Bond N 363.0-16.3-312.2 61.2-346.4-928.7 N-H1 1.6-3.5-2.0-6.7-1.1-3.1 N-CD 65.5-5.8-193.8 20.7-200.8-139.8 N-CA 559.5 1.5 261.7 12.3 231.1 658.9 CD 54.5-3.9-276.0 8.1-274.6-694.9 CD-HD1 60.4 5.2-46.6-45.0-76.1-118.9 CD-HD2 261.4 11.3-200.0-12.3-207.9-774.9 CD-CG 415.8 15.0 92.6-8.5 98.7-121.4 HD1 15.9-4.2-2.1-11.8-10.1-11.8 HD2 49.7 6.5-71.6 2.6-72.7-284.2 CG 24.4 5.2 127.4 7.7 123.6 172.5 CG-HG1 137.8-16.0 265.1-28.8 267.8 168.6 CG-HG2 58.5 18.6-130.7 7.6-119.2 98.3 CG-CB 202.7-7.7 72.8 17.2 42.9 464.8 HG1 29.7-5.0 73.6-7.7 76.5 121.7 HG2 16.4 4.9-40.1 2.0-39.1-54.9 CB 56.6 11.6 400.3-44.1 381.1 935.4 CB-HB1 313.5 4.7-11.0-13.2 14.8 1192.2 CB-HB2 90.1-0.8 156.5-16.5 158.5 316.6 CB-CA 149.7 22.7 126.5-10.9 119.3 212.9 HB1 57.1 1.0 51.2-6.7 58.0 394.6 HB2 15.7 1.6 25.4-2.7 26.8 12.5 CA 120.8 11.6-156.5 44.9-159.6-631.0 CA-HA 43.3 26.3-27.2 33.3-10.9-18.2 CA-C 332.4 6.1 5.0 20.0-14.4-294.0 HA 34.8 4.5 42.0 6.0 40.5-111.6 C 382.8-41.9-323.9 51.5-323.7-1430.9 C-O 83.2 1.0-20.7 12.9-21.3-2.5 O 221.0-17.3-69.0 31.6-68.4-578.1 C-OC1 32.0-11.4-18.1 8.6-21.5-20.9 C-HCO 4.8-26.7-2.0-2.0-5.5-4.3 OC1 10.7-6.0 13.3-20.1 15.6 81.3 HCO 1.4-9.1-2.5-0.2-3.5-7.1 S10

Table S7: TD-HF, Glycine, Atom N 185.5 15.3-69.5 12.0-62.8-383.8 CA 236.9 9.2-158.0 21.1-163.7-295.4 C 217.1 3.6-316.1 1.3-337.6-370.3 O 113.0-1.1-117.2-10.3-126.4 11.2 H 19.3 7.8 31.7 0.7 30.6 32.7 HA1 21.2 5.8 30.4 5.4 27.0-6.0 HA2 57.8 1.5-52.7 6.5-54.6-152.8 Table S8: TD-HF, Glycine, Bond N 135.0 9.9-135.2 3.9-131.8-422.6 N-CA 73.5-0.5 93.4 14.5 100.7 43.4 CA 27.1 4.3-150.0 7.2-152.6-224.3 CA-C 245.6 0.6-83.4 3.3-87.3-71.0 C 71.3 4.0-200.5-9.4-217.0-259.2 C-O 46.0-1.4-147.8 18.2-154.0-151.3 O 90.0-0.4-43.3-19.4-49.4 86.9 N-H 27.7 11.2 38.0 1.6 37.2 34.2 H 5.4 2.2 12.7-0.1 12.0 15.6 CA-HA1 21.0 6.5 41.6 3.1 34.7-36.8 CA-HA2 79.5 3.3-67.7 6.9-70.5-77.8 HA1 10.7 2.6 9.6 3.9 9.6 12.4 HA2 18.0-0.2-18.9 3.1-19.4-113.9 Table S9: TD-B3LYP, Glycine, Atom N 221.9 24.5 95.0 20.1 106.0-288.2 CA 288.4 17.9-305.8 50.1-307.4-898.6 C 268.5 4.9-371.2 0.8-390.3-598.8 O 123.5 0.5-154.9-16.0-162.4-166.9 H 22.0 11.1 57.6-0.7 55.9 84.5 HA1 23.4 6.9 23.3 8.2 20.0-28.6 HA2 61.4 2.8-63.4 7.5-65.6-208.6 S11

Table S10: TD-B3LYP, Glycine, Bond N 162.1 17.2-29.1 5.3-24.6-384.5 N-CA 88.9-1.9 176.8 29.6 191.6 91.9 CA 44.4 10.8-294.6 26.5-297.0-734.2 CA-C 294.1 2.8-142.0 4.3-144.0-199.7 C 98.7 4.1-217.0-8.7-233.7-310.6 C-O 45.7-1.2-166.3 14.8-169.2-376.7 O 100.6 1.1-71.7-23.4-77.8 21.4 N-H 30.8 16.5 71.4-0.1 69.6 100.6 H 6.6 2.9 21.9-0.6 21.1 34.1 CA-HA1 21.7 7.9 29.9 5.5 22.2-74.5 CA-HA2 83.3 5.5-87.1 7.7-90.6-146.6 HA1 12.5 2.9 8.3 5.4 8.9 8.7 Table S11: TD-CAMB3LYP, Glycine, Atom N 213.0 21.0 4.2 16.9 13.6-334.6 CA 273.0 14.9-253.7 37.5-257.7-623.6 C 254.2 4.9-358.4-5.1-380.7-482.5 O 122.6 0.8-131.1-19.6-139.5-90.4 H 21.3 9.4 42.5-0.1 41.2 63.7 HA1 22.8 6.2 27.0 7.2 23.8-20.2 HA2 60.5 2.6-57.4 7.2-59.4-178.7 Table S12: TD-CAMB3LYP, Glycine, Bond N 156.1 14.6-87.5 5.1-83.4-408.1 N-CA 83.7-1.0 131.9 22.9 143.6 71.8 CA 40.4 8.6-242.0 18.3-244.9-533.5 CA-C 278.3 1.5-113.7 3.4-117.4-89.1 C 92.2 4.5-232.9-11.5-251.6-301.9 C-O 45.7-0.6-137.3 9.4-140.9-272.1 O 99.8 1.1-62.5-24.3-69.0 45.7 N-H 30.0 13.9 51.5 0.7 50.3 75.1 H 6.3 2.5 16.8-0.4 16.0 26.2 CA-HA1 21.4 7.0 35.8 4.6 28.5-62.5 CA-HA2 82.0 5.2-77.2 7.3-80.3-100.4 HA1 12.2 2.7 9.1 4.9 9.6 11.0 S12

Properties of the collagen hyperpolarizability tensor Table S13: β Collagen components for the atomic additive model method β xxx β xxy β xxz β xyy β xyz β xzz β yyy β yyz β yzz β zzz TD-HF 20.4-4.6-1020.0 35.9 39.8-74.4 124.6-1154.8-33.4-2681.2 TD-B3LYP 87.0-25.8-547.2 55.5 40.7-87.4 155.9-719.8-39.2-2832.4 TD-CAMB3LYP 43.6-13.8-919.5 48.8 43.3-93.5 153.3-1080.9-46.8-3067.0 Table S14: β Collagen components for the atomic point model, i.e. no damping. method β xxx β xxy β xxz β xyy β xyz β xzz β yyy β yyz β yzz β zzz TD-HF 11.1 40.6-2383.9 34.2 100.0-209.3 154.9-2627.2-195.3-26113.7 TD-B3LYP 43.8 37.7-498.5 49.0 179.9-181.9 378.7-797.9-294.7-42116.5 TD-CAMB3LYP 20.4 53.9-2529.5 43.8 152.8-251.9 262.7-2861.6-345.8-45940.5 Table S15: β Collagen components for the bond point model, i.e. no damping. method β xxx β xxy β xxz β xyy β xyz β xzz β yyy β yyz β yzz β zzz TD-HF 41.9 39.9-2680.6 35.7 125.0-228.3 149.9-3035.3-262.7-36046.0 TD-B3LYP 77.8 44.6-367.6 49.3 242.8-106.8 409.9-912.0-537.5-70079.5 TD-CAMB3LYP 59.7 60.1-3143.5 45.7 204.4-247.1 262.6-3689.3-546.0-72749.1 S13

Table S16: β Collagen components for the atomic damped thole model method β xxx β xxy β xxz β xyy β xyz β xzz β yyy β yyz β yzz β zzz TD-HF 2.8 28.8-1554.9 26.7 79.5-164.6 143.5-1734.9-126.6-14559.2 TD-B3LYP 45.7 20.2-21.7 41.2 123.4-168.2 296.1-225.5-137.3-17328.3 TD-CAMB3LYP 14.9 31.3-1264.4 36.8 108.5-203.1 228.9-1481.7-179.9-20199.4 Table S17: β Collagen components for the bond damped thole model method β xxx β xxy β xxz β xyy β xyz β xzz β yyy β yyz β yzz β zzz TD-HF 15.9 33.8-1925.0 28.5 109.9-199.1 156.2-2192.9-180.8-23580.9 TD-B3LYP 53.1 23.8 346.1 41.7 184.0-161.2 365.4 2.2-248.1-32906.4 TD-CAMB3LYP 27.3 39.8-1631.5 38.8 161.2-233.2 263.5-1987.6-297.7-37334.4 S14

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