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The SPASIBA force field for some retinal conformers
Journal of Molecular Structure: THEOCHEM 777 (2006) 113–120 www.elsevier.com/locate/theochem
The SPASIBA force field for some retinal conformers A. Zanoun a
a,*
, S. Bouaziz a, A. Belaidi a, G. Vergoten
b
LaRTFM, De´partement de Me´canique, ENSET, BP 1523, Oran El M’naouer, Algeria b UMR CNRS 8576, USTLille, 59650 Villeneuve D’ Ascq, France Received 31 July 2006; accepted 1 August 2006 Available online 17 August 2006
Abstract In this work, we determine a reliable and transferable molecular force field for the chromophore of the visual pigments. We obtain this field by calculation using potential SPASIBA for a series of retinal conformers. The parameters were established thanks to various experimental information deduced from crystallography and more particularly from molecular vibration spectroscopy (Infra-red and Raman). The reproduction of the experimental spectra of vibrations remains always a criterion of evaluation of the reliability of a force field. If the latter is good, the field can be applied in all confidence to macromolecular blocks to undertake studies in molecular dynamics. 2006 Elsevier B.V. All rights reserved. Keywords: Molecular force field; Retinal isomers; SPASIBA; Molecular dynamics
1. Introduction Several works were carried out on retinal isomers, showing in particular the possibility of identifying isomers by their vibrational spectra [1]. In solution the frequencies of vibration very sensitive to ethylene isomerism make it possible to distinguish relatively well isomers between them [2,3]. For the same isomer, the intensities and the position of the lines do not vary according to solvents, except in the event of interaction solvent-aqueous solution. As an example, the establishment of a connection with the octanol lowers the frequency of vibration of valence C@O from 6 to 11 cm 1 [2]. For four isomers (all-trans, 9-cis, 13-cis, and 11-cis), the area of the fingerprint ranges between 900 and 1450 cm 1 [4]. The analysis of the spectra of Raman preresonance [5] shows that the vibration of valence C@C is characteristic for each isomer. On the other hand the vibration of valence C–CH3 plays a significant role for the interpretation of the resonance Raman spectra [6]. In 1977, Warshel calculated the Raman intensities of resonance for several models of retinal with the program
*
Corresponding author. Tel.: +213 71 56 46 12. E-mail address: [email protected] (A. Zanoun).
0166-1280/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2006.08.035
QCFF/Pi [7]. The latter makes it possible to obtain the optimized geometry and normal modes between the first excited states and fundamental (p fi p*). From a polyenic chain of given characteristics (length, subsistent, constants of forces) Cookingham established the dynamic equations according to the co-ordinates of each atom [8]. The complete vibrational analysis of retinal isomers was made by Saito and Tasumi [9], but the use of a simplified geometry (replacement of the cycle by methyl) for theoretical calculations shed a doubt concerning some attributions. On the basis of the same approximation, we carried out a calculation of the Raman intensities of resonance, on 7 isomers [10]. The evolution of data processing means enabled us to clearly improve the procedure of calculation compared to preceding work, by making less approximation. In the present study, the parameterization of the potential energy function SPASIBA [11] is extended to chromophore of visual pigments (isomer of the retinal). We carried out a complete calculation on the most frequent isomers i.e., all-trans, 9-cis, 11-cis and 13-cis. In addition to the structural of 11-cis and all-trans analysis, we carried out a spectral analysis of four isomers. The parameters of the field of forces are mainly given by the adjustment of the frequencies calculated on those observed. The results obtained are of very good quality (the average error is lower than
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Fig. 1. Charges and atom numbering.
10 cm 1). The force constants thus obtained are not only transferable at the similar molecular blocks (having the same chemical functions) but could also be used in studies by molecular dynamics. Following a calculation test in molecular dynamics we can affirm that the parameters thus obtained are of very good quality.
We note that the computed values are comparable with the experimental values. The standard deviation is about ˚ for the bounds of all-trans isomers and 0.05 and 0.03 A 11-cis, respectively. The latter is about 1.25 and 1.02 for the angles of valence. On the other hand, it is 5 and 3 for the plane angles.
2. Calculation procedure
3.2. Spectral analysis
To determine the new parameters of the force field, we used those determined previously for the aldehyde group [11,12] and those of the cyclic part represented by b-ionone [13]. The starting structural parameters for all-trans and 11cis are taken from the results of crystallography [14,15]. For the isomers 9-cis and 13-cis, these data are taken from all-trans, by making a rotation of 180 around the bounds C9@C10 and C13@C14, respectively. The non-positioned hydrogen in X-ray diffraction was placed while respecting the standards geometrical values. In order to simplify the calculation, the geometry of the CH3 groups was taken so that the latter were perfect tetrahedrons. The redundancies of the cycle and the CH3 groups were automatically cancelled. At the beginning an ab initio quantum calculation, based on the Hf/6-31g base ** and using the Gaussian98 software [16], enabled us to determine the atomic electronic charge (Fig. 1). The use of program SPASIBA allowed the minimization of the geometry of different molecules, the calculation of the vibration frequencies as well as the test in molecular dynamics.
In spite of the difference of the physical state between the experimental simulation and data, we obtained a good prediction of the vibration spectra for the four isomers (Table 2a, all-trans; b, 9-cis; c, 11-cis; d, 13-cis). Keeping in mind that we did not omit the cycle in our calculations, we held account in our attributions of the deformations related to the latter. Generally we note that the calculated frequencies fairly coincide the observed frequencies. The area of the high frequencies is attributed to the CH elongations. the detail of attributions for the other areas is:
3. Results and discussion The results that we obtain show the capacity of the force field SPASIBA to be reproduced at the same time, the structure and the frequencies of vibration with a good accuracy. 3.1. Structural analysis After optimization, the calculated geometry using SPASIBA is compared to the experimental data in Table 1.
• The 1620–1700 cm 1 range. The band which appears in this area is related to the vibration of valence C@O, which was confirmed by our calculations. The intensity of this band is identical for 4 isomers. The fact that it is intense in infra-red confirms that bound C@O is polar [17]. This terminal group takes part in the electronic delocalization. • The 1500–1620 cm 1 range. In this area we find the most intense Raman ray which corresponds to the vibrations of bounds C@C. It is the most concerned ray by resonance, because it corresponds to the mode of vibration having greatest Franck–Condon overlap between the fundamental and excited electronic states [18,19]. Several frequencies were calculated in this area, which corresponds to the various vibrations of existing bounds C@C in each isomer. • The 1300–1500 cm 1 range. Most of this area is allocated to the deformations methyl. We note in particular the band related to the asymmetrical deformations of the 9CH3 and 13CH3, these two methyl take part primarily in the isomerization phenomena.
A. Zanoun et al. / Journal of Molecular Structure: THEOCHEM 777 (2006) 113–120
115
Table 1 Structural Parameters Parameter in A
All-trans
11-cis
This work
Cal. [22]
Obs. [14]
This work
Cal. [22]
Obs. [15]
a. Bound length (A˚) 6A1 1A2 2A3 3A4 4A5 5@6 6A7 7@8 8A9 9@10 10A11 11@12 12A13 13@14 14A15 15@Oxy CACH3 (average) CACH3 (b average) CH (average) CH (b average) CH (CH3 average) CH (CH3 b average)
1.517 1.540 1.486 1.509 1.507 1.356 1.487 1.345 1.466 1.350 1.449 1.345 1.455 1.347 1.461 1.211 1.502 1.527 1.092 1.110 1.108 1.108
1.497 1.537 1.528 1.527 1.500 1.358 1.495 1.351 1.479 1.365 1.464 1.361 1.467 1.375 1.428 – – – – – – –
1.535 1.545 1.420 1.494 1.505 1.330 1.482 1.315 1.467 1.345 1.442 1.338 1.452 1.344 1.455 1.200 1.493 1.518 1.007 1.020 0.968 0.957
1.520 1.511 1.508 1.537 1.515 1.336 1.487 1.345 1.457 1.349 1.468 1.346 1.487 1.347 1.472 1.211 1.502 1.527 1.093 1.110 1.108 1.108
1.497 1.537 1.528 1.526 – 1.361 1.491 1.353 1.479 1.364 1.463 1.361 1.468 1.375 1.421 1.220 – – – – – –
1.528 1.523 1.498 1.532 1.521 1.333 1.486 1.339 1.461 1.347 1.454 1.339 1.472 1.358 1.467 1.213 – – – – – –
b. Angles of valence () 1A2A3 2A3A4 3A4A5 4A5@6 5@6A7 6@5A18 6A7@8 7@8A9 8A9@10 9@10A11 10@9A19 10A11@12 11@12A13 12A13@14 13@14A15 14A15@O C@CACH3 CACACH3
112.2 113.8 113.5 124.4 121.0 124.5 124.1 125.8 118.1 126.8 124.0 122.8 125.9 117.6 126.8 122.1 123.7 110.8
110.9 108.8 112.3 123.9 121.5 123.1 123.2 123.4 117.8 125.8 123.1 120.5 125.5 117.9 124.0 – – –
115.8 115.6 115.2 122.6 122.2 124.3 124.3 126.3 118.2 127.1 123.4 123.4 125.6 118.2 125.9 123.1 123.4 111.8
112.2 109.9 112.2 123.4 122.2 124.8 124.8 125.9 118.2 125.2 123.5 126.4 128.7 120.1 123.4 122.2 124.3 108.9
110.9 108.8 112.3 123.9 121.8 123.3 123.8 124.3 117.6 125.4 123.0 126.0 128.6 122.6 123.6 – – –
111.5 111.9 113.3 122.9 123.2 125.8 126.2 126.4 117.8 124.3 124.3 128.1 129.9 121.3 122.9 121.4 124.5 109.3
c. Angles of torsion () 6A1A2A3 1A2A3A4 2A3A4A5 3A4A5@6 4A5@6A7 5@6A7@8 6A7@8A9 7@8A9@10 8A9@10A11 9@10A11@12 10A11@12A13 11@12A13@14 12A13@14A15 5@6A1A2 13@14A15@Oxy 7@8A9A19 7A6A1A18
44.4 60.6 38.0 7.5 179.1 58.4 179.3 168.0 178.6 171.8 179.1 178.4 177.4 17.2 175.6 3.7 45.5
46 63 48 18 179 50 183 168 182 173 182 172 180 – – – –
42.6 50.0 31.8 6.8 178.6 58.3 180.7 175.8 179.1 180.1 175.5 181.6 177.7 – – – –
47 61.7 45.2 15.9 178.0 43.3 177.1 173.0 178.2 174.1 7.7 37.0 178.4 19.0 177.3 5.6 47.0
46 62 49 18 178 44 182 173 178 170 9 29 180 – – – –
47.4 59.1 39.8 11.5 180.4 41.4 179.6 174.0 175.5 179.3 2.1 38.7 179.8 18.2 174.5 7.2 42.8 (continued on next page)
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Table 1 (continued) Parameter
All-trans
7A6A1A17 4A5@6A1 7A6@5A16 15A14@13A20
11-cis
This work
Cal. [22]
Obs. [14]
This work
Cal. [22]
Obs. [15]
74.1 1.7 7.7 5.1
– – – –
– – – –
72.5 5.4 6.5 8.8
– – – –
74.3 1.1 3.9 3.1
Table 2 Comparison and attribution of the observed and calculated frequencies mC (cm 1) a. all-trans 1651 1620 1585 1464 1451 1443 1403 1391 1378 1357 1338 1302 1300 1286 1257 1219 1197 1196 1160 1151 1126 1092 1067 1036 1027 1003 972 964 961 908 885 856 853 842 826 rms b. 9-cis 1651 1619 1591 1551 1450 1438 1403 1387 1377 1366
mO (cm 1)
Dm (cm 1)
Attribution (PED)
Raman
IR
1665 – 1578 – 1449 –
– – – – – 1009 – 966 – 892 – 868 – 849 –
1655 1609 1573 1467 – 1443 1399 – 1375 1358 1332 1304 1281 1270 – 1215 – 1196 1163 1135 1122 1111 1070 1045 1027 1008 970 – 961 893 878 868 852 842 828
14 11 7 3 2 0 4 0 2 1 4 1 19 16 1 4 1 0 4 16 4 19 3 9 0 6 2 2 0 16 7 12 1 7 2 8.5
mC@O (76%) mC@C (22%) mC@C (cycle) (58%), mC@C (18%) daCH3 (49%), daCH2 (20%) da32CH3 (45%), da28CH3 (27%), da39CH2 (15%) daCH2 (72%) daCH3 (73%), dC–CH3 (19%) dS CH3 (29%), dCCH (12%) dS CH3 (69%), dC–CH3 (17%) q18CH3 (13%), d22C@CH (12%), d1C ¸ @CH (11%), m1C ¸ @C (11%) d22C@CH (16%), q18CH3 (12%), d26c-ch (11%), m22C@C (10%) d1C ¸ @CH (14%), m6CAC (10%) d27CACH2 (14%) m27CACH2 (12%), m24CAC (11%) dC–CH2 (25%), d42CCH (22%), m27CACH3 (12%) d39CH2 (15%), d42CCH (12%) m27CACH3 (13%), m6CAC (12%) m6CAC (32%) m27CACH3 (32%), d36CH2 (13%) m13CAC (25%), m24CAC (23%), m42CAC (18%) m13CAC (37%), m24CAC (18%) c2CAC (35%), c1C ¸ @C (34%), cC@C (14%) m36CAC (49%), m39CAC (25%) m2CAC (67%) q28CH3 (40%), q32CH3 (34%) cC@C (23%), d17CCH3 (19%), m45CACH3 (12%) cC@C (33%), dCCH (27%) dCCH (35%), mCAC (28%) cC@C (28%), mC–CH3 (cycle) (25%) mCAC (cycle) (17%), mC–CH3 (cycle) (13%), cC@C (13%) mCAC (cycle) (40%), dCCHM (17%) cC@C (66%), mC–CH3 (12%) cC@C (27%), mC–CH3 (18%) dCCH (20%), mC–CH3 (16%) sC@C (31%)
1665 – 1588 – 1447 1432 1405 – 1375 –
1662 1612 1589 1561 – 1339 – 1384 1376 1360
11 7 2 10 3 1 2 3 1 6
mC@O (76%) mC@C (66%) mC@C (47%), m26C@C (22%) mC@C (69%) da18CH3 (92%) da7CH3 (91%) dS 46CH3 (92%) dS 7CH3 (87%) dS 7CH3 (87%) q18CH3 (44%), d16HC@C (21%), m17CAC (21%) (continued on next page)
1391 – – 1334 1301 1281 1270 1256 – 1198 – 1164
A. Zanoun et al. / Journal of Molecular Structure: THEOCHEM 777 (2006) 113–120
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Table 2 (continued) mC (cm 1) 1346 1319 1304 1295 1284 1257 1216 1197 1196 1144 1095 1067 1036 1027 1002 961 910 886 867 844 838 829 rms c. 11-cis 1650 1615 1583 1573 1566 1526 1450 1429 1398 1385 1343 1328 1299 1271 1256 1214 1197 1177 1156 1142 1046 1036 1025 974 961 903 883 868 854 824 792 rms d. 13-cis 1655 1582 1550 1446
mO (cm 1)
Dm (cm 1)
Attribution (PED)
Raman
IR
– 1330 1295 – 1279 1261 1217 1201 1185 1148 1113 – 1046 1029 1008 960 – 883 872 852 – –
1340 1326 1306 1291 1277 1259 1220 1201 1173 1145 1113 1062 1037 1030 1014 963 896 884 874 854 845 821
6 7 9 4 5 2 1 4 11 4 18 5 1 2 6 1 14 2 5 10 7 8 7
d25HCC (19%) d39CH2 (29%) dCH2 (28%), mC–CH3 (18%) mC@C (18%), dHCC (29%) mbCAC (31%), mbC–CH3 (17%), dCH2 (16%) dCH2 (51%) dCCH2 (38%), m6CAC (13%) mbC–CH3 (18%), mbCAC (12%), m6CAC (38%), dCCH (12%) m24CAC (38%), m42CAC (23%) m4CAC (36%), m6CAC (22%) mbCAC (79%) m2CAC (66%) m28CH3 (47%), d32CH3 (40%) q18CH3 (41%), s15C@C (25%) c22C@C (22%) cC@C (23%) mbCAC (43%) m17CACH3 (22%), m17CAC (19%) sC@C (48%) sC@C (70%) s22C@C (32%)
1659 1600 1582 – 1558 1530 1453 1428 1402 1389 1347 1317 1295 1271 – 1211 1187 1173 1146 1132 – 1031 1018 976 965 903 877 866 847 831 769
1660 – – 1574 – – 1446 – – 1382 1338 – – 1268 1255 1203 1188 – 1140 – 1048 – 1018 – – 894 877 868 – – –
9 15 1 1 8 4 3 1 4 4 4 11 4 0 1 3 10 4 10 10 2 5 7 2 4 1 6 0 7 7 23 7.3
mC@O (78%) mC@C (68%) mbC@C (69%) m4C@C (22%), m1C ¸ @C (21%), m22C@C (21%) m4C@C (50%), m22C@C (12%) m1C ¸ @C (29%), m15C@C (28%), m22C@C (11%) da42CH2 (56%), da32CH3 (11%) dS 7CH3 (88%) dS 46CH3 (91%) q18CH3 (47%) d27CCH2 (21%), d39CCH2 (23%) d5HCC (61%), m6CACH3 (14%) mbC–C (25%) d12HCC (29%), d14HCC (24%), mC@C (11%) dbCCH2 (25%), mbC–C (25%) dHCO (37%), d3HCC (19%) m27CACH3 (19%) m27CACH3 (17%), qbCH3 (15%) m27CACH3 (20%), m45CACH3 (11%) m24CAC (40%), mb42CAC (23%) c2CAC (50%) mbCAC (69%), qbCH3 (13%) d27CH3 (77%) s1C ¸ @C (47%), d14HCC (10%) m27CACH3 (35%), d27CACH3 (27%%) dbHCC (11%), m27CACH3 (10%) mbCAC (32%), sC@C (16%) s15C@C (44%) s15C@C (19%) m27CACH3 (14%) s22C@C (60%)
1659 1582 1545 1450
1657 – – –
4 0 5 4
mC@O(75%) mbC@C (72%) m22C@C (30%), m4C@C (23%), m15C@C (11%) da18CH3 (85%) (continued on next page)
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Table 2 (continued) mC (cm 1) 1407 1372 1367 1343 1302 1333 1300 1283 1256 1228 1196 1177 1130 1125 1047 1024 1006 963 951 899 881 861 812 rms
mO (cm 1) Raman
IR
1403 – – 1350 1301 1337 1310 – – 1224 1193 1167 – 1117 1044 – 1014 972 958 893 887 866 –
1400 1380 1362 – 1304 1335 1310 1280 1254 1218 1192 1164 1130 1117 – 1025 1014 966 – – 883 862 820
Dm (cm 1)
Attribution (PED)
4 8 5 7 1 4 10 3 2 4 3 10 0 8 3 1 8 9 7 6 6 5 8 6
da18CH3 (47%) d25HCC (24%), d7CH3 (18%) d7CH3 (44%) dbHCC (67%) d1C ¸ @CH(14%), m6CAC (10%) d7CH3 (32%), d5HCC (18%), m6CAC (14%) mbCAC (23%) dbCCH (22%), m24CAC (11%), m27CAC (11%) dC–CH2 (25%), d42CCH (22%), m27CACH3 (12%) d16HCC (26%), d6CACH3 (15%) d16HCC (20%), d14HCC (13%) mbC–CH3 (28%), m24CAC (11%), m24CAC (23%), m13CAC (22%), mbCAC (21%) m13CAC (41%), m24CAC (15%) mbCCH (27%), mbCAC (18%) q7CH3 (73%) q18CH3 (29%), q23CH3 (18%), m17CAC (13%) s6CAC (30%), w14H (14%), w12H (10%) s22C@C (62%), w25H (13%), w23H (11%) s4C@C (64%), w5H (11%) m6CACH3 (27%), m6CAC (16%), m17CACH3 (13%) w16H (30%), s15C@C (15%), w12H (10%) w25H (23%), w12H (15%) w14H (14%)
mO from Saito and Tasumi [9].
• The 990–1300 cm 1 range. In this area we find the vibrations of valence C–C and of deformation CCH. This area contains also the fingerprint. • The low frequency range below 900 cm 1. It contains the deformations except CH plane, deformations CCC and the torsion modes. The results which we obtained show the capacity of the force field of SPASIBA to reproduce simultaneously, the structure with a good precision and the vibration frequencies with the best potential energy distribution (PED). The force constants are showed in Table 3 (a, K; b, H and F; c, Vn/2 for torsions; d, Vn/2 for the deformations out of the plane; e, lCH2, vCH2 and vCH3). 3.3. Test of the force field by molecular dynamics In order to test the validity of the field of forces which we determined, a molecular dynamics calculation (DM) was carried out. We chose a structure of all-trans isomer near to the experimental structure. Before launching the molecular dynamics module we followed the following stages: (a) Thermalization so that the system is led to the temperature of simulation. The equations of motion are then integrated by regularly increasing speeds using a multiplier in order to raise the temperature. Generally the thermalization is reached in about ten picoseconds (ps).
(b) Balancing in order to stabilize the system at the temperature of simulation. (c) Finally, the dynamic phase where the structures and speeds are saved every 1 ps to account for the DM history. Initial speeds of the atoms are assigned according to the Maxwell–Boltzman distribution. The cut-off distance used ˚ . During simulation, for the non-bound interaction is 8 A all the bound lengths are given values of balance by the Shake procedure [20]. In order to average the rapid fluctuations, it is more interesting to look at the evolution during a maximum of 50 fs. The analysis of atom at a time can be associated with the crystallographic temperature factors. These fluctuations are due to the absence of crystalline environment (the DM is carried out in the vacuum). The steps of integration are of 0.5 ps, speeds and the temperatures are calibrated every 10 ps to remain fixed around 300 K. the time of simulation is 500 ps. The thermalization time is approximately 10 ps, and be considered as our origin of times. The kinetic energy on the potential energy ratio indicates that the thermalization of our dynamics was carried out. We limit the calculation to 25 ps, knowing that in experiments the passage of the isomer 11-cis to all-trans is carried out at the end of 2 ps [21]. The first plane angle of interest is (5@6A7@8) because it is between the cycle and the linear part. Its computed value by SPASIBA is 58.4 (Fig. 2) and 43.3 for all-trans isomers and 11cis, the experimental values are 58.3 and 41.4, respectively [14,15]. The passage of the 11-cis to all-trans is carried
A. Zanoun et al. / Journal of Molecular Structure: THEOCHEM 777 (2006) 113–120 Table 3 The force constants Parameter
Table 3 (continued) K (kcal mol
a. Stretching (K) C-C CC-CC CC-C C-H CC-H C-CT C-C9 LC-HX LC-O C9-HM CT-CT CT-C9 C9-C9
1
˚ 1) A
r0 (A)
455.28 455.28 260.00 315.07 315.07 190.00 190.00 275.07 700.00 320.0 165.00 165.00 165.00
H (kcal mol
1
rad 2)
b. Bending (H and F) OALCAHX 20.00 CALCAHX 13.00 OCALCAC 23.00 LCACAH 10.00 LCACAC 6.00 CACAH 13.02 CCACCAH 13.02 CACCAH 10.02 CCACAH 10.02 CACTAHC 12.89 CAC9AHM 12.89 CACACC 18.70 CCACCAC 18.70 CACACT 14.70 CACAC9 14.70 CCACACT 12.70 CACTACT 18.10 CAC9AC9 18.10 CACTAC9 18.10 C9ACACT 12.70 HCACTAHC 29.60 HMAC9AHM 29.60 CTAC9AHM 15.10 C9AC9AHM 15.10 CTACTAHC 15.81 CTACTACT 18.70 CTACTAC9 18.70 CTAC9AC9 18.70 C9AC9AC9 18.70 CTACAH 12.82 CACTAHM 12.89 CTACACT 12.70
c. Torsion XACTACAC XACTACACC XAC9ACAC C9AC9ACACT C9ACACTAHC CTACAC9AHM XACTACTAX CTACACTAHC XACACCAH CACACCACC
119
1.34 1.34 1.47 1.09 1.49 1.49 1.10 1.21 1.11 1.11 1.53 1.53 1.53
F (kcal mol
1
10.50 53.00 140.00 53.00 60.00 75.70 75.70 70.70 70.70 70.70 70.70 50.47 50.47 40.47 40.47 47.47 47.47 47.47 47.47 47.47 10.07 10.07 69.43 69.43 69.43 47.47 47.47 47.47 47.47 50.70 90.70 47.47 Vn/2
c (deg.)
0.54 0.17 0.54 0.15 0.05 0.05 0.15 0.08 0.20 1.00
180.0 180.0 180.0 180.0 180.0 180.0 0.0 180.0 180.0 180.0
˚ 1) A
h0 (deg.) 120.9 115.0 123.0 117.3 120.0 120.0 120.0 120.0 120.0 110.2 110.2 124.7 124.7 127.7 127.7 124.0 109.0 109.0 109.0 118.0 108.5 108.5 109.5 109.5 109.5 111.8 111.8 111.8 111.8 117.0 110.2 118.0
Parameter
CTACACCACC XAXACAH XAX—CACT
d. Out of plane bending LCACACACT LCACACACC HACACAH HACCACCAH HACCACCAX HACACAX CTACACACC XACCACCAX XACACAX XAXALCAHX CTACACCACC Constants e. CH2 and CH3 lCH2 vCH2 vCH3
K (kcal mol
1
˚ 1) A
r0 (A)
Vn/2
c (deg.)
1.10 0.30 0.30
180.0 180.0 180.0 Vn/2
c (deg.)
5.75 6.10 5.40 5.40 4.60 4.60 5.75 6.10 6.10 11.00 2.50
180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0
n 2.0 2.0 2.0 N 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 Values 4.00 5.75 3.60
out using torsion (11@12). In experiments the torsion value is 2.1 for the 11-cis and 175.5 for the all-trans. They were calculated at 7.71 and 179.1, respectively. The angle of valence (1A13@14) is calculated at 120.1 (t-trans) and 117.6 (11-cis). The experimental values are 121.3 and 117.6, respectively. The most stable conformers are the 11-cis (0) and the t-trans (180). We conclude that the computed values by DM using SPASIBA are of excellent quality (good agreement with the experiment) which confirms the validity of the selected forces field and has a double aspects (spectroscopic and of molecular mechanics). The obtained results allow us to continue to study these molecules in biological environment and to compare with those given by Hayashi et al. [23]. 4. Conclusion
n 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 2.0 2.0
If we consider molecular dynamics as a welcomed application, it is essential that the field of forces reproduces at least the vibrational properties of a molecule in order to expect to study the dynamic behavior of this molecule. In the harmonic dynamics applications, the use of the usual Molecular Mechanics force fields led to intermediate results (bad agreement between theoretical frequencies and experimental results) simply because the commercially available force fields or an academic way does not have spectroscopic ‘‘quality’’. The SPASIBA force field was thus designed to reproduce simultaneously, the structures and the vibration spectra. SPASIBA, thus parameterized for the chromophore of the visual pigments gives very good results. The continua-
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Fig. 2. Angle between the cycle and linear part after MD.
tion of this work will be the study by molecular dynamics of chromophore of the pigments in a biological environment (with the opsin). References [1] E.R. Lipincott, T.E. Kenney, J. Am. Chem. Soc. 84 (1962) 3641. [2] L. Rimai, D. Gill, J.L. Parsens, J. Am. Chem. Soc. 93 (1971) 1353. [3] D. Gill, Mr. E. Heyde, L. Rimai, J. Am. Chem. Soc. 93 (1971) 6288. [4] R.H. Callender, A. Doukas, R. Crouch, K. Nakanishi, Biochemistry 15 (8) (1976) 1621. [5] R.E. Cookingham, A. Lewis, D.W. Collins, Mr. A. Marcus, J. Am. Chem. Soc. 98 (1976) 2757. [6] G. Eyring, B. Currey, R. Mathies, I. Palings, J. Lungtenburg, Biochemistry 19 (1980) 2410. [7] A. Warshel, P. Dauber, J. Chem. Phys. 66 (12) (1977) 5477. [8] R. E Cookingham, A. Lewis, A.T. Lemly, Biochemistry 17 (22) (1978) 4699. [9] S. Saito, Mr. Tasumi, J. Raman Spectrosc. 14 (4) (1983) 236. [10] A. Zanoun, Thesis 3eme Cycle LilleII (1986). [11] A. Zanoun, V. Durier, A. Belaidi, G. Vergoten, J. Mol. Struct. 476 (1999) 261. [12] V. Durier, A. Zanoun, A. Belaidi, G. Vergoten, J. Mol. Struct. 476 (1999) 271. [13] A. Zanoun, P. Lagant, G. Vergoten, J. Mol. Struct. 510 (1999) 85.
[14] T. Hamanaka, T. Mitsui, T. Ashida, Mr. Kkudu, Acta Crystallogr. B28 (1972) 214. [15] R.D. Gilardi, I.L. Karle, J. Karle, Acta Crystallogr. B28 (1972) 2605. [16] Gaussian 98 (Revision A.11.1), M.J. Frich, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.r. Cheeseman, V.G. Zakrzewski, G.A. Montgomery, Jr., R.E. Stramann, J. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Glifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, P. Salvador, J.J. Dannenberg, D.K. Malick, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaroni, R. Gomperts, D.J. Fox, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B.G. Johnson, W. Chen, M.W. Wong, J.L. Andres, G. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, Gaussian, Inc., Pittsburgh PA, 2001. [17] Y. Koyama, Y. Mukai, J. Umemura, M. Ito, K. Tsukida, J. Raman Spectrosc. 15 (5) (1984) 300. [18] A. Warshel, Mr. Karplus, J. Am. Chem. Soc. 96 (1974) 5676. [19] B. Brooks, R. Bruccoleri, B. Olafson, D. States, S. Samanathan, Mr. Karplus, J. Comput. Chem. 4 (1983) 187. [20] L. Verlet, Phys. Rev. 159 (1967) 98. [21] Q. Wang, R.W. Schoenlein, L.A. Peteanu, R.A. Mathis, C.V. Shank, Science 266 (1994) 422. [22] R. Rowan III, A. Warshel, B.D. Sykes, M. Karplus, Biochemistry 13 (5) (1974) 970. [23] S. Hayashi, E. Tajkhorshid, K. Schulten, Biophys. J. 85 (2003) 1440.
The SPASIBA force field for some retinal conformers A. Zanoun a
a,*
, S. Bouaziz a, A. Belaidi a, G. Vergoten
b
LaRTFM, De´partement de Me´canique, ENSET, BP 1523, Oran El M’naouer, Algeria b UMR CNRS 8576, USTLille, 59650 Villeneuve D’ Ascq, France Received 31 July 2006; accepted 1 August 2006 Available online 17 August 2006
Abstract In this work, we determine a reliable and transferable molecular force field for the chromophore of the visual pigments. We obtain this field by calculation using potential SPASIBA for a series of retinal conformers. The parameters were established thanks to various experimental information deduced from crystallography and more particularly from molecular vibration spectroscopy (Infra-red and Raman). The reproduction of the experimental spectra of vibrations remains always a criterion of evaluation of the reliability of a force field. If the latter is good, the field can be applied in all confidence to macromolecular blocks to undertake studies in molecular dynamics. 2006 Elsevier B.V. All rights reserved. Keywords: Molecular force field; Retinal isomers; SPASIBA; Molecular dynamics
1. Introduction Several works were carried out on retinal isomers, showing in particular the possibility of identifying isomers by their vibrational spectra [1]. In solution the frequencies of vibration very sensitive to ethylene isomerism make it possible to distinguish relatively well isomers between them [2,3]. For the same isomer, the intensities and the position of the lines do not vary according to solvents, except in the event of interaction solvent-aqueous solution. As an example, the establishment of a connection with the octanol lowers the frequency of vibration of valence C@O from 6 to 11 cm 1 [2]. For four isomers (all-trans, 9-cis, 13-cis, and 11-cis), the area of the fingerprint ranges between 900 and 1450 cm 1 [4]. The analysis of the spectra of Raman preresonance [5] shows that the vibration of valence C@C is characteristic for each isomer. On the other hand the vibration of valence C–CH3 plays a significant role for the interpretation of the resonance Raman spectra [6]. In 1977, Warshel calculated the Raman intensities of resonance for several models of retinal with the program
*
Corresponding author. Tel.: +213 71 56 46 12. E-mail address: [email protected] (A. Zanoun).
0166-1280/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2006.08.035
QCFF/Pi [7]. The latter makes it possible to obtain the optimized geometry and normal modes between the first excited states and fundamental (p fi p*). From a polyenic chain of given characteristics (length, subsistent, constants of forces) Cookingham established the dynamic equations according to the co-ordinates of each atom [8]. The complete vibrational analysis of retinal isomers was made by Saito and Tasumi [9], but the use of a simplified geometry (replacement of the cycle by methyl) for theoretical calculations shed a doubt concerning some attributions. On the basis of the same approximation, we carried out a calculation of the Raman intensities of resonance, on 7 isomers [10]. The evolution of data processing means enabled us to clearly improve the procedure of calculation compared to preceding work, by making less approximation. In the present study, the parameterization of the potential energy function SPASIBA [11] is extended to chromophore of visual pigments (isomer of the retinal). We carried out a complete calculation on the most frequent isomers i.e., all-trans, 9-cis, 11-cis and 13-cis. In addition to the structural of 11-cis and all-trans analysis, we carried out a spectral analysis of four isomers. The parameters of the field of forces are mainly given by the adjustment of the frequencies calculated on those observed. The results obtained are of very good quality (the average error is lower than
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Fig. 1. Charges and atom numbering.
10 cm 1). The force constants thus obtained are not only transferable at the similar molecular blocks (having the same chemical functions) but could also be used in studies by molecular dynamics. Following a calculation test in molecular dynamics we can affirm that the parameters thus obtained are of very good quality.
We note that the computed values are comparable with the experimental values. The standard deviation is about ˚ for the bounds of all-trans isomers and 0.05 and 0.03 A 11-cis, respectively. The latter is about 1.25 and 1.02 for the angles of valence. On the other hand, it is 5 and 3 for the plane angles.
2. Calculation procedure
3.2. Spectral analysis
To determine the new parameters of the force field, we used those determined previously for the aldehyde group [11,12] and those of the cyclic part represented by b-ionone [13]. The starting structural parameters for all-trans and 11cis are taken from the results of crystallography [14,15]. For the isomers 9-cis and 13-cis, these data are taken from all-trans, by making a rotation of 180 around the bounds C9@C10 and C13@C14, respectively. The non-positioned hydrogen in X-ray diffraction was placed while respecting the standards geometrical values. In order to simplify the calculation, the geometry of the CH3 groups was taken so that the latter were perfect tetrahedrons. The redundancies of the cycle and the CH3 groups were automatically cancelled. At the beginning an ab initio quantum calculation, based on the Hf/6-31g base ** and using the Gaussian98 software [16], enabled us to determine the atomic electronic charge (Fig. 1). The use of program SPASIBA allowed the minimization of the geometry of different molecules, the calculation of the vibration frequencies as well as the test in molecular dynamics.
In spite of the difference of the physical state between the experimental simulation and data, we obtained a good prediction of the vibration spectra for the four isomers (Table 2a, all-trans; b, 9-cis; c, 11-cis; d, 13-cis). Keeping in mind that we did not omit the cycle in our calculations, we held account in our attributions of the deformations related to the latter. Generally we note that the calculated frequencies fairly coincide the observed frequencies. The area of the high frequencies is attributed to the CH elongations. the detail of attributions for the other areas is:
3. Results and discussion The results that we obtain show the capacity of the force field SPASIBA to be reproduced at the same time, the structure and the frequencies of vibration with a good accuracy. 3.1. Structural analysis After optimization, the calculated geometry using SPASIBA is compared to the experimental data in Table 1.
• The 1620–1700 cm 1 range. The band which appears in this area is related to the vibration of valence C@O, which was confirmed by our calculations. The intensity of this band is identical for 4 isomers. The fact that it is intense in infra-red confirms that bound C@O is polar [17]. This terminal group takes part in the electronic delocalization. • The 1500–1620 cm 1 range. In this area we find the most intense Raman ray which corresponds to the vibrations of bounds C@C. It is the most concerned ray by resonance, because it corresponds to the mode of vibration having greatest Franck–Condon overlap between the fundamental and excited electronic states [18,19]. Several frequencies were calculated in this area, which corresponds to the various vibrations of existing bounds C@C in each isomer. • The 1300–1500 cm 1 range. Most of this area is allocated to the deformations methyl. We note in particular the band related to the asymmetrical deformations of the 9CH3 and 13CH3, these two methyl take part primarily in the isomerization phenomena.
A. Zanoun et al. / Journal of Molecular Structure: THEOCHEM 777 (2006) 113–120
115
Table 1 Structural Parameters Parameter in A
All-trans
11-cis
This work
Cal. [22]
Obs. [14]
This work
Cal. [22]
Obs. [15]
a. Bound length (A˚) 6A1 1A2 2A3 3A4 4A5 5@6 6A7 7@8 8A9 9@10 10A11 11@12 12A13 13@14 14A15 15@Oxy CACH3 (average) CACH3 (b average) CH (average) CH (b average) CH (CH3 average) CH (CH3 b average)
1.517 1.540 1.486 1.509 1.507 1.356 1.487 1.345 1.466 1.350 1.449 1.345 1.455 1.347 1.461 1.211 1.502 1.527 1.092 1.110 1.108 1.108
1.497 1.537 1.528 1.527 1.500 1.358 1.495 1.351 1.479 1.365 1.464 1.361 1.467 1.375 1.428 – – – – – – –
1.535 1.545 1.420 1.494 1.505 1.330 1.482 1.315 1.467 1.345 1.442 1.338 1.452 1.344 1.455 1.200 1.493 1.518 1.007 1.020 0.968 0.957
1.520 1.511 1.508 1.537 1.515 1.336 1.487 1.345 1.457 1.349 1.468 1.346 1.487 1.347 1.472 1.211 1.502 1.527 1.093 1.110 1.108 1.108
1.497 1.537 1.528 1.526 – 1.361 1.491 1.353 1.479 1.364 1.463 1.361 1.468 1.375 1.421 1.220 – – – – – –
1.528 1.523 1.498 1.532 1.521 1.333 1.486 1.339 1.461 1.347 1.454 1.339 1.472 1.358 1.467 1.213 – – – – – –
b. Angles of valence () 1A2A3 2A3A4 3A4A5 4A5@6 5@6A7 6@5A18 6A7@8 7@8A9 8A9@10 9@10A11 10@9A19 10A11@12 11@12A13 12A13@14 13@14A15 14A15@O C@CACH3 CACACH3
112.2 113.8 113.5 124.4 121.0 124.5 124.1 125.8 118.1 126.8 124.0 122.8 125.9 117.6 126.8 122.1 123.7 110.8
110.9 108.8 112.3 123.9 121.5 123.1 123.2 123.4 117.8 125.8 123.1 120.5 125.5 117.9 124.0 – – –
115.8 115.6 115.2 122.6 122.2 124.3 124.3 126.3 118.2 127.1 123.4 123.4 125.6 118.2 125.9 123.1 123.4 111.8
112.2 109.9 112.2 123.4 122.2 124.8 124.8 125.9 118.2 125.2 123.5 126.4 128.7 120.1 123.4 122.2 124.3 108.9
110.9 108.8 112.3 123.9 121.8 123.3 123.8 124.3 117.6 125.4 123.0 126.0 128.6 122.6 123.6 – – –
111.5 111.9 113.3 122.9 123.2 125.8 126.2 126.4 117.8 124.3 124.3 128.1 129.9 121.3 122.9 121.4 124.5 109.3
c. Angles of torsion () 6A1A2A3 1A2A3A4 2A3A4A5 3A4A5@6 4A5@6A7 5@6A7@8 6A7@8A9 7@8A9@10 8A9@10A11 9@10A11@12 10A11@12A13 11@12A13@14 12A13@14A15 5@6A1A2 13@14A15@Oxy 7@8A9A19 7A6A1A18
44.4 60.6 38.0 7.5 179.1 58.4 179.3 168.0 178.6 171.8 179.1 178.4 177.4 17.2 175.6 3.7 45.5
46 63 48 18 179 50 183 168 182 173 182 172 180 – – – –
42.6 50.0 31.8 6.8 178.6 58.3 180.7 175.8 179.1 180.1 175.5 181.6 177.7 – – – –
47 61.7 45.2 15.9 178.0 43.3 177.1 173.0 178.2 174.1 7.7 37.0 178.4 19.0 177.3 5.6 47.0
46 62 49 18 178 44 182 173 178 170 9 29 180 – – – –
47.4 59.1 39.8 11.5 180.4 41.4 179.6 174.0 175.5 179.3 2.1 38.7 179.8 18.2 174.5 7.2 42.8 (continued on next page)
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Table 1 (continued) Parameter
All-trans
7A6A1A17 4A5@6A1 7A6@5A16 15A14@13A20
11-cis
This work
Cal. [22]
Obs. [14]
This work
Cal. [22]
Obs. [15]
74.1 1.7 7.7 5.1
– – – –
– – – –
72.5 5.4 6.5 8.8
– – – –
74.3 1.1 3.9 3.1
Table 2 Comparison and attribution of the observed and calculated frequencies mC (cm 1) a. all-trans 1651 1620 1585 1464 1451 1443 1403 1391 1378 1357 1338 1302 1300 1286 1257 1219 1197 1196 1160 1151 1126 1092 1067 1036 1027 1003 972 964 961 908 885 856 853 842 826 rms b. 9-cis 1651 1619 1591 1551 1450 1438 1403 1387 1377 1366
mO (cm 1)
Dm (cm 1)
Attribution (PED)
Raman
IR
1665 – 1578 – 1449 –
– – – – – 1009 – 966 – 892 – 868 – 849 –
1655 1609 1573 1467 – 1443 1399 – 1375 1358 1332 1304 1281 1270 – 1215 – 1196 1163 1135 1122 1111 1070 1045 1027 1008 970 – 961 893 878 868 852 842 828
14 11 7 3 2 0 4 0 2 1 4 1 19 16 1 4 1 0 4 16 4 19 3 9 0 6 2 2 0 16 7 12 1 7 2 8.5
mC@O (76%) mC@C (22%) mC@C (cycle) (58%), mC@C (18%) daCH3 (49%), daCH2 (20%) da32CH3 (45%), da28CH3 (27%), da39CH2 (15%) daCH2 (72%) daCH3 (73%), dC–CH3 (19%) dS CH3 (29%), dCCH (12%) dS CH3 (69%), dC–CH3 (17%) q18CH3 (13%), d22C@CH (12%), d1C ¸ @CH (11%), m1C ¸ @C (11%) d22C@CH (16%), q18CH3 (12%), d26c-ch (11%), m22C@C (10%) d1C ¸ @CH (14%), m6CAC (10%) d27CACH2 (14%) m27CACH2 (12%), m24CAC (11%) dC–CH2 (25%), d42CCH (22%), m27CACH3 (12%) d39CH2 (15%), d42CCH (12%) m27CACH3 (13%), m6CAC (12%) m6CAC (32%) m27CACH3 (32%), d36CH2 (13%) m13CAC (25%), m24CAC (23%), m42CAC (18%) m13CAC (37%), m24CAC (18%) c2CAC (35%), c1C ¸ @C (34%), cC@C (14%) m36CAC (49%), m39CAC (25%) m2CAC (67%) q28CH3 (40%), q32CH3 (34%) cC@C (23%), d17CCH3 (19%), m45CACH3 (12%) cC@C (33%), dCCH (27%) dCCH (35%), mCAC (28%) cC@C (28%), mC–CH3 (cycle) (25%) mCAC (cycle) (17%), mC–CH3 (cycle) (13%), cC@C (13%) mCAC (cycle) (40%), dCCHM (17%) cC@C (66%), mC–CH3 (12%) cC@C (27%), mC–CH3 (18%) dCCH (20%), mC–CH3 (16%) sC@C (31%)
1665 – 1588 – 1447 1432 1405 – 1375 –
1662 1612 1589 1561 – 1339 – 1384 1376 1360
11 7 2 10 3 1 2 3 1 6
mC@O (76%) mC@C (66%) mC@C (47%), m26C@C (22%) mC@C (69%) da18CH3 (92%) da7CH3 (91%) dS 46CH3 (92%) dS 7CH3 (87%) dS 7CH3 (87%) q18CH3 (44%), d16HC@C (21%), m17CAC (21%) (continued on next page)
1391 – – 1334 1301 1281 1270 1256 – 1198 – 1164
A. Zanoun et al. / Journal of Molecular Structure: THEOCHEM 777 (2006) 113–120
117
Table 2 (continued) mC (cm 1) 1346 1319 1304 1295 1284 1257 1216 1197 1196 1144 1095 1067 1036 1027 1002 961 910 886 867 844 838 829 rms c. 11-cis 1650 1615 1583 1573 1566 1526 1450 1429 1398 1385 1343 1328 1299 1271 1256 1214 1197 1177 1156 1142 1046 1036 1025 974 961 903 883 868 854 824 792 rms d. 13-cis 1655 1582 1550 1446
mO (cm 1)
Dm (cm 1)
Attribution (PED)
Raman
IR
– 1330 1295 – 1279 1261 1217 1201 1185 1148 1113 – 1046 1029 1008 960 – 883 872 852 – –
1340 1326 1306 1291 1277 1259 1220 1201 1173 1145 1113 1062 1037 1030 1014 963 896 884 874 854 845 821
6 7 9 4 5 2 1 4 11 4 18 5 1 2 6 1 14 2 5 10 7 8 7
d25HCC (19%) d39CH2 (29%) dCH2 (28%), mC–CH3 (18%) mC@C (18%), dHCC (29%) mbCAC (31%), mbC–CH3 (17%), dCH2 (16%) dCH2 (51%) dCCH2 (38%), m6CAC (13%) mbC–CH3 (18%), mbCAC (12%), m6CAC (38%), dCCH (12%) m24CAC (38%), m42CAC (23%) m4CAC (36%), m6CAC (22%) mbCAC (79%) m2CAC (66%) m28CH3 (47%), d32CH3 (40%) q18CH3 (41%), s15C@C (25%) c22C@C (22%) cC@C (23%) mbCAC (43%) m17CACH3 (22%), m17CAC (19%) sC@C (48%) sC@C (70%) s22C@C (32%)
1659 1600 1582 – 1558 1530 1453 1428 1402 1389 1347 1317 1295 1271 – 1211 1187 1173 1146 1132 – 1031 1018 976 965 903 877 866 847 831 769
1660 – – 1574 – – 1446 – – 1382 1338 – – 1268 1255 1203 1188 – 1140 – 1048 – 1018 – – 894 877 868 – – –
9 15 1 1 8 4 3 1 4 4 4 11 4 0 1 3 10 4 10 10 2 5 7 2 4 1 6 0 7 7 23 7.3
mC@O (78%) mC@C (68%) mbC@C (69%) m4C@C (22%), m1C ¸ @C (21%), m22C@C (21%) m4C@C (50%), m22C@C (12%) m1C ¸ @C (29%), m15C@C (28%), m22C@C (11%) da42CH2 (56%), da32CH3 (11%) dS 7CH3 (88%) dS 46CH3 (91%) q18CH3 (47%) d27CCH2 (21%), d39CCH2 (23%) d5HCC (61%), m6CACH3 (14%) mbC–C (25%) d12HCC (29%), d14HCC (24%), mC@C (11%) dbCCH2 (25%), mbC–C (25%) dHCO (37%), d3HCC (19%) m27CACH3 (19%) m27CACH3 (17%), qbCH3 (15%) m27CACH3 (20%), m45CACH3 (11%) m24CAC (40%), mb42CAC (23%) c2CAC (50%) mbCAC (69%), qbCH3 (13%) d27CH3 (77%) s1C ¸ @C (47%), d14HCC (10%) m27CACH3 (35%), d27CACH3 (27%%) dbHCC (11%), m27CACH3 (10%) mbCAC (32%), sC@C (16%) s15C@C (44%) s15C@C (19%) m27CACH3 (14%) s22C@C (60%)
1659 1582 1545 1450
1657 – – –
4 0 5 4
mC@O(75%) mbC@C (72%) m22C@C (30%), m4C@C (23%), m15C@C (11%) da18CH3 (85%) (continued on next page)
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A. Zanoun et al. / Journal of Molecular Structure: THEOCHEM 777 (2006) 113–120
Table 2 (continued) mC (cm 1) 1407 1372 1367 1343 1302 1333 1300 1283 1256 1228 1196 1177 1130 1125 1047 1024 1006 963 951 899 881 861 812 rms
mO (cm 1) Raman
IR
1403 – – 1350 1301 1337 1310 – – 1224 1193 1167 – 1117 1044 – 1014 972 958 893 887 866 –
1400 1380 1362 – 1304 1335 1310 1280 1254 1218 1192 1164 1130 1117 – 1025 1014 966 – – 883 862 820
Dm (cm 1)
Attribution (PED)
4 8 5 7 1 4 10 3 2 4 3 10 0 8 3 1 8 9 7 6 6 5 8 6
da18CH3 (47%) d25HCC (24%), d7CH3 (18%) d7CH3 (44%) dbHCC (67%) d1C ¸ @CH(14%), m6CAC (10%) d7CH3 (32%), d5HCC (18%), m6CAC (14%) mbCAC (23%) dbCCH (22%), m24CAC (11%), m27CAC (11%) dC–CH2 (25%), d42CCH (22%), m27CACH3 (12%) d16HCC (26%), d6CACH3 (15%) d16HCC (20%), d14HCC (13%) mbC–CH3 (28%), m24CAC (11%), m24CAC (23%), m13CAC (22%), mbCAC (21%) m13CAC (41%), m24CAC (15%) mbCCH (27%), mbCAC (18%) q7CH3 (73%) q18CH3 (29%), q23CH3 (18%), m17CAC (13%) s6CAC (30%), w14H (14%), w12H (10%) s22C@C (62%), w25H (13%), w23H (11%) s4C@C (64%), w5H (11%) m6CACH3 (27%), m6CAC (16%), m17CACH3 (13%) w16H (30%), s15C@C (15%), w12H (10%) w25H (23%), w12H (15%) w14H (14%)
mO from Saito and Tasumi [9].
• The 990–1300 cm 1 range. In this area we find the vibrations of valence C–C and of deformation CCH. This area contains also the fingerprint. • The low frequency range below 900 cm 1. It contains the deformations except CH plane, deformations CCC and the torsion modes. The results which we obtained show the capacity of the force field of SPASIBA to reproduce simultaneously, the structure with a good precision and the vibration frequencies with the best potential energy distribution (PED). The force constants are showed in Table 3 (a, K; b, H and F; c, Vn/2 for torsions; d, Vn/2 for the deformations out of the plane; e, lCH2, vCH2 and vCH3). 3.3. Test of the force field by molecular dynamics In order to test the validity of the field of forces which we determined, a molecular dynamics calculation (DM) was carried out. We chose a structure of all-trans isomer near to the experimental structure. Before launching the molecular dynamics module we followed the following stages: (a) Thermalization so that the system is led to the temperature of simulation. The equations of motion are then integrated by regularly increasing speeds using a multiplier in order to raise the temperature. Generally the thermalization is reached in about ten picoseconds (ps).
(b) Balancing in order to stabilize the system at the temperature of simulation. (c) Finally, the dynamic phase where the structures and speeds are saved every 1 ps to account for the DM history. Initial speeds of the atoms are assigned according to the Maxwell–Boltzman distribution. The cut-off distance used ˚ . During simulation, for the non-bound interaction is 8 A all the bound lengths are given values of balance by the Shake procedure [20]. In order to average the rapid fluctuations, it is more interesting to look at the evolution during a maximum of 50 fs. The analysis of atom at a time can be associated with the crystallographic temperature factors. These fluctuations are due to the absence of crystalline environment (the DM is carried out in the vacuum). The steps of integration are of 0.5 ps, speeds and the temperatures are calibrated every 10 ps to remain fixed around 300 K. the time of simulation is 500 ps. The thermalization time is approximately 10 ps, and be considered as our origin of times. The kinetic energy on the potential energy ratio indicates that the thermalization of our dynamics was carried out. We limit the calculation to 25 ps, knowing that in experiments the passage of the isomer 11-cis to all-trans is carried out at the end of 2 ps [21]. The first plane angle of interest is (5@6A7@8) because it is between the cycle and the linear part. Its computed value by SPASIBA is 58.4 (Fig. 2) and 43.3 for all-trans isomers and 11cis, the experimental values are 58.3 and 41.4, respectively [14,15]. The passage of the 11-cis to all-trans is carried
A. Zanoun et al. / Journal of Molecular Structure: THEOCHEM 777 (2006) 113–120 Table 3 The force constants Parameter
Table 3 (continued) K (kcal mol
a. Stretching (K) C-C CC-CC CC-C C-H CC-H C-CT C-C9 LC-HX LC-O C9-HM CT-CT CT-C9 C9-C9
1
˚ 1) A
r0 (A)
455.28 455.28 260.00 315.07 315.07 190.00 190.00 275.07 700.00 320.0 165.00 165.00 165.00
H (kcal mol
1
rad 2)
b. Bending (H and F) OALCAHX 20.00 CALCAHX 13.00 OCALCAC 23.00 LCACAH 10.00 LCACAC 6.00 CACAH 13.02 CCACCAH 13.02 CACCAH 10.02 CCACAH 10.02 CACTAHC 12.89 CAC9AHM 12.89 CACACC 18.70 CCACCAC 18.70 CACACT 14.70 CACAC9 14.70 CCACACT 12.70 CACTACT 18.10 CAC9AC9 18.10 CACTAC9 18.10 C9ACACT 12.70 HCACTAHC 29.60 HMAC9AHM 29.60 CTAC9AHM 15.10 C9AC9AHM 15.10 CTACTAHC 15.81 CTACTACT 18.70 CTACTAC9 18.70 CTAC9AC9 18.70 C9AC9AC9 18.70 CTACAH 12.82 CACTAHM 12.89 CTACACT 12.70
c. Torsion XACTACAC XACTACACC XAC9ACAC C9AC9ACACT C9ACACTAHC CTACAC9AHM XACTACTAX CTACACTAHC XACACCAH CACACCACC
119
1.34 1.34 1.47 1.09 1.49 1.49 1.10 1.21 1.11 1.11 1.53 1.53 1.53
F (kcal mol
1
10.50 53.00 140.00 53.00 60.00 75.70 75.70 70.70 70.70 70.70 70.70 50.47 50.47 40.47 40.47 47.47 47.47 47.47 47.47 47.47 10.07 10.07 69.43 69.43 69.43 47.47 47.47 47.47 47.47 50.70 90.70 47.47 Vn/2
c (deg.)
0.54 0.17 0.54 0.15 0.05 0.05 0.15 0.08 0.20 1.00
180.0 180.0 180.0 180.0 180.0 180.0 0.0 180.0 180.0 180.0
˚ 1) A
h0 (deg.) 120.9 115.0 123.0 117.3 120.0 120.0 120.0 120.0 120.0 110.2 110.2 124.7 124.7 127.7 127.7 124.0 109.0 109.0 109.0 118.0 108.5 108.5 109.5 109.5 109.5 111.8 111.8 111.8 111.8 117.0 110.2 118.0
Parameter
CTACACCACC XAXACAH XAX—CACT
d. Out of plane bending LCACACACT LCACACACC HACACAH HACCACCAH HACCACCAX HACACAX CTACACACC XACCACCAX XACACAX XAXALCAHX CTACACCACC Constants e. CH2 and CH3 lCH2 vCH2 vCH3
K (kcal mol
1
˚ 1) A
r0 (A)
Vn/2
c (deg.)
1.10 0.30 0.30
180.0 180.0 180.0 Vn/2
c (deg.)
5.75 6.10 5.40 5.40 4.60 4.60 5.75 6.10 6.10 11.00 2.50
180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0
n 2.0 2.0 2.0 N 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 Values 4.00 5.75 3.60
out using torsion (11@12). In experiments the torsion value is 2.1 for the 11-cis and 175.5 for the all-trans. They were calculated at 7.71 and 179.1, respectively. The angle of valence (1A13@14) is calculated at 120.1 (t-trans) and 117.6 (11-cis). The experimental values are 121.3 and 117.6, respectively. The most stable conformers are the 11-cis (0) and the t-trans (180). We conclude that the computed values by DM using SPASIBA are of excellent quality (good agreement with the experiment) which confirms the validity of the selected forces field and has a double aspects (spectroscopic and of molecular mechanics). The obtained results allow us to continue to study these molecules in biological environment and to compare with those given by Hayashi et al. [23]. 4. Conclusion
n 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 2.0 2.0
If we consider molecular dynamics as a welcomed application, it is essential that the field of forces reproduces at least the vibrational properties of a molecule in order to expect to study the dynamic behavior of this molecule. In the harmonic dynamics applications, the use of the usual Molecular Mechanics force fields led to intermediate results (bad agreement between theoretical frequencies and experimental results) simply because the commercially available force fields or an academic way does not have spectroscopic ‘‘quality’’. The SPASIBA force field was thus designed to reproduce simultaneously, the structures and the vibration spectra. SPASIBA, thus parameterized for the chromophore of the visual pigments gives very good results. The continua-
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Fig. 2. Angle between the cycle and linear part after MD.
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