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DFT conformational study of cysteine in gas phase and aqueous solution
Journal of Molecular Structure (Theochem) 498 (2000) 191–200 www.elsevier.nl/locate/theochem
DFT conformational study of cysteine in gas phase and aqueous solution A. Ferna´ndez-Ramos a,b,*, E. Cabaleiro-Lago a, J.M. Hermida-Ramo´n a, E. Martı´nez-Nu´n˜ez a, A. Pen˜a-Gallego a a
Departamento de Quı´mica Fı´sica, Facultade de Quı´mica, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain b Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Canada K1A OR6 Received 20 April 1999; accepted 5 July 1999
Abstract Different conformers of cysteine in gas phase are investigated at the DFT B3LYP/6-31G p and B3LYP/6-31111G pp levels. The effect of the solvent is simulated by using the Onsager and polarizable continuum (PCM) models within the self-consistent reaction field method (SCRF) at the B3LYP/6-31G p level. Specifically, five neutral forms, two anions and one zwitterion were analysed. Both, in gas phase and solution the most stable normal form has the carboxyl group directed toward the amino group. In accord with the experiment, the PCM model predicts that the most stable structure in solution is a zwitterion, a species that does not exist or has a very small stability in gas phase. A major stabilization in solution is also predicted for the zwitterionic form of anionic cysteine. Thus the PCM model renders correct stability order of the different conformers in solution, while the Onsager model does not, which is due to the underestimation of the electrostatic contributions to the solute–solvent interaction for the zwitterions. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Cysteine; Hydrogen bond; Zwitterion; Continuum model
1. Introduction Amino acids are important to study because they are fundamental blocks of peptides and proteins. Cysteine (HS–CH2 –CH–NH2COOH), like all the amino acids, carries an amino and a carboxylic acid group. Besides, cysteine has a thiol functional group, which is capable of donating and accepting intramolecular or intermolecular hydrogen bonds. Specifically, the –SH group is highly polarizable and can contribute to the stabilization of protein structures
* Corresponding author. Departamento de Quı´mica Fı´sica, Facultade de Quı´mica, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain.
[1,2]. It is well known that amino acids exist in gas phase mainly as neutral forms but in solution [3] and in solid phase [4] exist chiefly as zwitterions—neutral forms with charge separation. Depending on the pH conditions, other forms of cysteine, like anions, can be present in solution, but the zwitterionic form is the most stable, as demonstrated by NMR experiments [3]. Therefore, it is of great interest to predict by theoretical methods the structure and relative stability of anionic, zwitterionic and neutral forms of cysteine in gas phase and solution and, which is more important, to prove that these theoretical methods serve as a reliable tool in the modelling of biological systems and processes. Concerning cysteine, there are three theoretical studies dealing with the possible conformations in
0166-1280/00/$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(99)00261-4
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Fig. 1. The five conformations of neutral cysteine obtained at the B31YP/6-31G p level. The hydrogen bonds are depicted in dotted lines.
gas phase [5–7], based mainly on Hartree–Fock (HF) calculations, and none in solution. Tarakeshwar et al. [5,6] performed HF/4-31G p calculations of zwitterionic and neutral forms in gas phase. Gronert et al. [7] found 58 different conformers with the AM1 semiempirical method. Several of these conformers were further optimized at HF/6-31G p level and the energy
of five of them evaluated with single point MP2/6311G p//HF/6-31G p calculations. These five more representative conformers are considered in the present study using Density Functional Theory (DFT). Specifically, hybrid functionals with density gradient corrections and part of the Hartree–Fock exchange, like B3LYP, were shown to yield reliable
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Table 1 Relative energies (in kcal/mol) of the configuration studied in gas phase and in solution. The calculations in solution were performed at the B3LYP/6-31G p level. The dipole moments (in Debye) correspond to the solvated species Gas-phase HF
NI NII NIII NIV NV Z1 Z2 AI AII
a
Solution MP2
b
B3LYP
6-31G p
6-311G p
6-31G pe
6-31111G ppf
0.00 20.89 20.15 22.66 5.97 – – – –
0.00 0.76 1.34 3.66 6.40 – – – –
0.00 1.59 2.60 5.14 6.03 – – 0.00 5.23
0.00 1.31 2.13 4.20 5.38 – – – –
Onsager c
PCM d
Dipole
0.00 2.53 3.47 6.74 6.38 8.11 17.66 0.00 6.78
0.00 g/1.99 0.81/2.92 2.30/4.39 5.04/6.82 5.24/7.11 21.21/20.20 7.19/7.68 0.00/0.84 23.54/23.82
5.09 3.14 3.29 1.52 4.14 9.60 7.92 7.31 5.61
a
From Ref. [7]. Single-point calculations MP2/6-311//HF/6-31G p taken from Ref. [7]. c Absolute energy of NI 2721:928768 a:u: Absolute energy of AI 2721:440272 a:u: d PCM energies based on Onsager model B3LYP/6-31G p geometries without/with non-electrostatic contributions. e Absolute energy of NI 2721:925935 a:u: Absolute energy of AI 2721:379778 a:u: f Absolute energy of NI 2722:071001 a:u: g Absolute energy of NI 2721:946318 a:u: Absolute energy of AI 2721:475617 a:u: b
results in the study of different conformers of glycine [8] in gas phase. Since correlation effects are important in these studies, DFT methods, which are less demanding computationally than post-HF methods, open a new way to deal with large systems like the one at hand. Starting from gas-phase results, the simulation of the effect of aqueous solution is usually done by using a supermolecule- or continuum-model approach. The supermolecule approach includes explicit water molecules surrounding the solute. It provides information about the structure of the solvation layer, but a large number of water molecules is needed in order to obtain a zwitterion more stable than the normal form because longrange interactions are neglected. Continuum models do not provide such information but they include long-range interactions, which are important in the stabilization of zwitterions. At the same time, continuum models can provide geometries and frequencies of cysteine in solution, being only marginally more intensive computationally than similar studies in vacuum. Therefore this is the model we adopt for the present analysis of cysteine.
2. Quantum chemical calculations We report calculations carried out at the B3LYP/6-31G p level of theory. All the structures were fully optimized with no symmetry restrictions. The neutral forms in gas phase were also optimized at the B3LYP/6-31111G pp to make sure that the size of the basis set does not change the relative stability of the conformers. The solvation effects were added using two continuum models: (a) the Onsager model and (b) the polarizable continuum model (PCM). (a) The Onsager model [9–11] considers a polarizable reference molecule as being in a vacuum spherical cavity. The surroundings of the molecule are treated as a continuum with the macroscopic dielectric constant of the solvent (1 80 for water at room temperature). The reference molecule is treated as a point dipole placed in the centre of the cavity. This model considers only the electrostatic interaction resulting from the change in the reaction field due to the polarization of the reference molecule by the surrounding medium. The
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Table 2 ˚ ) between the hydrogens Ha, Hb and Hc and the donor and acceptor, respectively. The hydrogens have the same labels as indicated Distances (in A in Figs. 1 and 2. All the distances were obtained to the B3LYP/6-31G p level Hb
Ha Gas phase NI NII NII a NIV NV AI AII Solution (Onsager model) NI NII NIII b NIV NV ZI ZII AI AII a b
Hc
0.991 0.976 0.976 0.970 0.982 1.005 1.088
1.898 2.293 2.278 2.272 2.326 1.790 1.726
1.022 1.021 1.018 1.018 1.021 1.005 1.088
2.745 2.437 2.435 2.236 2.489 2.336 2.038
1.350 1.352 1.349 1.348
2.761 2.479 2.621 2.386
0.995 0.977 0.976 0.977 0.977 1.087 1.025 0.999 1.061
1.869 2.307 2.297 2.275 2.285 1.623 2.030 1.832 1.748
1.021 1.021 1.018 1.018 1.017 1.029 1.107 1.031 2.096
2.770 2.389 2.475 2.207 2.558 2.668 2.011 2.473
1.250 1.353 1.349 1.348
2.720 2.397 2.512 2.373
1.352
2.638
˚ , respectively. Gas phase NHd and HdS distances are 1.020 and 2.800 A ˚ , respectively. Onsager model NHd and HdS distances are 1.20 and 2.831 A
Onsager model geometries, energies and frequencies were obtained by full optimization starting from the gas-phase geometry and using the self-consistent reaction field method [10,11]. (b) The PCM model [12] considers a charge distribution of the solute represented by a discrete number of point charges placed at the centres of the cavity surface elements of appropriate area, which consists of interlocking spheres. It is assumed that the electronic density vanishes outside the cavity, an approximation compensated by a correction factor to the charges. For this reason the method is sometimes called “the virtual charge scheme” and belongs to the so-called apparent-charge surface methods. The PCM model also includes nonelectrostatic contributions, namely cavitation, dispersion and repulsion energies. The PCM energies were obtained by single-point calculations over the Onsager model optimized geometries. All the calculations were performed with the gaussian 98 suite of programs [13].
3. Results and discussion 3.1. Gas phase The five neutral conformers depicted in Fig. 1 have several types of hydrogen bond (HB) interactions between the following functional groups: (a) carboxyl–amino; (b) carbonyl–amino; (c) carboxyl– carbonyl; (d) thiol–carboxyl; (e) thiol–carbonyl and (f) thiol–amino. Within this classification each functional group might operate as a HB donor or acceptor. Thus, the amino group acts as a HB acceptor in the structure NI but as a donor in the structure NII. Table 1 shows the relative stabilities of the various neutral forms and Table 2 lists the main parameters related to the hydrogen bond interactions. Contrary to the HF/631G p prediction but in agreement with MP2 calculations [7], B3LYP predicts NI is the most stable conformer (see Table 1). This conformer forms a strong hydrogen bond of type a, where the amino group is the acceptor and the carboxyl group is the donor. The strength of the hydrogen bond is reflected ˚ ) and in the short nitrogen–oxygen (2.598 A
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Table 3 Frequencies (in cm 21), zero-point energies (in kcal/mol) and infrared intensities (in km/mol) for the neutral forms in gas phase I
NI
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ZPE
77 94 198 275 318 358 381 490 539 570 661 758 783 836 877 919 982 1061 1118 1181 1236 1255 1299 1346 1414 1458 1482 1691 1866 2685 3039 3095 3160 3391 3458 3563 68.52
NII 2.1 5.5 2.3 24.5 27.2 1.4 19.5 6.8 3.6 3.9 1.4 6.7 0.5 36.3 104.6 75.5 60.0 44.8 13.9 4.9 16.5 1.5 5.1 38.9 4.5 438.8 23.7 32.3 235.3 2.8 12.2 15.3 2.0 223.9 11.2 8.7
49 98 276 222 238 304 336 385 505 600 648 697 768 796 872 939 951 1026 1148 1157 1181 1265 1315 1340 1372 1440 1502 1709 1839 2667 3071 3097 3144 3472 3555 3677 68.00
NIII 2.2 3.4 0.7 12.5 8.5 5.5 51.1 21.9 14.8 72.1 20.7 52.3 22.9 11.9 85.0 42.9 30.7 63.3 109.7 4.5 145.7 10.8 2.6 6.7 46.7 6.5 3.7 27.9 263.2 7.7 14.2 8.8 5.6 2.7 3.8 47.5
36 105 189 253 284 321 353 421 534 549 644 677 738 779 853 931 954 1054 1145 1171 1190 1276 1328 1339 1389 1407 1478 1696 1830 2691 3006 3113 3171 3474 3565 3683 68.11
˚ ) distances with regard to hydrogen–nitrogen (1.898 A other conformers. The NI conformer also forms hydrogen bonds of types e and f, where the thiol group acts as a donor and acceptor, respectively. In all the other conformers the amino group acts as a donor and the hydrogen bond interaction is weaker, a fact reflected in the corresponding distances. From that, it is straightforward to conclude that the amino group operates better as an acceptor than as a donor. The stability of the conformer NII is mainly due to the hydrogen bonds of types b and f. Specifically, in the
NIV 1.3 0.8 0.5 6.3 17.8 25.5 53.8 2.3 11.9 51.0 71.7 37.7 32.6 5.7 30.7 114.8 22.8 49.1 37.1 140.5 101.3 2.6 13.4 22.7 22.0 1.2 14.2 43.6 218.6 5.2 16.4 10.0 2.8 1.6 4.7 53.6
38 114 199 258 269 284 332 379 503 557 640 713 733 771 845 903 1007 1039 1122 1194 1208 1252 1295 1349 1367 1440 1496 1677 1842 2706 2952 3093 3144 3489 3580 3678 67.89
NV 2.9 2.5 1.2 41.1 19.0 12.2 4.1 13.9 15.7 28.8 52.1 25.2 66.1 32.1 68.0 110.5 4.4 10.7 37.3 187.2 9.9 11.5 12.3 11.3 5.4 12.0 7.8 62.2 261.2 5.3 26.6 12.9 7.0 6.3 6.5 58.4
56 121 160 207 273 305 331 355 496 616 669 696 758 775 848 942 1008 1035 1160 1194 1214 1230 1316 1346 1384 1428 1502 1715 1860 2677 3048 3092 3158 3464 3526 3539 67.94
10.4 3.5 38.0 12.5 9.3 15.0 15.6 12.8 1.4 21.5 67.4 29.2 9.0 10.9 13.9 120.6 21.8 74.1 12.1 12.1 23.9 4.1 22.2 47.4 223.7 8.4 6.9 19.3 285.3 11.6 11.6 9.6 1.8 1.6 301.9 4.2
amino acid serine (the same as cysteine, but with an hydroxyl group instead of a thiol group), NII is the most stable conformation due to the strong interaction between the hydroxyl and the amino groups [7]. This is not the case in cysteine because the sulphur is a weaker donor or acceptor. In the conformer NII there is also a hydrogen bond of type c, but this kind of interaction is weak in all conformers (NII, NIII and NIV). The HB is strongly bent and, usually, at similar values of the remaining parameters, the strength of the HB is larger in linear or quasi-linear
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Fig. 2. Zwitterions (ZI and ZII) and anions (AI and AII) obtained by the Onsager model at the B3LYP/6-31G p level. The hydrogen bonds are depicted in dotted lines.
dispositions, decreasing in bent HB. Conformer NIII is similar to conformer NI with the difference of a HB of type a, in which the carboxylic oxygen acts as an acceptor instead of donor. Thus the relative stability of the two conformers is mainly due to the strength of this HB, stronger in NI. As in NI, all the other HBs are ˚ ) and relatively weak since the distances HcO (2.621 A ˚ HdS (2.800 A) are quite large. Conformer NIV exhibits a strong HB of type d, with a Hc –O distance of ˚ ; in this conformation, however, the HB only 2.386 A of type f is broken, a possible reason for the higher energy of this conformer comparative to NIII. Finally, NV is the least stable of the studied conformers; its main dissimilarity with NIV being in the different kind of interaction between the thiol and the carboxyl groups and in the presence of two HB instead of three. In this case the sulphur acts as an acceptor, with a HB ˚ which is shorter than in NIV, an distance of 2.326 A indication that the thiol group in cysteine is a better acceptor than donor.
Several different starting geometries were tried in search for a stable zwitterion in gas phase, but without success. It seems that the stability of the zwitterionic forms, like in glycine or alanine [14,15], is small or null. Surprisingly, it was possible to obtain two anionic forms AI and AII (zwitterion with an overall negative charge), which result from the loss of the thiolgroup hydrogen. In both cases, the sulphur is oriented toward the amino group forming a relatively strong HbS HB. In this case the AII form is stable, since the positive charge residing on the amino group is reduced by the oxygen and the sulphur which bear negative charges. This affects the HaN and HbS distances making them shorter than in the neutral conformers. The increase of the basis set to B3LYP/631111G pp does not alter the relative stability of the conformers, although it does bring the remaining conformers closer to NI energetically. These four conformers have some strong HB involving the thiol
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Table 4 Frequencies (in cm 21), zero-point energies (in kcal/mol) and infrared intensities (in km/mol) for the neutral forms in solution obtained by the Onsager model I
NI
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ZPE
78 94 194 272 316 366 388 491 537 572 659 760 783 839 890 931 981 1061 1119 1180 1237 1256 1300 1345 1412 1462 1481 1690 1855 2681 3043 3100 3160 3328 3464 3569 68.49
NII 2.8 7.5 2.8 31.1 32.0 1.6 24.6 8.9 4.2 3.8 2.0 6.9 0.6 28.3 159.9 76.9 77.6 51.2 16.5 5.6 19.6 3.5 5.3 42.0 9.1 539.4 15.4 45.9 300.4 7.3 11.3 13.5 2.6 318.9 9.9 17.4
47 100 166 236 244 305 350 387 508 604 648 695 770 797 874 94.1 952 1027 1148 1158 1177 1264 1311 1341 1377 1443 1503 1709 1837 2649 3074 3103 3146 3466 3550 3671 68.04
NIII 3.1 5.9 1.3 10.2 12.9 6.1 71.2 32.5 21.0 91.2 35.2 73.1 28.2 17.1 126.0 28.0 66.4 113.8 115.8 2.7 210.3 15.8 5.4 7.1 67.5 12.4 52 44.8 346.1 21.6 19.8 10.0 7.1 6.1 6.7 88.5
35 115 189 252 294 324 352 407 541 558 639 676 737 779 852 927 954 1054 1144 1169 1188 1276 1325 1338 1397 1410 1479 1692 1821 2697 3017 3110 3168 3474 3565 3682 68.12
group, and due to the fact that the sulphur, although a poor donor or acceptor of HB, is highly polarizable and therefore more affected by diffuse orbitals, the basis set extension results in a further stabilization. Since the smaller 6-31G p basis set yields reasonable results, we adopted it for the calculations in solution. The frequencies and IR intensities are shown in Table 3. The zero-point energy contribution is larger in NI than in the remaining conformers but in spite of that this conformer is still the most stable. All confor-
NIV 1.5 1.6 1.0 7.8 46.2 15.3 83.4 1.8 45.1 48.2 103.9 44.6 44.7 9.2 36.1 163.8 24.2 51.9 77.4 223.1 76.6 3.3 15.8 34.2 32.3 1.0 17.2 55.8 304.8 3.8 15.9 16.0 5.2 1.1 7.7 89.1
36 112 196 228 270 282 333 3741 501 563 638 710 730 770 847 896 1007 1040 1122 1187 1206 1248 1293 1349 1363 1440 1497 1675 1839 2709 2966 3092 3142 3489 3580 3676 67.80
NV 3.7 3.8 4.6 56.8 29.6 10.3 4.6 16.7 23.8 45.0 66.8 41.1 75.5 49.1 80.8 158.7 5.7 13.8 54.8 247.7 10.9 19.4 19.3 15.5 5.3 14.0 7.8 85.3 370.3 5.6 28.6 18.9 9.9 11.5 11.1 86.4
66 96 128 204 277 309 328 353 498 623 675 702 756 775 848 906 1014 1024 1157 1196 1209 1231 1311 1347 1382 1433 1500 1715 1844 2689 3059 3094 3165 3473 3489 3553 67.83
15.5 54.8 3.5 6.2 11.1 20.5 19.5 16.3 3.5 23.7 80.3 60.0 23.2 16.5 25.5 215.3 27.3 43.8 19.8 11.6 29.3 14.9 8.4 63.7 297.2 16.8 9.5 32.9 407.8 7.2 9.6 13.7 1.5 6.5 473.8 6.4
mers present the characteristic frequency due to the CO stretching (approximately 1850 cm 21) which is very intense in the infrared region. Conformers NI and NV have another two frequencies intense in IR corresponding to the COHa bending and OHa stretching with values of 1458 and 1866 cm 21 for NI and 1384 and 3526 cm 21 for NV, respectively. These two frequencies are less intense in the other three conformers, where the hydrogen Ha is directed toward the oxygen. It is also interesting to note that the OHa stretching in conformer NI has lower frequencies
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Table 5 Frequencies (in cm 21), zero-point energies (in kcal/mol) and infrared intensities (in km/mol) for the zwitterions and anions I
ZI
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ZPE
74 97 182 269 331 389 425 492 524 591 661 776 793 836 891 1017 1064 1095 1134 1232 1283 1308 1346 1382 1397 1482 1615 1690 1801 2605 2673 3094 3105 3169 3393 3514 68.26
Z2 9.5 24.9 4.4 23.7 147.2 30.3 9.8 6.4 38.2 7.4 8.1 1.0 28.8 87.6 32.8 24.0 22.6 17.7 110.8 17.9 253.7 46.2 85.8 76.3 453.9 29.1 39.2 372. 336.2 593.1 5.6 6.2 11.8 1.1 82.7 121.0
41 178 222 304 318 361 385 566 650 720 755 826 888 910 927 977 1079 118 1163 1259 1298 1309 1366 1423 1483 1515 1594 1666 1844 2261 2726 3061 3110 3147 3444 3523 69.24
A1 9.3 50.5 23.4 55.0 87.1 16.5 7.7 9.0 6.1 12.6 8.3 12.8 0.1 56.1 23.0 7.3 166.7 50.4 8.0 68.7 49.8 122.6 82.6 421.5 205.6 9.0 34.4 27.8 600.0 916.9 1788.3 36.8 13.5 4.2 69.3 83.1
than the NH stretchings, which is an indication of strong HB in this species. 3.2. Solution The Onsager model geometries of all the studied conformers are very similar to their gas-phase structures and the analysis presented in the above paragraph is also valid here. In general, the HB distances are shorter in solution and the structures are tighter. Similar to gas phase, in aqueous solution
88 119 171 260 360 400 424 548 661 672 778 847 887 931 956 1022 1088 1146 1239 1253 1306 1335 1374 1477 1505 1687 1842 2992 3046 3063 3241 3316 3518
62.28
A2 8.9 14.7 25.9 24.9 23.6 6.8 30.5 5.3 11.7 14.9 12.6 1.0 13.6 51.7 59.8 232.0 70.4 19.7 15.1 61.6 27.0 4.3 21.3 602.1 4.9 41.2 474.2 89.8 28.3 79.5 447.1 166.5 6.4
93 98 188 288 334 404 437 550 686 692 789 835 897 920 1010 1088 1133 1230 1244 1283 1314 1375 1391 1509 1607 1652 1773 2623 2920 3018 3082 3125 3538
3.2 22.8 33.8 125.7 51.9 29.6 10.1 34.0 20.5 12.6 0.6 32.7 121.7 14.6 47.1 17.9 139.2 122.5 46.1 431.5 53.3 159.1 194.8 5.4 77.0 21.6 387.0 1176.2 446.9 89.6 35.9 40.7 33.2
61.67
NI remains the most stable neutral conformer. Comparing to gas phase, in conformer NIII the Hc – ˚ . The HaS distance in O distance is reduced by 0.109 A conformer NIV and the HbN distance in conformer NV are also shorter in solution, although in the latter the HbO distance increases. Conformers NI and NV are more stabilized by the Onsager model as a consequence of their larger dipole moments, as illustrated in Table 1. In addition to the neural forms, two zwitterions and two anions become stable when the Onsager model is
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applied (Fig. 2). The zwitterion ZI represents a HbO ˚ , respectively, and NHa distances of 1.623 and 1.087 A which indicates very strong HB. The zwitterion ZII has two HB involving sulphur, while the interaction between the amino and the carboxyl groups is broken and therefore this structure is less stable than ZI. Similarly, we have shown that a zwitterionic form with trans orientation with regard to the oxygen is unstable at B3LYP/6-31G p level. This zwitterion and the ZI conformer were obtained in Ref. [6] via gas-phase calculations at the HF/4-31G p level; it appears that this level of calculation overestimates the stability of the zwitterionic forms. Anions AI and AII are the only stable anionic forms where the sulphur bears negative charge. A disposition of the sulphur as in conformer NI yields an unstable structure because of the repulsion between the sulphur and the oxygen. Contrary to what happens to the neutral forms, in solution the anions have longer hydrogen-acceptor distances due to the stabilization effect of the solute–solvent interactions on charges held by the atoms. The frequencies and IR intensities of the neutral, zwitterionic and anionic forms of cysteine in solution are displayed in Tables 4 and 5, respectively. The frequencies of the neutral conformers are very similar to those in gas phase because of the small structural change. The zwitterions, ZI, ZII and zwitterionicanionic form AII have a single characteristic very intense IR frequency at 1397, 1423 and 1283 cm 21, respectively, which corresponds to the symmetric deformation (pyramidalization) of the NH31 group. These three forms also have characteristic low frequencies and with very intense IR activity for the NH and OH stretchings of the hydrogens which yield strong HBs. In the case of the NH31 group, the HBs break the degeneration of the NH stretchings, and the non-hydrogen bonded NH stretchings in these zwitterions and anions have the largest frequencies. Thus the frequency of 2605 cm 21 corresponds to the NHa stretching in ZI; the frequencies of 1844 and 2261 cm 21 correspond to the NHb and OHa stretchings, respectively, in ZII; the frequencies of 2623 and 2920 cm 21 correspond to the NHa and NHb stretchings, respectively, in AII. The anion AI has two characteristic frequencies at 1477 and 3241 cm 21 corresponding to the COHa bending and OHa stretching, respectively.
199
As illustrated in Table 1, the Onsager model underestimates significantly the electrostatic interaction and therefore ZI is still by 8.11 kcal/mol less stable than NI; similar relative stabilities are obtained for AI and AII, whereas it is known that the zwitterionic species are predominant in solution [3]. By means of the PCM model, it was found that in solution ZI and AII are already more stable by 1.21 and 3.54 kcal/mol, respectively, as regard to NI and AI; these values change to 2.19 and 4.66 kcal/mol, respectively, if non-electrostatic contributions are included. The PCM model considers a more realistic shape of the cavity and treats the solute–solvent interactions more accurately. As pointed out before, the major interaction is electrostatic, the non-electrostatic part being less than 20% of the total interaction energy in all cases. In the neutral conformers, however, the nonelectrostatic interactions are more destabilizing, an effect due mainly to the difference in the cavitation energies, while the dispersion–repulsion energies are quite similar in all the conformers. This results from the fact that the cavitation energy has a positive contribution, which reflects the free-energy change upon cavity formation. This contribution is larger in the neutral conformers because it is easier to create a cavity for more polar species like the zwitterions. Therefore, as expected, the zwitterionic species are stabilized by both electrostatic and non-electrostatic terms, although the electrostatic interactions are prevailing.
4. Conclusions A DFT study of cysteine conformers in gas phase and in aqueous solution was carried out. In both cases the most stable conformer is the neutral conformer NI shown in Fig. 1. The hydrogen bond between the amino and the carboxyl groups is strongest when the nitrogen acts as a HB acceptor. This seems to be also the case for the thiol group. In gas phase the zwitterionic species are not stable, although it is possible to obtain two stable anions with a negative charge on the sulphur. The solvent tightens the structure of the neutral forms and loosens that of the anions. Within the Onsager model two zwitterionic forms, ZI and ZII, are stable with negative charges upon the oxygen and sulphur, respectively. The Onsager model, which
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underestimates the electrostatic contributions to the solute–solvent interaction, is unable to reproduce the right energetics of the zwitterionic forms. A more elaborate treatment of these interactions is needed in this case, which is introduced by means of the PCM model. In agreement with the experiment, this model predicts rightly that the zwitterions are most stable both in the neutral, ZI, and in the anionic, AII, forms. Acknowledgements The authors thank Z. Smedarchina for helpful discussions. Support through Project XUGA20903 A98 from Xunta de Galicia is appreciated. A.F.-R. thanks NRC for the computational facilities. References [1] P. Kollman, J. McKelvey, A. Johansson, S. Rothengerg, J. Am. Chem. Soc. 97 (1975) 955. [2] H. Li, C. Wurrey, G.J. Thomas Jr, J. Am. Chem. Soc. 114 (1992) 7463. [3] K.C. Chang, E. Grunwald, J. Phys. Chem. 80 (1976) 1425. [4] K.A. Kerr, J.P. Ashmore, T.F. Koetzle, Acta Crystalogr. B31 (1975) 2022. [5] P. Tarakeshwar, S. Manogaran, J. Mol. Struct. (Theochem) 305 (1994) 205.
[6] P. Tarakeshwar, S. Manogaran, Spectrochim. Acta 51A (1995) 925. [7] S. Gronert, R.A.J. O’Hair, J. Am. Chem. Soc. 117 (1995) 2071. [8] V. Barone, C. Adamo, F. Lelj, J. Chem. Phys. 102 (1995) 364. [9] L. Onsager, J. Am. Chem. Soc. 58 (1936) 1486. [10] M.W. Wong, K.B. Wiberg, M.J. Frisch, J. Chem. Phys. 95 (1991) 8991. [11] M.W. Wong, M.J. Frisch, K.B. Wiberg, J. Am. Chem. Soc. 113 (1991) 4776. [12] C. Amovilli, V. Barone, R. Cammi, E. Cance`s, M. Cossi, B. Mennucci, C.S. Pomelli, J. Tomasi, Adv. Quant. Chem. 32 (1999) 227. [13] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery, Jr., R.E. Statmann, J.C. 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. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, gaussian 98, Revision A.3, Gaussian, Inc., Pittsburgh, PA, 1998. [14] J.H. Jensen, M.S. Gordon, J. Am. Chem. Soc. 117 (1995) 8159. [15] A.G. Csa´za´r, J. Phys. Chem. 100 (1996) 3541.
DFT conformational study of cysteine in gas phase and aqueous solution A. Ferna´ndez-Ramos a,b,*, E. Cabaleiro-Lago a, J.M. Hermida-Ramo´n a, E. Martı´nez-Nu´n˜ez a, A. Pen˜a-Gallego a a
Departamento de Quı´mica Fı´sica, Facultade de Quı´mica, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain b Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Canada K1A OR6 Received 20 April 1999; accepted 5 July 1999
Abstract Different conformers of cysteine in gas phase are investigated at the DFT B3LYP/6-31G p and B3LYP/6-31111G pp levels. The effect of the solvent is simulated by using the Onsager and polarizable continuum (PCM) models within the self-consistent reaction field method (SCRF) at the B3LYP/6-31G p level. Specifically, five neutral forms, two anions and one zwitterion were analysed. Both, in gas phase and solution the most stable normal form has the carboxyl group directed toward the amino group. In accord with the experiment, the PCM model predicts that the most stable structure in solution is a zwitterion, a species that does not exist or has a very small stability in gas phase. A major stabilization in solution is also predicted for the zwitterionic form of anionic cysteine. Thus the PCM model renders correct stability order of the different conformers in solution, while the Onsager model does not, which is due to the underestimation of the electrostatic contributions to the solute–solvent interaction for the zwitterions. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Cysteine; Hydrogen bond; Zwitterion; Continuum model
1. Introduction Amino acids are important to study because they are fundamental blocks of peptides and proteins. Cysteine (HS–CH2 –CH–NH2COOH), like all the amino acids, carries an amino and a carboxylic acid group. Besides, cysteine has a thiol functional group, which is capable of donating and accepting intramolecular or intermolecular hydrogen bonds. Specifically, the –SH group is highly polarizable and can contribute to the stabilization of protein structures
* Corresponding author. Departamento de Quı´mica Fı´sica, Facultade de Quı´mica, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain.
[1,2]. It is well known that amino acids exist in gas phase mainly as neutral forms but in solution [3] and in solid phase [4] exist chiefly as zwitterions—neutral forms with charge separation. Depending on the pH conditions, other forms of cysteine, like anions, can be present in solution, but the zwitterionic form is the most stable, as demonstrated by NMR experiments [3]. Therefore, it is of great interest to predict by theoretical methods the structure and relative stability of anionic, zwitterionic and neutral forms of cysteine in gas phase and solution and, which is more important, to prove that these theoretical methods serve as a reliable tool in the modelling of biological systems and processes. Concerning cysteine, there are three theoretical studies dealing with the possible conformations in
0166-1280/00/$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(99)00261-4
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Fig. 1. The five conformations of neutral cysteine obtained at the B31YP/6-31G p level. The hydrogen bonds are depicted in dotted lines.
gas phase [5–7], based mainly on Hartree–Fock (HF) calculations, and none in solution. Tarakeshwar et al. [5,6] performed HF/4-31G p calculations of zwitterionic and neutral forms in gas phase. Gronert et al. [7] found 58 different conformers with the AM1 semiempirical method. Several of these conformers were further optimized at HF/6-31G p level and the energy
of five of them evaluated with single point MP2/6311G p//HF/6-31G p calculations. These five more representative conformers are considered in the present study using Density Functional Theory (DFT). Specifically, hybrid functionals with density gradient corrections and part of the Hartree–Fock exchange, like B3LYP, were shown to yield reliable
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193
Table 1 Relative energies (in kcal/mol) of the configuration studied in gas phase and in solution. The calculations in solution were performed at the B3LYP/6-31G p level. The dipole moments (in Debye) correspond to the solvated species Gas-phase HF
NI NII NIII NIV NV Z1 Z2 AI AII
a
Solution MP2
b
B3LYP
6-31G p
6-311G p
6-31G pe
6-31111G ppf
0.00 20.89 20.15 22.66 5.97 – – – –
0.00 0.76 1.34 3.66 6.40 – – – –
0.00 1.59 2.60 5.14 6.03 – – 0.00 5.23
0.00 1.31 2.13 4.20 5.38 – – – –
Onsager c
PCM d
Dipole
0.00 2.53 3.47 6.74 6.38 8.11 17.66 0.00 6.78
0.00 g/1.99 0.81/2.92 2.30/4.39 5.04/6.82 5.24/7.11 21.21/20.20 7.19/7.68 0.00/0.84 23.54/23.82
5.09 3.14 3.29 1.52 4.14 9.60 7.92 7.31 5.61
a
From Ref. [7]. Single-point calculations MP2/6-311//HF/6-31G p taken from Ref. [7]. c Absolute energy of NI 2721:928768 a:u: Absolute energy of AI 2721:440272 a:u: d PCM energies based on Onsager model B3LYP/6-31G p geometries without/with non-electrostatic contributions. e Absolute energy of NI 2721:925935 a:u: Absolute energy of AI 2721:379778 a:u: f Absolute energy of NI 2722:071001 a:u: g Absolute energy of NI 2721:946318 a:u: Absolute energy of AI 2721:475617 a:u: b
results in the study of different conformers of glycine [8] in gas phase. Since correlation effects are important in these studies, DFT methods, which are less demanding computationally than post-HF methods, open a new way to deal with large systems like the one at hand. Starting from gas-phase results, the simulation of the effect of aqueous solution is usually done by using a supermolecule- or continuum-model approach. The supermolecule approach includes explicit water molecules surrounding the solute. It provides information about the structure of the solvation layer, but a large number of water molecules is needed in order to obtain a zwitterion more stable than the normal form because longrange interactions are neglected. Continuum models do not provide such information but they include long-range interactions, which are important in the stabilization of zwitterions. At the same time, continuum models can provide geometries and frequencies of cysteine in solution, being only marginally more intensive computationally than similar studies in vacuum. Therefore this is the model we adopt for the present analysis of cysteine.
2. Quantum chemical calculations We report calculations carried out at the B3LYP/6-31G p level of theory. All the structures were fully optimized with no symmetry restrictions. The neutral forms in gas phase were also optimized at the B3LYP/6-31111G pp to make sure that the size of the basis set does not change the relative stability of the conformers. The solvation effects were added using two continuum models: (a) the Onsager model and (b) the polarizable continuum model (PCM). (a) The Onsager model [9–11] considers a polarizable reference molecule as being in a vacuum spherical cavity. The surroundings of the molecule are treated as a continuum with the macroscopic dielectric constant of the solvent (1 80 for water at room temperature). The reference molecule is treated as a point dipole placed in the centre of the cavity. This model considers only the electrostatic interaction resulting from the change in the reaction field due to the polarization of the reference molecule by the surrounding medium. The
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Table 2 ˚ ) between the hydrogens Ha, Hb and Hc and the donor and acceptor, respectively. The hydrogens have the same labels as indicated Distances (in A in Figs. 1 and 2. All the distances were obtained to the B3LYP/6-31G p level Hb
Ha Gas phase NI NII NII a NIV NV AI AII Solution (Onsager model) NI NII NIII b NIV NV ZI ZII AI AII a b
Hc
0.991 0.976 0.976 0.970 0.982 1.005 1.088
1.898 2.293 2.278 2.272 2.326 1.790 1.726
1.022 1.021 1.018 1.018 1.021 1.005 1.088
2.745 2.437 2.435 2.236 2.489 2.336 2.038
1.350 1.352 1.349 1.348
2.761 2.479 2.621 2.386
0.995 0.977 0.976 0.977 0.977 1.087 1.025 0.999 1.061
1.869 2.307 2.297 2.275 2.285 1.623 2.030 1.832 1.748
1.021 1.021 1.018 1.018 1.017 1.029 1.107 1.031 2.096
2.770 2.389 2.475 2.207 2.558 2.668 2.011 2.473
1.250 1.353 1.349 1.348
2.720 2.397 2.512 2.373
1.352
2.638
˚ , respectively. Gas phase NHd and HdS distances are 1.020 and 2.800 A ˚ , respectively. Onsager model NHd and HdS distances are 1.20 and 2.831 A
Onsager model geometries, energies and frequencies were obtained by full optimization starting from the gas-phase geometry and using the self-consistent reaction field method [10,11]. (b) The PCM model [12] considers a charge distribution of the solute represented by a discrete number of point charges placed at the centres of the cavity surface elements of appropriate area, which consists of interlocking spheres. It is assumed that the electronic density vanishes outside the cavity, an approximation compensated by a correction factor to the charges. For this reason the method is sometimes called “the virtual charge scheme” and belongs to the so-called apparent-charge surface methods. The PCM model also includes nonelectrostatic contributions, namely cavitation, dispersion and repulsion energies. The PCM energies were obtained by single-point calculations over the Onsager model optimized geometries. All the calculations were performed with the gaussian 98 suite of programs [13].
3. Results and discussion 3.1. Gas phase The five neutral conformers depicted in Fig. 1 have several types of hydrogen bond (HB) interactions between the following functional groups: (a) carboxyl–amino; (b) carbonyl–amino; (c) carboxyl– carbonyl; (d) thiol–carboxyl; (e) thiol–carbonyl and (f) thiol–amino. Within this classification each functional group might operate as a HB donor or acceptor. Thus, the amino group acts as a HB acceptor in the structure NI but as a donor in the structure NII. Table 1 shows the relative stabilities of the various neutral forms and Table 2 lists the main parameters related to the hydrogen bond interactions. Contrary to the HF/631G p prediction but in agreement with MP2 calculations [7], B3LYP predicts NI is the most stable conformer (see Table 1). This conformer forms a strong hydrogen bond of type a, where the amino group is the acceptor and the carboxyl group is the donor. The strength of the hydrogen bond is reflected ˚ ) and in the short nitrogen–oxygen (2.598 A
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195
Table 3 Frequencies (in cm 21), zero-point energies (in kcal/mol) and infrared intensities (in km/mol) for the neutral forms in gas phase I
NI
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ZPE
77 94 198 275 318 358 381 490 539 570 661 758 783 836 877 919 982 1061 1118 1181 1236 1255 1299 1346 1414 1458 1482 1691 1866 2685 3039 3095 3160 3391 3458 3563 68.52
NII 2.1 5.5 2.3 24.5 27.2 1.4 19.5 6.8 3.6 3.9 1.4 6.7 0.5 36.3 104.6 75.5 60.0 44.8 13.9 4.9 16.5 1.5 5.1 38.9 4.5 438.8 23.7 32.3 235.3 2.8 12.2 15.3 2.0 223.9 11.2 8.7
49 98 276 222 238 304 336 385 505 600 648 697 768 796 872 939 951 1026 1148 1157 1181 1265 1315 1340 1372 1440 1502 1709 1839 2667 3071 3097 3144 3472 3555 3677 68.00
NIII 2.2 3.4 0.7 12.5 8.5 5.5 51.1 21.9 14.8 72.1 20.7 52.3 22.9 11.9 85.0 42.9 30.7 63.3 109.7 4.5 145.7 10.8 2.6 6.7 46.7 6.5 3.7 27.9 263.2 7.7 14.2 8.8 5.6 2.7 3.8 47.5
36 105 189 253 284 321 353 421 534 549 644 677 738 779 853 931 954 1054 1145 1171 1190 1276 1328 1339 1389 1407 1478 1696 1830 2691 3006 3113 3171 3474 3565 3683 68.11
˚ ) distances with regard to hydrogen–nitrogen (1.898 A other conformers. The NI conformer also forms hydrogen bonds of types e and f, where the thiol group acts as a donor and acceptor, respectively. In all the other conformers the amino group acts as a donor and the hydrogen bond interaction is weaker, a fact reflected in the corresponding distances. From that, it is straightforward to conclude that the amino group operates better as an acceptor than as a donor. The stability of the conformer NII is mainly due to the hydrogen bonds of types b and f. Specifically, in the
NIV 1.3 0.8 0.5 6.3 17.8 25.5 53.8 2.3 11.9 51.0 71.7 37.7 32.6 5.7 30.7 114.8 22.8 49.1 37.1 140.5 101.3 2.6 13.4 22.7 22.0 1.2 14.2 43.6 218.6 5.2 16.4 10.0 2.8 1.6 4.7 53.6
38 114 199 258 269 284 332 379 503 557 640 713 733 771 845 903 1007 1039 1122 1194 1208 1252 1295 1349 1367 1440 1496 1677 1842 2706 2952 3093 3144 3489 3580 3678 67.89
NV 2.9 2.5 1.2 41.1 19.0 12.2 4.1 13.9 15.7 28.8 52.1 25.2 66.1 32.1 68.0 110.5 4.4 10.7 37.3 187.2 9.9 11.5 12.3 11.3 5.4 12.0 7.8 62.2 261.2 5.3 26.6 12.9 7.0 6.3 6.5 58.4
56 121 160 207 273 305 331 355 496 616 669 696 758 775 848 942 1008 1035 1160 1194 1214 1230 1316 1346 1384 1428 1502 1715 1860 2677 3048 3092 3158 3464 3526 3539 67.94
10.4 3.5 38.0 12.5 9.3 15.0 15.6 12.8 1.4 21.5 67.4 29.2 9.0 10.9 13.9 120.6 21.8 74.1 12.1 12.1 23.9 4.1 22.2 47.4 223.7 8.4 6.9 19.3 285.3 11.6 11.6 9.6 1.8 1.6 301.9 4.2
amino acid serine (the same as cysteine, but with an hydroxyl group instead of a thiol group), NII is the most stable conformation due to the strong interaction between the hydroxyl and the amino groups [7]. This is not the case in cysteine because the sulphur is a weaker donor or acceptor. In the conformer NII there is also a hydrogen bond of type c, but this kind of interaction is weak in all conformers (NII, NIII and NIV). The HB is strongly bent and, usually, at similar values of the remaining parameters, the strength of the HB is larger in linear or quasi-linear
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Fig. 2. Zwitterions (ZI and ZII) and anions (AI and AII) obtained by the Onsager model at the B3LYP/6-31G p level. The hydrogen bonds are depicted in dotted lines.
dispositions, decreasing in bent HB. Conformer NIII is similar to conformer NI with the difference of a HB of type a, in which the carboxylic oxygen acts as an acceptor instead of donor. Thus the relative stability of the two conformers is mainly due to the strength of this HB, stronger in NI. As in NI, all the other HBs are ˚ ) and relatively weak since the distances HcO (2.621 A ˚ HdS (2.800 A) are quite large. Conformer NIV exhibits a strong HB of type d, with a Hc –O distance of ˚ ; in this conformation, however, the HB only 2.386 A of type f is broken, a possible reason for the higher energy of this conformer comparative to NIII. Finally, NV is the least stable of the studied conformers; its main dissimilarity with NIV being in the different kind of interaction between the thiol and the carboxyl groups and in the presence of two HB instead of three. In this case the sulphur acts as an acceptor, with a HB ˚ which is shorter than in NIV, an distance of 2.326 A indication that the thiol group in cysteine is a better acceptor than donor.
Several different starting geometries were tried in search for a stable zwitterion in gas phase, but without success. It seems that the stability of the zwitterionic forms, like in glycine or alanine [14,15], is small or null. Surprisingly, it was possible to obtain two anionic forms AI and AII (zwitterion with an overall negative charge), which result from the loss of the thiolgroup hydrogen. In both cases, the sulphur is oriented toward the amino group forming a relatively strong HbS HB. In this case the AII form is stable, since the positive charge residing on the amino group is reduced by the oxygen and the sulphur which bear negative charges. This affects the HaN and HbS distances making them shorter than in the neutral conformers. The increase of the basis set to B3LYP/631111G pp does not alter the relative stability of the conformers, although it does bring the remaining conformers closer to NI energetically. These four conformers have some strong HB involving the thiol
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197
Table 4 Frequencies (in cm 21), zero-point energies (in kcal/mol) and infrared intensities (in km/mol) for the neutral forms in solution obtained by the Onsager model I
NI
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ZPE
78 94 194 272 316 366 388 491 537 572 659 760 783 839 890 931 981 1061 1119 1180 1237 1256 1300 1345 1412 1462 1481 1690 1855 2681 3043 3100 3160 3328 3464 3569 68.49
NII 2.8 7.5 2.8 31.1 32.0 1.6 24.6 8.9 4.2 3.8 2.0 6.9 0.6 28.3 159.9 76.9 77.6 51.2 16.5 5.6 19.6 3.5 5.3 42.0 9.1 539.4 15.4 45.9 300.4 7.3 11.3 13.5 2.6 318.9 9.9 17.4
47 100 166 236 244 305 350 387 508 604 648 695 770 797 874 94.1 952 1027 1148 1158 1177 1264 1311 1341 1377 1443 1503 1709 1837 2649 3074 3103 3146 3466 3550 3671 68.04
NIII 3.1 5.9 1.3 10.2 12.9 6.1 71.2 32.5 21.0 91.2 35.2 73.1 28.2 17.1 126.0 28.0 66.4 113.8 115.8 2.7 210.3 15.8 5.4 7.1 67.5 12.4 52 44.8 346.1 21.6 19.8 10.0 7.1 6.1 6.7 88.5
35 115 189 252 294 324 352 407 541 558 639 676 737 779 852 927 954 1054 1144 1169 1188 1276 1325 1338 1397 1410 1479 1692 1821 2697 3017 3110 3168 3474 3565 3682 68.12
group, and due to the fact that the sulphur, although a poor donor or acceptor of HB, is highly polarizable and therefore more affected by diffuse orbitals, the basis set extension results in a further stabilization. Since the smaller 6-31G p basis set yields reasonable results, we adopted it for the calculations in solution. The frequencies and IR intensities are shown in Table 3. The zero-point energy contribution is larger in NI than in the remaining conformers but in spite of that this conformer is still the most stable. All confor-
NIV 1.5 1.6 1.0 7.8 46.2 15.3 83.4 1.8 45.1 48.2 103.9 44.6 44.7 9.2 36.1 163.8 24.2 51.9 77.4 223.1 76.6 3.3 15.8 34.2 32.3 1.0 17.2 55.8 304.8 3.8 15.9 16.0 5.2 1.1 7.7 89.1
36 112 196 228 270 282 333 3741 501 563 638 710 730 770 847 896 1007 1040 1122 1187 1206 1248 1293 1349 1363 1440 1497 1675 1839 2709 2966 3092 3142 3489 3580 3676 67.80
NV 3.7 3.8 4.6 56.8 29.6 10.3 4.6 16.7 23.8 45.0 66.8 41.1 75.5 49.1 80.8 158.7 5.7 13.8 54.8 247.7 10.9 19.4 19.3 15.5 5.3 14.0 7.8 85.3 370.3 5.6 28.6 18.9 9.9 11.5 11.1 86.4
66 96 128 204 277 309 328 353 498 623 675 702 756 775 848 906 1014 1024 1157 1196 1209 1231 1311 1347 1382 1433 1500 1715 1844 2689 3059 3094 3165 3473 3489 3553 67.83
15.5 54.8 3.5 6.2 11.1 20.5 19.5 16.3 3.5 23.7 80.3 60.0 23.2 16.5 25.5 215.3 27.3 43.8 19.8 11.6 29.3 14.9 8.4 63.7 297.2 16.8 9.5 32.9 407.8 7.2 9.6 13.7 1.5 6.5 473.8 6.4
mers present the characteristic frequency due to the CO stretching (approximately 1850 cm 21) which is very intense in the infrared region. Conformers NI and NV have another two frequencies intense in IR corresponding to the COHa bending and OHa stretching with values of 1458 and 1866 cm 21 for NI and 1384 and 3526 cm 21 for NV, respectively. These two frequencies are less intense in the other three conformers, where the hydrogen Ha is directed toward the oxygen. It is also interesting to note that the OHa stretching in conformer NI has lower frequencies
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198
Table 5 Frequencies (in cm 21), zero-point energies (in kcal/mol) and infrared intensities (in km/mol) for the zwitterions and anions I
ZI
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ZPE
74 97 182 269 331 389 425 492 524 591 661 776 793 836 891 1017 1064 1095 1134 1232 1283 1308 1346 1382 1397 1482 1615 1690 1801 2605 2673 3094 3105 3169 3393 3514 68.26
Z2 9.5 24.9 4.4 23.7 147.2 30.3 9.8 6.4 38.2 7.4 8.1 1.0 28.8 87.6 32.8 24.0 22.6 17.7 110.8 17.9 253.7 46.2 85.8 76.3 453.9 29.1 39.2 372. 336.2 593.1 5.6 6.2 11.8 1.1 82.7 121.0
41 178 222 304 318 361 385 566 650 720 755 826 888 910 927 977 1079 118 1163 1259 1298 1309 1366 1423 1483 1515 1594 1666 1844 2261 2726 3061 3110 3147 3444 3523 69.24
A1 9.3 50.5 23.4 55.0 87.1 16.5 7.7 9.0 6.1 12.6 8.3 12.8 0.1 56.1 23.0 7.3 166.7 50.4 8.0 68.7 49.8 122.6 82.6 421.5 205.6 9.0 34.4 27.8 600.0 916.9 1788.3 36.8 13.5 4.2 69.3 83.1
than the NH stretchings, which is an indication of strong HB in this species. 3.2. Solution The Onsager model geometries of all the studied conformers are very similar to their gas-phase structures and the analysis presented in the above paragraph is also valid here. In general, the HB distances are shorter in solution and the structures are tighter. Similar to gas phase, in aqueous solution
88 119 171 260 360 400 424 548 661 672 778 847 887 931 956 1022 1088 1146 1239 1253 1306 1335 1374 1477 1505 1687 1842 2992 3046 3063 3241 3316 3518
62.28
A2 8.9 14.7 25.9 24.9 23.6 6.8 30.5 5.3 11.7 14.9 12.6 1.0 13.6 51.7 59.8 232.0 70.4 19.7 15.1 61.6 27.0 4.3 21.3 602.1 4.9 41.2 474.2 89.8 28.3 79.5 447.1 166.5 6.4
93 98 188 288 334 404 437 550 686 692 789 835 897 920 1010 1088 1133 1230 1244 1283 1314 1375 1391 1509 1607 1652 1773 2623 2920 3018 3082 3125 3538
3.2 22.8 33.8 125.7 51.9 29.6 10.1 34.0 20.5 12.6 0.6 32.7 121.7 14.6 47.1 17.9 139.2 122.5 46.1 431.5 53.3 159.1 194.8 5.4 77.0 21.6 387.0 1176.2 446.9 89.6 35.9 40.7 33.2
61.67
NI remains the most stable neutral conformer. Comparing to gas phase, in conformer NIII the Hc – ˚ . The HaS distance in O distance is reduced by 0.109 A conformer NIV and the HbN distance in conformer NV are also shorter in solution, although in the latter the HbO distance increases. Conformers NI and NV are more stabilized by the Onsager model as a consequence of their larger dipole moments, as illustrated in Table 1. In addition to the neural forms, two zwitterions and two anions become stable when the Onsager model is
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applied (Fig. 2). The zwitterion ZI represents a HbO ˚ , respectively, and NHa distances of 1.623 and 1.087 A which indicates very strong HB. The zwitterion ZII has two HB involving sulphur, while the interaction between the amino and the carboxyl groups is broken and therefore this structure is less stable than ZI. Similarly, we have shown that a zwitterionic form with trans orientation with regard to the oxygen is unstable at B3LYP/6-31G p level. This zwitterion and the ZI conformer were obtained in Ref. [6] via gas-phase calculations at the HF/4-31G p level; it appears that this level of calculation overestimates the stability of the zwitterionic forms. Anions AI and AII are the only stable anionic forms where the sulphur bears negative charge. A disposition of the sulphur as in conformer NI yields an unstable structure because of the repulsion between the sulphur and the oxygen. Contrary to what happens to the neutral forms, in solution the anions have longer hydrogen-acceptor distances due to the stabilization effect of the solute–solvent interactions on charges held by the atoms. The frequencies and IR intensities of the neutral, zwitterionic and anionic forms of cysteine in solution are displayed in Tables 4 and 5, respectively. The frequencies of the neutral conformers are very similar to those in gas phase because of the small structural change. The zwitterions, ZI, ZII and zwitterionicanionic form AII have a single characteristic very intense IR frequency at 1397, 1423 and 1283 cm 21, respectively, which corresponds to the symmetric deformation (pyramidalization) of the NH31 group. These three forms also have characteristic low frequencies and with very intense IR activity for the NH and OH stretchings of the hydrogens which yield strong HBs. In the case of the NH31 group, the HBs break the degeneration of the NH stretchings, and the non-hydrogen bonded NH stretchings in these zwitterions and anions have the largest frequencies. Thus the frequency of 2605 cm 21 corresponds to the NHa stretching in ZI; the frequencies of 1844 and 2261 cm 21 correspond to the NHb and OHa stretchings, respectively, in ZII; the frequencies of 2623 and 2920 cm 21 correspond to the NHa and NHb stretchings, respectively, in AII. The anion AI has two characteristic frequencies at 1477 and 3241 cm 21 corresponding to the COHa bending and OHa stretching, respectively.
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As illustrated in Table 1, the Onsager model underestimates significantly the electrostatic interaction and therefore ZI is still by 8.11 kcal/mol less stable than NI; similar relative stabilities are obtained for AI and AII, whereas it is known that the zwitterionic species are predominant in solution [3]. By means of the PCM model, it was found that in solution ZI and AII are already more stable by 1.21 and 3.54 kcal/mol, respectively, as regard to NI and AI; these values change to 2.19 and 4.66 kcal/mol, respectively, if non-electrostatic contributions are included. The PCM model considers a more realistic shape of the cavity and treats the solute–solvent interactions more accurately. As pointed out before, the major interaction is electrostatic, the non-electrostatic part being less than 20% of the total interaction energy in all cases. In the neutral conformers, however, the nonelectrostatic interactions are more destabilizing, an effect due mainly to the difference in the cavitation energies, while the dispersion–repulsion energies are quite similar in all the conformers. This results from the fact that the cavitation energy has a positive contribution, which reflects the free-energy change upon cavity formation. This contribution is larger in the neutral conformers because it is easier to create a cavity for more polar species like the zwitterions. Therefore, as expected, the zwitterionic species are stabilized by both electrostatic and non-electrostatic terms, although the electrostatic interactions are prevailing.
4. Conclusions A DFT study of cysteine conformers in gas phase and in aqueous solution was carried out. In both cases the most stable conformer is the neutral conformer NI shown in Fig. 1. The hydrogen bond between the amino and the carboxyl groups is strongest when the nitrogen acts as a HB acceptor. This seems to be also the case for the thiol group. In gas phase the zwitterionic species are not stable, although it is possible to obtain two stable anions with a negative charge on the sulphur. The solvent tightens the structure of the neutral forms and loosens that of the anions. Within the Onsager model two zwitterionic forms, ZI and ZII, are stable with negative charges upon the oxygen and sulphur, respectively. The Onsager model, which
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underestimates the electrostatic contributions to the solute–solvent interaction, is unable to reproduce the right energetics of the zwitterionic forms. A more elaborate treatment of these interactions is needed in this case, which is introduced by means of the PCM model. In agreement with the experiment, this model predicts rightly that the zwitterions are most stable both in the neutral, ZI, and in the anionic, AII, forms. Acknowledgements The authors thank Z. Smedarchina for helpful discussions. Support through Project XUGA20903 A98 from Xunta de Galicia is appreciated. A.F.-R. thanks NRC for the computational facilities. References [1] P. Kollman, J. McKelvey, A. Johansson, S. Rothengerg, J. Am. Chem. Soc. 97 (1975) 955. [2] H. Li, C. Wurrey, G.J. Thomas Jr, J. Am. Chem. Soc. 114 (1992) 7463. [3] K.C. Chang, E. Grunwald, J. Phys. Chem. 80 (1976) 1425. [4] K.A. Kerr, J.P. Ashmore, T.F. Koetzle, Acta Crystalogr. B31 (1975) 2022. [5] P. Tarakeshwar, S. Manogaran, J. Mol. Struct. (Theochem) 305 (1994) 205.
[6] P. Tarakeshwar, S. Manogaran, Spectrochim. Acta 51A (1995) 925. [7] S. Gronert, R.A.J. O’Hair, J. Am. Chem. Soc. 117 (1995) 2071. [8] V. Barone, C. Adamo, F. Lelj, J. Chem. Phys. 102 (1995) 364. [9] L. Onsager, J. Am. Chem. Soc. 58 (1936) 1486. [10] M.W. Wong, K.B. Wiberg, M.J. Frisch, J. Chem. Phys. 95 (1991) 8991. [11] M.W. Wong, M.J. Frisch, K.B. Wiberg, J. Am. Chem. Soc. 113 (1991) 4776. [12] C. Amovilli, V. Barone, R. Cammi, E. Cance`s, M. Cossi, B. Mennucci, C.S. Pomelli, J. Tomasi, Adv. Quant. Chem. 32 (1999) 227. [13] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery, Jr., R.E. Statmann, J.C. 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. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, gaussian 98, Revision A.3, Gaussian, Inc., Pittsburgh, PA, 1998. [14] J.H. Jensen, M.S. Gordon, J. Am. Chem. Soc. 117 (1995) 8159. [15] A.G. Csa´za´r, J. Phys. Chem. 100 (1996) 3541.