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The Radical Cations of the Monomer and van der Waals Dimer of a Methionine Residue as Prototypes of (2 Center - 3 Electron) SN and SS Bonds. Molecular Simulations of their Absorption Spectra in Water. Pierre Archirel, Jacqueline Bergès, and Chantal Houée-Levin J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b06329 • Publication Date (Web): 26 Aug 2016 Downloaded from http://pubs.acs.org on August 29, 2016
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The Radical Cations of the Monomer and van der Waals Dimer of a Methionine Residue as Prototypes of (2 center - 3 electron) SN and SS bonds. Molecular Simulations of their Absorption Spectra in Water Pierre Archirel,∗,† Jacqueline Berg`es,‡ and Chantal Hou´ee-L´evin† †Laboratoire de Chimie Physique CNRS UMR 8000, Universit´e Paris-Sud F91405 Orsay France ‡Sorbonne Universit´es, UPMC Univ Paris 06, CNRS, Laboratoire de Chimie Th´eorique UMR 7616, CC 137 - 4, place Jussieu F75252 Paris Cedex 05 France E-mail: [email protected]
Abstract Oxidation of peptides or proteins by the OH. radicals produced by pulse radiolysis yields species identified by their absorption spectra in the UV-visible domain. However the case of methionine (Met) in peptides is complex since its oxidation can lead to various free radicals with (2 center - 3 electron) bonds. We have performed MonteCarlo / DFT molecular simulations of the radical cation Met.+ of the methylated methionine aminoacid, taken as a model of the methonine residue of peptides, and of the radical cation of its van der Waals dimer, Met.+ 2 . The cation of the methionine residue displays a (2 center - 3 electron) SN bond. The cation of the dimer Met.+ 2 displays three quasi degenerate conformers, one stabilized by a (2 center - 3 electron) SS bond and two other, stabilized by ion-molecule interactions and made of a neutral and a cationic unit. These conformers are characterized by their charge and spin density localization and their UV-visible absorption spectra. These spectra enable a discussion of absorption spectra of the literature, in particular we emphasize the role of dimers, before and after the oxidation process.
Introduction Protein maintenance is of vital importance. In particular the redox shuttle between the residues methionine sulfoxide and methionine, ensured by enzymes methionine sulfoxide reductase A and B, controls many events linked to oxidative stress, including ageing. 1–3 The oxidation of methionine residues has been the focus of numerous experimental and theoretical studies these last thirty years. In particular the nature of the transients has been investigated by pulse radiolysis, 4,5 but controversies still exist about their structure and about their link to the final products, which can differ from the sulfoxide. 6,7 Hence the extent to which the redox shuttle works is still unknown.
It has been stated that the free radicals created upon OH. attack should have a σ 2 σ ∗ (2 2 ACS Paragon Plus Environment
center - 3 electron) (2c − 3e) bond between the sulfur radical cation and any atom having a lone pair. 8 On the experimental side one has only the transient absorption spectra and their time evolution. Experiments are interpreted with the help of the measured spectra of model compounds, 9–13 but the two following questions arise: • are the transients observed by pulse radiolysis really radical cations in which the sulfur atom is complexed? • which atom is donating its lone pair? In particular in peptides the candidates are numerous: oxygen or nitrogen of the peptide bond, and/or from the N- or C- terminus. Quantum calculations indicate that the spectra are very structure dependent, in particular they depend on the distance between the S and the doublet donor atoms. 14–18 The situation is still complicated by the possibilty of van der Waals dimerization of the peptides in solution, either neutral - neutral, or neutral - cation. This is clearly suggested by kinetic studies, 4,5 and by the evidence that peptides are only poorly soluble in water. It can be argued that the neutral - cation dimers are formed through (2c, 3e) SS+ bonds, 4,8 but this hypothesis deserves investigations. Note that the previous discussion only deals with the oxidation of the methionine residue of peptides. The oxidation of the methionine aminoacid itself leads to no cation formation, a decarboxylation is observed instead. 19–21 The methionine aminoacid is therefore out of the present discussion. In the present article we focus on the absorption spectra of the radical cations of a model methionine residue and of its van der Waals dimer. This model has been obtained through the double methylation of the methionine aminoacid. By this procedure we prevent the decarboxylation. 16,22 We note Met and Met2 the neutral species and Met.+ and Met.+ 2 their radical cations. We emphasize that our Met2 dimer is made of two distinct Met entities and is thus different from the MetMet dipeptide. There is a great need of molecular simulations of absorption spectra of peptide cations. 3 ACS Paragon Plus Environment
This is the aim of the present work. We have developed a Monte Carlo / DFT (MC/DFT) method, and shown it to be equivalent and faster than the more common Molecular Dynamics (MD/DFT) method. 23 Since MC simulations can be done with small basis sets only we will compare their results to static quantum results obtained with very large basis sets. In the first section we outline our simulation method, then we discuss the case of the Met.+ monomer, then the case of the dimer Met.+ 2 . In the last section we discuss measured absorption spectra of the literature, in the light of our simulations.
Computational methods The present work associates two different approaches: the static quantum chemistry which yields only one (optimized) structures and the corresponding absorption lines λ1 , λ2 ... that we will note ”at 0 K” for the sake of simplicity, and the molecular simulation, which yields real absorption spectra at 300 K, with a λmax value and band widths and profiles due to a large part of the potential surface. Calculations at 0 K can be made with very large bases, and provide useful tests of the molecular simulations. We have performed molecular simulations of the monomer and dimer of the methionine cation M.+ and M.+ 2 . We have used a mixed classical/quantum method, based upon the following three choices: the sampling of the nuclear configurations is done with the classical MC (Monte-Carlo) method at 300 K as enabled by the GIBBS code, 24 the calculation of the electronic energy is done with the DFT method 25 and the solvent is modeled with the PCM (Polarized Continuum) method 26 in its SMD (Solvent Modeling using density) formalism. 27 DFT and SMD calculations are done with the help of the Gaussian 09 code. 25 This method has already been used with success for the simulation of radiolytic species such as alcalin earth perchlorates 28 and EDOT derivatives. 23 We have used the BH&HLYP functional 29 because it is widely used in the literature about (2 center - 3 electron) cationic systems. 30,31 Nevertheless recent investigations of disulfide radical anions, 32 though confirming the ability of the BH&HLYP functional, show
that the RSH (Range Separated Hybrid) functionals work better. The authors emphasize that these anionic systems display much dynamical correlation effects, for which the RSH functionals have been designed indeed. Since our systems are cationic they probably display much less dynamical effects, and for this reason we have used the simpler BH&HLYP functional. For the sake of reasonable simulation times we have done the sampling on frozen fragments rather than on atoms. In this way we have only two MC moves: the global translation and global rotation of the fragments, which have been given the same probability 0.5. The number of MC steps has been set to 10 000 for monomers and 15 000 for dimers, this results in simulation times ranging from a few days for the monomers to several weeks for the dimers on the 8 core machines of our computation platform. The spectra have been computed with a series of TDDFT calculations 25 on a sublist of MC configurations extracted from the full list with one configuration out of fifty. The number of transitions has been set to twenty and the convolution of the resulting lines done according to the formula of the literature 33 and with a fwhm (full width at half maximum) set to 0.2 eV. For the convolution we have replaced each transition line of each geometry by a gaussian, separately. For the structure analysis we have calculated the NBO (Natural Bond Analysis) 34 and atomic spin densities. 25 For the sake of acceptable computation times we have used a small basis set, using core pseudopotentials for every carbon, oxygen and nitrogen atoms, 35 and sulfur atoms. 36 Since the published basis include no polarization functions we have added one d gaussian on each heavy atom with exponents 0.626 (on C atoms), 0.913 (on N atoms), 1.292 (on O atoms) and 0.65 (on S atoms). This polarized SDD basis will be noted pSDD hereafter. For the calculation of the absorption spectra we have considered the extension of the basis set with diffuse s and p gaussians of exponents 0.07 and 0.08 (on C atoms), 0.10 and 0.10 (on N atoms), 0.15 and 0.035 (on O atoms) and 0.07 and 0.015 (on S atoms). These exponents have been obtained from the smallest ones of the SDD basis set, and a division by a factor 2. This augmented pSDD basis set will be noted pSDD+ hereafter. For the sake of comparison with other works
we have also used the larger 6-31g(d), 6-311g(d), 6-311+g(d,p) and aug-cc-pvdz basis sets. 25
Results The methionine radical cation Met.+ Geometry optimizations show that the methionine cation displays two conformers, with SN and SO intramolecular bonds. 8–13 16–18 We give their structures in figure 1 and the main properties of the SN conformer in table 1.
Figure 1: Equilibrium structures of the Met.+ cation in its conformers with intramolecular SN bond (left) and SO bond (middle). Molecular fragments used for the simulation (right). Carbon atoms are grey, oxygen red, sulfur yellow and nitrogen blue.
Table 1: Met+ cation in its SN conformer in water at 0 K: SN bond length (in ˚ A), atomic spin densities and spectral data (in nm) with BH&HLYP, the SMD model and four basis sets. d (SN) ρ(S) ρ(N) λ1
We have performed MC simulations of the methionine cation in its two SN and SO conformers, with the BH&HLYP functional and the pSDD basis set. The number of MC steps
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has been set to 10 000. We have dropped the first 1000 MC steps, as only performing equilibration, and verified that the absorption spectrum is converged, that is the last thousands of MC steps yield only a slight modification of the band position. As already stated we have considered rigid fragments: SCH3 , NHCH3 , CO2 , CH, CH2 and CH3 , also shown on figure 1. The energy fluctuations along the simulation are shown on figure 2, it can be seen that the SN conformer is much more stable than the SO one, with a difference of the average energies of 0.7 eV (68 kJ/mol). This result is in agreement with our previous work. 22 Since the SO conformer is very instable we will drop it from the present study. The rdf (radial distribution function) of figure 3 (bottom, red curve) clearly confirms
Figure 2: Energy fluctuations along the MC simulations of the Met.+ cation in its conformers with SN and SO intramolecular bonds. the SN bonding nature of this conformer, with a SN distance between 2.35 and 2.75 ˚ A in agreement with our previous work. 22 This nature is also proved by the orbital isovalues of figure 4, calculated for a geometry arbitrarily taken in the MC list. It can be seen that one bioccupied orbital is a SN bonding orbital, with no node between S and N atoms and that the SOMO (singly occupied molecular orbital) is the corresponding antibonding orbital, with a nodal surface between the S and N atoms. The electron configuration may be written,
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rdf (arbitarry unit)
dimer with SS bond .+ DMS2
2,9 3 3,1 SS distance (Å)
dimer with trans IM bond dimer with cis IM bond monomer with SN bond
Figure 3: Radial distribution functions of the SN distance of the Met.+ cation with an SN bond and of the dimers with trans and cis IM bonds (bottom). Rdf of the SS distance of the dimer with an SS bond (top). We add the SS data for the DMS.+ 2 as a reference. The distance mesh is 0.02 ˚ A.
Figure 5: Atomic NBO charges (top) and spin densities (bottom) of the S and N atoms of the Met.+ cation in its conformer with SN intramolecular bond. Correlation of the charges and spin densities between themselves.
We have also investigated the electron localization of this conformer with the help of both the NBO analysis 34 and the Mulliken spin density analysis, 25 looking for correlations between these atomic quantities and the SN bond length, and between themselves. We have found that the better correlations are obtained for the quantities between themselves. These results are shown on figure 5. It can be seen that there is a good correlation between the atomic charges on the S and N atoms, and a still better correlation between the atomic spin densities on the S and N atoms. Note the large fluctuations of population: the S charge is always positive, between 0.40 and 0.60 and the N charge is always negative, between -0.40 and -0.60. The atomic spin densities on the S and N atoms are both positive and fluctuate in the same range: 0.35 - 0.65 a.u.. We have found out that the NBO charges take large values on all the atoms, and that conversely the spin densities take significant values on the S and N atoms only. This explains why the best correlation is obtained between the spin densities. The corresponding regression line reads almost exactly x + y = 1, showing that one electron is shared by the S and N atoms.
Now concerning the absorption spectrum, we have found out that the calculated spectrum in the visible zone, is due to the only σg → σu intense transition: ∗1 1 ∗2 2 σSN → σSN σSN σSN
We have used the Met.+ system as a test for three different bases. We have done simulations with the small pSDD basis (193 functions), the larger 6-31g(d) basis (199 functions) and the still larger 6-311g(d) basis (251 functions). We have calculated the spectrum without and with diffuse functions, as given in the previous section. This results in six spectra, gathered in figure 6.
Figure 6: Absorption spectrum of the Met.+ cation in its conformer with SN bond, calculated with BH&HLYP, three different basis sets and with and without diffuse gaussians.
Table 2: Met+ cation in its SN conformer in water at 300 K: spectral data (in nm), wavelength shift between 0 K and 300 K (in nm), total nuclear energies at 300K, corrected for anharmonicity (in eV), with BH&HLYP, the SMD model and three basis sets. λmax ∆λ Eanharm
It can be seen that the three bases yield rather different spectra, and that the diffuse functions only have a marginal effect. The results are summarised in tables 1 and 2, where we also give the wavelength shift between 0 K and 300 K:
∆λ = λmax (300K) − λ1 (0K)
It can be seen that: 1. at 0 K the basis effect is tiny, in a 4 nm (i.e. 0.03 eV) range. 2. at 300 K the basis effect is much larger, in a 53 nm (i.e. 0.37 eV) range. 3. this temperature effect on ∆λmax is very basis set dependent, in the order: 6-311g(d) (8 nm) < 6-31g(d) (37 nm) < pSDD (59 nm) This last result suggests that the anharmonicity of the potential surface is also basis dependent, and that the pSDD basis set, yielding the largest discrepancy, also yields the most anharmonic potential surface. In order to test this statement we have performed anharmonic calculations of the nuclear energies of the molecule (Eanharm ), as enabled by the gaussian 09 code. 25,37 These anharmonic energies at 300 K are given in table 2, they increase in the following way: 6-311g(d) > 6-31g(d) > pSDD Since it can be expected that the smallest nuclear energy is provided by the most anharmonic potential surface, this result confirms our statement. Note that the absorption spectrum of the cation of the methionine aminoacid actually cannot be recorded. Since we actually have no choice of basis set because simulations for dimers are to be done, we have performed them with the smallest pSDD basis set. The basis set dependence of the absorption spectrum must be kept in mind, nevertheless. As for the dimer it will be discussed with the results at 0 K only. 13 ACS Paragon Plus Environment
The radical cation of the van der Waals dimer Met.+ 2 Evidence of two bonding modes In this section we consider the radical cation of the van der Waals dimer, noted Met.+ 2 . We first have investigated the low lying structures of this cation with extensive geometry optimizations in water, using a large number of initial geometries. We have obtained three different low lying conformers: one with a 2c − 3e (2 center - 3 electron) SS bond and two of the van der Waals type, with an ion - molecule (IM) bonding. The structures are shown in figure 7, the relative energies with basis sets of increasing size are given in table 3. The nature of these conformers is proved by figure 7 and by the structural data given in table 4:
(a) ion-molecule trans
(b) ion-molecule cis
(c) SS 2c − 3e bond
Figure 7: Three low-lying conformers of the Me.+ 2 cation. The hydrogen atoms have been dropped, except those engaged in H-bonds.
1. the most stable conformer is of the IM type, this is proved by the total NBO charges of the units: 0.02 and 0.98 | e | and by the values of the atomic spin densities on the S 14 ACS Paragon Plus Environment
Table 3: Met.+ 2 cation in its SS and IM (ion- molecule) conformers in water. Relative energies and free energies at 300 K (in eV), as given by BH&HLYP, the SMD model and four basis sets. All the structures have been obtained with tight convergence threshold and ultrafine integration grid mesh, and display only real frequencies. The most stable conformer is given the energy 0. conformer
pSDD 6-311g(d) 6-311+g(d,p) aug-cc-pvdz E G E G E G E G SS bond 0.214 0.239 0.197 0.227 0.095 0.133 0.074 0.053 cis IM bond 0.100 0.084 0.142 0.132 0.084 0.089 0.082 0.087 trans IM bond 0. 0. 0. 0. 0. 0. 0. 0.
Table 4: Met.+ 2 cation in its SS and IM (ion- molecule) conformers in water: bond distances (in ˚ A), atomic spin densities and absorption wavelengths (in nm), with BH&HLYP, the SMD model and four basis sets. We add the absorption wavelength from the MC simulation at 300 K. conformer
and N atoms of the cationic unit, both close to 0.50 a.u.. This conformer is shown on figure 7 (a). It is made of two units: a neutral methionine (on the left) and a cation Met.+ in its SN conformer (on the right), linked by both ion-molecule interactions and two interchain NH...OCO hydrogen bonds. These two units are upside down, so that we call it the trans IM conformer hereafter. Note that previous calculations on the MetMet dipeptide have led to a similar structure. 22 2. The second IM conformer (figure 7 (b)) displays two facing SS atoms, with a large SS distance and conformations of the chains, very different from the first IM conformer. We will note this conformer cis IM conformer hereafter. The IM nature of this conformer is proved by the total NBO charge of the two units: 0.00 and 1.00 | e | and by the spin densities on the S and N atoms of the cationic unit. 3. the SS conformer (figure 7 (c)) displays a short SS bond, with length 2.8 ˚ A, and two parallel chains, linked by two inter-fragment NH...OCO hydrogen bonds, just like the trans IM conformer. The 2c − 3e SS bond is proved by the values of the total NBO charges of the two units: 0.50 and 0.50 | e | and by the atomic spin densities on each S atom, close to each other. According to the basis set these values range from about 0.4 (for the smallest pSDD basis) to about 0.5 (for larger bases) and to about 0.6 a.u. (for the largest basis). 4. This 2c − 3e SS bond is also proved by the orbital isovalues of figure 4, showing that one bioccupied orbital has a SS bonding character, with no node between the S atoms, and that conversely the SOMO has a SS antibonding character, with a nodal surface between the S atoms. The electron configuration may be written therefore:
2 ∗1 σg,SS σu,SS
5. we have found that an intermolecular 3-electron SN bond is also possible, but at a still
higher energy than that of the SS conformer. Since this SN dimer lies 0.19 eV (18 kJ/mol) higher than the SS dimer, we will ignore it in the following discussions. We have found out other bonding modes with higher energies. Since these three conformers are quasidegenerate we have calculated their energies with four basis sets of increasing size, from the small pSDD basis used in the simulations, up to the very large aug-cc-pvdz basis which should yield the most realistic results. Note that our calculations are free from dispersion and of BSSE (basis set superposition error) correction. Since BSSE correction can be expected small in DFT calculations, and since the B97D functional, including dispersion, has been proved inefficient for disulfide anions, 32 we have used the BH&HLYP functional for all our dimers, and postponed a closer discussion of dispersion effects to a later, dedicated section. Energies and free energies obtained with BH&HLYP, SMD and these four bases are given in table 3. It can be seen that the trans IM conformer is the most stable conformer whatever basis set is used and that the SS and cis IM conformers are very close to each other and their relative stability depends on the basis. In particular if the pSDD basis is used (like in the MC simulation) the cis IM conformer is more stable than the SS conformer. The difference of the energies decreases as the basis set becomes larger and eventually the largest basis (aug-cc-pvdz) makes the SS conformer more stable than the cis IM one, but by 0.03 eV only. It is clear that the three conformers are quasidegenerate and that extending the present result to other peptides is hazardous.
Molecular Simulations Our MC simulations are made with the small pSDD basis, and use rigid molecular fragments, just like for the monomer. These fragments are the following: CH3 SCH2 CH2 , CHNHCH3 and COOCH3 , and their geometry have been taken in the optimized structures of the dimers. Within this procedure the number of fragments is the same for the monomers and dimers, namely six. This small number of fragments has been chosen so as to shorten the equilibration period. The energy fluctuations are shown in figure 8. It can be seen that the equilibration 17 ACS Paragon Plus Environment
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of these dimers requires a larger number of MC steps, than the monomer. For this reason we have set the number of MC steps to 15 000. Note that we have performed 15 000 MC steps
dimer with trans IM bond dimer with cis IM bond dimer with SS bond
Figure 8: MC simulations of the Met.+ 2 cation in its conformers with SS and trans and cis IM bonding. Energy fluctuations (in eV) along the simulation. The energy of the trans IM conformer has been shifted by -0.2 eV.
for the two IM dimers, but that we could not reach this number for the SS conformer. This is due to a simulation ”accident” soon after the step 13 000: the BH&HLYP energy suddenly diverged. This accident proved to be due to the reaction field, and could be circumvented through a temporary scaling (i.e. 100 MC steps) of all the SMD atomic radii by the factor 1.05. Since this procedure results in some bias in the simulation, we prefer to consider only 13 000 MC steps for the SS conformer. According to table 3 the three conformers are separated by ca 0.1 eV (10 kJ/mol). The average energies of the MC simulations follow a similar trend: the conformer average energies increase according to the sequence: trans IM (0.), cis IM (+0.05 eV, 5 kJ/mol) and SS conformer (+0.26 eV, 2.5 kJ/mol). The rdf are given in figure 3 and confirm the SS and IM structures of the conformers:
1. both IM conformers display a short SN bond in one of the two monomers, in the range 2.35 - 2.7 ˚ A, like the SN conformer of the Met.+ monomer. Of course the other (neutral) unit displays much larger SN distances, not visible on this figure. 2. the SN rdf of these IM dimers are markedly different from that of the SN monomer, namely they are narrower and shifted toward smaller values of the SN distance. This shows that the SN monomer is in some extent frozen by the neighborhood of the neutral monomer. 3. the SS conformer has a relatively short SS bond, fluctuating in the range 2.6 - 3.1 ˚ A. This range is in agreement with previous calculations on similar systems with 2c − 3e SS bonds. 16 4. this SS rdf displays an intriguing bimodal shape, with two maxima at about 2.8 and 2.95 ˚ A. The inner maximum is in agreement with the value given by geometry optimization, 2.81 ˚ A, see table 4. The complex shape of the rdf may be due to a poor convergence of the simulation, but extension of the simulation is impossible due to the simulation accident. It may be also due to a double minimum on the SS free energy curve: we have recently found a similar rdf function in the [Li(ClO4 )2 ]− system and pointed out that they are not rare in the literature. 38 5. as a test we have done the simulation of the simple DMS.+ 2 (dimethyl sulfur) cation which is well known in the literature. 39 We have done 20 000 MC steps with the BH&HLYP functional, the aug-cc-pvdz basis set and the SMD formalism in water. The SS rdf is added to the figure 3, top. It can be seen that it is much simpler than that of the SS dimer of methionine, with only one maximum. It is also shifted to smaller values of the SS distance, due to the fact that in this small system the inter fragments repulsions are smaller. We have investigated the correlation of the spin atomic densities along the MC simulation, see figure 9. It can be seen that in the IM conformer (on the right, top) the S and N atomic 19 ACS Paragon Plus Environment
spin densities of the cationic fragment display a good linear correlation, just like that of the cationic monomer, shown in figure 5. Conversely no correlation of the S atomic spin densities can be seen in the SS conformer (on the left, top). This discrepancy can be traced back to the distribution of the atomic spin densities, spreading over other atoms: 1. inspection of the MC configurations shows that apart from the S and N atoms engaged in the bonding, the α carbon atoms and their hydrogens also take little values of the spin density, ranging from 0. to ca 0.03 au. 2. these values are small compared to the difference of the values on the S and N atoms in the IM conformer, but large compared to the difference of the values on the two S atoms in the SS conformer (never larger than 0.06 a.u.). This explains the better correlation in the first case. 3. a good correlation can be obtained in both cases if the atomic spin densities of the α carbon atoms and their hydrogens is added to the values of the densities on the S and N atoms: see figure 9 (bottom).
Absorption Spectra The absorption spectra of the SS and IM conformers have been calculated with the pSDD+ basis set (pSDD supplemented with diffuse gaussians). All the species of interest in the present work are open shell cations, this means that our DFT and TDDFT calculations, being of the UHF type, cannot ensure that the ground and excited states are true doublets, with the average value < S 2 >=0.75 exactly. Spin contamination by quartet states can have dramatic consequences on absorption spectra, but we have recently proposed a simple way for minimizing this influence in a work on organic cations. 23 Application of this method to the present spectra yielded only tiny differences, so that we may consider that the present spectra are free from spin contamination. We have verified that the calculated absorption spectra in the visible are made of one tran21 ACS Paragon Plus Environment
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sition only, the σg → σu transition of equ. 2 in the case of IM conformers, and the σg → σu transition: 2 ∗1 1 ∗2 σg,SS σu,SS → σg,SS σu,SS
in the case of the SS conformer. We give the simulated spectra in figure 10 and their λmax values in table 4. We join the spectrum of the cation monomer Met.+ to figure 10 for comparison. It can be seen that:
15000 SN monomer trans IM dimer cis IM dimer SS dimer
Figure 10: Absorption spectra of the Met.+ cation in its SN conformer and of the Met.+ 2 cation in its conformers with SS and IM bonding.
1. the IM isomers display a band at around 400 nm. Comparison with the band of the SN monomer shows that they are narrower and shifted toward higher energies. This effect is due to the perturbation of the cationic chromophor by the neighboring neutral, and can be related to the SN rdf of figure 3, already discussed. It appears that the presence of the neutral in some extent freezes the cation. The shift of both the band and the SN rdf is larger for the trans IM dimer, which is the most stable conformer.
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2. the SS conformer displays a complex spectrum with apparently two main bands. It appears that this shape is to be related to the complex SS rdf of figure 3, with two maximas. As written above this complexity could be apparent and due to a lack of convergence of our simulation. In figure 11 we show two contributions to this spectrum,
Figure 11: Absorption spectrum of the Met.+ 2 cation in its SS conformer, with separation of the short and large SS distances. We add the spectrum of the DMS.+ 2 cation as a reference. corresponding to different values of the SS distance, shorter and larger than the value 2.85 ˚ A. It can be seen that shorter values of the SS distance contribute the high energy part of the spectrum, and that larger values contribute the low energy part. 38 This complex spectrum is quite similar to that of [Li(ClO4 )]− 2 , already discussed.
3. the values of table 4 show that calculations at 0 K yield λ1 values which are rather close to those of the λmax values yielded by the MC simulations at 300 K. For the IM conformers the λ1 value of the trans conformer is 16 nm too long, for the cis conformer it is 4 nm too short. As for the SS conformer the λ1 value is 9 nm too short if only the first band, corresponding to shorter values of the SS distance, is considered. Not 23 ACS Paragon Plus Environment
surprisingly, the second λmax value at 580 nm, corresponding to larger values of the SS distance, cannot be predicted by geometry optimizations. 4. we have added to figure 11 the absorption spectrum of the DMS.+ 2 cation. This spectrum displays only one band, with λmax =506 nm in good agreement with the recorded value: 485 nm. 39 This simple spectrum is obviously linked to the simple rdf function of .+ figure 3. The rdf and absorption spectra of the DMS.+ 2 and Met2 cations suggest that
the dimers linked by the (2c-3e) bond may be classified into two categories: (1) small dimers with simple SS rdf s and spectra with one simple band and (2) large dimers, like Met.+ 2 , with bimodal rdf s and one complex absorption band. Testing other dimers is an interesting task for the future. 5. we have investigated the influence of the solvation model on the value of the absorption wavelength, and compared the SMD model to the CPCM model (Conductor-like PCM) used with UFF atomic radii. 40 This influence has been found small as long as the ion - molecule conformers are considered. For the cis conformer the λ1 values amount to 397 nm (SMD) and 418 nm (CPCM), for the trans conformer they amount to 407 nm (SMD) and 412 nm (CPCM). The influence of the solvation model is more important for the SS conformer, for which these values amount to 482 nm (SMD) and 516 nm (CPCM), that is a 34 nm difference. Cross calculations have shown that this difference is due to the solvation formalism, not to the different radii which are used, SMD and UFF. We have taken the small DMS.+ 2 cation as a test and investigated the dependence of the λmax value upon the solvation model. At the equilibrium geometry we obtain different values of λ1 : 439 nm (SMD) and 458 nm (CPCM), with a 19 nm difference. The MC simulation, identical to that of figure 11, but with the CPCM model and UFF radii (not shown), enables the comparison of the λmax values: 506 nm (SMD) and 510 nm (CPCM), with a 4 nm difference. The influence of the solvation model, clearly seen in the 0K data, is largely attenuated if the absorption spectra at 300K are
considered, therefore. Of course in the case of the SS conformer of Met.+ 2 the influence of the solvation model at 0K is larger: 34 nm, and the influence of the solvation model on the absorption spectra cannot be predicted. Note also that the experimental values of the absorption wavelengths are known within 10-20 nm. Experimental data cannot help discriminate the solvation models, therefore. Inclusion of dispersion effects The inclusion of dispersion effects is of utmost importance in the description of van der Waals neutral dimers, 41 but its importance in cationic dimers is not established, because such systems also display large electrostatic and induction effects. For the sake of clarification we have introduced dispersion effects in both our calculations at 0K and our MC simulations. We first have performed geometry optimizations and TDDFT calculations of the SN cation and of the three conformers, SS, cis IM and trans IM, of the dimer. We have used the B97D 42 and B97D3 43 functionals (both inluding dispersion), the 6-311+g(d,p) basis and the SMD simulation of the water solvent. Absorption wave lengths and relative free energies are given in table 5. It can be seen that: Table 5: Influence of dispersion effects on absorption wave lengths at 0K (in nm) and relative free energies at 300K (in eV) of Met.+ and Met.+ 2 . DFT results with two functionals including dispersion, the 6-311+g(d,p) basis set and SMD simulation of the water solvent. The most stable dimer is given the energy 0. species Met.+ Met.+ 2 Met.+ 2
conformer B97D SN λ 495, 403 SS 484 trans IM λ 426 cis IM 419 SS 0.077 trans IM G 0.053 cis IM 0.
B97D3 485, 398 471 401 405 0.150 0. 0.104
1. the SN cation of Met.+ now displays two main absorption lines in the visible. These ∗ lines correspond to excitations from the σSN and the σSC toward the σSN orbital. This
result is in contradiction with the BH&HLYP results of table 1, showing only one ∗ . Since the BH&HLYP functional is widely accepted transition, from σSN toward σSN
for the description of the present system, we consider that the B97D and B97D3 functionals are not satisfactory, therefore. 2. the B97D and B97D3 G values of table 5 are close to each other and also close to those of table 4 in the same basis, with the IM dimers more stable, and the SS dimer less stable. We conclude that the inclusion of dispersion, though refining the interactions, does not change our conclusion about the quasidegeneracy of the SS and IM conformers of the dimer.
Figure 12: Absorption spectra of the SN conformer of Met.+ and the trans IM conformer of Met.+ 2 with the B97D functional.
We then have performed MC simulations of the SN conformer of Met.+ (with 10 000 MC steps) and of the trans IM conformer of Met.+ 2 (with 15 000 MC steps) with the B97D functional and the pSDD basis set. The corresponding spectra are given in figure 12. It can 26 ACS Paragon Plus Environment
be seen that the spectrum of the SN monomer displays two bands, as can be expected from the lines of table 5, and that the spectrum of the dimer also displays two bands, shifted toward higher energies. The B97D spectrum of the SN monomer is in contradiction with the measured spectra of cationic SN species, which only display one broad band in the visible. From this measured broad band it is not possible to say whether one or several transitions interfere, but the B97D spectrum with two bands is clearly not realistic. The B97D spectrum of the trans IM dimer, given in figure 12, also displays two bands, but shifted toward higher energies. Again this spectrum with two bands is in contradiction with measurements, where single broad bands are always observed. Nevertheless this shift toward higher energies is interesting, because it has also been observed with the BH&HLYP functional.
Discussion The oxidation of various methionine containing peptides by OH. radicals has been studied since the 90’s. Up to now the transient absorption spectra of numerous peptides, proteins or methionine derivatives have been recorded in the UV and visible regions. In what follows we concentrate on the visible part of the spectra but other minor bands in the UV region were also detected. The absorption spectra of the free radicals resulting from oxidation of the dipeptide MetMet by OH. radicals have been reported at several pH values. 44 4 µs after the pulse, in very acidic medium (pH 1), the spectrum exhibits a huge band peaking at 490 nm. At the same delay, the spectrum is modified by increasing the pH: a very large band with a kind of plateau between ca. 400 and 500 nm is visible at pH 2.9. At pH 5.2, the band peaks at 400 nm. These spectra undergo modifications: 74µs after the pulse, the maximum is shifted to 390 nm at pH 2.9. Later, the oxidation of various isomers of cyclo-MetMet gave somewhat different results. 11,45,46 At pH 4.3, 2 µs after the pulse, for several isomers of cyclo Met-Met and for cyclo Gly-Met,
the spectrum is made of several bands at 380 - 500 nm. 15-20 µs after the pulse, the spectrum displays only a huge band peaking at 480-500 nm which smoothly decays. The discrepancy between the single band observed for the linear isomer and the complex spectra for the cyclic ones even at rather close pH values (4.3 vs. 5.2) and for species of close nature (Met-Met, cyclo Met-Met and cyclo Gly-Met) is obvious. These spectra have been interpreted with the help of recorded spectra of small model molecules.
Our simulations, using a model of the methionine residue in peptides and proteins, can be used for the interpretation of the numerous data concerning dipeptides, but we here concentrate on the spectra published in ref. 44. From our figure 10 the visible band of the SN cation has a λmax at 450 nm, but it can be seen that interaction with a neutral partner provokes a noticeable shift toward shorter wavelengths: 400 nm or even 380nm. This result enables an interpretation of the recorded spectra of ref. 44, figure 1: 1. the intriguing plateau observed at short time (figure 1c) between 400 and 500 nm can be due to the superposition of several species, at least monomers (absorbing at about 500 nm) and dimers (absorbing at about 400 nm). 2. the band observed at longer time, at 380 nm (figure 1d), can be due to dimers, or maybe higher oligomers since the wavelength is very short. This interpretation comes from our simulated spectra and must be consolidated by thermochemical considerations. We have evaluated the reaction free energies of the oxidation process and also of the dimerization, subsequent to the oxidation, because this process appears to be of utmost importance: 1. the oxidation by the OH. radical results in an energy deposit of ca 1.eV, this is suggested by the values of the reduction potentials. 6 Nevertheless this argument does not take into account the complexity of the oxidation mechanism, which might involve an addition - elimination process. 28 ACS Paragon Plus Environment
2. we have evaluated the standard free energy change of the association reaction:
M et.+ + M et → M et.+ 2
We first have evaluated this quantity in the gas phase, because this calculation often yields a good evaluation of the value in solution. 41 A DFT calculation, with the BH&HLYP functional and the aug-cc-pvdz basis set yields a negative reaction free energy in one case only: the formation of the trans ion - molecule dimer, with the value -0.14 eV (-14. kJ/mol). This value can be transformed to the standard value in solution with the two following changes: • the gas phase value includes the -PV (=-RT) term, which must be subtracted if the (uncompressible) condensed phase is considered. • the standard concentrations amount to 1/24.5 mol/L in the gas phase and 1. mol/L in the solution. This results in a -RT Log(24.5) term. The standard reaction free energy of reaction 6 in solution now reads:
∆r G0sol = ∆r G∗gas
+ RT − RT Log(24.5)
The free energy for reaction 6 in solution now amounts to -0.20 eV (-20 kJ/mol). This value shows that the association of the oxidised product with a neutral residue is plausible. These thermochemical data support our interpretation, proposed above on the basis of spectral data. Since it is likely that the initial solution contains dimers, because the peptides are only slightly soluble in water, it is also very likely that these dimers are broken by the oxidation process, which releases much energy. Then it is also plausible that after some time some association of neutral and cationic peptides occurs, provoking the shift of the spectrum toward higher energies. Note that this shift is frequently observed in pulse radiolysis. It is 29 ACS Paragon Plus Environment
important to note that this dimerization occurs not only via the formation of a SS+ bond, as it has been proposed (see ref. 47 and references herein) but also via the simpler ion molecule association. This is clearly visible in table 3, showing that three conformers, one of the SS type and two of the IM type, lie within less than 0.10 eV (10 kJ/mol). Note also that on figure 1d of ref. 44 the shift toward higher energies at long time is accompanied by a drop of the extinction coefficient. Since our simulations show that the monomer and the dimer have roughly the same extinction coefficients (see figure 10), with the value for the dimer even larger than the value for the monomer, we conclude that between 4. and 74. µs a loss of absorbing species occurs.
Conclusion We have performed molecular simulations of the radical cations of a model of the methionine residue of peptides and of its van der Waals dimer. This model has been obtained through the double methylation of the methionine aminoacid. We have used the classical Monte-Carlo sampling of the nuclear configurations, the DFT (BH&HLYP) calculation of the electronic structure and the SMD modeling of the solvent. The UV-visible absorption spectra have been deduced from the Monte-Carlo simulations. The radical cation of the monomer displays an intramolecular (2 center - 3 electron) SN bond, this is proved by the atomic densities on the S and N atoms, and by the shape of the singly occupied orbital. In the case of the monomer, the basis effect on the absorption spectrum has been investigated and found moderate, but real. The spectrum lies in the zone, currently accepted for this type of cation. The radical cation of the van der Waals dimer displays three quasidegenerate conformers, lying within less than 0.1 eV (10 kJ/mol) at the BH&HLYP/aug-cc-pvdz DFT level. The most stable conformer is of the ion- molecule type, with one neutral partner and one cationic one, with an intramolecular SN bond. Another conformer is slightly less stable and displays
an intermolecular (2 center - 3 electron) SS bond. The third conformer is again of the ionmolecule type, with different orientations of the chains. Such a quasidegeneracy implies that the relative stabilities of the ion-molecule and SS conformers cannot be acertained, and all the more that it cannot be predicted for other methionine residues. These conformers have different absorption spectra. The spectrum of the ion-molecule dimer is analogous to that of the SN monomer, but shifted toward shorter wavelengths. The spectrum of the SS conformer lies in the zone of that of model compounds with SS bonds. A comparison with the DMS.+ 2 cation shows that it is actually more complex and shifted toward larger wavelengths. The evidence of conformers of two types is an important point because it is currently stated in the radiolysis literature that the dimerization only occurs via SS bond formation. The present results actually enable a new discussion of the literature, different from the previous ones. In particular we emphasize that the time evolution of some spectra of the literature, with a shift toward shorter wavelegths, can be due to the presence of neutral dimers before the oxidation process, and to the association of one cationic and one neutral species, after the oxidation process. This dimer, observed a long time after the pulse, can be of either the SS or the ion-molecule type.
Acknowledgements All the simulations have been done on the computation platform of the Laboratoire de Chimie Physique. We thank Jean-Marie Teuler for everyday technical assistance.
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