Ground Electronic State of Peptide Cation Radicals: A Delocalized

LETTER pubs.acs.org/JPCL

Ground Electronic State of Peptide Cation Radicals: A Delocalized Unpaired Electron? Amy I. Gilson,† Guillaume van der Rest,† Julia Chamot-Rooke,† Westin Kurlancheek,‡ Martin Head-Gordon,‡ Denis Jacquemin,§ and Gilles Frison*,† †

Laboratoire des M
ecanismes R
eactionnels, D
epartement de Chimie, Ecole Polytechnique and CNRS, 91128 Palaiseau Cedex, France Department of Chemistry, University of California, Berkeley, California 94720, United States § Laboratoire CEISAM - UMR CNRS 6230, Universit
e de Nantes, 2 Rue de la Houssiniere, BP 92208, 44322 Nantes Cedex 3, France ‡

bS Supporting Information ABSTRACT:

Electron capture and electron transfer dissociations are bioanalytical methods for fragmenting cations after reduction by an electron. Previous computational studies based on conventional DFT schemes have concluded that the first step of these processes, the attachment of the electron, leads to extensive delocalization of the spin density in the intermediate radical cation. Here we show that most DFT methods produce unphysical results when studying single electron reduction of a dicationic peptide. This is not the case for post-HF methods and long-range corrected functionals that show satisfying electron affinities, intermolecular interaction energies, and spin density trends. Our results suggest that the charged group with the highest electron affinity on the precursor cation is also the site of spin density in the electronic ground state after electron attachment. These findings have important implications for the interpretation of experimental data from electron-based processes in biomolecules and may guide the development of new functionals. SECTION: Molecular Structure, Quantum Chemistry, General Theory

lectron capture dissociation (ECD)1,2 and electron transfer dissociation (ETD)3 are efficient fragmentation techniques, available on Fourier transform ion cyclotron resonance and ion trap or Q-TOF mass spectrometers, respectively. These methods have an important potential for the structural analysis of peptides or proteins.4
6 Electron capture by, or transfer to, cationic peptides or proteins in the gas phase characteristically results in cleavage of N
CR bonds, which makes these techniques complementary to collision-induced dissociation (CID) where peptidic bonds are cleaved. ECD and ETD also have some advantages compared with CID: they preserve labile post-translational modifications, and they allow fragmentation of larger peptides and even entire proteins without prior digestion, making these approaches particularly suitable for top-down proteomics. In ECD and ETD, a multiply charged cation is partially reduced by receiving one electron, thereby converting it from a closed-shell specie to an intermediate cation-radical that undergoes fragmentation. The exact mechanism(s) implicated in such a process are still a matter of active discussion from both computational and experimental points of view.7
12 Although there is consensus that the spin must become localized on a backbone carbonyl carbon to precipitate cleavage of an adjacent

E

r 2011 American Chemical Society

N
CR bond, the pathway the electron takes to reach the carbonyl remains unresolved. Does the electron attach itself directly to an amide π* orbital, which may be an excited state (the Utah
Washington mechanism),13,14 or are preliminary structural rearrangement(s) needed (the Cornell mechanism)?1 Recent theoretical studies indicate that the vertical reduction of protonated peptides lead to a highly delocalized spin density in the ground state. Delocalization could extend to spatially remote charged groups (ammonium,15,16 guanidinium,17 histidinium,18 amide and/or carbonyl π* orbitals,18 and/or tag groups19,20); therefore, the incoming electron could not be strictly assigned to a specific chemical group in the reduced ion. Density functional theory (DFT) methods are important tools in computational studies of ECD/ETD fragmentation because of their advantageous accuracy/cost balance, which allows the thorough study of relatively large systems such as pentapeptides.18 However DFT methods have a number of shortcomings including self-interaction error (SIE), which refers to the coulomb Received: April 8, 2011 Accepted: May 19, 2011 Published: May 25, 2011 1426

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Figure 1. Studied molecular structures. Color code: blue, nitrogen; gray, carbon; red, oxygen; white, hydrogen.

Figure 2. Calculated cation
electron vertical recombination energies relative to CCSD(T) values. The basis set used is 6-311þþG(2d,p) in all cases except when indicated.

repulsion and exchange interaction of an electron with itself. In Hartree
Fock theory, the energies due to an electron’s selfrepulsion and self-exchange cancel exactly by construction. This balance does not exist in “conventional” DFT functionals such as B3LYP. SIE thus leads to difficulties in describing cases such as transition-state energies and two-center three-electron systems.21,22 Most relevantly, it also induces an overly disperse spin density when adding or removing an electron from closedshell systems.23 These shortcomings are well-documented, and some theoretical studies on ECD/ETD have used more reliable but more expensive post-Hartree
Fock methods.7,12,24 However most studies have relied on DFT calculations. The effect of these errors and thus the suitability of different methods has not, to the best of our knowledge, yet been assessed. In this Letter, we evaluate the ability of a variety of computational methods to describe accurately the energetics of singleelectron reduction of ammonium groups and models of

protonated peptides as well as to describe the spin density in the resulting electronic ground state. DFT methods, including a local spin density approximation (LSDA) functional, generalized gradient approximation (GGA) functionals, meta-GGA, global hybrid (GH) functionals, as well as range-separated hybrids (RSHs) have been tested. In RSH, the amount of exact exchange included increases with interelectronic distance, therefore limiting the long-range Coulomb SIE.25
27 We have also tested double-hybrid functionals that include second-order perturbation theory correlation.28 Several post-HF methods have also been tested which, of course, do not suffer from SIE but may over localize spin density. (See the Supporting Information for a full description of the methodology.) Methylammonium (1), protonated glycine N-methyl amide (2), and a complex of the two (3d) that models interacting groups in a peptide/protein (Figure 1) are used as simple chemical models of cationic peptides, allowing extended basis 1427

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Figure 3. Interaction energy in 3d•þ relative to fully separated 1• and 2þ fragments.

sets CCSD(T) to be used as benchmarks for energetics. For models 3d (d = 5, 7, 10, 15, or 20 Å), the distance between the two nitrogen atoms is fixed at a value d. These models are used to study the interaction energy (IE) and spin density distribution between the two partners. We also use the dipeptide [GlyHis þ 2H]2þ (4),15 in which the N
N distance between the ammonium moieties is 9.910 Å, as a more realistic model. For cations 1þ, 2þ, 3d2þ (d = 5, 10, and 20 Å), and 42þ, we have computed the vertical ion-electron recombination energies, and the results are collated in Figure 2 and Table S2 in the Supporting Information. Most methods give rather good agreements with CCSD(T)/ 6-311þþG(2d,p) in predicting the vertical recombination energy (VRE) of cations 1þ and 2þ with a free electron (Figure 2). Furthermore, all methods correctly predict that 1þ has a higher electron affinity than 2þ (62 ( 5 kJ/mol greater) and also that the VRE of 3d2þ decreases as the distance d increases (Table S2 in the Supporting Information). However, for pure functionals, the discrepancy with the reference method may be large for dications and clearly tends to increase with d. This confirms that LSDA (SVWN5) and GGA (BLYP and PBEPBE) functionals as well as HF are inadequate in the present case. In contrast, RSH and post-HF methods nicely match the reference method, notably LC-BLYP, MP2, and MP4(SDQ), and to a lesser extent, LC-ωPBE and ωB97X-D. GH functionals give mixed performances at large d, and functionals including more exact exchange, for example, BH&HLYP, M06-2X, and BMK, clearly outperform the standard hybrids like B3LYP. To get more insight into the performance of these methods, we evaluate the IE between the two ammonium groups in 3d2þ

and also in its reduced counterpart 3d•þ. The IE between methylammonium (1) and protonated glycine N-methyl amide (2) in 3d2þ is described to within 2 kJ/mol of the reference method by all levels of calculation, regardless of d, and it decreases from þ220 kJ/mol to þ122 kJ/mol to þ65 kJ/mol at d = 5, 10, and 20 Å, respectively (Table S3 in the Supporting Information). This almost perfect adequacy is lost when studying the IE in 3d•þ (Figure 3 and Table S4 in the Supporting Information). At short distance, the electron could be shared by both ammonium groups, but at large distances it should be localized on the methylammonium, owing to its larger electron affinity. The IE in 3d•þ relative to fully separated 1• and 2þ fragments should thus tend to zero as the separation between the two groups approaches infinity. This convergence to zero is only obtained for methods including 100% HF exchange, at least at long interelectronic distances. This includes the RSHs LC-BLYP, LC-ωPBE, ωB97, ωB97X, and ωB97X-D, as well as HF, post-HF methods, and the M06-HF functional. Unlike the other RSHs, CAM-B3LYP performs less adequately in this case because it includes a smaller portion of exact HF exchange (65%) at long-range. These trends clearly parallel the ones obtained for the charge-transfer excitation energy of ethylenetetrafluoroethylene dimer over long intermolecular distance,29,30 even though it is the ground electronic state studied here. All other methods have a limited range of validity after which they yield unphysical results. Most striking are the cases where the IE begins to decline with increasing distance as with BLYP and TPSS. With such functionals, the lone electron is distributed across both groups 1 and 2 of 3d•þ to decrease the Coulomb repulsion of the electron with itself (Figure 4 and Table S5 in the Supporting Information). The general effect of including HF 1428

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Figure 4. Extent of spin delocalization is reflected by the spin density on partner 2 in 3d•þ and by the spin density on all atoms of the dipeptide except the lysine side chain in 4•þ.

exchange can be seen by comparing these results (no exact exchange) with the B3LYP results (20% of exact exchange), with the BH&HLYP or M06-2X results (50 and 54%, respectively), and finally with the post-HF methods and RSH, which include 100% of exact exchange at long distance (e.g., LC-BLYP or ωB97X-D). This comparison of methods shows that the more severe the SIE error is (i.e., the smaller the amount of exact exchange), the less reliably the IE and spin density (vide infra) can be calculated. It should, however, be noticed that addressing only the longrange Coulomb SIE solves this delocalization problem. SIE still present in the local exchange31 and correlation functionals does not lead to spurious results here (Figure 3). Indeed, the nature of the correlation functional (LYP vs P86 or PW91) does not influence our results. Calculations including only Becke’s exchange functional (B and LC-B) give similar results with those performed with BLYP and LC-BLYP, respectively, confirming that IE is not influenced by the correlation functional. Furthermore, the use of HFLYP, a modified functional in which local and nonlocal exchanges included in BLYP have been substituted by HF-exchange, leads to similar results than LC-BLYP, showing that the remaining SIE due to the exchange functional in RSHs or M06-HF does not play any role in our results. The same qualitative behavior of IE that is observed for fragments 1• and 2þ is observed for the reduction of a dimer built from two ammoniums 1 (Figure S1 in the Supporting Information). The fact that many methods break down after 7 Å indicates that they are not well-suited to model the reduction of any but the most compact multiply charged peptides. The analysis of the spin density in 3d•þ (Figure 4 and Table S5 in the Supporting Information) indicates that for HF, postHF methods, and M06-HF and RSH methods (excluding

CAM-B3LYP), the electron is no longer delocalized over both ammonium groups once the distance between them exceeds 7 Å. It is striking that the spin density is delocalized for all other methods whatever the value of d in the 5
20 Å range. In 42þ, the distance between the two nitrogen atoms is 9.9 Å. Consequently, the capture of an electron is not well-reproduced by classical DFT approaches. Previous conclusions on the electronic structure of 4•þ based on B3LYP calculations15 must thus be reevaluated with more appropriate methods. As shown in Figures 4 and 5, the previously described electron delocalization over the remote charged groups of the dipeptide is no longer retrieved when using long-range corrected functionals and postHF methods. It has been proposed that the electron attachment step could initially populate higher electronic states.9 Therefore, excited states and the kinetics of electron transfer between orbitals should be considered to understand fully the dynamics of the electron capture event. Preliminary TDDFT calculations indicate that (i) RSH methods predict fewer low-lying excited states than B3LYP, (ii) the first excited state has the spin density localized on the charged site not populated in the ground state and is ∼0.55 eV (∼0.65 eV) above the ground state for 310•þ (4•þ, respectively), and (iii) higher states (>1 eV) show electron density delocalization over various sites, including amide and/or carboxyl π* orbitals. Further work is needed to have a complete view on these points. These results are very important for the understanding of ECD/ETD mechanisms keeping in mind that the first step is electron attachment and that the fragmentations patterns observed in mass spectra are intrinsically linked to the radical cation’s structure and energetics. We show for the cases under study here that the question of where the electron goes in the 1429

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Figure 5. SOMO (0.025 au isovalue surface) of 4•þ at the (A) B3LYP/6-311þþG(2d,p) and (B) LC-BLYP/6-311þþG(2d,p) levels.

electronic ground state of the reduced radical cation can be estimated by assigning the unpaired electron to the group with the largest electronic affinity in the precursor cation. This is in contrast with the spin delocalization over several charge sites that was previously proposed in the literature. Our results highlight the shortcomings of conventional DFT methods to describe properly radical protonated peptides and suggest that rangeseparated functionals drastically improve the description of these peptides. These results represent a major breakthrough in the understanding of the ECD/ETD mechanisms and should be carefully considered for future theoretical studies on radical biological systems in general.32
34

’ COMPUTATIONAL METHODS VREs and IEs have all been calculated with Gaussian09.35 We used the 6-311þþG(2d,p) basis set throughout the study in combination with a large panel of DFT functional, HF, and post-HF methods (Table S1 in the Supporting Information). Calculations on all open-shell species used the spin-unrestricted formalism, and the resulting spin operator ÆS2æ values are between 0.750 and 0.755. Atomic spin density was calculated using the natural population analysis method.36 More details can be found in the Supporting Information. ’ ASSOCIATED CONTENT

bS

Supporting Information. Complete authors list for refs 18 and 35. Description of the computational methods used, VRE and IE values for model peptide cations, and spin density of their reduced form. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Tel: þ33 (0)1 69 33 48 34. Fax: þ33 (0)1 69 33 48 03.

’ ACKNOWLEDGMENT This work was performed using HPC resources from GENCICINES (grant 2011-c2011085107). D.J. is indebted to the R
egion des Pays de la Loire for financial support in the framework of a recrutement sur poste strat
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