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Charge transfer dynamics of carbon ions with uracil and halouracil targets at low collision energies
Chemical Physics Letters 503 (2011) 45–48
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Charge transfer dynamics of carbon ions with uracil and halouracil targets at low collision energies Marie-Christine Bacchus-Montabonel ⇑, Yvette Suzanne Tergiman Laboratoire de Spectrométrie Ionique et Moléculaire, Université de Lyon I et CNRS-UMR5579, 43, Bd. Du 11 Novembre 1918, 69622 Villeurbanne Cedex, France
a r t i c l e
i n f o
Article history: Received 15 December 2010 In final form 5 January 2011 Available online 7 January 2011
a b s t r a c t A theoretical treatment is derived at low-energies for the single charge transfer process in collision of C4+ ions with uracil and halouracil targets using ab-initio molecular methods. The radiosensitivity properties of halouracils and the anisotropy of the process are analyzed and compared to previous calculations at keV energies. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Interaction of ionizing radiation with biological tissues may induce lesions in DNA, as single- and double-strand breaks or base damage [1]. However, for high-energy photons or electrons, most of the damage is not due to the primary radiation itself, but to the secondary particles generated along the track after interaction of the ionizing radiation with the biological medium [2]. It has been shown in particular that low-energy secondary electrons could induce severe damage to DNA via dissociative attachment [3–5]. In addition, ionizing radiations can also produce ballistic low-energy ions and neutral radical fragments. Most of the experimental studies, up to now, have been focused on DNA degradation induced by secondary electrons and free radicals, however secondary ions may drive also physico-chemical reactions with the biological medium and the understanding of such processes is of main interest. In that sense, experimental and theoretical studies at the molecular level have been developed recently on ion–biomolecule interactions, essentially in the 1–500 keV energy range [6–13]. At lower energies, fragmentation of condensed thymine by low-energy (10–200 eV) Ar+ ions has been investigated [14]. However, such studies remain isolated and interaction of secondary ions with the biological medium at low collision energies is almost unexplored. In previous work, we have developed a theoretical treatment for the collision of carbon ions with uracil and halouracil targets in the [3–100] keV energy range [11–13]. In such collisions between an ion and a biomolecular target, different processes may be considered: excitation and fragmentation of the molecule, ionization of the gaseous target, and also possible charge transfer from the multicharged ion towards the biomolecule. From the experimental point of view, excitation and fragmentation cross ⇑ Corresponding author. Fax: +33 472431507. E-mail address: [email protected] (M.-C. Bacchus-Montabonel). 0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.01.013
sections are determined from mass spectra. But charge transfer has been shown to be a complementary process [11] and may be investigated theoretically in the framework of the molecular representation of the collisions [11,15,16]. The single charge transfer process between carbon ions and uracil or halouracil targets has thus been developed using ab-initio molecular calculations for the potential energies and corresponding coupling matrix elements followed by a semiclassical dynamics. Such reactions have been shown to be highly anisotropic [12], with electron delocalization from the target to the colliding ion [11]. For halouracil targets, we have in particular analyzed the anisotropy of the process with regard to the radiosensitization properties of halouracils [13]. The work is now extended to lower collision energies for which no data are available, in order to explore the evolution of the cross sections with regard of the collision energy. An interesting point is, first of all, to have an order of magnitude of the corresponding cross sections to evaluate the efficiency of the single charge transfer process in this energy range. Besides, it is particularly important to check if some new behaviour may be pointed out at low energies by comparison with the mechanism exhibited in the keV energy range.
2. Molecular treatment The study has been performed on the C4+ projectile carbon ion with the different uracil, 5-fluorouracil, 5-chlorouracil and 5-bromouracil targets as such ion has been shown to induce more efficient charge transfer than other carbon ions [11,12]. The collision is treated in the framework of the one-dimensional reaction coordinate approximation [11]. The evolution of the C4+ biomolecule system is thus driven by the reaction coordinate R corresponding to the distance between the centre-of-mass of the target molecule and the colliding carbon ion as presented in Figure 1a. Such an approach does not, of course, take into
46
M.-C. Bacchus-Montabonel, Y.S. Tergiman / Chemical Physics Letters 503 (2011) 45–48
g KL ðRÞ ¼ hwK j@=@RjwL i ¼ lim D 0
Figure 1. (a) Internal coordinates for the C4+ + biomolecule system. (b) Geometry of the uracil (X = H) and 5-halouracil molecules (5-fluorouracil, X = F; 5-chlorouracil, X = Cl; 5-bromouracil, X = Br).
account the internal motions of the biomolecule but has been widely used [17] and may be reasonable for fast collision processes where nuclear vibration and rotation periods are assumed to be much longer than the collision time. The different molecular states of the collision system are calculated for different approaches h from the perpendicular (h = 90°) to a planar or near-planar geometry in order to take into account the anisotropy of the process. The molecular calculations have been carried out by means of the MOLPRO suite of ab-initio programs [18]. An all-electron calculation has been performed, assuming no symmetries and using Cartesian coordinates with origin of coordinates at the centre-ofmass of the biomolecule. The potentials have been determined for a large number of R distances in the 0.5–9 Å range for a number of specific values of the angle h = [90°, 70°, 45°, 20°, 0° for uracil]; the angle u has been kept fixed at u = 60° which corresponds to an opposite direction to the X atom, hydrogen or halogen atom. The geometry of the ground state of uracil and halouracil molecules has been optimized by means of the DFT (Density Functional Theory) method with B3LYP functional using the 6-311G⁄⁄ basis sets. As shown in Table 1, this leads to vertical ionization potentials in good agreement with experimental [19] and previous theoretical results [20,21] using more extended basis sets and assumes the validity of the basis sets used in this study. The biomolecular targets have been kept frozen in the optimized geometry during the collision process. The molecular orbitals were optimized in state-averaged CASSCF (Complete Active Space Self Consistent Field) calculations using the same basis sets. Dynamical correlation effects are not taken into account at this level of theory, but we can expect a correct description of the relative energies of the different excited states. The active space includes the six highest valence orbitals constructed mainly on the 2pz, 3pz, 4pz orbitals centred respectively on fluorine, chlorine and bromine, the 2p orbitals centred on the oxygen atoms, the 2pz(C5) and 2pz(C6) orbitals (pC5C6, as shown in Figure 1b), and the 2px, 2py and 2pz orbitals of the colliding carbon ion. The 1s orbitals are treated as frozen core as well as the s and p doubly occupied orbitals on the halogen atoms. The charge transfer process is driven mainly by non-adiabatic interactions in the vicinity of avoided crossings [22]. The radial coupling matrix elements have thus been calculated by means of the finite difference technique:
1 hw ðRÞjwL ðR þ DÞi; D K
with the parameter D = 0.0012 a.u. previously tested [23] and using the three-point numerical differentiation method for reasons of numerical accuracy. The centre-of-mass of the biomolecule has been chosen as origin of electronic coordinates. An example of the potential energy curves is presented in Figure 2 for the C4+ on 5-chlorouracil collision for an orientation h = 45°. The main feature is an avoided crossing around 4–5 Å between the 41A entry channel and the excited 51A, 61A, 71A charge transfer levels. It corresponds to a double excitation of both electrons of the 2pO orbital on 5-chloroouracil (the 2pO orbital is a linear combination of the 2pz orbitals on atoms O2 and O4 with a contribution of the pz orbitals on chlorine) to the 2p components of the colliding carbon, and to the pC5C6 orbital constructed on 2pz(C5) and 2pz(C6) orbitals of 5-chlorouracil. Such interaction is the driving step in the charge transfer process. The interaction is relatively smooth and widespread on a wide distance range for this orientation h = 45°, it is much stronger and localized, and moves towards longer internuclear distances for a perpendicular geometry as previously pointed out [13]. Of course, the potential energy
Figure 2. Adiabatic potential energy curves for the C4+ + 5-chlorouracil collision. 1 . . .. . .., 1A state corresponding to the configuration {2pO 2pz}; 2 - - - -, 1A state corresponding to the configuration {2pO 2py}; 3 _____, 1A state corresponding to the configuration {2pO 2px}; 4 _____, 1A state corresponding to the configuration {(2pO)2}; 5 . . .. . .., 1A state corresponding to the configuration {pC5C6 2pz}; 6 - - - -, 1A state corresponding to the configuration {pC5C6 2py}; 7 _____, 1A state corresponding to the configuration {pC5C6 2px}.
Table 1 Vertical ionization potentials for the uracil and 5-halouracil molecules (in eV). Species
Our calculation
Wetmore et al. [20]
Crespo-Hernandez et al. [21]
Experiment [19]
Uracil 5-Fluorouracil 5-Chlorouracil 5-Bromouracil
9.56 9.55 9.35 9.12
9.47 9.46 9.21 9.07
9.43
9.50 Figure 3. Charge transfer cross sections averaged over the different orientations for the C4+ + uracil and halouracil targets (in 1016 cm2). _____, C4+ + uracil; - - - -, C4+ + 5-fluorouracil;. -. - ., C4+ + 5-chlorouracil; . . .. . .., C4+ + 5-bromouracil.
M.-C. Bacchus-Montabonel, Y.S. Tergiman / Chemical Physics Letters 503 (2011) 45–48
curves, position and intensity of the avoided crossings, depend on the collision system and of the orientation angle, however the same dominant interaction may be observed for the collision with uracil [11] and other halouracil molecules [13]. With regard to the orientation of the collision system, generally speaking, the interaction appears at lower internuclear distances when the approach angle h decreases and moves from the perpendicular geometry (h = 90°) to a geometry closer to the planar one. It is strong around the perpendicular geometry, and becomes smoother and more widespread, as seen on Figure 2, when the approach angle reaches h = 45° to near-planar geometries.
Table 2 Charge transfer cross sections averaged over the different orientations for the C4+ + uracil and halouracil collision systems (in 1016 cm2). v (a.u.)
Elab (eV)
Uracil
5-Fluorouracil
5-Chlorouracil
5-Bromouracil
0.01 0.015 0.02 0.03 0.04 0.05 0.07 0.1
30 67.5 120 270 480 750 1470 3000
5.732 6.141 6.449 7.744 7.631 6.671 6.282 5.788
0.015 0.015 0.020 0.029 0.025 0.028 0.032 0.031
0.085 0.070 0.072 0.056 0.045 0.051 0.052 0.047
0.006 0.007 0.009 0.008 0.009 0.011 0.012 0.013
47
3. Collision dynamics The collision dynamics has been performed in the framework of the sudden approximation hypothesis assuming electronic transitions to occur so fast that vibration and rotation motions could be considered as frozen during the collision. The total and partial cross sections are thus determined by solving the impact-parameter equation considering the geometry of the system frozen during the collision process. Such an approach has been widely used in the keV energy range in the framework of semi-classical methods using the EIKONXS code [24] and has proved its efficiency for energies greater than 10 eV/amu [25,26]. The approach has been extended in the present work to lower collision energies, down to 30 eV–3 keV, where the straight-line approximation may be questionable. However, in very recent calculations, we have shown that semiclassical methods could give quite reasonable cross sections up to ECM = 10–20 eV, the discrepancy with quantal calculations appearing for lower energies [27]. We can thus expect such semiclassical approach to give a correct order of magnitude of the charge transfer cross sections, and in particular allow a reliable comparison of the series of uracil and halouracil targets. The collision dynamics has been performed for the different orientations taking into account all the transitions driven by radial coupling matrix elements with origin of electronic coordinates at the centre-of-mass of the biomolecule. In the energy range we are
Figure 4. Charge transfer cross sections with regard to the orientation angle h (in 1016 cm2). (a) C4+ + uracil; (b) C4+ + 5-fluorouracil; (c) C4+ + 5-chlorouracil; (d) C4+ + 5bromouracil. _____, Elab = 3 keV; -. - ., Elab = 750 eV; - - - -, Elab = 120 eV; . . .. . .., Elab = 30 eV.
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interested in, rotational interaction can be neglected with good accuracy [28,29]. The charge transfer cross sections for the collision of C4+ ions on uracil and halouracil targets, averaged over the different orientations, are presented in Figure 3 and Table 2 for impact energies in the 30 eV–3 keV range. As far as absolute values are concerned, the cross sections are almost two orders of magnitude higher for C4+–uracil than for the halouracil targets, and up to three orders of magnitude higher for bromouracil. As charge transfer and fragmentation have been shown to be complementary processes [11], such behaviour induces a strong enhancement of the fragmentation process with halouracil targets, in quite agreement with the radiosensitivity properties of halouracils [30,31]. In particular, bromouracil appears to be a strong radiosensitizer, this is the case at keV energies, as previously pointed out [13], but even at low eV impact energies as shown by the present work. The mechanism of the charge transfer process may be detailed by looking at the dependence of the cross sections with regard to the orientation of the target towards the projectile ion. The results are presented in Figure 4. As already pointed out at keV collision energies, the charge transfer process is significantly favoured in an orientation close to the perpendicular geometry for the uracil and 5-fluorouracil targets. The cross sections appear maximum around h = 70° for the series of selected collision energies. For these targets, the X atom, hydrogen or fluorine, is light with a small atomic radius and may not induce significant steric effect. On the contrary, for 5-chlorouracil or 5-bromouracil targets, steric effects have to be considered, as already pointed out at keV energies. In that case, new features may be observed at low collision energies. For the 5-chlorouracil, the charge transfer process is favoured for an orientation angle h = 45°, opposite to the X = Cl heavy atom, for collision energies higher than 750 eV as previously observed at keV energies [13]. This anisotropy is certainly driven by steric effects; anyway at very low collision energies one observes that the charge transfer process is favoured at still lower h orientation angle, corresponding to near-planar geometries. Furthermore, the charge transfer with 5-bromouracil appears also to be clearly anisotropic, which was not so evident at keV energies [13], markedly favoured for an orientation angle around h = 40°. At low collision, the steric effect appears thus to be a driving parameter in the charge transfer process mechanism, even more efficient than at higher keV energies. The different targets may be separated into two groups, uracil and 5-fluorouracil on a one hand for which steric effect is negligible and charge transfer favoured close to the perpendicular direction, and, on the other hand, 5-chlorouracil and 5-bromouracil targets for which the steric effect is dominant and the charge transfer more efficient in a direction opposite to the heavy atom. 4. Conclusions This work provides to our knowledge the first theoretical data on ion–biomolecule collisions at low energies. In collisions of C4+ ions with uracil and halouracil, the charge transfer appears to be significantly less efficient for the halouracil targets than for uracil. The fragmentation process is thus markedly enhanced, in good agreement with the radiosensitivity properties of halouracils. The process is highly anisotropic, driven by steric effects. It is clearly favoured in the near-perpendicular orientation for light X atoms,
H or F, and more likely in the opposite orientation for more heavy targets as 5-chloro and 5-bromouracil. Up to now, very few data are available for ballistic ion–biomolecule interactions at a molecular level and the development of such studies, in particular at low energies, would be determinant. Acknowledgements We acknowledge support from the HPC resources of CCRT/ CINES/IDRIS under the allocation 2010-[i2010081566] made by GENCI [Grand Equipement National de Calcul Intensif] as well as from the COST action CM0702 CUSPFEL. References [1] C. von Sonntag, The Chemical Basis for Radiation Biology, Taylor & Francis, London, UK, 1987. [2] B.D. Michael, P.D. O’Neill, Science 287 (2000) 1603. [3] B. Boudaïffa, P. Cloutier, D. Hunting, M.A. Huels, L. Sanche, Science 287 (2000) 1658. [4] H. Abdoul-Carime, M.A. Huels, E. Illenberger, L. Sanche, J. Am. Chem. Soc. 123 (2001) 5354. [5] L. Sanche, Mass Spectrom. Rev. 21 (2002) 349. [6] J. de Vries, R. Hoekstra, R. Morgenstern, T. Schlathölter, J. Phys. B 35 (2002) 4373. [7] T. Schlatölter et al., ChemPhysChem 7 (2006) 2339. [8] J. de Vries, R. Hoekstra, R. Morgenstern, T. Schlathölter, Phys. Rev. Lett. 91 (2003) 053401. [9] R. Cabrera-Trujillo, E. Deumens, Y. Ohrn, O. Quinet, J.R. Sabin, N. Stolterfoht, Phys. Rev. A 75 (2007) 052702. [10] P. Sobocinski et al., J. Phys. B 39 (2006) 927. [11] M.-C. Bacchus-Montabonel, M. Łabuda, Y.S. Tergiman, J.E. Sienkiewicz, Phys. Rev. A 72 (2005) 052706. [12] M.-C. Bacchus-Montabonel, Y.S. Tergiman, Phys. Rev. A 74 (2006) 054702. [13] M.C. Bacchus-Montabonel, Y.S. Tergiman, D. Talbi, Phys. Rev. A 79 (2009) 012710. [14] Z. Deng, M. Imhoff, M.A. Huels, J. Chem. Phys. 123 (2005) 144509. [15] E. Bene, Á. Vibók, G.J. Halász, M.C. Bacchus-Montabonel, Chem. Phys. Lett. 455 (2008) 159. [16] E. Rozsályi, E. Bene, G.J. Halász, Á. Vibók, M.C. Bacchus-Montabonel, Phys. Rev. A 81 (2010) 062711. [17] L. Salem, Electrons in Chemical Reactions: First Principles, Wiley Interscience, New York, 1982. [18] MOLPRO (version 2009.1) is a package of ab initio programs written by H.-J. Werner, P.J. Knowles, F.R. Manby, M. Schütz, P. Celani, G. Knizia, T. Korona, R. Lindh, A. Mitrushenkov, G. Rauhut, T.B. Adler, R.D. Amos, A. Bernhardsson, A. Berning, D.L. Cooper, M.J.O. Deegan, A.J. Dobbyn, F. Eckert, E. Goll, C. Hampel, A. Hesselmann, G. Hetzer, T. Hrenar, G. Jansen, C. Köppl, Y. Liu, A.W. Lloyd, R.A. Mata, A.J. May, S.J. McNicholas, W. Meyer, M. E. Mura, A. Nicklaß, P. Palmieri, K. Pflüger, R. Pitzer, M. Reiher, T. Shiozaki, H. Stoll, A.J. Stone, R. Tarroni, T. Thorsteinsson, M. Wang, A. Wolf. [19] V.M. Orlov, A.N. Smirnov, Y.M. Varshavsky, Tetrahedron Lett. 48 (1976) 4377. [20] S.D. Wetmore, R.J. Boyd, L.A. Eriksson, Chem. Phys. Lett. 343 (2001) 151. [21] C.E. Crespo-Hernandez, R. Arce, Y. Ishikawa, L. Gorb, J. Leszczynski, D.M. Close, J. Phys. Chem. A 108 (2004) 6373. [22] N. Vaeck, M.C. Bacchus-Montabonel, E. Baloïtcha, M. Desouter-Lecomte, Phys. Rev. A 63 (2001) 042704. [23] M.C. Bacchus-Montabonel, C. Courbin, R. McCarroll, J. Phys. B 24 (1991) 4409. [24] R.J. Allan, C. Courbin, P. Salas, P. Wahnon, J. Phys. B 23 (1990) L461. [25] P.C. Stancil, B. Zygelman, K. Kirby, Photonic, electronic, and atomic collisions, in: F. Aumayr, H.P. Winter (Eds.), World Scientific, Singapore, 1998. [26] V. Sidis, Adv. At. Mol. Opt. Phys. 26 (1990) 161. [27] A. Chenel, E. Mangaud, Y. Justum, D. Talbi, M.C. Bacchus-Montabonel, M. Desouter-Lecomte, J. Phys. B 43 (2010) 245701. [28] E. Bene, P. Martínez, G.J. Halász, Á. Vibók, M.C. Bacchus-Montabonel, Phys. Rev. A 80 (2009) 012711. [29] M.C. Bacchus-Montabonel, Phys. Rev. A 59 (1999) 3569. [30] S. Zamenhof, R. DeGiovanni, S. Greer, Nature (London) 181 (1959) 827. [31] T.S. Lawrence, M.A. Davis, J. Maybaum, P.L. Stetson, W.D. Ensminger, Radiat. Res. 123 (1990) 192.
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Charge transfer dynamics of carbon ions with uracil and halouracil targets at low collision energies Marie-Christine Bacchus-Montabonel ⇑, Yvette Suzanne Tergiman Laboratoire de Spectrométrie Ionique et Moléculaire, Université de Lyon I et CNRS-UMR5579, 43, Bd. Du 11 Novembre 1918, 69622 Villeurbanne Cedex, France
a r t i c l e
i n f o
Article history: Received 15 December 2010 In final form 5 January 2011 Available online 7 January 2011
a b s t r a c t A theoretical treatment is derived at low-energies for the single charge transfer process in collision of C4+ ions with uracil and halouracil targets using ab-initio molecular methods. The radiosensitivity properties of halouracils and the anisotropy of the process are analyzed and compared to previous calculations at keV energies. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Interaction of ionizing radiation with biological tissues may induce lesions in DNA, as single- and double-strand breaks or base damage [1]. However, for high-energy photons or electrons, most of the damage is not due to the primary radiation itself, but to the secondary particles generated along the track after interaction of the ionizing radiation with the biological medium [2]. It has been shown in particular that low-energy secondary electrons could induce severe damage to DNA via dissociative attachment [3–5]. In addition, ionizing radiations can also produce ballistic low-energy ions and neutral radical fragments. Most of the experimental studies, up to now, have been focused on DNA degradation induced by secondary electrons and free radicals, however secondary ions may drive also physico-chemical reactions with the biological medium and the understanding of such processes is of main interest. In that sense, experimental and theoretical studies at the molecular level have been developed recently on ion–biomolecule interactions, essentially in the 1–500 keV energy range [6–13]. At lower energies, fragmentation of condensed thymine by low-energy (10–200 eV) Ar+ ions has been investigated [14]. However, such studies remain isolated and interaction of secondary ions with the biological medium at low collision energies is almost unexplored. In previous work, we have developed a theoretical treatment for the collision of carbon ions with uracil and halouracil targets in the [3–100] keV energy range [11–13]. In such collisions between an ion and a biomolecular target, different processes may be considered: excitation and fragmentation of the molecule, ionization of the gaseous target, and also possible charge transfer from the multicharged ion towards the biomolecule. From the experimental point of view, excitation and fragmentation cross ⇑ Corresponding author. Fax: +33 472431507. E-mail address: [email protected] (M.-C. Bacchus-Montabonel). 0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.01.013
sections are determined from mass spectra. But charge transfer has been shown to be a complementary process [11] and may be investigated theoretically in the framework of the molecular representation of the collisions [11,15,16]. The single charge transfer process between carbon ions and uracil or halouracil targets has thus been developed using ab-initio molecular calculations for the potential energies and corresponding coupling matrix elements followed by a semiclassical dynamics. Such reactions have been shown to be highly anisotropic [12], with electron delocalization from the target to the colliding ion [11]. For halouracil targets, we have in particular analyzed the anisotropy of the process with regard to the radiosensitization properties of halouracils [13]. The work is now extended to lower collision energies for which no data are available, in order to explore the evolution of the cross sections with regard of the collision energy. An interesting point is, first of all, to have an order of magnitude of the corresponding cross sections to evaluate the efficiency of the single charge transfer process in this energy range. Besides, it is particularly important to check if some new behaviour may be pointed out at low energies by comparison with the mechanism exhibited in the keV energy range.
2. Molecular treatment The study has been performed on the C4+ projectile carbon ion with the different uracil, 5-fluorouracil, 5-chlorouracil and 5-bromouracil targets as such ion has been shown to induce more efficient charge transfer than other carbon ions [11,12]. The collision is treated in the framework of the one-dimensional reaction coordinate approximation [11]. The evolution of the C4+ biomolecule system is thus driven by the reaction coordinate R corresponding to the distance between the centre-of-mass of the target molecule and the colliding carbon ion as presented in Figure 1a. Such an approach does not, of course, take into
46
M.-C. Bacchus-Montabonel, Y.S. Tergiman / Chemical Physics Letters 503 (2011) 45–48
g KL ðRÞ ¼ hwK j@=@RjwL i ¼ lim D 0
Figure 1. (a) Internal coordinates for the C4+ + biomolecule system. (b) Geometry of the uracil (X = H) and 5-halouracil molecules (5-fluorouracil, X = F; 5-chlorouracil, X = Cl; 5-bromouracil, X = Br).
account the internal motions of the biomolecule but has been widely used [17] and may be reasonable for fast collision processes where nuclear vibration and rotation periods are assumed to be much longer than the collision time. The different molecular states of the collision system are calculated for different approaches h from the perpendicular (h = 90°) to a planar or near-planar geometry in order to take into account the anisotropy of the process. The molecular calculations have been carried out by means of the MOLPRO suite of ab-initio programs [18]. An all-electron calculation has been performed, assuming no symmetries and using Cartesian coordinates with origin of coordinates at the centre-ofmass of the biomolecule. The potentials have been determined for a large number of R distances in the 0.5–9 Å range for a number of specific values of the angle h = [90°, 70°, 45°, 20°, 0° for uracil]; the angle u has been kept fixed at u = 60° which corresponds to an opposite direction to the X atom, hydrogen or halogen atom. The geometry of the ground state of uracil and halouracil molecules has been optimized by means of the DFT (Density Functional Theory) method with B3LYP functional using the 6-311G⁄⁄ basis sets. As shown in Table 1, this leads to vertical ionization potentials in good agreement with experimental [19] and previous theoretical results [20,21] using more extended basis sets and assumes the validity of the basis sets used in this study. The biomolecular targets have been kept frozen in the optimized geometry during the collision process. The molecular orbitals were optimized in state-averaged CASSCF (Complete Active Space Self Consistent Field) calculations using the same basis sets. Dynamical correlation effects are not taken into account at this level of theory, but we can expect a correct description of the relative energies of the different excited states. The active space includes the six highest valence orbitals constructed mainly on the 2pz, 3pz, 4pz orbitals centred respectively on fluorine, chlorine and bromine, the 2p orbitals centred on the oxygen atoms, the 2pz(C5) and 2pz(C6) orbitals (pC5C6, as shown in Figure 1b), and the 2px, 2py and 2pz orbitals of the colliding carbon ion. The 1s orbitals are treated as frozen core as well as the s and p doubly occupied orbitals on the halogen atoms. The charge transfer process is driven mainly by non-adiabatic interactions in the vicinity of avoided crossings [22]. The radial coupling matrix elements have thus been calculated by means of the finite difference technique:
1 hw ðRÞjwL ðR þ DÞi; D K
with the parameter D = 0.0012 a.u. previously tested [23] and using the three-point numerical differentiation method for reasons of numerical accuracy. The centre-of-mass of the biomolecule has been chosen as origin of electronic coordinates. An example of the potential energy curves is presented in Figure 2 for the C4+ on 5-chlorouracil collision for an orientation h = 45°. The main feature is an avoided crossing around 4–5 Å between the 41A entry channel and the excited 51A, 61A, 71A charge transfer levels. It corresponds to a double excitation of both electrons of the 2pO orbital on 5-chloroouracil (the 2pO orbital is a linear combination of the 2pz orbitals on atoms O2 and O4 with a contribution of the pz orbitals on chlorine) to the 2p components of the colliding carbon, and to the pC5C6 orbital constructed on 2pz(C5) and 2pz(C6) orbitals of 5-chlorouracil. Such interaction is the driving step in the charge transfer process. The interaction is relatively smooth and widespread on a wide distance range for this orientation h = 45°, it is much stronger and localized, and moves towards longer internuclear distances for a perpendicular geometry as previously pointed out [13]. Of course, the potential energy
Figure 2. Adiabatic potential energy curves for the C4+ + 5-chlorouracil collision. 1 . . .. . .., 1A state corresponding to the configuration {2pO 2pz}; 2 - - - -, 1A state corresponding to the configuration {2pO 2py}; 3 _____, 1A state corresponding to the configuration {2pO 2px}; 4 _____, 1A state corresponding to the configuration {(2pO)2}; 5 . . .. . .., 1A state corresponding to the configuration {pC5C6 2pz}; 6 - - - -, 1A state corresponding to the configuration {pC5C6 2py}; 7 _____, 1A state corresponding to the configuration {pC5C6 2px}.
Table 1 Vertical ionization potentials for the uracil and 5-halouracil molecules (in eV). Species
Our calculation
Wetmore et al. [20]
Crespo-Hernandez et al. [21]
Experiment [19]
Uracil 5-Fluorouracil 5-Chlorouracil 5-Bromouracil
9.56 9.55 9.35 9.12
9.47 9.46 9.21 9.07
9.43
9.50 Figure 3. Charge transfer cross sections averaged over the different orientations for the C4+ + uracil and halouracil targets (in 1016 cm2). _____, C4+ + uracil; - - - -, C4+ + 5-fluorouracil;. -. - ., C4+ + 5-chlorouracil; . . .. . .., C4+ + 5-bromouracil.
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curves, position and intensity of the avoided crossings, depend on the collision system and of the orientation angle, however the same dominant interaction may be observed for the collision with uracil [11] and other halouracil molecules [13]. With regard to the orientation of the collision system, generally speaking, the interaction appears at lower internuclear distances when the approach angle h decreases and moves from the perpendicular geometry (h = 90°) to a geometry closer to the planar one. It is strong around the perpendicular geometry, and becomes smoother and more widespread, as seen on Figure 2, when the approach angle reaches h = 45° to near-planar geometries.
Table 2 Charge transfer cross sections averaged over the different orientations for the C4+ + uracil and halouracil collision systems (in 1016 cm2). v (a.u.)
Elab (eV)
Uracil
5-Fluorouracil
5-Chlorouracil
5-Bromouracil
0.01 0.015 0.02 0.03 0.04 0.05 0.07 0.1
30 67.5 120 270 480 750 1470 3000
5.732 6.141 6.449 7.744 7.631 6.671 6.282 5.788
0.015 0.015 0.020 0.029 0.025 0.028 0.032 0.031
0.085 0.070 0.072 0.056 0.045 0.051 0.052 0.047
0.006 0.007 0.009 0.008 0.009 0.011 0.012 0.013
47
3. Collision dynamics The collision dynamics has been performed in the framework of the sudden approximation hypothesis assuming electronic transitions to occur so fast that vibration and rotation motions could be considered as frozen during the collision. The total and partial cross sections are thus determined by solving the impact-parameter equation considering the geometry of the system frozen during the collision process. Such an approach has been widely used in the keV energy range in the framework of semi-classical methods using the EIKONXS code [24] and has proved its efficiency for energies greater than 10 eV/amu [25,26]. The approach has been extended in the present work to lower collision energies, down to 30 eV–3 keV, where the straight-line approximation may be questionable. However, in very recent calculations, we have shown that semiclassical methods could give quite reasonable cross sections up to ECM = 10–20 eV, the discrepancy with quantal calculations appearing for lower energies [27]. We can thus expect such semiclassical approach to give a correct order of magnitude of the charge transfer cross sections, and in particular allow a reliable comparison of the series of uracil and halouracil targets. The collision dynamics has been performed for the different orientations taking into account all the transitions driven by radial coupling matrix elements with origin of electronic coordinates at the centre-of-mass of the biomolecule. In the energy range we are
Figure 4. Charge transfer cross sections with regard to the orientation angle h (in 1016 cm2). (a) C4+ + uracil; (b) C4+ + 5-fluorouracil; (c) C4+ + 5-chlorouracil; (d) C4+ + 5bromouracil. _____, Elab = 3 keV; -. - ., Elab = 750 eV; - - - -, Elab = 120 eV; . . .. . .., Elab = 30 eV.
48
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interested in, rotational interaction can be neglected with good accuracy [28,29]. The charge transfer cross sections for the collision of C4+ ions on uracil and halouracil targets, averaged over the different orientations, are presented in Figure 3 and Table 2 for impact energies in the 30 eV–3 keV range. As far as absolute values are concerned, the cross sections are almost two orders of magnitude higher for C4+–uracil than for the halouracil targets, and up to three orders of magnitude higher for bromouracil. As charge transfer and fragmentation have been shown to be complementary processes [11], such behaviour induces a strong enhancement of the fragmentation process with halouracil targets, in quite agreement with the radiosensitivity properties of halouracils [30,31]. In particular, bromouracil appears to be a strong radiosensitizer, this is the case at keV energies, as previously pointed out [13], but even at low eV impact energies as shown by the present work. The mechanism of the charge transfer process may be detailed by looking at the dependence of the cross sections with regard to the orientation of the target towards the projectile ion. The results are presented in Figure 4. As already pointed out at keV collision energies, the charge transfer process is significantly favoured in an orientation close to the perpendicular geometry for the uracil and 5-fluorouracil targets. The cross sections appear maximum around h = 70° for the series of selected collision energies. For these targets, the X atom, hydrogen or fluorine, is light with a small atomic radius and may not induce significant steric effect. On the contrary, for 5-chlorouracil or 5-bromouracil targets, steric effects have to be considered, as already pointed out at keV energies. In that case, new features may be observed at low collision energies. For the 5-chlorouracil, the charge transfer process is favoured for an orientation angle h = 45°, opposite to the X = Cl heavy atom, for collision energies higher than 750 eV as previously observed at keV energies [13]. This anisotropy is certainly driven by steric effects; anyway at very low collision energies one observes that the charge transfer process is favoured at still lower h orientation angle, corresponding to near-planar geometries. Furthermore, the charge transfer with 5-bromouracil appears also to be clearly anisotropic, which was not so evident at keV energies [13], markedly favoured for an orientation angle around h = 40°. At low collision, the steric effect appears thus to be a driving parameter in the charge transfer process mechanism, even more efficient than at higher keV energies. The different targets may be separated into two groups, uracil and 5-fluorouracil on a one hand for which steric effect is negligible and charge transfer favoured close to the perpendicular direction, and, on the other hand, 5-chlorouracil and 5-bromouracil targets for which the steric effect is dominant and the charge transfer more efficient in a direction opposite to the heavy atom. 4. Conclusions This work provides to our knowledge the first theoretical data on ion–biomolecule collisions at low energies. In collisions of C4+ ions with uracil and halouracil, the charge transfer appears to be significantly less efficient for the halouracil targets than for uracil. The fragmentation process is thus markedly enhanced, in good agreement with the radiosensitivity properties of halouracils. The process is highly anisotropic, driven by steric effects. It is clearly favoured in the near-perpendicular orientation for light X atoms,
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