Theoretical study of charge transfer dynamics in collisions of C6+ carbon ions with pyrimidine nucleobases

Eur. Phys. J. D (2012) 66: 175 DOI: 10.1140/epjd/e2012-30022-8

Theoretical study of charge transfer dynamics in collisions of C6+

carbon ions with pyrimidine nucleobases

M.C. Bacchus-Montabonel

Eur. Phys. J. D (2012) 66: 175DOI: 10.1140/epjd/e2012-30022-8

Regular Article

THE EUROPEANPHYSICAL JOURNAL D

Theoretical study of charge transfer dynamics in collisions of C6+

carbon ions with pyrimidine nucleobases

M.C. Bacchus-Montabonela

Laboratoire de Spectrometrie Ionique et Moleculaire, Universite de Lyon (Lyon I), CNRS-UMR5579,43 Bd. du 11 novembre 1918, 69622 Villeurbanne Cedex, France

Received 10 January 2012 / Received in final form 30 March 2012Published online 10 July 2012 – c© EDP Sciences, Societa Italiana di Fisica, Springer-Verlag 2012

Abstract. A theoretical approach of the charge transfer dynamics induced by collision of C6+ ions withbiological targets has been performed in a wide collision energy range by means of ab-initio quantumchemistry molecular methods. The process has been investigated for the target series thymine, uracil and5-halouracil corresponding to similar molecules with different substituent on carbon C5. Such a study maybe related to hadrontherapy treatments by C6+carbon ions and may provide, in particular, informationon the radio-sensitivity of the different bases with regard to ion-induced radiation damage. The resultshave been compared to a previous analysis concerning the collision of C4+ carbon ions with the samebiomolecular targets and significant charge effects have been pointed out.

1 Introduction

Severe damage to DNA may be caused by the action ofionizing radiations with biological tissues [1]. Direct dam-age may be driven by the radiation itself, but it has beenshown that important damage may also be induced bythe secondary particles, low-energy electrons or ions, gen-erated along the track after interaction of the ionizing ra-diation with the biological medium [2]. In order to explorethe mechanism underlying radiation-induced DNA dam-age at the molecular level, numerous studies focused onthe behaviour of the DNA building blocks under irradia-tion with slow-electrons, photons or ions have thus beendeveloped. Low-energy electrons have been widely inves-tigated and have shown to drive single- and double-strandbreaks of plasmid DNA [3,4], even at very low kinetic ener-gies, down to 3 eV, via dissociative attachment [5,6]. Butimportant interest has also been focused on collisions ofions on biomolecular targets, in particular DNA buildingblocks. Recent experimental and theoretical investigationshave been performed at kinetic energies in the keV rangesince these energies are relevant for the heavy-ion-inducedbiological radiation damage in the region of the Braggpeak where the induced damage is maximum [7–14]. Thisis this selectivity that makes heavy-ion therapy such apromising technique in cancer treatments [15]. In partic-ular, hadrontherapy by C6+ carbon ions appears particu-larly efficient for the treatment of deeply seated tumours[16,17]. Specific physico-chemical interactions with the bi-ological medium could however occur at lower energies,and a few experimental and theoretical studies have beenperformed recently in the eV energy range [18–21].

a e-mail: [email protected]

Different processes may be induced in reactions of ionswith biomolecular targets: excitation and fragmentation ofthe target, direct ionization of the biomolecule, and alsopossible charge transfer from the multiply charged ion to-wards the molecular target. From the experimental pointof view, excitation and fragmentation processes have beenmainly investigated and fragmentation cross sections aredetermined from mass spectra [7]. But these experimentalmeasurements may not give any information on chargetransfer between the incident ion and the biomoleculartarget [10]. We propose thus in this paper to investigatethe charge transfer mechanism in collisions of C6+ ionson a series of DNA and RNA bases, thymine, uracil andhalouracil. Such ions used in hadrontherapy by carbonions may reach an effective charge state when crossingthe biological medium; anyway, they may provide poten-tial candidates for the collision process. The moleculartargets investigated present similar structures and differonly by the substituent on the carbon C5 (see Fig. 1b),CH3 for thymine, hydrogen or halogen atom for uracil and5-halouracil molecules. We can thus analyze the chargetransfer process with regard to the possible steric or elec-tronic effects induced by the substituent. The theoreticaltreatment is driven in the framework of the molecular rep-resentation of the collisions [22,23] with ab-initio molecu-lar calculations of the potential energies and non-adiabaticcoupling matrix elements. The collision dynamics has beenperformed in a wide energy domain, from keV to eV ener-gies, in order to investigate the region of the Bragg peakas well as possible specific behaviour at low energies, aspointed out for low-energy secondary electrons [6].

These results may be compared to a previous studyon collisions of C4+ ions on the same biomolecular

Page 2 of 7 Eur. Phys. J. D (2012) 66: 175

(a) (b)

Fig. 1. (Color online) (a) Internal coordinates for the C6+ + biomolecule system; (b) geometry of the biomolecule: thymine,X = CH3; uracil, X = H; 5-fluorouracil, X = F; 5-chlorouracil, X = Cl, 5-bromouracil, X = Br.

targets [24]. The collision with the C4+ projectile ion forthis series of biomolecules has shown a complete differ-ent order of magnitude for the charge transfer cross sec-tions for thymine or uracil compared to halouracil tar-gets. The charge transfer cross sections are effectivelylower by at least a factor 100 for halouracil targets com-pared to uracil or thymine. This may drive an enhance-ment of the fragmentation process for halouracil targets, inagreement with the radiosensitization properties of thesebiomolecules [25,26]. The charge transfer process has be-sides been shown to be highly anisotropic, and steric ef-fects have been pointed out for the heavy halouracil tar-gets, 5-chlorouracil and 5-bromouracil [14,20]. An analysisof these features with the C6+ projectile ion, would drivemore realistic results on the mechanism involved in theseion-induced collisions, in particular it may provide an or-der of magnitude of the different cross sections and charac-terize numerically the efficiency of the different processes.

2 Molecular calculations

In the molecular description of the collisions, the chargetransfer process is described as the evolution of a quasi-molecular system formed by the projectile ion and themolecular target. For complex targets, a simple modelmay be proposed in the framework of the one-dimensionreaction coordinate approximation used in a number ofcases [27,28]. The ion-biomolecule system may thus beconsidered as a pseudo-diatomic molecule which evolu-tion is driven by the reaction coordinate corresponding tothe distance between the centre-of-mass of the biomoleculeand the colliding carbon ion. Of course such an approachdoes not consider the internal motions of the biomoleculebut it appears reasonable for very fast collision processeswhere nuclear vibration and rotation periods are assumedto be much longer than the collision time.

The geometry of the collision system is presented inFigures 1a and 1b. The different molecular states involved

in the process are calculated along the reaction coordinateR for different approaches θ in order to take into accountthe anisotropy of the process. The potentials have beendetermined for a large number of R distances, every 0.1 Ain the interacting region from 0.5 A to 9 A, for a numberof specific values of the angle θ. The potentials have thenbeen extrapolated to reach the asymptotic region. Thecalculation has been performed every θ = 10◦, from theperpendicular (θ = 90◦) to the planar geometry (θ = 0◦)providing a regular orientation description. The angle ϕhas been kept fixed at ϕ = 60◦ which corresponds to a di-rection opposite to the X substituent and thus minimizesthe steric hindrance in the collision process. The geome-try of the ground state of the different targets have beenoptimized and kept frozen during the collision process.

The molecular calculations have been carried out us-ing the MOLPRO suite of ab-initio programs [29]. Spin-orbit coupling being negligible in the energy range of in-terest, the electron spin can be assumed to be conservedduring the collision process and only singlet states havebeen considered. An all-electron calculation has been per-formed with no symmetries and using Cartesian coordi-nates with origin of coordinates at the centre-of-mass ofthe biomolecule. The potential energies and non-adiabaticcoupling matrix elements (NACME) have been deter-mined by state-averaged CASSCF (complete active spaceself consistent field) calculations. Although, dynamicalcorrelation effects are not taken into account at this levelof theory, we can expect a correct description of the rel-ative energies of the different excited states. Effectively,some calculations at a higher MRCI (Multireference Con-figuration Interaction) level of theory have been performedin the long distance range and around the main avoidedcrossing in the case of the C6+ + uracil collision system.At the MRCI level of theory, the potentials are lowered byabout 0.02 a.u. for all the molecular states involved in theprocess. This moves by less than 0.1 A the position of theavoided crossings towards shorter internuclear distances

Eur. Phys. J. D (2012) 66: 175 Page 3 of 7

Fig. 2. (Color online) Adiabatic potential energy curves for the C6+ + biomolecule collision systems in the perpendicularorientation. Labels are given by increasing energy; 1 (blue), 1A state {2pO 2pz}; 2 (magenta dotted line), 1A state {2pO 2py};3 (green dotted line), 1A state {2pO 2px}; 4 (black dotted line), 1A state {(2pO)2}; 5 (blue), 1A state {πC5C6 2pz}; 6 (green),1A state {πC5C6 2py}; 7 (red), 1A state {πC5C6 2px}.

and does not change the relative position of the differentmolecular states. A similar lowering is observed for theother targets assessing a coherent comparison for the se-ries of biomolecules. Seven molecular states have been de-termined by means of state-averaged CASSCF(2,6) cal-culations. Similar active spaces have been considered forthe different targets in order to compare each system atthe same level of accuracy including the 2px, 2py and 2pz

orbitals of the colliding carbon ion, the HOMO (highestoccupied molecular orbital) mainly constructed on the 2pz

orbitals centred on both oxygen atoms and the 2pz(C5)

and 2pz(C6) orbitals describing the molecular orbital calledby extension π(C5C6) (see Fig. 1b). This excited orbitalπ(C5C6) is delocalized also on the 2pz orbital on CH3 forthymine, and on the 2pz, 3pz, 4pz orbitals centered, re-spectively, on fluorine, chlorine, and bromine for halouracilmolecules. The 1s orbitals of carbon, nitrogen and oxygenare treated as frozen core. The valence electrons have beendescribed using the 6-311G** basis set of atomic orbitals.

The charge transfer process being driven mainly bynon-adiabatic interactions in the vicinity of avoided cross-ings [30], the non-adiabatic radial coupling matrix ele-ments between all pairs of states have been calculatednumerically by means of the finite difference technique:

gKL(R) = 〈ψK |∂/∂R|〉=

⟨ψK(R)

∣∣∣∣ limΔ→0

1Δ

∣∣∣∣ψL(R+Δ) − ψL(R)⟩,

which, taking account of the orthogonality of the eigen-functions |ψK(R)〉 and |ψL(R)〉 for K �= L reduces to

gKL(R) = 〈ψK |∂/∂R|ψL〉= limΔ→0

1Δ

〈ψK(R) |ψL(R +Δ)〉 .(1)

The stability with regard to the differentiation step Δ hasbeen tested and the value of Δ = 0.0012 a.u. has beenchosen [31] using the three-point numerical differentiationmethod for reasons of numerical accuracy. The centre ofmass of the thymine molecule has been chosen as originof electronic coordinates.

The potential energy curves for the different C6+ –biomolecule collision systems are presented in Figure 2for the perpendicular geometry. Strong non-adiabatic in-teractions may be observed between the different molecu-lar states, in particular between the entry channel corre-sponding to the {(2pO)2} configuration (the 2pO orbitalis mainly described by a linear combination on the 2pz

orbitals on both oxygen atoms) and the charge transferlevels towards the 2px, 2py, 2pz orbitals of the projectilecarbon ion. A direct charge transfer may be observed withan excitation of a 2pO orbital of the biomolecular target toa 2px, 2py, 2pz orbital of the colliding carbon ion, leadingto 1, 2, 3 1A1 states corresponding to a complex formedby the C5+(2p) ion and the ionized biomolecule. The pro-cess involves also the excited 5, 6, 7 1A1 charge transferlevels which correspond to a double excitation process,


with simultaneously an electron exchange from the 2pO

orbital to the 2p components of the colliding carbon, to-gether with an excitation to the πC5C6 orbital constructedmainly on the 2pz(C5) and 2pz(C6) orbitals of the ring,with contributions of the 2pz orbital on CH3 for thymine,and the 2pz, 3pz, 4pz orbitals centred, respectively, onfluorine, chlorine, and bromine for halouracil molecules.Such transfer excitation process has also been observedin collisions of C4+ ions with the same biomolecular tar-gets [10,14,21], and even in ion-atom collisions [32]. Theposition and shape of the non-adiabatic interaction de-pends of course on the collision system.

3 Collision treatment

The collision dynamics has been developed using a semi-classical method in the framework of the sudden approx-imation hypothesis assuming that the electronic transi-tions occur so fast that vibration and rotation motionsremain unchanged. The total and partial cross sections,corresponding to purely electronic transitions, may thenbe determined by solving the impact-parameter equationwith a frozen geometry for the molecular target. Sucha treatment is, of course, relatively crude, but it hasproved its efficiency in a number of ion-diatomic or poly-atomic collisions for energies higher than ∼10 eV/amu[10,21,33]. Taking account of our recent analysis of time-dependent quantal wave packet and semiclassical ap-proaches in charge transfer processes [34], the method hasbeen extended recently to lower collision energies, downto the eV range [20,35].

In the semiclassical approach, the nuclei are consideredto follow a classical trajectory R(t) = b + vt with regardto the impact parameter b and the velocity v. The time-dependent Schrodinger equation reduces thus to:

(Hel [r,R(t)] − i

∂

∂t

)Ψ(r, b, v, t) = 0, (2)

where Hel is the electronic Born-OppenheimerHamiltonian and r stands for the electronic coordi-nates. It may be solved for each velocity v and impactparameter b by expanding the total wave function on theeigenfunctions ψadia

mΛ of Hel with eigenvalues εmΛ wherem is the number of electronic states ψadia

mΛ and Λ is thequantum number for the projection on the molecular axisof the total electronic orbital angular momentum L:

Ψ(r, b, v, t) =∑mΛ

amΛ(b, v, t)ψadiamΛ [r,R(t)]

× exp

⎛⎝−i

t∫0

εmΛ [R(t′)] dt′

⎞⎠ .

By integration of equation (2), the probabilities are givenby P (b, v) =

∑mΛ

|amΛ (b, v,∞)|2 with summation over all

Fig. 3. (Color online) Variation of the charge transfer cross-sections averaged over the different orientations with regardto the collision energy, for the C6+ + biomolecule systems(full lines) and for the corresponding C4+ + biomolecule sys-tems (broken lines) (in 10−16 cm2). ___ thymine; ___,uracil; ___, 5-fluorouracil;

___, 5-chlorouracil;___, 5-

bromouracil.

charge exchange channels. The cross section is then de-fined by:

σ(v) =14π

∫P (b, v)db. (3)

The collision dynamics has been performed using theEIKONXS program based on an efficient propagationmethod [36]. The calculation has been carried out in the[7.5 eV–48keV] laboratory energy range for the 7 statesinvolved in the process, taking into account all the transi-tions driven by radial coupling matrix elements with ori-gin of electronic coordinates at the centre-of-mass of themolecular target. The coupled equations have been solvedwith a step size such that an accuracy of 10−4 for thesymmetry of the S matrix is achieved. Such a calcula-tion does not take into account the charge transfer frominner valence states, but involves the excited charge trans-fer levels 5, 6, 7 1A1 as described in previous paragraphs.The charge transfer cross sections averaged over the dif-ferent orientations are presented in Table 1 and Figure 3.They are compared to the corresponding data for the C4+

collision with thymine, uracil and halouracil targets.As previously stated with the C4+ projectile ion, the

cross sections with the C6+ projectile are of the same orderof magnitude for uracil and thymine targets. The processis clearly favoured with thymine, with values up to 6.6 ×10−16 cm2, although they never exceed 1.8×10−16 cm2 forthe uracil target. The process is mainly driven by the suc-cession of avoided crossings between the entry channel41 A state corresponding to the {(2pO)2} configuration


Table 1. Charge transfer cross sections averaged over the different orientations for a series of C6+-biomlecule collision systems(in 10−16 cm2). Comparison with corresponding data for C4+-biomlecule collision systems.

Elab v C4++ C6++ C4++ C6++ C4++ C6++ C4++ C6++ C4++ C6++(eV) (a.u.) thymine thymine uracil uracil fluoro- fluoro- chloro- chloro- bromo- bromo-

[21] [21,24] uracil uracil uracil uracil uracil uracil[21,24] [21,24] [21,24]

7.5 0.005 6.05 1.32 2.45 0.050 0.002 4.9 × 10−5

14.7 0.007 6.60 1.92 5.55 2.01 0.024 0.075 0.092 0.004 0.003 9.8 × 10−5

30 0.01 9.10 1.84 5.73 1.90 0.015 0.099 0.085 0.006 0.006 1.5 × 10−4

67.5 0.015 9.02 3.35 6.14 1.93 0.015 0.117 0.070 0.008 0.007 2.1 × 10−4

120 0.02 8.68 4.38 6.45 2.01 0.020 0.124 0.072 0.011 0.009 2.2 × 10−4

270 0.03 9.01 5.22 7.74 1.70 0.029 0.098 0.056 0.023 0.008 2.8 × 10−4

480 0.04 10.66 6.05 7.63 1.67 0.025 0.075 0.045 0.028 0.009 4.0 × 10−4

750 0.05 11.62 6.53 6.67 1.51 0.028 0.058 0.051 0.036 0.011 3.8 × 10−4

1.47 × 103 0.07 13.53 6.66 6.28 1.48 0.032 0.042 0.052 0.098 0.012 4.9 × 10−4

3.0 × 103 0.1 14.93 6.28 5.79 1.85 0.031 0.028 0.047 0.121 0.013 6.0 × 10−4

12.0 × 103 0.2 13.24 4.32 5.04 1.08 0.024 0.018 0.038 0.067 0.007 4.0 × 10−4

27.0 × 103 0.3 12.12 3.03 3.97 0.56 0.018 0.011 0.025 0.038 0.004 2.2 × 10−4

48.0 × 103 0.4 10.16 2.05 3.56 0.33 0.013 0.007 0.017 0.024 0.003 1.4 × 10−4

75.0 × 103 0.5 11.89 1.43 3.28 0.22 0.010 0.005 0.012 0.016 0.002 9.1 × 10−5

108.0 × 103 0.6 11.33 1.05 2.85 0.16 0.007 0.003 0.009 0.011 0.002 6.5 × 10−5

147.0 × 103 0.7 10.88 0.79 2.42 0.12 0.006 0.002 0.006 0.008 0.001 4.8 × 10−5

and the excited exit channels 5, 6, 7 1A states. A significantinteraction is also observed in the case of the thymine tar-get with the 1, 2, 3 1A states corresponding to a directcharge transfer {2pO 2pC}, which may lead to a more effi-cient charge transfer than observed with the uracil target.As observed for processes driven by radial couplings, thecross sections present a maximum, which is in the presentcase very smooth as several non-adiabatic interactionsare involved. As expected with regard to the radiosen-sibility of halouracil molecules [14,20], the charge trans-fer process is significantly less efficient with 5-fluoro and5-chlorouracil targets, with a factor about 10−2 comparedto uracil or thymine. The effect is particularly significantfor the 5-chlorouracil target at low collision energy whichpresents very low charge transfer cross sections around0.005×10−16 cm2 in the eV range. On the contrary, chargetransfer cross sections appear higher at keV energies withthe 5-chlorouracil target than with the 5-fluorouracil one.The significant increase of the charge transfer cross sec-tions up to Elab = 3 keV observed for the 5-chlorouraciltarget is worth to be noticed, as the variation with col-lision energy of the corresponding cross sections for theother biomolecular targets appear rather smooth. It maybe associated to the direct charge transfer, already pointedout for the thymine target. Effectively, in the case of the5-chloro and 5-bromouracil targets, the process is morelikely driven by the non-adiabatic interactions betweenthe entry channel and the direct charge transfer {2pO

2pC} levels, inducing an increase of the charge transfercross sections at higher collision energies than the interac-tion involving the excited 5, 6, 7 1A states. Conversely, for5-fluorouracil, such interactions with excited charge trans-fer states are more important and the maximum of chargetransfer cross sections appears at lower collision energies.

In all cases, the charge transfer cross sections decrease asusual at higher energies, above 10 keV. The most impor-tant feature is however the extremely low values obtainedfor the charge transfer cross sections in the collision ofC6+ ions with the 5-bromouracil molecule. The values areof the order of 10−4 × 10−16 cm2, with a maximum of4.9×10−4×10−16 cm2, so about 10−4 lower than the val-ues calculated with the thymine target. Such result maybe discussed with regard to a previous analysis on theCq++ uracil collision system involving theoretical deter-mination of charge transfer cross sections [10] and exper-imental fragmentation yield [7]. In such ion-biomoleculecollisions, excitation, ionization, fragmentation and chargetransfer are clearly strongly related processes and dependon a great number of factors, velocity, projectile charge,target state, but a qualitative correlation may be pointedout between fragmentation and charge transfer. For ex-ample, at low collision energy, the C2+ + uracil systemappears experimentally to drive almost complete fragmen-tation, in relation with a very low charge transfer crosssection and the fragmentation yield decreases with in-creasing collision energy, when the charge transfer crosssection increases [7,10]. Conversely, for the same reactionswith the C4+ projectile ion, the experimental fragmenta-tion yield is lower, almost independent of the collision en-ergy, and the calculated charge transfer cross sections aresignificantly higher than in the collision with the C2+ pro-jectile, and similarly almost independent of the collisionenergy. These observations remain of course completelyqualitative and have to be handled with care, anyway theywould suggest that the fragmentation process would beexpected to be significantly more efficient in collisions ofC6+ ions with 5-bromouracil, compared for example, withthe similar reaction with thymine. This result agrees with


medical observations, as the replacement of thymine by5-bromouracil in cellular DNA has been shown to inducea strong enhancement of DNA damage through ionizingradiations [25]. The effect, already noticed with C4+, issignificantly stronger, by at least a factor 10, with theC6+ projectile used in ion cancer therapy, corroboratingthe radio-sensitization properties of 5-bromouracil. Moregenerally, the charge transfer cross sections appear to belower with the C6+ projectile than with C4+ for the seriesthymine, uracil and 5-bromouracil targets. By extensionof the analysis developed on the uracil target, fragmen-tation may thus be expected qualitatively to be more ef-ficient with this projectile chosen in medical treatments.On another hand, the charge transfer cross sections with5-fluoro and 5-chlorouracil targets are almost of the sameorder of magnitude with C4+ and C6+projectiles. Theydepend significantly of the collision energy, as pointedout previously, which could be correlated to a compet-ing mechanism involving interactions between direct orexcited charge transfer levels. The present treatment be-ing restricted to only a few molecular states and molecularorientations, further calculations would be expected.

4 Concluding remarks

The charge transfer in the collision of C6+ carbon ionswith thymine, uracil and halouracil targets has been in-vestigated in a wide collision energy range using ab-initiomolecular calculations. Some qualitative tendency may beexhibited from a compared analysis of these charge trans-fer calculations with previous theoretical and experimen-tal results which could be useful in the interpretation ofsuch collision processes. For example, an enhancement ofthe fragmentation process with the 5-bromouracil target,compared with the same reaction with thymine or uracil,could be expected. The effect appears higher with thepresent C6+ projectile ion than with the C4+ projectilesuggesting a special interest in the use of such carbon ionin experiments. More generally, the present results pro-vide a qualitative order of magnitude of the charge trans-fer cross sections for the series of targets investigated, to-gether with both C6+ and C4+ projectile ions, which mayestablish a hierarchy between the different ion-target col-lision systems.

We acknowledge support from the HPC resources ofCCRT/CINES/IDRIS under the allocation 2011-[i2011081566]made by GENCI [Grand Equipement National de Calcul In-tensif] as well as from the COST actions MP1002 Nano-IBCT.

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Theoretical study of charge transfer dynamics in collisions of C6+ carbon ions with pyrimidine nucleobases