Quantum-mechanical predictions of DNA and RNA ionization by energetic proton beams

Quantum-mechanical predictions of DNA and RNA ionization by energetic proton beams

This article has been downloaded from IOPscience. Please scroll down to see the full text article.

2012 Phys. Med. Biol. 57 2081

(http://iopscience.iop.org/0031-9155/57/7/2081)

Download details:

IP Address: 195.220.226.21

The article was downloaded on 21/03/2012 at 09:40

Please note that terms and conditions apply.

View the table of contents for this issue, or go to the journal homepage for more

Home Search Collections Journals About Contact us My IOPscience

IOP PUBLISHING PHYSICS IN MEDICINE AND BIOLOGY

Phys. Med. Biol. 57 (2012) 2081–2099 doi:10.1088/0031-9155/57/7/2081

Quantum-mechanical predictions of DNA and RNAionization by energetic proton beams

M E Galassi1, C Champion2,4, P F Weck3, R D Rivarola1, O Fojon1

and J Hanssen2

1 Instituto de Fısica Rosario, CONICET and Universidad Nacional de Rosario,Avenida Pellegrini 250, 2000 Rosario, Argentina2 Laboratoire de Physique Moleculaire et des Collisions, ICPMB (FR CNRS 2843),Institut de Physique, Universite de Lorraine, 1 rue Arago, 57078 Metz Cedex 3, France3 Department of Chemistry and Harry Reid Center for Environmental Studies,University of Nevada Las Vegas, 4505 Maryland Parkway, Las Vegas, NV 89154, USA

E-mail: champion@univ-metz.fr

Received 22 September 2011, in final form 30 January 2012Published 21 March 2012Online at stacks.iop.org/PMB/57/2081

AbstractAmong the numerous constituents of eukaryotic cells, the DNA macromoleculeis considered as the most important critical target for radiation-induceddamages. However, up to now ion-induced collisions on DNA componentsremain scarcely approached and theoretical support is still lacking fordescribing the main ionizing processes. In this context, we here report atheoretical description of the proton-induced ionization of the DNA andRNA bases as well as the sugar–phosphate backbone. Two different quantum-mechanical models are proposed: the first one based on a continuum distortedwave–eikonal initial state treatment and the second perturbative one developedwithin the first Born approximation with correct boundary conditions (CB1).Besides, the molecular structure information of the biological targets studiedhere was determined by ab initio calculations with the Gaussian 09 softwareat the restricted Hartree–Fock level of theory with geometry optimization.Doubly, singly differential and total ionization cross sections also providedby the two models were compared for a large range of incident and ejectionenergies and a very good agreement was observed for all the configurationsinvestigated. Finally, in comparison with the rare experiment, we have noted alarge underestimation of the total ionization cross sections of uracil impactedby 80 keV protons, whereas a very good agreement was shown with the recentlyreported ionization cross sections for protons on adenine, at both the differentialand the total scale.

(Some figures may appear in colour only in the online journal)

4 Author to whom any correspondence should be addressed.

0031-9155/12/072081+19$33.00 © 2012 Institute of Physics and Engineering in Medicine Printed in the UK & the USA 2081

2082 M E Galassi et al

Introduction

The double-stranded deoxyribonucleic acid (DNA) has just four nucleobases, namely adenine,cytosine, thymine and guanine, which provide the code for cellular information. A fifthnucleobase, uracil, is also found in the single-stranded ribonucleic acid (RNA) that replacesthymine during DNA transcription due to its efficient base pairing with adenine through theformation of hydrogen bonds. Conversely, uracil possesses the ability to turn into thyminethrough methylation in order to protect the DNA and improve DNA replication. Therefore,RNA plays a fundamental role in protein synthesis.

Irradiation of biological matter by ion and electron beams produces secondary speciesalong the radiation track which can further react within irradiated cells to provoke criticalRNA/DNA lesions such as base damages, single- or double-strand breaks and then induceradiation effects such as arrest of cell division, chromosomal aberrations, mutation and celldeath. Indeed, DNA lesions and more particularly those involved in clustered damages arenowadays considered of prime importance for describing the post-irradiation cellular survival.Under these conditions, improved theoretical models as well as experimental data on ion-induced collisions at the DNA level remain crucial still today, especially to go beyond thesimple approximation which consists in describing the biological matter by water as usuallydone in the existing track–structure numerical simulations.

On the experimental side, ionization and fragmentation of isolated DNA and RNAconstituents are well-documented subjects. In this context, let us mention the work of Coupieret al (2002) on nucleosides impacted by 25–100 keV protons, that of Moretto-Capelle and LePadellec (2006) dealing with the determination of doubly and singly ionization differentialcross sections (DDCS and SDCS, respectively) for impact of 20, 50 and 100 keV protonson dry gas-phase uracil and the investigations provided by Alvarado et al (2007) on chargedand neutral species of slow light ions interacting with DNA building blocks. More recently,Tabet et al (2010a, 2010b, 2010c) have reported total cross sections (TCS) for the ionizationof uracil and DNA bases impacted by protons. Finally, let us mention the extensive studiesrecently reported by Iriki et al (2011a, 2011b), where a large set of absolute DDCS and SDCSis provided for 500 keV, 1 MeV and 2 MeV protons impacting adenine.

On the theoretical side, a classical model combining a classical trajectory Monte Carlo(CTMC) approach with a classical over-barrier (COB) criterion was recently employedto analyze single and multiple ionizing processes induced by an impact of fast H+,He2+ and C6+ ions on RNA uracil and DNA bases in terms of TCS (Abbas et al 2008,Lekadir et al 2009). Simultaneously, two quantum-mechanical approaches, both developedwithin the first-order Born approximation with correct boundary conditions (CB1)5, wererecently proposed: the first one provided by Dal Cappello et al (2008) dedicated tocomputations of doubly, singly differential and total ionization cross sections for protonsimpacting on cytosine and the second more recent one proposed by Champion et al (2010),where ionization induced by light ions (H+, He2+ and C6+) on the four DNA bases wasinvestigated. At this stage, let us mention that besides the ionization modeling which isradically different within the classical and the quantum approaches, the description of theimpacted biological targets also hugely differs between both theories. Indeed, in the classicalapproach (Abbas et al 2008, Lekadir et al 2009), it is simply reduced to the knowledgeof the ionization energies of the different molecular subshells of the targets, whereas acomplete description of the molecular wavefunctions—in terms of linear combinations ofatomic orbitals (LCAO)—is usually needed in the quantum approaches. In this context, the

5 The reader is referred to the works developed by Tachino (2011) and Champion et al (2012) for a detailedformulation.

Quantum-mechanical predictions of DNA and RNA ionization by energetic proton beams 2083

two above-cited works differ from one another since a LCAO-SCF (self-consistent field)method was used by Dal Cappello et al (2008) while Champion et al (2010) employeda simplified LCAO approach, similar to that reported by Bernhardt and Paretzke (2003),describing the impacted biological targets by their five highest occupied molecular orbitals(HOMOs).

In this work, doubly, singly differential and TCS are computed within the continuumdistorted wave–eikonal initial state (CDW-EIS) model (Crothers and McCann 1983, Fainsteinet al 1988a) for protons impacting on DNA/RNA components. The biological targets aredescribed by a LCAO representation expanded on a large set of molecular orbitals, which arehere calculated from first principles. CB1 calculations employing this extended orbital basis aswell as available classical predictions are also reported for comparison. Finally, comparisonswith existing experimental measurements are reported in terms of differential and total crosssections.

Atomic units will be used hereafter except where otherwise stated.

Theory

As in our previous works, an independent active electron approximation is employed here(see for example Fainstein et al (1988b) and Galassi et al (2004)). Under these conditions, thepassive target electrons (those non-ionized) are considered as frozen in their initial orbitalsduring the collision process, which is generally assumed to overcome the difficulty of takinginto account the dynamical correlation between active and passive electrons in particular forlarge molecules like those investigated here6. Thus, within this approximation, the interactionbetween the projectile and the passive electrons only affects the trajectory of the incidentparticle. Consequently, its contribution to the ionization reaction itself is neglected, whichis independent of the quantum approximation used for describing the ion-induced ionizationprocess of atoms and molecules, all the more that we here only consider calculations of crosssections integrated over the projectile scattering angle (Stolterfoht et al 1997). Then, we focuson the following in the theoretical description of the dynamics of the active (ejected) electron.

In the CDW-EIS model, the initial and final distorted wavefunctions are chosen as

χ+α = exp(iKα · R)

(2π)3/2ϕα(x) exp

[−i

ZP

vln(vs + v · s)

](1)

and

χ−β = exp(iKβ · R)

(2π)3/2ϕβ(x)N∗(Z∗

T /k)1F1(−iZ∗T /k; 1;−i kx − ik · x)

×N∗(ZP/p)1F1(−iZP/p; 1;−ipx − ip · x), (2)

where the vectors x and s give the positions of the active electron with respect to the center ofmass of the residual target and to the projectile, respectively, whereas R denotes the positionof the projectile with respect to the center of mass of the target. Furthermore, εα denotes theactive electron orbital energy, v the collision velocity, k the momentum of the ejected electronseen from the target, p = k − v the momentum of this electron with respect to the projectileand Kα and Kβ the momenta of the reduced particle of the complete system in the entry andexit channels, respectively, ZP being the projectile charge and Z∗

T an effective target charge. Inequation (2), N(a) = exp(πa/2)�(1 − ia) and N∗(a) indicates the conjugate of N(a).

The function ϕα(x) describes the bound electron wavefunction and the multiplicativeprojectile eikonal phase in equation (1) (depending on the electronic coordinate s of the

6 Nevertheless, let us add that for more information about the influence of electron correlation on ionization of atomictargets, we refer the reader to the detailed analysis recently given by Monti et al (2009).

2084 M E Galassi et al

Figure 1. Ball-and-stick representation of the equilibrium geometries of DNA/RNA componentscomputed at the RHF/3-21G level of theory.

active electron) indicates that the active electron moves simultaneously in a bound state ofthe target and implicitly in a projectile eikonal continuum one. The eikonal form of theprojectile–active electron continuum is chosen to preserve the normalization of the initialdistorted wavefunction (Fainstein et al 1988b). In the exit channel, ϕβ(x) is a plane wavethat when multiplied by the effective Coulomb continuum factor (see equation (2)) gives thecontinuum of the ionized electron in the field of the residual target, while the inclusion of amultiplicative projectile continuum factor indicates that the electron is moving in a continuumstate of the residual target and projectile combined fields, both considered on equal footing(Fainstein et al 1991). Thus, initial and final distorted wavefunctions in CDW-EIS are chosenas two-center ones in the sense that the active electron is considered to feel the simultaneouspresence of the projectile and residual target potentials in the entry and exit channels at alldistances between aggregates. It avoids the presence of disconnected diagrams associatedwith the separated consideration of these potentials, which could induce to the presence of

Quantum-mechanical predictions of DNA and RNA ionization by energetic proton beams 2085

Table 1. Population and binding energies of the adenine molecular orbitals.

Molecular Ionizationorbital energies (eV) Population (effective number of electrons ξ )

1 8.44 0.98 N(2p) + 1.02 C(2p)2 9.98 1.18 N(2p) + 0.8 C(2p)3 10.55 0.10 N(2s) + 1.54 N(2p) + 0.30 C(2p)4 11.39 1.64 N(2p) + 0.36 C(2p)5 11.71 0.22 N(2s) + 1.36 N(2p) + 0.24 C(2p) + 0.08 H(1s) + 0.02 C(2s)6 12.88 0.38 N(2s) + 1.22 N(2p) + 0.18 C(2p) + 0.08 H(1s) + 0.06 C(2s)7 13.5 1.24 N(2p) + 0.78 C(2p)8 15.23 1.22 N(2p) + 0.76 C(2p)9 16.34 0.66 N(2p) + 0.92 C(2p) + 0.36 H(1s)

10 16.85 0.62 N(2p) + 0.98 C(2p) + 0.34 H(1s) + 0.02 N(2s)11 17.29 0.04 N(2s) + 0.82 N(2p) + 0.84 C(2p) + 0.26 H(1s) + 0.02 C(2s)12 17.5 0.88 N(2p) + 1.10 C(2p)13 18.42 1.06 N(2p) + 0.74 C(2p) + 0.10 H(1s) + 0.02 C(2s)14 18.99 0.12 C(2s) + 0.74 N(2p) + 0.56 C(2p) + 0.48 H(1s) + 0.02 N(2s)15 20.1 1.02 N(2p) + 0.52 C(2p) + 0.30 H(1s) + 0.12 C(2s)16 21.32 0.02 N(2s) + 1.00 N(2p) + 0.54 C(2p) + 0.24 H(1s) + 0.12 C(2s)17 22.86 0.30 N(2s) + 0.66 N(2p) + 0.46 C(2p) + 0.24 H(1s) + 0.24 C(2s)18 23.89 0.12 N(2s) + 0.66 N(2p) + 0.36 C(2p) + 0.12 H(1s) + 0.66 C(2s)19 24.4 0.14 N(2s) + 0.60 N(2p) + 0.40 C(2p) + 0.20 H(1s) + 0.66 C(2s)20 28.35 0.18 N(2s) + 0.26 N(2p) + 0.26 C(2p) + 0.06 H(1s) + 1.18 C(2s)21 31.41 1.64 N(2s) + 0.06 N(2p) + 0.16 C(2p) + 0.04 H(1s) + 0.06 C(2s)22 32.3 1.66 N(2s) + 0.04 N(2p) + 0.26 C(2p) + 0.08 H(1s) + 0.18 C(2s)23 33.98 1.36 N(2s) + 0.12 N(2p) + 0.06 C(2p) + 0.08 H(1s) + 0.38 C(2s)24 35.68 1.32 N(2s) + 0.16 N(2p) + 0.12 C(2p) + 0.42 C(2s)25 37.47 1.26 N(2s) + 0.22 N(2p) + 0.04 C(2p) + 0.02 H(1s) + 0.50 C(2s)26 303.09 1.98 C(1s)27 304.5 2.0 C(1s)28 304.85 2.0 C(1s)29 304.85 1.98 C(1s)30 305.33 1.98 C(1s)31 418.63 1.98 N(1s)32 418.84 1.98 N(1s)33 419.22 1.98 N(1s)34 419.27 1.98 N(1s)35 420.79 1.98 N(1s)

divergences in the corresponding Lippmann–Schwinger development (Gayet 1972, Belkic1978). Moreover, CDW-EIS includes in the initial and final distorted wavefunctions the long-range coulomb character of the interaction of the active electron with the projectile in theentry channel and also with the residual target in the exit one, so that they satisfy correctasymptotic conditions in both channels (Crothers and McCann 1983). This property is crucialto avoid the presence of the divergent contribution of the intermediate elastic channel in theionization reaction (Dewangan and Eichler 1985). For more details on the distorted initial andfinal wavefunctions and the corresponding perturbation potentials, the reader is referred toStolterfoht et al (1997).

In the CB1 model, which can be considered as an extension of the approximationintroduced by Belkic et al (1986) for electron capture, the initial and final wavefunctionsare chosen as

ϕ+α = exp(iKα · R)

(2π)3/2φα(x) exp

[−i

ZP

vln(vR − v · R)

](3)

2086 M E Galassi et al

Table 2. Population and binding energies of the cytosine molecular orbitals.

IonizationMolecular energiesorbital (eV) Population (effective number of electrons ξ )

1 8.94 0.70 C(2p) + 0.72 N(2p)+ 0.56 O(2p)2 10.05 1.58 N(2p) + 0.38 C(2p)+ 0.04 O(2p)3 10.67 1.22 N(2p) + 0.38 O(2p)+ 0.26 C(2p)+ 0.08 N(2s)4 11.42 1.24 O(2p) + 0.40 N(2p)+ 0.18 N(2s)+ 0.14 C(2p)5 13.15 0.62 O(2p) + 0.98 C(2p)+ 0.42 N(2p)6 14.53 1.24 N(2p) + 0.62 C(2p)+ 0.12 O(2p)7 15.61 0.92 O(2p) + 0.44 C(2p)+ 0.24 O(2s)+ 0.26 N(2p)+ 0.08 H(1s)8 16.47 1.14 C(2p) + 0.38 N(2p)+ 0.34 H(1s)+ 0.04 N(2s)+ 0.04 C(2s)9 16.8 0.88 C(2p) + 0.44 H(1s)+ 0.22 O(2p)+ 0.26 N(2p)+ 0.08 O(2s)+ 0.02 C(2s)

10 17.02 0.86 N(2p) + 0.96 C(2p)+ 0.16 O(2p)11 18.31 0.86 N(2p) + 0.52 H(1s)+ 0.40 C(2p)+ 0.08 O(2p)+ 0.12 C(2s)12 19.47 0.90 N(2p) + 0.52 C(2p)+ 0.32 H(1s)+ 0.04 O(2p)+ 0.04 O(2s)+ 0.12 C(2s)13 20.63 0.94 N(2p) + 0.78 C(2p)+ 0.20 H(1s)+ 0.06 O(2p)14 20.74 0.76 N(2p) + 0.54 C(2p)+ 0.46 H(1s)+ 0.10 C(2s)+ 0.06N(2s)+ 0.02 O(2s)15 23.79 0.90 N(2p) + 0.48 C(2s)+ 0.28 C(2p)+ 0.16 H(1s)+ 0.06 O(2s)+ 0.04 N(2s)16 24.28 0.02 O(2p) + 0.20 H(1s)+ 0.68 C(2s)+ 0.46 N(2p)+ 0.42 C(2p)+ 0.18 N(2s)17 28.93 1.20 C(2s) + 0.26 N(2s)+ 0.32 C(2p)+ 0.06 N(2p)+ 0.10 H(1s)+ 0.04 O(2s)18 31.79 1.58 N(2s) + 0.12 C(2p)+ 0.08 N(2p)+ 0.06 C(2s)+ 0.10 H(1s)+ 0.02 O(2s)19 34.14 1.38 N(2s) + 0.34 C(2s) + 0.08 O(2s) + 0.06 C(2p) + 0.08 H(1s) + 0.06 N(2p)20 35.33 0.44 O(2s) + 0.92 N(2s) + 0.40 C(2s) + 0.16 N(2p) + 0.04 O(2p) + 0.02 C(2p)21 37.7 0.92 O(2s) + 0.38 C(2s)+ 0.48 N(2s)+ 0.14 O(2p)+ 0.06 N(2p) + 0.08 C(2p)22 302.18 1.98 C(1s)23 304.47 2.00 C(1s)24 305.09 2.00 C(1s)25 305.69 2.00 C(1s)26 417.42 1.98 N(1s)27 418.83 1.98 N(1s)28 419.8 1.98 N(1s)29 550.88 2.00 O(1s)

and

ϕ−β = exp(iKβ · R)

(2π)3/2φβ(x)N∗(Z∗

T /k)1F1(−iZ∗T /k; 1;−ikx − ik · x)

× exp

[+i

ZP

vln(vR + v · R)

]. (4)

Let us note that the main difference between the initial wavefunction described by equation(3) and that given in the CDW-EIS approach resides in an eikonal phase depending on R insteadof s, so that the asymptotic boundary conditions associated with the projectile–active electroninteraction are now preserved but ϕ+

α presents a one-target center character. In the exit channel(see equation (4)), an asymptotic version of this interaction is also considered (dependingagain on R), which will be valid under the dynamic condition k � v (x � R) (Tachino 2011).So, in the CB1 approximation for ionization, correct boundary conditions are only satisfied inthis restricted coordinate space region. Thus, ϕ−

β also presents a one-target center character. Itmust also be mentioned that the application of the active electron Schrodinger equation on thewavefunction given in equation (3) results in

(Hα − Eα )φ+α = Vαφ+

α (5)

Quantum-mechanical predictions of DNA and RNA ionization by energetic proton beams 2087

Table 3. Population and binding energies of the guanine molecular orbitals.

IonizationMolecular energiesorbital (eV) Population (effective number of electrons ξ )

1 8.24 1.20 C(2p) + 0.56 N(2p) + 0.22 O(2p)2 11.14 0.40 C(2p) + 1.48 N(2p) + 0.10 O(2p)3 11.36 0.26 C(2p) + 1.24 N(2p) + 0.20 O(2p) + 0.02 H(1s) + 0.16 N(2s)4 11.80 1.28 N(2p) + 0.46 O(2p) + 0.24 C(2p)5 11.83 1.28 O(2p) + 0.38 N(2p) + 0.18 C(2p) + 0.04 C(2s) + 0.02 N(2s)6 12.39 1.52 N(2p) + 0.42 C(2p) + 0.02 O(2p)7 13.08 0.16 C(2p) + 1.40 N(2p) + 0.30 N(2s) + 0.02 H(1s)8 15.34 0.78 C(2p) + 0.62 N(2p) + 0.58 O(2p)9 16.62 1.08 O(2p) + 0.44 C(2p) + 0.10 N(2p) + 0.26 O(2s)

10 16.76 1.22 N(2p) + 0.74 C(2p)11 16.93 0.96 C(2p) + 0.64 N(2p) + 0.28 H(1s) + 0.08 O(2p)12 17.62 0.94 N(2p) + 0.76 C(2p) + 0.22 H(1s) + 0.04 O(2p)13 18.51 0.98 N(2p) + 0.96 C(2p) + 0.06 O(2p)14 18.87 0.68 N(2p) + 0.80 C(2p) + 0.18 O(2p) + 0.22 H(1s) + 0.04 C(2s)

+ 0.02 O(2s)15 19.71 0.98 N(2p) + 0.54 H(1s) + 0.20 C(2p) + 0.06 O(2p) + 0.10 C(2s)

+ 0.04 O(2s) + 0.02 N(2s)16 20.60 1.12 N(2p) + 0.46 C(2p) + 0.18 H(1s) + 0.16 C(2s)17 20.88 0.98 N(2p) + 0.30 H(1s) + 0.10 C(2s) + 0.50 C(2p)18 22.66 1.08 N(2p) + 0.58 C(2p) + 0.22 H(1s) + 0.04 C(2s) + 0.04 O(2p)19 23.30 0.70 N(2p) + 0.30 C(2s) + 0.28 N(2s) + 0.38 C(2p) + 0.26 H(1s)20 24.80 0.46 C(2s) + 0.22 C(2p) + 0.18 N(2s) + 0.88 N(2p) + 0.16 H(1s)

+ 0.02 O(2p)21 25.30 0.74 N(2p) + 0.58 C(2s) + 0.42 C(2p) + 0.06 O(2s) + 0.12 H(1s)

+ 0.04 N(2s)22 28.98 1.10 C(2s) + 0.30 C(2p) + 0.28 N(2p) + 0.18 N(2s) + 0.02 O(2s)

+ 0.02 H(1s)23 32.88 1.68 N(2s) + 0.12 C(2s) + 0.08 H(1s) + 0.06 N(2p) + 0.22 C(2p)24 34.05 1.52 N(2s) + 0.14 O(2s) + 0.10 C(2p) + 0.10 C(2s) + 0.06 H(1s)25 34.24 1.48 N(2s) + 0.14 C(2s) + 0.14 H(1s) + 0.12 N(2p) + 0.04 C(2p)26 37.55 1.18 N(2s) + 0.32 C(2s) + 0.18 O(2s) + 0.12 C(2p) + 0.20 N(2p)27 38.28 0.46 O(2s) + 0.06 C(2p) + 0.02 H(1s) + 0.14 N(2p) + 0.42 C(2s)

+ 0.94 N(2s) + 0.04 O(2p)28 39.2 0.74 O(2s) + 0.62 N(2s) + 0.46 C(2s) + 0.10 O(2p) + 0.02 N(2p)29 311.53 1.98 C(1s)30 313.15 2.00 C(1s)31 313.79 2.00 C(1s)32 314.93 2.00 C(1s)33 315.93 2.00 C(1s)34 431.02 1.98 N(1s)35 431.10 1.98 N(1s)36 432.32 1.98 N(1s)37 432.91 2.00 N(1s)38 432.94 2.00 N(1s)39 568.45 1.98 O(1s)

with the perturbative potential given by

Vα = −ZP

s+ ZP

R. (6)

In this expression the second added term results from the inclusion, in the initialwavefunction, of the projectile–active electron interaction at large asymptotic separation

2088 M E Galassi et al

Table 4. Population and binding energies of the thymine molecular orbitals.

Molecular Ionizationorbital energies (eV) Population (effective number of electrons ξ )

1 9.14 1.12 C(2p) + 0.46 N(2p) + 0.34 O(2p) + 0.08 H(1s)2 10.93 0.90 N(2p) + 1.08 O(2p) + 0.02 C(2p)3 11.35 1.46 O(2p) + 0.20 N(2p) + 0.26 C(2p) + 0.02 C(2s)4 12.13 1.44 O(2p) + 0.20 N(2p) + 0.22 C(2p) + 0.04 N(2s) + 0.04 H(1s)5 13.29 0.60 N(2p) + 0.50 O(2p) + 0.12 H(1s) + 0.76 C(2p)6 14.47 1.06 C(2p) + 0.70 H(1s) + 0.14 O(2p)7 14.68 0.52 O(2p) + 0.76 C(2p) + 0.58 N(2p) + 0.12 H(1s)8 14.81 1.32 C(2p) + 0.22 O(2p) + 0.12 N(2p) + 0.08 C(2s) + 0.14 H(1s)9 15.57 1.18 C(2p) + 0.48 H(1s) + 0.24 O(2p) + 0.08 N(2p)

10 15.99 0.84 O(2p) + 0.14 O(2s) + 0.68 C(2p) + 0.18 H(1s) + 0.08 N(2p)11 16.36 0.96 O(2p) + 0.26 O(2s) + 0.56 C(2p) + 0.02 C(2s) + 0.06 H(1s)

+ 0.06 N(2p)12 17.44 0.58 O(2p) + 0.48 C(2p) + 0.34 N(2p) + 0.20 O(2s) + 0.24 H(1s)

+ 0.10 C(2s)13 17.62 0.90 C(2p) + 0.82 N(2p) + 0.26 O(2p)14 18.59 0.76 N(2p) + 0.52 C(2p) + 0.54 H(1s) + 0.06 C(2s) + 0.02 O(2p)15 20.28 0.88 N(2p) + 0.40 C(2p) + 0.34 H(1s) + 0.26 C(2s) + 0.08 O(2p)

+ 0.04 O(2s)16 20.38 0.62 N(2p) + 1.06 C(2p) + 0.16 O(2p) + 0.04 C(2s)17 23.51 0.90 N(2p) + 0.38 C(2s) + 0.30 C(2p) + 0.12 H(1s) + 0.12 O(2s)

+ 0.06 N(2s) + 0.06 O(2p)18 24.08 0.50 N(2p) + 0.64 C(2s) + 0.46 C(2p) + 0.22 H(1s) + 0.06 N(2s)

+ 0.04 O(2s) + 0.02 O(2p)19 25.53 1.24 C(2s) + 0.24 N(2p) + 0.20 C(2p) + 0.22 H(1s) + 0.04 O(2s)20 29.23 1.44 C(2s) + 0.12 N(2s) + 0.22 C(2p) + 0.04 N(2p) + 0.06 O(2s)21 32.65 1.52 N(2s) + 0.12 O(2s) + 0.12 C(2s) + 0.12 C(2p) + 0.10 H(1s)22 34.46 1.04 N(2s) + 0.52 O(2s) + 0.20 C(2s) + 0.12 C(2p) + 0.08 N(2p)

+ 0.04 H(1s)23 37.09 1.40 O(2s) + 0.34 C(2s) + 0.18 O(2p) + 0.04 N(2p) + 0.02 N(2s)24 37.85 0.92 O(2s) + 0.38 C(2s) + 0.46 N(2s) + 0.14 O(2p) + 0.02 N(2p)

+ 0.02 C(2p)25 293.56 1.98 C(1s)26 294.27 1.98 C(1s)27 296.03 1.98 C(1s)28 297.42 2.00 C(1s)29 298.44 2.00 C(1s)30 408.28 1.98 N(1s)31 408.68 1.98 N(1s)32 536.74 2.00 O(1s)33 536.87 1.98 O(1s)

between both particles. Thus, only the short-range part of this interaction contributes to theperturbative potential. It is easy to show that the corresponding eikonal phases appearing inthe initial and final wavefunctions and depending on R in CB1 may be neglected when crosssections integrated over the projectile scattering angle are considered (Champion et al 2011).

As mentioned above, the input parameters for the occupied molecular orbitals (MOs)of adenine, cytosine, guanine, thymine and uracil bases as well as of the sugar–phosphatebackbone unit were here obtained by using similar ab initio methods as the ones described byBernhardt and Paretzke (2003). For each DNA/RNA component, all the occupied MOs wereincluded in the present calculations, i.e. N = 35, 29, 39, 33, 29 and 48 MOs for adenine,cytosine, guanine, thymine, uracil and sugar–phosphate backbone unit, respectively; this

Quantum-mechanical predictions of DNA and RNA ionization by energetic proton beams 2089

Table 5. Population and binding energies of the uracile molecular orbitals.

Molecular Ionizationorbital energies (eV) Population (effective number of electrons ξ )

1 9.5 0.48 N(2p) + 0.42 O(2p) + 1.10 C(2p)2 10.97 0.90 N(2p) + 1.06 O(2p) + 0.02 C(2p)3 11.36 0.20 N(2p) + 1.50 O(2p) + 0.22 C(2p) + 0.04 C(2s)4 12.23 0.04 N(2s) + 0.20 N(2p) + 1.48 O(2p) + 0.20 C(2p) + 0.02 H(1s)5 13.7 0.70 N(2p) + 0.84 C(2p) + 0.40 O(2p)6 14.93 0.48 N(2p) + 0.74 C(2p) + 0.76 O(2p)7 15.64 0.78 C(2p) + 0.48 O(2p) + 0.40 H(1s) + 0.22 N(2p) + 0.04 O(2s)

+ 0.04 C(2s)8 15.82 0.96 O(2p) + 0.60 C(2p) + 0.18 O(2s) + 0.12 N(2p) + 0.12 H(1s)9 16.82 0.76 O(2p) + 0.62 C(2p) + 0.24 O(2s) + 0.20 H(1s)+ 0.06 N(2p)

+ 0.04 C(2s)10 17.48 0.52 O(2p) + 0.40 N(2p) + 0.54 C(2p) + 0.18 O(2s)+ 0.24 H(1s)

+ 0.06 C(2s)11 17.63 0.86 C(2p) + 0.88 N(2p) + 0.26 O(2p)12 18.71 0.56 C(2p) + 0.68 N(2p) + 0.54 H(1s) + 0.06 C(2s)13 20.23 0.58 N(2p) + 1.06 C(2p) + 0.20 O(2p) + 0.08 C(2s)14 21.20 0.92 N(2p) + 0.20 C(2s) + 0.42 H(1s) + 0.36 C(2p)+ 0.04 O(2s)15 23.62 0.88 N(2p) + 0.44 C(2s) + 0.32 C(2p) + 0.16 O(2s)+ 0.08 H(1s)

+ 0.04 N(2s) + 0.08 O(2p)16 24.46 0.62 N(2p) + 0.64 C(2s) + 0.40 C(2p) + 0.20 H(1s)+ 0.06 N(2s)

+ 0.02 O(2p)17 28.71 1.28 C(2s) + 0.14 N(2s) + 0.30 C(2p) + 0.08 N(2p)+ 0.06 O(2s)

+ 0.08 H(1s)18 32.70 1.50 N(2s) + 0.16 O(2s) + 0.12 C(2p) + 0.10 C(2s)+ 0.10 H(1s)19 34.56 1.04 N(2s) + 0.08 N(2p) + 0.22 C(2s) + 0.04 H(1s)+ 0.12 C(2p)

+ 0.52 O(2s)20 37.08 1.40 O(2s) + 0.04 N(2s) + 0.34 C(2s) + 0.16 O(2p)+ 0.04 N(2p)21 37.92 0.94 O(2s) + 0.38 C(2s) + 0.46 N(2s) + 0.02 C(2p) + 0.02 N(2p)

+ 0.12 O(2p)22 293.85 1.98 C(1s)23 296.08 1.98 C(1s)24 297.28 2.00 C(1s)25 298.31 2.00 C(1s)26 407.98 1.98 N(1s)27 408.5 1.98 N(1s)28 536.44 1.98 O(1s)29 536.44 1.98 O(1s)

represents a significant improvement over the only five HOMOs originally used in Championet al 2010. Total-energy calculations for all targets were performed in the gas phase with theGaussian 09 software at the RHF/3-21G level of theory (Frisch et al 2009). The equilibriumgeometries of the nucleobases depicted in figure 1 were obtained without symmetry constraintsapplied. The structure of the sugar–phosphate backbone unit was optimized following theprocedure suggested by Colson et al (1993) for a typical B-DNA fiber conformation: as shownin figure 1, a sodium counter ion was placed between the two oxygen atoms opposite to thephosphorus, the hydroxyl group of the deoxyribose was replaced with a terminal hydrogen toavoid double-counting of the O atom in the backbone unit, H atoms were added to terminatethe bonds to the adjacent groups, and the backbone and deoxyribose torsion angles were keptfixed during relaxation calculations with the values given by Colson et al (1993). The resulting

2090 M E Galassi et al

Table 6. Population and binding energies of the sugar–phosphate backbone molecular orbitals.

Molecular Ionizationorbital energies (eV) Population (effective number of electrons ξ )

1 10.53 1.20 O(2p) + 0.32 H(1s) + 0.38 C(2p)2 10.64 1.88 O(2p) + 0.06 P(3p)3 10.88 1.98 O(2p)4 11.65 1.66 O(2p) + 0.08 P(3p) + 0.04 H(1s) + 0.06 C(2p)5 11.73 0.72 O(2p) + 1.04 C(2p) + 0.10 H(1s) + 0.04 O(2s)6 11.97 1.62 O(2p) + 0.08 P(3p) + 0.14 C(2p) + 0.02 H(1s)7 12.27 0.92 O(2p) + 0.60 C(2p) + 0.26 H(1s) + 0.02 P(3p)8 12.41 1.48 O(2p) + 0.12 H(1s) + 0.12 C(2p) + 0.12 P(3p)9 12.73 0.88 C(2p) + 0.38 H(1s) + 0.42 O(2p) + 0.04 P(3p)

10 12.7 1.22 C(2p) + 0.20 H(1s) + 0.46 O(2p)11 13.06 0.96 C(2p) + 0.64 O(2p) + 0.20 H(1s) + 0.04 P(3p)12 13.69 1.40 O(2p) + 0.16 P(3p) + 0.22 C(2p) + 0.04 H(1s)13 14.31 1.16 O(2p) + 0.50 C(2p) + 0.10 H(1s) + 0.06 P(3p) + 0.02 O(2s)14 14.91 1.02 C(2p) + 0.32 O(2p) + 0.42 H(1s)15 15.13 1.20 O(2p) + 0.38 C(2p) + 0.12 H(1s) + 0.06 O(2s) + 0.12 P(3p)16 15.56 0.82 O(2p) + 0.60 C(2p) + 0.16 P(3p) + 0.08 O(2s) + 0.06 H(1s)

+ 0.02 P(3s)17 15.84 0.88 O(2p) + 0.58 C(2p) + 0.16 P(3p) + 0.26 H(1s) + 0.04 O(2s)18 16.54 0.92 O(2p) + 0.16 H(1s) + 0.20 O(2s) + 0.34 C(2p) + 0.10 P(3s)

+ 0.18 P(3p)19 17.39 0.78 C(2p) + 0.70 O(2p) + 0.32 H(1s) + 0.06 P(3p) + 0.02 O(2s)20 17.52 0.98 C(2p) + 0.48 O(2p) + 0.24 H(1s) + 0.04 C(2s) + 0.02 P(3p)

+ 0.02 O(2s)21 17.96 1.02 C(2p) + 0.48 O(2p) + 0.20 H(1s) + 0.04 P(3s) + 0.04 P(3p)

+ 0.02 O(2s)22 18.86 0.86 O(2p) + 0.48 C(2p) + 0.18 P(3p) + 0.16 H(1s) + 0.08 C(2s)23 20.84 0.58 O(2p) + 0.48 C(2s) + 0.22 H(1s) + 0.28 C(2p) + 0.08 P(3s)

+ 0.08 P(3p) + 0.10 O(2s)24 21.69 0.54 O(2p) + 0.50 C(2s) + 0.06 O(2s) + 0.20 H(1s) + 0.30 C(2p)

+ 0.04 P(3p) + 0.16 P(3s)25 21.80 0.80 C(2s) + 0.28 H(1s) + 0.26 O(2p) + 0.34 C(2p) + 0.06 O(2s)

+ 0.08 P(3s)26 24.76 1.24 C(2s) + 0.20 O(2p) + 0.14 C(2p) + 0.20 H(1s) + 0.02 P(3s)

+ 0.02 O(2s) + 0.02 P(3p)27 27.84 1.52 C(2s) + 0.12 O(2p) + 0.10 H(1s) + 0.06 C(2p) + 0.04 O(2s)28 28.33 1.48 C(2s) + 0.18 O(2s) + 0.14 C(2p) + 0.04 O(2p) + 0.02 H(1s)29 33.17 1.78 O(2s) + 0.14 P(3p) + 0.08 O(2p)30 34.67 1.64 O(2s) + 0.10 P(3s) + 0.06 P(3p) + 0.10 O(2p) + 0.02 C(2s)31 36.35 1.66 O(2s) + 0.16 C(2s) + 0.02 P(3p) + 0.02 O(2p)32 36.76 1.54 O(2s) + 0.30 C(2s) + 0.04 O(2p)33 38.18 1.52 O(2s) + 0.22 P(3s) + 0.06 C(2s) + 0.08 O(2p)34 149.58 2.00 P(2p)35 149.61 2.00 P(2p)36 149.61 2.00 P(2p)37 207.08 2.00 P(2s)38 303.73 1.98 C(1s)39 304.55 1.98 C(1s)40 304.90 1.98 C(1s)41 305.23 1.98 C(1s)42 305.48 1.98 C(1s)43 554.24 2.00 O(1s)44 554.24 2.00 O(1s)45 555.91 2.00 O(1s)46 556.77 2.00 O(1s)47 556.80 2.00 O(1s)48 2165.16 2.00 P(1s)

Quantum-mechanical predictions of DNA and RNA ionization by energetic proton beams 2091

100 101 102 10310-5

10-4

10-3

10-2

10-1

100

Ejected electron energy (eV)

DD

CS

(10

-16 c

m2 /e

V.s

r)

Figure 2. CDW-EIS and CB1 DDCS (solid and dashed lines, respectively) for 100 keV protonscolliding with uracil at a fixed electron emission angle θe = 35◦. Experimental data (solid circles)as well as CTMC predictions (open circles) both taken from Moretto-Capelle and Le Padellec(2006) are also reported for comparison.

first ionization potential of the backbone unit was 10.53 eV, in close agreement with the scaledvalue of 10.52 eV obtained by Bernhardt and Paretzke (2003).

The computed ionization energies of the occupied MOs of the biological targetsinvestigated here were scaled so that their calculated Koopmans ionization energy, i.e. theionization energy of their HOMO, coincides with the experimental value of the ionizationpotential measured by Hush and Cheung (1975). For each MO labeled j, the effective numberof electrons ξ j,i relative to the atomic component i, was derived from a standard Mullikenpopulation analysis and their sum for each occupied MO is very close to 2, since only atomicshells with very small population have been discarded (see tables 1–6).

In the laboratory frame, triply differential cross sections, σ (3)( s, e, Ee), differentialwith respect to the scattering direction s, the ejected electron direction e and the emittedelectron energy, can be written as

σ (3)( s, e, Ee) =N∑

j=1

σ(3)j ( s, e, Ee), (7)

where N is the number of MOs used in the description of the target and σ(3)j refers to the

triply differential cross section for the jth orbital, the latter being obtained as a weighted sum

2092 M E Galassi et al

100 101 102 10310-18

10-16

10-14

10-12

10-10

10-8

10-6

10-4

10-2

DD

CS

(10-1

6 cm2 /e

V.s

r)

Ejected electron energy (eV)

15° (x10-1) 30° (x10

-2)

45° (x10-3) 60° (x10

-4)

75° (x10-5) 90° (x10

-6)

105° (x10-7) 120° (x10

-8)

135° (x10-9) 150° (x10

-10)

165° (x10-11)

Figure 3. CDW-EIS and CB1 DDCS (solid and dashed lines, respectively) for 500 keV protonscolliding with adenine at different electron emission angles. Experimental data taken from Irikiet al (2011b) are reported for comparison. Multiplicative factors have been used for clarity reasons.

of atomic triply differential cross sections corresponding to the different atomic componentsinvolved in the CNDO description, namely

σ(3)j ( s, e, Ee) =

∑i

ξ j,i.σ(3)at,i ( s, e, Ee), (8)

where the effective number of electrons ξ j,i (as well as the corresponding binding energy) islisted in tables 1–6 for each MO of all the biological targets of interest.

Then, triply differential cross sections can be calculated from the corresponding transitionmatrix element whereas DDCS σ (2)( e, Ee) and SDCS σ (1)(Ee) are obtained by successiveintegrations of σ (3)( s, e, Ee) over the solid angles s and e, respectively. Finally, TCSare computed by integration over the energy transferred to the ejected electron Ee.

Finally, note that in the present quantum-mechanical calculations, the effective targetcharge Z∗

T is taken as Z∗T = √−2n2

αεα, where nα refers to the principal quantum number ofeach atomic orbital component used in each MO expansion whereas the active electron orbitalenergy εα is related to the ionization energies Bj of the occupied MOs by εα = −Bj. Each ofthe different MOs is thus described by using a basis of effective atomic ones.

Quantum-mechanical predictions of DNA and RNA ionization by energetic proton beams 2093

100 101 102 10310-18

10-16

10-14

10-12

10-10

10-8

10-6

10-4

10-2

15° (x10-1) 30° (x10

-2)

45° (x10-3) 60° (x10

-4)

75° (x10-5) 90° (x10

-6)

105° (x10-7) 120° (x10

-8)

135° (x10-9) 150° (x10

-10)

165° (x10-11)

DD

CS

(10-1

6 cm2 /e

V.s

r)

Ejected electron energy (eV)

Figure 4. CDW-EIS and CB1 DDCS (solid and dashed lines, respectively) for 1 MeV protonscolliding with adenine at different electron emission angles. Experimental data taken from Irikiet al (2011a) are reported for comparison. Multiplicative factors have been used for clarity reasons.

Results and discussions

To the best of our knowledge, the literature concerned by experimental ionization cross sectionsof DNA and RNA components impacted by protons is poor and exclusively limited to (i) the 25,50 and 100 keV DDCS measurements on uracil reported by Moretto-Capelle and Le Padellec(2006), (ii) the absolute total and partial cross sections provided by Tabet et al (2010c) fornucleobases in the Bragg peak velocity range, namely here at 80 keV incident, and finally(iii) the DDCS, SDCS and TCS recently reported by Iriki et al (2011a, 2011b) for adenineimpacted by protons at three particular incident energies, namely 500 keV, 1 MeV and 2MeV. In this context, we focused this section to an extensive comparison of our theoreticalpredictions to these existing measurements in order to point out the reliability of the twomodels presented here.

Thus, CDW-EIS and CB1 DDCS for proton beams with 100 keV kinetic energy collidingwith uracil (C4H4N2O2) are shown in figure 2 (solid and dashed lines, respectively) for a fixedelectron emission angle θ e = 35◦, i.e. under kinematical conditions similar to those reported byMoretto-Capelle and Le Padellec (2006). A very good agreement may be observed betweenthe two theoretical sets. Besides, in comparison with the experimental data (solid circles)taken from Moretto-Capelle and Le Padellec (2006), we observe that both sets of results(CB1 and CDW-EIS) largely overestimate the measurements, with a disagreement reaching

2094 M E Galassi et al

100 101 102 10310-18

10-16

10-14

10-12

10-10

10-8

10-6

10-4

10-2

15° (x10-1) 30° (x10

-2)

45° (x10-3) 60° (x10

-4)

75° (x10-5) 90° (x10

-6)

105° (x10-7) 120° (x10

-8)

135° (x10-9) 150° (x10

-10)

165° (x10-11)

DD

CS

(10-1

6 cm2 /e

V.s

r )

Ejected electron energy (eV)

Figure 5. CDW-EIS and CB1 DDCS (solid and dashed lines, respectively) for 2 MeV protonscolliding with adenine at different electron emission angles. Experimental data taken from Irikiet al (2011b) are reported for comparison. Multiplicative factors have been used for clarity reasons.

two orders of magnitude for low ejection energies. However, once compared to the CTMCpredictions also given by Moretto-Capelle and Le Padellec (2006) the agreement of the presentcalculations appears better both in magnitude and slope, even considering that the classicalcalculations present a pronounced decrease for low ejection energies (Ee < 20 eV) whichis not reproduced by the present calculations. We are currently investigating the possibleorigin of this disagreement between theory and experiments, which appears all the moresurprising and not understandable so as in comparison with the recent measurements of Irikiet al (2011a, 2011b) for adenine interacting with 500 keV, 1 MeV and 2 MeV protons, ourCB1 predictions exhibit a very good agreement (see figures 3–5) for a large range of ejectionangles (15◦ � θe � 165◦) and ejected electron energies (5eV � Ee � 1keV). A generalgood agreement with experiments is also observed for CDW-EIS results except for backwardscattering. For atomic targets, this undesirable behavior, which is characteristic of the CDW-EIS model, can be partially avoided including in the calculations the dynamical screeningproduced by the electrons remaining bound to the target on the ionized one (Monti et al 2010).Moreover, the use of numerical target continuum wavefunctions in the exit channel has beenshown to improve the agreement between CDW-EIS results and experiments at large emissionangles (Fainstein et al 1994, Gulyas et al 1995) for atomic targets. To test the validity ofthis comportment for the large molecules treated here, the formidable task of consideringnumerical target continuum wavefunctions for each of the atomic states employed to describethe numerous MOs should be included in the dynamical description of the collision.

Quantum-mechanical predictions of DNA and RNA ionization by energetic proton beams 2095

100 101 102 10310-5

10-4

10-3

10-2

10-1

100

SD

CS

(cm

2 /eV

)

Ejected electron energy (eV)

Figure 6. CDW-EIS and CB1 SDCS (solid and dashed lines, respectively) for 500 keV, 1 MeVand 2 MeV protons colliding with adenine. Experimental data taken from Iriki et al (2011a) and(2011b) are reported for comparison.

In figure 6, CDW-EIS and CB1 SDCS for adenine impacted by 500 keV, 1 MeV and 2 MeVprotons are reported and compared with the measurements of Iriki et al (2011a, 2011b). Hereagain, the agreement between the CB1 theoretical set and experiments for ejected energieslarger than 10 eV is very good. Additionally, we clearly observe that CDW-EIS results agreevery well with the experimental data, provided that the ejected energy is greater than about100 eV.

In figure 7, TCS are presented for all the DNA/RNA bases as well as the sugar–phosphatebackbone impacted by protons. Thus, for adenine, in accord with the SDCS reported above,we note that the CDW-EIS and the CB1 predictions are in reasonable agreement providedthat the impact energies are larger than 100 keV, even considering that the CB1 calculationsoverestimate CDW-EIS ones all the more that the collision velocity increases. Furthermore, incomparison to our previously published classical CTMC-COB predictions taken from Lekadiret al (2009), we still observe agreement with the present quantum-mechanical predictionsexcept at low incident energies where the CDW-EIS TCS show a characteristic drop inamplitude as the energy decreases. The very good description of experimental DCCS andSDCS obtained for the collisional system {H+ + adenine} is extended for TCS with themeasurements of Iriki et al, namely at 1 MeV (open up triangles) taken from Iriki et al (2011a)and at 500 keV and 2 MeV (solid up triangles) taken from Iriki et al (2011b). However, incomparison with the TCS reported by Tabet et al (2010c), we observe that our theoretical

2096 M E Galassi et al

101 102 103 10410-1

100

101

102

101 102 103 104100

101

102

101 102 103 104100

101

102

101 102 103 104100

101

102

101 102 103 104100

101

102

101 102 103 104100

101

102

CB1

CB1

CB1

CB1

CB1

electron

electronelectron

electron

H+ + Backbone H+ + Uracil

H+ + ThymineH+ + Guanine

H+ + CytosineT

CS

(10-1

6 cm2 )

H+ + Adenine

electron

CTMC-COB

CB1

CDW-EIS CDW-EIS

CTMC-COB

CTMC-COB

CTMC-COB

CTMC-COB

CDW-EIS

TC

S(1

0-16 cm

2 )

CDW-EIS

CDW-EISTC

S(1

0-16 cm

2)

Incident proton energy (keV)

CDW-EIS

Incident proton energy (keV)

Figure 7. CDW-EIS and CB1 TCS (solid and dashed lines, respectively) for the DNA/RNA basesas well as the sugar–phosphate backbone all impacted by protons. Previously published classicalCTMC-COB predictions taken from Lekadir et al (2009) are also reported. The experimentalmeasurements reported are taken from Tabet et al (2010c) (solid circles), Iriki et al (2011a)(open up triangle), Iriki et al (2011b) (solid up triangles) and Iriki et al (private communication)(open circles). Electron impact TCS taken from Mozejko and Sanche (2005) are also included forcomparison.

results largely underestimate the measurement (solid circles), which is also evident for thethymine and uracil bases. Let us note that for cytosine, the agreement between the Tabet et al’smeasurement and our calculations seems better, while for uracil, very good agreement maybe observed with the recent measurements of Iriki et al (private communication). Similarly,figure 8 clearly reveals that the CDW-EIS and the CB1 predictions in terms of TCS for thesugar–phosphate backbone are both in reasonable agreement provided that the impact energiesare larger than 100 keV, even considering that the CB1 calculations overestimate CDW-EISones all the more that the collision velocity increases.

Besides, for comparison we have also included the TCS predictions reported by Mozejkoand Sanche (2005) for electron projectiles. As they have been calculated using a first-order

Quantum-mechanical predictions of DNA and RNA ionization by energetic proton beams 2097

101 102 103 10410-2

10-1

100

Incident proton energy (keV)

AdenineCytosineThymineGuanine

SugarPhosphate BackboneWater

TC

S/N

e (1

0-16 cm

2 )

Figure 8. CDW-EIS and CB1 ‘normalized’ TCS (solid and dashed lines, respectively) for theDNA/RNA components compared to the homologous for water (see the text for details). In bothcases, the targets have been described within the CNDO approach.

model, they seem to follow better the CB1 than the CDW-EIS results at high-enough collisionvelocities.

Finally, in comparison to the corresponding cross sections in water, the latter being alsodescribed within the CNDO approach (see Champion et al 2012), we clearly observe that thetotal ionization cross sections are roughly within the ratio of the number of target electrons(denoted as Ne), in particular for the CDW-EIS approach, while slight discrepancies are pointedout when CB1 predictions are superimposed, certainly due to calculation artifices encounteredalong the procedures of numerical integrations. This observation obviously suggests that themean free path for protons in water will be similar to that in DNA and that account of suchaccurate cross sections of DNA components would lead to no modification in the transportmodeling of protons in non-homogeneous biological medium. However, this statement isonly valid for ‘spatial’ considerations since strong differences were pointed out when energytransfers (kinetic as well as potential) were intra-compared between water and DNA. This willbe the subject of a forthcoming paper where the proton-induced energetic cartography in a‘realistic’ biological medium will be studied in detail.

Conclusions

Single ionization of DNA/RNA components impacted by fast protons has been theoreticallystudied by employing two different quantum-mechanical models based on the CDW-EISand CB1 approaches. Each molecular orbital is described by using ab initio calculationsdeveloped in this work. A good agreement is observed between the two approaches forall cases reported and also with previous classical predictions at impact energies larger than100 keV. Furthermore, these models are shown to give an adequate description of experimentalmeasurements in terms of doubly and singly differential cross sections for 500 keV, 1 MeVand 2 MeV protons impacting on adenine. However, let us mention that large discrepancieswere found with uracil experimental doubly differential cross sections. The origin of thisdisaccording is still under consideration. For total cross sections an excellent agreement withexperiments by Iriki et al (2011a, 2011b) is obtained, whereas discrepancies with the ones by

2098 M E Galassi et al

Tabet et al (2010c) were found. This disagreement between measurements remains an openquestion and more experiments appear as necessary to answer it. It is also predicted that thetheoretical total ionization cross sections are roughly within the ratio of the number of targetelectrons.

Acknowledgments

This work has been developed as part of the activities planned in the Programme deCooperation ECOS-Sud A09E04, the Project Simulation Monte Carlo Haute Performancepour l’Hadrontherapie partially funded by the Conseil Regional de Lorraine and the FrenchAgence Nationale de la Recherche Contract No ANR-09-BLAN-0135-01. Furthermore, someof the authors (MEG, OF and RDR) acknowledge partial support from the Agencia Nacional dePromocion Cientıfica y Tecnologica (Project PICT 2006 No 1912) and the Consejo Nacionalde Investigaciones Cientificas y Tecnicas (PIP-CONICET No 1026/10 and No 0033/10), bothinstitutions from the Republica Argentina.

References

Abbas I, Champion C, Zarour B, Lasri B and Hanssen J 2008 Single and multiple cross sections for ionizingprocesses of biological molecules by protons and α-particle impact: a classical Monte Carlo approach Phys.Med. Biol. 53 N41

Alvarado F, Bari S, Hoeckstra R and Schaltholter T 2007 Interactions of neutral and singly charged keV atomicparticles with gas-phase adenine molecules J. Chem. Phys. 127 034301

Belkic Dz 1978 A quantum theory of ionization in fast collisions between ions and atomic systems J. Phys. B: At.Mol. Phys. 11 3529

Belkic Dz, Gayet R, Hanssen J and Salin A 1986 The first Born approximation for charge transfer collisions J. Phys.B: At. Mol. Phys. 19 2945

Bernhardt Ph and Paretzke H G 2003 Calculation of electron impact ionisation cross sections of DNA using theDeutsch-Mark and binary-encounter-Bethe formalisms Int. J. Mass Spectrom. 223–4 599

Champion C, Galassi M E, Weck P F, Fojon O, Hanssen J and Rivarola R D 2012 Quantum-mechanical contributionsto numerical simulations of charged particle transport at the DNA scale in Radiation Damage in BiomolecularSystems, Biological and Medical Physics, Biomedical Engineering ed G C Gomez-Tejedor and M C FussSpringer Science chap 16 pp 263–89

Champion C, Hanssen J and Rivarola R D 2011 Theories on high-energy heavy ion collisions with applications inhadron therapy Adv. Quantum Chem. at press

Champion C, Lekadir H, Galassi M E, Fojon O, Rivarola R D and Hanssen J 2010 Theoretical predictions forionization cross sections of DNA nucleobases impacted by light ions Phys. Med. Biol. 55 6053–67

Colson A O, Besler B and Sevilla M D 1993 Ab-initio molecular-orbital calculations on DNA radical ions: 3.Ionization-potentials and ionization sites in components of the DNA sugar–phosphate backbone J. Phys.Chem. 97 8092–7

Coupier B et al 2002 Inelastic interactions of protons and electrons with biologically relevant molecules Eur. Phys. J.D 20 459

Crothers D S F and McCann J F 1983 Ionisation of atoms by ion impact J. Phys. B: At. Mol. Phys. 16 3229Dal Cappello C, Hervieux P A, Charpentier I and Ruiz-Lopez F 2008 Ionization of the cytosine molecule by protons:

ab initio calculation of differential and total cross sections Phys. Rev. A 78 042702Dewangan D P and Eichler J 1985 Boundary conditions and the strong potential Born approximation for electron

capture J. Phys. B: At. Mol. Phys. 18 L65Fainstein P D, Ponce V H and Rivarola R D 1991 Two-centre effects in ionization by ion impact J. Phys. B: At. Mol.

Opt. Phys. 24 3091Fainstein P D, Gulyas L and Salin A 1994 Angular distribution of electrons ejected from argon by 350 keV proton

impact: CDW-EIS approximation J. Phys. B: At. Mol. Opt. Phys. 27 L259Fainstein P D, Ponce V H and Rivarola R D 1988a A theoretical model for ionization in ion-atom collisions.

Application for the impact of multicharged projectiles on helium J. Phys. B: At. Mol. Opt. Phys. 21 287Fainstein P D, Ponce V H and Rivarola R D 1988b Two-center effects in ionization by ion impact J. Phys. B: At. Mol.

Opt. Phys. 24 3091

Quantum-mechanical predictions of DNA and RNA ionization by energetic proton beams 2099

Frisch M J et al 2009 Gaussian 09 Revision A.02 (Wallingford, CT: Gaussian, Inc.)Galassi M E, Rivarola R D and Fainstein P D 2004 Multicenter character in single-electron emission from

H2 molecules by ion impact Phys. Rev. A 70 032721Gayet R 1972 Charge exchange scattering amplitude to first order of a three body expansion J. Phys. B: At. Mol.

Phys. 5 483Gulyas L, Fainstein P D and Salin A 1995 CDW-EIS theory of ionization by ion impact with Hartree–Fock description

of the target J. Phys. B: At. Mol. Opt. Phys. 28 245Hush N S and Cheung A S 1975 Ionization potentials and donor properties of nucleic acid bases and related compounds

Chem. Phys. Lett. 34 11Iriki Y, Kikuchi Y, Imai M and Itoh A 2011a Absolute doubly differential cross sections for ionization of adenine by

1.0 MeV protons Phys. Rev. A 84 032704Iriki Y, Kikuchi Y, Imai M and Itoh A 2011b Proton-impact ionization cross sections of adenine measured at 0.5 and

2.0 MeV by electron spectroscopy Phys. Rev. A 84 052719Lekadir H, Abbas I, Champion C, Fojon O, Rivarola R D and Hanssen J 2009 Single electron loss cross sections

of DNA/RNA bases impacted by energetic multi-charge ions: a classical Monte Carlo approach Phys. Rev.A 79 062710

Monti J M, Fojon O A, Hanssen J and Rivarola R D 2009 Ionization of helium targets by proton impact: a four-body distorted wave-eikonal initial state model and electron dynamic correlation J. Phys. B: At. Mol. Opt.Phys. 42 195201

Monti J M, Fojon O A, Hanssen J and Rivarola R D 2010 Influence of the dynamic screening on single-electronionization of multi-electron atoms J. Phys. B: At. Mol. Opt. Phys. 43 205203

Moretto-Capelle P and Le Padellec A 2006 Electron spectroscopy in proton collisions with dry gas-phase uracil basePhys. Rev. A 74 062705

Mozejko P and Sanche L 2005 Cross sections for electron scattering from selected components of DNA and RNARadiat. Phys. Chem. 73 77

Stolterforht N, DuBois R D and Rivarola R D 1997 Electron Emission in Heavy Ion–Atom Collisions ed G Ecker,P Lambropoulos, I I Sobel’man and H Walther (Berlin: Springer)

Tabet J, Eden S, Feil S, Abdoul-Carime H, Farizon B, Farizon M, Ouaskit S and Mark T D 2010a 20–150-keVproton-impact-induced ionization of uracil: fragmentation ratios and branching ratios for electron capture anddirect ionization Phys. Rev. A 81 012711

Tabet J, Eden S, Feil S, Abdoul-Carime H, Farizon B, Farizon M, Ouaskit S and Mark T D 2010b Absolute molecularflux and angular distribution measurements to characterize DNA/RNA vapor jets Nucl. Instrum. Methods Phys.Res. B 268 2458

Tabet J, Eden S, Feil S, Abdoul-Carime H, Farizon B, Farizon M, Ouaskit S and Mark T D 2010c Absolute total andpartial cross sections for ionization of nucleobases by proton impact in the Bragg peak velocity range Phys. Rev.A 82 022703

Tachino C 2011 Single and multiple ionization in diatomic molecules PhD Thesis Universidad Nacional de Rosario(unpublished)