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International Journal of Mass Spectrometry 360 (2014) 1– 7

Contents lists available at ScienceDirect

International Journal of Mass Spectrometry

j ourna l ho me page: www.elsev ier .com/ locate / i jms

Electron impact total cross sections for components of DNA and RNAmolecules

Minaxi Vinodkumara,∗, Chetan Limbachiyab, Mayuri Barota, Avani Barota, Mohit Swadiab

a V.P. & R.P.T.P. Science College, VallabhVidyanagar 388120, Gujarat, Indiab P.S. Science College, Kadi 382715, Gujarat, India

a r t i c l e i n f o

Article history:Received 24 October 2013Received in revised form31 December 2013Accepted 31 December 2013Available online 8 January 2014

Keywords:Spherical complex optical potentialTotal cross sectionsBiomoleculesDNARNA30.84-Bm.

a b s t r a c t

Present paper reports electron impact total cross sections (QT), total elastic cross sections (Qel) and totalinelastic cross sections (Qinel) for DNA and RNA nucleic bases as well as Phosphoricacid from 20 eV to2000 eV. These components include uracil (C4H4N2O2), thymine (C5H6N2O2), cytosine (C4H5N3O), ade-nine (C5H5N5), guanine (C5H5N5O) and phosphoric acid (H3PO4). We have employed spherical complexoptical potential (SCOP) formalism to calculate these total cross sections. Since DNA and RNA are complexmolecules, we have used the group additivity rule which incorporates molecular properties of the targetto evaluate these cross sections rather than the atomic properties as in case of independent atom model(IAM) and screened corrected additivity rule (SCAR) employed in previous works. The present results forthese complex biomolecules are compared with previous data wherever available.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

Electron induced reactions represent some of the most fun-damental processes as they drive nearly all the importantphysico-chemical processes in various sectors of applied fieldssuch as radiation chemistry, plasma etching in semiconductors,biochemistry, stability of waste repositories, dynamics of the atmo-sphere and interstellar clouds, dissociative recombination andelectron attachment processes. In recent times, low energy electronimpact studies on biomolecules have gained prominence due to thepioneering work of Sanche and coworkers [1,2]. Biomolecules, inparticular DNA/RNA components are prone to high energy radia-tion damage which can occur due to primary, secondary or reactiveprocesses [3].The components of DNA and RNA, uracil (C4H4N2O2),thymine (C5H6N2O2) and cytosine (C4H5N3O) as well as adenine(C5H5N5) and guanine (C5H5N5O) are some of the simplest pyrim-idine and purine bases, respectively. These nucleic acids, whosefunction is storage and transfer of genetic information [4] are essen-tial components of all living cells. When the living cells get exposedto radiation such as �-rays, X-rays and �-rays, single and multipleionization processes produce large number of secondary electrons.These electrons carry large fraction of the energy of the impinging

∗ Corresponding author. Tel.: +91 9723309739 (mob); fax: +91 2692 235207.E-mail address: minaxivinod@yahoo.co.in (M. Vinodkumar).

radiation. These low energy electrons (9–20 eV) [5] interact reso-nantly or directly with the irradiated biomolecules through seriesof sequential reactions causing damage to DNA and RNA in termsof either single or double strand breaks. The direct interaction canbreak the backbone of the DNA while the resonances or transientanion formation will dissociate it into neutral and anionic frag-ments [6]. Such electron interactions cause modifications of cellularDNA and RNA and promote cytotoxic, mutagenic and carcinogeniclesions. To arrive at a complete description of the biological effectsof radiation, the entire sequence of events leading to the final chem-ical state of the cell must be known and the mechanisms involvedmust be understood. This sequence of events occurs on a timescaleranging from atto seconds to macroscopic times. The complete setof cross sections resulting from low and intermediate energy elec-tron collisions with DNA molecules or its building blocks are neededas input in Monte Carlo simulations to study damage of living cellsinduced by ionizing radiations [7,8].

Despite the importance of electron interaction studies with DNAand RNA based molecules, the data is limited particularly on theexperimental front. This is attributed to the fact that the electronscattering experiments with complex biomolecules in the gas phaseare challenging because of the difficulties in the preparation ofwell-characterized pure gas targets of these molecules and also thesubsequent quantitative determination of the target densities [8].Theoretical differential and integral cross sections for elastic elec-tron collision (Qel) with adenine, guanine, thymine and cytosine are

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2 M. Vinodkumar et al. / International Journal of Mass Spectrometry 360 (2014) 1– 7

Table 1Target properties [23,24].

Molecule Ionizationthreshold(eV)

Polarizability (Å)3 Bond lengths (Å)

Adenine 8.84 14.63 C–C 1.14C - N 1.34

N–H 1.07C–H 1.04C–H 1.09C–O 1.27

Guanine 8.48 14.06 C–C 1.49C - N 1.37

Cytosine 9.01 10.82 N–H 1.07C–H 1.04C–H 1.09

C–C 1.39C–O 1.27N–C 1.47

Thymine 9.48 11.77Uracil 9.25 9.91Phosphoric acid 11.72 5.36 P–O 1.59 O–H 1.04

reported by Mozejko and Sanche [9] while total cross sections (QT)as a sum of total elastic and ionization cross section are reportedby Mozejko et al. [10] for impact energies 50 eV to 4000 eV. They[10] also reported total cross sections for uracil using the sum ofintegral elastic cross sections obtained by independent atom model[11,12] and ionization cross sections obtained using the BEB formal-ism [13,14]. Blanco and Garcia [15] reported total elastic and totalinelastic cross sections for adenine, guanine, cytosine and thyminemolecules using screening corrected additivity rule. Integral elas-tic cross sections for phosphoric acid at low energy are reportedby three groups Bryjko et al. [16], Winstead and Mckoy [17] andTonzani and Greene [18] while at intermediate to high energy totalelastic cross sections are reported by Mozejko and Sanche [9] andtotal cross section is reported by Mozejko et al. [10]. Recently Bryjkoet al. [16] performed low energy calculations up to 12 eV using R-matrix and computed total integral elastic cross sections. Winsteadand Mckoy [17] used Schwinger multichannel method (SWM) andcomputed integral elastic cross sections up to 30 eV, while Tonzaniand Greene [18] used R-matrix formalism to calculate total elasticcross sections for five DNA and RNA bases viz. adenine, guanine,thymine, uracil and cytosine for low impact energies up to 14 eV.Recently Minaxi Vinodkumar and Chetan Limbachiya [19] reportedelectron impact total cross section and total ionization cross sec-tions for uracil and phosphate group from ionization threshold to2000 eV. Vinodkumar et al. [20] also reported total ionization crosssections for all components of the DNA and RNA molecules viz. ade-nine, guanine, thymine, cytosine, uracil and backbone units (sugarphosphate) from threshold of the target to 2000 eV.

In the present paper, we extend the work and report thetotal cross sections for the DNA and RNA nucleic bases viz. ade-nine, guanine, thymine, cytosine, uracil and phosphoric acid from20 eV to 2000 eV. For computing the total elastic cross sectionsand total inelastic cross sections, we have employed group addi-tivity rule (GAR) in the frame work of SCOP [21,22] formalism.Fig. 1 shows the complete geometrical structure of various com-ponents of DNA/RNA molecule and phosphoric acid along withthe bonding structure [23]. It is shown that while DNA structureconsists of thymine, adenine, guanine and cytosine as nitrogenbases and deoxyribose and phosphate as sugar phosphate backbonemolecules, in RNA, thymine is replaced by uracil and deoxyriboseis replaced by Ribose molecules.

Table 1 lists various target properties of all the components ofDNA and RNA used for the computation of total cross sections. Thedetailed theoretical methodology is discussed in the next section.

2. Theoretical methodology

The electron atom/molecule scattering phenomenon is charac-terized quantitatively by two important cross sections viz. total

elastic and total inelastic cross sections and they combine to rep-resent the total cross sections. Accordingly, we write

QT (Ei) = Qel (Ei) + Qinel (Ei) (1)

where, the first term on the right hand side accounts for all elasticprocesses while the second term takes care of loss of flux in the out-going channels resulting from electronic excitations and ionization.The complete spherical complex optical potential is represented by[21,22]

Vopt (Ei, r) = VR (Ei, r) + iVI (Ei, r) (2)

where the real part of the potential VR consists of static poten-tial (Vst), exchange potential (Vex), and polarization potential (Vp).Owing to the fixed nuclei approximation, the static potential, (Vst)is calculated at the Hartree–Fock level. The exchange potential (Vex)is responsible for electron exchange between the incoming projec-tile and one of the target-electrons. The polarization potential (Vp)combines the short range correlation and the long range polariza-tion effect that arises due to the momentary redistribution of targetcharge cloud which gives rise to dipole and quadrupole moments.The second term of Eq. (2) is the imaginary part of the potentialwhich takes into account all absorption processes. It is to be notedhere that the SCOP as such does not require any fitting parame-ters. All the potentials described vide Eq. (2) are charge-densitydependent. Hence, representation of target charge density is verycrucial. We have employed atomic charge density derived from theHartree–Fock wave functions of Bunge and Barrientos [25].HereDNA/RNA molecules are very complex and their constituents arealso large in size. The single center approach will not be feasi-ble and hence we have employed the group additivity rule [26,27]which is better compared to the independent atom model or simpleadditivity rule [12,13] that overestimates particularly at low impactenergies. Here, the target molecule is represented as an aggregateof scattering centers, which is assumed to scatter the electron inde-pendently. In group additivity rule employed here the geometricalstructure of the molecule is taken into account. The groups where alighter hydrogen atom is bonded with heavier atom such as C, N andO, the charge density of lighter hydrogen atom is expanded at thecenter of heavier atom by employing the Bessel function expan-sion [28].This is a good approximation since hydrogen atoms donot significantly act as scattering center and the cross sections aredominated by the central atom size. In case of the groups havingboth heavier atoms, the molecular charge density is derived fromthe atomic charge densities by expanding them at the center ofmass of the system. Thus, the single-center molecular charge den-sity is obtained as a linear combination of constituent atomic chargedensities, renormalized to account for covalent molecular bonding.The molecular charge density �(r)so obtained is renormalized toincorporate the covalent bonding as described in our earlier paper[29–31].In the SCOP formalism [21,22], the spherical part of thecomplex optical potential is used to solve the Schrödinger equa-tion using partial wave analysis to yield complex phase shifts atdifferent energies. For the present study our absorption potentialis treated elastic to both vibrational and rotational excitations ofthe target.

As discussed earlier the absorption potential takes care of lossof flux into all allowed inelastic channels. For this we have usedmodel potential of Staszewska et al. [32] which is non-empirical,quasi-free, Pauli-blocking and dynamic in nature. The full form ofmodel potential is represented by,

Vabs(r, Ei) = −�(r)

√Tloc

2×

(8�

10k3F Ei

)× �(p2 − k2

F − 2�) · (A1 + A2 + A3) (3)

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M. Vinodkumar et al. / International Journal of Mass Spectrometry 360 (2014) 1– 7 3

Fig. 1. Geometrical structure of different components of DNA/RNA.

The parameters A1, A2 and A3 are defined as

A1 = 5k3

f

2�; A2 =

k3f

(5p2 − 3k2

f

)(

p2 − k2f

)2;

A3 =2�

(2k2

f+ 2� − p2

)(2k2

f+ 2� − p2

)5/2

(p2 − k2

f

)2(4)

The local kinetic energy of the incident electron is given by

Tloc = Ei − (Vst + Vex) (5)

The absorption potential is a function of molecular charge den-sity �(r), incident energy (Ei) and the parameter � of the target.It is not sensitive to long range potentials like Vpol and hence isneglected in local kinetic energy term of Eq. (5). In Eq. (3), p2 = 2Ei, isthe kinetic energy of incident electron in Hartree, kF = [3�2�(r)]1/3

is the Fermi wave vector. Further �(x) is the Heaviside unit step-function, such that �(x) = 1 for x ≥ 0, and is zero otherwise. Thedynamic functions A1, A2 and A3 of Eq. (4) depend differently on�(r), I, � and Ei. The parameter � determines a threshold belowwhich Vabs = 0, and the ionization or excitation is prevented ener-getically. This means � parameter represents the threshold energyfor continuum states i.e. only ionization processes are taken intoaccount, excitation to discrete levels being ignored by the originalmodel [32]. So in order to include the excitations due to discretelevels at lower energy, we have considered � as the energy depend-ent parameter. So, � as a variable accounts for more penetration ofthe absorption potential in the target charge–cloud region [33–36].Following the earlier works in this regard [35], we express � as afunction of Ei around I as

� (Ei) = 0.8I + ˇ (Ei − I) (6)

Here, ̌ is obtained by requiring that � = I at Ei = Ep, where Ep isthe value of Ei at which Qinel attains maximum value. For Ei > Ep,� is held constant equal to Ionization energy of the target as sug-gested in the original model of Staszewska et al. [32]. The choice of� = I throughout the incident energy range would not allow evenexcitation at Ei ≤ I. On the other hand, if parameter � is much lessthan the ionization threshold, then Vabs becomes exceedingly high

near the peak position. The choice of 0.8I is discussed elaboratelyin earlier work by Vinodkumar et al. [35].

After generating the full complex optical potential given in Eq.(2) for a given electron molecule system, we solve the Schrödingerequation numerically with Numerov method using partial waveanalysis. Presently our optical potential is elastic to dipole potentialwhich means we have not considered the Born Closure for higherpartial waves. Hence at low incident electron energies with shortrange potentials, only few partial waves are significant for conver-gence, e.g. at ionization threshold of the target around 5–6 partialwaves are sufficient but as the incident energy increases largenumber of partial waves (∼40 for absorption potential and 200for polarization potential at 2000 eV) are needed for convergence.Using these partial waves the complex phase shifts are obtainedwhich are key ingredients to find the relevant cross sections.

3. Result and discussion

The theoretical approach of Spherical Complex Optical Poten-tial is employed to determine total elastic, and total inelastic crosssections. The total cross section is obtained by taking the algebraicsum of Qel and Qinel. Due to the model potentials adopted and thepartial wave analysis used for the calculations the present resultsinvolve uncertainties of 10% for low energies below 100 eV and5% above it. The total cross sections of adenine, guanine, thymine,cytosine, uracil, and phosphoric acid are plotted as function of pro-jectile energy from 25 eV to 2000 eV, vide Figs. 2–7, respectively.Fig. 8 represents the mutual comparison of total cross sectionsfor all these targets studied in this work. The numerical values ofthe total elastic, inelastic and total cross sections for adenine, gua-nine, and thymine are tabulated in Table 2 and cytosine, uracil andphosphoric acid in Table 3 for ready reference.

Fig. 2 shows comparison of the present total elastic as well astotal cross sections for e–adenine scattering with available results.No experimental data for total elastic as well as total cross sec-tions are available in the literature to the best of our knowledge.The theoretical results for total elastic cross sections are providedby Mozejko and Sanche [9] and Blanco and Garcia [15]. Moze-jko et al. [10] have used independent atom model [11,12] fortotal elastic cross sections and BEB method [13,14] for total ion-ization cross sections, while Blanco and Garcia [15] have usedscreening corrected additivity rule to compute total cross sections.They also [15] presented total cross sections for adenine using AR.The AR results overestimate at low energies (below 100 eV). This

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Table 2Various total cross sections for adenine, guanine and thymine in Å2.

Energy (eV) Adenine Guanine Thymine

Qel Qinel QT Qel Qinel QT Qel Qinel QT

25 92.05 18.54 110.59 86.25 22.34 108.59 70.75 14.45 85.2130 75.94 22.45 98.39 75.26 25.82 101.08 62.96 17.86 80.8240 56.57 26.45 83.02 60.47 29.04 89.51 52.01 21.56 73.5750 45.62 27.58 73.20 50.89 29.78 80.67 44.20 22.95 67.1660 38.96 27.53 66.49 44.51 29.46 73.97 38.39 23.21 61.6070 34.40 26.98 61.38 39.98 28.68 68.66 34.14 22.83 56.5780 30.80 26.25 57.05 35.82 27.82 63.64 30.89 22.16 53.0590 27.87 25.49 53.36 32.71 26.91 59.63 27.58 21.60 49.19100 25.67 24.71 50.38 30.41 25.98 56.39 25.19 20.93 46.12150 19.04 20.95 39.99 23.25 22.02 45.27 18.32 17.90 36.23300 10.86 14.81 25.67 11.76 17.44 29.20 11.61 12.60 24.22500 8.75 9.29 18.04 9.45 11.88 21.34 8.13 9.23 17.361000 4.16 6.17 10.33 4.31 7.78 12.10 4.80 5.64 10.452000 3.14 3.71 6.85 4.02 2.30 6.32 2.71 3.20 5.92

Fig. 2. Total cross section for e-adenine. Solid line: present QT results, short dashline: present Qel results, dash–dot–dot: Mozejko and Sanche Qel [9], dash line: Moze-jko et al. QT [10], dash-dot line: Blanco and Garcia QT [15], short-dot line: Blanco andGarcia Qel [15] (For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.).

overestimation in molecular cross section can be attributed to twofacts: first, the close packed molecule is not fully transparent for lowenergy electrons (Ei < 100 eV) and second, the mutual overlappingby neighbouring atoms is ignored and hence the inner atoms arepartially screened by the outer atoms [37]. Mozejko and Sanche[9] presented total elastic cross sections above 50 eV where IAM[11,12] results are better.

Inspecting the curve one finds that AR results reported fortotal cross sections by Blanco and Garcia [15] are the highest asexpected at low incident energies and gradually it merges withpresent results of QT beyond 100 eV. It is clearly seen from thecurve, that present total cross section results find excellent agree-ment with the results of Mozejko and Sanche [9] throughout theenergy (50–2000 eV). Actually the AR results of Mozejko et al. [10]should slightly overestimate the present results. Instead they are invery good agreement. The reason for this agreement is attributedto the fact that they obtained their total cross section as sum oftotal elastic cross sections obtained using IAM [11,12] and totalionization cross sections obtained using BEB method [13,14] butcontribution resulting from electronic excitations are excluded inthis sum. Hence instead of overestimating slightly they merge withpresent results. The present results show similar nature with theSCAR results of Blanco and Garcia [15] but the SCAR results aremuch lower compared to present results as well as results of Moze-jko et al. [10] below 100 eV. While the SCAR treatment succeedspartially in accounting for geometrical screening corrections atmedium-to-large energies, reliable results are not to be expectedat very low energies due to its semiclassical nature [15,38]. Typi-cal values for screening correction are more than 60% at 10 eV, 30%

Table 3Various total cross sections for cytosine, uracil and phosphoric acid in Å2.

Energy (eV) Cytosine Uracil Phosphoric acid

Qel Qinel QT Qel Qinel QT Qel Qinel QT

25 46.95 11.99 58.94 52.26 13.72 118.32 81.46 9.78 91.2430 43.17 14.55 57.72 42.01 15.83 108.59 70.75 14.45 85.2140 36.75 17.38 54.13 32.22 17.81 101.08 62.96 17.86 80.8250 31.69 18.44 50.14 27.06 18.39 89.51 52.01 21.56 73.5760 27.82 18.64 46.46 24.09 18.36 80.67 44.20 22.95 67.1670 24.95 18.38 43.32 21.75 18.04 73.97 38.39 23.21 61.6080 22.67 17.92 40.59 19.55 17.72 68.66 34.14 22.83 56.5790 20.46 17.49 37.95 18.11 17.28 63.64 30.89 22.16 53.05100 18.86 16.98 35.84 16.87 16.77 59.63 27.58 21.60 49.19150 14.24 14.63 28.87 12.28 15.30 56.39 25.19 20.93 46.12300 10.00 8.24 18.24 4.52 12.81 45.27 18.32 17.90 36.23500 7.44 5.23 12.67 2.85 9.335 29.20 11.61 12.60 24.221000 4.73 2.87 7.60 0.47 5.22 21.34 8.13 9.23 17.362000 2.85 1.53 4.38 0.25 1.32 12.10 4.80 5.64 10.45

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Fig. 3. Total cross section for e-guanine. Solid line: present QT results, short dashline: present Qel results, dash–dot–dot: Mozejko and Sanche Qel [9], Dash line: Moze-jko et al. QT [10], dash-dot line: Blanco and Garcia QT [15], and short dot: Blanco andGarcia Qel [15]. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of this article.)

at 100 eV, 10% at 1 keV [15]. Above 200 eV, their QT results are invery good agreement with the present results as well as results ofMozejko et al. [10]. This agreement at high energies beyond 200 eVis expected as the effect of screening will be reduced gradually withincrease in incident energy. Blanco and Garcia [15] expected 10%errors in their total cross sections.

For total elastic cross sections in Fig. 2, results of Mozejkoand Sanche [9] are slightly higher compared to present results asexpected since they have used IAM [11,12]. SCAR results of Blancoand Garcia [15] are similar in shape but they are very low at lowenergies below 200 eV for the reasons stated earlier for QT. Beyond500 eV all the results tend to merge with present results revealingthe fact that these approximations are much effective only at lowincident energies and their effect gradually decreases with increasein energy.

Figs. 3 and 4 show the present total elastic and total cross sec-tions for e-guanine and e-thymine scattering, respectively, with theavailable comparisons. In case of guanine as well as thymine weobserve similar results with similar comparisons as adenine andthe discussion remains the same and hence not repeated.

Fig. 5 shows comparison of the present total elastic and totalcross sections for e-cytosine scattering along with other availableresults. Total cross sections for e-cytosine scattering are reportedby Mozejko et al. [10] and Blanco and Garcia [15]. The AR plus BEBresults of Mozejko et al. [10] are slightly higher compared to presentresults as expected. However the nature of the curve is similar. TheSCAR results of Blanco and Garcia [15] are lower to the presentresults below 200 eV and are slightly higher thereafter. The samebehavior is also observed for the present total elastic cross sec-tions with results of Mozejko and Sanche [9] whereas the presentresults tend to merge with the SCAR results of Blanco and Garcia[15] beyond 200 eV.

Theoretical results of the total elastic as well as total crosssections for uracil are already published by present authors,Vinodkumar et al. [19]. However, for the sake of complete discus-sion of DNA/RNA units we have presented our earlier publishedresults of the total elastic as well as the total cross sectionsfor uracil [19] in Fig. 6. No measurements for total cross sec-tions are reported for uracil. There are two theoretical datafor total elastic and total cross sections reported by Mozejko

Fig. 4. Total cross section for e-thymine. solid line: present QT results, short dashline: present Qel results, dash line: Mozejko et al. QT [10], dash–dot–dot: Mozejkoand Sanche Qel [9], dash–dot line: Blanco and Garcia QT [15], and Short-Dot: Blancoand Garcia Qel [15]. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of this article.)

and Sanche [9] and Mozejko et al. [10], respectively. The totalcross section of Mozejko et al. [10] is higher compared presentdata of total cross section due to the reason discussed ear-lier for cytosine. The SCAR data for QT and Qel of Blanco andGarcia [15] overestimate the present data beyond 150 eV. Elasticcross sections of Mozejko and Sanche [9] are slightly higher com-pared to present elastic cross sections as expected because thedata produced by IAM overestimates the present data producedby group additivity rule.

In Fig. 7 we compare present results of the total elastic and thetotal cross section for e-phosphoric acid scattering with available

Fig. 5. Total cross section for e-cytosine. Solid line: present QT results, short dashline: present Qel results, dash–dot–dot: Mozejko and Sanche Qel [9], dash line: Moze-jko et al. QT [10], dash-dot line: Blanco and Garcia QT [15], and short-dot: Blanco andGarcia Qel [15]. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of this article.)

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Fig. 6. Total cross section for e-uracil. solid line: present QT results, short dash line:present Qel results, dash–dot–dot: Mozejko and Sanche Qel [9], dash line: Mozejkoet al. QT [10], dash-dot line: Blanco and Garcia QT [15], and short-dot: Blanco andGarcia Qel [15]. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of this article.)

data. The low energy electron scattering is done by Bryjko et al. [16],Winstead and McKoy [17] and Tonzani and Greene [18]. We haveincluded this data to show the trend of the present results withthe low energy calculations as present results are above thresh-old to 2000 eV. One important structure as predicted by Winsteadand McKoy [17] and Tonzani and Greene [18] is clearly seen in thepresent results around 15 eV. Qualitatively, the present results arein good agreement with results of Winstead and McKoy [17] andTonzani and Greene [18] while quantitatively results of Tonzaniand Greene [18] are very high while that of Winstead and McKoy[17] are little higher than present results. Integral elastic cross sec-tions of Mozejko and Sanche [10] are much higher than present

Fig. 7. Total cross section for e-phosphoric acid. solid line: present QT results, shortdash line: present Qel results, dash–dot–dot: Mozejko and Sanche [9], dash-dot line:Bryjko et al. [16], dash line: Tonzani and Greene [18], and short dash–dot line: Win-stead and McKoy [17]. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

Fig. 8. Total cross sections for e -(guanine, adenine, thymine, cytosine, uracil andphosphoric acid. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of this article.)

results near threshold and with the increase in impact energy thedifference is reduced successively.

Finally in Fig. 8 we represent the comparison of DNA/RNAnucleic bases and phosphoric acid collectively. The figure clearlyreflects the facts that total cross sections increases with increasein geometrical size of the target which largely depends on totalnumber of electrons. Apart from the geometric size the other fac-tor which governs the magnitude of the total cross section is theionization threshold. This can be clearly seen in case of cytosineand uracil. Both the targets have the same N, but the ionizationthreshold of cytosine is slightly lower (9.01 eV) compared to uracil(9.25 eV) and hence the cross sections of cytosine is slightly highercompared to uracil. The cross sections for all the targets tend tomerge at high energies reflecting the fact that the time spent bythe projectile with the target decreases, hence decreasing the totalcross sections.

4. Conclusion

Present paper reports comprehensive study of electron impacttotal cross sections for DNA and RNA nucleic bases and phos-phoric acid. SCOP formalism is employed to compute total elasticand total inelastic cross sections. Total cross section is obtainedas an algebraic sum of these two cross sections. Due to the modelpotentials adopted and the partial wave analysis used for the cal-culations the present results involve uncertainties of 10% for lowenergies below 100 eV and 5% above it. It is quite evident from theplots (Figs. 2–8) given in the previous section that present theoryaccounts for the total cross sections very well. Since DNA and RNAare complex molecules, we have used the group additivity approachto evaluate these cross sections which is probably done for thefirst time. Group additivity approach makes use of molecular prop-erties of target rather than atomic properties as in AR and SCARapproaches. One important structure observed in total cross sec-tion results of Winstead and McKoy [17] and Tonzani and Greene[18] is clearly observed in the present results around 15 eV for e-H3PO4. While the present total cross section data compares wellwith AR plus BEB results of Mozejko et al. [10] for adenine, gua-nine and thymine it overestimates slightly (within 10%) for resultsof cytosine and uracil. Similarly the SCAR results of Blanco and

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M. Vinodkumar et al. / International Journal of Mass Spectrometry 360 (2014) 1– 7 7

Garcia [15] underestimates present results considerably at lowenergy as expected for adenine, guanine and thymine but over-estimates beyond 100 eV(within 10%) for cytosine and uracil. Thesituation is similar for total elastic cross section also. In Fig. 8 wehave reported the mutual comparison of total cross sections for thecomponents of DNA and RNA molecules. The study reflects the factthat total cross section increases with increase in geometric sizeof the target as well as ionization threshold of the target. It is thusbelieved that this effort will be more appreciated by the technologywhere cross section data is necessary for further modeling of theirsystems. Also, we hope that our results act as bench mark for theexperimentalists to perform cross section measurements for thesebiologically important targets.

Acknowledgments

Minaxi Vinodkumar acknowledges DST, New Delhi, for themajor research project (SR/S2/LOP/26-2008) and Chetan Lim-bachiya thanks UGC, New Delhi, for the major research project [F.no. 40-429/2011 (SR)] for financial support under which part of thiswork is carried out.

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