54

CHAPTER 3

Atomic P & Phosphorus molecules – The DNA

relevance

3.1 Introduction and motivation

It is well known that the biogenic elements (H, C, N, O, S, P) and organic

molecules [1] are some of the important constituents of the universe. The question of how

life began on Earth does not have an exact answer and inevitably there is scientific

speculation. There is evidence [2, 3] to support the view that a vast array of exotic but

important chemicals have been delivered to Earth through impacts from interstellar

objects.

Gulick [4] recognised a central role of phosphorus in the origin-of-life question

and pointed out a major problem. The principal source of prebiotic phosphorus present on

Earth crust was inorganic phosphate (containing the PO43- unit), which is insoluble in

water. Presumably, the solution phase of phosphates would be poorly available as a

biological nutrient on the early Earth. This question leads to consider extraterrestrial

sources of phosphorus and indeed, such sources exist. The phosphorus-containing

molecules like PH, PH2, PH3, PO, PO2, PN and PCradicals, have been observed in

interstellar gas clouds [5 - 7] and they are proposed to be present under appropriate

conditions. In a landmark paper of Cooper et al [8], the first account of the presence of

phosphonic acids in meteorites was published. Specifically, they observed water soluble

alkyl-phosphonic acids. Thus, Phosphorus is a bio-element important in the development

of life [9] and hence this chapter is aims to explore atomic phosphorus and its

compounds.

55

The present chapter addresses theelectron scattering cross sections, starting from

atomic P and several diatomic and large polyatomic phosphorus bearing molecules. After

atomic P, the next target of our study is Phosphorus monoxide (PO) which is an

important constituent of carbon rich stellar atmosphere [10]. Then, the dimer P2, is

principally an exotic gas phase species of astrophysical interest [11].Recently, Cummins

et al [12] have discussed direct inclusion of phosphorus atoms into organic substrates

that can have application in electronics.

It is interesting to study electron impact processes by Phosphorous hydrides

because of numerous applications. PH is major form of Phosphorus bearing molecule

near the photosphere as the spectrum of PH is observed in the Sun [13]. These radicals

are also detected in cool stellar atmosphere [14] and circumstellar envelopes. Phosphine

(PH3) has a wide range of industrial application, as for example it is used for the

production of P2 dimer. It is also an important doping agent in the semiconductor industry

and is widely used as source of phosphorus for InP and GaP thin film production [15]. It

is used to achieve devices for quantum computing. Also, presence of these molecules was

reported in the atmosphere of Jupiter, Saturn [16, 17] and Earth [18]. So, these

moleculesmust be playing important role in reaction mechanisms and atmospheric

chemistry of the interstellar and planetary systems [5, 19].

High energy ionizing radiation entering human body quickly attenuates via some

energy -loss process that liberates a large number of low energy (0–20 eV) secondary

electrons. These electrons then interact with bio-molecules such as water [20, 21], sugars

[22] and DNA bases [23 - 26], and have been shown to cause significant damage to DNA

through the process of dissociative attachment [27, 28]. This either directly leads to

single or double DNA strand breaks or it results into the formation of free radicals, which

can then chemically react with DNA to leading to strand break. Therefore, for complete

understanding and better physical description of all events leading to DNA damage we

must examine process induced by ionizing radiation. Comprehensive studies of Low

Energy Electron (LEE) interactions with deoxyribonucleic acid DNA, ribonucleic acid

RNA, their subunits, and molecular constituents of these biomolecules are necessary.

56

Especially, LEE interactions with components of DNA backbone, which consists of

repeated sugar-phosphate units, should be studied extensively.

Electron interactions with tetrahydrofuran (THF) – C4H8O have been studied

because it serves as a convenient model for the sugar ring in the DNA backbone. In

particular, the backbone of DNA may be viewed as a series of THF molecules held

together by phosphate bonds to which the bases are attached. Phosphate anion (PO4-)

forms the backbone of DNA. So in a way phosphoric acid – H3PO4 and trimethyl

phosphate (TMP) - OP(OCH3)3 is analogous to phosphate group present in DNA, and an

important constituent of DNA. Moreover, Phosphoric acid exists in atmosphere in form

of aerosols at lower altitudes (<30 km), whereas at higher altitudes it present in gaseous

form. Thus, Phosphates play an important role in terrestrial biochemistry, since they form

in combination with sugars; they form the backbone component of DNA and RNA.

Knowledge of ionization cross sections of Phosphorus bearing compounds can be an

important tool to study the damage of living cells; and study of Phosphorus chemistry for

‘Panspermia’ (hypotheses on the origin of life). With this background we were motivated

to investigate electron scattering with atomic P and related molecules.

3.2 Atomic Phosphorus

This atom is member of group 15 in the periodic table, wherein Nitrogen is the

lightest atom in this column. The stable molecular form of nitrogen is triply bonded

N2nitrogen molecule, whereas the stable molecular form of phosphorus is the tetrahedral

P4 molecule, which is an interesting dichotomy. Atomic P is less studied target in terms

of electron interactions. Here we have calculated the total ionization cross sections for

atomic P in its ground state as well as the metastable state. Our theoretical method of

calculations has been adequately discussed in chapters 2. In essence, we calculate by

SCOP and deduce by CSP- ic, vide equations (2.5.1) to (2.5.4).

In table 3.1 we have shown target properties of atomic P along with the

parameters used for CSP- ic. In table 3.1 EP is the incident energy at which Qinel gets its

maximum and using this value of EP in CSP- ic method we derived a, C1 and C2

parameters which are also mentioned in the table.

57

Table 3.1 Target properties of P atom in its ground state

Atom Ionization

potential (eV)

Ep a C1 C2

P 10.48 45 12.22 -1.61 -8.20

Table 3.2 Ionization cross sections Qion (in Å2) of Atomic P in their ground state

as well as mixture of ground and metastable state.

Ei(eV) P(GS) P(80% GS & 20% MP)

15 0.62 0.83

20 1.73 2.17

25 2.62 3.23

30 3.23 3.94

40 3.89 4.69

50 4.06 4.84

60 4.07 4.78

70 3.94 4.59

80 3.78 4.38

90 3.62 4.17

100 3.47 3.99

150 2.90 3.28

200 2.52 2.81

300 2.03 2.23

400 1.72 1.87

500 1.50 1.62

600 1.34 1.44

700 1.21 1.30

800 1.11 1.18

900 1.02 1.09

1000 0.95 1.01

2000 0.57 0.60

58

Atomic P has ground as well as two significant metastable states, which give rise

to the probability of presence of metastable state in the atomic beam used for cross

sections measurement[29]. For this reason Santos and Parente [30] have calculated the

ionization cross sections of Phosphorus at ground and metastable state as well. They

assumed that 60% phosphorus atom in their ground state 4S and 40% in 2P state and

found better agreement with experimental measurements of Freund et al [29]. In similar

manner, we have taken 80 % phosphorus atoms in their ground state and 20 % atoms in

excited 2P state, which seems to be reasonable. It appears that presence of 40 % atoms in 2P state in the experimental beam is rather larger fraction, and the experiment does not

spell out this clearly. Our results are well matched with Freund et al [29] at peak position

as shown in figure 3.1.

Figure 3.1: Total ionization cross sections of Phosphorus atom by electron impact. Green solid line Present results of Qion (80 % G.D + 20 % M.P); Dash dot dotQion for ground state; Dash dot Qionfor P state; Circle Qion of Freund et al [29].

10 100 10000

1

2

3

4

5

6

Phosphorus

cros

s-se

ctio

n(Å2 )

E(eV)

Qion

Ground State Qion Metastable P state Total Q

ion (80% G.D +20% M.P)

Freund

59

Here for atomic P we have also applied the same analogy. We have calculated the

cross sections of ground state phosphorus. We have also computed the cross sections for 2P metastable (MP) states as shown in figure 3.1. To reach the experimental scenario, we

have taken a mixture of 80 % G.D and 20 % M.P. As seen in the figure at lower and at

higher energies the experimental measurements are higher than the present results. Apart

from this our result basically highlights the cross sections for the ground state Phosphorus

atoms. In table 3.2 we have tabulated ionization cross sections of ground state as well as

mixture of ground and metastable state of P atom. In general experimental results on

atomic beams are more or less influenced by metastable contaminations [29].

3.3 Simple compounds of phosphorus

Let us now examine electron scattering with small molecules constituting

Phosphorus. We choose the molecules of astrophysical significance such as PO and P2.

The most stable form of Phosphorus element that is tetrahedral P4 molecule commonly

known as whitephosphorus is also included in the list.

In the previous chapter we have discussed the basic theoretical formalism to

calculate scattering cross sections. The method basically starts with simultaneous elastic

and inelastic electron scattering represented in the complex potential V(r, Ei) = VR(r, Ei) +

iVI(r, Ei), where r is the radial distance from the mass-centre of the target, VR(r, Ei) is the

real part and VI (r, Ei) is the imaginary part of the total potential. The real part consists of

static, exchange and polarization terms and the imaginary term is the absorption potential

Vabs as described in [31, 32]. The basic input required in constructing all these model

potentials is the atomic or molecular charge density. Since the targets are small

molecules, we have applied single centre expansion in order to obtain the charge density

of the molecules. Then we have computed the potentials to be used in Schrodinger

equation and solve it to obtain the cross sections QT,Qel andQinel.

Next, from our method CSP-ic the ionization cross sections and total excitation

cross sections are computed from Qinel. In the forthcoming sub-sections ionization cross

sections of the molecules PO, P2 and P4 are reported along with the comparison of the

60

results. Physical properties of the targets and parameters obtained from CSP-ic are

tabulated in Table 3.3.

Table 3.3 Molecular properties and parameters used for simple phosphorus

bearing molecules PO, P2 and P4

Target Ionization

potential (eV)

Bond

Length (Å)

Polarizability

(Å3)

Ep a C1

C2

PO 8.39 1.476 2.304 80 6.919 -0.955 -8.289

P2 10.53 1.893 5.155 100 6.192 -0.998 -7.204

P4 9.9 2.22 11.33 65 10.064 -1.635 -6.766

3.3.1 Phosphorus oxide radical (PO)

10 100 10000

2

4

6

8

10

12

ioni

zatio

n cs

(Å2 )

Ei (eV)

Present Qion P4 P2 PO

Figure 3.2: Total ionization cross sections (in Å2) of PO, P2 and P4 by electron impact. Blue solid line - present Qion of P4; green solid line - present Qion of P2; red solid line -Qion for PO.

61

Much work is done on spectroscopic data of the PO molecule but electron impact

processes are almost untouched in this case. To the best of our knowledge, there is no

data available for the target in the literature up to date. The cross sections of electron

impact on PO may supplement essential input formation of phosphonic acids in

meteorites. In figure 3.2 we have plotted our present ionization cross section for PO. We

have also compared the cross sections of PO with those of P2 and P4. It is clear from the

figure that cross sections Qionof PO are smallest while that of P4 are thelargest amongst

the three targets. This is because out of the three molecules PO is smallest and its

polarizability is also the smallest (table 3.3). We can also infer that the magnitude of

ionization cross sections depends on size and polarizability of molecules. The number of

electrons and ionization threshold of PO is smaller than P2 and P4 molecules. These facts

are reflected and explained by the peak positions and magnitudes of all the three targets

studied. Present ionization cross sections of PO, P2 and P4 are listed in Table 3.4.

3.3.2 P2 and P4

Not much literature is available on the ionization cross sections forP2 and P4

molecules. Molecular properties of these targets are listed in table 3.3. Monnon et al [33]

has measured direct ionization and dissociative ionization cross section of P2 and P4

molecules and these are the only measured data available till date. Bettaga et al [34]

have computed elastic cross section for electron scattering at low energy implementing

Schwinger Multichannel Method with Pseudopotentials. Scott [35] has calculated peak of

ionization cross sections of these molecules applying the binary-encounter-Bethe (BEB)

method and used effective core potential. Here we discuss our electron impact ionization

cross sections of these exotic species. The cross sections Qion of these molecular targets

are exhibited in table 3.4.

In figure 3.2 we have shown our present results on cross section calculation of P2

and P4. In the figure 3.3 we have also plotted our present ionization cross section of P2

and P4 as against our Qion of atomic phosphorus. The sequence shown in the figure 3.3

appears satisfactory and has broad peak. Adding the cross section of atomic P twice, we

obtain the cross section of P2 and is called Independent Atom Model (IAM). In similar

manner using IAM ionization cross section of P4 is obtained and plotted, as shown in the

62

figure. There is some discrepancy of in the data of ionization cross section for P4

published in earlier works. Peak of ionization cross section for P4 measured and reported

by Monnom[33] is 21 Å2, and calculated peak of ionization potential using BEB for

effective core potential is 15.1 as stated in Scott [35]. On the other hand, from the figure

we can see that the ionization peak for P4 using IAM is 15.65. So, this aspect needs

further detailed study, in order to verify and explain such variations.

Table 3.4: Ionization cross sections (in Å2) of phosphorus bearing molecules in

their ground state

Ei PO P2 P4 15 0.69 0.28 0.81

20 1.77 1.31 2.98

25 2.68 2.59 5.31

30 3.39 3.77 7.34

40 4.40 5.10 9.75

50 4.80 5.68 10.36

60 5.05 6.01 10.65

70 5.22 6.18 10.63

80 5.31 6.29 10.52

90 5.30 6.36 10.38

100 5.25 6.41 10.24

150 4.96 6.23 9.62

200 4.62 5.91 9.03

300 4.04 5.18 8.12

400 3.60 4.58 7.38

500 3.24 4.10 6.78

600 2.97 3.71 6.27

700 2.73 3.38 5.83

800 2.52 3.10 5.45

900 2.35 2.87 5.11

1000 2.19 2.66 4.81

2000 1.26 1.55 2.97

63

10 100 10000

2

4

6

8

10

12

14

16

ioni

zatio

n cs

(Å2 )

Ei (eV)

QionP

4 present IAM (P4)

P2 present IAM (P2)

Atomic P

Figure 3.3: Present Qion for Atomic P, molecular P2 and P4, also ground state P-atom. Black dot- Atomic P; Orange line - P2Qion using single centre expansion; Pink line -Qion for P4 using single centre approach; Green dash - P2Qion using Independent Atom Model (IAM) ; Blue dash - P4Qion using IAM.

3.4 Hydrides of Phosphorus PHx(x=1–3)

For hydrides of Phosphorus, we intend to compute various total cross sections, viz.,

QT= Qel+ Qinel (3.4.1)

With Qinel = ΣQexc + Qion (3.4.2)

As we know Qinel(Ei) ≥ Qion(Ei) (3.4.3)

This is the basis for the CSP-ic method, already discussed in Chapter 2. Our

calculation of all these TCSs is based on a complex scattering potential, generated from

64

spherically averaged charge densities of the target molecules obtained by the single

centre. The molecular charge density ( )r . Here in table 3.5 and 3.6 we have shown

target properties andCSP-ic parameters (a, C1, C2) respectively for PH3 molecule.

As can be seen from table 3.5 these molecules are weakly dipolar and possess

very small dipole moment. A molecule with dipole moment D will exhibit long range

dipole potential at large r , and the form is given by [36]

2

ˆr

rDrV rD

(3.4.4)

The cross section for rotational excitation (J → J’) in a linear rigid rotator can be

calculated analytically [36] by applying the Born approximation to VD, and is given by

2

2

8( ) ( , ) ln3 2 1rot i JJ i

D J k kQ E Q D Ek J k k

(3.4.5)

Where, D is the dipole moment;k and k’ are the initial and final wave-vector

magnitudes of the scattering electron. Thus, Qrot calculated this way are added to the

QTto acquire the grand total cross sections QTOT of polar molecules. Thus we have,

( ) ( ) ( )TOT i T i rot iQ E Q E Q E (3.4.6)

Table 3.5 Molecular properties of phosphorus hydrides

Targets Ionization

potential (eV)

Bond

Length (Å)

Polarizability

(Å3)

Dipole

moment

(Debye)

PH 10.26 1.422 2.41 0.769

PH2 9.82 1.428 2.329 0.863

PH3 10.11 1.421 3.043 0.580

65

Table 3.6 Table of parameters for hydrides of phosphorus

Targets Ep a C1 C2

PH 55 8.707 -1.603 -6.056

PH2 70 8.796 -1.602 -6.113

PH3 55 5.873 -1.037 -6.629

3.4.1 PH3

Hardly any experimental work on phosphine (PH3) and other targets is carried out

due to its poisonous nature. Grand total cross sections of electron impact on PH3 are

reported by Aryasinghe et al [37] for electron energy range of 90 – 3500 eV. Absolute

cross section was measured by Szmytkowski et al [38] in energy range of 0.5 – 370 eV.

Mark et al [39] measured ionization cross sections PH3 upto 183 eV.

Many theoretical works on PH3 has been reported till date. Integral and

differential elastic CS for the hydrides of the V group (PH3, AsH3, SbH3) of the periodic

table is calculated by Bettega et al.[40, 41]. The differential, integral elastic and

momentum transfer cross sections for PH3 at 1–40 eV were calculated by Winstead et al.

[42] using Schwinger Multichannel (SMC) method. Bettega and Lima also estimated

integral elastic cross sections for low energy range 0.5 – 8 eV through SMC method. Jain

[43] used complex optical potential method to evaluate elastic and inelastic cross sections

for intermediate electron energy range. Varella et al [44] have reported cross sections for

rotational excitation by implementing SMC with pseudopotentails. Munjal and Baluja

[45] calculated the cross sections within 0.025–15 eV using R-matrix method. Recently,

Limbachiya et al [46] reported only the total elastic cross sections over a wide energy

range.

66

Table 3.7: Elastic and grand total cross sections (in Å2) of various phosphorus

hydrides PHx (x = 1, 3)

Ei PH3 PH2 PH

Qel QTOT Qel QTOT Qel QTOT

15 31.19 32.49 29.91 31.30 28.62 29.56

20 25.49 29.04 23.39 26.89 22.12 24.68

25 20.77 26.33 18.78 24.04 17.63 21.59

30 17.09 24.08 15.46 21.89 14.51 19.44

40 12.27 20.49 11.01 18.50 10.29 16.29

50 9.08 17.59 8.07 15.86 7.43 13.91

60 7.58 15.78 6.71 14.22 6.09 12.44

70 6.82 14.60 5.98 13.09 5.38 11.43

80 6.27 13.62 5.49 12.21 4.92 10.65

90 5.85 12.80 5.12 11.48 4.58 10.01

100 5.52 12.11 4.82 10.85 4.31 9.47

150 4.42 9.66 3.86 8.66 3.45 7.57

200 3.75 8.13 3.28 7.28 2.94 6.38

300 2.94 6.27 2.58 5.65 2.32 4.98

400 2.44 5.16 2.15 4.66 1.94 4.12

500 2.10 4.40 1.86 3.99 1.68 3.53

600 1.85 3.87 1.64 3.51 1.49 3.12

700 1.67 3.46 1.48 3.15 1.34 2.80

800 1.53 3.14 1.36 2.87 1.21 2.52

900 1.41 2.89 1.26 2.64 1.12 2.32

1000 1.32 2.69 1.18 2.46 1.07 2.20

2000 0.83 1.59 0.76 1.48 0.70 1.35

67

10 100 10000

10

20

30

40

50

60QTOT

present Aryasinghe Szmytkowski

Qel

present Jain Bettaga

Qion present Mark

TCS(

Å2 )

Ei (eV)

Figure 3.4: Present QTOT, Qel and Qion for e – PH3 scattering. QTOT → solid line present QTOT, circle – Aryasinghe et al [37], star – Szmytkowski et al [38]. Qel → Dash – present Qel, dash dot –Jain et al[45], dotted line- Bettaga [40], Qion → dash dot dot - present Qion; left triangle – Mark et al [39].

The numerical values of elastic and grand total cross sections of PH3 in the energy

range of 10 – 2000 eV are displayed in Table 3.7. Consider now figure 3.4 corresponding

to e – PH3 scattering. The grand total cross sections are below the measured values of

cross sections at lower energies, but at higher energies above 200 eV it is in good accord

with the reported measurements of Aryasinghe et al [37]. The ionization cross sections

are slightly greater than the only experimental measurement of Mark et al [39]. In this

figure we have also shown Qel which is again lesser than the other theoretical data given

by Jain et al [45].

68

From the figure 3.4 we observe a reasonable agreement between our present

calculations and the only experimental ionization cross section reported by Mark et

al[39]. At higher energies elastic cross sections and ionization cross sections have almost

an equal value. The values Qionfor PH3 are tabulated in table 3.8.

Table 3.8: Present Qion (in Å2) for various phosphorus hydrides PHx (x = 1, 3)

Ei PH3 PH2 PH

15 0.44 0.49 0.31

20 1.72 1.71 1.23

25 3.09 2.94 2.20

30 4.21 3.89 2.97

40 5.44 4.95 3.97

50 5.95 5.45 4.54

60 5.98 5.48 4.63

70 5.86 5.36 4.55

80 5.68 5.19 4.43

90 5.49 5.02 4.29

100 5.30 4.85 4.15

150 4.49 4.11 3.53

200 3.89 3.55 3.06

300 3.08 2.84 2.46

400 2.57 2.37 2.06

500 2.20 2.04 1.78

600 1.95 1.81 1.58

700 1.74 1.62 1.42

800 1.58 1.48 1.28

900 1.45 1.35 1.18

1000 1.35 1.26 1.11

2000 0.75 0.72 0.64

69

10 100 10000

1

2

3

4

5

6

ioni

zatio

n cs

(Å2 )

Ei (eV)

Qion PH3 PH2 PH

Figure 3.5: Comparison of Present Qion for PHx (x =1 – 3). Solid line – present for Qion PH3; dash – present for Qion PH2; dotted line – present cross sections for PH.

Figure 3.5 compares ionization cross sections of all the three hydrides of Phosphorus.

The figure clearly indicates dependence of cross sections on polarizability of the targets.

Here we observe, Qion (PH3) >Qion (PH2) >Qion (PH).

Also, we know polarizability (α0) trend as follows.

α0 (PH3) >α0 (PH2) >α0 (PH),

This implies that cross sections (apart from the number of electrons) are directly

proportional to polarizability of the targets under study. This leads to interesting aspect of

relation between Qion and polarizability, which will be discussed in depth in chapter 6 of

the thesis.

70

3.4.2 PH and PH2

For PH the only available electron impact calculation is reported by Rajvanshi

and Baluja [47] that too for low energy region (0 – 10eV) using R – matrix method. To

best of our knowledge there is no work on Phosphino (PH2) for electron impact. Till now

figure 3.6 and 3.7 describes the cross sections of these molecules in the incident energy

range of 15 to 2000 eV.

10 100 10000

5

10

15

20

25

30

TCS(

Å2 )

Ei (eV)

Present QTOT Present Q

el Present Q

ion

Figure 3.6: Present QTOT, Qel and Qion for e – PH2 scattering.

71

10 100 10000

5

10

15

20

25

30

35

TCS(

Å2 )

Ei (eV)

present QTOT

present Qel

present Qion

Figure 3.7: Present QTOT, Qel and Qion for e – PH scattering.

3.5 DNA sugar phosphate backbone

Nucleic acids molecules are essential for life on Earth, as these are building

blocks for living cells and define characteristics of a living being. There are two basic

types of nucleic acid, DNA (deoxyribonucleic acid) and RNA (ribonucleic acid). Nucleic

acids have the same basic structure in all organisms. DNA the basic unit of life consists

of two long polymers of simple units called nucleotides. A nucleotide comprises

nitrogenous base with backbone made of sugars and a phosphate groups as shown in

figure 3.8.

72

Figure 3.8 Structure of DNA nucleotide and double helix structure of DNA

The mutagenic effects associated with change in genetic expression of DNA or

DNA strands breaks by ionizing radiation has become the subject of considerable

research. The strand break caused by ionizing radiation is primarily due to collisions with

secondary electrons produced after interaction of high energy radiation with the target.

The mechanisms by which such degradation occurs has become an important area for

considerable research effort. Owing to the size and complexity of the DNA molecule,

details on the mechanisms involved in the bond breaking processes is usually inferred by

comparing the results of LEE experiments on DNA and the results of LEE impact on

basic building blocks of DNA by several theoretical and experimental methods. Hence,

there is a need to perform measurements/ calculations on its isolated constituents, such as

nucleic bases and nucleosides, applying different experimental or theoretical methods.

73

Figure 3.9: Structure of trimethyl phosphate, tetrahydrofuran (THF) and

phosphoric acid molecules.

First experiment of low-energy electron scattering from condensed DNA was

performed by Boudaiffa et al [48]. Experiments with DNA were performed with thin

films of short strands or plasmids [49]. Gas and solid phase experiments have been

performed with isolated components of DNA (the base, phosphate, sugar and water

subunits) [50]. Sodium dihydrophosphate and tetrahydrofuran with its derivatives were

chosen as analogs of the phosphate group and the sugar ring of DNA, respectively [50,

51]. Recently, Quantum mechanical models developed to describe LEE scattering from

DNA and its subunits has been completely summarized recently [52].

However electron scattering experiments with bio-molecules e.g., nucleotide

bases, nucleosides, amino acids, peptides in the gas phase remain sparse since there are

many practical difficulties in preparing well characterized pure gas targets of these

molecules and it is difficult to determine target number densities. Hence there is need for

more comprehensive theoretical investigations of electron scattering from such targets,

with the models of radiation damage requiring an evaluation/estimation of the various

cross sections for such bio-molecules.

We have used the theory of modified group additivity method to calculate QTand

Qion for all large stable molecules of biological relevance. In this method, the cross

sections for different chemical functional groups in the molecule were calculated by the

single centre approach and then contributions are added together to get the total cross

section of the molecule. The number of scattering centres and their positions depend on

the geometrical structure of the molecule.

74

Table 3.9: Molecular properties for THF, H3PO4 and TMP

Target Ionization

potential

(eV)

Bond Length (Å) Polarizability

(Å3)

Dipole

moment

(Debye)

Geometric

correction

factor Z

THF 9.55

CH 1.11

7.22 1.63 0.771 CO 1.42

CC 1.53

H3PO4 11.72

PO1 1.46

5.67 3.461 0.831 PO2,3,4 1.58

OH 0.96

TMP 9.99

PO1 1.47

10.86 3.3 0.683 PO2,3,4 1.61

OC 1.44

CH 1.08

For example the phosphoric acid (H3PO4) molecule will have four scattering

centres one at P and three at O atoms (refer figure 3.9). It has got three OH groups and

one PO group, and hence four scattering centres. The charge density for the OH group is

obtained by expanding H on O and is re-normalized to get the total number of electrons

in that group. Similarly the charge density for the other centre at P is also obtained.

Electron impact cross sections for each of these groups are obtained using the ionization

potential of the molecule. Then the cross section contributions from each of the centre are

added together to get the total cross section for the molecule. Simple addition of the cross

sections computed for the constituent groups overestimates the cross section values of the

molecules. This is because the bonding effects amongst the functional groups are not

taken into considerations that lead to overestimation. Here we are implementing Modified

Group Additivity Rule with Z correction, in order to reduce the overestimation. So we are

multiplying the added cross sections with Z factor and incorporate the geometric

75

correction as explained in chapter 2. The molecular properties of all the three targets are

listed in table 3.9. Also, in table 3.10 the parameters obtained from CSP-ic are displayed.

3.5.1 Tetra Hydrofuran (THF)- C4H8O

THF represents an analogue to the furan structure of the sugar in DNA backbone.

Due to this reason, a number of papers have been published on this target till date. Zecca

et al [53] and Mozejko et al [54] measured the absolute total cross section for electron

scattering by gas-phase THF. The elastic differential cross section (DCS) at 20 eV and

above was measured by Milosavljevi´c et al [55]. Absolute elastic cross-sections in the

energy range of 6.5–50 eV and angular range between 10◦ and 130◦ were measured by

Colyer et al [56], in the ranges 6–20 eV and 20◦–180◦ by Dampc et al [57]. Allan [58]

reported measurements of differential elastic, total elastic and vibrational excitation cross

sections over energy range from 0.1 eV to 20 eV. Homem et al [59] reported absolute

differential elastic cross section for THF at intermediate energy range (50 – 1000) eV.

Vibrational excitation cross sections have been measured very recently by Dampc et al

[60]. Several high-level scattering calculations on THF have been reported. Trevisan et al

[61] reported an ab initio calculation of the elastic differential and momentum-transfer

cross sections using the complex Kohn variational method. Winstead and McKoy [62]

calculated the elastic differential and momentum-transfer cross sections using the

Schwinger multichannel method. Bouchiha et al [63] used the R-matrix method with

Born correction to calculate the angle-integrated elastic cross section, inelastic cross

sections and the energies for a number of resonances. Tonzani and Greene [64] calculated

the integral elastic cross section and gained further insight into the resonant structure by

considering time delay. Pawel [65] reported elastic and ionization cross sections for THF

and H3PO4 within intermediate energy range. The only experimental measurement for

ionization cross section is recently reported by Dampc et al [66].

76

Table 3.10 Present values of parameters Ep, a, C1and C2

Targets Ep a C1 C2

THF 55 9.786 -1.625 -6.640

H3PO4 90 6.53 -0.974 -7.734

TMP 85 7.003 -0.952 -8.402

Table 3.11: Present QT, Qel and Qion (in Å2) for tetrahydrofuran (THF)

Ei QT Qel Qion

15 42.86 40.79 1.07

20 43.40 37.15 4.16

25 42.73 32.87 7.17

30 41.21 28.71 9.47

40 38.18 22.86 12.01

50 35.51 19.42 12.80

60 33.10 17.06 12.89

70 30.90 15.22 12.72

80 29.03 13.96 12.34

90 27.46 13.05 11.90

100 26.00 12.11 11.56

150 20.29 8.79 9.91

200 17.25 7.57 8.57

300 13.67 6.26 6.79

400 11.43 5.40 5.65

500 9.85 4.75 4.84

600 8.67 4.24 4.24

700 7.75 3.83 3.78

800 7.01 3.50 3.41

900 6.40 3.21 3.11

1000 5.89 2.97 2.85

2000 3.26 1.69 1.55

77

Now consider the electron scattering with THF using Modified Group Additivity

Rule with Z correction. Figure 3.10 shows elastic cross section for the molecule at an

energy range from ionization threshold to 2000 eV. From the figure we can see that there

is very good matching of our results with that of all available experimental cross section.

Starting from low energy, the present results are in excellent matching with the

theoretical data of Tonzani et al who used R- matrix method for cross section

calculations. As expected, result from our calculations are much lower than values

reported by Pawel et al [65], this is because Pawel group has used independent atom

model to calculate the cross sections which are going to be higher. At high energies also

the cross sections are within the error bar of measurements reported by Homem et al. In

table 3.11 we have tabulated the numerical values of present cross sections for THF.

10 100 10000

10

20

30

40

TCS(

Å2 )

Ei (eV)

Qel

present Pawel Tonzani Winstead Homen Allan Coyler Dampc

Figure 3.10:Qel for e – tetrahydrofuran scattering Dash dotted line- present result, dash - Pawel et al [65], solid line Tonzani et al [64], dotted line Winstead et al [68]; star – Homem et al [59], Pentagon – M Allan [58], inverted triangle – Coyler et al [56], circle – Dampc et al [57].

78

In figure 3.11 total cross sections and ionization cross sections are displayed. At

low and high energies, our cross sections are within the error bar of measurements

reported by Pawel etal. But at intermediate energies present result is slightly lower than

the measurements. Moreover, measured cross section published by Zecca et al is much

lower than Pawel et al and hence is lower than our result also. The ionization cross

section for THF as reported in figure 3.11 is in excellent matching with BEB result by

Pawel et al and also with the measurements of Dampc et al. This shows that the

modification introduced in this cyclic molecule is yielding good results and is showing a

good match with the previous work reported for the target THF.

10 100 10000

10

20

30

40

50

TCS(

Å2 )

Ei (eV)

QT

Present Mozejko et al Zecca

Qion

present Pawel DampC

Figure 3.11:QT and Qionfor e – tetrahydrofuran scattering.

QT → solid line – present results; star – Mozejko et al [54]; Diamond – Zecca et al [53]. Qion → Dash – present results; solid line – Dampc et al [60]; Dash dot – Pawel et al [65].

79

3.5.2 Phosphoric Acid - H3PO4

Mozejkoet al [65] computed ionization cross section of H3PO4 using BEB model

and computed differential elastic, total elastic cross sections through independent atom

model. They also calculated differential and integral elastic cross section for the target.

Tozani et al [64] and Bryjko et al [67] applied R-matrix method to calculate elastic cross

section of phosphoric acid. Calculations on low energy collisions with H3PO4 were

performed by Winstead and McKoy [68], who studied electron collisions with conformer

uuu. Phosphoric acid has several conformers or geometrical structures. The uuu

corresponds to conformer with symmetric positions of OH functional groups.

10 100 10000

5

10

15

20

25

30

35

40

45

TCS(

Å2 )

Ei (eV)

QT

Qel

present Pawel Winstead Tonzani Bryjko

Qion present Pawel

Figure 3.12: Present QT, Qel and Qion for e – H3PO4 scattering. QT → green solid line present cross sections. Qel → green solid line present results; Dash – Pawel et al [65]; dotted line – Winstead et al [68]; short dot –Tonzani et al[64]; Blue solid line – Bryjko et al [67]. Qion → green solid line present results; dash dot dot - Pawel et al [65].

80

As shown in figure 3.12 our present result of ionization cross section matches

well with the theoretically calculated cross sections based on BEB by Pawel et al [65].

H3PO4 is a polar molecule having permanent dipole moment of 3.461 debye, due to this

the total cross section shows a peak at lower energies; further the magnitude of QT is

lesser than Qel calculated by other theoretical groups.

Again, at low energy region, present Qel is much less than cross sections

calculated and reported by Tonzani et al [64]. Cross sections reported by Bryjko et al

[67] are slightly greater than the present Qel. As expected, the elastic cross sections by

Pawel et al are greater than the present cross sections, because they used IAM to evaluate

the cross sections. No experimental data of the target is available for comparison.

3.5.3 Trimethyl phosphate - OP(OCH3)3

Another anologue for the phoasphate group of DNA is trimethyl phosphate as in

figure 3.9. Recently Aflatooni et al. [69] have reported DA measurements for TMP,

while Burrow et al. [70] have reported electron transmission measurements for TMP.

Winstead et al [68] computed cross sections for low-energy elastic collisions of electrons

with trimethyl phosphate and phosphoric acid.

The numerical values of present cross sections for TMP and H3PO4 are given in

table number 3.12. The figure 3.13 portrays the cross sections of TMP within the energy

range from 10 eV to 2000 eV. Our present result for Qel at low energies below 20 eV is

much smaller than the values reported in Winstead et al [68]. This may be primarily due

to absence of rotational cross sections at lower energies and TMP being a polar molecule,

the addition of Qrot can improve cross section values at low energy regime. This is again

reflected in present total absolute cross sections of the target. There are no comparisons

of ionization cross sections for the present target.

81

Table 3.12: Present QT, Qel and Qion (in Å2) for phosphoric acid and trimethyl

phosphate

Ei H3PO4 TMP

QT Qel Qion QT Qel Qion

15 30.00 29.22 0.17 45.92 42.96 0.95

20 32.06 28.52 1.38 57.06 48.89 3.64

25 34.11 27.84 2.99 66.00 53.29 6.51

30 34.73 26.28 4.47 69.94 53.79 8.95

40 19.04 22.51 6.73 69.71 49.08 12.56

50 32.25 19.69 7.96 65.95 43.53 14.49

60 30.50 17.63 8.54 61.59 38.70 15.46

70 28.52 15.35 9.07 57.16 34.11 16.13

80 26.74 13.58 9.35 53.41 30.73 16.35

90 25.28 12.37 9.40 50.25 28.14 16.34

100 24.01 11.42 9.37 46.60 24.64 16.58

150 19.04 7.94 8.93 35.43 15.77 16.00

200 15.97 6.24 8.20 27.30 24.61 14.74

300 12.62 4.85 6.91 21.33 20.73 12.63

400 10.64 4.13 5.96 18.05 17.87 11.04

500 9.23 3.62 5.23 15.70 15.71 9.79

600 8.17 3.22 4.67 13.92 14.02 8.79

700 7.33 2.91 4.22 12.50 12.66 7.97

800 6.65 2.64 3.84 11.34 11.53 7.29

900 6.08 2.43 3.52 10.39 10.57 6.71

1000 5.62 2.24 3.27 9.58 9.82 6.22

2000 3.16 1.27 1.86 5.37 5.59 3.42

82

10 100 10000

10

20

30

40

50

60

70

TCS(

Å2 )

Ei (eV)

present QT

Qel

present Winstead

present Qion

Figure 3.13: Present QT, Qel and Qion for e – TMP scattering. dash present cross sections QT;short Dash – present results of Qel; dash dot dot – present Qion

3.5.4 Sugar phosphate

Consider finally the sugar phosphate unit of the DNA polymer. On the theoretical

side, Bernhardt and Paretzke [71] calculated total ionization cross-sections for the DNA

and RNA bases and sugar-phosphate backbone using both the semi-classical Deutsch-

Märk (DM) formalism [72] and the Binary-Encounter Bethe (BEB) formalism [73]. The

figure 3.14 displays present ionization cross sections of DNA sugar phosphate analogue

by adding Qion of THF and H3PO4, and also the cross section of THF added with that of

TMP is also plotted in the same graph. Qion obtained by adding THF and H3PO4 is

slightly lesser than values reported by BEB and DM method in Bendhardt and Paretzke

83

[71]. Whereas, Qion obtained by adding THF and TMP are slightly greater than cross

sections obtained by applying BEB and DM method.

10 100 10000

5

10

15

20

25

30

35

io

niza

tion

cs (Å

2 )

Ei (eV)

Present additivity THF + TMP THF + H

3PO

4DNA sugar phosphate

DM BEB

Figure 3.14:Qion for electron scattering by DNA sugar phosphate unit. Green solid line - present Qion by adding cs of THF and TMP; red solid line - present Qionby adding cs of THF and H3PO4; brown dash dot -Qionusing DM formalism by Bendhardt [71]; blue dash -Qion applying BEB reported by Bendhardt [71]

3.6 Conclusions

In nature, phosphorus compounds are present in both biosphere and minerals, so

knowledge of phosphorus is a part of the prehistoric chemistry. Indispensable for the

global understanding, the studies of electron-induced processes for gas-phase molecules

are also involved in chemical change. The main objective of the chapter is to link the

mechanisms responsible for the damage induced to DNA by electrons by finding the

84

contribution of these surrogates of its constituent building blocks and discuss potential

applications. To achieve this objective Modified Group Additivity Rule has been applied

successfully on large polyatomic molecules to calculate various cross sections. Initially

we started with sugar phosphate backbone, in this the idea of adding cross section of

sugar analog THF with phosphate analogues H3PO4 and TMP worked out quiet

satisfactorily. More work towards this direction can possibly produce some intuitive

proposition of DNA damage by electrons. Large magnitude of ionization cross section for

sugar phosphate unit supports the notion that phosphate backbone plays an important role

in electron induced damage of DNA. A number of analogs of DNA components are

awaited for the calculation, which can be a key to understand radiation damage

mechanism. The field however is infantile and the physics of life sciences is wide open

and challenging.

85

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