Electron scattering from pyridine.

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Electron Scattering from Pyridine Agnieszka Sieradzka, Francisco Blanco, Martina C. Fuss, Zdenek Masin, Jimena Gorfinkiel, and Gustavo Garcia J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 09 Jun 2014 Downloaded from http://pubs.acs.org on June 16, 2014

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The Journal of Physical Chemistry

Electron Scattering from Pyridine Agnieszka Sieradzka,† F. Blanco,‡ M. C. Fuss,¶ Zdenˇek Maˇs´ın,† J. D. Gorfinkiel,∗,† and G. Garc´ıa¶,§ Department of Physical Sciences, The Open University, Walton Hall, Milton Keynes, MK7 6AA, United Kingdom, Departamento de F´ısica At´omica, Molecular y Nuclear, Universidad Complutense de Madrid, 28040 Madrid, Spain, Instituto de F´ısica Fundamental, Consejo Superior de Investigaciones Cient´ıficas, Serrano 113-bis, 28006 Madrid, Spain, and Centre for Medical Radiation Physics, University of Wollongong, 2522 NSW, Australia E-mail: [email protected].

Abstract We have calculated cross sections for elastic and inelastic electron scattering from pyridine in the energy range 1 eV to 1 keV. The R-matrix and IAM-SCAR methods have been used for low and higher collision energies respectively. Agreement with available theoretical data is good. We have also looked at the formation of shape resonances and compared our results with existing experimental data. We compare the results with data for electron scattering with pyrimidine. ∗

To whom correspondence should be addressed Department of Physical Sciences, The Open University, Walton Hall, Milton Keynes, MK7 6AA, United Kingdom ‡ Departamento de F´ısica At´ omica, Molecular y Nuclear, Universidad Complutense de Madrid, 28040 Madrid, Spain ¶ Instituto de F´ısica Fundamental, Consejo Superior de Investigaciones Cient´ıficas, Serrano 113-bis, 28006 Madrid, Spain § Centre for Medical Radiation Physics, University of Wollongong, 2522 NSW, Australia †

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Keywords 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

electron-molecule collisions, cross sections, resonances, organic compounds

Introduction Understanding and characterizing electron scattering from molecules is crucial in a number of applied fields (e.g. plasma processes in both technological and astrophysical environments, radiation damage in biological matter, etc.). Experimental and theoretical/computational techniques continue to be developed and improved in order to provide more accurate quantitative information and detailed insight into the molecular processes induced by electron collisions. 1 Increased interest in understanding, at a microscopic level, the effect of radiation on biological systems has led to the study of electron scattering from biological molecules: 2 nucleobases, deoxyribose, amino acids, etc.. Much of this work has focused on the dissociative electron attachment (DEA) process known to lead to DNA-strand breaks. 3,4 Low energy experimental work has looked at the anions produced in DEA from DNA components. Theoretical work has been mostly restricted to studying resonance (or temporary negative ion) formation, with a few studies investigating the dissociation step in one dimension (e.g. Gallup and Fabrikant 5 ). At the same time, the accurate determination of cross sections for all the possible processes (elastic scattering, target excitation, DEA, ionization, etc.) for a broad energy range is also receiving increased attention. This is due to the need for these data in single-track structure simulations used for modelling radiation-induced damage in biological matter. 6 These simulations require quantitative data for all the possible processes that take place over the whole range of available kinetic energies. Key among these processes are electron collisions, as large quantities of electrons are produced by the primary radiation. 7 Many recent studies, particularly theoretical ones, have focused on model molecules: for 2


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example, tetrahydrofuran was initially studied instead of deoxyribose 8–12 because it has fewer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

electrons (particularly helpful for ab initio calculations) and higher symmetry. Similarly, pyrimidine (C4 H4 N2 ) and its isomers (pyrazine and pyridazine) have attracted significant attention as models for the pyrimidinic nucleobases: thymine, cytosine, and uracil (see Sanz et al. 13 and references therein). These studies provide useful information that can be extrapolated to the scattering processes with the molecules of interest. 14 Differences in the collision processes and cross sections for the diazines are mainly due to their different dipole moment (other properties, like polarizability and ionization energy are very similar for the three of them); low energy resonances are very similar and can be traced back to benzene. It seemed therefore of interest to study pyridine, C5 H5 N, that possesses similar physicochemical properties to the diazines, in order to ascertain how the single (instead of double) substitution of a carbon atom in the benzene ring affects the collision processes and its theoretical description. Low energy electron scattering from pyridine has been studied computationally 15 using the Schwinger multichannel method. The authors reported elastic cross sections as well as the positions of the low-lying π ∗ resonances. Modelli and Burrow 16 and Nenner and Schulz 17 performed electron transmission spectroscopy experiments (ETS) on substituted pyridines and azabenzenes, among them pyridine, respectively. This allowed them to characterize three low-lying (below 5 eV) π ∗ resonances in all these targets.

The R-matrix method The R-matrix method 18 and its application to electron-molecule scattering 19 have recently been described in detail. We will nonetheless briefly summarize the method here. The R-matrix calculations reported in this work have been performed within the fixed-nuclei approximation. The key idea of the R-matrix method is the division of configuration space into two

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regions, an inner and an outer region. These are separated by a sphere of radius r = a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

centred on the centre of mass of the system. The R-matrix sphere must be large enough to contain the charge density of the target states of interest and that associated to the target orbitals used to build the L2 functions (see below). The more complex inner region problem is solved first. In this region, the wave function for the (N + 1) electron system can be written as a linear combination:

ΨΓk (X1 ....XN+1 )

= A +

nc n X X

Φi (X1 ....XN ; ˆ rN+1 ; σN +1 ) ×

i=1 j=1 m X

χi (X1 ....XN+1 )bik ,

uij (rN +1 ) aijk rN +1 (1)

i=1

where Xi represent the space and spin coordinates of electron i and σN+1 indicates the spin coordinates of the (N + 1)th electron. The operator A ensures the antisymmetrization of the whole wavefunction. The functions Φi (XN ; ˆ rN+1 ; σN +1 ) are built as products of the target wavefunctions Φi of each of the n states included in the calculation and the angular (spherical harmonics) and spin functions of the scattering electron. The functions uij describe the radial behaviour of the scattering electron and are generated as linear combinations of Gaussian functions centred on the centre of mass of the molecule. The L2 -integrable functions χi are built as products of target orbitals and they are crucial for the representation of shortrange correlation and polarization effects. The spin-space symmetry of the wavefunctions is denoted by Γ. In order to obtain the coefficients aijk and bik , the matrix obtained from the sum of the (N + 1) Hamiltonian and the Bloch operator 18 is diagonalized. This generates a set of ΨΓk and their associated eigenvalues, Ek , that allow us to describe the (N + 1) system in the inner region. In the outer region, where exchange between the scattering and target electrons can be neglected, a single centre expansion of the electron-molecule interaction potential is used. 4


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The radial functions describing the behaviour of the scattering electron are determined by 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

solving a set of coupled differential equations. This is done by propagating the R-matrix, constructed using inner region (ΨΓk and Ek ) and target (to define the channels) information. This propagation is carried out to a radius large enough so that an asymptotic expansion for the radial wavefunctions of the scattering electron in each channel can be used. K-matrices are determined by matching these to known analytical asymptotic solutions. Integral and differential cross sections, resonances’ properties, etc. can be obtained from these. In our calculations we have used the UKRmol suite 20 and, in order to calculate elastic differential cross sections (DCS), POLYDCS. 21 For polar targets, the fixed-nuclei cross sections diverge due to the long-range nature of the electron-dipole interaction. POLYDCS, implemented by Sanna and Gianturco, uses a frame-transformation method (based on the multipole-extracted adiabatic-nuclei procedure proposed by Norcross and Padial 22 ) to overcome this problem (see Gianturco and Jain 23 for more details). This is one of several first Born approximation based ’top up’ procedures: those partial waves not included in the ab initio calculation are incorporated in an approximate way. (Another way of seeing this approach is by interpreting the ab initio contribution as a correction to the Born cross section.)

The IAM-SCAR method The IAM-SCAR method is based on an independent atom representation (IAM) complemented with a screening corrected additivity rule (SCAR) and it has already been extensively employed to calculate electron scattering cross sections for a wide variety of molecular targets 24–26 over a broad energy range (0.1-1000 eV). We only briefly reiterate the key points of this approach here. Initially, this approximation does not consider the molecule as a single target but as an aggregate of atoms which scatter independently assuming that molecular binding does not affect their electronic distribution. The first subjects of these calculations

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are therefore the constituent atoms, namely H, C and N. Each atomic target is represented 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

by an interacting complex (optical) potential, Vopt (r), whose real part accounts for the elastic scattering of the incident electrons while the imaginary part represents the inelastic processes that are considered as “absorption” from the incident beam. This optical potential can be expressed as: Vopt (r) = Vs (r) + Vex (r) + Vpol (r) + iVabs (r)

(2)

where Vs (r) is the static term derived from the Hartree-Fock calculation of the atomic charge density. 27 Vex (r) is the exchange term which accounts for the indistinguishability between the incident and target electrons. The expression chosen for this term is the semi-classical energy-dependent formula derived by Riley and Truhlar. 28 Vpol (r) is the polarization term which describes the long-range interactions and depends on the target dipole polarizibility, in the form given by Zhang et al. 29 Finally, the absorption potential Vabs (r), which accounts for the inelastic processes, is based on Staszewska’s quasi-free model. 30 Initially some divergences were found when results were compared to the available atomic scattering data. After including some improvements such as many-body and relativistic corrections, screening effects inside the atom, local velocity correction and in the description of the electrons’ indistinguishability, the model proved to provide a good approximation for electron-atom scattering 31,32 over a broad energy range. An excellent example of this is elastic electron– atomic iodine (I) scattering, 33 where the optical potential results compare very favourably with those from a sophisticated Dirac-B-spline R-matrix computation. Within this model we numerically integrate the radial scattering equation and obtain the complex partial wave phase shifts δl . 34 Using these phase shifts, in combination with the optical theorem, we can generate the atomic scattering amplitudes: lmax 1 X (2l + 1)(e2iδl + 1)Pl (cos θ) f (θ) = 2ik l=0

(3)

where θ is the scattering angle and k the momentum of the incident electron. From these we

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can determine differential (dσel /dΩ) and integral (σel ) elastic cross sections, as well as the 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

total scattering cross sections using standard scattering expressions. In order to obtain molecular cross sections, the IAM has been followed by applying a coherent addition procedure, commonly known as the additivity rule (AR). In this approach, the molecular scattering amplitude, F (θ), is derived from the sum of the above atomic molec amplitudes which lead to the differential elastic cross section for the molecule (dσel /dΩ),

according to

F (θ) =

X

fi (θ)eiq·ri

atoms

molec X dσel sin qrij = fi (θ)fj∗ (θ) dΩ qrij i,j

(4)

where q is the momentum transferred in the scattering process and rij is the distance between atoms i and j. molec Integral elastic cross sections for the molecule can be determined by integrating (dσel /dΩ).

Alternatively, elastic cross sections can be derived from the atomic scattering amplitudes in conjunction with the optical theorem 31 giving

molec σel =

X

atoms σel

(5)

atoms

Unfortunately, in its original form, we found an inherent contradiction between the integral cross section derived from those two approaches, which suggested that the optical theorem was being violated. 29 The main limitation of the AR is that no molecular structure is considered, thus it is really only applicable when the incident electrons are fast enough to effectively “see” the target molecule as a sum of the individual atoms (typically above ∼100 eV). To reduce this limitation we developed the SCAR method 32,35 which considers the geometry of the corresponding molecule (atomic positions and bond lengths) by introducing some screening coefficients which modify both differential and integral cross sections, especially for lower energies. With this correction the range of validity of the IAM-SCAR method might be

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extended down to about 10 eV, depending on the target. For intermediate and high energies 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(20-5000 eV), this method has been proved to be a powerful tool to calculate electron scattering cross sections from a high variety of molecules of very different sizes, from diatomic to complex biomolecules. 36 From the above description of the IAM-SCAR procedure it is obvious that vibrational and rotational excitations are not considered in this calculation. However, for polar molecules such as pyridine, additional dipole-induced excitation cross sections can be calculated following the procedure suggested by Jain: 37 differential and integral rotational excitation cross sections for a free electric dipole are calculated in the framework of the first Born approximation (FBA). These are incorporated to our IAM-SCAR calculation in an incoherent way, adding the results as an independent channel. Although rotational excitation energies are, in general, very low (typically a few meV) in comparison with the incident electron energies, in order to validate the Born approximation the latter energies should be higher than about 10 eV. Under these circumstances, rotational excitation cross sections J → J’ are calculated by weighting the population for the Jth rotational quantum number at 300 K and estimating the average excitation energy from the corresponding rotational constants. We call the whole procedure, that it has been successfully used for other polar molecules such as H2 O, HCN, and pyrimidine, 38–40 the IAM-SCAR+Rotations method. Additionally, when the permanent dipole moment of the molecule is relatively large, as is the case of pyridine, the FBA also fails for medium and large scattering angles. In order to partially solve this situation, we introduced a correction based on that suggested by Dickinson, 41 which brings a substantial improvement for electron scattering cross sections with strongly polar molecules. This procedure introduces a first-order corrective term Dck dσ to the differential cross sections for medium and large angles but maintaining the dΩ B FBA correction dσ for lower angles: dΩ dσ B µ2 1 θ ≤ θc ≃ 2 dΩ 6Ei sin (θ/2)

dσ Dck πµ 1 θ ≥ θc ≃ 3 dΩ 64Ei sin (θ/2) 8


(6)

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Here µ is the permanent dipole moment of the molecule and Ei the energy of the projectile. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Providing that the dipole moment is bigger than µ =0.75 Debye, both curves smoothly join together at θc , the critical angle at which they cross each other.

Details of the calculations Pyridine, C5 H5 N, has a vertical ionization energy 42 of around 9.51 eV, a dipole moment of 2.19 Debye 43 and its experimentally determined spherical polarizability 42 is 64 a30 . It has 42 electrons and belongs to the C2v point group. Pyridine is an asymmetric top, but two of its rotational constants differ by less than 5%, so it can be approximated as a symmetric top. Its first electronic excitation threshold is around 4 eV. 44 The calculations presented here are based on the experience gained in the study of electron collisions with diazines, both at low 45,46 and intermediate and high energies. 13,47

R-matrix calculations We used the ground state equilibrium geometry optimized at the QCISD level 42 (other equilibrium geometries were tested with no difference in the scattering results). Following our earlier work, 46 we performed calculations with two different basis sets: a compact, ccpVDZ, and a diffuse one, 6-311+G**. Hartree-Fock SCF (HF) orbitals were generated using MOLPRO 48 and used in the scattering calculation. The calculated ground state energy and dipole moment are listed in Table 1. The agreement of the HF energy with the accurate value for the energies is, as expected, not very good. The dipole moment (very important in the scattering description) agrees much better with the experimental value. We used an R-matrix radius a=13 a0 for calculations with the compact basis set and a=18 a0 for the diffuse one and the appropriate continuum basis sets. 49,50 For the smaller R-matrix radius, we tested the effect of including an extra partial wave (l = 5) in the calculations. We performed the calculations at the Static-Exchange plus Polarization (SEP)

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Table 1: Energy (in Hartree) and dipole moment (in Debye) of the ground state of pyridine calculated at the HF level, using the basis sets indicated in the table. Also listed are the experimental value of the ground state dipole moment 43 and the calculated energy at B3LYP level using the 6-311+G(3df,2p) basis set. 42 E µ

cc-pVDZ 6-311+G** Acc. value −246.71 −246.75 -248.37 2.22 2.43 2.19

level: only the ground state of the target, described at HF level, is included in expression (1). In order to describe short range correlation-polarization effects, we include in the set of L2 functions (χi in expression (1)) configurations of this type: (core)Nd (valence)N −Nd (virtual)1

(7)

with N=42 and Nd =34. Here, ’valence’ denotes all those orbitals occupied in the ground state configuration from which single excitations are allowed, ’virtual’ denotes a subset of those HF orbitals that are unoccupied in the ground state configuration. Unfortunately, it is not possible to determine a priori the optimal number of virtual orbitals to include; if too many are used the calculations can be ’overcorrelated’. 46 Our approach for the diazines and uracil, that we have followed here, is to start with a small number of the lowest energy virtual orbitals and increase this number (always adding orbitals in increasing energy order) until we achieve good agreement with the experimental positions of the π ∗ resonances; for pyridine, we have used the resonance positions of Nenner and Schulz. We have determined as optimal the use of 35 virtual orbitals in the calculations with the compact basis set and 50 when the diffuse basis set is used. These are consistent with those required to obtain the best agreement with experiment in the case of the diazines: 35 and 40 virtuals respectively were enough in that case (although published data 46 used 25 and 35 we have since found out 51 that better agreement is reached when using a few more orbitals). The larger number of virtual orbitals required in the pyridine case when the diffuse basis is used set can probably be ascribed to the fact that these orbitals (due to the absence of the second nitrogen atom) 10


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are more diffuse than those of the diazines. It should be noted that the effect on the cross 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

sections of varying the number of virtual orbitals is weak and smaller than the differences due to employing the compact or diffuse basis sets.

Results Cross sections Figure 1 shows the integral elastic cross section for energies up to 15 eV calculated with the R-matrix method using several models. Both (rotationally summed) Born corrected and uncorrected results are shown. Above the first excitation threshold, our R-matrix SEP calculations suffer from the presence of pseudo-resonances which appear as very narrow spikes in the cross section as can be seen in the Figure. Comparison of the various R-matrix cross sections allows us to conclude that: (i) both compact and diffuse basis sets produce almost identical cross sections, the most noticeable difference being the position of the visible shape resonances (see below), (ii) including an extra partial wave in the R-matrix calculation does not affect the Born-corrected results. Schwinger multichannel results from Barbosa et al. 15 are also plotted in Figure 1. As is the case for the R-matrix results, both an uncorrected cross section and one corrected to include additional partial waves are presented. We can see in the Figure that for energies below 5 eV the uncorrected Schwinger cross section is smaller than the R-matrix one and fairly different in shape. A similar difference in the shape of the cross section obtained with both methods was found for the non-dipolar pyrazine and attributed to the differences in the description of the polarization. 51 We can see that the diffuse basis set R-matrix calculation shows some small indication of a decrease in the 2-3 eV range. Above 5 eV, the size and shape of both uncorrected cross sections is similar. There are a number of differences between the R-matrix and Schwinger calculations that could explain the difference in the uncorrected cross sections: use of different basis sets, of different configurations for the description of the 11



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short-range polarization, different number of partial waves included in the expansion and 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

the fact that R-matrix calculations do not take into account the polarization potential in the outer region. The Schwinger cross section obtained using a Born-closure procedure (’corrected’) is smaller than the R-matrix one in the whole energy range. This is partly due to the fact that the Schwinger integral cross section is obtained integrating the corresponding DCS between 1◦ and 180◦ , whereas the R-matrix cross sections correspond to the integration over the whole energy range (but they are not obtained from a numerical integration of the DCS). Integrating our DCS in the range 1◦ and 180◦ for 6 eV, results in a cross section of around 187 a20 , a smaller value than that of the corrected Schwinger cross section (211 a20 ). The difference between these two values, however, is the same as that between the uncorrected R-matrix and Schwinger cross sections. This means that the difference in the corrected cross sections is therefore mainly due to the different integration ranges. It also indicates that it is unlikely that a different number of partial waves included in the (uncorrected) R-matrix and Schwinger is responsable for the differences between these two cross sections. Figure 2 shows the elastic integral cross section for the whole energy range studied in this work. We see that the size of IAM-SCAR and IAM+Rotations cross sections around 10 eV is reasonably consistent with the R-matrix and Schwinger multichannel uncorrected and corrected cross sections respectively. The shape of the uncorrected cross section is different, but this is not surprising: the IAM-SCAR method is not expected to provide reliable results for energies much lower than ∼30 eV. Nonetheless, the slope of the IAMSCAR cross section above 30 eV and the low energy cross sections below ∼6 eV indicate that a smooth interpolation between both energy ranges is possible. This agreement is similar to that obtained for pyrimidine. 13 The cross section for electron scattering from pyrimidine is similar in size to the pyridine one (the dipole moment of pyrimidine is fairly similar too: 2.334D 52 ). Also plotted in Figure 2 is the total electronically inelastic cross section obtained with the IAM-SCAR method. This cross section is somewhat bigger than

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that for pyrimidine. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

13

Note that this cross section is zero below ∼10 eV, when in fact, the

first electronic excitation thresholds is around 4 eV. This is due to the fact that in the present IAM-SCAR model, electronic excited states lying below 10 eV are ignored. It should be noted that the IAM-SCAR+Rotations cross section is obtained, as explained above, assuming a 300 K population for the initial rotational states. The Born-corrected Rmatrix cross section is determined assuming the molecule is initially in its ground rotational state and summed over all possible final states with J < 9. The comparison of these cross sections is, in principle, not ’like-with-like’. However, recent work on positron scattering from pyrimidine 53 showed that for a rigid rotor with parameters similar to those of pyridine, temperature effects on the cross section are very small below 20 eV. Figure 3 shows DCS for several energies. We observe minor difference between the Rmatrix DCS calculated with different basis sets. For the lower energies we have plotted the R-matrix results together with those of Barbosa et al. 15 The agreement between R-matrix and Schwinger results is good, and fairly independent of the energy. Note that the agreement for small angles (≤ 10◦ ) looks very good, but this is due to the scale of the figure; in fact, although the shape of the DCS is very similar, the size is not. The Schwinger cross section is smaller than the R-matrix one. For 10 eV we have also plotted the IAM-SCAR results: once again, the differences in the shape of ab initio and IAM-SCAR DCS are not surprising as this energy is beyond the range of validity of the method. At higher energies, only the IAM-SCAR/IAM-SCAR+Rotations method is able to provide results. The shape and size of the DCS is very similar to that of pyrimidine below 50 eV. Above this energy, however, the DCS for pyridine seems to be much bigger.

Low energy results: shape resonances The integral elastic cross section in Figure 1 shows clearly the presence of three resonances in both the uncorrected R-matrix and Schwinger results (the resonant peaks are less obvious in 13



Table 2: Positions (and widths), in eV, of the π resonances in pyridine calculated in this work at the SEP level using the basis sets and number of virtual orbitals (Nr. V) indicated. The parameters have been determined using RESON, 54 a Breit-Wigner profile fitting program. Also listed are the positions of the resonances calculated by Barbosa et al. 15 at the SEP level considering only singlet-coupled excitations and the experimental results of Nenner and Schulz 17 and Modelli and Burrow. 16 ∗

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nr. V Basis set cc-pVDZ 25 Basis set cc-pVDZ 35 Basis set cc-pVDZ 40 Basis set 6-311+G** 50 Barbosa et al. Nenner and Schulz Modelli and Burrow

2

B1 1.15 (0.057) 0.77 (0.022) 0.48 (0.01) 0.67 (0.027) 0.90 0.62 0.72

2

2 A2 B1 1.46 (0.058) 5.8 (0.60) 1.11 (0.025) 5.51 (0.48) 0.96 (0.016) 5.32 (0.48) 1.07 (0.030) 5.33 (0.47) 1.33 5.80 1.20 4.58 1.18 4.48

the Born corrected cross sections but visible nonetheless) below 6 eV. The pseudoresonances present in the R-matrix results prevent us from providing reliable information on any physical resonances that may appear above this energy region. In the diazines, both calculations and experiments indicate the presence of a fourth π ∗ resonance. 46 We are unable to determine whether a fourth π ∗ resonance is also present in electron-pyridine scattering. The resonance positions are listed in Table 2, together with results from ETS experiments. 16,17 Also listed is the symmetry of the resonances. For the calculations with the compact basis set, we have listed results with three different numbers of virtual orbitals. As already stated, 35 virtual orbitals give the best agreement with the results of Nenner and Schulz. Increasing the number of virtual orbitals included in the calculations with the compact basis set to 40 causes the two lowest resonances to become overcorrelated. The R-matrix resonances appear somewhat lower in energy than the Schwinger ones (addition of triplet-coupled excitations has been shown to lower the position of the 2 B1 resonances in the Schwinger calculations). The diffuse basis set seems to give positions in better agreement with both experiments. The third resonance appears too high in energy in all the calculations quoted: this resonances is likely to have a mixed shape and core-excited character (as does the third resonance in diazines 46,55 ) and therefore, the inclusion of configurations 14


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describing electronically excited states of the target are needed to describe it accurately. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Conclusions We report elastic cross sections for electron scattering from pyridine in the energy range 1 eV to 1 keV using the R-matrix (low energy) and IAM-SCAR (higher energy) methods, together with electronically inelastic cross sections calculated with the IAM-SCAR method. These cross sections agree reasonably well. Earlier, Schwinger calculations, produce cross sections that are significantly smaller than our Born-corrected cross sections. We show that this discrepancy is mainly due to the choice of angular range ( 1◦ and 180◦ ) for which the Schwinger DCS is integrated to obtain the integral cross section. However, the uncorrected cross sections also show some quantitative and qualitative differences that we believe are mainly due to differences in the description of the polarization. Three shape resonances (of π ∗ character) are identified and characterized: their positions agree well with experimental results and prior calculations. The elastic pyridine cross sections are fairly similar in size to those of pyrimidine for energies below 50 eV. There are, however, however small differences in the shape of the DCS for angles > 30 − 40◦ . Pyrimidine has an additional nitrogen in the 6-atom ring and therefore an additional lone pair. This may increase slightly the exchange effects and lead to the changes in the DCS. Above 50 eV, the DCS seem to be larger for pyridine. Similarly the inelastic cross section obtained with the IAM-SCAR method is somewhat bigger than that for pyrimidine. On the whole, however, the substitution of a carbon atom for a nitrogen one in going from pyridine to pyrimidine seems to have a small effect on the scattering data presented here.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Cross sections (a0 )


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compact compact (l=5) diffuse Ab intio compact (l=5) Ab intio diffuse Schwinger corrected Schwinger

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Figure 1: Low energy integral elastic cross section for electron scattering from pyridine calculated using the R-matrix method using the basis sets indicated in the figure. The cross sections labelled ’Ab initio’ and ’Schwinger’ do not incorporate a Born-based correction; for those labelled l=5 the ab initio calculation contains the extra partial wave. Also plotted are the multichannel Schwinger results of Barbosa et al..

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diffuse Ab initio diffuse Schwinger Schwinger corrected IAM-SCAR IAM-SCAR+Rotations Inelastic (IAM-SCAR) 1

10 E (eV)

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Figure 2: Integral elastic cross section for electron scattering from pyridine for the whole energy range studied in this work for the methods and models indicated in the figure. Also plotted are the Schwinger results of Barbosa et al..The cross sections labelled ’Ab initio’ and ’Schwinger’ do not incorporate a Born-based correction.

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3 eV

6 eV

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1 R-matrix diffuse R-matrix compact IAM-SCAR+Rot. Schwinger

10 eV 100 100

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DCS (10 cm sr )

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10

30 eV

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50 eV

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0.1 0.01 0

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90

120 150 180

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E (eV)

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90

120 150 180

E (eV)

Figure 3: Elastic differential cross section for electron scattering from pyridine for the energies indicated in the panels calculated using the R-matrix and IAM-SCAR+Rotations methods. The R-matrix results are Born-corrected. Also plotted are the multichannel Schwinger results of Barbosa et al.. The bottom right-hand panel shows IAM-SCAR+Rotations cross sections for several energies.

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Figures 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Acknowledgement This work was partially supported by the Spanish Ministerio de Econom´ıa y Competitividad (Project FIS2012-31230) and the European Commission COST Action MP1002 (NanoIBCT) and Action CM1301 (CELINA). The research carried out at The Open University was funded by EPSRC. We thank Prof. Marcio Bettega for providing us with their calculated data in order to produce the plots.

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tronically excited states: CASPT2, CC2, CCSD, and CC3. The Journal of Chemical Physics 2008, 128, 134110–25. (45) Maˇs´ın, Z.; Gorfinkiel, J. D.; Jones, D. B.; Bellm, S. M.; Brunger, M. J. Elastic and inelastic cross sections for low-energy electron collisions with pyrimidine. The Journal of Chemical Physics 2012, 136, 144310. (46) Maˇs´ın, Z.; Gorfinkiel, J. D. Shape and core excited resonances in electron collisions with diazines. The Journal of Chemical Physics 2012, 137, 204312. (47) Sanz, A. G.; Fuss, M. C.; Blanco, F.; Gorfinkiel, J. D.; Almeida, D.; da Silva, F. F.; Limao-Vieira, P.; Brunger, M. J.; Garc´ıa, G. An investigation into electron scattering from pyrazine at intermediate and high energies. The Journal of Chemical Physics 2013, 139, 184310. (48) Werner, H.-J.; Knowles, P. J.; Lindh, R.; Manby, F. R.; Sch¨ utz, M.; et al., MOLPRO, version 2009.1, a package of ab initio programs. 2009. (49) Faure, A.; Gorfinkiel, J. D.; Morgan, L. A.; Tennyson, J. GTOBAS: fitting continuum functions with Gaussian-type orbitals. Comp. Phys. Commun. 2002, 144, 224–241. (50) Tarana, M.; Tennyson, J. Polarization effects in electron collisions with Li2 : application of the molecular R-matrix method with pseudostates. J. Phys. B: At., Mol. Opt. Phys. 2008, 41, 205204. (51) Maˇs´ın, Z. Resonance formation in electron collisions with pyrimidine-like targets. Ph.D. thesis, The Open University, 2012. (52) Blackman, G.; Brown, R.; Burden, F. Microwave spectrum, dipole moment, and nuclear quadruple coupling constants of pyrimidine. Journal of Molecular Spectroscopy 1970, 35, 444. 24


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(53) Franz, J.; Gianturco, F. A. Low-energy positron scattering from gas-phase pyrimidine: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

A quantum treatment of the dynamics and a comparison with experiments. Phys. Rev. A 2013, 88, 042711. (54) Tennyson, J.; Noble, C. J. RESON–A program for the detection and fitting of BreitWigner resonances. Comput. Phys. Commun. 1984, 33, 421–424. (55) Winstead, C.; McKoy, V. Resonant Channel Coupling in Electron Scattering by Pyrazine. Phys. Rev. Lett. 2007, 98, 113201.

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Graphical TOC Entry 1000

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10

1 0.1

diffuse Ab initio diffuse Schwinger Schwinger corrected IAM-SCAR IAM-SCAR+Rotations Inelastic (IAM-SCAR)

1

10 E (eV)

100

1000

Integral elastic cross section for

electron scattering from pyridine.

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Low energy elastic electron scattering from CF3Br molecules.

The role of electron donors generated from UV photolysis for accelerating pyridine biodegradation.

Phthalate dioxygenase reductase: a modular structure for electron transfer from pyridine nucleotides to [2Fe-2S].

Inelastic electron scattering from a helical potential: transverse polarization and the structure factor in the single scattering approximation.

Association and liquid structure of pyridine-acetic acid mixtures determined from neutron scattering using a 'free proton' EPSR simulation model.

Resonant light scattering from a single dielectric nano-antenna formed by electron beam-induced deposition.

Absolute vibrational cross sections for 1-19 eV electron scattering from condensed tetrahydrofuran (THF).

Differential cross sections for intermediate-energy electron scattering from α-tetrahydrofurfuryl alcohol: excitation of electronic-states.

An investigation into electron scattering from pyrazine at intermediate and high energies.

Measurement of parity violation in electron-quark scattering.

Carrier density independent scattering rate in SrTiO3-based electron liquids.

Critical binding and electron scattering by symmetric-top polar molecules.

Spin-dependent electron scattering at graphene edges on Ni(111).

Electron shell ionization of atoms with classical, relativistic scattering.

Muscle thick filament mass measured by electron scattering.

Multiscale phase mapping of LiFePO4-based electrodes by transmission electron microscopy and electron forward scattering diffraction.

No surprise in the first Born approximation for electron scattering.

Dynamic scattering of electron vortex beams--a Bloch wave analysis.

Similarity between positronium-atom and electron-atom scattering.

A complete comparison of simulated electron diffraction patterns using different parameterizations of the electron scattering factors.

Theory of light emission from quantum noise in plasmonic contacts: above-threshold emission from higher-order electron-plasmon scattering.

Ultrasound scattering from spherical tumours.

A DFT study of the ionization and electron attachment of 2-azido pyridine.

Electron-Phonon Coupling Strength at Metal Surfaces Directly Determined from the Helium Atom Scattering Debye-Waller Factor.