Elastic scattering of low-energy electrons by 1,4-dioxane Alessandra Souza Barbosa and Márcio H. F. Bettega Citation: The Journal of Chemical Physics 140, 184303 (2014); doi: 10.1063/1.4874646 View online: http://dx.doi.org/10.1063/1.4874646 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/18?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A joint theoretical and experimental study for elastic electron scattering from 1,4-dioxane J. Chem. Phys. 139, 014308 (2013); 10.1063/1.4812215 Low-energy electron scattering from the aza-derivatives of pyrrole, furan, and thiophene J. Chem. Phys. 138, 234311 (2013); 10.1063/1.4811218 Low-energy electron collisions with pyrrole J. Chem. Phys. 132, 204301 (2010); 10.1063/1.3428620 A comparative study of elastic scattering of low-energy electrons by boron, aluminum and gallium trihalides J. Chem. Phys. 118, 75 (2003); 10.1063/1.1523902 Elastic scattering of low-energy electrons by benzene J. Chem. Phys. 112, 8806 (2000); 10.1063/1.481529
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THE JOURNAL OF CHEMICAL PHYSICS 140, 184303 (2014)
Elastic scattering of low-energy electrons by 1,4-dioxane Alessandra Souza Barbosa and Márcio H. F. Bettegaa) Departamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, 81531-990 Curitiba, Paraná, Brazil
(Received 18 March 2014; accepted 22 April 2014; published online 8 May 2014) We report calculated cross sections for elastic collisions of low-energy-electrons with 1,4-dioxane. Our calculations employed the Schwinger multichannel method with pseudopotentials and were carried out in the static-exchange and static-exchange plus polarization approximations for energies up to 30 eV. Our results show the presence of three shape resonances belonging to the Bu , Au , and Bg symmetries and located at 7.0 eV, 8.4 eV, and 9.8 eV, respectively. We also report the presence of a Ramsauer-Townsend minimum located at around 0.05 eV. We compare our calculated cross sections with experimental data and R-matrix and independent atom model along with the additivity rule corrected by using screening coefficients theoretical results for 1,4-dioxane obtained by Palihawadana et al. [J. Chem. Phys. 139, 014308 (2013)]. The agreement between the present and the R-matrix theoretical calculations of Palihawadana et al. is relatively good at energies below 10 eV. Our calculated differential cross sections agree well with the experimental data, showing only some discrepancies at higher energies. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4874646] I. INTRODUCTION
The cross sections resulting from electron collisions with molecules represent an input in the description and modeling of processes involving plasmas in astrophysics1 and in technology.2 More recently, due to the discovery that lowenergy electrons can cause single- and double-strand breaks in the DNA,3 the community of electron-molecule collisions has changed its attention to molecules of biological relevance. Namely, to those which are of DNA subunits or molecules related to these subunits, e.g., sugars, alcohols, acids, and ethers.4 In particular, since the strand breaks in DNA occur through a dissociative electron attachment (DEA)5 which involves a transient negative ion (resonance),6 the proper description of the resonance spectra of these molecules is desired. 1,4-dioxane is a heterocyclic ether with C2h symmetry. It can be viewed as a benzene derivative, with the two oxygens replacing the C–H group in the positions 1 and 4 along the ring, as can be seen in Fig. 1. One important difference between these two molecules is that benzene is unsaturated while 1,4-dioxane is a saturated molecule. This difference has a direct impact if we consider electron collisions with benzene and 1,4-dioxane, more precisely in the shape resonance spectra of these molecules. As is well known, benzene has two π * shape resonances (the low-lying resonance being twofold degenerate) associated with the unoccupied π * orbitals, where the higher lying resonance has a mixed shape and core-excited character.8–10 If we consider the interactions of low-energy electrons with 1,4-dioxane, the literature is still very scarce. The resonance spectra of 1,4-dioxane have been investigated by Bremner et al.11 using the near-threshold electron energya) Electronic mail: [email protected]
0021-9606/2014/140(18)/184303/6/$30.00
loss (EEL) spectra. The authors reported negative ion signals at around 6.4 eV, 7.2-7.6 eV, and 7.8 eV. Recently, Palihawadana et al.12 published a joint theoretical and experimental work on electron collisions with 1,4-dioxane. The experiment was performed with a crossed electron-molecular beam device and reported elastic differential (DCSs) and integral cross sections (ICSs) at 10, 15, 20, and 30 eV. The theoretical calculations employed two different methods: the ab initio R-matrix method and the independent atom model along with the additivity rule corrected by using screening coefficients (known as IAM-SCAR). Both calculations provided integral and differential cross sections. The R-matrix calculations of Palihawadana et al.12 reported the presence of two shape resonances in the integral cross section, one belonging to the Bg symmetry located at 8.30 eV and the other belonging to the Au symmetry located at 8.36 eV. The authors found another structure in the R-matrix integral cross section which resulted from the overlap of two structures belonging to the Au and Bu symmetries. They suggested that this structure could be related to a (higher-lying) resonance with a mixed character (shape and core-excited), as found in benzene and pyrazine.8–10 The resonance locations provided by the R-matrix calculations of Palihawadana et al.12 are in qualitative agreement with the EEL spectra. The IAMSCAR integral cross section is structureless, and shows qualitative agreement with the R-matrix results and with the experiment at higher energies. Regarding the differential cross sections, the agreement with the theoretical results and the experimental data is in general good. Palihawadana et al.12 suggested that pyrazine and 1,4-dioxane can be thought of as benzene derivatives. In view of that, the authors also compared their theoretical and experimental differential cross sections with the experimental data for benzene and pyrazine. The differences found between the DCSs of 1,4-dioxane and the DCSs of benzene and pyrazine were discussed in
140, 184303-1
© 2014 AIP Publishing LLC
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A. S. Barbosa and M. H. F. Bettega
J. Chem. Phys. 140, 184303 (2014)
electron basis set (direct space) is given by |χm = A(|1 ⊗ |ϕm ),
(2)
where |1 is the target ground state, |ϕ m is a single-particle function, and A is the antisymmetrizer. For the calculations carried out in the SEP approximation, the direct space is augmented by CSFs constructed as |χm = A(|r ⊗ |ϕs ),
FIG. 1. Geometrical structure of 1,4-dioxane (generated with MacMolPlt7 ).
terms of the exchange interaction and the non-planarity of 1,4-dioxane. In this work, we present calculated elastic integral, momentum transfer (MTCS), and differential cross sections for low-energy-electron collisions with 1,4-dioxane. We employed the Schwinger multichannel method (SMC) method13 implemented with the pseudopotentials (SMCPP)15 of Bachelet, Hamann, and Schlüter.18 The calculations were carried out in the static-exchange (SE) and static-exchange plus polarization (SEP) approximations for energies up to 30 eV. We compare our calculated cross sections with theoretical and experimental results of Palihawadana et al.12 Our aim is to provide a set of cross sections obtained with a well established ab initio method and consequently obtain further insight into the resonance spectra of 1,4-dioxane. It is also interesting to compare the differential cross sections of 1,4dioxane with available theoretical and experimental differential cross sections for benzene and for other benzene derivatives, such as pyridine, pyrimidine, and pyrazine, in order to search for similarities among them. The remainder of this paper is as follows. In Sec. II, we present the theoretical method and computational procedure of this calculation. In Sec. III, we present and discuss the results. In Sec. IV, we close the paper with a brief summary of the present results.
II. COMPUTATIONAL DETAILS
Our calculations employed the SMC method13, 14 with pseudopotentials.15 The details of the method have been discussed elsewhere16 and here we will only provide the relevant points for the present calculations. The SMC method is a variational approximation to the scattering amplitude, and the resulting expression in the body-frame is given by 1 Skf |V |χm d −1 mn χn |V |Ski , fSMC (kf , ki ) = − 2π m,n (1) where the {|χ m } represents a basis set of (N + 1)-electron symmetry-adapted Slater determinants, also referred to as configuration state functions (CSFs). The CSFs are built from products of target states with single-particle functions. For the calculations carried out in the SE approximation, the (N + 1)-
(3)
where |r are the N-electron Slater states obtained by performing single excitations of the target from the occupied (hole) orbitals to a set of unoccupied (particle) orbitals. Here, |ϕ s is also a single-particle function and A is the antisymmetrizer. In Eq. (1), the dmn matrix elements are given by dmn = χm |A(+) |χn
(4)
and the A( + ) operator is given by 1 1 Hˆ − Hˆ P +P Hˆ + (P V +V P )−V G(+) P V. N +1 2 2 (5) In the above equations, Ski(f ) is a product of a target state and a plane wave with momentum ki(f ) , which is an eigenstate of the unperturbed Hamiltonian H0 ; V is the interaction potential between the incident electron and the target; Hˆ ≡ E − H is the collision energy minus the full Hamiltonian of the system, with H = H0 + V ; P is a projection operator onto the openchannel space; and G(+) P is the free-particle Green’s function projected on the P-space. Our scattering calculations were carried out in the optimized chair structure of C2h symmetry of 1,4-dioxane, since this is the most stable conformer. In order to optimize the geometrical structure, we employed the package GAMESS17 at the second order Møller-Plesset perturbation theory using the TZV++(2d,1p) basis set, in the C2h point group. In Fig. 1, we present the optimized structure of 1,4-dioxane. We used the pseudopotentials of Bachelet, Hamman, and Schlüter18 to replace the core electrons of carbon and oxygen atoms and the valence target electrons are represented by Cartesian Gaussian functions which were generated according to Bettega et al.19 We used six s-type functions, five p-type functions, and one d-type function (6s5p1d) for carbon and five s-type and p-type functions and three d-type functions (5s5p3d) for the oxygen. The Cartesian Gaussian functions for carbon and oxygen are show in Table I. For hydrogen, we used the 4s/3s basis set of Dunning20 augmented by one p-type function with exponent 0.75, as is shown in Table II. The symmetric combinations of the d-type orbital were excluded to avoid linear dependency in the basis set. To represent particle and scattering orbitals in the SEP calculations, we employed the improved virtual orbitals (IVOs).21 We selected IVOs satisfying the relation22 A(+) =
εpar − εhole + εscat < ,
(6)
where εpar is the particle orbital energy, εhole is hole orbital energy, εscat is the scattering orbital energy, and is the energy cut off. We used = 1.95 hartrees and considered all singlet and triplet coupled excitation for all symmetries, such
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J. Chem. Phys. 140, 184303 (2014)
TABLE I. Uncontracted Cartesian Gaussian functions used for carbon and oxygen. C
O
s s s s s s
12.49408 2.470291 0.614027 0.184029 0.036799 0.013682
16.05878 5.920242 1.034907 0.316843 0.065203
p p p p p
5.228869 1.592058 0.568612 0.210326 0.072250
10.14127 2.783023 0.841010 0.232940 0.052211
d d d
0.126278
1.698024 0.455259 0.146894
60 50 40 30 20 10
2 -16
30 20 10 0
TABLE II. Cartesian Gaussian functions used for hydrogen. Exponent
s s s s
13.3615 2.0133 0.4538 0.1233
p
0.75
Coefficient 0.130844 0.921539 1.00 1.00 1.00
10 15 20 energy (eV)
25
30
and located at 7 eV, to the Au symmetry and located at 8.4 eV, and to the Bg symmetry and located at 9.8 eV. We performed the partial wave analysis of the ICSs of these symmetries and obtained the corresponding eigenphase sum (not shown here). We found that there is a major contribution from the = 3 partial wave for the Bu and Au cross sections and from = 4 for the Bg cross section. Through the behavior of the eigenphase sum we concluded that those structures correspond to broad shape resonances. We also investigated the structures
15 Au
Ag 40
12
30
9
20
6
10
3
-16
2
cross section (10 cm )
50
0
0
5
10
15
20
25
30
20 2
In Fig. 2, we present our calculated ICS and MTCS in the SE and in the SEP approximations, for energies up to 30 eV. We also present the experimental data and the theoretical results, obtained with the IAM-SCAR and R-matrix methods, of Palihawadana et al.12 All R-matrix results shown here for comparison were obtained with 40 virtual orbitals. In the present ICS, we note a pronounced broad structure in the SE cross section that moves down in energy in the SEP calculations. Another feature that is worth mentioning is the rapid fall, as the energy decreases, shown by the present ICS. This point will be discussed in detail later. The agreement between our results and the results obtained with the R-matrix method is in general good. In the low-energy regime, the R-matrix ICS presents a structure that is absent in our ICS. For energies above 12 eV, the two cross sections start to differ, the Rmatrix ICS being lower than ours and showing several pseudoresonances. The ICS obtained with the IAM-SCAR method is structureless, increasing at lower energies and following the shape of our ICS and the experimental data at higher energies. In order to obtain additional information about the structures in the present ICS, we show in Fig. 3 the symmetry decomposition of the ICS according to the C2h point group. We observe that the pronounced structure in the ICS results from the overlap of three structures belonging to the Bu symmetry
5
0
0
5
10
15
20
25
30
12 Bu
16
Bg
10
-16
III. RESULTS
0
FIG. 2. Integral cross section (upper panel) and momentum transfer cross section (lower panel) for elastic scattering of electrons by 1,4-dioxane. We compare our results with calculated cross sections obtained by Palihawadana et al.12 using the R-matrix and IAM-SCAR methods. We also compare the theoretical results with the experimental data of Palihawadana et al.12
cross section (10 cm )
that we obtained 10 502 CSFs for the Ag and the Bu symmetries, 10 426 for the Au symmetry, and 10 417 CSFs for the Bg symmetry.
Type
SE SEP R-matrix IAM-SCAR expt.
70
400 cross section (10 cm )
Type
-16
2
cross section (10 cm )
80
8 12 6 8 4 4 0
SE SEP
2 0
5
10 15 20 energy (eV)
25
30
0
0
5
10 15 20 energy (eV)
25
30
FIG. 3. Symmetry decomposition of the integral cross section within the C2h group for elastic scattering of electrons by 1,4-dioxane obtained in the SE and SEP approximations.
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J. Chem. Phys. 140, 184303 (2014)
2
s-wave cross section (10 cm )
-16
A’
30
-16
2
cross section (10 cm )
35
25 20 15 10
SEP R-matrix
5
8 7 6 5 4 3 2 1 0
0
0.1
0.2 0.3 energy (eV)
0.4
0
0.1
0.2 0.3 energy (eV)
0.4
A’’
30
s-wave eigenphase (radians)
cross section (10
-16
2
cm )
0
25 20 15 10 5 0
0
5
10 15 20 energy (eV)
25
30
FIG. 4. Symmetry decomposition of the integral cross section in the Cs group. We compare our SEP results with the results obtained with the Rmatrix method.
that appear in the ICS of the Ag symmetry and concluded that they are not shape resonances. Palihawadana et al.12 reported two shape resonances, one in the Bg symmetry at 8.3 eV and the other in the Au symmetry at 8.36 eV. Our location for the Au resonance agrees well with the R-matrix calculations of Palihawadana et al.,12 while for the Bg symmetry our computed resonance position of 9.8 eV is much higher than the R-matrix results. This discrepancy may be due to the different treatments of polarization used in both calculations. Our resonance locations are higher compared to the EEL spectra of Bremner et al.,11 which show negative ion signals at around 6.4 eV, 7.2-7.6 eV, and 7.8 eV. Figure 4 shows a comparison between the symmetry decomposition of the present ICS and the R-matrix results in the Cs group.23 To obtain the A ICS, we summed the ICSs of the Ag and Bu symmetries and of the A ICS we summed the ICSs of the Au and Bg symmetries of Fig. 3. The agreement between the two theoretical results is good. Palihawadana et al.12 also reported a feature in the ICS at around 7 eV as being an overlap of two shape resonances belonging to the Au and Bu symmetries. They also suggested that the higher-lying resonance would be a mixing of shape and core-excited resonances. This behavior has been found in benzene and its aza-derivatives.8–10 In order to investigate this suggestion, we carried out a configuration interaction calculation on the anion of the Bu , Au , and Bg symmetries of 1,4-dioxane, similar to that carried out by Winstead and McKoy9 in pyrazine. The calculation employed the package GAMESS17 at the optimized geometry of the ground state of the neutral molecule (as described above) with the 6-311+G(d,p) basis set and up to quadruple excitations. The active space was comprised with the last three occupied and
0.05 0 -0.05 -0.1 -0.15 -0.2
FIG. 5. s-wave cross section and the corresponding s-wave eigenphase.
the first three unoccupied orbitals. The results of these calculations show that the dominant configuration for each symmetry has a pure shape-resonance configuration, that is the molecular ground state configuration with the extra electron in the first unoccupied orbital of the corresponding symmetry. The present ICS for 1,4-dioxane shows a rapid decrease in magnitude with decreasing energy. As shown in Fig. 3, this feature is due to the Ag symmetry. To investigate this behavior of the ICS for the Ag symmetry, we obtained the swave ( = 0) ICS and computed the corresponding s-wave eigenphase. The results are shown in Fig. 5 and indicate the presence of a Ramsauer-Townsend (RT) minimum at around 0.05 eV. The s-wave eigenphase changes sign, crossing zero at around 0.05 eV, which is the same energy where the s-wave ICS is zero. The behavior of the eigenphase suggests that the net interaction felt by the incoming electron changes from attractive, when the eigenphase is positive, to repulsive, when the eigenphase is negative. The interactions between the incoming electron and the molecule are the Coulomb (static), polarization, and the exchange potentials. The polarization interaction is always attractive to the incident electron, and the exchange is repulsive, in the sense that the incoming electron is not allowed to occupy a doubly occupied orbital (according to Pauli’s exclusion principle). The static potential is attractive when the incoming electron visits the target electronic cloud (by the Gauss law).24, 25 This is the signature of a RT minimum, which was not reported by Palihawadana et al.12 In Figures 6 and 7, we present our calculated DCSs in the SE and SEP approximations. We compare our DCSs with experimental and calculated data from Palihawadana et al.12 for 1,4-dioxane. Unpublished results obtained with the R-matrix method at 2, 3, 4, 6, and 8.5 eV are also included for comparison.23 We also compare our DCSs with
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A. S. Barbosa and M. H. F. Bettega
J. Chem. Phys. 140, 184303 (2014)
3 eV
4 eV
-16
2
cross section (10 cm /sr)
-16
2 eV
15 eV
6 eV
8.5 eV
30 60 90 120 150 180 30 60 90 120 150 180 30 60 90 120 150 180 scattering angle (degrees)
FIG. 6. Differential cross sections for elastic scattering of electrons by 1,4-dioxane at 2, 3, 4, 6, 8.5, and 10 eV. Dotted-dashed (blue) and solid (green) lines, present results obtained in the SE and SEP approximations; short-dashed (red) line, R-matrix results for 1,4-dioxane; dashed (indigo) line, IAM-SCAR results from Ref. 12; circles (magenta), experimental data for benzene from Ref. 27; triangles (cyan), experimental data for pyrazine from Ref. 28; stars (orange), experimental data for 1,4-dioxane from Ref. 12. The short-dashed (red) line at 2, 3, 4, 6, and 8.5 eV corresponds to DCSs from Ref. 23 and at 10 eV is from Ref. 12.
experimental data for benzene27 and pyrazine.28 1,4-dioxane and pyrazine can be thought as benzene derivatives, with the carbons on positions 1 and 4 replaced by oxygens in 1,4-dioxane and by nitrogen atoms in pyrazine. At low energies, there is a good agreement between our calculated DCSs and the R-matrix results.23 At 10 eV our calculated data also agree well with the calculated R-matrix DCS of Palihawadana et al.12 and with the experimental data for 1,4-dioxane. At higher energies, the present computed DCSs and those obtained with the R-matrix method by Palihawadana et al.12 differ in magnitude and present a different oscillatory behavior. It is worth to mention that the shape of our calculated DCS agrees better with experimental data, mainly at 20 eV and 30 eV. The differences in magnitude observed at these energies between the theory and the experiment can be explained by the fact that our calculations consider only the elastic channel, and therefore there is no flux loss from the elastic channel into the (closed) inelastic channels.26 Figure 8 shows a comparison between the experimental DCSs of 1,4-dioxane and the experimental data of benzene,27 pyrazine,28 and pyrimidine29 and the calculated results for
100 20 eV
30 eV
-16
2
15 eV
10
1 0
30 eV
1
30 60 90 120 150 180 30 60 90 120 150 180 30 60 90 120 150 180 scattering angle (degrees)
10 eV
10
0
20 eV
10
0
1
1
cross section (10 cm /sr)
100
2
10
cross section (10 cm /sr)
184303-5
30 60 90 120 150 180 30 60 90 120 150 180 30 60 90 120 150 180 scattering angle (degrees)
FIG. 7. As in Figure 6 at 15, 20, and 30 eV. The short-dashed (red) line are from Ref. 12.
FIG. 8. Differential cross sections for elastic scattering of electrons by 1,4-dioxane, benzene, pyrimidine, pyrazine, and pyridine at 15, 20, and 30 eV. Stars (orange), experimental data for 1,4-dioxane;12 circles (magenta), experimental data for benzene;27 triangles (cyan), experimental data for pyrazine;28 squares (brown), experimental data for pyrimidine;29 dashed (red) line, calculated results for benzene obtained in the SE approximation;30 solid (green) line, calculated results for pyridine obtained in the SE approximation.31
benzene30 and pyridine31 at 15, 20, and 30 eV. Pyrazine and pyrimidine differ from benzene by the replacement of two C–H groups by two nitrogen atoms in the ring (in the positions 1 and 4, and 1 and 3, respectively), while pyridine has only one nitrogen in place of the C–H group. This figure shows that the experimental DCSs of benzene, pyridine, and pyrazine are very similar to each other. It also shows that the calculated DCSs for benzene and pyridine, which were obtained in the SE approximation, agree with each other and also agree in shape with the experimental data of benzene, pyrimidine, and pyrazine, although they are higher in magnitude. This behavior is also explained by absence of flux loss from the elastic channel to the inelastic ones. The DCSs of 1,4-dioxane differ from the DCSs of the other molecules, especially at 15 eV, where the DCS of 1,4-dioxane presents a f-wave behavior while the other DCSs present a d-wave behavior. This comparison suggests that the DCSs of the planar molecules do not depend on the location of the nitrogen atoms in the ring. IV. SUMMARY
We presented calculated elastic cross sections for lowenergy electron collisions with 1,4-dioxane. Our calculations employed the Schwinger multichannel method and were performed in the static-exchange and in the static-exchangepolarization approximations. Our results are compared with other relevant experimental and theoretical results. We found three shape resonances in the Bu , Au , and Bg symmetries located at 7.0 eV, 8.4 eV, and 9.8 eV, respectively, which qualitatively agree with the R-matrix results and with the EEL spectra. We also found a Ramsauer-Townsend minimum located at around 0.05 eV. We compared the present computed DCSs with R-matrix and IAM-SCAR calculations and with the experimental data. Our results agree in general with the R-matrix results for energies up to 10 eV, and also agree with the experimental data. We also compared the DCSs of 1,4-dioxane with results for benzene and some benzene derivatives, namely, pyrimidine, pyrazine, and pyridine. Although the DCSs for the benzene and the benzene derivatives agree with each other, they differ from the DCSs of 1,4-dioxane.
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ACKNOWLEDGMENTS
A.S.B. acknowledges support from Brazilian Agency Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES). M.H.F.B. acknowledges support from Brazilian agency Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), and from FINEP (under project CTInfra). The authors acknowledge computational support from Professor Carlos M. de Carvalho at LFTC-DFis-UFPR and at LCPAD-UFPR, and from CENAPAD-SP. The authors would also like to thank Professor Jimena D. Gorfinkiel for providing the published and unpublished R-matrix cross sections in tabulated form. 1 L.
Campbell and M. J. Brunger, Plasma Sources Sci. Technol. 22, 013002 (2013); A. Garcia-Sanz, F. Carelli, F. Sebastianelli, F. A. Gianturco, and G. Garcia, New J. Phys. 15, 013018 (2013). 2 J.-S. Yoon, M.-Y. Song, H. Kato, M. Hoshino, H. Tanaka, M. J. Brunger, S. J. Buckman, and H. Cho, J. Phys. Chem. Ref. Data 39, 033106 (2010). 3 B. Boudaïffa, P. Cloutier, D. Hunting, M. A. Huels, and L. Sanche, Science 287, 1658 (2000). 4 See, for instance, D. Bouchiha, J. D. Gorfinkiel, L. G. Caron, and L. Sanche, J. Phys. B 40, 1259 (2007); M. A. Khakoo, J. Muse, H. Silva, M. C. A. Lopes, C. Winstead, V. McKoy, E. M. de Oliveira, R. F. da Costa, M. T. do N. Varella, M. H. F. Bettega, and M. A. P. Lima, Phys. Rev. A 78, 062714 (2008); T. C. Freitas, M. T. do N. Varella, R. F. da Costa, M. A. P. Lima, and M. H. F. Bettega, ibid. 79, 022706 (2009); M. A. Khakoo, L. Hong, B. Kim, C. Winstead, and V. McKoy, ibid. 81, 022720 (2010). 5 X. Pan, P. Cloutier, D. Hunting, and L. Sanche, Phys. Rev. Lett. 90, 208102 (2003). 6 F. Martin, P. D. Burrow, Z. Cai, P. Cloutier, D. Hunting, and L. Sanche, Phys. Rev. Lett. 93, 068101 (2004). 7 B. M. Bode and M. S. Gordon, J. Mol. Graph. Model. 16, 133 (1998). 8 I. Nenner and G. J. Schulz, J. Chem. Phys. 62, 1747 (1975). 9 C. Winstead and V. McKoy, Phys. Rev. Lett. 98, 113201 (2007); Phys. Rev. A 76, 012712 (2007)
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Mažín and J. D. Gorfinkiel, J. Chem. Phys. 135, 144308 (2011).
11 L. J. Bremner, M. G. Curtis, and I. C. Walker, J. Chem. Soc., Faraday Trans.
87, 1049 (1991). 12 P. Palihawadana, J. P. Sullivan, S. J. Buckman, Z. Masin, J. D. Gorfinkiel, F.
Blanco, G. Garcia, and M. J. Brunger, J. Chem. Phys. 139, 014308 (2013). Takatsuka and V. McKoy, Phys. Rev. A 24, 2473 (1981); 30, 1734 (1984). 14 M. A. P. Lima, L. M. Brescansin, A. J. R. da Silva, C. Winstead, and V. McKoy, Phys. Rev. A 41, 327 (1990). 15 M. H. F. Bettega, L. G. Ferreira, and M. A. P. Lima, Phys. Rev. A 47, 1111 (1993). 16 R. F. da Costa, F. J. da Paixão, and M. A. P. Lima, J. Phys. B 37, L129 (2004); 38, 4363 (2005). 17 M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. J. Su, T. L. Windus, M. Dupuis, and J. A. Montgomery, J. Comput. Chem. 14, 1347 (1993). 18 G. B. Bachelet, D. R. Hamann, and M. Schlüter, Phys. Rev. B 26, 4199 (1982). 19 M. H. F. Bettega, A. P. P. Natalense, M. A. P. Lima, and L. G. Ferreira, Int. J. Quantum Chem. 60, 821 (1996). 20 T. H. Dunning, Jr., J. Chem. Phys. 53, 2823 (1970). 21 W. J. Hunt and W. A. Goddard III, Chem. Phys. Lett. 3, 414 (1969). 22 F. Kossoski and M. H. F. Bettega, J. Chem. Phys. 138, 234311 (2013). 23 Z. Mažín and J. D. Gorfinkiel, private communication (2013). 24 M. A. P. Lima, K. Watari, and V. McKoy, Phys. Rev. A 39, 4312 (1989). 25 B. M. Nestmann, K. Pfingst, and S. D. Peyerimhoff, J. Phys. B 27, 2297 (1994). 26 R. F. da Costa, M. H. F. Bettega, M. A. P. Lima, M. C. A. Lopes, L. R. Hargreaves, G. Serna, and M. A. Khakoo, Phys. Rev. A 85, 062706 (2012). 27 H. Cho, R. J. Gulley, K. Sunohara, M. Kitajima, L. J. Uhlmann, H. Tanaka, and S. J. Buckman, J. Phys. B 34, 1019 (2001). 28 P. Palihawadana, J. P. Sullivan, S. J. Buckman, and M. J. Brunger, J. Chem. Phys. 137, 204307 (2012). 29 P. Palihawadana, J. Sullivan, M. Brunger, C. Winstead, V. McKoy, G. Garcia, F. Blanco, and S. Buckman, Phys. Rev. A 84, 062702 (2011). 30 M. H. F. Bettega, C. Winstead, and V. McKoy, J. Chem. Phys. 112, 8806 (2000). 31 A. S. Barbosa, D. F. Pastega, and M. H. F. Bettega, Phys. Rev. A 88, 022705 (2013). 13 K.
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THE JOURNAL OF CHEMICAL PHYSICS 140, 184303 (2014)
Elastic scattering of low-energy electrons by 1,4-dioxane Alessandra Souza Barbosa and Márcio H. F. Bettegaa) Departamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, 81531-990 Curitiba, Paraná, Brazil
(Received 18 March 2014; accepted 22 April 2014; published online 8 May 2014) We report calculated cross sections for elastic collisions of low-energy-electrons with 1,4-dioxane. Our calculations employed the Schwinger multichannel method with pseudopotentials and were carried out in the static-exchange and static-exchange plus polarization approximations for energies up to 30 eV. Our results show the presence of three shape resonances belonging to the Bu , Au , and Bg symmetries and located at 7.0 eV, 8.4 eV, and 9.8 eV, respectively. We also report the presence of a Ramsauer-Townsend minimum located at around 0.05 eV. We compare our calculated cross sections with experimental data and R-matrix and independent atom model along with the additivity rule corrected by using screening coefficients theoretical results for 1,4-dioxane obtained by Palihawadana et al. [J. Chem. Phys. 139, 014308 (2013)]. The agreement between the present and the R-matrix theoretical calculations of Palihawadana et al. is relatively good at energies below 10 eV. Our calculated differential cross sections agree well with the experimental data, showing only some discrepancies at higher energies. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4874646] I. INTRODUCTION
The cross sections resulting from electron collisions with molecules represent an input in the description and modeling of processes involving plasmas in astrophysics1 and in technology.2 More recently, due to the discovery that lowenergy electrons can cause single- and double-strand breaks in the DNA,3 the community of electron-molecule collisions has changed its attention to molecules of biological relevance. Namely, to those which are of DNA subunits or molecules related to these subunits, e.g., sugars, alcohols, acids, and ethers.4 In particular, since the strand breaks in DNA occur through a dissociative electron attachment (DEA)5 which involves a transient negative ion (resonance),6 the proper description of the resonance spectra of these molecules is desired. 1,4-dioxane is a heterocyclic ether with C2h symmetry. It can be viewed as a benzene derivative, with the two oxygens replacing the C–H group in the positions 1 and 4 along the ring, as can be seen in Fig. 1. One important difference between these two molecules is that benzene is unsaturated while 1,4-dioxane is a saturated molecule. This difference has a direct impact if we consider electron collisions with benzene and 1,4-dioxane, more precisely in the shape resonance spectra of these molecules. As is well known, benzene has two π * shape resonances (the low-lying resonance being twofold degenerate) associated with the unoccupied π * orbitals, where the higher lying resonance has a mixed shape and core-excited character.8–10 If we consider the interactions of low-energy electrons with 1,4-dioxane, the literature is still very scarce. The resonance spectra of 1,4-dioxane have been investigated by Bremner et al.11 using the near-threshold electron energya) Electronic mail: [email protected]
0021-9606/2014/140(18)/184303/6/$30.00
loss (EEL) spectra. The authors reported negative ion signals at around 6.4 eV, 7.2-7.6 eV, and 7.8 eV. Recently, Palihawadana et al.12 published a joint theoretical and experimental work on electron collisions with 1,4-dioxane. The experiment was performed with a crossed electron-molecular beam device and reported elastic differential (DCSs) and integral cross sections (ICSs) at 10, 15, 20, and 30 eV. The theoretical calculations employed two different methods: the ab initio R-matrix method and the independent atom model along with the additivity rule corrected by using screening coefficients (known as IAM-SCAR). Both calculations provided integral and differential cross sections. The R-matrix calculations of Palihawadana et al.12 reported the presence of two shape resonances in the integral cross section, one belonging to the Bg symmetry located at 8.30 eV and the other belonging to the Au symmetry located at 8.36 eV. The authors found another structure in the R-matrix integral cross section which resulted from the overlap of two structures belonging to the Au and Bu symmetries. They suggested that this structure could be related to a (higher-lying) resonance with a mixed character (shape and core-excited), as found in benzene and pyrazine.8–10 The resonance locations provided by the R-matrix calculations of Palihawadana et al.12 are in qualitative agreement with the EEL spectra. The IAMSCAR integral cross section is structureless, and shows qualitative agreement with the R-matrix results and with the experiment at higher energies. Regarding the differential cross sections, the agreement with the theoretical results and the experimental data is in general good. Palihawadana et al.12 suggested that pyrazine and 1,4-dioxane can be thought of as benzene derivatives. In view of that, the authors also compared their theoretical and experimental differential cross sections with the experimental data for benzene and pyrazine. The differences found between the DCSs of 1,4-dioxane and the DCSs of benzene and pyrazine were discussed in
140, 184303-1
© 2014 AIP Publishing LLC
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184303-2
A. S. Barbosa and M. H. F. Bettega
J. Chem. Phys. 140, 184303 (2014)
electron basis set (direct space) is given by |χm = A(|1 ⊗ |ϕm ),
(2)
where |1 is the target ground state, |ϕ m is a single-particle function, and A is the antisymmetrizer. For the calculations carried out in the SEP approximation, the direct space is augmented by CSFs constructed as |χm = A(|r ⊗ |ϕs ),
FIG. 1. Geometrical structure of 1,4-dioxane (generated with MacMolPlt7 ).
terms of the exchange interaction and the non-planarity of 1,4-dioxane. In this work, we present calculated elastic integral, momentum transfer (MTCS), and differential cross sections for low-energy-electron collisions with 1,4-dioxane. We employed the Schwinger multichannel method (SMC) method13 implemented with the pseudopotentials (SMCPP)15 of Bachelet, Hamann, and Schlüter.18 The calculations were carried out in the static-exchange (SE) and static-exchange plus polarization (SEP) approximations for energies up to 30 eV. We compare our calculated cross sections with theoretical and experimental results of Palihawadana et al.12 Our aim is to provide a set of cross sections obtained with a well established ab initio method and consequently obtain further insight into the resonance spectra of 1,4-dioxane. It is also interesting to compare the differential cross sections of 1,4dioxane with available theoretical and experimental differential cross sections for benzene and for other benzene derivatives, such as pyridine, pyrimidine, and pyrazine, in order to search for similarities among them. The remainder of this paper is as follows. In Sec. II, we present the theoretical method and computational procedure of this calculation. In Sec. III, we present and discuss the results. In Sec. IV, we close the paper with a brief summary of the present results.
II. COMPUTATIONAL DETAILS
Our calculations employed the SMC method13, 14 with pseudopotentials.15 The details of the method have been discussed elsewhere16 and here we will only provide the relevant points for the present calculations. The SMC method is a variational approximation to the scattering amplitude, and the resulting expression in the body-frame is given by 1 Skf |V |χm d −1 mn χn |V |Ski , fSMC (kf , ki ) = − 2π m,n (1) where the {|χ m } represents a basis set of (N + 1)-electron symmetry-adapted Slater determinants, also referred to as configuration state functions (CSFs). The CSFs are built from products of target states with single-particle functions. For the calculations carried out in the SE approximation, the (N + 1)-
(3)
where |r are the N-electron Slater states obtained by performing single excitations of the target from the occupied (hole) orbitals to a set of unoccupied (particle) orbitals. Here, |ϕ s is also a single-particle function and A is the antisymmetrizer. In Eq. (1), the dmn matrix elements are given by dmn = χm |A(+) |χn
(4)
and the A( + ) operator is given by 1 1 Hˆ − Hˆ P +P Hˆ + (P V +V P )−V G(+) P V. N +1 2 2 (5) In the above equations, Ski(f ) is a product of a target state and a plane wave with momentum ki(f ) , which is an eigenstate of the unperturbed Hamiltonian H0 ; V is the interaction potential between the incident electron and the target; Hˆ ≡ E − H is the collision energy minus the full Hamiltonian of the system, with H = H0 + V ; P is a projection operator onto the openchannel space; and G(+) P is the free-particle Green’s function projected on the P-space. Our scattering calculations were carried out in the optimized chair structure of C2h symmetry of 1,4-dioxane, since this is the most stable conformer. In order to optimize the geometrical structure, we employed the package GAMESS17 at the second order Møller-Plesset perturbation theory using the TZV++(2d,1p) basis set, in the C2h point group. In Fig. 1, we present the optimized structure of 1,4-dioxane. We used the pseudopotentials of Bachelet, Hamman, and Schlüter18 to replace the core electrons of carbon and oxygen atoms and the valence target electrons are represented by Cartesian Gaussian functions which were generated according to Bettega et al.19 We used six s-type functions, five p-type functions, and one d-type function (6s5p1d) for carbon and five s-type and p-type functions and three d-type functions (5s5p3d) for the oxygen. The Cartesian Gaussian functions for carbon and oxygen are show in Table I. For hydrogen, we used the 4s/3s basis set of Dunning20 augmented by one p-type function with exponent 0.75, as is shown in Table II. The symmetric combinations of the d-type orbital were excluded to avoid linear dependency in the basis set. To represent particle and scattering orbitals in the SEP calculations, we employed the improved virtual orbitals (IVOs).21 We selected IVOs satisfying the relation22 A(+) =
εpar − εhole + εscat < ,
(6)
where εpar is the particle orbital energy, εhole is hole orbital energy, εscat is the scattering orbital energy, and is the energy cut off. We used = 1.95 hartrees and considered all singlet and triplet coupled excitation for all symmetries, such
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184303-3
A. S. Barbosa and M. H. F. Bettega
J. Chem. Phys. 140, 184303 (2014)
TABLE I. Uncontracted Cartesian Gaussian functions used for carbon and oxygen. C
O
s s s s s s
12.49408 2.470291 0.614027 0.184029 0.036799 0.013682
16.05878 5.920242 1.034907 0.316843 0.065203
p p p p p
5.228869 1.592058 0.568612 0.210326 0.072250
10.14127 2.783023 0.841010 0.232940 0.052211
d d d
0.126278
1.698024 0.455259 0.146894
60 50 40 30 20 10
2 -16
30 20 10 0
TABLE II. Cartesian Gaussian functions used for hydrogen. Exponent
s s s s
13.3615 2.0133 0.4538 0.1233
p
0.75
Coefficient 0.130844 0.921539 1.00 1.00 1.00
10 15 20 energy (eV)
25
30
and located at 7 eV, to the Au symmetry and located at 8.4 eV, and to the Bg symmetry and located at 9.8 eV. We performed the partial wave analysis of the ICSs of these symmetries and obtained the corresponding eigenphase sum (not shown here). We found that there is a major contribution from the = 3 partial wave for the Bu and Au cross sections and from = 4 for the Bg cross section. Through the behavior of the eigenphase sum we concluded that those structures correspond to broad shape resonances. We also investigated the structures
15 Au
Ag 40
12
30
9
20
6
10
3
-16
2
cross section (10 cm )
50
0
0
5
10
15
20
25
30
20 2
In Fig. 2, we present our calculated ICS and MTCS in the SE and in the SEP approximations, for energies up to 30 eV. We also present the experimental data and the theoretical results, obtained with the IAM-SCAR and R-matrix methods, of Palihawadana et al.12 All R-matrix results shown here for comparison were obtained with 40 virtual orbitals. In the present ICS, we note a pronounced broad structure in the SE cross section that moves down in energy in the SEP calculations. Another feature that is worth mentioning is the rapid fall, as the energy decreases, shown by the present ICS. This point will be discussed in detail later. The agreement between our results and the results obtained with the R-matrix method is in general good. In the low-energy regime, the R-matrix ICS presents a structure that is absent in our ICS. For energies above 12 eV, the two cross sections start to differ, the Rmatrix ICS being lower than ours and showing several pseudoresonances. The ICS obtained with the IAM-SCAR method is structureless, increasing at lower energies and following the shape of our ICS and the experimental data at higher energies. In order to obtain additional information about the structures in the present ICS, we show in Fig. 3 the symmetry decomposition of the ICS according to the C2h point group. We observe that the pronounced structure in the ICS results from the overlap of three structures belonging to the Bu symmetry
5
0
0
5
10
15
20
25
30
12 Bu
16
Bg
10
-16
III. RESULTS
0
FIG. 2. Integral cross section (upper panel) and momentum transfer cross section (lower panel) for elastic scattering of electrons by 1,4-dioxane. We compare our results with calculated cross sections obtained by Palihawadana et al.12 using the R-matrix and IAM-SCAR methods. We also compare the theoretical results with the experimental data of Palihawadana et al.12
cross section (10 cm )
that we obtained 10 502 CSFs for the Ag and the Bu symmetries, 10 426 for the Au symmetry, and 10 417 CSFs for the Bg symmetry.
Type
SE SEP R-matrix IAM-SCAR expt.
70
400 cross section (10 cm )
Type
-16
2
cross section (10 cm )
80
8 12 6 8 4 4 0
SE SEP
2 0
5
10 15 20 energy (eV)
25
30
0
0
5
10 15 20 energy (eV)
25
30
FIG. 3. Symmetry decomposition of the integral cross section within the C2h group for elastic scattering of electrons by 1,4-dioxane obtained in the SE and SEP approximations.
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184303-4
A. S. Barbosa and M. H. F. Bettega
J. Chem. Phys. 140, 184303 (2014)
2
s-wave cross section (10 cm )
-16
A’
30
-16
2
cross section (10 cm )
35
25 20 15 10
SEP R-matrix
5
8 7 6 5 4 3 2 1 0
0
0.1
0.2 0.3 energy (eV)
0.4
0
0.1
0.2 0.3 energy (eV)
0.4
A’’
30
s-wave eigenphase (radians)
cross section (10
-16
2
cm )
0
25 20 15 10 5 0
0
5
10 15 20 energy (eV)
25
30
FIG. 4. Symmetry decomposition of the integral cross section in the Cs group. We compare our SEP results with the results obtained with the Rmatrix method.
that appear in the ICS of the Ag symmetry and concluded that they are not shape resonances. Palihawadana et al.12 reported two shape resonances, one in the Bg symmetry at 8.3 eV and the other in the Au symmetry at 8.36 eV. Our location for the Au resonance agrees well with the R-matrix calculations of Palihawadana et al.,12 while for the Bg symmetry our computed resonance position of 9.8 eV is much higher than the R-matrix results. This discrepancy may be due to the different treatments of polarization used in both calculations. Our resonance locations are higher compared to the EEL spectra of Bremner et al.,11 which show negative ion signals at around 6.4 eV, 7.2-7.6 eV, and 7.8 eV. Figure 4 shows a comparison between the symmetry decomposition of the present ICS and the R-matrix results in the Cs group.23 To obtain the A ICS, we summed the ICSs of the Ag and Bu symmetries and of the A ICS we summed the ICSs of the Au and Bg symmetries of Fig. 3. The agreement between the two theoretical results is good. Palihawadana et al.12 also reported a feature in the ICS at around 7 eV as being an overlap of two shape resonances belonging to the Au and Bu symmetries. They also suggested that the higher-lying resonance would be a mixing of shape and core-excited resonances. This behavior has been found in benzene and its aza-derivatives.8–10 In order to investigate this suggestion, we carried out a configuration interaction calculation on the anion of the Bu , Au , and Bg symmetries of 1,4-dioxane, similar to that carried out by Winstead and McKoy9 in pyrazine. The calculation employed the package GAMESS17 at the optimized geometry of the ground state of the neutral molecule (as described above) with the 6-311+G(d,p) basis set and up to quadruple excitations. The active space was comprised with the last three occupied and
0.05 0 -0.05 -0.1 -0.15 -0.2
FIG. 5. s-wave cross section and the corresponding s-wave eigenphase.
the first three unoccupied orbitals. The results of these calculations show that the dominant configuration for each symmetry has a pure shape-resonance configuration, that is the molecular ground state configuration with the extra electron in the first unoccupied orbital of the corresponding symmetry. The present ICS for 1,4-dioxane shows a rapid decrease in magnitude with decreasing energy. As shown in Fig. 3, this feature is due to the Ag symmetry. To investigate this behavior of the ICS for the Ag symmetry, we obtained the swave ( = 0) ICS and computed the corresponding s-wave eigenphase. The results are shown in Fig. 5 and indicate the presence of a Ramsauer-Townsend (RT) minimum at around 0.05 eV. The s-wave eigenphase changes sign, crossing zero at around 0.05 eV, which is the same energy where the s-wave ICS is zero. The behavior of the eigenphase suggests that the net interaction felt by the incoming electron changes from attractive, when the eigenphase is positive, to repulsive, when the eigenphase is negative. The interactions between the incoming electron and the molecule are the Coulomb (static), polarization, and the exchange potentials. The polarization interaction is always attractive to the incident electron, and the exchange is repulsive, in the sense that the incoming electron is not allowed to occupy a doubly occupied orbital (according to Pauli’s exclusion principle). The static potential is attractive when the incoming electron visits the target electronic cloud (by the Gauss law).24, 25 This is the signature of a RT minimum, which was not reported by Palihawadana et al.12 In Figures 6 and 7, we present our calculated DCSs in the SE and SEP approximations. We compare our DCSs with experimental and calculated data from Palihawadana et al.12 for 1,4-dioxane. Unpublished results obtained with the R-matrix method at 2, 3, 4, 6, and 8.5 eV are also included for comparison.23 We also compare our DCSs with
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A. S. Barbosa and M. H. F. Bettega
J. Chem. Phys. 140, 184303 (2014)
3 eV
4 eV
-16
2
cross section (10 cm /sr)
-16
2 eV
15 eV
6 eV
8.5 eV
30 60 90 120 150 180 30 60 90 120 150 180 30 60 90 120 150 180 scattering angle (degrees)
FIG. 6. Differential cross sections for elastic scattering of electrons by 1,4-dioxane at 2, 3, 4, 6, 8.5, and 10 eV. Dotted-dashed (blue) and solid (green) lines, present results obtained in the SE and SEP approximations; short-dashed (red) line, R-matrix results for 1,4-dioxane; dashed (indigo) line, IAM-SCAR results from Ref. 12; circles (magenta), experimental data for benzene from Ref. 27; triangles (cyan), experimental data for pyrazine from Ref. 28; stars (orange), experimental data for 1,4-dioxane from Ref. 12. The short-dashed (red) line at 2, 3, 4, 6, and 8.5 eV corresponds to DCSs from Ref. 23 and at 10 eV is from Ref. 12.
experimental data for benzene27 and pyrazine.28 1,4-dioxane and pyrazine can be thought as benzene derivatives, with the carbons on positions 1 and 4 replaced by oxygens in 1,4-dioxane and by nitrogen atoms in pyrazine. At low energies, there is a good agreement between our calculated DCSs and the R-matrix results.23 At 10 eV our calculated data also agree well with the calculated R-matrix DCS of Palihawadana et al.12 and with the experimental data for 1,4-dioxane. At higher energies, the present computed DCSs and those obtained with the R-matrix method by Palihawadana et al.12 differ in magnitude and present a different oscillatory behavior. It is worth to mention that the shape of our calculated DCS agrees better with experimental data, mainly at 20 eV and 30 eV. The differences in magnitude observed at these energies between the theory and the experiment can be explained by the fact that our calculations consider only the elastic channel, and therefore there is no flux loss from the elastic channel into the (closed) inelastic channels.26 Figure 8 shows a comparison between the experimental DCSs of 1,4-dioxane and the experimental data of benzene,27 pyrazine,28 and pyrimidine29 and the calculated results for
100 20 eV
30 eV
-16
2
15 eV
10
1 0
30 eV
1
30 60 90 120 150 180 30 60 90 120 150 180 30 60 90 120 150 180 scattering angle (degrees)
10 eV
10
0
20 eV
10
0
1
1
cross section (10 cm /sr)
100
2
10
cross section (10 cm /sr)
184303-5
30 60 90 120 150 180 30 60 90 120 150 180 30 60 90 120 150 180 scattering angle (degrees)
FIG. 7. As in Figure 6 at 15, 20, and 30 eV. The short-dashed (red) line are from Ref. 12.
FIG. 8. Differential cross sections for elastic scattering of electrons by 1,4-dioxane, benzene, pyrimidine, pyrazine, and pyridine at 15, 20, and 30 eV. Stars (orange), experimental data for 1,4-dioxane;12 circles (magenta), experimental data for benzene;27 triangles (cyan), experimental data for pyrazine;28 squares (brown), experimental data for pyrimidine;29 dashed (red) line, calculated results for benzene obtained in the SE approximation;30 solid (green) line, calculated results for pyridine obtained in the SE approximation.31
benzene30 and pyridine31 at 15, 20, and 30 eV. Pyrazine and pyrimidine differ from benzene by the replacement of two C–H groups by two nitrogen atoms in the ring (in the positions 1 and 4, and 1 and 3, respectively), while pyridine has only one nitrogen in place of the C–H group. This figure shows that the experimental DCSs of benzene, pyridine, and pyrazine are very similar to each other. It also shows that the calculated DCSs for benzene and pyridine, which were obtained in the SE approximation, agree with each other and also agree in shape with the experimental data of benzene, pyrimidine, and pyrazine, although they are higher in magnitude. This behavior is also explained by absence of flux loss from the elastic channel to the inelastic ones. The DCSs of 1,4-dioxane differ from the DCSs of the other molecules, especially at 15 eV, where the DCS of 1,4-dioxane presents a f-wave behavior while the other DCSs present a d-wave behavior. This comparison suggests that the DCSs of the planar molecules do not depend on the location of the nitrogen atoms in the ring. IV. SUMMARY
We presented calculated elastic cross sections for lowenergy electron collisions with 1,4-dioxane. Our calculations employed the Schwinger multichannel method and were performed in the static-exchange and in the static-exchangepolarization approximations. Our results are compared with other relevant experimental and theoretical results. We found three shape resonances in the Bu , Au , and Bg symmetries located at 7.0 eV, 8.4 eV, and 9.8 eV, respectively, which qualitatively agree with the R-matrix results and with the EEL spectra. We also found a Ramsauer-Townsend minimum located at around 0.05 eV. We compared the present computed DCSs with R-matrix and IAM-SCAR calculations and with the experimental data. Our results agree in general with the R-matrix results for energies up to 10 eV, and also agree with the experimental data. We also compared the DCSs of 1,4-dioxane with results for benzene and some benzene derivatives, namely, pyrimidine, pyrazine, and pyridine. Although the DCSs for the benzene and the benzene derivatives agree with each other, they differ from the DCSs of 1,4-dioxane.
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184303-6
A. S. Barbosa and M. H. F. Bettega
ACKNOWLEDGMENTS
A.S.B. acknowledges support from Brazilian Agency Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES). M.H.F.B. acknowledges support from Brazilian agency Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), and from FINEP (under project CTInfra). The authors acknowledge computational support from Professor Carlos M. de Carvalho at LFTC-DFis-UFPR and at LCPAD-UFPR, and from CENAPAD-SP. The authors would also like to thank Professor Jimena D. Gorfinkiel for providing the published and unpublished R-matrix cross sections in tabulated form. 1 L.
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