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UKRmol+: a suite for modelling of electronic processes in molecules interacting with electrons, positrons and photons using the R-matrix method

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read UKRmol+ reengineers the molecular R-matrix codes to model electron and positron scattering, photoionization, and time-dependent laser inputs with mixed Gaussian/B-spline continua.

desk verdict A substantial open-source release that delivers real new capability; referees should focus on documenting the integral library that the headline B-spline results depend on. read the letter →

arxiv 1908.03018 v1 pith:WKJY6KFG submitted 2019-08-08 physics.comp-ph physics.atom-ph

Zdeněk Mašín , Jakub Benda , Jimena D. Gorfinkiel , Alex G. Harvey , Jonathan Tennyson This is my paper · ORCID
classification physics.comp-phphysics.atom-ph
keywords electron-moleculescatteringpositronphotoionizationR-matrixmethodB-splineorbitalsGaussian-typequantumchemistryinterfaceMPIparallelization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper reports UKRmol+, a completely rewritten implementation of the UK polyatomic molecular R-matrix scattering codes. It claims that one suite can compute low-energy electron and positron scattering from molecules and clusters, photoionization cross sections, and input for time-dependent R-matrix (RMT) calculations. The key advance is an optional mixed Gaussian-type-orbital and B-spline continuum, which permits much larger R-matrix spheres and higher photoelectron energies than the previous GTO-only code. A sympathetic reader would care because this is the public, reproducible foundation for a widely used method in molecular collision and photoionization physics.

What carries the argument

The central mechanism is the R-matrix division of space combined with the mixed Gaussian/B-spline continuum implemented in GBTOlib. BTOs, defined as radial B-splines multiplied by real spherical harmonics, represent the continuum at higher kinetic energies and support much larger R-matrix radii, while GTOs describe target and low-energy continuum regions. The load-bearing step is the construction and diagonalization of the energy-independent inner-region Hamiltonian: one diagonalization supplies all scattering energies, and subsequent outer-region propagation and matching produce the observables.

What would settle it

Compare GBTOlib's mixed Gaussian/B-spline integrals with high-order numerical quadrature on a small molecule at the suite's stated R-matrix parameters, and run its free-scattering eigenphase test across a wide energy range; eigenphase sums consistently above the paper's $10^{-2}$ rad rule of thumb would falsify the continuum representation.

Watch

Extended reading notes

Core claim

On its own terms, the central assertion is that UKRmol+ is a completely reengineered and extended version of the previous UKRmol codes, not an incremental patch. It takes target molecular orbitals from external quantum chemistry packages, builds the inner-region Hamiltonian with the GBTOlib integral library, diagonalizes it serially or in parallel, and feeds the eigenpairs to outer-region modules that yield K-matrices, cross sections, eigenphase sums, resonance parameters, photoionization dipoles, or RMT input. The demonstration cases are electron-impact excitation of thiophene, electron scattering from BeH at an R-matrix radius of $35\,a_0$ using a mixed GTO/BTO continuum, positron-H2 scattering with pseudostates, and photoionization of benzene. The paper argues that the suite reproduces earlier UKRmol results and that the BTO capability extends the reliable energy range beyond what double-precision GTO-only calculations allow.

Load-bearing premise

If the unpublished integral library used for the mixed Gaussian/B-spline basis has numerical errors, the B-spline continuum results collapse, since no independent published reference for those integrals yet exists.

Editorial extensions

If this is right

  • Diffuse targets with R-matrix radii of tens of bohr become practical, as demonstrated by the BeH calculation at $35\,a_0$ with 50 target states.
  • Photoionization calculations reach higher photoelectron energies: the mixed GTO/BTO basis removes unphysical oscillations that break down the double-precision GTO-only benzene results near 50 eV.
  • Positron scattering with pseudostates improves the treatment of polarization and can be extended to larger targets through the parallel MPI-SCATCI diagonalizer.
  • The same inner-region data feed the RMT code, so intense-laser time-dependent studies share an identical molecular description with the scattering and photoionization calculations.
  • The distributed test suite covers all supported Abelian point groups, serial and parallel runs, and benchmark outputs for Hamiltonian eigenvalues, cross sections, and eigenphase sums.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper's examples, the BTO continuum could become a systematic convergence tool: varying the R-matrix radius and the B-spline grid start gives a direct route to checking continuum completeness rather than merely extending the energy range.
  • The benzene comparison suggests a cheap diagnostic: because the Legendre truncation parameters $L_{\mathrm{Leg}}=12$ and $24$ visibly change results above 25 eV, one could monitor convergence of the free-scattering eigenphase sum while raising these parameters in any new calculation.
  • The phase-matching tools for geometry-dependent photoionization amplitudes imply a natural test: apply the suite to a molecule with a known conical intersection and verify that the matched dipoles vary smoothly along a closed loop around the intersection.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript describes UKRmol+, a Fortran 95/2003 suite for molecular R-matrix calculations of electron and positron scattering, molecular photoionization, and generation of input for the RMT time-dependent suite. The presentation covers the standard inner-/outer-region R-matrix formalism in Section 2, the individual programs and their namelists in Section 3, and the workflows for scattering, photoionization, and RMT input in Sections 4-6. A test suite is described in Section 7, and Section 8 presents illustrative applications: electron-impact excitation of thiophene compared with EELS data, electron scattering from BeH with a mixed GTO/BTO continuum at R = 35 a0, positron-H2 scattering with pseudostates, and photoionization of benzene comparing GTO-only and mixed GTO/BTO continuum bases.

Significance. If the central claims hold, UKRmol+ is a substantial community resource: it is open-source, distributed with a build system and test suite, supports MPI parallelization through MPI-SCATCI and MPI-RSOLVE, accepts target orbitals from external quantum chemistry packages, and extends the continuum representation to mixed Gaussian/B-spline bases. The Section 2.1 derivation is standard and correct, and the comparisons against independent experimental EELS and positron-beam data, together with reproduction of previously published BeH results, provide meaningful grounding. The authors are also candid about the limitations of the benzene demonstration. The main risk is that the new mixed GTO/BTO integral capability rests on GBTOlib, which is cited only as "In preparation", and the in-paper validation of that component is incomplete.

major comments (3)
  1. [Section 3.1.2 and Section 3.1.6] The free-scattering test (Section 3.1.2) checks overlap, kinetic-energy, and Bloch integrals in a one-electron problem with H = -nabla^2/2, but it cannot detect errors in the mixed two-electron integral classes <CC||TT> and <CC||CT>, which are precisely the numerically delicate classes needed for the BTO continuum capability. Since GBTOlib is described only as "In preparation" (Ref. [10]) and no independent analytical or numerical validation of these integral classes is reported, the headline BTO results rest on an unverified foundation. I recommend adding explicit convergence tests of these integral classes against known values, or against an independent implementation, and reporting the sensitivity to delta_r and the Legendre truncation parameters.
  2. [Section 8.4, Figure 12] The benzene photoionization example is the only in-paper molecular demonstration that exercises the mixed two-electron integrals, but the authors state that the calculation "is not to present accurate observables" and acknowledge that the results are not converged with respect to continuum angular momentum above about 50 eV. The visible differences between LLeg = 12 and LLeg = 24 in the 2E2g panel additionally show incomplete convergence in the Legendre truncation. As published evidence for the correctness of the mixed integral library this is weak; I ask for one converged benchmark, or a quantitative statement of the expected errors in the displayed curves.
  3. [Section 1 and Section 7] The claim that UKRmol+ "should be able to reproduce virtually all the old results" and that this "has indeed been tested for a number of targets" is not quantified, and the Section 7 test-suite benchmark outputs are generated by the same code, so they demonstrate reproducibility rather than correctness. A table comparing UKRmol and UKRmol+ results for at least one representative target, with stated tolerances, would make the backward-compatibility claim concrete and would strengthen the paper's central assertion.
minor comments (4)
  1. [Abstract] The abstract contains the typo "photionisation" in place of "photoionisation".
  2. [Section 2.2] The text reads "The next section shows shows how this leads"; the duplicated word should be removed.
  3. [Sections 3.1.5, 3.2, 3.4, 8.1, 8.2] There are several grammatical and typographical errors that should be corrected: "all the orbitals used for m a single orthonormal set" in Section 3.1.5, "differnet" in Section 3.2, "quadropole" in Section 3.4, "This calculations was" in Section 8.1, and "Hamilonians" in Section 8.2.
  4. [Figure 9] The caption ends with an incomplete phrase "[72] and." which should be completed or removed.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the paper's derivation chain is standard R-matrix algebra and its illustrative results are either compared with unnormalized experiment or labelled non-benchmark; the main self-reference is an in-preparation GBTOlib citation, a support gap rather than a circular reduction.

full rationale

The paper is a software-description/code-release article. Its Section 2 derivation follows the standard R-matrix embedding algebra (Eqs. 8-18): the Bloch operator converts the boundary-value problem into an eigenvalue problem, and the R-matrix is defined by projecting the spectral decomposition of the inner-region Green's function. Nothing in this chain is fitted, and no physical observable is defined in terms of the result it is supposed to predict. The illustrative calculations in Section 8 provide external anchoring where they claim it: the thiophene excitation function is compared to EELS data that the paper explicitly states were not normalized to theory, and the positron-H2 cross sections are compared to measurements by Zecca et al. and Hoffman et al. The BeH and benzene panels are explicitly capability demonstrations, not validated predictions (Section 8.4 says its purpose 'is not to present accurate observables'). The only load-bearing self-reference is GBTOlib (Ref. [10], 'In preparation'), which supplies the mixed GTO/BTO integrals used by the BTO continuum examples; the in-suite free-scattering test exercises only a one-electron zero-potential Hamiltonian and therefore cannot independently validate the mixed two-electron classes. That is a missing-support/correctness risk, not a circular reduction: the paper does not derive any result from GBTOlib, define a target quantity in terms of GBTOlib output, or invoke a uniqueness theorem. The test-suite 'benchmark outputs' are regression references produced by the same code and are presented as compilation tests, i.e. reproducibility checks rather than first-principles predictions. Hence no derivation in the paper reduces to its own inputs by construction; the appropriate finding is no significant circularity, with the GBTOlib dependency noted as the weak point.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The paper contains no fitted parameters in the sense of constants tuned to reproduce experimental data. The computational model choices (R-matrix radius, basis sets, deletion thresholds) are user inputs that the paper guides, but they are not derived from the central claim. The main axioms are standard domain assumptions of the R-matrix method. No new physical entities are postulated.

assumptions (5)
  • domain assumption Fixed-nuclei non-relativistic Hamiltonian (Eq. 5) is used for the inner region.
    All equations and codes in Sections 2-5 rely on this Hamiltonian; relativistic effects and nuclear motion are excluded from the central claim.
  • domain assumption Target electronic wavefunctions are assumed to have negligible amplitude on the R-matrix sphere boundary.
    Stated in Section 2 opening and Section 3.1.1 ('the spatial extent of the target electronic orbitals determines the size of the R-matrix sphere required'); the method's matching condition requires target orbitals to vanish at r=a.
  • domain assumption Outer-region projectile-target interaction is represented by a single-centre multipole expansion.
    Used in Section 2.2 for propagation to asymptotic radius, and in SWINTERF (Section 3.6.1). The paper refers to Appendix A.2 of [13] for the potential form. Outside the R-matrix sphere, exchange is neglected.
  • domain assumption For photoionization, the initial bound state is fully contained within the R-matrix sphere.
    Section 5 states 'In the current implementation we consider the initial state to be fully contained within the R-matrix sphere', which is a good approximation only for ground and low-lying states of cations.
  • domain assumption Symmetric orthogonalization of continuum orbitals with user-selected deletion thresholds preserves the physical description.
    Section 3.1.5 states that continuum orbitals with overlap eigenvalues below del_thresh are deleted; the accuracy of results depends on choosing thresholds correctly, and quad precision is sometimes required. The examples depend on this numerics.

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Cite this review

Pith. "Pith review of UKRmol+: a suite for modelling of electronic processes in molecules interacting with electrons, positrons and photons using the R-matrix method." pith.science (2026). https://pith.science/paper/WKJY6KFG

@misc{pith2026190803018,
  author       = {Pith},
  title        = {Pith review of: UKRmol+: a suite for modelling of electronic processes in molecules interacting with electrons, positrons and photons using the R-matrix method},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WKJY6KFG}},
  note         = {Machine review of arXiv:1908.03018}
}
read the original abstract

UKRmol+ is a new implementation of the UK R-matrix electron-molecule scattering code. Key features of the implementation are the use of quantum chemistry codes such as Molpro to provide target molecular orbitals; the optional use of mixed Gaussian -- B-spline basis functions to represent the continuum and improved configuration and Hamiltonian generation. The code is described, and examples covering electron collisions from a range of targets, positron collisions and photionisation are presented. The codes are freely available as a tarball from Zenodo.

Figures

Figures reproduced from arXiv: 1908.03018 by the authors.

Figure 1
Figure 1. The BTOs and GTOs are defined as follows: [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 1
Figure 1. Set-up of the continuum basis in a UKRmol+ calculation. The G [PITH_FULL_IMAGE:figures/full_fig_p016_1.png] view at source ↗
Figure 2
Figure 2. Workflow of the orbital orthogonalization. The steps 2 an [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗
Figures from the paper (10 more)
Figure 3
Figure 3. Figure 3: Parameters for finite-difference discretization of the inn [PITH_FULL_IMAGE:figures/full_fig_p037_3.png]
Figure 4
Figure 4. Figure 4: Workflow for the inner region and interface parts of a sca [PITH_FULL_IMAGE:figures/full_fig_p039_4.png]
Figure 5
Figure 5. Figure 5: Workflow for the outer region of a scattering calculation. [PITH_FULL_IMAGE:figures/full_fig_p042_5.png]
Figure 6
Figure 6. Figure 6: Workflow for a photoionization calculation. Red indicates th [PITH_FULL_IMAGE:figures/full_fig_p048_6.png]
Figure 7
Figure 7. Figure 7: Workflow for production of the RMT input file. Red indicates [PITH_FULL_IMAGE:figures/full_fig_p056_7.png]
Figure 8
Figure 8. Figure 8: Alternative workflow for production of the RMT input file us [PITH_FULL_IMAGE:figures/full_fig_p057_8.png]
Figure 9
Figure 9. Figure 9: Cross sections for excitation into the second triplet stat [PITH_FULL_IMAGE:figures/full_fig_p059_9.png]
Figure 10
Figure 10. Figure 10: Cross sections for electron scattering from BeH (doub [PITH_FULL_IMAGE:figures/full_fig_p060_10.png]
Figure 11
Figure 11. Figure 11: Total cross sections for positron-H2 collisions. Calculations including pseu￾docontinuum orbitals with angular momenta up to 2 (’spd’) and up to 5 (’spdfgh’) are compared with experimental results [93, 94]. suite (in particular MPI-SCATCI) will enable both electron an…
Figure 12
Figure 12. Figure 12: Cross sections (on log-scale) and β asymmetry parameters (angular distribu￾tions) for photoionization of benzene into the two lowest-lying states (2E1g and 2E2g) as calculated using GTO-only continua (lmax = 6, double and quad precision) and mixed GTO/BTO continua (lm…

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Works this paper leans on

91 extracted references · 76 canonical work pages

  1. [10]

    Z. Maˇ s ´ ın, et al, GBTOlib: library for evaluation of molecular integrals in the basis of multicentric gaussian and single-centre B-spline orbita ls., Computer Physics CommunicationIn preparation

  2. [1]

    P. G. Burke, K. A. Berrington (Eds.), Atomic and Molecular Proce sses, an R-matrix Approach, Institute of Physics Publishing, Bristol, 199 3. 67 Table B.22: Multiplication table for combinations of irreducible represe ntations of the Abelian groups supported with UKRmol+. Numbers are the M -values introduced in Table B.21. 0 1 2 3 4 5 6 7 0 0 1 2 3 4 5 6 ...

  3. [3]

    Descouvemont, D

    P. Descouvemont, D. Baye, The R-matrix theory, Rep. Prog. P hys. 73 (2010) 036301. doi:{10.1088/0034-4885/73/3/036301}

    doi:10.1088/0034-4885/73/3/036301 2010

  4. [4]

    Tennyson, L

    J. Tennyson, L. K. McKemmish, T. Rivlin, Low temperature chem- istry using the R-matrix method, Faraday Discuss. 195 (2016) 31– 48. doi:10.1039/c6fd00110f

    work page doi:10.1039/c6fd00110f 2016

  5. [5]

    Zhang, K

    R. Zhang, K. L. Baluja, J. Franz, J. Tennyson, Positron collision s with molecular hydrogen: cross sections and annihilation parameters ca lcu- lated using the R-matrix with pseudo-states method, J. Phys. B: At. Mol. Opt. Phys. 44 (2011) 035203

    2011

  6. [6]

    C. J. Gillan, J. Tennyson, P. G. Burke, The UK molecular R-matrix scattering package: a computational perspective, in: W. Huo, F. A. Gi- anturco (Eds.), Computational methods for Electron-molecule co llisions, Plenum, New York, 1995, pp. 239–254

    1995

  7. [7]

    L. A. Morgan, C. J. Gillan, J. Tennyson, X. Chen, R-matrix calcula tions for polyatomic molecules: electron scattering by N 2O, J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 4087–4096

    1997

  8. [8]

    J. M. Carr, P. G. Galiatsatos, J. D. Gorfinkiel, A. G. Harvey, M. A . Lysaght, D. Madden, Z. Maˇ s ´ ın, M. Plummer, J. Tennyson, H. N. Varambhia, UKRmol: a low-energy electron- and positron-molecule scattering suite, The European Physical Journal D 66 (3) (2012) 58. doi:10.1140/epjd/e2011-20653-6

    work page doi:10.1140/epjd/e2011-20653-6 2012

Show all 91 references
  1. [9]

    Werner, P

    H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. Sch¨ utz, Mol- pro: a general-purpose quantum chemistry program package, WI REs Comput. Mol. Sci. 2 (2012) 242–253. doi:10.1002/wcms.82

    2012 doi

  2. [11]

    A. G. Harvey, D. S. Brambila, F. Morales, O. Smirnova, An R-mat rix approach to electron-photon-molecule collisions: photoelectron a ngular 69 distributions from aligned molecules, J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 215005. doi:{10.1088/0953-4075/47/21/215005}

    2014 doi

  3. [12]

    D. S. Brambila, A. G. Harvey, Zdenˇ ek, J. D. Gorfinkiel, O. Smirn ova, The role of multichannel effects in the photoionization of the no 2 molecule: an ab initio r -matrix study, J. Phys. B: At. Mol. Opt. Phys. 48 (2015) 245101

    2015

  4. [13]

    Brown, et al., RMT: R-matrix with time-dependence

    A. Brown, et al., RMT: R-matrix with time-dependence. Solving the semi-relativistic, time-dependent Schr¨ odinger equation for g eneral, multi-electron atoms and molecules in intense, ultrashort, arbitrar ily polarized laser pulses., Comput. Phys. Commun.In preparation

  5. [14]

    Burke, C

    P. Burke, C. Noble, V. Burke, R-matrix theory of atomic, molec - ular and optical processes, in: P. Berman, C. Lin, E. Ari- mondo (Eds.), Advances In Atomic, Molecular, and Opti- cal Physics, Vol. 54, Academic Press, 2007, pp. 237 – 318. doi:https://doi.org/10.1016/S1049-250X(...

    2007 doi

  6. [15]

    P. G. Burke, R-Matrix Theory of Atomic Collisions: Application to Atomic, Molecular and Optical Processes, Springer, 2011

    2011

  7. [16]

    Gailitis, New forms of asymptotic expansions for wavefunctio ns of charged-particle scattering, J

    M. Gailitis, New forms of asymptotic expansions for wavefunctio ns of charged-particle scattering, J. Phys. B: At. Mol. Opt. Phys. 9 (1 976) 843

  8. [17]

    K. L. Baluja, P. G. Burke, L. A. Morgan, R-matrix propagation program for solving coupled second-order differential-equations, Compute r Phys. Comm. 27 (1982) 299–307

    1982

  9. [18]

    L. A. Morgan, A generalized r-matrix propagation program for solv- ing coupled 2nd-order differential-equations, Computer Phys. Com m. 31 (1984) 419–422

    1984

  10. [19]

    P. G. Burke, C. J. Noble, A. G. Sunderland, V. M. Burke, Electr on Collisions with Iron Peak Elements: A Computational Grand Challenge, Physica Scripta T100 (2002) 55–63

    2002

  11. [20]

    C. J. Noble, R. K. Nesbet, Cfasym, a program for the calculatio n of the asymptotic solutions of the coupled equations of electron collisio n- theory, Computer Phys. Comm. 33 (1984) 399. 70

    1984

  12. [21]

    Szmytkowski, J

    R. Szmytkowski, J. Hinze, Convergence of the non-relativistic and rela- tivistic R -matrix expansions at the reaction volume boundary, Jour nal of Physics B: Atomic, Molecular and Optical Physics 29 (4) (1996) 76 1. doi:10.1088/0953-4075/29/4/018

    1996 doi

  13. [22]

    Bachau, E

    H. Bachau, E. Cormier, P. Decleva, J. E. Hansen, F. Martin, Ap plica- tions of b-splines in atomic and molecular physics, Rep. Prog. Phys. 6 4 (2001) 1815–1943

    2001

  14. [23]

    Faure, J

    A. Faure, J. D. Gorfinkiel, L. A. Morgan, J. Tennyson, GTOBAS : fitting continuum functions with Gaussian-type orbitals, Comp. Phys. Com - mun. 144 (2002) 224–241

    2002

  15. [24]

    Tennyson, Electron - molecule collision calculations using the R- matrix method, Phys

    J. Tennyson, Electron - molecule collision calculations using the R- matrix method, Phys. Rep. 491 (2010) 29–76

    2010

  16. [25]

    M. M. Fujimoto, W. J. Brigg, J. Tennyson, R-matrix calculations of differential and integral cross sections for low-energy electron c ollisions with ethanol, The European Physical Journal D 66 (2012) 204

    2012

  17. [26]

    W. J. Brigg, J. Tennyson, M. Plummer, R-matrix calculations of lo w- energy electron collisions with methane, J. Phys. B: At. Mol. Opt. Ph ys. 47 (2014) 185203

    2014

  18. [27]

    Tennyson, R-matrix calculation of Rydberg states of CO, J

    J. Tennyson, R-matrix calculation of Rydberg states of CO, J. Phys. B: At. Mol. Opt. Phys. 29 (1996) 6185–6201

    1996

  19. [28]

    A. Dora, J. Tennyson, L. Bryjko, T. van Mourik, R-matrix calc ulation of low-energy electron collisions with uracil, J. Chem. Phys. 130 (16) (2009) 164307–8. doi:10.1063/1.3119667

    2009 doi

  20. [29]

    Bartschat, E

    K. Bartschat, E. T. Hudson, M. P. Scott, P. G. Burke, V. M. B urke, Electron-atom scattering at low and intermediate energies using a pseudo-state R-matrix basis, J. Phys. B: At. Mol. Opt. Phys. 29 ( 1996) 115–123

    1996

  21. [30]

    J. D. Gorfinkiel, J. Tennyson, Electron-H + 3 collisions at intermediate energies, J. Phys. B: At. Mol. Opt. Phys. 37 (2004) L343–L350

    2004

  22. [31]

    J. D. Gorfinkiel, J. Tennyson, Electron impact ionisation of small molecules at intermediate energies: the R-matrix with pseudostate s method, J. Phys. B: At. Mol. Opt. Phys. 38 (2005) 1607–1622. 71

    2005

  23. [32]

    Halmov´ a, J

    G. Halmov´ a, J. D. Gorfinkiel, J. Tennyson, Low and intermediate energy electron collisions with the C − 2 molecular anion, J. Phys. B: At. Mol. Opt. Phys. 41 (2008) 155201

    2008

  24. [33]

    Jones, J

    M. Jones, J. Tennyson, On the use of pseudostates to calcula te molecular polarizabilities, J. Phys. B: At. Mol. Opt. Phys. 43 (2010) 045101

    2010

  25. [34]

    Zhang, P

    R. Zhang, P. G. Galiatsatos, J. Tennyson, Positron collisions wit h acetylene calculated using the R-matrix with pseudo-states metho d, J. Phys. B: At. Mol. Opt. Phys. 44 (2011) 195203

    2011

  26. [35]

    Schaftenaar, J

    G. Schaftenaar, J. H. Noordik, Molden: a pre- and post- processing program for molecular and electronic structures, Jou r- nal of Computer-Aided Molecular Design 14 (2) (2000) 123–134. doi:10.1023/A:1008193805436

    2000 doi

  27. [36]

    R. M. Parrish, L. A. Burns, D. G. A. Smith, A. C. Simmonett, A. E . DePrince, E. G. Hohenstein, U. Bozkaya, A. Y. Sokolov, R. Di Remig io, R. M. Richard, J. F. Gonthier, A. M. James, H. R. McAlexander, A. K u- mar, M. Saitow, X. Wang, B. P. Pritchard, P. Verma, H. F. Schaefe r...

    2017

  28. [37]

    H. H. H. Homeier, E. O. Steinborn, Some properties of the coup ling co- efficients of real spherical harmonics and their relation to Gaunt co effi- cients, Journal of Molecular Structure: THEOCHEM 368 (1996) 31 –37. doi:16/S0166-1280(96)90531-X

    1996

  29. [38]

    Darby-Lewis, Z

    D. Darby-Lewis, Z. Maˇ s ´ ın, J. Tennyson, R-matrix calculation s of electron impact electronic excitation of {BeH}, Journal of Physics B: Atomic, Molecular and Optical Physics 50 (17) (2017) 175201. doi:10.1088/1361-6455/aa8161

    2017 doi

  30. [39]

    Szab´ o, N

    A. Szab´ o, N. S. Ostlund, Modern quantum chemistry: introdu ction to advanced electronic structure theory, Courier Dover Publication s, 1996. 72

    1996

  31. [42]

    Sieradzka, J

    A. Sieradzka, J. D. Gorfinkiel, Theoretical study of resonanc e formation in microhydrated molecules. i. pyridine-(h 2o)n, n = 1,2,3,5, The Journal of Chemical Physics 147 (3) (2017) 034302. doi:10.1063/1.4993941

    2017 doi

  32. [43]

    Sieradzka, J

    A. Sieradzka, J. D. Gorfinkiel, Theoretical study of resonanc e formation in microhydrated molecules. ii. thymine-(h 2o)n, n = 1,2,3,5, The Journal of Chemical Physics 147 (3) (2017) 034303. doi:10.1063/1.4993946

    2017 doi

  33. [45]

    Tennyson, A new algorithm for Hamiltonian matrix constructio n in electron-molecule collision calculations, J

    J. Tennyson, A new algorithm for Hamiltonian matrix constructio n in electron-molecule collision calculations, J. Phys. B: At. Mol. Opt. Phy s. 29 (1996) 1817–1828

    1996

  34. [46]

    Yoshimine, CONSTRUCTION OF HAMILTONIAN MATRIX IN LARGE CONFIGURATION INTERACTION CALCULATIONS, J

    M. Yoshimine, CONSTRUCTION OF HAMILTONIAN MATRIX IN LARGE CONFIGURATION INTERACTION CALCULATIONS, J. Comput. Phys. 11 (1973) 449–454

    1973

  35. [47]

    A. D. McLean, in: W. A. Lester Jr (Ed.), Potential Energy Surf aces in Chemistry, San Jose: IBM Research Laboratory, 1971, p. 87

    1971

  36. [48]

    A. F. Al-Refaie, J. Tennyson, A parallel algorithm for Hamilto- nian matrix construction in electronmolecule collision calculations: MPI-SCATCI, Computer Physics Communications 221 (2017) 53–62 . doi:10.1016/j.cpc.2017.07.023

    2017 doi

  37. [49]

    Stathpoulos, F

    A. Stathpoulos, F. C. F, A DA VIDSON PROGRAM FOR FINDING A FEW SELECTED EXTREME EIGENPAIRS OF A LARGE, SPARSE, 73 REAL, SYMMETRICAL MATRIX, Computer Phys. Comm. 79 (1994) 268–290. doi:10.1016/0010-4655(94)90073-6

    1994 doi

  38. [50]

    Lehoucq, D

    R. Lehoucq, D. Sorensen, C. Yang, ARPACK Users’ Guide: Solu tion of Large-scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, Software, Environments, Tools, Society for Industria l and Ap- plied Mathematics, 1998

    1998

  39. [51]

    J. Choi, J. Demmel, I. Dhillon, J. Dongarra, S. Ostrouchov, A. P etitet, K. Stanley, D. W. Walker, R. C. Whaley, ScaLAPACK: A Portable Lin- ear Algebra Library for Distributed Memory Computers - Design Iss ues and Performance, in: Proceedings of the Second International W orks...

    1996

  40. [52]

    Hernandez, J

    V. Hernandez, J. E. Roman, V. Vidal, SLEPc: A scalable and flexi- ble toolkit for the solution of eigenvalue problems, ACM Trans. Math. Software 31 (3) (2005) 351–362

    2005

  41. [53]

    Tennyson, Phase factors in electron-molecule collision calcula tions, Computer Phys

    J. Tennyson, Phase factors in electron-molecule collision calcula tions, Computer Phys. Comm. 100 (1997) 26–30

    1997

  42. [54]

    C. J. Gillan, J. Tennyson, B. M. McLaughlin, P. G. Burke, Low ene rgy electron impact excitation of the nitrogen molecule: optically forbidd en transitions, J. Phys. B: At. Mol. Opt. Phys. 29 (1996) 1531–1547

    1996

  43. [55]

    Tashiro, K

    M. Tashiro, K. Morokuma, J. Tennyson, r-matrix calculation of electron collisions with electronically excited o 2 molecules, Phys. Rev. A 73 (2006) 052707. doi:10.1103/PhysRevA.73.052707. URL https://link.aps.org/doi/10.1103/PhysRevA.73.052707

    2006 doi

  44. [56]

    Tennyson, Partitioned R-matrix theory for molecules, J

    J. Tennyson, Partitioned R-matrix theory for molecules, J. Ph ys. B: At. Mol. Opt. Phys. 37 (2004) 1061–1071

    2004

  45. [57]

    A. G. Harvey, D. S. Brambila, F. Morales, O. Smirnova, CDENPRO P: Transition matrix elements involving continuum states, arXiv e-print s (2013) arXiv:1401.0229 arXiv:1401.0229. 74

    2013 arXiv

  46. [58]

    Loupas, J

    A. Loupas, J. D. Gorfinkiel, Shape and core-excited resonanc es in elec- tron scattering from alanine, The Journal of Chemical Physics 150 (6) (2019) 064307. doi:10.1063/1.5081813

    2019 doi

  47. [59]

    Tarana, J

    M. Tarana, J. Tennyson, Polarization effects in electron collision s with Li2: application of the molecular R-matrix method with pseudostates, J. Phys. B: At., Mol. Opt. Phys. 41 (2008) 205204

    2008

  48. [60]

    Sukuba, J

    I. Sukuba, J. D. Gorfinkiel, Phys. Rev. A

  49. [61]

    Maˇ s ´ ın, J

    Z. Maˇ s ´ ın, J. D. Gorfinkiel, Shape and core excited resonances in electron collisions with diazines, The Journal of Chemical Physics 137 (20) (20 12) 204312. doi:10.1063/1.4767345

    doi

  50. [62]

    P. G. Burke, H. M. Schey, Elastic scattering of low-energy electrons by atomic hydrogen, Phys. Rev. 126 (1962) 147–162. doi:10.1103/PhysRev.126.147

    1962 doi

  51. [63]

    Tennyson, C

    J. Tennyson, C. J. Noble, Reson–a program for the detection and fitting of breit-wigner resonances, Comput. Phys. Commun. 33 (1984) 4 21–424

    1984

  52. [64]

    D. T. Stibbe, J. Tennyson, TIMEDEL: a program for the detection and parameterization of resonances using the time- delay matrix, Computer Phys. Comm. 114 (1-3) (1998) 236–242. doi:{10.1016/S0010-4655(98)00070-8}

    1998 doi

  53. [65]

    D. A. Little, J. Tennyson, M. Plummer, C. J. Noble, A. G. Sunderland, TIMEDELn: A programme for the detection and parametrization of overlapping resonances using the time-delay method, Computer Physics Communications 215 (2017) 137 – 148. doi:https://doi.org/10.1016/j.cpc.2017.01.005

    2017 doi

  54. [66]

    Tennyson, Continuum and bound states of the e − – CH + system using the R–Matrix method, J

    J. Tennyson, Continuum and bound states of the e − – CH + system using the R–Matrix method, J. Phys. B: At. Mol. Opt. Phys. 21 (198 8) 805–816

  55. [67]

    Sanna, F

    N. Sanna, F. A. Gianturco, Differential cross sections for elec - tron/positron scattering for polyatomic molecules, Computer Phy s. Comm. 114 (1998) 142–167. 75

    1998

  56. [68]

    F. A. Gianturco, A. Jain, The theory of electron scattering fr om polyatomic molecules, Physics Reports 143 (6) (1986) 347–425. doi:10.1016/0370-1573(86)90125-0

    1986 doi

  57. [69]

    Regeta, M

    K. Regeta, M. Allan, C. Winstead, V. McKoy, Z. Maˇ s ´ ın, J. D. Gorfinkiel, Resonance effects in elastic cross sections for electron scatterin g on pyrimidine: Experiment and theory, The Journal of Chemical Physic s 144 (2). doi:http://dx.doi.org/10.1063/1.4937790

    doi

  58. [70]

    Zhang, A

    R. Zhang, A. Faure, J. Tennyson, Electron and positron collisio ns with polar molecules: studies with the benchmark water molecule, Phys. Scripta 80 (2009) 015301

    2009

  59. [71]

    Regeta, M

    K. Regeta, M. Allan, Z. Maˇ s ´ ın, J. D. Gorfinkiel, Abso- lute cross sections for electronic excitation of pyrimidine by electron impact, The Journal of Chemical Physics 144 (2). doi:http://dx.doi.org/10.1063/1.4939077

    doi

  60. [72]

    Loupas, K

    A. Loupas, K. Regeta, M. Allan, J. D. Gorfinkiel, Shape and core -excited resonances in thiophene, The Journal of Physical Chemistry A 122 (4) (2018) 1146–1155. doi:10.1021/acs.jpca.7b11865

    2018 doi

  61. [73]

    D. A. Little, J. Tennyson, Singlet and triplet ab initio Rydberg states of N 2, J. Phys. B: At. Mol. Opt. Phys. 46 (2013) 145102

    2013

  62. [74]

    B. K. Sarpal, S. E. Branchett, J. Tennyson, L. A. Morgan, Bo und states using the R-matrix method: Rydberg states of HeH, J. Phys. B: At . Mol. Opt. Phys. 24 (1991) 3685–3699

    1991

  63. [75]

    M. J. Seaton, USE OF THE R-MATRIX METHOD FOR BOUND-STATE CALCULATIONS .1. GENERAL-THEORY, J. Phys. B: At. Mol. Opt. Phys. 18 (1985) 2111–2131. doi:{10.1088/0022-3700/18/11/008}

    1985 doi

  64. [76]

    Rabad´ an, J

    I. Rabad´ an, J. Tennyson, R-Matrix calculation of the bound a nd con- tinuum states of the e − – NO + system, J. Phys. B: At. Mol. Opt. Phys. 29 (1996) 3747–3761

    1996

  65. [77]

    R. W. Brankin, I. Gladwell, J. R. Dormand, P. J. Prince, W. L. Seward, A RUNGE-KUTTA-NYSTROM CODE, ACM TRANS- ACTIONS ON MATHEMATICAL SOFTW ARE 15 (1989) 31–40. doi:{10.1145/62038.69650}. 76

    1989

  66. [78]

    W. J. Brigg, A. G. Harvey, A. Dzarasova, S. Mohr, D. S. Bramb ila, F. Morales, O. Smirnova, J. Tennyson, Calculated photoionization c ross sections using Quantemol-N, Jap. J. Appl. Phys. 54 (2015) 06GA02

    2015

  67. [79]

    Khamesian, N

    M. Khamesian, N. Douguet, S. F. dos Santos, O. Dulieu, M. Raou lt, W. J. Brigg, V. Kokoouline, Formation of CN-, C3N-, and C5N- Molecules by Radiative Electron Attachment and their Destruc- tion by Photodetachment, Phys. Rev. Lett. 117 (2016) 123001. doi:{10.1103/PhysRevLett.1...

    2016 doi

  68. [80]

    D. S. Brambila, A. G. Harvey, Z. Maˇ s ´ ın, J. D. Gorfinkiel, O. Smirnova, The role of multichannel effects in the photoionization of the NO 2 molecule: An ab initio R -matrix study, J. Phys. B: At. Mol. Opt. Phys. 48 (24) (2015) 245101. doi:10.1088/0953-4075/48/24/245101

    2015 doi

  69. [81]

    D. S. Brambila, A. G. Harvey, K. Houfek, Z. Maˇ s ´ ın, O. Smirnova, Role of electronic correlations in photoionization of NO2 in the vicinity of the 2A1/2B2 conical intersection, Phys Chem Chem Phys 19 (30) (2017 ) 19673–19682. doi:10.1039/c7cp01643c

    2017 doi

  70. [83]

    Rouz´ ee, A

    A. Rouz´ ee, A. G. Harvey, F. Kelkensberg, D. Brambila, W. K. S iu, G. Gademann, O. Smirnova, M. J. J. Vrakking, Imaging the elec- tronic structure of valence orbitals in the XUV ionization of aligned molecules, J. Phys. B: At. Mol. Opt. Phys. 47 (12) (2014) 124017. doi:10.108...

    2014 doi

  71. [84]

    B. D. Bruner, Z. Maˇ s ´ ın, M. Negro, F. Morales, D. Brambila, M.Devetta, D. Faccial` a, A. G. Harvey, M. Ivanov, Y. Mairesse, S. Patchkovs kii, V. Serbinenko, H. Soifer, S. Stagira, C. Vozzi, N. Dudovich, O. Smir nova, Multidimensional high harmonic spectroscopy of polyatomi...

    2016 doi

  72. [85]

    Maˇ s ´ ın, A

    Z. Maˇ s ´ ın, A. G. Harvey, M. Spanner, S. Patchkovskii, M. Iva nov, O. Smirnova, Electron correlations and pre-collision in the re-collision picture of high harmonic generation, J. Phys. B: At. Mol. Opt. Phys . 51 (13) (2018) 134006. doi:10.1088/1361-6455/aac598

    2018 doi

  73. [86]

    D. R. Austin, F. McGrath, L. Miseikis, D. Wood, P. Hawkins, A. S. Johnson, M. Vacher, Z. Maˇ s ´ ın, A. Harvey, M. Ivanov, O. Smirno va, J. P. Marangos, Role of tunnel ionization in high harmonic generation from substituted benzenes, Faraday Discuss. 194 (0) (2016) 34 9–368. d...

    2016 doi

  74. [87]

    D. M. Brink, G. R. Satchler, Angular Momentum, Clarendon Pres s ; Oxford University Press, Oxford; New York, 1993

    1993

  75. [88]

    Ritchie, Theory of the angular distribution of photoelectron s ejected from optically active molecules and molecular negative ions, Phys

    B. Ritchie, Theory of the angular distribution of photoelectron s ejected from optically active molecules and molecular negative ions, Phys. Rev . A 13 (4) (1976) 1411–1415. doi:10.1103/PhysRevA.13.1411

    1976 doi

  76. [89]

    Richter, J

    M. Richter, J. Gonzalez-Vazquez, Z. Maˇ s ´ ın, D. S. Brambila, A . Har- vey, F. Morales, F. Martn, Ultrafast imaging of laser-controlled no n- adiabatic dynamics in NO 2 from time-resolved photoelectron emission, Physical Chemistry Chemical Physics doi:10.1039/C9CP00649D

    doi

  77. [90]

    Mayer, Simple Theorems, Proofs, and Derivations in Quantum Chem- istry, US, Springer Science + Business Media New York, 2003

    I. Mayer, Simple Theorems, Proofs, and Derivations in Quantum Chem- istry, US, Springer Science + Business Media New York, 2003

    2003

  78. [91]

    K. L. Baluja, R. Zhang, J. Franz, J. Tennyson, Low-energy p ositron collisions with water: elastic and rotationally inelastic scattering, J. Phys. B: At. Mol. Opt. Phys. 40 (2007) 3515–3524

    2007

  79. [92]

    A. G. Sanz, M. C. Fuss, F. Blanco, Z. Maˇ s ´ ın, J. D. Gorfinkiel, R. P. McEachran, M. J. Brunger, G. Garc ´ ıa, Cross-section cal- culations for positron scattering from pyrimidine over an energy range from 0.1 to 10000 ev, Phys. Rev. A 88 (2013) 062704. doi:10.1103/PhysRevA....

    2013 doi

  80. [93]

    K. R. Hoffman, M. S. Dababneh, Y.-F. Hsieh, W. E. Kauppila, V. Po l, J. H. Smart, T. S. Stein, Total-cross-section measurements for positrons and electrons colliding with h 2, n 2, and co 2, Phys. Rev. A 25 (1982) 1393–1403. doi:10.1103/PhysRevA.25.1393. 78

    1982 doi

  81. [94]

    Zecca, L

    A. Zecca, L. Chiari, A. Sarkar, K. L. Nixon, M. J. Brunger, Tot al cross sections for positron scattering from h 2 at low energies, Phys. Rev. A 80 (2009) 032702. doi:10.1103/PhysRevA.80.032702

    2009 doi

  82. [95]

    Tennyson, D

    J. Tennyson, D. B. Brown, J. J. Munro, I. Rozum, H. N. Varam b- hia, N. Vinci, Quantemol-N: an expert system for performing electr on molecule collision calculations using the R-matrix method, J. Phys. Conf. Ser. 86 (2007) 012001

    2007

  83. [96]

    Cooper, M

    B. Cooper, M. Tudorovskaya, S. Mohr, A. O’Hare, M. Hanicinec , A. Dzarasova, J. Gorfinkiel, J. Benda, Z. Maˇ s ´ ın, A. Al-Refaie, P. J. Knowles, J. Tennyson, Quantemol Electron Collision: an expert sys - tem for performing UKRmol+ electron molecule collision calculations, Atoms. 79

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