Simplest-level Electron Nuclear Dynamics Research Articles

Electron Nuclear Dynamics of H+ + C2H2 at ELab = 30, 200, and 450 eV.

We present a complete simplest-level electron nuclear dynamics (SLEND) investigation of H+ + C2H2 at collision energies ELab = 30, 200, and 450 eV. This reaction is relevant in astrophysics and provides a computationally feasible prototype for proton cancer therapy reactions. SLEND is a time-dependent, variational, direct, and nonadiabatic method that adopts a classical-mechanics description for the nuclei and a Thouless single-determinantal wave function for the electrons. We perform this study with our code PACE, which incorporates the One Electron Direct/Electron Repulsion Direct (OED/ERD) atomic integrals package developed by the Bartlett group. Current SLEND simulations with the 6-31G** basis set involves 2,646 trajectory calculations from 9 nonredundant, symmetry-inequivalent projectile-target orientations. For H+ + C2H2 at ELab = 30 eV, SLEND/6-31G** simulations predict one simple scattering process, and three reactive ones: C2H2 hydrogen substitution, C2H2 fragmentation into two CH moieties, and C2H2 fragmentation into CHC and H moieties, respectively. We reveal and analyze the mechanisms of these processes through computer animations; this valuable chemical information is inaccessible by experiments. The SLEND/6-31G** scattering angle functions exhibit primary and secondary rainbow scattering features that vary with the projectile-target orientations and collision energies. SLEND/6-31G** predicts 1-electron-transfer (1-ET) integral cross sections at ELab = 30, 200, and 450 eV in good agreement with their experimental counterparts. SLEND/6-31-G** predicts 1-ET differential cross sections (DCSs) at ELab = 30 eV that agree well with their experimental counterparts over all the measured scattering angles. In addition, SLEND/6-31G** predicts 0-ET DCSs at ELab = 30 eV that agree well with their experimental counterparts at low scattering angles, but less satisfactorily at higher ones. Remarkably, both the 0- and 1-ET DCSs from SLEND/6-31G** exhibit distinct primary rainbow scattering signatures in excellent agreement with their experimentally inferred counterparts. Furthermore, both SLEND/6-31G** and the experiment indicate that the primary rainbow scattering angles from the 0- and 1-ET DCSs are identical (an unusual fact in proton-molecule collisions). Through these rainbow scattering predictions, SLEND has also validated a procedure to extract primary rainbow angles from structureless DCSs. We analyze the obtained theoretical results in comparison with available experimental data and discuss forthcoming developments in the SLEND method.

Testing standard basis sets for direct ionizations: H+ + H at ELab = 0.1-100 keV.

With the simplest-level electron nuclear dynamics (SLEND) method, we test standard Slater-type-orbital/contracted-Gaussian-functions (STO/CGFs) basis sets for the simulation of direct ionizations (DIs), charge transfers (CTs), and target excitations (TEs) in H+ + H at ELab = 0.1-100 keV. SLEND is a time-dependent, variational, on-the-fly, and nonadiabatic method that treats nuclei and electrons with classical dynamics and a Thouless single-determinantal state, respectively. While previous tests for CTs and TEs exist, this is the first SLEND/STO/CGFs test for challenging DIs. Spin-orbitals with negative/positive energies are treated as bound/unbound states for bound-to-bound (CT and TE) and bound-to-unbound (DI) transitions. SLEND/STO/CGFs simulations correctly reproduce all the features of DIs, CTs and TEs over all the considered impact parameters and energies. SLEND/STO/CGFs simulations correctly predict CT integrals cross-sections (ICSs) over all the considered energies and predict satisfactory DI and TE ICSs within some energy ranges. Strategies to improve SLEND/STO/CGFs for DI predictions are discussed.

Electron nuclear dynamics with plane wave basis sets: complete theory and formalism.

Electron nuclear dynamics (END) is an ab initio quantum dynamics method that adopts a time-dependent, variational, direct, and non-adiabatic approach. The simplest-level (SL) END (SLEND) version employs a classical mechanics description for nuclei and a Thouless single-determinantal wave function for electrons. A higher-level END version, END/Kohn-Sham density functional theory, improves the electron correlation description of SLEND. While both versions can simulate various types of chemical reactions, they have difficulties to simulate scattering/capture of electrons to/from the continuum due to their reliance on localized Slater-type basis functions. To properly describe those processes, we formulate END with plane waves (PWs, END/PW), basis functions able to represent both bound and unbound electrons. As extra benefits, PWs also afford fast algorithms to simulate periodic systems, parametric independence from nuclear positions and momenta, and elimination of basis set linear dependencies and orthogonalization procedures. We obtain the END/PW formalism by extending the Thouless wave function and associated electron density to periodic systems, expressing the energy terms as functionals of the latter entities, and deriving the energy gradients with respect to nuclear and electronic variables. END/ PW has a great potential to simulate electron processes in both periodic (crystal) and aperiodic (molecular) systems (the latter in a supercell approach). Following previous END studies, END/PW will be applied to electron scattering processes in proton cancer therapy reactions.

Symmetry-breaking effects on time-dependent dynamics: correct differential cross sections and other properties in H+ + C2H4 at ELab = 30 eV.

We present a computational procedure that introduces low degrees of symmetry breaking into a restricted Hartree-Fock (RHF) state in order to induce higher symmetry breaking during the state's subsequent dynamics. The symmetries herein considered are those of electronic HF states as classified by Fukutome; those symmetries affect bond dissociations and internal rotations among other phenomena. Therefore, this investigation extends a part of Fukutome's time-independent analysis of symmetry breaking to the time-dependent (dynamical) regime. The procedure is formulated in the framework of the simplest-level electron nuclear dynamics, a time-dependent, variational, on-the-fly and non-adiabatic method that employs classical dynamics for the nuclei and a Thouless single-determinantal state for the electrons. We test this procedure on the H+ + C2H4 reaction at 30 eV due to its conspicuous display of symmetry-breaking effects; this reaction is relevant in astrophysics and proton cancer therapy. Fukutome's axial spin density wave (ASDW) HF state is used to represent the symmetry-broken initial states. Through a Thouless parameter, small degrees of symmetry breaking are introduced into the initial ASDW states in a controlled manner. After starting the dynamics from those states, higher degrees of symmetry breaking emerge or not as determined by the direct-dynamics equations without external interventions. Simulations starting from symmetry-conforming states preserve symmetry features during dynamics, whereas simulations starting from symmetry-broken states display an upsurge of symmetry breaking when the reactants collide. Initial symmetry breaking increases the total integral cross sections of collision-induced fragmentations and of target-to-proton 1-electron-transfer reactions and decreases the scattering angle function and primary rainbow angle of the outgoing projectile. Remarkably, symmetry-breaking simulations reproduce the correct relative order and values of the experimental 0- and 1-electron-transfer differential cross sections, whereas symmetry-conforming simulations predict incorrect order and values. Our calculated scattering angle functions and differential cross sections also exhibit expected primary and secondary rainbow angle features that experiments fail to detect. A detailed discussion on the description of symmetry-breaking processes with the ASDW and Thouless states is included to provide a rigorous theoretical basis for this investigation.

Non-adiabatic molecular dynamics simulations of non-charge-transfer and charge-transfer scattering in H+ +CO2 at ELab=30 eV

The H+ +CO2 reaction at high energies is relevant in atmospheric chemistry, astrophysics, and proton cancer therapy research. Therefore, we present herein a complete investigation of H+ +CO2 at ELab=30 eV with the simplest-level electron nuclear dynamics (SLEND) method. SLEND describes nuclei via classical mechanics and electrons with a single-determinantal Thouless wavefunction. The 3402 SLEND conducted simulations from 42 independent CO2 target orientations provide a full description of all the reactive processes and their mechanisms in this system: non-charge-transfer scattering (NCTS), charge-transfer scattering (CTS), and single C=O bond dissociation; all this valuable information about reactivity is not accessible experimentally. Numerous details of the projectile scattering patterns are provided, including the appearance and coalescence of primary and secondary rainbow angles as a function of the target orientation. SLEND NCTS and CTS differential cross sections (DCSs) are evaluated in conjunction with advanced semi-classical techniques. SLEND NCTS DCS agrees well with its experimental counterpart at all the measured scattering angles, whereas SLEND CTS DCS agrees well at high scattering angles but less satisfactorily at lower ones. Remarkably, both NCTS and CTS SLEND DCSs predict the primary rainbow angle signatures in agreement with the experiment.

A screened independent atom model for the description of ion collisions from atomic and molecular clusters

We apply a recently introduced model for an independent-atom-like calculation of ion-impact electron transfer and ionization cross sections to proton collisions from water, neon, and carbon clusters. The model is based on a geometrical interpretation of the cluster cross section as an effective area composed of overlapping circular disks that are representative of the atomic contributions. The latter are calculated using a time-dependent density-functional-theory-based single-particle description with accurate exchange-only ground-state potentials. We find that the net capture and ionization cross sections in p-X$_n$ collisions are proportional to $n^\alpha$ with $2/3 \le \alpha \le 1$. For capture from water clusters at 100 keV impact energy $\alpha$ is close to one, which is substantially different from the value $\alpha=2/3$ predicted by a previous theoretical work based on the simplest-level electron nuclear dynamics method. For ionization at 100 keV and for capture at lower energies we find smaller $\alpha$ values than for capture at 100 keV. This can be understood by considering the magnitude of the atomic cross sections and the resulting overlaps of the circular disks that make up the cluster cross section in our model. Results for neon and carbon clusters confirm these trends. Simple parametrizations are found which fit the cross sections remarkably well and suggest that they depend on the relevant bond lengths.

Exploring water radiolysis in proton cancer therapy: Time-dependent, non-adiabatic simulations of H+ + (H2O)1-6.

To elucidate microscopic details of proton cancer therapy (PCT), we apply the simplest-level electron nuclear dynamics (SLEND) method to H+ + (H2O)1-6 at ELab = 100 keV. These systems are computationally tractable prototypes to simulate water radiolysis reactions—i.e. the PCT processes that generate the DNA-damaging species against cancerous cells. To capture incipient bulk-water effects, ten (H2O)1-6 isomers are considered, ranging from quasi-planar/multiplanar (H2O)1-6 to “smallest-drop” prism and cage (H2O)6 structures. SLEND is a time-dependent, variational, non-adiabatic and direct method that adopts a nuclear classical-mechanics description and an electronic single-determinantal wavefunction in the Thouless representation. Short-time SLEND/6-31G* (n = 1–6) and /6-31G** (n = 1–5) simulations render cluster-to-projectile 1-electron-transfer (1-ET) total integral cross sections (ICSs) and 1-ET probabilities. In absolute quantitative terms, SLEND/6-31G* 1-ET ICS compares satisfactorily with alternative experimental and theoretical results only available for n = 1 and exhibits almost the same accuracy of the best alternative theoretical result. SLEND/6-31G** overestimates 1-ET ICS for n = 1, but a comparable overestimation is also observed with another theoretical method. An investigation on H+ + H indicates that electron direct ionization (DI) becomes significant with the large virtual-space quasi-continuum in large basis sets; thus, SLEND/6-31G** 1-ET ICS is overestimated by DI contributions. The solution to this problem is discussed. In relative quantitative terms, both SLEND/6-31* and /6-31G** 1-ET ICSs precisely fit into physically justified scaling formulae as a function of the cluster size; this indicates SLEND’s suitability for predicting properties of water clusters with varying size. Long-time SLEND/6-31G* (n = 1–4) simulations predict the formation of the DNA-damaging radicals H, OH, O and H3O. While “smallest-drop” isomers are included, no early manifestations of bulk water PCT properties are observed and simulations with larger water clusters will be needed to capture those effects. This study is the largest SLEND investigation on water radiolysis to date.

In honour of N. Yngve Öhrn: surveying proton cancer therapy reactions with Öhrn's electron nuclear dynamics method. Aqueous clusters radiolysis and DNA-base damage by proton collisions

Proton cancer therapy (PCT) utilises high-energy H+ projectiles to cure cancer. PCT healing arises from its DNA damage in cancerous cells, which is mostly inflicted by the products from PCT water radiolysis reactions. While clinically established, a complete microscopic understanding of PCT remains elusive. To help in the microscopic elucidation of PCT, Professor Öhrn's simplest-level electron nuclear dynamics (SLEND) method is herein applied to H+ + (H2O)3–4 and H+ + DNA-bases at ELab = 1.0 keV. These are two types of computationally feasible prototypes to study water radiolysis reactions and H+-induced DNA damage, respectively. SLEND is a time-dependent, variational, non-adiabatic and direct-dynamics method that adopts a nuclear classical-mechanics description and an electronic single-determinantal wavefunction. Additionally, our SLEND + effective-core-potential method is herein employed to simulate some computationally demanding PCT reactions. Due to these attributes, SLEND proves appropriate for the simulation of various types of PCT reactions accurately and feasibly. H+ + (H2O)3–4 simulations reveal two main processes: H+ projectile scattering and the simultaneous formation of H and OH fragments; the latter process is quantified through total integrals cross sections. H+ + DNA-base simulations reveal atoms and groups displacements, ring openings and base-to-proton electron transfers as predominant damage processes.

Electron nuclear dynamics of proton collisions with DNA/RNA bases at ELab = 80 keV: A contribution to proton cancer therapy research

The reactions: H++B, B=adenine, cytosine, thymine and uracil, at ELab=80keV, relevant in proton cancer therapy, are investigated with the simplest-level electron nuclear dynamics (SLEND) and SLEND/Kohn-Sham-density-functional-theory (SLEND/KSDFT) methods. These time-dependent, direct, and non-adiabatic methods utilize nuclear classical mechanics and electronic single-determinantal wavefunctions. Results from this study include snapshots of the simulated reactions depicting base-to-proton electron transfers, base-to-proton total electron-transfer probabilities from various reactants’ initial conditions, and base-to-proton 1-electron-transfer total integral cross sections. The last properties are compared with results from the only available experiment on these systems and from three alternative theories.

H+ + NO(vi = 0) → H+ + NO(vf = 0–2) at ELab = 30 eV with canonical and Morse coherent states

H++NO(vi=0)=H++NO(vf=0–2) at ELab=30eV is investigated with the simplest-level electron nuclear dynamics (SLEND) method. In a direct, time-dependent, variational, and non-adiabatic framework, SLEND adopts nuclear classical mechanics and an electronic single-determinantal wavefunction. A coherent-states (CS) procedure recovers quantum vibrational properties from classical mechanics. Besides canonical CS, SU(1,1), SU(2), and Gazeau–Klauder Morse CS are innovatively introduced to treat anharmonicity. SLEND vibrational differential cross, rainbow scattering angles, and H+ energy loss spectra compare well with experimental data and with vibrational close-coupling rotational infinite-order sudden approximation results obtained at a higher computational cost.

Dynamics of H+ + CO at ELab = 30 eV

The astrophysically relevant system H+ + CO (vi = 0) → H+ + CO (vf) at ELab = 30 eV is studied with the simplest-level electron nuclear dynamics (SLEND) method. This investigation follows previous successful SLEND studies of H+ + H2 and H+ + N2 at ELab = 30 eV [J. Morales, A. Diz, E. Deumens, and Y. Öhrn, J. Chem. Phys. 103(23), 9968 (1995)10.1063/1.469886; C. Stopera, B. Maiti, T. V. Grimes, P. M. McLaurin, and J. A. Morales, J. Chem. Phys. 134(22), 224308 (2011)10.1063/1.3598511]. SLEND is a direct, time-dependent, variational, and non-adiabatic method that adopts a classical-mechanics description for the nuclei and a single-determinantal wavefunction for the electrons. A canonical coherent-states (CS) procedure associated with SLEND reconstructs quantum vibrational properties from the SLEND classical dynamics. Present SLEND results include reactivity predictions, snapshots of the electron density evolution, average vibrational energy transfers, rainbow angle predictions, total and vibrationally resolved differential cross sections (DCS), and average vibrational excitation probabilities. SLEND results are compared with available data from experiments and vibrational close-coupling rotational infinite-order sudden (VCC-RIOS) approximation calculations. Present simulations employ four basis sets: STO-3G, 6-31G, 6-31G**, and cc-pVDZ to determine their effect on the results. SLEND simulations predict non-charge-transfer scattering and CO collision-induced dissociation as the main reactions. SLEND/6-31G, /6-31G**, and /cc-pVDZ predict rainbow angles and total DCS in excellent agreement with experiments and more accurate than their VCC-RIOS counterparts. SLEND/6-31G** and /cc-pVDZ predict vibrationally resolved DCS for vf = 0–2 in satisfactory experimental agreement, but less accurate than their comparable H+ + CO VCC-RIOS and H+ + H2 and H+ + N2 SLEND results. SLEND/6-31G** and /cc-pVDZ predict qualitatively correct average vibrational excitation probabilities, which are quantitatively correct for vf = 2, but under(over)estimated for vf = 0(1). Discrepancies in some H+ + CO SLEND vibrational properties, not observed in H+ + H2 and H+ + N2 SLEND results, are attributed to the moderately overestimated SLEND vibrational energy through its effect upon the canonical CS probabilities. Correction of that energy to its experimental values produces a remarkable improvement in the average vibrational excitation probabilities. Ways to obtain more accurate vibrational properties with higher-level versions of electron nuclear dynamics are discussed.

Dynamics of H+ + N2 at E Lab = 30 eV

The H+ + N2 system at ELab = 30 eV, relevant in astrophysics, is investigated with the simplest-level electron nuclear dynamics (SLEND) method. SLEND is a time-dependent, direct, variational, non-adiabatic method that employs a classical-mechanics description for the nuclei and a single-determinantal wavefunction for the electrons. A canonical coherent-states procedure, intrinsic to SLEND, is used to reconstruct quantum vibrational properties from the SLEND classical mechanics. Present simulations employ three basis sets: STO-3G, 6-31G, and 6-31G**, to determine their effect on the results, which include reaction visualizations, product predictions, and scattering properties. Present simulations predict non-charge-transfer scattering and N2 collision-induced dissociation as the main reactions. Average vibrational energy transfer, H+ energy-loss spectra, rainbow angle, and elastic vibrational differential cross sections at the SLEND/6-31G** level agree well with available experimental data. SLEND/6-31G** results are comparable to those calculated with the vibrational close-coupling rotational infinite-order sudden approximation and the quasi-classical trajectory method.

Time-dependent density-functional theory method in the electron nuclear dynamics framework

A time-dependent density-functional theory (DFT) dynamics method in the electron nuclear dynamics (END) framework is presented. This time-dependent variational method treats simultaneously the nuclei and electrons of a system without utilizing predetermined potential energy surfaces. Like the simplest-level END, this method adopts a classical-mechanics description for the nuclei and a Thouless single-determinantal representation for the electrons. However, the electronic description is now expressed in a Kohn–Sham DFT form that provides electron correlation effects absent in the simplest-level END. Current implementation of this method employs the adiabatic approximation in the exchange–correlation action and potential. Simulations of molecular vibrations and proton–molecule reactions attest to the accuracy of the present method.