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.

Electron nuclear dynamics of time-dependent symmetry breaking in H+ + H2O at ELab = 28.5-200.0 eV: a prototype for ion cancer therapy reactions.

Following our preceding research [P. M. McLaurin, R. Merritt, J. C. Domínguez, E. S. Teixeira and J. A. Morales, Phys. Chem. Chem. Phys., 2019, 21, 5006], we present an electron nuclear dynamics (END) investigation of H+ + H2O at ELab = 28.5-200.0 eV in conjunction with a computational procedure to induce symmetry breaking during evolution. The investigated system is a computationally feasible prototype to simulate water radiolysis reactions in ion cancer therapy. END is a time-dependent, variational, non-adiabatic, and on-the-fly method, which utilizes classical mechanics for nuclei and a Thouless single-determinantal state for electrons. In this study, a procedure inherent to END introduces low degrees of symmetry breaking into the reactants' restricted Hartree-Fock (RHF) state to induce a higher symmetry breaking during evolution. Specifically, the Thouless exponential operator acting on the RHF reference generates an axial spin density wave (ASDW) state according to Fukutome's analysis of HF symmetry breaking; this state exhibits spatial and spin symmetry breaking. By varying a Thouless parameter, low degrees of symmetry breaking are introduced into ASDW states. After starting the dynamics from those states, higher degrees of symmetry breaking may subsequently emerge as dictated by the END equations without ad hoc interventions. Simulations starting from symmetry-conforming states preserve the symmetry features during dynamics, whereas simulations starting from symmetry-broken states display an upsurge of symmetry breaking once the reactants collide. Present simulations predict three types of reactions: (I) projectile scattering, (II) hydrogen substitution, and (III) water radiolysis into H + OH and 2H + O fragments. Remarkably, symmetry breaking considerably increases the extent of the target-to-projectile electron transfers (ETs) occurring during the above reactions. Then, with symmetry breaking, 1-ET differential and integral cross sections increase in value, whereas 0-ET differential cross sections and primary rainbow scattering angles decrease. More importantly, END properties calculated from symmetry-breaking simulations exhibit better agreement with the experimental data. Notably, END 1-ET integral cross sections with symmetry breaking compare better with their experimental counterparts than 1-ET integral cross sections from high-level close-coupling calculations; moreover, END validates an undetected rainbow scattering peak inferred from the experimental data. A discussion of our symmetry-breaking procedure in the context of Fukutome's analysis of HF symmetry breaking is also presented.

Statistical-law formulas for zero- to two-electron-transfer probabilities in proton-molecule and proton cancer therapy reactions from electron nuclear dynamics theory.

We present the first quantum-mechanical derivation of statistical-law formulas to calculate zero- to two-electron transfers (ETs) in proton-molecule reactions. The original statistical derivation assumed that the n-ET probabilities of N electrons in a shell obey an N-trial binomial distribution with success probability equal to an individual one-ET probability; the latter was heuristically identified with the number of transferred electrons from the integrated charge density. The obtained formulas proved accurate to calculate ET cross sections in proton-molecule and proton cancer therapy (PCT) reactions. We adopt the electron nuclear dynamics (END) theory in our quantum-mechanical derivation due to its versatile description of ETs via a Thouless single-determinantal state. Since non-orthogonal Thouless dynamical spin-orbitals pose mathematical difficulties, we first present a derivation for a model system with N ≥ 2 electrons where only two with opposite spins are ET active; in that scheme, the Thouless dynamical spin-orbitals become orthogonal, a fact that facilitates a still intricate derivation. In the end, we obtain the number of transferred electrons from the Thouless state charge density and the ETs probabilities from the Thouless state resolution into projectile-molecule eigenstates describing ETs. We prove that those probabilities and numbers of electrons interrelate as in the statistical-law formulas via their common dependency on the Thouless variational parameters. We review past ET results of proton-molecule and PCT reactions obtained with these formulas in the END framework and present new results of H+ + N2O. We will present the derivation for systems with N > 2 electrons all active for ETs in a sequel.