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.

Electron nuclear dynamics of H+ + CO2 (000) → H+ + CO2 (v1v2v3) at ELab = 20.5-30 eV with coherent-states quantum reconstruction procedure.

The simplest-level electron nuclear dynamics (SLEND) method with the coherent-states (CSs) quantum reconstruction procedure (CSQRP) is applied to the scattering system H+ + CO2 (000) → H+ + CO2 (v1v2v3) at ELab = 20.5-30 eV. Relevant for astrophysics, atmospheric chemistry and proton cancer therapy, this system undergoes collision-induced vibrational excitations in CO2. SLEND is a time-dependent, variational, direct, and non-adiabatic method that adopts a classical-mechanics description for nuclei and a single-determinantal wavefunction for electrons. The CSQRP employs the canonical CS to reconstruct quantum state-to-state vibrational properties from the SLEND classical nuclear dynamics. Overall, the calculated collision-induced vibrational properties agree well with experimental data. SLEND total differential cross sections (DCSs) agree remarkably well with their experimental counterparts and accurately display rainbow scattering angles structures. SLEND averaged target excitation energies for vibrational + rotational and rotational motions exhibit reasonable and good agreements with experimental data, respectively. These properties show that rotational excitation is low and that the asymmetric stretch normal mode of CO2 is much more excited than the others. SLEND/CSQRP state-to-state vibrational DCSs agree reasonably well with the sparse experimental data for final states v1v2v3 = 000-002, but less satisfactorily for 003. These DCSs also accurately display rainbow scattering angles structures. Finally, SLEND/CSQRP vibrational proton energy loss spectra agree remarkably well with their experimental counterparts for various final vibrational states of CO2, collisions energies and scattering angles. Present results demonstrate the accuracy of SLEND/CSQRP to predict state-to-state vibrational properties in scattering systems with multiple normal modes.

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.

Electron Nuclear Dynamics Simulations of Proton Cancer Therapy Reactions: Water Radiolysis and Proton- and Electron-Induced DNA Damage in Computational Prototypes.

Proton cancer therapy (PCT) utilizes high-energy proton projectiles to obliterate cancerous tumors with low damage to healthy tissues and without the side effects of X-ray therapy. The healing action of the protons results from their damage on cancerous cell DNA. Despite established clinical use, the chemical mechanisms of PCT reactions at the molecular level remain elusive. This situation prevents a rational design of PCT that can maximize its therapeutic power and minimize its side effects. The incomplete characterization of PCT reactions is partially due to the health risks associated with experimental/clinical techniques applied to human subjects. To overcome this situation, we are conducting time-dependent and non-adiabatic computer simulations of PCT reactions with the electron nuclear dynamics (END) method. Herein, we present a review of our previous and new END research on three fundamental types of PCT reactions: water radiolysis reactions, proton-induced DNA damage and electron-induced DNA damage. These studies are performed on the computational prototypes: proton + H2O clusters, proton + DNA/RNA bases and + cytosine nucleotide, and electron + cytosine nucleotide + H2O. These simulations provide chemical mechanisms and dynamical properties of the selected PCT reactions in comparison with available experimental and alternative computational results.

Dynamics of H+ + CO at E(Lab) = 30 eV.

The astrophysically relevant system H(+) + CO (v(i) = 0) → H(+) + CO (v(f)) at E(Lab) = 30 eV is studied with the simplest-level electron nuclear dynamics (SLEND) method. This investigation follows previous successful SLEND studies of H(+) + H(2) and H(+) + N(2) at E(Lab) = 30 eV [J. Morales, A. Diz, E. Deumens, and Y. Öhrn, J. Chem. Phys. 103(23), 9968 (1995); C. Stopera, B. Maiti, T. V. Grimes, P. M. McLaurin, and J. A. Morales, J. Chem. Phys. 134(22), 224308 (2011)]. 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 v(f) = 0-2 in satisfactory experimental agreement, but less accurate than their comparable H(+) + CO VCC-RIOS and H(+) + H(2) and H(+) + N(2) SLEND results. SLEND∕6-31G** and ∕cc-pVDZ predict qualitatively correct average vibrational excitation probabilities, which are quantitatively correct for v(f) = 2, but under(over)estimated for v(f) = 0(1). Discrepancies in some H(+) + CO SLEND vibrational properties, not observed in H(+) + H(2) and H(+) + N(2) 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(+) + N(2) system at E(Lab) = 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 N(2) 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.