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

Recurrent Neural Network/Machine Learning Predictions of Reactive Channels in H+ + C2H4 at ELab = 30 eV: A Prototype of Ion Cancer Therapy Reactions

We present a simplest-level electron nuclear dynamics/machine learning (SLEND/ML) approach to predict chemical properties in ion cancer therapy (ICT) reactions. SLEND is a time-dependent, variational, on-the-fly, and nonadiabatic method. In SLEND, nuclear and electronic parameters determine reactants-to-products trajectories in a quantum phase space; this establishes a mapping between reactants' initial conditions and products' properties. To accelerate simulations, SLEND/ML utilizes a modicum of SLEND trajectories to train ML methods on the aforesaid mapping and employs them to predict chemical properties. We employ SLEND/ML to predict reaction types and products' charges in H+ + C2H4 at ELab = 30 eV, a prototype of ICT reactions involving double-bonded compounds. For reaction predictions, a recurrent neural network (RNN) and k-nearest neighbor method are the best models with 98.23% and 95.13% accuracy. RNN correctly predicts frequent and infrequent reaction types and generalizes over data sets. For charge predictions, the RNN exhibits low mean absolute errors of 0.02-0.07.

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 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.

First-Principles Simulations of Biological Molecules Subjected to Ionizing Radiation

Ionizing rays cause damage to genomes, proteins, and signaling pathways that normally regulate cell activity, with harmful consequences such as accelerated aging, tumors, and cancers but also with beneficial effects in the context of radiotherapies. While the great pace of research in the twentieth century led to the identification of the molecular mechanisms for chemical lesions on the building blocks of biomacromolecules, the last two decades have brought renewed questions, for example, regarding the formation of clustered damage or the rich chemistry involving the secondary electrons produced by radiolysis. Radiation chemistry is now meeting attosecond science, providing extraordinary opportunities to unravel the very first stages of biological matter radiolysis. This review provides an overview of the recent progress made in this direction, focusing mainly on the atto- to femto- to picosecond timescales. We review promising applications of time-dependent density functional theory in this context.

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.

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.

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.