Electron nuclear dynamics of H++H2 collisions at Elab=30 eV

Quasi-Classical Trajectory Calculations on a Two-State Potential Energy Surface Including Nonadiabatic Coupling Terms as Friction for D+ + H2 Collisions

Akin to the traditional quasi-classical trajectory method for investigating the dynamics on a single adiabatic potential energy surface for an elementary chemical reaction, we carry out the dynamics on a 2-state ab initio potential energy surface including nonadiabatic coupling terms as friction terms for D+ + H2 collisions. It is shown that the resulting dynamics correctly accounts for nonreactive charge transfer, reactive non-charge transfer and reactive charge transfer processes. In addition, it leads to the formation of triatomic DH2+ species as well.

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.

Multi-configuration electron-nuclear dynamics: An open-shell approach

The multi-configuration electron-nuclear dynamics for open shell systems with a spin-unrestricted formalism is described. The mean fields are evaluated using second-order reduced density matrices for electronic and nuclear degrees of freedom. Applications to light-element diatomics including equilibrium geometries, electronic energies, dipole moments, and absorption spectra are presented. The von Neumann entropies for different spin states of a LiH molecule are compared.

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.

Temporally stable rotational coherent states for molecular simulations. I. Spherical and linear rotor cases

We reformulate a previous rotational coherent state (CS) to obtain temporally stable (TS) CSs for the spherical rotor (SR) and linear rotor (LR): TSSR and TSLR CSs, respectively. Being TS, the new CSs remain within their own classes during dynamics by evolving exclusively through their CS parameters. The new TS CSs are now appropriate to reconstruct quantum rotational properties from classical-mechanics simulations of chemical reactions. Following literature precedents, we enforce temporal stability by incorporating action-angle-related phase factors into the parameters of the original CS. In addition, to elucidate CS quantum reconstruction procedures, we derive one more rotational CS from a quantum electron nuclear dynamics description of a diatomic rotor (DR). The DR CS and the TSLR CS are not identical but display similar structures and properties. We rigorously demonstrate and examine the key properties of the three CSs: continuity, resolution of unity, temporal stability, action identity, minimum uncertainty relationships, and quasi-classical behavior. Finally, we present computer simulations of the CSs dynamics and an application of them to predict CO rotational excitation probabilities in the Li⁺ + CO reaction. CS results agree satisfactorily with experimental ones and encourage future applications in chemical dynamics, statistical mechanics, spectroscopy, nuclear physics, quantum coherence, and quantum computing.

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.

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 E_Lab = 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.

Collision dynamics of proton with formaldehyde: fragmentation and ionization

Using time-dependent density functional theory, applied to the valence electrons and coupled non-adiabatically to molecular dynamics of the ions, we study the ionization and fragmentation of formaldehyde in collision with a proton. Four different impact energies: 35 eV, 85 eV, 135 eV, and 300 eV are chosen in order to study the energy effect in the low energy region, and ten different incident orientations at 85 eV are considered for investigating the steric effect. Fragmentation ratios, single, double, and total electron ionization cross sections are calculated. For large impact parameters, these results are close to zero irrespective of the incident orientations due to a weak projectile-target interaction. For small impact parameters, the results strongly depend on the collision energy and orientation. We also give the kinetic energy releases and scattering angles of protons, as well as the cross section of different ion fragments and the corresponding reaction channels.

New light shed on charge transfer in fundamental H+ + H2 collisions

There is no consensus on the magnitude and shape of the charge transfer cross section in low-energy H+ + H2 collisions, in spite of the fundamental importance of these collisions. Experiments have thus been carried out in the energy range 15≤E≤5000  eV. The measurements invalidate previous recommended data for E≤200  eV and confirm the existence of a local maximum around 45 eV, which was predicted theoretically. Additionally, vibrationally resolved cross sections allow us to investigate the evolution of the underlying charge transfer mechanism as a function of E.

Influence of nuclear exchange on nonadiabatic electron processes in H(+)+H2 collisions

H(+)+H(2) collisions are studied by means of a semiclassical approach that explicitly accounts for nuclear rearrangement channels in nonadiabatic electron processes. A set of classical trajectories is used to describe the nuclear motion, while the electronic degrees of freedom are treated quantum mechanically in terms of a three-state expansion of the collision wavefunction. We describe electron capture and vibrational excitation, which can also involve nuclear exchange and dissociation, in the E = 2-1000 eV impact energy range. We compare dynamical results obtained with two parametrizations of the potential energy surface of H(3)(+) ground electronic state. Total cross sections for E > 10 eV agree with previous results using a vibronic close-coupling expansion, and with experimental data for E < 10 eV. Additionally, some prototypical features of both nuclear and electron dynamics at low E are discussed.

A study of conical intersections for the H3(+) system

A parametrization of the three asymptotic conical intersections between the energies of the H3(+) ground state and the first excited singlet state is presented. The influence of an additional, fourth conical intersection between the first and second excited states at the equilateral geometry on the connection between the three conical regions is studied, for both diatomics-in-molecules and ab initio molecular data.

Study of ab initio molecular data for inelastic and reactive collisions involving the H3+ quasimolecule

The lowest two ab initio potential energy surfaces (PES), and the corresponding nonadiabatic couplings between them, have been obtained for the H3+ system; the molecular data are compared to those calculated with the diatomic in molecules (DIM) method. The form of the couplings is discussed in terms of the topology of the molecular structure of the triatomic. The method of Baer is employed to generate "diabatic" states and the residual nonadiabatic couplings are calculated. The ab initio results for these are markedly different from the corresponding DIM data, and show the need to consider the third PES.

Charge exchange and threshold effect in the energy loss of slow projectiles

In this Letter, we study charge exchange and energy loss of protons, taking into account the dynamics of both nuclei and electrons during the collision with atomic hydrogen, helium, and neon targets. We obtain the nuclear and electronic contributions to the energy loss as well as the charge exchange probability, and the total cross section for charge exchange. We find a low-energy threshold in the electronic energy loss due to the quantization of excited states. We find that the electronic stopping cross section is not proportional to the velocity of the projectile at very low velocities (energies), as is predicted by electron gas theory. This confirms recent experimental results.