An accurate three‐dimensional potential energy surface for H3

Simulation of Chemical Reactions on a Quantum Computer

Studying chemical reactions, particularly in the gas phase, relies heavily on computing scattering matrix elements. These elements are essential for characterizing molecular reactions and accurately determining reaction probabilities. However, the intricate nature of quantum interactions poses challenges, necessitating the use of advanced mathematical models and computational approaches to tackle the inherent complexities. In this study, we develop and apply a quantum computing algorithm for the calculation of scattering matrix elements. In our approach, we employ the time-dependent method based on the Møller operator formulation where the S-matrix element between the respective reactant and product channels is determined through the time correlation function of the reactant and product Møller wavepackets. We successfully apply our quantum algorithm to calculate scattering matrix elements for 1D semi-infinite square well potential and on the colinear hydrogen exchange reaction. As we navigate the complexities of quantum interactions, this quantum algorithm is general and emerges as a promising avenue, shedding light on new possibilities for simulating chemical reactions on quantum computers.

A Q-learning method based on coarse-to-fine potential energy surface for locating transition state and reaction pathway

Transition state (TS) on the potential energy surface (PES) plays a key role in determining the kinetics and thermodynamics of chemical reactions. Inspired by the fact that the dynamics of complex systems are always driven by rare but significant transition events, we herein propose a TS search method in accordance with the Q-learning algorithm. Appropriate reward functions are set for a given PES to optimize the reaction pathway through continuous trial and error, and then the TS can be obtained from the optimized reaction pathway. The validity of this Q-learning method with reasonable settings of Q-value table including actions, states, learning rate, greedy rate, discount rate, and so on, is exemplified in 2 two-dimensional potential functions. In the applications of the Q-learning method to two chemical reactions, it is demonstrated that the Q-learning method can predict consistent TS and reaction pathway with those by ab initio calculations. Notably, the PES must be well prepared before using the Q-learning method, and a coarse-to-fine PES scanning scheme is thus introduced to save the computational time while maintaining the accuracy of the Q-learning prediction. This work offers a simple and reliable Q-learning method to search for all possible TS and reaction pathway of a chemical reaction, which may be a new option for effectively exploring the PES in an extensive search manner.

Time-dependent quantum mechanical wave packet dynamics

Starting from a model study of the collinear (H, H₂) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH₄. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H₂) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.

Effect of Reagent Vibration and Rotation on the State-to-State Dynamics of the Hydrogen Exchange Reaction, H + H2 → H2 + H

State-to-state dynamics of the benchmark hydrogen exchange reaction H + H₂ (v = 0-4, j = 0-3) → H₂ (v', j') + H is investigated with the aid of the real wave packet approach of Gray and Balint-Kurti (J. Chem. Phys. 1998, 108, 950-962) and electronic ground BKMP2 potential energy surface of Boothroyd et al. (J. Chem. Phys. 1996, 104, 7139-7152). Initial state-selected and product state-resolved reaction probabilities, integral cross section, and product diatom vibrational and rotational level populations at a few collision energies are reported to elucidate the energy disposal mechanism. State-specific thermal rate constants are also calculated and compared with the available literature results. Coriolis coupling terms of the nuclear Hamiltonian are included, and calculations are parallelized over the helicity quantum number, Ω'. Attempts are made, in particular, to study the effect of reagent vibrational and rotational excitations on the dynamical attributes. It is found that the calculations become computationally expensive with reagent vibrational and rotational excitation. Reagent vibrational excitation is found to enhance the reactivity and has significant impact on the energy disposal to the vibrational and rotational degrees of freedom of the product. The interplay of reagent translational and vibrational energy on the product vibrational distribution unfolds an important aspect of the energy disposal mechanism. The effect of reagent rotation on the state-to-state dynamics is found not to be very significant, and the weak effect turns out to be specific to v'.

Prediction of a Feshbach Resonance in the Below-the-Barrier Reactive Scattering of Vibrationally Excited HD with H

Quantum reactive scattering calculations on the vibrational quenching of HD due to collisions with H were carried out employing an accurate potential energy surface. The state-to-state cross sections for the chemical reaction HD(v = 1, j = 0) + H → D + H₂(v' = 0, j') at collision energies between 1 and 10 000 cm^-1 are presented, and a Feshbach resonance in the low-energy regime, below the reaction barrier, is observed for the first time. The resonance is attributed to coupling with the vibrationally adiabatic potential correlating to the v = 1, j = 1 level of the HD molecule, and it is dominated by the contribution from a single partial wave. The properties of the resonance, such as its dynamic behavior, phase behavior, and lifetime, are discussed.

Spiers Memorial Lecture : Introductory lecture: quantum dynamics of chemical reactions

This Spiers Memorial Lecture discusses quantum effects that can be calculated and observed in the chemical reactions of small molecules.

Beyond energies: geometry predictions with the XYG3 type of doubly hybrid density functionals

The scaled mean absolute deviations (s-MADs) of the optimized geometric parameters for covalent bondings (the CCse set), nonbonded interactions (the S22G30 set) and the transition state structures (the TSG36 set), with Tot referring to the averaged s-MAD for general performances.

Vibrationally Inelastic Collision Between Li2(ν = 0) and Li: Direct and Postponed Elongation Mechanisms

The mechanism for vibrational inelastic excitation during the collision between Li2(ν = 0) and Li was investigated exploiting classical trajectory simulations over a potential energy surface generated by fitting valence full configuration interaction calculations employing a large basis set. From the trajectory results, it emerges that the vibrational excitation in noncapture collisions presents uniquely a forward-scattered projectile for the highest levels of excitation (ΔE(0 → ν') ≃ Ecoll). For lower ν', a minor contribution presenting a backward-scattered projectile appears, which, however, has its major contribution coming from a "slingshot"-like (orbiting) mechanism exploiting the attractive features of the Li3 potential energy surface rather than a direct recoil.

Which Is Better at Predicting Quantum-Tunneling Rates: Quantum Transition-State Theory or Free-Energy Instanton Theory?

Quantum transition-state theory (QTST) and free-energy instanton theory (FEIT) are two closely related methods for estimating the quantum rate coefficient from the free-energy at the reaction barrier. In calculations on one-dimensional models, FEIT typically gives closer agreement than QTST with the exact quantum results at all temperatures below the crossover to deep tunneling, suggesting that FEIT is a better approximation than QTST in this regime. Here we show that this simple trend does not hold for systems of greater dimensionality. We report tests on several collinear and three-dimensional reactions, in which QTST outperforms FEIT over a range of temperatures below crossover, which can extend down to half the crossover temperature (below which FEIT outperforms QTST). This suggests that QTST-based methods such as ring-polymer molecular dynamics (RPMD) may often give closer agreement with the exact quantum results than FEIT.

Adiabatic potential energy surfaces for the low-energy collisional dynamics of C(+)((2)P) ions with H2 molecules

The low-energy electronic states of the CH2(+) molecular ion are investigated with multireference configuration interaction calculations based on complete active space self-consistent field reference wave functions using a large C(6s5p4d3f)/H(8s6p3d1f) basis set. The focus is on the three lowest-lying states describing formation and destruction of the astrophysically relevant methylidine cation CH(+). Both processes are discussed in light of the topology of the relevant potential energy surfaces and their intersections.

A MATLAB-based finite-element visualization of quantum reactive scattering. I. Collinear atom-diatom reactions

We restate the application of the finite element method to collinear triatomic reactive scattering dynamics with a novel treatment of the scattering boundary conditions. The method provides directly the reactive scattering wave function and, subsequently, the probability current density field. Visualizing these quantities provides additional insight into the quantum dynamics of simple chemical reactions beyond simplistic one-dimensional models. Application is made here to a symmetric reaction (H+H2), a heavy-light-light reaction (F+H2), and a heavy-light-heavy reaction (F+HCl). To accompany this article, we have written a MATLAB code which is fast, simple enough to be accessible to a wide audience, as well as generally applicable to any problem that can be mapped onto a collinear atom-diatom reaction. The code and user's manual are available for download from http://www2.chem.umd.edu/groups/alexander/FEM.

Relative efficacy of vibrational vs. translational excitation in promoting atom-diatom reactivity: rigorous examination of Polanyi's rules and proposition of sudden vector projection (SVP) model

To provide a systematic and rigorous re-examination of the well-known Polanyi's rules, excitation functions of several A + BC(v = 0, 1) reactions are determined using the Chebyshev real wave packet method on accurate potential energy surfaces. Reactions with early (F + H2 and F + HCl), late (Cl + H2), and central (H∕D∕Mu + H2, where Mu is a short-lived light isotope of H) barriers are represented. Although Polanyi's rules are in general consistent with the quantum dynamical results, their predictions are strictly valid only in certain energy ranges divided by a cross-over point. In particular, vibrational excitation of the diatomic reactant typically enhances reactivity more effectively than translational excitation at high energies, while reverse is true at low energies. This feature persists irrespective of the barrier location. A sudden vector projection model is proposed as an alternative to Polanyi's rules. It is found to give similar, but more quantitative, predictions about mode selectivity in these reactions, and has the advantage to be extendible to reactions involving polyatomic molecules.

Reactive scattering dynamics of rotational wavepackets: a case study using the model H+H2 and F+H2 reactions with aligned and anti-aligned H2

We propose a method to steer the outcome of reactive atom-diatom scattering, using rotational wavepackets excited by strong non-resonant laser pulses. Full close-coupled quantum mechanical scattering calculations of the D+H2 and F+H2 reactions are presented, where the H2 molecule exists as a coherent superposition of rotational states. The nuclear spin selective control over the molecular bond axis alignment afforded by the creation of rotational wavepackets is applied to reactive scattering systems, enabling a nuclear spin selective influence to be exerted over the reactive dynamics. The extension of the conventional eigenstate-to-eigenstate scattering problem to the case in which the initial state is composed of a coherent superposition of rotational states is detailed, and a selection of example calculations are discussed, along with their mechanistic implications. The feasibility of the corresponding experiments is considered, and a suitable simple two pulse laser scheme is shown to strongly differentiate the reactivities of o-H2 and p-H2.

Isotopes and analogs of hydrogen--from fundamental investigations to practical applications

Hydrogen has a central role in the story of the universe itself and also in the story of our efforts to understand it. This paper retells the story of the part played by hydrogen and its stable isotope deuterium in the primordial synthesis of the elements, then goes on to describe how the spectrum of atomic hydrogen led to insights into the laws governing matter at the most fundamental level, from the quantum mechanics of Schrödinger and Heisenberg, through quantum electrodynamics, to the most recent work investigating the underlying structure of the proton itself. Atomic hydrogen is unique among the elements in that the concept of isotopy--atoms having the same nuclear charge but different masses--is stretched to its limit in the isotopes of hydrogen, ranging from the well-known isotopes deuterium and tritium to exotic species such as muonium, muonic helium, and positronium. These atoms, or atom-like objects, have much to tell us about fundamental aspects of the universe. In recent years the idea of utilizing hydrogen either as an energy source (through nuclear fusion) or as an energy storage medium (bound in hydrides or other materials) has attracted much attention as a possible avenue to a post-oil energy future. Some of the more interesting recent developments are described here. Dedicated to the memory of Brian C. Webster (1939-2008).

Hydrogen-abstraction reactivity patterns from A to Y: the valence bond way

"Give us insight, not numbers" was Coulson's admonition to theoretical chemists. This Review shows that the valence bond (VB)-model provides insights and some good numbers for one of the fundamental reactions in nature, the hydrogen-atom transfer (HAT). The VB model is applied to over 50 reactions from the simplest H + H(2) process, to P450 hydroxylations and H-transfers among closed-shell molecules; for each system the barriers are estimated from raw data. The model creates a bridge to the Marcus equation and shows that H-atom abstraction by a closed-shell molecule requires a higher barrier owing to the additional promotion energy needed to prepare the abstractor for H-abstraction. Under certain conditions, a closed-shell abstractor can bypass this penalty through a proton-coupled electron transfer (PCET) mechanism. The VB model links the HAT and PCET mechanisms conceptually and shows the consequences that this linking has for H-abstraction reactivity.

The classical Wigner method with an effective quantum force: application to the collinear H + H2 reaction

To improve the classical Wigner (CW) model, we recently proposed the classical Wigner model with an effective quantum force (CWEQF). The results of the CWEQF model are more accurate than those of the CW model. Still the simplicity of the CW model is retained. The quantum force was obtained by defining a characteristic distance η(0) between two Feynman paths that enter the expression for the flux-flux correlation function. η(0) was considered independent of the position along the reaction path. The CWEQF leads to a lowering of the effective potential barrier. Here we develop the method to use position dependent η(0) values. The method is also generalized to two dimensions. Applications are carried out on one-dimensional model problems and the two-dimensional H + H(2) collinear reaction.

Tersoff-Type Potentials for Carbon, Hydrogen and Oxygen

The application of Tersoff-type potentials are illustrated for examples from three distinct classes of chemical systems: a covalently-bonded solid (carbon), a gas-phase few-body reactive system (H3), and a molecular solid (oxygen). For carbon, the potential energy expression yields stable planar graphite layers as well as a stable diamond phase, both with correct densities and binding energies. The potential also predicts the π-bonded chain structure to be the energetically-preferred reconstruction on the {111} surface of diamond, in agreement with ab initio studies. For hydrogen the potential provides a quantitative description of accurate ab initio energies. The oxygen potential describes both the O2 and O3 molecules, and qualitatively describes intramolecular bonding in the condensed phase.

Molecular Dynamics Simulation of Hydrogenated Amorphous Silicon with Tersoff Potential

A Molecular dynamics method with a Many-body Tersoff-type interatomic potential has been being applied to analyses of hydrogenated Amorphous silicon (a-Si:H) thin-film growth processes. As a first step toward film growth simulations, Molecular dynamics simulations of SiH3 radical, which would be a significant precursor for the a-Si:H thin-film growth processes, and a-Si:H formation with a rapid quenching method have been performed by developing new Tersoff-type interatomic potential between Si and H in this study. Visualization of SiH3 radical dynamics by computer graphics has made it possible to observe the inversion and rotation of SiH3 radical, which had been predicted by infrared diode-laser spectroscopie measurement in other group. In addition, visualization of the a-Si:H sample has helped us to find that there are some microcavities in the sample and that there are two kinds of hydrogen in the sample, gathering closely together while lying scattered, which had been predicted in IR absorption experimental results.

Valence bond perturbation theory. A valence bond method that incorporates perturbation theory

A post-VBSCF method, called valence bond second-order perturbation theory (VBPT2), is developed in this paper and is shown to be (i) economical and (ii) at par with more sophisticated VB and MO-based methods. The VBPT2 method starts with VBSCF using a minimal structure set. Subsequently, the Møller-Plesset (MP) partition of the zeroth-order Hamiltonian is obtained by introducing a generalized Fock matrix constructed from the VBSCF density matrix. The first-order wave function is expressed in terms of singly and doubly excited VB structures, which are generated by replacing occupied orbitals by virtual orbitals, the latter being defined as orthogonal to the occupied orbitals. The VBPT2 method retains the simplicity of a VB presentation by condensing contributions from the excited structures into the minimal number of fundamental structures that are involved in the VBSCF calculation. The method is tested by calculating the bond energies of H(2), F(2), N(2), O(2), the barrier of identity hydrogen abstraction reaction, the atomization energy and a potential energy curve for the water molecule and the structural weights and covalent-ionic resonance energy of F(2). It is shown that the VBPT2 method gives results in good agreement with those of the VBCI method and molecular-orbital based methods such as MRPT and MRCI at the same truncation levels. However, the computational effort is greatly reduced, compared to that of VBCI. Future potential directions for the development of the VBPT2 method are outlined.