Nonadiabatic chemical dynamics in an intense laser field: electronic wave packet coupled with classical nuclear motions

Dynamics of molecules in an intense laser field is studied in terms of the quantum electronic wave packet coupled with classical nuclear motions. The equations of motion are derived taking a proper account of molecular interactions with the vector potential of a classical electromagnetic field, along with the nonadiabatic interaction due to the breakdown of the Born-Oppenheimer approximation. With the aid of electronic structure calculations, the present method enables us to track, in an ab initio manner, the dynamics of polyatomic molecules in an intense field. Preliminary calculations are carried out for the vibrational state of LiF and a collision of Li+F under an intense laser pulse, which are limited to the domain of no ionization.     

Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions

An ab initio electronic wave-packet dynamics coupled with the simultaneous classical dynamics of nuclear motions in a molecule is studied. We first survey the dynamical equations of motion for the individual components. Reflecting the nonadiabatic dynamics that electrons can respond to nuclear motions only with a finite speed, the equations of motion for nuclei include a force arising from the kinematic (nuclear momentum) coupling from electron cloud. To materialize these quantum effects in the actual ab initio calculations, we study practical implementation of relevant electronic matrix elements that are related to the derivatives with respect to the nuclear coordinates. Applications of the present scheme are performed in terms of the configuration state functions (CSF) using the canonical molecular orbitals as basis functions without transformation to particular diabatic basis. In the CSF representation, the nonadiabatic interaction due to the kinematic coupling is anticipated to be rather small, and instead it should be well taken into account through the off-diagonal elements of the electronic Hamiltonian matrix. Therefore it is expected that the nonadiabatic dynamics based on this CSF basis neglecting the kinematic coupling may work. To verify this anticipation and to quantify the actual effects of the kinematic coupling, we compare the dynamics with and without the kinematic-coupling terms using the same CSF set. Applications up to the fifth electronically excited states in a nonadiabatic collision between H(2) and B(+) shows that the overall behaviors of these two calculations are surprisingly similar to each other in an average sense except for a fast fluctuation reflecting the electronic time scale. However, at the same time, qualitative differences in the collision events are sometimes observed. Therefore it turns out after all that the kinematic-coupling terms cannot be neglected in the CSF-basis representation. The present applications also demonstrate that the nonadiabatic electronic wave-packet dynamics within ab initio quantum chemical calculation is feasible.     

Exploring potential energy surfaces for chemical reactions: an overview of some practical methods

Potential energy surfaces form a central concept in the application of electronic structure methods to the study of molecular structures, properties, and reactivities. Recent advances in tools for exploring potential energy surfaces are surveyed. Methods for geometry optimization of equilibrium structures, searching for transition states, following reaction paths and ab initio molecular dynamics are discussed. For geometry optimization, topics include methods for large molecules, QM/MM calculations, and simultaneous optimization of the wave function and the geometry. Path optimization methods and dynamics based techniques for transition state searching and reaction path following are outlined. Developments in the calculation of ab initio classical trajectories in the Born-Oppenheimer and Car-Parrinello approaches are described.     

Bifurcations on potential energy surfaces of organic reactions

A single transition state may lead to multiple intermediates or products if there is a post-transition-state reaction pathway bifurcation. These bifurcations arise when there are sequential transition states with no intervening energy minimum. For such systems, the shape of the potential energy surface and dynamic effects, rather than transition-state energetics, control selectivity. This Minireview covers recent investigations of organic reactions exhibiting reaction pathway bifurcations. Such phenomena are surprisingly general and affect experimental observables such as kinetic isotope effects and product distributions.     

Semi-empirical potential energy surfaces for hydrogen-atom transfer reactions

A method for constructing potential energy surfaces previously proposed by the author has been extended to hydrogen transfer reactions between halide, oxygen, and carbon atoms. A qualitative relation was found between the repulsive energy and the number of anti-bonding electrons. In general, the calculated kinetic isotope effect is in satisfactory agreement with observed values and the contributions by H-atom tunneling to the rate of reaction is smaller than that obtained from other surfaces.     

A topological stochastic approach to the study of multidimensional potential energy surfaces of chemical reactions

In this article we propose a new approach for investigating the properties of multidimensional potential energy surfaces in chemical reactions, based on relations of each multidimensional surface to its one-dimensional image which is the chemical reaction tree. This approach makes it possible to find a common number of independent channels in chemical reactions for complex systems and to construct the probable models.     

Non-Hermitian quantum mechanics: wave packet propagation on autoionizing potential energy surfaces

The correspondence between the time-dependent and time-independent molecular dynamic formalisms is shown for autoionizing processes. We demonstrate that the definition of the inner product in non-Hermitian quantum mechanics plays a key role in the proof. When the final state of the process is dissociative, it is technically favorable to introduce a complex absorbing potential into the calculations. The conditions which this potential should fulfill are briefly discussed. An illustrative numerical example is presented involving three potential energy surfaces.     

Improved direct diabatization and coupled potential energy surfaces for the photodissociation of ammonia

Diabatic potential energy surfaces are a convenient starting point for dynamics calculations of photochemical processes, and they can be calculated by the fourfold way direct diabatization scheme. Here we present an improved definition of the reference orbital for applying the fourfold way direct diabatization scheme to ammonia. The improved reference orbital is a geometry-dependent hybrid orbital that allows one to define consistent dominant configuration lists at all geometries important for photodissociation. Using diabatic energies calculated with the new reference orbital and consistent dominant configuration lists, we have refitted the analytical representations of the ground and the first electronically excited singlet-state potential energy surfaces and the diabatic coupling surface. Improved functional forms were used to reproduce the experimental dissociation energies and excitation energies, which will be important for subsequent simulations of photochemical dynamics. We find that the lowest-energy conical intersection point is at 5.16 eV, with C _2v symmetry. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users. This article is part of the special issue dedicated to the memory of the late Professor Fernando Bernardi.     

Comparison of classical mechanics and the coupled states approximation for Li+-CO scattering on an ab initio calculated CI potential energy surface

The dynamics of rotational excitation on an ab initio calculated CI rigid rotor potential energy surface for Li⁺-CO are investigated using classical mechanics and the quantum mechanical coupled-states (CS) approximation. Transition probabilities out of the j = 0 initial level are calculated for various impact parameters between b = 0 and 40a_o for 1 eV collisions. The classical results agree well with the average of Δj-even and Δj-odd quantum transition probabilities except for a few lower impact parameters where CS seems to underestimate the large Δ transitions. No propensity rule is observed for the preference of the Δj-even versus Δj-odd transitions as might have been expected.     

Potential energy surfaces for gas-surface reactions

A method for constructing the potential energy surface for reactions of a molecule with the surface of cleaved non-conducting crystals is reported. The method uses systematic fragmentation to express the total potential in terms of potential energy surfaces which describe reactions of relatively small molecules in the gas phase. The approach is illustrated by an application to the reaction of hydrogen atoms with a hydrogen-terminated silicon(111) surface.     

Interpolating moving least-squares methods for fitting potential energy surfaces: applications to classical dynamics calculations

As a continuation of our efforts to develop efficient and accurate interpolating moving least-squares (IMLS) methods for generating potential energy surfaces, we carry out classical trajectories and compute kinetics properties on higher degree IMLS surfaces. In this study, we have investigated the choice of coordinate system, the range of points (i.e., the cutoff radius) used in fitting, and strategies for selections of data points and basis elements. We illustrate and test the method by applying it to hydrogen peroxide (HOOH). In particular, reaction rates for the O-O bond breaking in HOOH are calculated on fitted surfaces using the classical trajectory approach to test the accuracy of the IMLS method for providing potentials for dynamics calculations.     

General methodology in two dimensions for classical simulation of reactive and nonreactive events on ab initio potential energy surfaces

A completely general two-dimensional (2D) methodology for the classical simulation of reactive and nonreactive events on ab initio potential energy surfaces is introduced and tested. The methodology requires the minimum amount of information given a priori—geometries and energies at these geometries. From a list of ab initio geometries and energies, simulations may be executed and a distribution of outcomes obtained. The method introduced attempts a local approach at simulating the dynamics of the system, rather than a global analytic fit to the potential energy surface. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1431–1444, 1998     

Solvated potential energy surfaces for MePC

A conformational study of methylphosphocholine (MePC) was performed from a conformational map calculated considering the dihedral angles that most affected the energy of the system. This conformational map was obtained from interpolations of energy values found from calculations that took into account the presence of solvent through a dielectric continuum approach. We used a quantum–mechanical method based on the Density Functional Theory (DFT) and the 6-31G(d,p) basis set. Conformational samplings were performed in stability regions and the most stable conformers were identified. Comparisons of samplings in solvated and non-solvated conformational maps were performed, and although very different from each other, they furnish equivalent final conformational sets. Both the sets reproduced satisfactorily the experimental shift observed for the vibrational modes of –[P(O₂)]⁻– and –CH₂– methylene groups of MePC when the system was solvated.