Adiabatic Electronic Potential Energy Surfaces Research Articles

Machine Learning Representations of the Three Lowest Adiabatic Electronic Potential Energy Surfaces for the ArH2+ Reactive System.

In this work, we present Gaussian process regression machine learning representations of the three lowest coupled 2A' adiabatic electronic potential energy surfaces of the ArH2+ reactive system in full dimensionality. Additionally, the nonadiabatic coupling matrix elements were calculated. These adiabatic potentials and their nonadiabatic couplings are necessary ingredients in the theoretical investigation of the nonadiabatic reaction dynamics of the Ar + H2+ → ArH+ + H and Ar+ + H2 → ArH+ + H reactions, as well as the competing charge transfer process, Ar + H2+↔ Ar+ + H2. Accurate ab initio electronic structure calculations (ic-MRCI+Q/aug-cc-pVQZ), whereby the effect of spin-orbit coupling in Ar+ has been accounted for through the state interaction method, serve as input for the machine learning training process. The potential energy surfaces are fitted with high accuracies, with root-mean-square errors on the order of 10-7 eV for the three surfaces, which meet the requirements for chemical dynamics at low temperature. It was found that quite a large number of training points (of the order of 5000 ab initio points) are needed in order to achieve these accuracies due to the complex topography of these electronic surfaces.

Importance of Geometric Phase Effects in Ultracold Chemistry.

It is demonstrated that the inclusion of the geometric phase has an important effect on ultracold chemical reaction rates. The effect appears in rotationally and vibrationally resolved integral cross sections as well as cross sections summed over all product quantum states. The effect arises from interference between scattering amplitudes of two reaction pathways: a direct path and a looping path that encircle the conical intersection between the two lowest adiabatic electronic potential energy surfaces. It is magnified when the two scattering amplitudes have comparable magnitude and they scatter into the same angular region which occurs in the isotropic scattering characteristic of the ultracold regime (s-wave scattering). Results are presented for the O + OH → H + O2 reaction for total angular momentum quantum number J = 0-5. Large geometric phase effects occur for collision energies below 0.1 K, but the effect vanishes at higher energies when contributions from different partial waves are included. It is also qualitatively demonstrated that the geometric phase effect can be modulated by applying an external electric field allowing the possibility of quantum control of chemical reactions in the ultracold regime. In this case, the geometric phase plays the role of a "quantum switch" which can turn the reaction "on" or "off".

Ultracold Rydberg atoms in a magneto-electric trap

We investigate the quantum properties of an ultracold Rydberg atom exposed to a magnetic quadrupole field and a homogeneous electric field. The properly transformed Hamiltonian explicitly depends on the conserved total angular momentum and couples the centre of mass and electronic degrees of freedom. The corresponding Schrödinger equation is solved by an adiabatic separation focusing on a fixed n-manifold. The shape of the adiabatic electronic potential energy surfaces is analysed. With increasing electric field strength, avoided crossings among them become ubiquitous and the electric field-dominated regime spreads out within the centre-of-mass coordinate space. A transition from smooth surfaces for weak electric fields to surfaces involving a cusp-like behaviour in the strong field regime is observed. The latter involves a characteristic splitting behaviour of the surfaces due to the competition of the Stark and magnetic interactions. In contrast to previous investigations, our setup allows for the trapping of quantum states with a comparatively small electronic angular momentum.

Inelastic scattering matrix elements for the nonadiabatic collision B(P1∕22)+H2(Σg+1,j)↔B(P3∕22)+H2(Σg+1,j′)

Inelastic scattering matrix elements for the nonadiabatic collision B(P1∕22)+H2(Σg+1,j)↔B(P3∕22)+H2(Σg+1,j′) are calculated using the time dependent channel packet method (CPM). The calculation employs 1A′2, 2A′2, and 1A″2 adiabatic electronic potential energy surfaces determined by numerical computation at the multireference configuration-interaction level [M. H. Alexander, J. Chem. Phys. 99, 6041 (1993)]. The 1A′2 and 2A′2, adiabatic electronic potential energy surfaces are transformed to yield diabatic electronic potential energy surfaces that, when combined with the total B+H2 rotational kinetic energy, yield a set of effective potential energy surfaces [M. H. Alexander et al., J. Chem. Phys. 103, 7956 (1995)]. Within the framework of the CPM, the number of effective potential energy surfaces used for the scattering matrix calculation is then determined by the size of the angular momentum basis used as a representation. Twenty basis vectors are employed for these calculations, and the corresponding effective potential energy surfaces are identified in the asymptotic limit by the H2 rotor quantum numbers j=0, 2, 4, 6 and B electronic states Pja2, ja=1∕2, 3∕2. Scattering matrix elements are obtained from the Fourier transform of the correlation function between channel packets evolving in time on these effective potential energy surfaces. For these calculations the H2 bond length is constrained to a constant value of req=1.402a.u. and state to state scattering matrix elements corresponding to a total angular momentum of J=1∕2 are discussed for j=0↔j′=0,2,4 and P1∕22↔P1∕22, P3∕22 over a range of total energy between 0.0 and 0.01a.u.

Accurate first-derivative nonadiabatic couplings for the H3 system

A conical intersection exists between the ground (1 A′2) and the first-excited (2 A′2) electronic potential energy surfaces (PESs) of the H3 system for C3v geometries. This intersection induces a geometric phase effect, an important factor in accurate quantum mechanical reactive scattering calculations, which at low energies can be performed using the ground PES only, together with appropriate nuclear motion boundary conditions. At higher energies, however, such calculations require the inclusion of both the 1 2A′ and 2 2A′ electronic PESs and the corresponding nuclear derivative couplings. Here we present ab initio first-derivative couplings for these states obtained by analytic gradient techniques and a fit to these results. We also present a fit to the corresponding 1 2A′ and 2 2A′ adiabatic electronic PESs, obtained from the ab initio electronic energies. The first-derivative couplings are compared with their approximate analytical counterparts obtained by Varandas et al. [J. Chem. Phys. 86, 6258 (1987)] using the double many-body expansion method. As expected, the latter are accurate close to conical intersection configurations but not elsewhere. We also present the contour integrals of the ab initio couplings along closed loops around the above-mentioned conical intersection, which contain information about possible interactions between the 2 2A′ and 3 2A′ states.

Exploring the topology of potential energy surfaces of the H2+ ion in the presence of a strong magnetic field

We discuss the symmetries, the behavior of the diabatic energy curves, as well as the static aspects of vibronic interaction for diatomic molecules in the presence of a strong magnetic field. Our central subject of investigation is the topology of the adiabatic electronic potential energy surfaces of diatomic molecules which are discussed using some selected examples of the surfaces of the H2+ ion. Global equilibrium configurations corresponding to stable molecular states are found both for the parallel as well as for the perpendicular configurations. For a higher degree of excitation, we observe that the global minimum can belong to the lowest possible symmetry of the ion in the presence of a magnetic field. As an example, we discuss the topology of the 3u potential energy surface. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 553–560, 1997

Exploring the topology of potential energy surfaces of the H2 ion in the presence of a strong magnetic field

We discuss the symmetries, the behavior of the diabatic energy curves, as well as the static aspects of vibronic interaction for diatomic molecules in the presence of a strong magnetic field. Our central subject of investigation is the topology of the adiabatic electronic potential energy surfaces of diatomic molecules which are discussed using some selected examples of the surfaces of the H2+ ion. Global equilibrium configurations corresponding to stable molecular states are found both for the parallel as well as for the perpendicular configurations. For a higher degree of excitation, we observe that the global minimum can belong to the lowest possible symmetry of the ion in the presence of a magnetic field. As an example, we discuss the topology of the 3u potential energy surface. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 553–560, 1997

On the topology of the adiabatic potential energy surfaces of the H 2+-ion in a strong magnetic field

The electronic structure of diatomic molecules in strong magnetic fields is investigated by means of the example of the hydrogen molecular ion. A variety of different possibilities for the topological behaviour of the two-dimensional adiabatic electronic potential energy surfaces are derived and discussed. Global as well as local equilibrium configurations of the ion are shown to occur not only for the positions with higher symmetry, i.e. for the parallel and perpendicular positions, but also for configurations which correspond to an inclination of the internuclear axis with respect to the external field.

Spectral Theory of Physical and Chemical Binding,

A spectral method which provides unified quantum mechanical descriptions of both physical and chemical binding phenomena is reported for constructing the adiabatic electronic potential energy surfaces of aggregates of atoms or other interacting fragments. The formal development, based on use of a direct product of complete sets of atomic spectral eigenstates and the pairwise-additive nature of the total Hamiltonian matrix in this basis, is seen to be exact when properly implemented and to provide a separation theorem for N-body interaction energies in terms of response matrices which can be calculated once and for all for atoms and other fragments of interest. Its perturbation theory expansion provides a generalization of familiar (Casimir−Polder) second-order pairwise-additive and (Axilrod−Teller) third-order nonadditive interaction energies, expressions which are recovered explicitly in the long-range-dipole expansion limit. A program of ab initio computational implementation of the formal development i...

Quantum study of electronically non-adiabatic collinear reactions. III. Influence of vibrational and electronic excitations on the Cs + HH → CsH + H reaction

A new hyperspherical close-coupling method, involving non-orthogonal diabatic electronic bases adapted to each arrangement, is developed to compute collisional transition probabilities for the collinear Cs + HH system, close to the threshold of the reactions Cs *(7p) + HH(υ = 0) → CsH(υ = 0) + H. A simple model, taking into account the overall rotation of the linear CsHH complex, provides estimates of inelastic and reactive cross sections. A hyperspherical adiabatic analysis, based on adiabatic electronic potential energy surfaces, points out two prominent features in the dynamics of the CsHH system namely: (i) Approximate electrovibrational adiabaticity, which gives rise to large cross sections (≈ 5 Å 2), for both the vibrationally adiabatic process Cs *(7p) + HH(υ = 0) → CsH(υ = 0) + H and the vibrational-into-electronic energy conversion Cs(6s) + HH(υ = 6) → CsH(υ = 0) + H. (ii) Sharp resonances, which yield rapid oscillations on total cross sections, related to the rotational structure of an intermediate linear long-lived complex.

Nonadiabatic semiclassical scattering. II. Solution of two-dimensional models and comparison with quantum results

The generalized surface-hopping procedure for semiclassical nonadiabatic scattering is applied to a two dimensional model for comparison with quantum results. The model consists of two adiabatic electronic potential energy surfaces with a radial nonadiabatic coupling between the electronic states. Both adiabatic potential surfaces are taken to be constant. The coupling is assumed to be weak. This model is sufficient to explore many of the important features of the generalized surface-hopping procedure. Comparison of the semiclasssical and quantum results demonstrates good agreement, and the first order quantum scattering amplitude is analytically found to be the ℏ→0 limit of the first order semiclassical scattering amplitude. The behavior of the wave function near singularities in the transition amplitudes is explored in a general context, independent of these simplified models. These singularities are found to be necessary to produce the correct behavior in the wave function.

Spectroscopic effects of conical intersections of molecular potential energy surfaces

A simple vibronic coupling model involving two electronic states and two vibrational modes is considered. The model is based on harmonic diabatic potentials and linear coupling of the diabatic electronic states. It is shown that the adiabatic electronic potential energy surfaces exhibit, in general, a conical intersection. The well known E × E and E × B Jahn-Teller problems are contained as special cases. Using numerical methods the optical absorption spectrum is calculated exactly. Extremely complex vibronic spectra are obtained when the conical intersection occurs within the Franck-Condon (FC) zone. The exact vibronic spectra are compared with spectra calculated in the adiabatic and FC approximation. The genuine spectroscopic effects of conical intersections are revealed by a comparison with the results of standard one-dimensional vibronic coupling calculations. The presence of a conical intersection limits the applicability of the adiabatic and FC approximations much more strongly than in the one-dimen...