Diabatic Representation Research Articles

Adiabatic energies and perturbative non-adiabatic corrections for Coulombic three-particle systems in the hyperspherical harmonics formalism

The adiabatic energies and non-adiabatic corrections of the bound and lowest-lying quasi-bound S states of the light Coulombic three-particle systems, the negative positronium and muonium ions and the neutral He atom, are evaluated using the hyperspherical harmonics formalism. The calculations are based on the adiabatic separation of the hyperradial and the hyperangular degrees of freedom. The non-adiabatic corrections are determined using high-order Rayleigh-Schrödinger perturbation theory. Although the adiabatic perturbation series do not always converge, they can be accurately summed for isolated states applying Wynn's algorithm. The perturbation treatment exhibits high numerical stability with respect to the number of basis functions and it is therefore possible to perform these calculations employing very large basis set expansions. The perturbation series pertaining to the well-isolated ground states are summable even in the diabatic representation.

Coupled ab initio potential energy surfaces for the reaction Cl(2P)+HCl→ClH+Cl(2P)

We have constructed the 12A′, 22A′ and 12A″ potential energy surfaces for the Cl(2P)+HCl→ClH+Cl(2P) reaction, together with the non-adiabatic coupling surface between the 12A′ and 22A′ states. All our calculations used the MOLPRO quantum chemistry package, with Dunning's correlation consistent augmented valence triple zeta 1-electron basis set. The 12A′ and 12A″ energies are calculated at the restricted open shell coupled cluster singles doubles with perturbative triples (RCCSD-T) level, whilst the 22A′–12A′ energy difference and the non-adiabatic coupling are calculated via the multireference configuration interaction (MRCI) technique. The non-adiabatic coupling is evaluated from transition matrix elements of the angular momentum operator, namely 〈12A″∣Lx∣12A′〉 and 〈12A″∣Lx∣22A′〉. The surfaces in a diabatic representation are fitted to rotated-Morse cubic-spline functions. The empirical long-range potentials of Dubernet and Hutson (J. Phys. Chem., 1994, 98, 5844), together with empirical short range potentials, are then combined with the fitted abinitio surfaces to produce a set of global potential energy surfaces. Convergence tests show that the height of the barrier at C2v geometries is 0.4361 eV for the 12B1 state, and occurs at a ClHCl bond angle of 137°. The collinear barrier heights are 0.4939 eV on the 2Σu+ surface and 0.9416 eV on the 2Πg surface.

Ab initio study of charge transfer in low-energy collisions with helium

Charge transfer cross sections for collisions of ground state and excited state ) with atomic helium are presented for energies less than 250 eV . Using a fully quantum mechanical, molecular-orbital, close-coupling approach, the cross sections are calculated in a diabatic representation. Completely ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond method are utilized. Rate coefficients for temperatures between 100 and 100 000 K and cross sections for collisions with isotopic are presented. Results for the reverse process, , are also given.

A theoretical study of mutual neutralization in Li + H collisions

First principles calculations of mutual neutralization in and collisions have been performed for low energies (0.68-50.0 eV). A diabatic representation is used for eight electronic states determined directly within an ab initio calculation. For the comparison with the recent merged-beam experiment the finite acceptance angle of the detector has been taken into account. An improved ionic diabatic curve, corrected for deficiencies in the ab initio electron affinity of H, has also been used. The large cross section at low energy for this mutual neutralization is due predominantly to the almost optimal efficiency for the non-adiabatic transition to the neutral Li(3s)H(1s) state. The calculated cross section exceeds experiment by no more than about 20%, indicating that the neutral-ionic diabatic crossings and couplings are accurately evaluated by the ab initio approach.

Theoretical analysis of electron capture and electron loss in Be 4++H2 and H++H2 collisions

Dynamical calculations are carried out within the framework of the Frank-Condon approximation, for collisions between H+ and Be4+ ions with H2 molecules within the range of energies . For the higher impact energies, we employ single-particle models, using semiclassical and classical trajectory Monte Carlo adapted methods. The accuracy of the single-particle models is checked by comparing molecular data, transition probabilities and cross sections, with those obtained with an ab initio approach and with experiment. We conclude that a central potential approximation for the H2 molecule yields accurate capture and electron-loss cross sections for , and good ones in the energy region . An analysis of the equivalent and non-equivalent-electrons bielectronic interpretations of the model potential probabilities has been performed; for both reactions, comparison of the Hamiltonian matrix elements in a diabatic representation supports the conclusion that an equivalent-electron picture is adequate to describe the active electron of the H2 molecule with an H2+ `core'.

Spectra and time-dependent dynamics of H3 near the conical intersection in the (2p)1E′ ground electronic manifold

We report on the spectra and dynamics of H3 near the conical intersection in its (2p)1E′ ground electronic manifold. The time-dependent wave packet approach and the double many-body expansion (DMBE) potential energy surface (PES) are employed for this purpose. We use Jacobi coordinates (R,r,γ) and employ the fast Fourier transform method for R and r, and the discrete variable representation method for γ, in conjunction with the split-operator formalism to describe the evolution of the wave packet (WP) in space and time, respectively. While the main focus of the present work is to explicitly reveal the effects of nonadiabatic coupling between the two sheets of the DMBE PES, companion calculations are also carried out to investigate the dynamics on the uncoupled upper and lower adiabatic sheets, both in two and three dimensions (for total angular momentum J=0). A set of pseudospectra is calculated by Fourier transforming the time autocorrelation function of suitably chosen Gaussian wave packets located initially at the minimum energy point of the seam of conical intersections. The eigenstates thus obtained are assigned by computing their eigenfunctions by spectral quantization. In the coupled states treatment the WP is propagated in the diabatic representation. The time dependence of the adiabatic populations is calculated by using suitable adiabatic projection operators. We find strong effects of nonadiabatic coupling on the discrete vibrational energy levels of the upper adiabatic sheet, which all change to quasibound states in the coupled manifold. The comparison of the decay dynamics of various levels of the upper adiabatic sheet indicates considerable mode specificity (their lifetimes typically vary between 3 and 6 fs). On the other hand, resonances are seen to be less pronounced near the conical intersection on the lower adiabatic sheet (when compared to those in the literature, obtained near the collinear saddle point region). The effect of nonadiabatic coupling on them is only minor. We also report preliminary results on the optical emission spectrum of H3 and compare them with the experimental findings.

Charge transfer in He++-He collisions at keV energies in an intense laser field: A theoretical close-coupled study using a diabatic molecular representation

We carry out a theoretical study of the effect of a strong laser field on charge transfer in collisions of doubly charged helium ions with helium at keV energies, using a close-coupled treatment with a diabatic molecular wave function basis in the semiclassical impact parameter approximation. Our results show significant effects of the laser intensity, wavelength and the orientation of the (linear) laser polarization on the charge transfer cross-sections. Our results also indicate the possibility of an experimental test for differentiating between the effects of the minimal coupling and the multipolar matter-radiation interactions on ion-atom collision processes.

A quenching method in mixed quantum-classical dynamics calculations on nonadiabatic problems

A quenching method [Chem. Phys. Lett. 262, 284 (1996)] is extended to study nonadiabatic reactive scattering within a mixed quantum-classical molecular dynamics simulation based on the time dependent self-consistent field. The quenching method is more straightforward for nonadiabatic reactive scattering than for the adiabatic case. A rigorous diabatic-adiabatic transformation for nonadiabatic problems is presented. It provides a theoretical basis for decoupling the bifurcating wavepacket in adiabatic reactive scattering and a new decoupling technique. The derivation illustrates clearly that a diabatic representation is convenient for both adiabatic and nonadiabatic reactive scattering within the mixed quantum-classical formulation. Two model examples are used to demonstrate the advantages of the quenching method for nonadiabatic reactive scattering. A comparison with the full quantum treatment is also made.

Quantum and semiclassical calculations of cold-atom collisions in light fields

We derive and apply an optical Bloch equation (OBE) model for describing collisions of ground and excited laser cooled alkali atoms in the presence of near-resonant light. Typically these collisions lead to loss of atoms from traps. We compare the results obtained with a quantum mechanical complex potential treatment, semiclassical Landau-Zener models with decay, and a quantum time-dependent Monte-Carlo wave packet (MCWP) calculation. We formulate the OBE method in both adiabatic and diabatic representations. We calculate the laser intensity dependence of collision probabilities and find that the adiabatic OBE results agree quantitatively with those of the MCWP calculation, and qualitatively with the semiclassical Landau-Zener model with delayed decay, but that the complex potential method or the traditional Landau-Zener model fail in the saturation limit.

Time-dependent self-consistent-field dynamics based on a reaction path Hamiltonian. I. Theory

A method that combines the time-dependent self-consistent-field (TDSCF) method with the reaction path Hamiltonian (RPH) derived by Miller, Handy, and Adams [J. Chem. Phys. 72, 99 (1980)] is proposed. This TDSCF-RPH method allows the calculation of the real-time quantum dynamics of chemical reactions involving polyatomic molecules. When both the coupling between the normal modes and the curvature are zero, the dynamics of an F-dimensional system is shown to reduce to a one-dimensional numerical time propagation. When the reaction path curvature is zero and the coupling between the normal modes is non-zero, the dynamics is shown to still reduce to a one-dimensional problem for a specific choice of initial wavepacket (which can have an arbitrary component for the reaction coordinate), but F coupled one-dimensional equations of motion must be propagated for a general initial wavepacket (unless the RPH is transformed to the diabatic representation). When the coupling between the normal modes is zero and the reaction path curvature is non-zero but small, the dynamics is shown to reduce to a one-dimensional numerical time propagation for an arbitrary initial wavepacket. The derivations of the equations of motion for these cases are presented in this paper, and numerical tests are presented in a separate paper.

Potential energy surfaces of NaFH

High-level ab initio calculations of the ground and several excited-state adiabatic potential surfaces of the NaFH system are reported. These calculations were performed by multireference configuration interaction on a large grid of geometries which allowed them to be used for constructing an accurate analytic representation of the NaFH potential surfaces. For the ground and first excited states, using a genetic algorithm, an analytic 2×2 matrix fit was obtained corresponding to a diabatic representation. The off-diagonal coupling was obtained by fitting the energy gap between the surfaces in the region of their avoided crossing, and the diagonal elements were then fit to reproduce the ab initio adiabatic energy at 1530 points. The full fit was used to locate the barrier and the van der Waals well on the ground-state potential surface, the exciplex on the first-excited-state potential surface, and the minimum energy path for the ground-state Na+HF→NaF+H reaction. Additional calculations on the van der Waals and saddle point regions were carried out by a variety of ab initio methods as a check on accuracy. Major topological features of the potential energy surfaces representing higher-than-first excited states were examined.

Theoretical investigation of weakly-bound complexes of O(3P) with H2

We report multireference configuration interaction (CI), as well as coupled-cluster, calculations for the three O(3P)H2 potential-energy surfaces (two of A″ symmetry and one of A′ symmetry in Cs geometry) in the region relevant to the weakly bound O(3P)⋯H2 complex. The two electronically adiabatic states of A″ symmetry correspond to an orthogonal transformation of two orthogonal electronic occupations of the O 2p orbitals. The transformation of the three electronically adiabatic states to an approximate diabatic representation, which involves four potential-energy functions, can be obtained, either from calculated matrix elements of the electronic orbital angular momentum or from analysis of the expansion coefficients of the CI wave functions. An exact treatment of the nuclear motion including spin–orbit coupling, based on the diabatic PES’s (potential energy surfaces), is used to determine the energies of the lowest bend–stretch levels of complexes of O(3P) with both nuclear spin isomers of H2 and D2. The predicted dissociation energies (D0) are 15.4 and 22.4 cm−1 for the complexes with pH2 and oH2, respectively, and 22.3 and 31.4 cm−1 for the complexes with oD2 and pD2, respectively.

Ab initio study of charge transfer in low energy collisions with atomic hydrogen

Charge transfer cross sections for collisions of ground state and excited state with atomic hydrogen are presented for energies less than . The cross sections are calculated in a diabatic representation using a fully quantum-mechanical, molecular-orbital, close-coupled method. Completely ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond method are incorporated. Inclusion of the and closed-channels results in oscillations in the charge transfer cross section for collision energies above the separated-atom energy of the lowest closed-channel . Rate coefficients for temperatures between 500 and 100 000 K and cross sections for collisions with isotopic D are presented. Results for the reverse process, charge transfer ionization, are also given.

Test of Trajectory Surface Hopping Against Accurate Quantum Dynamics for an Electronically Nonadiabatic Chemical Reaction

This paper presents the first test of the popular trajectory surface-hopping (TSH) method against accurate three-dimensional quantum mechanics for a reactive system. The system considered is a model system in which an excited atom with an excitation energy of 0.76 eV reacts with or is quenched by the H2 molecule. The electronically nonadiabatic collisions occur primarily near a conical intersection of an exciplex with a repulsive ground state. The accurate quantal results are calculated using the outgoing wave variational principle in an electronically diabatic representation. Four variants of the TSH method are tested, differing in the criteria for hopping and the component of momentum that is adjusted in order to conserve energy when a hop occurs. Coupling between the ground and excited surface occurs primarily in the vicinity of a conical intersection and is mediated by an exciplex found on the upper surface. We find that the overall TSH quenching probabilities are in good agreement with quantum mechanical results, but the branching ratios between reactive and nonreactive trajectories and many of the state-selected results are poorly reproduced by trajectory calculations. The agreement between trajectory surface hopping and quantal results is on average worse for the relatively more “quantum mechanical” j ) 0 initial state and M + H2 quenching process and better for

Mixed quantum–classical dynamics

We present a unified derivation of the mean-field (Ehrenfest) and surface-hopping approaches to mixed quantum–classical dynamics that elucidates the underlying approximations of the methods and their strengths and weaknesses. We then report a quantitative test of alternative mixed quantum–classical methods against accurate quantum mechanical calculations for a simple one-dimensional curve-crossing model. We conclude that, for this model, surface-hopping with the adiabatic representation is decidedly superior to either mean-field or surface-hopping with the diabatic representation.

Quantum dynamics of multiple modes for reactions in complex systems

Two different approaches for investigating the quantum dynamics of multiple modes for reactions in complex systems are presented. The first is time-dependent self-consistent-field dynamics based on a reaction path Hamiltonian (TDSCF-RPH), which allows the calculation of the real-time quantum dynamics of gas-phase chemical reactions involving polyatomic molecules. The TDSCF-RPH equations of motion are derived for straight-line diabatic reaction path Hamiltonians, including the case in which the minimum-energy path has negligible curvature and the case in which the minimum-energy path has large curvature but the system follows a straight-line path instead of the minimum-energy path. The advantage of the diabatic representation is that the TDSCF dynamics reduces to a one-dimensional numerical time propagation, even for the case of large coupling between the vibrational modes. The second approach is the multiconfigurational molecular dynamics with quantum transitions (MC-MDQT) method, which combines a multiconfigurational self-consistent-field (MC-SCF) formulation for the vibrational wavefunction with the MDQT non-adiabatic mixed quantum–classical molecular dynamics method. The MC-MDQT method allows the quantum dynamical treatment of multiple modes within a mixed quantum–classical framework for reactions in condensed-phase systems. The advantages of the MC-MDQT method are that it incorporates the significant correlation between the quantum modes, is valid in the adiabatic and non-adiabatic limits and the intermediate regime, and provides real-time dynamical information. The application of MC-MDQT to simulate the real-time non-equilibrium quantum dynamics of proton transport along protonated chains of water molecules is presented.

Quasibound states in long-range alkali dimers: Grid method calculations

A local minimum is found in the 0g+ long range potential curves of the K2 and Rb2 alkali dimers. This well-of magnitude 42 cm−1 for K2 and 93 cm−1 for Rb2—is located above the first ns+n2P3/2 dissociation limit and metastable states could be populated using laser light blue detuned compared to the resonance line. To compute the previously unknown energies and lifetimes of these quasibound states, two grid methods are employed. One method is based on diagonalizing a Fourier grid Hamiltonian, the other uses a propagation technique in imaginary time to filter out vibrational eigenfunctions. Equivalent results are given by both methods. Then the lifetimes are extracted from the correlation function obtained by propagation in real time of these numerical vibrational wave functions. The methods are employed both in adiabatic representation with one electronic potential curve and in diabatic representation with two potential curves. Two quasibound states are found for K2, and three for Rb2 above seven stable bound states. Their lifetimes vary from 20 ps to 3 ns.

Photodissociation of ozone in the Chappuis band. I. Electronic structure calculations

Potential-energy surfaces of the 1 1A′, 1 1A′′, and 2 1A′′ states of ozone and corresponding transition-dipole-moment surfaces have been computed as a function of the two bond distances and the bond angle. The calculations are based on the complete-active-space self-consistent field (CASSCF) and multiconfigurational second-order perturbation theory (CASPT2) electronic-structure models. For the calculations of the A″1 surfaces, which exhibit a conical intersection, a diabatic representation has been constructed, employing a direct diabatization method implemented at the CASSCF level. The slow variation of the diabatic potentials and transition dipole moments with nuclear geometry allows us to perform the ab initio calculations on a widely spaced grid. The complete potential-energy and transition-dipole-moment surfaces are then efficiently obtained by interpolation. This procedure leads to very significant savings of computing time compared to the mapping of the rapidly varying potentials and derivative couplings in the conventional adiabatic representation. Diabatic potentials at the CASPT2 level have been obtained by applying the adiabatic-to-diabatic transformation constructed at the CASSCF level to the adiabatic CASPT2 potentials. The properties of the resulting adiabatic and diabatic A″1 potential-energy surfaces are discussed, with emphasis on the 1 1A′′–2 1A′′ conical intersection, which is of relevance for the photodissociation dynamics of ozone in the Chappuis band. The computation of the photoabsorption cross section and the comparison between theory and experiment are discussed in the accompanying paper.

Photodissociation of ozone in the Chappuis band. II. Time-dependent wave-packet calculations and interpretation of diffuse vibrational structures

We present time-dependent wave-packet calculations describing the photodissociation of ozone in the Chappuis band, which evolves in the two lowest states of A″1 symmetry. The calculations are performed in the diabatic representation and include the coupling between the two relevant states. All three nuclear degrees of freedom are taken into account. The two potential-energy surfaces, the coupling potential, and the two transition-dipole-moment functions with the electronic ground state have been calculated previously by ab initio methods [Woywod et al., J. Chem. Phys. 107, 7282 (1997)]. The coupling between the two diabatic states is exceedingly strong, resulting in very fast dissociation into O+O2 on the time scale of only one symmetric stretch period. A small portion of the initially created wave packet is temporarily trapped leading to three tiny recurrences, which reflect basically symmetric stretch motion plus some amount of bending motion. The experimentally observed diffuse vibrational structures superimposed to the broad absorption spectrum are satisfactorily reproduced and discussed both in the time-independent and the time-dependent picture of spectroscopy. In view of the very short lifetime in the excited states, the correspondingly large widths of the diffuse structures, and the participation of all three vibrational modes we conclude that an unique assignment in terms of three quantum numbers is not possible. The main structures are due to symmetric stretch excitation, but bending and even asymmetric stretch motion are also involved. A one-state model, in which only the upper (bound) adiabatic potential is employed, provides a qualitatively correct explanation of the absorption spectrum and the diffuse structures.

Semiclassical wave packet calculations on ion–molecule reactions: Studies on B+(3Pu)+H2 reaction

We present the investigations of nonadiabatic scattering processes (reactive as well charge-transfer) occurring in B++H2 reaction in the gas phase on the triplet electronic surfaces utilizing a mixed quantum-classical approach to scattering of three particle systems in hyperspherical coordinates. The time-dependent Schrödinger equation is solved in diabatic representation using wave packet propagation method on a grid in two quantum dimensions. The potential-energy surfaces have been obtained using the valence-bond diatomics-in-molecule approach.