Mise au point. Theorie des effets de couplage vibronique multimodes. Probleme a 2 etats. Couplage vibronique mettant en jeu des modes et des etats degeneres. Effets du couplage vibronique multimodes en spectroscopie. Comportement statistique des niveaux d'energie vibroniques. Intersections coniques et evolution temporelle de la fluorescence

Multimode molecular dynamics beyond the Born-Oppenheimer approximation

Starting from our earlier model [J. Chem. Phys. 66, 1496 (1977)] a simple expression is derived for the radial dependent damping functions for the individual dispersion coefficients C2n for arbitrary even orders 2n. The damping functions are only a function of the Born–Mayer range parameter b and thus can be applied to all systems for which this is known or can be estimated. For H(1S)–H(1S) the results are in almost perfect agreement with the very accurate recent ab initio damping functions of Koide, Meath, and Allnatt. Comparisons with less accurate previous calculations for other systems also show a satisfactory agreement. By adding a Born–Mayer repulsive term [A exp(−bR)] to the damped dispersion potential, a simple universal expression is obtained for the well region of the atom–atom van der Waals potential with only five essential parameters A, b, C6, C8, and C10. The model has been tested for the following representative systems: H2 3Σ, He2, and Ar2 as well as NaK 3Σ and LiHg, which include four che...

An improved simple model for the van der Waals potential based on universal damping functions for the dispersion coefficients

Previous calculation of the ground‐state energy of H2 has been extended to include large internuclear distances and accurate potential‐energy curve for 0.4≤R≤10.0 a.u. is presented. For 0.4≤R≤4.0 a.u. expectation values of several operators have also been calculated. The calculation was made using a wavefunction in the form of an expansion in elliptic coordinates. The wavefunction depends on the interelectronic distance but, in contrast to the James—Coolidge expansion, is flexible enough to describe properly the dissociation of the molecule. Extensive calculations have also been made for the repulsive 3Σu+ state (1.0≤R≤10.0) and for the 1Πu state (1.0≤R≤10.0). In the former case a van der Waals minimum has been found at R=7.85 a.u. and 4.3 cm−1 below the dissociation limit. For the 1Πu state the computed binding energy De=20 490.0 cm−1 and the equilibrium internuclear distance Re=1.0330 A are in a satisfactory agreement with the experimental values De=20 488.5 cm−1 and Re=1.0327 A. In this case a van der ...

Potential‐Energy Curves for the X 1Σg+, b3Σu+, and C 1Πu States of the Hydrogen Molecule

The ground‐state energies of H2, LiH, Li2, and H2O are calculated by a fixed‐node quantum Monte Carlo method, which is presented in detail. For each molecule, relatively simple trial wave functions ΨT are chosen. Each ΨT consists of a single Slater determinant of molecular orbitals multiplied by a product of pair‐correlation (Jastrow) functions. These wave functions are used as importance functions in a stochastic approach that solves the Schrodinger equation by treating it as a diffusion equation. In this approach, ΨT serves as a ‘‘guiding function’’ for a random walk of the electrons through configuration space. In the fixed‐node approximation used here, the diffusion process is confined to connected regions of space, bounded by the nodes (zeros) of ΨT. This approximation simplifies the treatment of Fermi statistics, since within each region an electronic probability amplitude is obtained which does not change sign. Within these approximate boundaries, however, the Fermi problem is solved exactly. The e...

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Fixed-node quantum Monte Carlo for molecules

A review of the various possible definitions of diradicals leads the authors to describe these systems as having two odd electrons in degenerate or nearly-degenerate molecular orbitals. A study of the wave-function for the two odd electrons shows that its form depends entirely on whether the diradical is homo- or heterosymmetric. Energy schemes are given in these two cases, as well as in the intermediate “non-symmetric” case. The extent of zwitterionic character in diradical states is also investigated. This is followed by a discussion of intersystem crossing between singlet and triplet diradical states via spin-orbit coupling and other mechanisms. The electronic matrix elements for spin-orbit coupling are calculated and evaluated numerically for various model cases. It is then possible to establish general rules for favorable (electronic) intersystem crossing. In 1,3 or 1,4 diradicals its efficiency is estimated to be comparable with that in aromatics. The role of the electron-nuclear hyperfine interaction in mixing singlet and triplet states, particularly in CIDNP, is explained.

Finally the question of whether diradicals actually occur as secondary minima on potential energy surfaces is examined. Recent quantum-mechanical calculations, in contradiction to some thermochemical and kinetic evidence, lead to flat singlet surfaces without significant minima.

The Electronic Properties of Diradicals

Accurate ground‐state energies of the hydrogen molecule have been computed using wavefunctions in the form of expansions in elliptic coordinates and including explicitly the interelectronic distance. The computations have been made with 54‐term expansions (0.4≤R≤3.7) and with 80‐term expansions (0.5≤R≤2.0). For the equilibrium internuclear distance, the best total energies obtained in the two cases are —1.1744701 a.u. and —1.1744746 a.u., respectively, the corresponding binding energies being 38 291.8 and 38 292.7 cm—1. Employing the 54‐term wavefunctions, the relativistic corrections and the diagonal corrections for nuclear motion have been computed for several internuclear distances. For equilibrium their contributions to the binding energy have been found to be —0.526 and 4.947 cm—1, respectively. Thus the final theoretical binding energy for H2 amounts to 38 297.1 cm—1 and is a little larger than the experimental value 38 292.9±0.5 cm—1. The discrepancy may be due to the adiabatic approximation.

Accurate Adiabatic Treatment of the Ground State of the Hydrogen Molecule

The potential‐energy curve for the electronic ground state of the hydrogen molecule has been calculated for 1 ≤ R ≤ 3.2 a.u. in double precision and using a 100‐term expansion for the electronic wavefunction. Accuracy of the previously computed diagonal corrections for nuclear motion has been tested. The vibrational equation has been solved for all isotopes of the hydrogen molecule and for the rotational quantum number J ≤ 10. The calculated adiabatic dissociation energy of H2, corrected for relativistic and radiative effects, is by 3.8 cm−1 larger than the experimental value, hence the theoretical total energy is by the same amount lower than the experimental value. The calculated vibrational quanta for H2 are by 0.5–0.9 cm−1 larger than the experimental ones.

Improved Theoretical Ground‐State Energy of the Hydrogen Molecule

A variation perturbation method has been employed to calculate the static dipole polarizabilities of the hydrogen molecule. The wavefunction was represented by an expansion in elliptic coordinates including the interelectronic distance. A 54‐term expansion was used for the zero‐order wavefunction and 34 terms for the first‐order corrections. The polarizabilities computed for several values of the internuclear distance (0.4≤R≤4.0) were averaged for various vibrational and rotational states of H2, HD, and D2. The results are in a satisfactory agreement with the experimental values.

Polarizability of the Hydrogen Molecule

Relativistic corrections, Born–Oppenheimer energies and adiabatic corrections are computed for R ≤ 120 bohr for the electronic ground state of the hydrogen molecule The Born–Oppenheimer potential is slightly lower than ever reported The problem of linear dependencies in the basis set is removed and the same set is used for all internuclear distances which assures continuity of the results The radiative corrections are evaluated approximately and—for that purpose—the polarizability of the molecule is also computed Vibrational energies are computed and— corrected for nonadiabatic effects—compared with experiment for several isotopes It is argued on the basis of the remaining discrepancies that an improvement in the ab initio nonadiabatic corrections is necessary

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Relativistic energies of the ground state of the hydrogen molecule

The electronic -vibrational wave functions are obtained from the Schrodinger equation for the relative motion of the electrons and nuclei in a diatomic molecule. Numerical computation for the ground state of the hydrogen molecule is carried out. (R.E.U.)

L. Wolniewicz

Papers

Accurate Adiabatic Treatment of the Ground State of the Hydrogen Molecule

Improved Theoretical Ground‐State Energy of the Hydrogen Molecule

Polarizability of the Hydrogen Molecule

Relativistic energies of the ground state of the hydrogen molecule

Nonadiabatic Theory for Diatomic Molecules and Its Application to the Hydrogen Molecule