F. Spiegelmann

Ab initio molecular calculations including spin-orbit coupling. I. Method and atomic tests

Abstract Ab initio pseudopotentials accounting for monoelectronic spin-orbit effects are derived. The spin-orbit coupling is introduced through an effective hamiltonian in a basis of L - S states. Results are presented for some states of the argon and indium atoms.

Mechanisms of phase transitions in sodium clusters: From molecular to bulk behavior

The thermodynamics of sodium clusters is investigated by means of a classical empirical potential and a simple quantal tight-binding model. Neutral and singly charged clusters of sizes ranging from 8 to 147 atoms are considered. A very particular attention is paid to the optimization and sampling problems. We determine the lowest-energy structures (global minima) with the “basin-hopping” technique, and the finite-temperature simulations are improved by using the “q-jumping” method and put together with the multiple histogram method. The clusters geometries may be very different on the model used, but also on the ionic charge, up to the size of about 40 atoms. The thermodynamical analysis is performed near the solid–liquid transition by calculating the complete calorific curves (heat capacities) as well as some microscopic parameters to probe the dynamics on the energy landscapes, including the spectra of isomers found by periodic quenching, isomerization indexes and the Lindemann parameter δ. Up to the la...

Comparison between experimentally and theoretically determined potential curves of the Ar2* lowest states

Accurate potential curves have been determined for the (3p54s)Ar*+(1S0) Ar excimer, with extended basis sets, large CI and the Cohen–Schneider spin–orbit coupling scheme. Using the synchrotron radiation, measurements of the quantitative absorption temperature dependence of the wings of the 3P1 and 1P1 lines have been made and parts of the potential curves have been derived through the quasistatic treatment. The theoretical work shows that the complex and detailed shapes of the curves result from the action of various physical phenomena (electronic correlation, van der Waals dispersion forces, R−3 resonance interaction, and spin–orbit coupling); however a sufficiently accurate calculation and analysis allows a state by state comparison with absorption and emission experimental results and an attempt to gather and clarify the present knowledge.

Theoretical study of an unusual reactive collision Cs(7p)+H2→CsH+H. Diabatic approach of the collinear collision potential energy surfaces

The Cs(7p)+(X 1∑+g, v=0) H2→(X 2∑+, v=0) CsH+H reactive collision was recently experimentally observed from a crossed beam experiment by Crepin et al. This reaction is rather unusual since it starts from a highly excited state of the system (11th potential surface) and must reach the ground state surface in the product channel without energy loss. Accurate nonempirical CI calculations of the potential energy surface for the collinear collision are reported, using large basis sets and a nonempirical relativistic pseudopotential for the Cs atom. The adiabatic potential surfaces, which exhibit irregular behavior, are reinterpreted in terms of an ab initio nearly diabatic effective Hamiltonian spanned by five neutral repulsive channels Cs(6s)×H2, Cs(6p)×H2,..., Cs(7p)×H2 and an ionic very flat Cs+H−2 channel which tends to the product wave function (Cs+H−)×H. The intersection of these diabatic potential surfaces are accessible from the entrance energy and this picture supports a harpooning mechanism, the 7p e...

Ab initio molecular calculations including spin-orbit coupling. II. Molecular test on the InH molecule and application to the g states of the Ar2* excimer

Abstract Ab initio CI relativistic calculations with non-empirical core pseudopotentials are achieved for the valence states of InH and the gerade Rydberg states of the Ar2* excimer using the quasi-degenerate perturbation theory in the Λ · Σ coupling scheme.

Theoretical study of spectroscopical properties of Na and Na2 in argon clusters and matrices

We present a calculation of the structure and the optical transitions of sodium atoms and dimers embedded in argon clusters and matrices. We studied several different systems: A single sodium atom in a dodecahedral argon cluster, a Na atom in a substitutional site of a fcc (face-centered-cubic) Ar lattice containing 63 atoms and a sodium dimer in a 9-atom vacancy of the same fcc lattice (Na2@Ar54). For optimizing the system geometry in its ground state, we use a simplified tight-binding scheme of a metal cluster dressed by the metal-matrix and matrix-matrix van der Waals interactions. A procedure closer to ab initio methodology is then applied using e-Na+ and e-Ar semi-local pseudopotentials and core-polarization operators to determine the electronic structure of the metal valence electrons in the environment of the rare-gas atoms. The electronic transitions and oscillator strengths are obtained by a full two-electron configuration interaction (CI) treatment in the case of Na2@Ar54. The A1Σu+→X1Σg+ transi...

Theoretical and experimental determination of the lowest excited states of the Kr*2 excimer

The potential energy curves of the Kr*2 excimer dissociating into Kr (4s24p6 1S0)+Kr*(4s24p55s) are determined (i) theoretically from ab initio CI calculation and semiempirical SO coupling and (ii) experimentally from the temperature dependence of absorption profiles. The results are carefully examined with the help of theoretical simulation of line profiles using semiclassical or quantal models.

Structural properties of sodium microclusters (n=4-34) using a Monte Carlo growth method

The structural and electronic properties of small sodium clusters are investigated using a distance‐dependent extension of the tight‐binding (Huckel) model and a Monte Carlo growth algorithm for the search of the lowest energy isomers. The efficiency and advantages of the Monte Carlo growth algorithm are discussed and the building scheme of sodium microclusters around constituting seeds is explained in details. The pentagonal‐based seeds (pentagonal bipyramids and icosahedral structures) are shown to play an increasing role beyond n=12. Optimized geometries of Nan clusters are obtained in the range n=4–21 and for n=34. In particular, Na20 is found to have C3 symmetry, hardly prolate with all axial ratios almost equivalent, whereas Na34 has D5h symmetry and consists of a doubly icosahedral seed of 19 atoms surrounded by a ring of 15 atoms. Stabilities, fragmentation channels, and one‐electron orbital levels are derived for the lowest isomers and shown to be characterized by a regular odd–even alternation. The present results are in generally good correspondence with previous nuclei‐based calculations when available. The global shapes of clusters, as well as the shape‐induced fine structure splitting of the spherical electronic jellium shell are found, with a few exceptions, to be also consistent with the ellipsoidal or spheroidal versions of the jellium model.The structural and electronic properties of small sodium clusters are investigated using a distance‐dependent extension of the tight‐binding (Huckel) model and a Monte Carlo growth algorithm for the search of the lowest energy isomers. The efficiency and advantages of the Monte Carlo growth algorithm are discussed and the building scheme of sodium microclusters around constituting seeds is explained in details. The pentagonal‐based seeds (pentagonal bipyramids and icosahedral structures) are shown to play an increasing role beyond n=12. Optimized geometries of Nan clusters are obtained in the range n=4–21 and for n=34. In particular, Na20 is found to have C3 symmetry, hardly prolate with all axial ratios almost equivalent, whereas Na34 has D5h symmetry and consists of a doubly icosahedral seed of 19 atoms surrounded by a ring of 15 atoms. Stabilities, fragmentation channels, and one‐electron orbital levels are derived for the lowest isomers and shown to be characterized by a regular odd–even alternation. ...

A pseudopotential hole‐particle treatment of neutral rare gas excimer systems. I. Formalism

A pseudopotential hole‐particle formalism is developed for the treatment of rare‐gas excimers and excited rare‐gas clusters. The formalism relies on the definition of a model Hamiltonian on the basis of single hole‐particle excitations (from the neutral closed shell ground state) involving localized np hole orbitals and any orthogonal molecular orbital (MO) basis set for the excited particle. Hole contributions in the Hamiltonian matrix elements are taken into account via distance‐ and orientation‐dependent transfer integrals (hole delocalization) and repulsion integrals like in diatomic in molecules treatments of rare gas ions, while the contribution of the excited particle is included through an explicit quantal treatment via one‐electron e‐Rg and averaged e‐Rg+ pseudopotentials. Core‐polarization pseudopotentials are also added to account for core‐polarization and core‐Rydberg correlation effects. Some approximated core‐Rydberg two‐electron integrals needed for adequate space and spin multiplicity of t...

Isomerisation and phase transitions in small sodium clusters

Using a distance-dependent tight-binding hamiltonian, we have studied the influence of the temperature on the geometries of small alkali clusters (Na4, Na8, and Na20). We have applied a Monte-Carlo thermodynamical method which consists in performing canonical samplings for various temperatures, these samplings being reexpressed in the microcanonical ensemble. This method provides thermodynamical values such as the entropy and the specific heat. Their behaviour shows one phase transition in the case of Na4 and Na8, and two phase transitions for Na20. As concerns Na4 and Na8, the transition occurs at ≈200 K, between a solid-like phase and a phase for which the geometry of these clusters oscillates between numerous shapes. In the case of Na20, the two observed phase transitions can be described as a melting of the surface atoms (at ≈200 K) preliminarily to the fluctuation of an inner icosahedron seed (at ≈300 K).