Model Potential Approach Research Articles

Multiphoton ionization through the triplet states of Mg by linearly and circularly polarized laser pulses

We theoretically study multiphoton ionization through the triplet states of Mg by linearly polarized and circularly polarized fs laser pulses. After the construction of the atomic basis using the frozen-core Hartree-Fock potential as well as the model potential approaches for both singlet and triplet series which show rather good agreements with the existing data in terms of state energies and dipole matrix elements, we solve time-dependent Schr\"odinger equations with $3s3p$ $^{3}P_{1}$ as an initial state, and calculate the total ionization yield and photoelectron energy spectra.

Model Potential Approaches for Describing the Interaction of Excess Electrons with Water Clusters: Incorporation of Long-Range Correlation Effects

In this work we focus on the binding of excess electrons to water clusters, a problem for which dispersion interactions, which originate from long-range correlation effects, are especially important. Two different model potential approaches, one using quantum Drude oscillators and the other using polarization potentials, are investigated for describing the long-range correlation effects between the weakly bound excess electron and the more tightly bound electrons of the monomers. We show that these two approaches are related in that the polarization potential models can be derived from the quantum Drude model approach by use of an adiabatic separation between the excess electron and the Drude oscillators. The model potential approaches are applied to clusters containing up to 45 water monomers. Where possible, comparison is made with the results of ab initio electronic structure calculations. Overall, the polarization potential approach is found to give electron binding energies in good agreement with those from the Drude model and ab initio calculations, with the greatest discrepancies being found for "cavity-bound" anion states.

Theoretical complex Stark energies of lithium by a complex scaling plus the B-spline approach

The B-spline-based coordinate rotation method plus the model potential approach is applied to investigate the complex energies of low-lying resonances of the lithium atom in an electric field. Our results are compared with two recent calculations by a state-specific complex eigenvalue Schrödinger equation (CESE) (Themelis and Nicolaides 2001 J. Phys. B: At. Mol. Opt. Phys. 34 2905) and complex absorbing potential (CAP) (Sahoo and Ho 2000 J. Phys. B: At. Mol. Opt. Phys. 33 5151) methods, which are in controversy. The positions of resonances by the present calculation are found to be in agreement with theoretical data obtained by both the CESE and CAP methods. Our investigation clarifies that the contradiction about ‘4f0’ resonant position varies with the electric field. However, for the width of resonances, our results are only consistent with those by the CESE method for all strengths of the electric field under consideration. A detailed comparison on the m = 0 state among these three calculations shows that the unusual behaviour of width of resonances in the weak-field case by the CAP method is not a ‘new’ finding but a misguiding resulting from nonconvergent results. The systematic agreement between our model potential calculation and the ab initio calculation by the CESE for lithium indicates that the present proposed method is reliable and appropriate to simplify the calculation of the alkali metal atom in external fields.

Embedding Fragment ab Initio Model Potentials in CASSCF/CASPT2 Calculations of Doped Solids: Implementation and Applications.

In this article, we present a fragment model potential approach for the description of the crystalline environment as an extension of the use of embedding ab initio model potentials (AIMPs). The biggest limitation of the embedding AIMP method is the spherical nature of its model potentials. This poses problems as soon as the method is applied to crystals containing strongly covalently bonded structures with highly nonspherical electron densities. The newly proposed method addresses this problem by keeping the full electron density as its model potential, thus allowing one to group sets of covalently bonded atoms into fragments. The implementation in the MOLCAS 7.0 quantum chemistry package of the new method, which we call the embedding fragment ab inito model potential method (embedding FAIMP), is reported here, together with results of CASSCF/CASPT2 calculations. The developed methodology is applied for two test problems: (i) the investigation of the lowest ligand field states (2)A1 and (2)B1 of the Cr(V) defect in the YVO4 crystal and (ii) the investigation of the lowest ligand field and ligand-metal charge transfer (LMCT) states at the Mn(II) substitutional impurity doped into CaCO3. Comparison with similar calculations involving AIMPs for all environmental atoms, including those from covalently bounded units, shows that the FAIMP treatment of the YVO4 units surrounding the CrO4(3-) cluster increases the excitation energy (2)B1 → (2)A1 by ca. 1000 cm(-1) at the CASSCF level of calculation. In the case of the Mn(CO3)6(10-) cluster, the FAIMP treatment of the CO3(2-) units of the environment give smaller corrections, of ca. 100 cm(-1), for the ligand-field excitation energies, which is explained by the larger ligands of this cluster. However, the correction for the energy of the lowest LMCT transition is found to be ca. 600 cm(-1) for the CASSCF and ca. 1300 cm(-1) for the CASPT2 calculation.

Two-, three-, and four-photon ionization of Mg in the circularly and linearly polarized laser fields: Comparative study using the Hartree–Fock and model potentials

We theoretically study multiphoton ionization of Mg in the circularly polarized (CP) as well as the linearly polarized (LP) laser fields. Specifically two-, three-, and four-photon ionization cross sections from the ground and first excited states are calculated as a function of photon energy. Calculations are performed using the frozen-core Hartree–Fock (FCHF) and also the model potential (MP) approaches and the results are compared. We find that the MP approach provides results as good as or even slightly better than those by the FCHF. We also report the relative ratios of the ionization cross sections by the CP and LP laser fields as a function of photon energy, which exhibit clear effects of electron correlations.

Local field corrections in the lattice dynamics of chromium

s – d hybridizing effects constitute the major part of local field effects in transition metals. Therefore local field corrections to phonon frequencies in transition metals are taken to be mainly as a result of these hybridizing effects. This work extends the inclusion of local field corrections in the calculation of the phonon dispersion curves to the transition metal, chromium (Cr3+) using the formalism of lattice dynamics based on the transition metal model potential approach in the adiabatic and hatmonic approximations. The results obtained here have a good fit with experimental values. Nigerian Journal of Physics Vol. 16(2) 2004: 86-96

Single- and two-photon ionization of Sr

Using the R-matrix Floquet approach we have calculated single- and two-photon ionization cross sections for Sr within a model potential approach. The frequency ranges investigated range from 0.21 to 0.27 au and from 0.105 to 0.158 au. The results are in reasonable agreement with previous experimental and theoretical work. The two-photon cross sections are dominated by the 5s6p 1Po resonance. For the m = 0 level of this resonance, we obtain photoionization cross sections ranging typically between 5 and 20 Mb. A comparison with results for Ca shows good similarity for single-photon ionization, but significantly less agreement for two-photon ionization.

Scattering of low- to intermediate-energy positrons from molecular hydrogen

Using a complex model potential, we have calculated the total, integrated elastic, momentum transfer, absorption, and differential cross sections for positrons scattered from molecular hydrogen. The widely available software package GAUSSIAN is used to generate the radial electronic charge density of the molecule which is used to produce the interaction potentials. The quasifree absorption potential, previously developed and used for positron-atom scattering, is extended to positron scattering from molecular targets. It is shown that this model potential approach produces accurate results even into the low-energy regime.

Spin–orbit effects on the electronic spectroscopy of transition metal dihydrides H2M(CO)4 (M=Fe, Os)

The influence of spin–orbit (SO) effects on the transition energies to the low-lying singlet and triplet electronic states of H2M(CO)4 (M = Fe, Os) are calculated by means of a two-step procedure in which CASSCF/MS-CASPT2 method using relativistic effective core potentials in the ab initio model potential (AIMP) approach was used to obtain the spin-free vertical transitions in a first step. Spin–orbit effects are taken into account in the second step by building a determinantal model space which includes a set of reference configurations able to represent all the desired states along with singly excited configurations selected with respect to the SO operator within the atomic mean-field approximation. The results of the first step calculation are exploited in order to include correlation effects via an effective Hamiltonian technique and diagonalize the full matrix on the determinantal basis. It is shown that while the SO has little influence on the absorption spectrum of H2Fe(CO)4 it does affect significantly the electronic spectroscopy of the third row transition metal complex H2Os(CO)4 leading to a large mixing between the low-lying states and to a splitting exceeding 3000 cm−1 for the lowest 3B2 state.

Application of spectral intensities through a model potential approach to the prediction of photodissociation rate constants of CFC molecules in the ionosphere

AbstractAbsorption of high‐frequency radiation by chlorofluorocarbon (CFC) compounds in the ionosphere leads to their photoionization and photodissociation. Rydberg states are known to play an essential role in the initiation of photochemical processes. The photoabsorption intensities in both bound and continuous spectral regions, through all the allowed Rydberg channels, of two Freon molecules, have been first calculated. Then, through the use of the intensity data, photolysis rate constants corresponding to dissociation pathways in zones E and D of the ionosphere have been determined. An extension of the molecular quantum defect orbital approach has been used to supply these rate constants for the first time. Neither previous measurements nor theoretical calculations on these properties have, to our knowledge, been reported. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Model-potential calculations for ground and excitedΣ statesof Rb2+, Cs2+ and RbCs+ ions

A model-potential approach successfully employed in the past for describingpotential curves of light alkali dimers is extended to calculate potential curves ofΣ symmetry for theheavy molecular ions Rb2+, Cs2+ and RbCs+. The results are in agreement with those calculated using a pseudopotential method, except for theCs++Cs(5d) dissociation limit. The limits of the present model-potential calculations and the ways ofimproving them are carefully analysed.

The electronic spectroscopy of transition metal di-hydrides H2M(CO)4(M = Fe,Os): a theoretical study based on CASSCF/MS-CASPT2 and TD-DFT

Transition energies to the low-lying singlet electronic excited states of H2M(CO)4 (M = Fe,Os) are calculated at the CASSCF/MS-CASPT2 level of theory using relativistic effective core potentials in the ab initio model potential (AIMP) approach. The main features of the absorption spectra of both molecules differ significantly. The spectrum of H2Fe(CO)4 is dominated by low-lying excited states corresponding mainly to 3dFe → σ*u and 3dFe → σ*g excitations calculated between 39 310 cm−1 (4.9 eV) and 43 210 cm−1 (5.4 eV). These allowed transitions contribute to the shoulder observed in the experimental spectrum around 270 nm (37 040 cm−1) and are responsible for the photoreactivity of H2Fe(CO)4 at 254 nm (39 370 cm−1). In contrast the lowest part of the absorption spectrum of the osmium analog H2Os(CO)4 is characterized by a high density of metal–ligand-charge-transfer (MLCT) states between 47 220 cm−1 (5.9 eV) and 52 430 cm−1 (6.55 eV) and corresponding to 5dOs → π*CO excitations. The transitions corresponding to 5dOs → σ*u and 5dOs → σ*g excitations are displaced to the upper part of the absorption spectrum of H2Os(CO)4 (beyond 60 000 cm−1 or 166 nm) and cannot induce H2 elimination under irradiation at 254 nm like in the iron complex. A series of sigma-bond–ligand-charge-transfer (SBLCT) states corresponding to σg → π*CO and σu → π*CO excitations not present in H2Fe(CO)4 is found exclusively in the spectrum of H2Os(CO)4 beyond 55 000 cm−1. The upper part of the spectrum of H2Fe(CO)4 (below 220 nm) is assigned to intense MLCT transitions corresponding to 3dFe → π*CO excitations. The MS-CASPT2 and TD-DFT methods agree qualitatively as far as the assignment and transition energies of the low-lying states are concerned in both molecules whereas a comparison of the calculated oscillator strengths is more problematic. The transitions are generally underestimated at the TD-DFT level, an effect that is even more pronounced for the charge transfer excitations to the carbonyl ligands. The high density of singlet electronic states in these simple transition metal hydrides carbonyls illustrates the complexity of the electronic spectroscopy in this class of molecules. This explains the poor resolution of these overcrowded spectra and the difficulty in understanding the photoreactivity of these molecules.

A Model Potential Approach to Charge Resonance Phenomena in Aromatic Cluster Ions

This work proposes a simple yet accurate methodology to account for charge resonance in ionic clusters. The supersystem's model Hamiltonian is described via a basis set of valence bond structures for which the charge is localized on a given monomer, and whose intermolecular binding energies are computed using a polarizable model potential. The coupling elements between these structures are proportional to an overlap integral between relevant nonorthogonal monomer molecular orbitals. Ab initio calculations are employed to calibrate and validate the model, but also to define its limits. The methodology is then applied to the global exploration of potential energy surfaces for small homocluster ions of benzene, naphthalene, and anthracene. The structural and electronic properties of these systems are discussed, with emphasis on important trends such as the polarization vs charge-transfer competition or the difference between adiabatic and vertical ionization potentials. Extensions to stacked cluster ions of ...

Application of a Drude model to the binding of excess electrons to water clusters

A one-electron model potential approach for calculating the binding energies of an excess electron interacting with water clusters is presented. Drude oscillators are employed on the water monomers to describe electron–water polarization and dispersion interactions. It is demonstrated that the resulting model gives electron binding energies very close to the predictions of ab initio CCSD(T) calculations. Dispersion interactions and high-order renormalization effects are found to make large contributions to the electron binding energies.

Annihilation rate in positronic systems by quantum Monte Carlo: e+LiH as test case

An accurate method to compute the annihilation rate in positronic systems by means of quantum Monte Carlo simulations is tested and compared with previously proposed methods using simple model systems. This method can be applied within all the quantum Monte Carlo techniques, just requiring the accumulation of the positron–electron distribution function. The annihilation rate of e+LiH as a function of the internuclear distance is studied using a model potential approach to eliminate the core electrons of Li, and explicitly correlated wave functions to deal with all the remaining particles. These results allow us to compute vibrationally averaged annihilation rates, and to understand the effect of the Li+ electric field on positron and electron distributions.

Model Potential Approach to Core Polarisation in SCF Calculations

The paper discusses the applicability of simple model potentials used to describe the valence-core electron correlation (core polarisation in a semiclassical picture) within fully relativistic self-consistent-field Dirac-Fock calculations. The influence of core polarisation on oscillator strengths is demonstrated for medium and heavy systems with one and two valence electrons and is compared with other correlation effects (e.g. intravalence correlation), where applicable. Different forms of core polarisation potential and induced transition dipole moment are presented and discussed, together with limitations of the core polarisation picture. Though the emphasis is on the use of core polarisation potentials within SCF calculations, these potentials are also widely employed within a valence electron effective model potential approach. Some recent results obtained with different effective model potentials for Ag and Au isoelectronic sequences are presented and compared with SCF calculations. Finally, our earlier results obtained with the core polarisation picture are compared with the most recent unpublished results where the valence-core electron correlation (core polarisation) is explicitly represented in the configuration interaction (CI) scheme and spin-orbitals are generated by employing an ab initio model potential technique with noninteger outermost core shell occupation number, intended to improve the efficiency of the CI representation of the valence-core correlation.

Crash-Conformational Kinematics of the Covalent Lattice of Diamond on Melting

Using the model potential approach we have obtained a generalized potential of interatomic interactions for two condensed states providing an abrupt change in thermodynamic functions at a point of a solid to liquid transition. A kinematic model is considered for the transition of the diamond lattice with pure covalent bonds to the melted state. The model is based on the concept of crash destruction of the lattice during the conformational transformation of the initial symmetry of the chosen atomic group. The kinetic energy of the thermal motions of atoms does not exceed the potential energy of lattice atomization. The kinematic patterns of the positions of 150 atoms at T ≲ Tm and T ≳ Tm are given for the two-dimensional hexagonal net.

A model-potential approach for bismuth (I). Densification and melting curve calculation

In spite of the intricacy of its phase diagram, a pertinent investigation of bismuth at high pressure is possible with the help of a model-potential, if perturbation expansion is extended up to third order, as evidenced by the calculations presented here (phonon spectrum of phase I, prediction of volume collapse in the vicinity of 25 kbar, structure factor of liquid Bi, melting curve, etc.).

A model-potential approach for bismuth: II. behaviour under shock loading

Using a model-potential introduced in a previous paper, properties of bismuth under shock loading at high pressure are studied here theoretically. In addition to the usual hydrodynamic behaviour for compact and porous material, our investigation extends to dynamical temperature determination, a quite intricate but rewarding topic.

Collapse versus growth for a Bose-Einstein condensate with attractive interactions

Using a model potential approach, we study the time-dependent behavior of a Bose-Einstein condensate with negative scattering length during its collapse in the zero-temperature limit. The condensate is modeled through an effective potential, which linearizes the Schr\"odinger equation, in order to obtain an intuitive visualization of the dynamics of the condensate. We find that a substantial fraction of the condensate survives the collapse. The origin for this survival is the reappearance of a barrier in the effective potential during the collapse. In contrast to previous calculations, the present calculations indicate that the size of the residual condensate strongly depends on the growth rate of the condensate. The present results are compared to other theoretical calculations and to experimental work.