Model Potential Method Research Articles

Third-order Douglas–Kroll ab initio model potential for actinide elements

A relativistic ab initio model potential (AIMP) method with the third-order Douglas–Kroll (DK3) approximation has been developed for the whole series of the actinide elements from Th to Lr. Two different cores, i.e., [Xe, 4f,5d] and [Xe, 4f], have been employed and the corresponding valence basis sets, (14s10p11d9f)/[6s5p5d4f] and (14s10p12d9f)/[6s5p6d4f], are presented for all actinides. The mean absolute errors of the AIMP relative to the all-electron results for the atomic SCF valence orbital energies (ε) and the radial expectation values (〈r〉) are 0.003 (0.001) hartree and 0.004 (0.006) bohr with the small (large) core set. The spectroscopic properties of the Σ+1 ground state of thorium monoxide, ThO, are calculated at the SCF and complete active space SCF levels. The DK3-AIMP results again satisfactorily reproduce the all-electron DK3 results. The large core set gives almost the same results as the small set for atomic and molecular calculations, suggesting that the 5d electrons can safely be omitted from the valence electrons in actinide chemistry.

Model Potential Calculations for Various Electronic Excited States of Li- and Na-

Energies and wave functions for the ground state and several excited electronic states are reported for Li- and Na- negative ions. Calculations have been achieved in the framework of a model potential method using s, p, d, and f atomic Slater-type basis orbitals. The electronic correlation has been considered through configuration interaction calculations. Present results are compared with available experimental and theoretical data.

The ab initio model potential method with the spin-free relativistic scheme by eliminating small components Hamiltonian

A relativistic ab initio model potential (AIMP) for Pt, Au, and Hg atoms has been developed using a relativistic scheme by eliminating small components (RESC) in which the 5p, 5d, and 6s electrons are treated explicitly. The quality of new RESC–AIMP has been tested by calculating the spectroscopic properties of the hydrides of these elements using the Hartree–Fock and coupled cluster with singles and doubles (CCSD) methods. The agreement with reference all-electron RESC calculations is excellent. The RESC–AIMP method is applied successfully in the investigation of the spectroscopic constants of Au2 and Hg2 using the CCSD method with a perturbative estimate of the contributions of triples. The ground state of Pt2 is also determined by RESC–AIMP with the second-order complete active space perturbation method. The results show that scalar relativistic effects on the valence properties are well described by the RESC–AIMP method. The effect on the basis set superposition error on the spectroscopic constants is also examined.

Model Potential Calculations for the Ground and Various Excited States of LiNa+

A theoretical investigation of the electronic structure of the molecular ion LiNa+ (adiabatic potential energy curves, rovibrational energies, spectroscopic constants and dipole moments) has been performed in the framework of a model potential method. Such information, not yet available to the best of our knowledge except for the ground state, constitutes the input data for simulations of above threshold dissociation of LiNa+. Although most of the energy curves are found to be dissociative, some present potential wells located at intermediate internuclear distances. A long-range extrapolation is proposed for the lowest states.

Many-body and model-potential calculations of low-energy photoionization parameters for francium

The photoionization cross section $\sigma$, spin-polarization parameters $P$ and $Q$, and the angular-distribution asymmetry parameter $\beta$ are calculated for the $7s$ state of francium for photon energies below 10 eV. Two distinct calculations are presented, one based on many-body perturbation theory and another based on the model potential method. Although predictions of the two calculations are similar, the detailed energy dependence of the photoionization parameters from the two calculations differ. From the theoretical p-wave phase shifts, we infer quantum defects for $p_{1/2}$ and $p_{3/2}$ Rydberg series, permitting us to calculate positions of experimentally unknown $p$ states in francium.

Structure and spectroscopy of Cr3+ defects in KMgF3, KZnF3, and CsCaF3 crystals. An ab initio model potential embedded cluster study

The ab initio model potential (AIMP) method has been proven to produce effective one-electron operators that accurately represent the embedding effects of the cations and anions that consititute crystalline lattices like the KMgF3, KZnF3, and CsCaF3 cubic fluoroperovskites. The combination of these quantum mechanical embedding potentials with highly sophisticated molecular quantum chemical calculations of the CrF\documentclass{article}\pagestyle{empty}\begin{document}$^{3-}_{6}$\end{document} defect cluster enables theoretical study of the structure and spectroscopy of promising laser materials like the Cr3+-doped KMgF3, KZnF3, and CsCaF3 crystals at the level of quality attainable in molecular quantum chemistry. The combination of the theoretical results with available experimental data [electron paramagnetic resonance (EPR), electron spin resonance (ESR), absorption, and emission spectra at ambient and high pressures] can contribute to clarifying the electronic structure of these systems, where different interpretations of the very sophisticated spectroscopic data exist, mainly due to the difficulty associated with the existence of cubic, trigonal, and tetragonal Cr3+ defects contributing to the spectra. The results of AIMP embedded-cluster studies of the cubic defects are presented here as one more useful and independent source of information that serves to clarify the divergent assignments and to provide new spectroscopic information, which shows that the laser emission of Cr3+ defects in all three crystals should be free from excited state absorption losses if the pumping process is done through selective excitation to the 4T2g laser level, below the 2Eg higher excited state. Since the Cr3+ substitutional impurities create an excess positive charge, the effects of lattice site relaxation and dipole polarization on the local structure have been investigated and are presented here. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 961–972, 2000

Ground and excited states of PtCH2+: assessment of the no-pair Douglas–Kroll ab initio model potential method

Relativistic all-electron and ab initio model potential (AIMP) calculations have been performed on the PtCH2+ ground and low-lying excited states employing a one-component Hamiltonian. Electron correlation is taken into account by means of a multireference configuration interaction treatment whereas spin–orbit coupling effects have been added as a perturbation. The no-pair Douglas–Kroll ab initio model potential method is found to reproduce all-electron results excellently. The one-center spin–orbit mean-field Douglas–Kroll ab initio model potential approach appears to be a competitive means for electronic structure calculations on compounds containing heavy elements. An analysis of the PtCH2+ electronic ground state structure reveals that both the Pt+ configurations d9 and d8s1 participate in the double bond. This finding differs to some extent from a model postulating that a d8s1 structure is preferred.

Higher-order Stark effect on an excited helium atom

Degenerate perturbation theory is used to study dipole susceptibilities of an excited helium atom in an external electric field. The dependence of the perturbed energy of levels in atoms on fine-structure effects and on the higher-order Stark effect is investigated. Numerical results have been obtained for the (1s3p) P0 and (1s3p) P2 states of helium. The magnitude of the electric field and the energy separation at the 0 30 anticrossing are calculated. Calculations of polarizabilities and hyperpolarizabilities are carried out using sums of oscillator strengths and, alternatively, with the excited electron Green function. An estimate is given based on the model potential method for the contribution of an infinite series over the bound states, including the integral over the continuum, for secondand higher-order matrix elements. The relativistic approach for evaluating reduced dipole matrix elements based on the relativistic no-pair Hamiltonian and including both the Coulomb and Breit interactions ~configuration-interaction method! is analyzed. @S1050-2947~99!06108-9#

Potential energy curves of 58 states of Li 2+

Adiabatic potential curves for all electronic states correlated to Li ++Li[2s] up to Li ++Li[6g] have been computed in the framework of a model potential method, over a rather large range of internuclear distances (4 a.u.< R<40 a.u.). A good agreement has been obtained with previous theoretical determinations as well as with available experimental results for the ground and the first excited states. Long-range-type predictions for the lowest states have been considered.

Photoionization suppression by continuum coherence: Experiment and theory

We present experimental and theoretical results of a detailed study of laser-induced continuum structures (LICS) in the photoionization continuum of helium out of the metastable state 2s $^1S_0$. The continuum dressing with a 1064 nm laser, couples the same region of the continuum to the {4s $^1S_0$} state. The experimental data, presented for a range of intensities, show pronounced ionization suppression (by as much as 70% with respect to the far-from-resonance value) as well as enhancement, in a Beutler-Fano resonance profile. This ionization suppression is a clear indication of population trapping mediated by coupling to a contiuum. We present experimental results demonstrating the effect of pulse delay upon the LICS, and for the behavior of LICS for both weak and strong probe pulses. Simulations based upon numerical solution of the Schr\"{o}dinger equation model the experimental results. The atomic parameters (Rabi frequencies and Stark shifts) are calculated using a simple model-potential method for the computation of the needed wavefunctions. The simulations of the LICS profiles are in excellent agreement with experiment. We also present an analytic formulation of pulsed LICS. We show that in the case of a probe pulse shorter than the dressing one the LICS profile is the convolution of the power spectra of the probe pulse with the usual Fano profile of stationary LICS. We discuss some consequences of deviation from steady-state theory.

Oscillator Strengths for Bound States of Beryllium Isoelectronic Sequence

A model-potential method using selecting B-spline basis functions in a configuration-interaction (CI) scheme is applied to study the bound states of the beryllium isoelectronic sequence (Z = 5–7). The energies and wave functions of the bound 1s22snl (l ≤ 2), and 1s22pnl L (L ≤ 2, L ≠ l) states are calculated and used to calculate the oscillator strengths. Our length results of the oscillator strengths for electric dipole transitions are accurate and can be achieved efficiently for various states.

The energies and oscillator strengths of bound states of Be

The energies and wavefunctions of the , and states of beryllium are calculated with a model-potential method by using selected B-spline basis functions in a configuration-interaction (CI) scheme. Our length results of the oscillator strengths for electric dipole transitions and the energies, which are set to be zero at the ground state of Be III, are compared with the experimental and other theoretical results. The agreement showed that our method is capable of giving accurate results for various states of beryllium efficiently.

Ab initio spin-free-state-shifted spin-orbit configuration interaction calculations on singly ionized iridium

This work presents a systematic test of the performance of a spin-orbit operator founded upon the Wood-Boring-based ab initio model potential method [J. Chem. Phys. 102, 8078 (1995)]. Assuming a separability of the problem into a spin-free correlation treatment and a spin-orbit calculation part, this aim can be reached. We shall show in this publication both the separability and the high level of quality of the spin-orbit operator applying our method to the even spectrum of Ir+. We shall treat the spin-orbit part by means of the above mentioned spin-orbit operator and cope with the spin-free correlation problem through introducing a spin-free-state-shifting operator, shifting the spin-free energies to empirical values obtained from experiment. The quality of the spin-orbit operator is very high, actually better than estimated in previous calculations which were contaminated by an insufficient treatment of correlation. The procedure established is most efficient: Spin-free-state-shifted spin-orbit CI calculations employing a space of the significant reference configurations plus single excitations lead to very reliable spin-orbit splittings provided that the spin-free states are calculated at a high level of quality.

The ab initio model potential method. Relativistic Wood-Boring valence spin-orbit potentials and spin-orbit-corrected basis sets from B( Z = 5) to Ba( Z = 56)

The spin-orbit-CI WB-AIMP method[Chem. Phys. Lett., 147 (1988) 597; J. Chem. Phys., 102 (1995) 8078] has been recently proposed, monitored and applied, as a means to include spin-orbit relativistic effects in molecular and solid state effective core potential calculations. Necessary ingredients of the method are the valence spin-orbit model potentials and the spin-orbit-corrected valence basis sets, which are available in the literature for FI, TlRn, Ni and Pt; in this work, we obtain and compile the ones of all the remaining elements of the Periodic Table from boron to barium.

Model potentials for main group elements Li through Rn

Model potential (MP) parameters and valence basis sets were systematically determined for the main group elements Li through Rn. For alkali and alkaline-earth metal atoms, the outermost core (n−1)p electrons were treated explicitly together with the ns valence electrons. For the remaining atoms, only the valence ns and np electrons were treated explicitly. The major relativistic effects at the level of Cowan and Griffin’s quasi-relativistic Hartree–Fock method (QRHF) were incorporated in the MPs for all atoms heavier than Kr. The valence orbitals thus obtained have inner nodal structure. The reliability of the MP method was tested in calculations for X−, X, and X+ (X=Br, I, and At) at the SCF level and the results were compared with the corresponding values given by the numerical HF (or QRHF) calculations. Calculations that include electron correlation were done for X−, X, and X+ (X=Cl and Br) at the SDCI level and for As2 at the CASSCF and MRSDCI levels. These results were compared with those of all-electron (AE) calculations using the well-tempered basis sets. Close agreement between the MP and AE results was obtained at all levels of the treatment.

Model potential calculations for the excited and Rydberg states of the Na2+ molecular ion: Potential curves, dipole and quadrupole transition moments

Molecular potential curves for many excited states of the Na2 molecule are presently available for a wide range of internuclear distances, in the framework of a two-electron model potential method. The energies were obtained through an extensive configuration interaction procedure using Na+ 2 orbitals, and the quality of the results was controlled by the accuracy of the wavefunctions of the molecular ion. In this work, computed potential energy curves and transition moments are presented for the ground, excited and Rydberg Σ, Π and Δ states of Na+ 2 up to the Na(7i) + Na+ dissociation limit. The accuracy of the first excited states is checked by comparing with available experimental data. Figures are presented for the molecular quantum defects as a function of internuclear distance, showing an interesting pattern of pseudo-crossings.

The ab initio model potential method and the optimized orbitals for the multiconfiguration self-consistent field-configuration interaction approach

The ab initio model potential method and the optimized orbitals for the multiconfiguration self-consistent field-configuration interaction approach

Energies of neon-like n = 4 to n = 2 resonance lines

A multi-configuration Dirac-Fock method is used to calculate the energies of the n = 4 → n = 2 resonance lines for neon-like ions with nuclear charge Z from 18 to 92. These results are compared with calculations done by the Z-expansion method and the model potential method. High resolution measurements done at the EBIT facility are presented for several high-Z ions and provide an important benchmark against which the various code results are compared.

Investigation of short-range order in magnesium-terbium alloy

Using the model potential method with Ashcroft form factors, we predict the existence of short-range order in the alloy Mg−2.9 at. % Tb, which is experimentally confirmed by diffuse x-ray scattering. We use the diffuse x-ray scattering method to determine the characteristic temperature of the alloy: θ D = 325 K.

The quartet levels of lithium

We studied the 1s2s nl and quartet states of the lithium atom by a model-potential method with B-spline basis functions in the CI scheme. The transition wavelengths and probabilities, and lifetimes for electric dipole decay are calculated and compared with experimental and other theoretical results. A large number of transitions, which can possibly be observed, are presented. Our calculated transition wavelengths and lifetimes are in good agreement with the available experimental results. Including relativistic, radiative, and mass-polarization corrections for 1s2p and 1s2s cores, we calculated for - transitions. Some of these agreed with experimental results within 1 Å. The lifetime of [1s2p3s] is calculated to be 9.89 ns, which is the best agreement with the experimental result, ns, among the present theoretical results. The lifetime of [1s2s3s] is also improved.