Atomic spin-orbit pseudopotential definition and its relation to the different relativistic approximations

A critical analysis of usual shape-consistent spin-orbit pseudopotential extraction procedures is presented, considering the basic requirements of the atomic pseudopotentials. It is based on a perturbative analysis of both reference all-electron Dirac-Coulomb and pseudopotential calculations by means of the formalism developed by Lindgren and Morrisson. In the light of this analysis, we propose a new hybrid extraction of spin-orbit pseudopotentials, taking advantage of both shape-consistent and energy-consistent procedures. These new pseudopotentials are extracted and checked for the (2)P ground state of the halogens.     

Electron-density-dependent fused-sphere surfaces derived from pseudopotential calculations

Fused-sphere surfaces can be used to mimic a molecular boundary associated with a constant value of the electron density. The simplest of such fused-sphere models are constructed by using the atomic radii for the spherical isodensity surfaces of individual atoms. In this work, we discuss the extension of this model to molecules containing atoms beyond the second row. In these many- electron systems, the computation of electron densities is usually simplified by adopting a pseudopotential (or effective-core potential) approach. Here, we discuss the performance of large- and small-core pseudo-potential calculations as a tool to derive atomic radii. Our results provide an optimum set of variable radii that can be used to build fused-sphere surfaces. This continuum of surfaces provides a simple approximation to the low-electron-density regions around molecules with heavy atoms.     

Real space pseudopotential calculations for copper clusters

Neutral and anion clusters of copper, Cu(n) (n=3-11), are examined using real space pseudopotentials constructed within the local spin density approximation. We predict the ground state structure for each cluster, the binding energy, and the corresponding photoelectron spectra, which we compare to experiment. We find strong final state effects in the photoelectron spectra, especially for the smaller clusters. The binding energy as a function of cluster size tracks well with the measured values, although the magnitude of the binding energy exceeds the experimental values by approximately 20%, as expected for the local spin density approximation.     

Note on the generation of Gaussian bases for pseudopotential calculations

We present a technique to generate Cartesian Gaussian bases for electronic configuration and cross-section calculations on molecules. The technique is specially useful for pseudopotential work, when the bases cannot be tabulated because they depend on the specific choice of the pseudopotential. © 1996 John Wiley & Sons, Inc.     

Gombás pseudopotential SCF calculations for atoms

The Simplified SCF Method of Gombás, in which the orbital orthogonality conditions are replaced by statistical pseudopotentials, has been tested for the first time by accurate numerical calculations without any further approximation. Whereas the original version of the method leads to characteristic error trends, a correction factor recently introduced by Gombás into the pseudopotential expression, produces surprisingly good results.

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Zusammenfassung Das sog. Vereinfachte SCF-Verfahren von Gombás, bei welchem die Orthogonalitätsbedingungen der Orbitale durch statistische Pseudopotentiale ersetzt werden, wird erstmalig durch saubere numerische Rechnungen getestet. Während die unkorrigierte Version der Methode Resultate mit charakteristischen Fehlern liefert, führt der kürzlich von Gombás abgeleitete Korrekturfaktor im Besetzungsverbotpotential zu überraschend guten Ergebnissen.

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Résumé La «méthode SCF simplifiée» de Gombás, où les conditions d'orthogonalité des orbitales sont remplacées par des pseudo potentiels statistiques, a été pour la première fois éprouvée avec des calculs numériques précis sans aucune autre approximation. Alors que la version originale de la méthode conduit à des tendances d'erreurs caractéristiques, un facteur de correction récemment introduit par Gombás dans l'expression du pseudo-potential, produit des résultats remarquablement bons.

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Dedicated to the memory of Professor Paul Gombás.

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This work has been stimulated by discussions with Prof.P. Gombás. Computer time on the IBM 7090 of the GMD at Bonn is gratefully acknowledged.     

Parallel processing forab initio total energy pseudopotential calculations

Summary The total energy pseudopotential method is well suited to parallel processing. This paper discusses a procedure for calculating the valence electronic wavefunction in a given ionic configuration, and considers the exploitation of parallel processing using a data parallel approach. The implementation of this procedure on two message passing i860 based machines, containing up to 64 nodes, is described, and the prospects for massively parallel execution are examined.     

Spectroscopic and spin-orbit calculations on the SO+ radical cation

Highly correlated ab initio methods were used in order to generate the potential-energy curves of the SO+ electronic states correlating to S+(4Su)+O(3Pg) and S+(2Du)+O(3Pg). These curves were used for deducing accurate spectroscopic properties for these electronic states. Our calculations predict the existence of a 2Phi state lying close in energy to the well-characterized b 4Sigma- state and several weakly bound quartet and doublet states located in the 6-9 eV internal energy range not identified yet. The spin-orbit integrals between these electronic states were evaluated using these highly correlated wave functions, allowing the discussion of the metastability and the predissociation processes forming S+ +O in their electronic ground states. Multistep spin-orbit-induced predissociation pathways are suggested. More specifically, the experimentally determined dissociative potential-energy curve [H. Bissantz et al., Z. Phys. D 22, 727 (1992)] proposed to explain the rapid SO+(b 4Sigma-, v> or =13)-->S+(4Su)+O(3Pg) reaction is found to coincide with the 2 4Pi potential-energy curve for short internuclear distances and with the repulsive 1 6Pi state for longer internuclear separations.     

Spectroscopic data for the LiH molecule from pseudopotential quantum Monte Carlo calculations

Quantum Monte Carlo and quantum chemistry techniques are used to investigate pseudopotential models of the lithium hydride (LiH) molecule. Interatomic potentials are calculated and tested by comparing with the experimental spectroscopic constants and well depth. Two recently developed pseudopotentials are tested, and the effects of introducing a Li core polarization potential are investigated. The calculations are sufficiently accurate to isolate the errors from the pseudopotentials and core polarization potential. Core-valence correlation and core relaxation are found to be important in determining the interatomic potential.     

Ab initio spin-orbit calculations on the lowest states of the nickel dimer

Potential energy curves of the lowest electronic states of the Ni(2) dimer are calculated near the equilibrium using the multireference ab initio methods including the spin-orbit interaction. Scalar-relativistic results fully confirm previous qualitative interpretations based on the correlation with atomic limits and the symmetry of vacancies in the atomic 3d(9) shells. Spin-orbit calculations firmly establish the symmetry of the ground state as 0(+)(g) and give the excitation energies 70 ± 30 cm(-1) and 200 ± 80 cm(-1) for the lowest 0(-)(u) and 5(u) states, respectively. The model electronic spectrum of the Ni(2) shows some trends that might be observed in matrix isolation far-infrared and electron spin resonance spectra.     

Modified carbon pseudopotential for use in ONIOM calculations of alkyl-substituted metallocenes

Nonrelativistic carbon 1s core pseudopotentials are optimized for substituted cyclopentadienide ring carbons for use in integrated molecular orbital molecular orbital (IMOMO) and integrated molecular orbital molecular mechanics (IMOMM) calculations where the Cp ring substituents are not included in the high-level IMOMO or IMOMM subsystem. Use of the optimized pseudopotential within the IMOMO framework leads to significant improvements in predicted carbonyl stretching frequencies for a series of Cp-ring-methylated zirconocenes compared to using a standard carbon pseudopotential. The technology is less successful in the IMOMM implementation.     

Full spin-orbit configuration interaction calculations on electronic states of LiBe

Ab initio calculations are reported for the simplest heteronuclear metal cluster, LiBe. Full spin-orbit configuration interaction calculations in the context of relativistic effective core potentials lead to accurate potential energy curves for low-lying states. Results are compared with recent experimental observations and with all electron multi-reference configuration interaction calculations.     

Ab initio calculations of spin-orbit coupling in the SnH+4 ion

Ab initio configuration interaction calculations (CI) have been performed in order to evaluate the spin-orbit coupling associated with the Jahn-Teller distortion of the SnH⁺₄ ion. Optimizing all geometric parameters at the CI (MP2) level leads to two stable forms, C_3v and C_2v. Spin-orbit coupling, which is 0.29 eV for the tetrahedral form of SnH⁺₄, decreases sharply with distortion by vibronic interaction and becomes very low in stable forms.     

Daubechies wavelets as a basis set for density functional pseudopotential calculations

Daubechies wavelets are a powerful systematic basis set for electronic structure calculations because they are orthogonal and localized both in real and Fourier space. We describe in detail how this basis set can be used to obtain a highly efficient and accurate method for density functional electronic structure calculations. An implementation of this method is available in the ABINIT free software package. This code shows high systematic convergence properties, very good performances, and an excellent efficiency for parallel calculations.     

Ab initio and pseudopotential calculations on the singlet and triplet states of the disilyne isomers

Ab initio SCF as well as pseudopotential calculations were performed for determining equilibrium structures and relative stabilities of several disilyne isomers. For the singlet state there are only two structures, the bridged and the silavinylidene carbene, which correspond to minima on the energy hypersurface. The most stable of the six isomeric structures investigated is the bridged conformer in the ¹A₁ electronic state, followed by the silavinylidene carbene in the ¹A₁ and ³A₂ electronic states. Inclusion of electron correlation by MRD-CI calculations has no qualitative influence on the relative stabilities found in the SCF calculations.     

On the existence of SH3, SeH3, and TeH3: Discrepancies between all-electron and pseudopotential calculations

Ab initio calculations using both pseudopotential and double and triple-ζ all-electron basis sets, with and without electron correlation (MP2, QCISD), have been performed on the λ⁴-sulfanyl (SH₃), λ⁴-selanyl (SeH₃), and λ⁴-tellanyl (TeH₃) radicals. All-electron basis sets of double-ζ quality predict that SH₃ and SeH₃ correspond to transition states on their respective potential energy surfaces. In contrast, the pseudopotentials of Hay and Wadt predict that SH₃ and SeH₃ correspond to local minima at the QCISD level of theory while the pseudopotentials of Christiansen and Stevens predict transition states. By comparison, TeH₃ proved to be a local minimum at all levels of theory. Interestingly, when a very large (triple-ζ) all-electron basis set was used, SH₃ proved to be a transition state; however, in this instance the potential energy surface was found to be much flatter than in the case for which a double-ζ basis set was used, suggesting that further improvements in the basis set may lead to a local minimum. Further improvements in the all-electron selenium basis also led to a local minimum for SeH₃ at the QCISD level of theory. © 1995 by John Wiley & Sons, Inc.     

A combination of quasirelativistic pseudopotential and ligand field calculations for lanthanoid compounds

Summary Improved energy-adjusted quasirelativistic pseudopotentials for lanthanoid atoms with fixed valency are presented and tested in molecular calculations for CeO, CeF, EuO, GdO, YbO, and YbF. The pseudopotential calculations treat the lanthanoid 4f shell as part of the core and yield accurate estimates for average bond lengths, vibrational frequencies and dissociation energies of all states belonging to a superconfiguration. Information for each individual state of the considered superconfiguration may be obtained from subsequent ligand field model calculations. The results of this combined pseudo-potential and ligand field approach (PPLFT) are compared to more accurate calculations with ab initio pseudopotentials that include the lanthanoid 4f orbitals explicitly in the valence shell and to available experimental data.     

Semi-empirical molecular orbital calculations the electronic structure and the spin-orbit coupling in azabenzenes

Electronic structures of pyridine, pyrazine, pyrimidine and pyridazine are studied by a semiempirical SCF method for valence electron systems previously proposed by the present authors. The charge distributions, transition energies and oscillator strengths of these compounds are calculated. The calculated results show fairly good agreement with the observed ones. Using these results, we have further calculated the oscillator strengths of singlet-triplet transitions and the life times of the triplet states (). In this treatment, we have considered the mixing of various singlets with T ₁ and triplets with S ₀, and the effect of -electrons is studied.

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Zusammenfassung Es werden nach einer von den Autoren dieser Arbeit vorgeschlagenen Methode die Elektronenstrukturen von Pyridin, Pyrazin, Pyrimidin und Pyridazin studiert. Die halbempirische SCF-Methode für Valenzelektronensysteme gestattet die Berechnung der Ladungsverteilungen, Übergangsenergien und Oszillatorstärken, die in recht guter Übereinstimmung mit der Beobachtung stehen. Ferner werden die Oszillatorstärken von Singulett-Triplett-Übergängen und die Lebensdauer von Triplett-Zuständen () berechnet.

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Résumé Les structures électroniques de la pyridine, de la pyrazine, de la pyrimidine et de la pyridazine sont étudiées par une méthode SCF semiempirique pour les électrons de valence proposée précédemment par les auteurs. Les distributions de charge, les énergies de transition et les forces oscillatrices de ces composés sont calculées, donnant des résultats en bon accord avec l'expérience. De plus nous avons calculé les forces oscillatrices des transitions singulet-triplet et les durées de vie des états triplets (). Dans ce calcul nous avons inclus l'interaction de configuration et l'étude de l'effet des électrons .

     

Ab initio spin-orbit configuration interaction calculations for high-lying states of the HeNe quasimolecule

Multireference configuration interaction (MRD-CI) calculations are reported for a large series of electronic states of the HeNe quasimolecule up to 170000 cm(-1) excitation energy, including those that dissociate to the 3S1 and 2 1S0 excited states of the He atom. Spin-orbit coupling is included through the use of relativistic effective core potentials (RECPs). Good agreement is obtained with experimental spectroscopic data for the respective atomic levels, although there is a tendency to systematically underestimate the energies of the Ne atom by 1000-1500 cm(-1) because of differences in the correlation effects associated with its ground and Rydberg excited states. Potential curves are calculated for each of these states, and a number of relatively deep minima are found. The CI Omega-state wave functions are sufficiently diabatic until r = 4-5 a0 to allow for a clear identification of the He 1s-2s excited states. Electric dipole transition moments are computed between these states and the HeNe X 0+ ground state up to r = 4.0 a0, and it is found that the 2 (1)S0 - X maximum value is over an order of magnitude larger than that for the corresponding (3)S1 - X excitation process.     

Capability of pseudopotential methods to simulate all-electron calculations with floating spherical gaussian orbitals

A pseudopotential method has been applied to the calculation of local molecular orbitals for the water molecule in its ground state. Calculated values of the bond length and of the bond angle are in good agreement with those obtained from analogous calculations involving all the electrons. Comparison with experimental data is of the same quality in the two types of calculations.