Relativistic calculations of the low-lying electronic states of the ZnO molecule are performed for the Λ–Σ states, 1Σ+, 1Π, 1Δ, 3Π and 3Σ−, at the CCSD(T) or MRCI level, using scalar relativistic energy-consistent pseudopotentials, and the EPCISO method for spin–orbit CI coupling. The ZnO ground state is assigned to 0+ symmetry and has 1Σ+ character around the equilibrium region. The spectroscopic constants (re, ωe) of the 0+ ground state are in good agreement with experimental results. Interpenetration of the vibrational levels of the two lowest 0+ states is also shown.

A hybrid procedure to extract spin-orbit pseudo-potentials is proposed, taking information from both the orbital shape in the valence region and the atomic spin-orbit splitting. An effective atomic spin-orbit parameter is derived from a Dirac-Coulomb-Fock reference atomic calculation and is then used to extract the spin-orbit pseudo-potential. This method is tested for the ground-state configuration (5s(2)5p(4)) of the tellurium atom. (c) 2005 Wiley Periodicals, Inc.

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.

Improvements on current one-component extraction procedures of spin-orbit pseudopotentials are investigated for high accuracy computation of spin-orbit coupling energies. By means of the perturbation-theory formalism we first show that spin-orbit pseudopotentials, extracted at the one-component self-consistent-field level from a reference all-electron Dirac-Coulomb or Dirac-Coulomb-Breit calculation, include valence spin-orbit polarization and relaxation effects. As a consequence the use of these pseudopotentials in uncontracted spin-orbit configuration interaction (CI) with singles from the reference ground-state configuration gives rise to double counting of these spin-orbit effects. Two new methods that avoid such double counting have been investigated. The first, so-called “explicit” method, calculates explicitly, by means of a four-component spin-orbit CI, the double-counted spin-orbit effects and removes them from the pseudopotentials. Due to the nonadditivity of the core and valence spin-orbit effects as well as the so-called “pseudovariational collapse,” this method is shown to be cumbersome. In the second “implicit” method the spin-orbit pseudopotential is extracted at the spin-orbit polarized and relaxed level by means of a single-excitation spin-orbit CI calculation. Atomic tests on iodine demonstrate the ability of the latter method to solve the double-counting problem.

Large core (seven-valence electrons) shape-consistent averaged relativistic pseudopotentials (AREP) including core effects have been derived for the halogen series (Cl,Br,I,At). The influence of core effects on the spin-orbit splitting of the halogen and alkali atoms is clearly demonstrated within an all-electron four-component atomic reference calculation by means of a perturbation analysis. In particular, it is shown that AREPs extracted at the Dirac-Coulomb-Fock level, which already include spin-orbit polarization effects, give excellent results for atomic spectroscopy and equilibrium distances of halogen dimers. We also show that in our approach the core effects, included by configuration interaction using the numerical GRASP code, are transferred to the averaged orbital one-electron energy, defined in a perturbational way. This leads to a modification of the extracted AREPs by core effects, which is illustrated by calculations of the first atomic excited states using these AREPs. These results support the validity of including core effects directly in the AREPs extracted in a shape-consistent scheme. The transferability to the atomic excited states as well as to the molecular case is also verified.

Relativistic and electron correlation effects play an important role in the electronic structure of molecules containing heavy elements (main group elements, transition metals, lanthanide and actinide complexes). It is therefore mandatory to account for them in quantum mechanical methods used in theoretical chemistry, when investigating for instance the properties of heavy atoms and molecules in their excited electronic states. In this chapter we introduce the present state-of-the-art ab initio spin-orbit configuration interaction methods for relativistic electronic structure calculations. These include the various types of relativistic effective core potentials in the scalar relativistic approximation, and several methods to treat electron correlation effects and spin-orbit coupling. We discuss a selection of recent applications on the spectroscopy of gas-phase molecules and on embedded molecules in a crystal environment to outline the degree of maturity of quantum chemistry methods. This also illustrates the necessity for a strong interplay between theory and experiment.

A quasirelativistic perturbative method of ab initio calculations on ground and excited molecular electronic states and transition properties within the relativistic effective core potential approximation is presented and discussed. The method is based on the construction of a state-selective many-electron effective Hamiltonian in the model space spanned by an appropriate set of Slater determinants by means of the second-order many-body multireference perturbation theory. The neglect of effective spin-orbit interactions outside of the model space allows the exploitation of relatively high nonrelativistic symmetry during the evaluation of perturbative corrections and therefore dramatic reduction of the cost of computations without any contraction of the model-space functions. One-electron transition properties are evaluated via the perturbative construction of spin-free transition density matrices. Illustrative calculations on the X0(+) - A1, B0(+), and (ii)1 transitions in the ICl molecule are reported. (C) 2002 Wiley Periodicals, Inc.

We present a quasirelativistic method of ab initio calculations on molecular excited states and electronic transition moments within the relativistic effective potential approximation, based on the construction of intermediate Hamiltonians and spin-foe one-particle transition density matrices by means of the many-body multipartitioning perturbation theory. The method is applied to describe the electronic transitions involved in the radiative decay of the A0(u)(+), B0(u)(+), and B1(u), states of Te-2. Good agreement of the computed transition dipole moment functions with their empirical counterparts is achieved. Theoretical radiative lifetime estimates for several low-lying rovibrational levels of the states under study are reported and compared with experimental collisionless lifetimes.

Very accurate ab initio electronic + spin-orbit calculations of the lowest-lying states of the Ag atom and Ag+ cation have been performed through the CASSCF + ACPF + EPCISO method, using the Stuttgart small-core (19 active electrons) relativistic effective core potential (RECP) as well as its associated 2D spin-orbit effective potential. An ad hoc spin-orbit P-symmetry pseudopotential for the 2P state adapted to this 19-e RECP and basis set was extracted. The Stuttgart basis set was augmented to a large valence Gaussian basis set (8s8p7d3f3g/6s6p4d3f3g) in order to reproduce at best the experimental 2S-2D and 2S-2P transition energies as well as the ionization potential (IP) of Ag, which play a crucial role for the accurate description of the spectroscopy in silver-containing molecular systems. A detailed discussion on the multiple schemes used to deal with the differential d10 vs d9 electronic correlation for these two excited states is given. The role of the 4s and 4p (core) shells on the 2S-2D and 2S-2P transition energies and the IP is carefully studied and discussed. The core–core correlation is found to play a minor role while an insufficient treatment of the core-valence electronic correlation is responsible for the main differential d10 vs d9 correlation energy error between the 2S-2D and 2S-2P transition energies. For the neutral atom, the 2D5/2-2D3/2 and 2P3/2-2P1/2 splittings are in excellent agreement with the experimental ones. However, the relative calculated energetic ordering for the 2D5/2,2D3/2,2P3/2, and 2P1/2 fine structure components is critically dependent on the J-averaged purely electronic ACPF 2P and 2D energies of the parent states. The 3D fine-structure splitting for the ion is also found in good agreement with the experiment.

We present a new two-step uncontracted spin-orbit configuration interaction (CI) method which automatically accounts for spin-orbit polarization effects on multiconfigurational wave functions by selecting the single excitations having a significant spin-orbit interaction with a chosen determinantal reference space. This approach is in the line of a conventional two-step method, as a sophisticated correlation treatment in a scalar relativistic approximation is carried out in the first step. In the second step, we define a model space which includes a set of reference configurations able to represent all the wanted states along with singly excited configurations selected with the spin-orbit (SO) operator. We then exploit the first-step calculation in order to include correlation effects via an effective Hamiltonian technique and diagonalize the full matrix on the determinantal basis. The method combines the advantages of both one-step and conventional two-step SO–CI methods; it intends to treat efficiently the cases where both relativity and extended CI treatments are needed. The new code EPCISO is tested on the spin-orbit splitting of the P2 electronic ground state of the thallium atom which, in spite of its very simple electronic structure is a well-known difficult case study for SO–CI methods. The EPCISO code yields results in excellent agreement with the experimental splitting value; they are compared to those obtained using the conventional two-step CIPSO code.

Recent progress on atomic and chemical group effective potentials is presented. The reviewed effective potentials follow a shape-consistent extraction technique from ab initio data, within a scalar relativistic approximation. Two types of averaged relativistic effective core potentials are considered: the correlated ones where a part of the correlation energy is included in the effective potential, and the polarized ones for which only the core polarization effects are taken into account. In addition spin-orbit polarized pseudopotentials have been extracted, and the effects of the core polarization are tested on the atomic spectroscopy of iodine. Finally a very recent chemical group effective methodology is presented, reducing the number of both electrons and nuclei explicitly treated. Chemical transferability is investigated, and test calculations on a cyclopentadienyl effective group potential are presented.

Ab initio quasirelativistic calculations on the B0(u)(+)-X0(g)(+), A 1(u)-X0(g)(+) and B'1(u)((1)Pi (u))-X 0(g)(+) transition dipole moment functions for the I-2 molecule are reported. The computational approach combines a description of relativistic effects through core pseudopotentials with correlation treatment by many-body multipartitioning perturbation theory. The resulting functions are used to simulate the absorption spectra of I-2 and to estimate the radiative decay rates of the B0(u)(+), nu' states.

A simple method of ab initio quasirelativistic calculations on electronic transition moments in molecules is presented. The description of relativistic effects through effective core potentials is combined with the use of the second-order many-body multipartitioning perturbation theory for correlation treatment. Transition moment estimates are obtained by the finite-field technique. Pilot applications to the B0(+)((3)Pi) --> X0(+)((1)Sigma(+)) transitions in IF and ICl are reported and the results are compared to experimental data. A new fit of the observed visible absorption spectra of ICl gives results in excellent agreement with our ab initio results. (C) 1999 Elsevier Science B.V. All rights reserved.

A comprehensive deperturbation analysis is made of the singlet—triplet D 1Δ ∼ d3Δ complex of the 23Na39K molecule. The deperturbation model takes into account direct spin—orbit coupling between the singlet and triplet states plus a spin—rotational interaction between different Ω components of the triplet state. The direct inversion procedure provides a self-consistent set of the Dunham molecular constants for both states and for the matrix elements of the spin—orbit interaction. The deperturbation analysis is supported by electronic structure calculations performed in the framework of the relativistic effective potential method combined with many-body multipartitioning perturbation theory. The theoretical spin—orbit matrix elements agree well with their experimental counterparts.

We present a theoretical study of the first low-lying excited states of plutonium, Pu(VI)O22+. Their geometries were optimized and found to be basically unchanged due to the local character of the excitations. Vertical spin-free excitation energies were calculated for all (23) states below 240 kcal/mol. Fine-structure levels were obtained for all states in the f-manifold below 105 kcal/mol. The ground state of the plutonyl(VI) ion is a 3Hg at the spin-free level, and its Ω=4 component at the spin-orbit level. The spin-orbit interaction was calculated at the quasi-degenerate perturbation level, using `the one-to-one correspondence of the integrals' method proposed, combined with a shift technique. We propose a simpler approach avoiding the use of generalised contracted ECP basis sets. This is, to our knowledge, the first systematic study of the low-lying excited states of the plutonyl ion including spin-orbit effects.

We investigate in this paper the reduction properties of:the early actinyl ions. Geometry optimization and reaction energies were calculated at the correlated level, using effective core potentials. In a second step we included spin-orbit interaction calculated at the quasi-degenerate perturbation level. We report a general trend which is in agreement with experiment.

A simple method of ab initio quasirelativistic calculations on electronic transition moments in molecules is presented. The description of relativistic effects through effective core potentials is combined with the use of the second-order many-body multipartitioning perturbation theory for correlation treatment. Transition moment estimates are obtained by the finite-field technique. Pilot applications to the B0+(3Π)→X0+(1Σ+) transitions in IF and ICl are reported and the results are compared to experimental data. A new fit of the observed visible absorption spectra of ICl gives results in excellent agreement with our ab initio results.

We present in this paper a systematic investigation of the accuracy of different theoretical approaches to uranyl reduction. All-electron and RECP results are compared at the SCF and different correlated levels, including density functional methods. The comparison is done for geometries and reaction energies. The influence of spin-orbit interaction on energies is also investigated.

Spin-orbit interaction in ab initio calculations using effective core potentials is usually treated with pseudo-spin-orbit-operators, which are fitted on relativistic all-electron data. This procedure has been applied successfully for many systems. However, in combination with all-electron calculations, a recently developed atomic mean-field spin-orbit code succeeded in reproducing spectroscopic data with high accuracy. We propose a new way to combine these approaches in order to benefit from their conceptual and computational advantages. We present applications on two experimentally and/or theoretically well-known atomic systems, platinum and thallium, to prove the validity and precision of this new ansatz.