A two-step uncontracted determinantal effective Hamiltonian-based SO–CI method

Abstract

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.

On the multi-reference nature of plutonium oxides: PuO22+, PuO2, PuO3 and PuO2(OH)2

“…Note that optCAS could be further reduced by excluding 5 molecular orbitals (nos. 4,8,14,15, and 18 in Fig. 5(b-ii) units, the plutonium 5f and 6d orbitals hybridize considerably with each other as well as with all oxygen p orbitals.…”

“…[6,7] As scalar relativistic effects are nowadays relatively straightforward to treat, and there are sufficiently accurate approaches to treat spinorbit interactions perturbatively [8], a remaining difficulty is the large number of competing highly-correlated electronic states resulting from distributing electrons among the energetically close-lying 5f, 6d, and 7s atomic orbitals, which requires a multi-reference treatment. In addition, the so-called inner valence orbitals, 6s and 6p, are highly polarizable and yield non-negligible contribution to the electron correlation energy.…”

On the accuracy of one-component pseudopotential spin-orbit calculations

“…Vallet et al 6 with the energy-consistent relativistic pseudopotentials from Leininger et al 7 and the corresponding corepolarization potential ͑CPP͒. At the one-component SCF level, the SO splitting of the 2 P ground state was found to be equal to 7334.4 cm −1 .…”

“…Then the introduction of single excitations from the reference configuration 6s 2 6p into the SO-CI space gave a splitting of 7943.4 cm −1 which is significantly higher ͑by 609 cm −1 ͒ than the SCF value. Therefore the combination of our current SOPPs with uncontracted SO-CI calculations 6 may lead to a non-negligible doublecounting problem if singles from the reference ground-state configuration are included in the SO-CI space. This serious problem concerns in general the one-component extraction procedures of relativistic effective core potentials using as reference four-component DC total-energy splittings.…”

Inclusion of mean-field spin–orbit effects based on all-electron two-component spinors: Pilot calculations on atomic and molecular properties

“…Restriction to this part of the DK Hamiltonian is common and has made the DK approach the most widely relativistic approach in quantum chemical calculations. 18,19 When spin-orbit effects are to be included the spinorbit operator is applied usually at the post-one-component HF step 5,[20][21][22][23][24][25][26] to couple multiplets with different spin and space symmetries. This is done either by a quasidegenerate perturbation theory ͑QDPT͒ where configuration interaction ͑CI͒ or MCSCF states are taken as zero-order wave functions ͑so-called LS coupling͒ or by an intermediate coupling scheme in spin-orbit CI ͑SO-CI͒ or by fully variational treatment of spin-orbit coupling in configuration space.…”