Reliable Electronic Structure Calculations for Heavy Element Chemistry: Relativistic Pseudopotentionals for Application to Lanthanide and Actinide Systems

Walter C. Ermler
Maria M. Marino
University of Memphis

Summary

A new computational methodology based on relativistic pseudopotentionals (RPPs) that is needed to treat molecules that contain heavy elements at accuracy comparable to what can be achieved for molecules containing first- and second-row atoms has been developed. We are in the process of implementing the RPP method into high-performance software that is portable and scalable on massively parallel computer systems, and are calculating structures, properties and spectra of heavy-metal complexes .

We have completed the development of a relativistic pseudopotentional (RPP), a new form of relativistic effective core potential (RECP) that requires only the smallest number of molecular electrons to be treated explicitly. We are also coding the modules needed to implement the RPP in molecular calculations. We are studying the AmCl + molecule, a system that highlights the need for incorporation of the RPP if both high accuracy and computational tractability are to be maintained.

We are continuing the derivations of RPPs for individual elements, initially Am, Eu, Er and Cl. Like their RECP counterparts, RPPs are derived by back-solving the Dirac-Fock equation using nodeless pseudospinors. To derive RPPs essentially devoid of non-local errors, we apply our nodeless valence pseudospinor method, which uses the small core RECPs in the node-removal process. This procedure eliminates the nodes in an outer core atomic spinor while retaining the form of the spinor as a bona-fide eigenvector of the valence electron Fock matrix over its entire radial range (from the atomic nucleus to infinity).

Codes authored by Ermler and collaborators for the calculation of RECPs, namely SCREPCV, ATOMIC, LPJ, JJT, and JJSCF, have served as models and resources for the development of the RPP method at PNNL during the initial period of the grant. Notably, the use of two-component atomic spinors in the context of RECP generation is transformed over to a basis-set driven process, rather than the original one that was derived in terms of numerical spinors output from a Dirac-Fock code (ACRV). This permits the outer-core basis function coefficients that define the atomic spinors (ATOMIC) to be segregated during the generation of the RPP for a specific element. These coefficients are made available for variation in molecular calculations that incorporate RPPs, with their embedded small-core RECPs. These are the functionals that are used in the molecular applications planned for the Columbus and NWChem suites during the final year of the current project. The subtleties associated with the simultaneous incorporation of small-core RECPs, nodeless valence pseudospinors, and atomic one- and two-electron integrals associated with outer core spinors have required the development of extensive new algorithms and circuitry in the SRECPCV and ATOMIC codes, in terms of both computation and storage and retrieval.

We are also generating new angular momentum projection operators to be associated with the RPPs. Unlike their RECP counterparts, these operators are not defined in the context of the Wigner-Eckart theorem, thus allowing for the symmetry breaking that takes place when outer core electrons polarize in response to interatomic environments. This results in operators containing additional angular degrees of freedom, as opposed to the two angular-component-based operators of the RECPs.

Upon completion of algorithm development and coding, implementation of the RPP formalism into the Columbus and NWChem suites will be carried out in collaboration with OSU and PNNL, respectively. Additionally, code optimization and parallelization, as well as the efficient two-, three- and four-center extensions of the RPP molecular codes will be carried out in collaboration with the SciDAC Computer Science Integrated Software Infrastructure Centers.

A valence full-configuration-interaction study with a polarized double-zeta quality basis set was also completed for the lowest 49 electronic states of AmCl⁺ . The resulting electronic potential energy curves are mostly repulsive. For those states that are bound, the chemical bonding is ionic in character with negligible participation of 5f electrons. The molecular f-f spectroscopy of AmCl⁺ arises essentially from an in situ Am⁺² core with states slightly red-shifted by the presence of chloride ion. Am⁺¹ + Cl asymptotes which give rise to the few attractive potential energy curves can be predicted by analysis of the f-f spectroscopy of isolated Am⁺¹ and Am⁺² . The attractive curves have substantial binding energies, on the order of 75-80 kcal/mole, and are noticeably lower than recent indirect measurements on the isovalent EuCl⁺ . An independent empirical study supports the predicted reduction in AmCl⁺ binding energy. The energies of the repulsive curves are strongly dependent on the selection of the underlying atomic orbitals while those of the attractive curves are not. The calculations were carried out using our recently developed parallel spin-orbit configuration-interaction Columbus package.

Affiliated SciDAC researchers are Russell M. Pitzer, Bruce E. Bursten and Isaiah Shavitt of Ohio State University. This group is expanding and enhancing the Columbus suite of electronic structure codes for efficient parallel computations of electronic wave functions for polyatomic systems containing heavy elements. Core and outer core electrons are represented by RECPs and RPPs that we are developing.

We continue our contacts with Theresa. L. Windus of PNNL regarding code development in the context of the NWChem system. Additionally, we collaborate with Jeffrey L. Tilson, Center for Computational Research, SUNY, Buffalo and Albert F. Wagner and Ron Shepard of ANL on applications using our parallel spin-orbit configuration interaction modification of Columbus.

For further information on this subject contact:
Walter C. Ermler
Department of Chemistry
University of Memphis
Memphis, TN 38152
Phone: 901-678-4422
wermler@memphis.edu

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