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>