Development of a New Spin-Orbit Coupling Program Package

The inclusion of spin-orbit coupling effects in quantum chemical calculations has been subject to intense research in Bonn since several years. The Bonn spin-orbit coupling suite of programs (BNSOC, see Fig. 5 for an overview) offers a choice of various spin-orbit Hamiltonians (Breit-Pauli, no-pair, molecular or atomic mean-field) to be combined with a non-relativistic or no-pair spin-free all-electron Hamiltonian as well as ab initio model potentials (AIMPs). Fine-structure splittings and spin-orbit coupled wavefunctions are evaluated optionally by quasi-degenerate perturbation theory (QDPT) in the basis of configuration interaction (CI) wavefunctions, by direct solution of perturbation equations in the basis of spin-symmetry adapted functions (SAFs, or configuration state functions, CSFs), or in a spin-orbit CI (SOCI). Rates of spin-forbidden radiative transitions are available at present only at the QDPT level. Furthermore, it is possible to simultaneously consider rotational and spin-orbit interaction (ROSO) in diatomic molecules at this level of theory. Current versions of BNSOC are capable of describing small molecules very accurately, but larger systems experience unmanageable requirements of storage and computation time. This is true for the calculation of spin-orbit matrix elements over CI wavefunctions in the SPOHR program (feasible for a maximum of about seven non-hydrogen atoms) as well as the more sophisticated SOCI program SPDIAG (only diatomics have been addressed so far). The BNSOC programs are presently linked to the old MOLECULE-SWEDEN program package, which provides the spin-free integrals and Molecular Orbitals (MOs). Correlated wavefunctions are determined with the MRD-CI program, devised originally by Buenker and Peyerimhoff and coworkers in the 1970s and developed further by Buenker and coworkers in the 1980s. Storage requirements of the integrals and of the Hamiltonian matrix are the most severe bottlenecks there, as well as in the SOCI code currently available.

Figure 5: Modules of the Bonn spin-orbit coupling (BNSOC) code (hatched) and linkage to other program packages.

The DFT/MRCI program, developed by S. Grimme and M. Waletzke during the last years, is a selecting multi-reference CI program that utilizes modern techniques such as the RI (Resolution of the Identity) approximation and a direct diagonalization algorithm, thus eliminating the above mentioned restrictions. Integrals and MOs for the DFT/MRCI program are taken from the TURBOMOLE package. The most interesting feature of the program is the possibility to use Kohn Sham (KS) orbitals as one-particle basis instead of Hartree Fock (HF) orbitals. In this way, major parts of the dynamic electron correlation that have been obtained in the DFT treatment are carried over to the subsequent CI step, in which now only static correlation has to be considered. This fact drastically reduces the length of the CI expansion, allowing for calculations beyond one hundred active electrons.

We are currently developing spin-orbit coupling modules for this program, which will allow the calculation of spin-orbit matrix elements over CI wavefunctions and SOCI calculations for larger molecules, both with HF and KS orbitals.