| Contents: | ||
|---|---|---|
| – | Relativistic Configuration Interaction Methods | |
| – | Large-Scale Relativistic Multi-Configuration SCF Program | |
| – | Devising a Relativistic Multi-Reference Coupled-Cluster Program | |
Despite the advance of density functional theory and coupled-cluster methods in quantum
chemistry, configuration interaction (CI) methods remain an indispensable and general
tool to determine the electronic structure and the correlation energy especially of
open-shell atoms and molecules. Our primal motivation is to draw general heavy-element
species (including lanthanide and actinide compounds) into the reach of relativistic CI
methods by a refined definition of active orbital/spinor spaces and a direct implementation
allowing for large-scale applications.
Common to all our CI approaches is the Hamiltonian-direct Davidson-Olsen algorithm. The Hamiltonian matrix is not explicitly set up, but instead linear transformations (sigma vectors) of a chosen number of reference vectors (CI vectors) are computed and a subspace eigenvalue problem is solved, the final solutions being obtained by iterating the procedure with newly-determined reference vectors. Dynamical blocking of the involved vectors allows for CI expansions of up to roughly 15 million terms (spin-dependent relativistic, program LUCIAREL) and 1 billion terms (spin-averaged scalar relativistic, program LUCITA). The wave functions are defined in the most flexible way, by dividing the orbital/spinor space into an arbitrary number of subspaces with arbitrary occupation constraints (Generalized Active Spaces, GAS, see figure).
States and one-particle functions are defined fully in terms of double group symmetry and employing time-reversal symmetry for computational savings (spin-dependent CI); the latter can both be applied in a 2- or 4-component relativistic framework.
The programs are constantly improved and have been interfaced to the MOLECULE-SWEDEN (spin-dependent CI), MOLCAS, and DIRAC program packages. They have found and are finding a number of interesting applications both in atomic and molecular structure. As to the scalar relativistic approach, LUCITA has been applied to determine spectroscopic properties of the Au2 molecule within the spin-free formalism of 4-component Dirac theory and to support an (electric property study) determining the permanent dipole moment of the HI molecule. The first calculation of dipole polarizabilities in spin-orbit split states (of the heavy halogen atoms) has been performed with LUCIAREL recently, and a similar molecular treatment is currently being carried out (on ScO).
| Project: | Timo Fleig |
| Collaborators: | Jeppe Olsen, Aarhus |
| Christel Marian | |
| Lucas Visscher, Amsterdam |
Key publications:
Relativistic MCSCF theory allows for the treatment of molecules containing heavy atoms and exhibiting near-degeneracy configurations (static correlation) in their electronic valence. An MCSCF optimization of the wave function can be depicted as follows:
In the course of 2002, a 4-component MCSCF program has been brought to completion using the CI
program GOSCI in an upgraded version, allowing for determinant expansions of roughly up to 300.000
terms. The spinor optimization is carried out in the traditional picture of Dirac-Hartree-Fock
(DHF) theory where the negative energy solutions are kept unoccupied and a minimax principle for
the spinor rotations ensures convergence to the desired electronic state with maximum variational
freedom. Double point group and time-reversal symmetries are exploited throughout for computational
savings, and a quaternion algebra formalism ensures an efficient storage and addressing of the
additional classes of two-electron integrals in the relativistic case.
Several pilot applications have been carried out with the newly developed code. The multi-configurational character of the Beryllium atom in its ground state is investigated using active spaces of increasing size. Spinor/orbital occupation numbers are compared to those obtained with a non-relativistic program package (Molcas) and found to match these very well as expected in such a ``non-relativistic'' system. Further, a finite-field study of the molecular dipole moment of the HBr and HI molecules is carried out, demonstrating the sufficiently improved results upon opening a suitable active space for valence correlation as compared to DHF and experimental values.
The program system is currently being extended by incorporation of the above-mentioned relativistic CI code LUCIAREL to allow for large-scale CI calculations within the MCSCF procedure, an important bottleneck in practice. It will be possible to correlate many electrons and to treat large CI expansions of, e.g., more than 30 million determinants.
| Project: | Timo Fleig |
| Collaborators: | Hans Jørgen Aa. Jensen, Odense |
| Jeppe Olsen, Aarhus | |
| Lucas Visscher, Amsterdam |
Key publications:
Most current implementations lack applicability, though, when a state of interest is described by several determinants of similar weights, like typically in (low-spin) open-shell compounds or such excited states of closed-shell molecules. The most elegant solution is to employ a multi-reference CC ansatz, but this has several drawbacks. Especially in relativistic theory, the formalism becomes non-commutative, and thus significantly more complicated. To account for this increased complexity, a novel route in CC methodology is pursued: Instead of explicity programming the highly complex and vast amount of formulas or letting the program generate the formulas, the evaluation of the CC exponentials in the amplitude equations is carried out by manipulations of spin(or) strings directly exploiting general principles accounting for the varying excitation levels.
The approach has been implemented in non-relativistic theory in the LUCIA code (Jeppe Olsen, University of Aarhus) and will be extended to the relativistic framework in the near future.
| Project: | Timo Fleig |
| Collaborators: | Jeppe Olsen, Aarhus |
Key publications: