Columbus Program System for Molecular Electronic Structure

1. Columbus Program SystemforMolecular Electronic Structure Relativistic Quantum Chemistry Capabilities Russell M. Pitzer Department of Chemistry Ohio State University Work done in collaboration with R. Shepard, Argonne National Lab T. Mueller, Research Center Jülich W.C. Ermler, University of Memphis I. Shavitt, University of Illinois B. Bursten, Ohio State University

2. Columbus Program SystemInteractions - Energies One-electron Kinetic Energy of Electrons Electron-Nucleus Coulomb Attraction Spin-orbit Interaction Two-electron Electron-Electron Coulomb Repulsion

3. Columbus Program SystemFormulation One-electron basis functions (orbitals): Atomic orbitals (AOs)  linear combinations  Molecular orbitals (MOs) Many-electron basis functions: Linear combinations of products of MOs and spin functions chosen to be antisymmetric (Pauli Principle) and eigenfunctions of electron spin  Configuration State Functions (CSFs) Wavefunctions (solutions to Schrödinger Eq.): Linear combinations of CSFs (Large, sparse matrix diagonalization)  energies etc.

4. Columbus ProgramsReal Symmetric Eigenvalue Problem • Sparse matrix; dimensions 104 to 109 • Need only small number of lowest eigenvalues • Matrix elements generated on the fly in computing matrix-vector products • (Iterative) Davidson method

5. Columbus ProgramsParallelization • Extraction of eigenvalues requires almost all of the computer time • Sub-blocks of matrix handled in parallel in forming matrix-vector products • Global Arrays software used • Load balancing by assigning tasks in decreasing order of length

6. Timing of CI Iteration Programming: T. Mueller, Research Center, Juelich Tuning and Benchmarking: M. Minkoff and R. Shepard, Argonne National Lab

7. Columbus Programs Expect to incorporate pseudopotentionals from W.C. Ermler and M. Marino (SciDAC). Effectively, large-core pseudopotentials with outer core flexible and simply coupled to valence electrons

8. Columbus Programs Applications UO22+ in Cs2UO2Cl2 X-ray spectra (O K-edge) in 500 eV range. Excitation to valence orbitals including 5g. UO2 Characterized lowest 32 electronic states. Low-lying states thermally populated  electronic hot bands Comparison with spectra of M. Heaven group Antisymmetric stretch frequencies found to be 776 cm-1(Ar matrix), 915 cm-1 (Ne matrix) by L. Andrews group. Calculations and gas-phase experiments give results close to the high value (several groups). Ar matrix electronic spectra give same electronic ground state as in gas phase (Heaven group).

9. Columbus ProgramsApplications • CUO – Observed shifts in matrix-isolation stretching frequencies (68,195 cm-1) between Ne and Ar hosts suggest different electronic ground states; support with DFT calculations without SO (Li et al. 2002). CASPT2 + SO calculations give no explanation (Roos et al. 2003). • Er3+ doped into GaN – example of laser material for optical-fiber signals. Transition is 4I15/2  4I13/2. Crystal field causes splittings and intensities.

10. Atomic Self-Consistent-Field Program • Original version by C.C.J. Roothaan and P.S. Bagus 1963 (assembler) • Many later versions in fortran • Mainly used to optimize AO basis sets • Version now available with fortran 90 memory allocation improved integral formulas simple vectorization features generalization to angular momenta 0 to 24 some states with two open shells of the same symmetry simplified open-shell energy coefficients • Correlation-consistent basis sets for core potentials now available: http://www.chemistry.osu.edu/~pitzer