Columbus Program System for Molecular Electronic Structure

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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

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Columbus Program SystemInteractions - Energies

• One-electron
• Kinetic Energy of Electrons
• Electron-Nucleus Coulomb Attraction
• Spin-orbit Interaction
• Two-electron
• Electron-Electron Coulomb Repulsion

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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.

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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

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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

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

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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).

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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.

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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.os
  u.edu/pitzer