Canonical Tensors Applied to Ab Initio Electronic Structure: Exact electron correlation via full-dimensional calculation
Abstract
Recent decades have seen a veritable explosion in the importance of computational chemistry methodsÑparticularly density functional theory (DFT). The starting point for virtually all such methods has been the single-electron states (e.g. molecular orbitals), and their associated Slater determinants. Achieving reasonable, ÒchemicalÓ accuracy requires an expansion over multiple configurations. However, even the most accurate ab initio methods in existence [e.g., coupled cluster] employ restricted expansions, rendering bona fide error analysis impossible. As a result, no standard, practical computational chemistry methods developed to date can provide a rigorous treatment of electron correlation. This is not only problematic in its own right, it also makes it difficult to establish reliably accurate benchmark calculations for purposes of testing and characterizing more approximate methods such as DFT. To remedy this state of affairs, the proposed research project explores a radical new approach in which the electronic structure problem is attacked directly, via exact solution of the many-electron Schroedinger equation in full dimensionality. Unthinkably difficult in the past, recent developments render such an approach at least feasible, going forward. The risks are high, but the potential benefitsÑthose above, as well as others not yet imaginedÑcould be enormous. No longer would it be necessary to ÒguessÓ where electronic structure error comes fromÑor worse, to rely on a cancellation of errors to get the right result. Even risky projects must have carefully considered objectives, and a well-thought-out rationale for likely success. Using a combination of new and old techniques (specifically, Gaussian-Sinc, Alternating Least Squares, Block Krylov, Band Pass Staging, and Optimal Separable Basis) the ground and many excited states of the He atom have recently been computedÑboth energy levels and wave functions, in full, two-electron, six-dimensionality (6D)Ñto a ÒchemicalÓ accuracy of ~1 millihartree. Moreover, this was achieved using the simplest, least efficient basis set imaginable (plane waves), on a single computational node with limited RAM, in a matter of hours. At least three planned refinements will radically improve the above performance: (a) incremental band-pass staging; (b) optimal component-separable bases; (c) symmetry adaptation. In addition, the code will be generalized for multiple nuclei, and for more than two electrons. These developments are expected to lead to microhartree convergence for He, as well as chemical accuracy or better for Li, Be, and H2Ñall with rigorous error bars, exact treatment of electron correlation, and full-dimensional electronic wavefunctions. Application to the electron gas and Ewald sums will also be essayed. Larger systems are beyond the scope of this initial exploratory effort. However, the benefits of explicit four-electronÑand even two-electronÑ calculations in the context of larger systems are becoming increasingly well recognized, especially vis-ˆ-vis efforts to determine universal functionals for DFT.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 14, 2019
- Source ID
- W911NF1910023
Entities
People
- Lionel Poirier
Organizations
- Army Contracting Command
- Texas Tech University
- United States Army