Bethe Salpeter Equation Spectra for Very Large Systems with Thousands of Electrons or More

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With support from the Chemical Theory, Models and Computational Methods program in the Division of Chemistry, Professor Daniel Neuhauser of UCLA is developing methods for determining the optical properties of very large molecular systems. These properties play a critical role in broad applications of organic and inorganic energy materials, including semiconducting nanoparticles, organic supramolecular structures, and organic photovoltaic nanostructures. The ability to characterize very large systems with thousands of atoms computationally is critical for the manipulation and control of these new materials and systems, and for the design of future systems. Toward this end, the Neuhauser group will develop a stochastic formalism to solve the Bethe-Salpeter Equation (BSE) for characterizing the absorption spectrum of very large chemical systems. BSE is known to predict accurately the absorption properties of molecular and solid-state systems. The use of these proposed stochastic methods is expected to enable scaling up to very large systems of thousands of atoms with tens of thousands of electrons. This work will be incorporated into a new code-based General Chemistry course and outreach activities to underserved groups.Typically the BSE is too computationally costly to consider for molecules larger than few hundred atoms due to the generation and application of the screened Coulomb exchange, W. The Neuhauser research group will undertake to develoop three specific methodology advances to the BSE: linear scaling generation of the action of W, sparse stochastic compression and sampling for storage of huge W matrices, practically quadratic scaling of the stochastic application of W within the BSE, a time-dependent Hartree-Fock (TDHF) with W-based exchange kernels, and stochastic representation of first-order dynamic corrections. Specifically, the action of the screened Coulomb interaction will be separated into a convolutional exchange-like portion that is to be systematically improved to resemble the true effective interaction, and a small remainder that should easily be stochastically sampled. Together, these innovations are expected to couple to yield a method for simulating nanoscale systems of thousands of electrons in active orbitals. If successful, these modification of the Bethe-Salpeter Equation are expected to have far-reaching scientific impact.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.