Recorded 31 March 2025. Eugene De Prince of Florida State University presents "Lower Bounds in Quantum Chemistry" at IPAM's Optimal Transport for Density Operators: Theory and Numerics Workshop. Abstract: Any electronic Hamiltonian can be decomposed into a sum of squares (SOS) of products of fermionic creation and annihilation operators plus a constant shift. The constant shift is a lower-bound to the ground-state energy of the Hamiltonian, and a tighter lower-bound can be obtained as the pool of fermionic operators becomes more complete. The SOS decomposition problem is a complement to a more well-known approach in quantum chemistry based on the variational optimization of the two-electron reduced density matrix (2RDM). In this approach, the 2RDM is optimized subject to a set of ensemble N-representability conditions, and, as the set of conditions becomes more complete, the trace of the 2RDM against the Hamiltonian approaches the full configuration interaction energy from below. In this talk, I will discuss the similarities and differences between the SOS and variational 2RDM approaches. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-i-optimal-transport-for-density-operators-theory-and-numerics/?tab=schedule