主講人：Prof. Ka Un Lao (Department of Chemistry, Virginia Commonwealth University)
題目： Accelerating Quantum Chemistry Calculations Using Grassmannians
地點: Rm. 504, Institute of Atomic and Molecular Sciences, Academia Sinica (中研院原分所5樓504室)
Quantum chemistry is now widely used by a diverse community of scientists to study chemical properties and processes. However, accurate quantum mechanical methods are resource-intensive and time-consuming, especially for large and complex systems. Recently, we have integrated Grassmannian mathematics with electronic structure theory to overcome this computational bottleneck. The key idea of this manifold-based method is to map density matrices, which are the central components in self-consistent field (SCF) methods, from a non-linear Grassmann manifold to its tangent space. Such abstract mappings from differential geometry can be achieved through Grassmann logarithms and exponentials based on the singular value decomposition. Afterward, direct interpolation/extrapolation of density matrices with the correct non-linear physical constraints can be processed on the tangent space of a Grassmann manifold to obtain an accurate density matrix at the desired geometry. Exploring the complementary synergies between Grassmannians and electronic structure theory can open multiple research avenues from chemistry to physics to biology. One promising application of this “manifold-aware” method is accurately and efficiently constructing multi-dimensional ab initio-based potential energy surfaces (PESs) without the time-consuming SCF iterations. Such PESs can then be used for quantum dynamics studies where numerous conformations must be explored to study product distributions, elucidate reaction mechanisms, and evaluate the rates of chemical reactions.