(To open PDF: 5 sig figs of *π*)

Two major research directions:

(1) Constructing a Multi-Scale Bridge, *ψπφ*, for Quantum Free-Energy Simulations

(2) AMAZE Theory: New Theory of Centroid Path Integral

**1. Constructing a Multi-Scale Bridge, ψπφ, for Quantum Free-Energy Simulations**

Biochemical and biomolecular free-energy simulation of DNA, RNA, and protein molecules is one of the most explicit and realistic computational methods to unravel the (reaction) mechanisms underlying biological events. Computer simulations (in quantum biochemistry), which are performed at multiple scales and based on fundamental laws in Physics, e.g., [1] density-functional theory (DFT) for electronic scale, [2] path integral (PI) for nuclear scale, and [3] Monte Carlo/molecular dynamics for phase-space scale, can provide us with penetrating insight complementary to experimental results.

In order to render such computationally-expensive multi-scale simulations be a practical and conventional approach for biomolecular simulations, we have been constructing a multi-scale bridge that fuses electronic, nuclear, and phase-space scales altogether by creating a new series of intermediate levels of theory. These new intermediate levels of theory can systematically lead us to have accurate quantum free-energy profiles (very important physical quantities in quantum biochemistry), in accordance with the available computing power. We name our multi-scale bridge as *ψπφ* because it is a Systematic *Ab Initio* Path-Integral Free-Energy Expansion (SAI-PI-FEE) method [Free PDF].

**2. AMAZE Theory: New Theory of Centroid Path Integral**

In addition to our automated integration-free path-integral (AIF-PI) method that is based on the powerful Kleinert’s variational perturbation (KP) theory {[DOI] [PDF] [Supp. Material], [DOI] [PDF]}, we now have been working on a new centroid path-integral theory at the minimum of the absolute-zero energy (AMAZE). Using this new AMAZE theory, along with other centroid-path-integral properties reported in the literature, it is possible that we can accurately calculate many-body quantum free energies, tunneling splittings, and molecular (anharmonic) spectroscopy simply by minimization. Furthermore, the long-existing problem in free-energy simulations, which is caused by multiple conformers orthogonal to the reaction coordinate, could also potentially be solved by our new AMAZE theory [Free PDF] [another Free PDF].