Developing the Multilayer Multiconfiguration Time-dependent Hartree Theory

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Haobin Wang of University of Colorado Denver is supported by an award from the Chemical Theory, Models and Computational Methods program in the Division of Chemistry to develop a computer simulation method called multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory for studying quantum dynamics in chemical systems. Here, quantum dynamics deals with the motions, energy, and momentum exchanges of chemical systems that are governed by the laws of quantum mechanics. Quantum dynamics is relevant to quantum computing and atomic optics. Professor Wang is developing ML-MCTDH as an advanced numerical tool for reducing the huge parameter space in large chemistry and physics problems to a manageable level using a combination of physical modeling, mathematical reformulation, and computer software engineering. ML-MCTDH is among the most mature and efficient contraction schemes for studying ultrafast motions in complex systems. In some strongly systems, ML-MCTDH is the only known approach that can provide reliable results for quantitative predictions and analysis. The problems studied here can also offer a fundamental understanding of photochemical processes and the design of chiral molecules. Haobin Wang’s research also has a broader impact associated with science, technology, software engineering, and mathematics education used in pharmaceuticals (and other applications). Professor Wang is training graduate and undergraduate students and providing research experiences for high school STEM teachers and students. The numerical techniques and software developed in this project have potential application to a broad array of applied problems, such a numerical solution of differential equations, numerical linear algebra, and parallel computation.The goal of this research is to further develop the powerful tensor contraction scheme, the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory, for studying complex molecular systems in more difficult physical regimes. Along this line, Haobin Wang is developing techniques to solve pressing technical difficulties to make ML-MCTDH amendable to very demanding problems: appropriate regularization of the equations of motion and effective ways for choosing proper tree structures in ML-MCTDH simulations. He is extending ML-MCTDH from simulating wave functions to corresponding density matrices or equivalent wave functions in a fictitious dual Hilbert space. The key to this possibility is to iteratively or recursively implement ML-MCTDH with many more layers than before, which would not be possible without solving the technical difficulties addressed in this research. In addition, Haobin Wang is generalizing ML-MCTDH to handle other classes of problems that require effective contraction of high-rank tensors. He is employing the ML-MCTDH methodology to simulate hierarchy equations of motion (HEOM) that aim at significantly pushing its limit. Variational principle will be applied to derive the working equations by mapping the HEOM dynamics onto a non-Hermitian Hamiltonian operator, which can then simulate quantum dynamics for open systems. The development and practical implementation of ML-MCTDH will make it applicable to truly challenging problems. The examples can also offer a fundamental understanding of the relevant photochemical processes, which can help control specific reactions as well as design new materials for enantioselective phase transfer of chiral molecules.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.