Highly efficient time-domain quantum chemistry algorithms

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The current state of Theoretical and Computational Chemistry is a paradox -- the fundamental equations governing physical reality in the chemical energy range (1-100 eV) are known completely, yet their exact solutions are in most cases far too complex to be computed: the best we can currently do, even with the largest modern supercomputers, is about the size of the benzene molecule.This basic computational problem is solved using physical approximations: calculating a given property to a given accuracy is often a much simpler task than obtaining the full molecular wavefunction. Computational Chemistry currently employs a large array of such approximations -- from the crudest (molecular dynamics) to medium accuracy (semi-empirics and density functional theory) to high accuracy (configuration interaction and high-order preturbation theory) to extreme precision (full configuration interaction). The primary parameter that makes an approximation computable is known as "scaling": polynomial (ideally linear) scaling makes an approximation computationally acceptable, whereas exponential scaling generally means that further theoretical work is required before meaningful calculations can be performed.This project will enable knowledge transfer between three sub-disciplines of Computational Chemistry -- time-domain electronic structure theory, spin dynamics and density matrix renormalization group (DMRG) -- that will bring some of the exponentially scaling computation stages down to polynomial scaling. Specifically, the latest DMRG algorithms will be adopted for dissipative spin dynamics (Cornell --> Oxford, Edinburgh), the state space restriction algorithms from spin dynamics will be adopted for time-domain electronic structure theory (Oxford, Edinburgh --> Stanford, Bristol) and the tensor factorization algorithms used in electronic structure theory will be applied to spin dynamics (Bristol, Cornell, Cardiff --> Edinburgh, Oxford). The six research groups (two US groups and four UK groups) involved in this project have extensive independent publication records on the subjects listed above, and view the possibility of joining forces on the computational scaling problem as a crucial opportunity in the ongoing effort towards improving the efficiency of Quantum Chemistry algorithms.Faster and more accurate simulation algorithms benefit all application areas of Quantum Chemistry -- computational drug design, biomolecular structure determination, MRI contrast agent design, metabolomics, magnetic resonance and optical spectroscopy, materials chemistry, etc. Our primary objective is to lift the (presently rather low) ceiling of what is possible to accurately compute using Quantum Chemistry techniques.