Highly efficient time-domain quantum chemistry algorithms

理论和计算化学的现状是一个悖论——在化学能范围（1-100 eV）内控制物理现实的基本方程是完全已知的，但它们的精确解在大多数情况下太复杂而无法计算：我们目前能做的最好的，即使是最大的现代超级计算机，也只有苯分子的大小。这个基本的计算问题是用物理近似来解决的：以给定的精度计算给定的性质通常比获得完整的分子波函数要简单得多。计算化学目前采用大量这样的近似——从最原始的（分子动力学）到中等精度（半经验和密度泛函理论），再到高精度（构型相互作用和高阶预扰动理论），再到极端精度（全构型相互作用）。使近似值可计算的主要参数被称为“缩放”：多项式（理想情况下是线性）缩放使近似值在计算上可接受，而指数缩放通常意味着在执行有意义的计算之前需要进一步的理论工作。该项目将实现计算化学三个子学科之间的知识转移——时域电子结构理论、自旋动力学和密度矩阵重整化群（DMRG）——这将使一些指数缩放的计算阶段降低到多项式缩放。具体而言，耗散自旋动力学将采用最新的DMRG算法（Cornell—> Oxford, Edinburgh），时域电子结构理论将采用自旋动力学中的状态空间限制算法（Oxford, Edinburgh—> Stanford, Bristol），自旋动力学将采用电子结构理论中的张量分解算法（Bristol, Cornell, Cardiff—> Edinburgh, Oxford）。参与该项目的六个研究小组（两个美国小组和四个英国小组）在上述主题上有广泛的独立出版记录，并且认为在计算缩放问题上联合起来的可能性是正在努力提高量子化学算法效率的关键机会。更快、更精确的模拟算法有利于量子化学的所有应用领域——计算药物设计、生物分子结构测定、MRI造影剂设计、代谢组学、磁共振和光谱学、材料化学等。我们的主要目标是提高使用量子化学技术精确计算的可能性（目前相当低）。

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.