Highly efficient time-domain quantum chemistry algorithms

理论和计算化学的现状是一个悖论--在化学能范围内(1-100 eV)控制物理现实的基本方程是完全已知的，但在大多数情况下，它们的精确解太复杂而无法计算：我们目前所能做的最好的事情，即使是使用最大的现代超级计算机，也是关于苯分子的大小。这个基本的计算问题是使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。计算化学目前使用了大量这样的近似--从最粗略的(分子动力学)到中等精度(半经验和密度泛函理论)到高精度(组态相互作用和高阶预扰动理论)到极高精度(全组态相互作用)。使近似值可计算的主要参数称为“标度”：多项式(理想线性)标度使近似值在计算上可接受，而指数标度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。这个项目将使计算化学的三个子学科--时间域电子结构理论、自旋动力学和密度矩阵重整化群(DMRG)--之间的知识转移--这将使一些指数标度计算阶段降至多项式标度。具体地说，耗散自旋动力学将采用最新的DMRG算法(康奈尔--&GT；牛津，爱丁堡)，自旋动力学的状态空间限制算法将被用于时域电子结构理论(牛津，爱丁堡--&GT；斯坦福，布里斯托尔)，电子结构理论中使用的张量分解算法将应用于自旋动力学(布里斯托尔，康奈尔，卡迪夫--&GT；爱丁堡，牛津)。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)在上面列出的主题上有广泛的独立发表记录，并将在计算比例问题上联合起来的可能性视为正在努力提高量子化学算法效率的一个重要机会。更快和更准确的模拟算法受益于量子化学的所有应用领域--计算药物设计、生物分子结构确定、磁共振造影剂设计、代谢组学、磁共振和光学光谱学、材料化学等。我们的主要目标是取消使用量子化学技术进行准确计算的(目前相当低的)上限。

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.