Tensor hypercontraction for electronic structure and first principles molecular dynamics

斯坦福大学的托德马丁内斯得到了化学系化学理论、模型和计算方法项目的一个奖项的支持，以开发研究大分子电子性质的有效和准确的方法。 为了描述分子的量子力学行为，需要求解电子薛定谔方程。不幸的是，即使用现代计算机，这个方程也很难求解。主要的问题是，最精确的方法的计算工作量随着分子大小的六次方而增长。 Martinez和他的同事们设计了一些方法，大大减少了这种扩展。需要这样的方法来达到设计具有定制特性的分子的目标，例如有效结合蛋白质的药物和具有有利荧光特性的分子，以用于生物成像。 如果这项工作是成功的，分子的大小，其性质可以准确地预测将大大扩大相比，目前的方法。 本计画主要发展电子结构与从头算分子动力学的张量超压缩方法。张量超收缩将电子排斥积分和波函数振幅转换为可因子分解的形式，导致基于波函数的电子结构方法（如微扰理论和耦合簇）的标度减少多达分子尺寸的两倍。 Martinez小组正在开发新的网格，用于超收缩的最小二乘变体，并扩展超收缩方法，以包括第一原理分子动力学所需的能量分析梯度。 他们正在探索超收缩在自洽场方法（如Hartree-Fock和密度泛函理论）中的应用。超压缩强调关联量的秩稀疏性。这是一种强大的方法，但同时利用空间局部性（元素稀疏性）也很有用。 新的方法，可以同时利用秩和元素稀疏性，即局部形式的张量超收缩，正在考虑。 这些新的和改进的超收缩方法用于预测荧光蛋白的荧光能量和寿命，可用于生物成像应用。

Todd Martinez of Stanford University is supported by an award from the Chemical Theory, Models and Computational Methods Program in the Chemistry Division to develop efficient and accurate methods for studying the electronic properties of large molecules. To describe the quantum mechanical behavior of molecules, it is necessary to solve the electronic Schrodinger equation. Unfortunately, this equation is very difficult to solve, even with modern computers. The main problem is that computational effort for the most accurate methods grows with the sixth power of molecular size. Martinez and coworkers design methods that reduce that scaling considerably. Such methods are needed to reach the goal of designing molecules with tailored properties, such as drugs that bind effectively to proteins and molecules with favorable fluorescent properties for use in biological imaging. If this work is successful, the size of molecules whose properties can be accurately predicted will be greatly enlarged compared to present approaches. This project focuses on the development of the tensor hypercontraction method for electronic structure and ab initio molecular dynamics. Tensor hypercontraction casts the electron repulsion integrals and wave function amplitudes in a factorizable form, leading to scaling reductions by as much as two powers of the molecular size for wave function-based electronic structure methods like perturbation theory and coupled cluster. The Martinez group is developing new grids for least-squares variants of hypercontraction and extending the hypercontraction methodology to include analytic gradients of the energy that are needed in first principle molecular dynamics. They are exploring the application of hypercontraction to self-consistent field methods like Hartree-Fock and density functional theory. Hypercontraction emphasizes rank sparsity in the associated quantities. This is a powerful approach, but it is also useful to simultaneously exploit spatial locality (element sparsity). New approaches which can exploit both rank and element sparsity simultaneously, i.e. a local form of tensor hypercontraction, are being considered. These new and improved hypercontraction methods are used to predict fluorescence energies and lifetimes for fluorescent proteins that may be used in bioimaging applications.