Tensor hypercontraction for electronic structure and first principles molecular dynamics

斯坦福大学的托德·马丁内斯获得了化学部化学理论、模型和计算方法项目的支持，以开发高效而准确的方法来研究大分子的电子性质。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，这个方程式也很难解。主要的问题是，最精确的方法的计算工作量与分子大小的6次方有关。马丁内斯和他的同事设计的方法大大减少了这种伸缩性。为了达到设计具有定制特性的分子的目标，需要这种方法，例如有效地与蛋白质和具有良好荧光特性的分子结合的药物，用于生物成像。如果这项工作成功，与目前的方法相比，可以准确预测其性质的分子的尺寸将大大扩大。本项目致力于发展电子结构和从头算分子动力学的张量超收缩方法。张量超收缩使电子排斥积分和波函数振幅以可因式分解的形式出现，使得基于波函数的电子结构方法(如微扰理论和耦合团簇)的标度缩减率高达分子尺寸的2次方。马丁内斯小组正在为超收缩的最小二乘变量开发新的网格，并将超收缩方法扩展到包括第一性原理分子动力学所需的能量的解析梯度。他们正在探索超收缩在自洽场方法中的应用，如Hartree-Fock和密度泛函理论。超收缩强调关联量的秩稀疏性。这是一种强大的方法，但对于同时利用空间局部性(元素稀疏性)也很有用。可以同时利用秩稀疏性和元素稀疏性的新方法，即张量超压缩的局部形式，正在被考虑。这些新的和改进的超收缩方法被用来预测可能用于生物成像应用的荧光蛋白质的荧光能量和寿命。

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.