Quantum Monte Carlo meets Quantum Chemistry

电子薛定谔方程是控制原子、分子、固体和材料性质的基本(量子力学)方程。这个方程的一个关键特征是电子-电子相互作用的存在，这解释了这样一个事实，即电子(它提供了将原子结合到分子和固体中的“粘合剂”)根据库仑势相互排斥。这一点，再加上电子是费米子的事实(量子物体，两个粒子的交换导致波函数的符号变化)，导致了电子的复杂关联运动。事实证明，对化学键的准确描述需要对这种相互关联的运动有一个很好的，有时是非常好的解释。不幸的是，将许多电子关联起来所需的复杂性是巨大的，这是量子化学和凝聚态物理中无数(不受控制的)近似的来源。在许多最有趣的系统中，这些近似都不能提供结果，因为它们甚至没有提供电子结构的定性正确的图像。我的团队在过去几年的工作是开发一种全新的方法来解决关联电子带来的问题。我们发展了一种新的基于“生命游戏”概念的量子蒙特卡罗方法来模拟电子系统。在这种方法中，我们模拟了一群正负符号的步行者，他们生活在一个被称为斯莱特决定空间(这是一个适当地解释了电子的费米子性质的空间)的抽象晶格上。这些步行者根据一套简单、定义明确的规则随机繁殖、灭绝和死亡。对于给定的化学系统，薛定谔哈密顿量定义了步行者死亡和繁殖的速率，但除此之外，规则对所有系统都是相同的。反复执行这些规则的计算机模拟导致步行者的数量不断变化。值得注意的是(我们已经明确表明)这样的模拟可以求解电子薛定谔方程，在系统可改进的近似范围内，充分考虑电子系统的关联性质。换句话说，我们发现有可能利用一个特别设计的“生命游戏”的力量来做一些非常有用的事情，即求解电子薛定谔方程。这一发现开辟了一个巨大而非常重要的研究领域，因为它提供了一种新的方法来接近物理科学的基本方程之一，这已经引起了国际上该领域一些顶尖研究人员的注意。该奖学金的目的是为我提供时间和资源，充分发展这些想法，促进合作，并保持在竞争中的领先地位。从过渡金属分子的分子物理学到过渡金属氧化物领域，从过渡金属分子的分子物理到过渡金属氧化物的电子结构继续对现有方法构成最严峻的挑战，这项研究的影响可能在广泛的技术重要学科中都能感受到。

The electronic Schrödinger equation is the fundamental (quantum mechanical) equation which governs the properties of atoms, molecules, solids and materials. A key feature of this equation is the presence of electron-electron interactions, which account for the fact that the electrons (which provide the "glue" that binds atoms into molecules and solids), repel each other according to a Coulomb potential. This, together with the fact that electrons are fermions (quantum objects such that an exchange of two particles lead to a sign change in the wavefunction), results in an intricate correlated motion of the electrons. It turns out that an accurate description of the chemical bond requires a good, sometimes very good, account of this correlated motion. Unfortunately, the necessary complexity introduced to correlate many electrons is immense, and has been the source of countless (uncontrolled) approximations in quantum chemistry and condensed-matter physics. In many of the most interesting systems, these approximations fail to deliver, in that they do not provide even a qualitatively correct picture of the electronic structure.The work of my group in the past few years has been to develop a radically new way to approach to the problem posed by correlated electrons. We have developed a new Quantum Monte Carlo approach based on a "Game of Life" concept to the simulation of of electronic systems. In this approach, we simulate a population of walkers of positive and negative sign which live on an abstract lattice called Slater determinant space (which is a space that accounts properly for the fermion nature of electrons). These walkers stochastically procreate, as well as annihilate and die, according to a simple, well-defined, set of rules. For a given chemical system, the Schrodinger Hamiltonian defines the rates at which the walkers die and procreate, but otherwise the rules stay the same for all systems. A computer simulation which repeatedly executes these rules leads to an evolving population of walkers. What is remarkable (and which we have shown explicitly) is that such a simulation can solve the electronic Schrodinger equation, to within systematically improveable approximations, taking full account of the correlated nature of electronic systems. In other words, we have discovered that it is possible to harness the power of a specially designed "Game of Life" to do something very useful, namely to solve electronic Schrodinger equations.This discovery opens up a huge and very important field of research, as it provides a new way to approach one of the fundamental equations of physical science, and which has already attracted the attention of some of the top researchers in the field, internationally. The purpose of this fellowship is provide me the time and resources to develop these ideas to full, to foster collaborations, and to keep ahead of the competition. The impact of this research may be felt across a broad range of technologically important disciplines, from the molecular physics of transition metal molecules, to the field of transition-metal oxides, whose electronic structure continue to pose the severest challenge to existing methods.