Quantum Monte Carlo meets Quantum Chemistry

量子蒙特卡罗遇上量子化学

• 批准号: EP/J003867/1
• 负责人: Ali Alavi
• 金额: $ 123.36万
• 依托单位: University of Cambridge
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2011
• 资助国家: 英国
• 起止时间: 2011 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FJ003867%2F1
• 关键词: Quantum; Monte; Carlo; meets; Chemistry

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.

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。该方程的一个关键特征是电子-电子相互作用的存在，这解释了电子（提供将原子粘合成分子和固体的“胶水”）根据库仑势相互排斥的事实。再加上电子是费米子（量子物体，两个粒子的交换导致波函数的符号变化），导致电子发生复杂的相关运动。事实证明，对化学键的准确描述需要对这种相关运动有良好的、有时非常好的解释。不幸的是，关联许多电子所需的复杂性是巨大的，并且是量子化学和凝聚态物理中无数（不受控制的）近似的根源。在许多最有趣的系统中，这些近似无法实现，因为它们甚至不能提供电子结构的定性正确图像。过去几年我的团队的工作是开发一种全新的方法来解决相关电子带来的问题。我们开发了一种基于“生命游戏”概念的新量子蒙特卡罗方法来模拟电子系统。在这种方法中，我们模拟了一群具有正号和负号的步行者，它们生活在一个称为斯莱特行列式空间（这是一个正确解释电子费米子性质的空间）的抽象晶格上。这些步行者根据一套简单、明确的规则随机地繁殖、消灭和死亡。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，所有系统的规则保持不变。重复执行这些规则的计算机模拟会导致步行者群体的不断演变。值得注意的是（我们已经明确表明），这种模拟可以在系统可改进的近似范围内求解电子薛定谔方程，并充分考虑电子系统的相关性质。换句话说，我们发现可以利用专门设计的“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且非常重要的研究领域，因为它提供了一种处理物理科学基本方程之一的新方法，并且已经引起了国际上该领域一些顶尖研究人员的关注。该奖学金的目的是为我提供时间和资源来充分发展这些想法，促进合作并在竞争中保持领先。这项研究的影响可能遍及广泛的技术重要学科，从过渡金属分子的分子物理学到过渡金属氧化物领域，其电子结构继续对现有方法构成最严峻的挑战。

项目成果

An explicitly correlated approach to basis set incompleteness in Full Configuration Interaction Quantum Monte Carlo

全配置交互量子蒙特卡罗中基组不完整性的显式相关方法

• DOI: 10.48550/arxiv.1208.0980
• 发表时间: 2012
• 作者: Booth G

Semi-stochastic full configuration interaction quantum Monte Carlo: developments and application

半随机全构型相互作用量子蒙特卡罗：发展与应用

• DOI: 10.48550/arxiv.1502.04847
• 发表时间: 2015
• 作者: Blunt N

Nonlinear biases, stochastically sampled effective Hamiltonians, and spectral functions in quantum Monte Carlo methods

• DOI: 10.1103/physrevb.98.085118
• 发表时间: 2018-08-09
• 期刊: PHYSICAL REVIEW B
• 影响因子: 3.7
• 作者: Blunt, Nick S.;Alavi, Ali;Booth, George H.
• 通讯作者: Booth, George H.

Linear-scaling and parallelisable algorithms for stochastic quantum chemistry

• DOI: 10.1080/00268976.2013.877165
• 发表时间: 2014-01-01
• 期刊: MOLECULAR PHYSICS
• 影响因子: 1.7
• 作者: Booth, George H.;Smart, Simon D.;Alavi, Ali
• 通讯作者: Alavi, Ali

An excited-state approach within full configuration interaction quantum Monte Carlo

全构型相互作用量子蒙特卡罗中的激发态方法

• DOI: 10.48550/arxiv.1508.04680
• 发表时间: 2015
• 作者: Blunt N