Full Configuration Interaction Quantum Monte Carlo: from Molecules to Materials

控制原子、分子和材料性质的基本方程是多电子薛定谔方程，它的解通过求解组成电子的相关运动给出所考虑的系统的能量。考虑这种相关性已被证明对材料的有用建模至关重要，同时也极难计算。在本提案中，我们将开发一种全新的方法来解决这个问题，该方法基于一种算法，该算法传播驻留在能够解释这种相关性的抽象状态空间（斯莱特决定因素）的行走者的进化分布。算法是一套非常简单的规则（但经过特殊设计），类似于生命游戏。该算法已被PI证明对孤立分子有效，将fci级计算的范围扩展了许多数量级。本文的建议是将FCIQMC扩展到无限重复系统，该系统可用于模拟金刚石或石墨等材料。这种扩展需要的方法是在一个基本的方式进行扩展，以允许复杂的，而不是纯粹的真正的步行者。在支持案例中提出了这样做的方法。如果成功，该方法将改变材料建模领域，因为它将首次提供一种计算相关能的方法，而无需强加不受控制的近似。在开发这种新技术的经验中，我们希望有一天能够解决快速发展的相关材料领域所带来的一些问题，这些问题到目前为止已被证明是现有方法无法解决的。

The fundamental equation governing the properties of atoms, molecules and materials is the many-electron Schr\ odinger equation, whose solution gives the energy of the system under consideration, by solving for the correlated motions of the constituent electrons. Accounting for this correlation has proven to be both essential for useful modelling of materials, as well as extremely difficult to calculate. In this proposal, we will develop a radically new approach to this problem based an algorithm which propagates an evolving distribution of walkers which inhabit an abstract space of states (Slater determinants) which are able to account for this correlation.The algorithm is a remarkably simple set of rules (but specially devised), akin to a Game of Life. This algorithm has been shown by the PI to work efficiently for isolated molecules, extending the range of FCI-level calculations by many orders of magnitude. The proposal here is to extend FCIQMC for an infinitely repeating system, which can be used to model a material such as diamond or graphite. This extension requires the method to be extended in a fundamental way, to allow for complex rather than purely real walkers. A method to do this is proposed in the Case for Support. If successful, this method could transform the field of modelling of materials, in that it would give access, for the first time, a way to compute the correlation energy without the imposition of uncontrolled approximations. In developing experience with this new technique, we hope one day to be able to solve some of the problems posed by the rapidly developing field of correlated materials, which have so far proven impervious to existing methods.