Expanding the scope and scale of first-principles quantum-mechanical simulations with the ONETEP linear-scaling method on high performance computers

计算机模拟在我们的社会中起着重要的作用，例如飞行模拟器可以让飞行员比在空中更便宜和安全地接受培训。在科学和技术领域，计算机模拟是理解和预测材料复杂过程的有力工具。模拟通常与常规实验一起使用，但也可以用于实验成本太高或甚至无法进行的情况，例如在极端条件下（如地球中心的高温和高压）研究材料时。上个世纪之交，随着量子力学（QM）的发现，科学革命开始了。在非常小的尺度上，大自然的行为方式与我们的日常经验完全不同。如果我们缩小到原子大小，导航将变得非常困难，因为不确定性原理说，不可能同时精确地知道你在哪里和你要去哪里！尽管有这种奇怪的行为，量子力学是非常精确的，并为我们所有的科学和技术提供了基础。除非量子力学的方程可以解决今天科学家和工程师感兴趣的问题，否则这种说法是没有用的。挑战在于方程非常复杂-即使是两个电子也太多了，无法在纸上找到解决方案。在某种程度上，量子力学本身提供了答案，因为它导致了晶体管的发明，从而导致了计算机的发明。然而，即使在最快的计算机上，也只能精确地解决小分子的QM方程，而今天科学家感兴趣的系统涉及数千个。即使是计算机技术的快速和无情的进步也不能提供完整的答案，因为问题的规模。完成某项任务所需的工作通常随着其规模的增加而增加。例如，修剪草坪所需的时间与其面积成正比：如果你的花园面积增加一倍，那么你将花费两倍的时间。这是一个线性扩展的例子，但许多任务所涉及的工作量增加得比这更快。将一套书或CD按字母顺序排列，或者在纸牌游戏中排列你的手牌，通常与所涉及的对象数量的平方成比例：如果你将数量增加三倍，则需要九倍（三平方）。有一些任务要糟糕得多，例如解决旅行推销员问题，以找到访问给定地点的最快路线。多添加一个位置会使求解时间加倍。即使你能在一分钟内解决三个地点的问题，仅仅22个就需要你一整年的时间。求解量子力学方程的规模就是这样的。然而，在20世纪60年代，随着密度泛函理论（DFT）的引入，Walter Kohn获得了1998年诺贝尔化学奖。不利的缩放的起源是电子是带电粒子。电荷相斥，所以一个电子的轨迹取决于所有其他电子的轨迹，因为它想避开它们。因此，随着涉及的电子越来越多，求解描述这些轨迹的方程就变得越来越困难。但DFT的显著结果是，整个系统的物理性质，我们想要的问题的答案，不依赖于这些单个轨迹的细节，而只是平均值。因此，一个线性标度的解决方案的方程是可能的，这承诺大大扩大规模的量子simulationaccessibility.The工作的目的是适应最近开发的线性标度DFT代码称为ONETEP，以利用最新的发展，在计算机技术，使它有效地运行在最强大的计算机上现在可用。利用线性尺度方法和现代计算机的力量，科学家们将首次对由数万个原子组成的系统进行基于QM的模拟。

Computer simulations play an important part in our society e.g. flight simulators allow pilots to be trained more cheaply and safely than in the air. In science and technology, computer simulation is a powerful tool for understanding and predicting complex processes in materials. Simulations are often used alongside conventional experiments, but they can also be used when experiments are too expensive or even impossible to perform, e.g. when studying materials in extreme conditions such as the high temperatures and pressures at the centre of the Earth.The turn of the last century saw the start of a scientific revolution with the discovery of quantum mechanics (QM). On very small scales, nature behaves in a radically different way from our everyday experience. If we were shrunk down to the size of an atom navigation would become very difficult, as the uncertainty principle says that it is impossible to know at the same moment precisely where you are and where you are going! In spite of this bizarre behaviour, QM is astonishingly accurate, and provides the foundation for all our science and technology.Such claims are of no use unless the equations of QM can be solved for problems of interest to scientists and engineers today. The challenge is that the equations are very complicated - even two electrons are too much for finding a solution on paper. In a way, QM has itself provided the answer as it led to the invention of the transistor and so to the computer. However, even on the fastest computers it is only possible to solve the equations of QM exactly for small molecules, whereas the systems of interest to scientists today involve many thousands. Even the rapid and relentless progress of computer technology cannot provide the whole answer, because of the scaling of the problem.The work needed to accomplish a certain task generally increases with its size e.g. the time taken to mow a lawn is proportional to its area: if you double the size of your garden it will take you twice as long. This is an example of linear scaling, but the effort involved in many tasks increases faster than this. Sorting a set of books or CDs into alphabetical order or arranging your hand in a game of cards usually scales as the square of the number of objects involved: if you triple the number it will take nine (three squared) times as long. There are some tasks which are much worse, such as solving the travelling salesman problem to find the quickest route to visit a given set of places. Adding one more location doubles the time it takes to solve. Even if you can solve the problem for three locations in one minute, just 22 will take you a whole year. Solving the equations of QM exactly scales like this. However, in the 1960s a significant leap forwards was made with the introduction of density-functional theory (DFT), for which Walter Kohn won the 1998 Nobel Prize in chemistry. The origin of the unfavourable scaling is that electrons are charged particles. Like charges repel, so one electron's trajectory depends on all the others', as it wants to avoid them. So solving the equations which describe these trajectories becomes much harder as more electrons are involved. But the remarkable result of DFT is that the physical properties of the whole system, the answers to the questions we want, do not depend upon the details of these individual trajectories, but only on the average. So a linear-scaling solution of the equations is possible, which promises dramatically to expand the scale of quantum simulations accessible.The aim of this work is to adapt a recently-developed linear-scaling DFT code called ONETEP to take advantage of recent developments in computer technology so that it runs efficiently on the most powerful computers now available. Harnessing the power of linear-scaling methods and modern computers will allow scientists to perform simulations based on QM for systems made of tens of thousands of atoms for the first time.