RUI: CDS&E: Fast Treecode Methods for Particle-Particle Multipolar Electrostatic Interactions in Molecular Simulations

贝茨学院的Henry Boateng获得了化学系化学理论、模型和计算方法项目的奖励，他开发了加速原子和分子模拟的算法。该奖项还得到了数学科学部和美国国家科学基金会建立的刺激竞争性研究计划（EPSCoR）的支持。科学家模拟物理系统，并通过将模拟结果与实验结果进行比较来验证他们的模型。一旦这些模型得到验证，它们就会被用来对实验无法达到的状态做出预测，或者集中实验的方向。这些模型的范围从原子和分子的亚原子尺度到全球尺度，例如天气预报。这个建议的重点是在原子和分子尺度上。分子模拟的一个典型用途是测定蛋白质的结构。分子模拟实践者的理想将是在实验空间尺度上模拟系统，大约一万亿亿个原子，在实验时间上，秒。当今最强大的计算机（10万个以上的处理器）只能模拟10亿个原子和万分之一秒的量级。这项工作的首要目标是开发有助于缩小并最终消除这一瓶颈的方法。生物化学系统的精确分子模拟需要精确计算静电相互作用。将原子建模为球体，从而将电子密度建模为点电荷的主要方法未能捕获静电相互作用中固有的各向异性。多极静电学提供了对电子环境更精细的描述，因此有望更精确地模拟生化系统。在多极静电相互作用中，化学物质的电荷密度用高阶多极来描述，而不仅仅是用定点电荷来描述。定点电荷是多极静电模型的零阶或单极项。模型的精度随多极阶数的增加而增加，计算成本也随之增加。多极相互作用的高昂成本一直是该模型被广泛采用的障碍。与二阶多极的相互作用通常比相应的定点电荷昂贵一个数量级。Boateng和同事开发了三种相关但不同的并行树码方法来加速分子模拟的多极静电学。这些方法是基于博阿滕教授为固定点电荷模型开发和研究的类似方法。该方法将粒子-粒子相互作用分为近场和远场相互作用。对近场相互作用进行了精确的计算，对远场相互作用用笛卡尔泰勒展开进行了近似计算。这些算法是为自由空间和周期边界条件开发的，以确保它们适用于广泛的分子模拟应用。除了它提供的加速之外，树码的优点还包括良好的并行可伸缩性、低内存需求、适合复杂几何形状以及相对容易实现。所开发的方法将在化学、生物化学和生物物理学的几个实际例子中进行测试。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Henry Boateng from Bates College is supported by an award from the Chemical Theory, Models and Computational Methods program in the Division of Chemistry to develop algorithms for speeding up atomic and molecular simulations. The award is also supported by the Division of Mathematical Sciences and the NSF Established Program to Stimulate Competitive Research (EPSCoR). Scientists simulate physical systems and validate their models by comparing the simulation results to experimental results. Once the models have been validated, they are then used to make predictions for regimes inaccessible by experiments or to focus the direction of experiments. These models can range from the subatomic scale of atoms and molecules to global scale, for example weather prediction. The focus of this proposal is at the atomic and molecular scale. A typical use for molecular simulation is in the determination of the structure of proteins. The ideal for practitioners of molecular simulation will be to simulate systems at experimental spatial scale, about a trillion trillion atoms, and at experimental times, for seconds. The most powerful computers today (upwards of 100000 processors) only allow for simulations on the order of a billion atoms and one-ten thousandth of a second. The overarching goal of this work is to develop methods that help shrink and ultimately eliminate this bottleneck.Accurate molecular simulations of biochemical systems require accurate computations of the electrostatic interactions. The predominant approach of modeling an atom as a sphere and thus the electron density as a point charge fails to capture the anisotropy inherent in electrostatic interaction. Multipolar electrostatics provides a much more refined description of the electronic environment and hence the promise of more accurate simulations of biochemical systems. In multipolar electrostatic interactions the charge densities of chemical species are described by higher order multipoles instead of only fixed-point charges. The fixed-point charge is the zero order or monopole term of a multipolar electrostatic model. The accuracy attained by the model increases with increasing multipole order with a related increase in computational cost. The prohibitive cost of multipolar interactions has been a barrier to the model being widely adopted. Interactions with multipoles up to second order are typically an order of magnitude more expensive than corresponding fixed-point charges. Boateng and coworkers develop three related but different parallel treecode methods to accelerate multipolar electrostatics for molecular simulations. The methods are based on similar methods developed and studied by Professor Boateng for fixed point charge models. The methods split particle-particle interactions into near and far field interactions. The near-field interactions are evaluated exactly and the far-field interactions are approximated using a Cartesian Taylor expansion. The algorithms are developed for both free space and periodic boundary conditions to ensure they are useful for a broad range of molecular simulation applications. The advantages of the treecode, aside from the speedup it offers, includes good parallel scalability, low memory requirement, suitability for complex geometries and relative ease of implementation. The methods developed will be tested on several practical examples in chemistry, biochemistry and biophysics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.