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An O(n) framework for internal coordinate molecular dynamics applicable to molecules with arbitrary constraints and geometries

机译：用于内部坐标分子动力学的O（n）框架，适用于具有任意约束和几何形状的分子

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摘要

For molecules with constraints such as fixed lengths and angles, it is more efficient to consider the molecular movement in the space of generalised internal coordinate than in Cartesian coordinate. This paper presents a new framework in the simulation of molecular movement, especially for macro-molecules with massive length and angle constraints. The generalised forces are calculated to invert the dense mass matrix for integrating the constraints equation. The inverting of the mass matrix was made based on distance descending ordering method. The method does an reordering of the internal variables to make the Cholesky decomposition need no fill-in, which promises the time complexity in doing mass matrix inverting. The method was extended for application to loop structures. It is found that the mass matrix would become singular when the bond angles approach 0 or pi; thus a rotation convention switch method was proposed to resolve the singularity. The time complexity has been demonstrated and the length and angle constraints can be arbitrarily applied. The long-time energy conservation in NVE ensemble was compared for results from symplectic and non-symplectic time integrators. The non-symplectic fourth-order Runge-Kutta method still has satisfactory long-time energy conservation if using small time step.
机译：对于具有固定长度和角度的具有约束的分子，考虑广义内部坐标空间的分子运动比在笛卡尔坐标上更有效。本文介绍了分子运动模拟的新框架，特别是对于具有大规模长度和角度约束的宏观分子。计算广义力以反转致密质量矩阵，用于积分约束方程。基于距离下降排序方法制造质量基质的反相。该方法对内部变量进行重新排序，使Cholesky分解无需填充，这承诺在进行质量矩阵反转时的时间复杂性。该方法被扩展以用于循环结构。结果发现，当键角接近0或pi时，质量基质将变得奇异;因此，提出了一种旋转约定切换方法来解决奇点。已经证明了时间复杂性，并且可以任意地应用长度和角度约束。将NVE合奏的长时间节能进行了比较，以效果和非互相时间集成商的结果。如果使用少的时间步长，则非辛的第四阶runge-Kutta方法仍然具有令人满意的长时间节能。

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