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Numerical calculations using the hyper-molecular dynamics simulation method

机译：使用超分子动力学模拟方法进行数值计算

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摘要

Hyper-molecular dynamics (H-MD) is a new simulation method developed to increase the time scale over which a molecular dynamics simulation can be carried out. Adding a bias potential to the interatomic potential, the simulated time can be boosted by a factor dependent upon the temperature of the system. A bias potential which gives a substantial 'boost' can be defined as a function of the lowest eigenvalue of the Hessian matrix of the total interatomic potential with respect to the atom coordinates and the projection of the gradient of the potential onto the eigenvector. In order to obtain a numerical approximation for these quantities without the diagonalization of the Hessian matrix, numerical minimization methods have been proposed. The performance of a hyper-molecular dynamics simulation depends on the accuracy and speed of such minimization methods. Here we present a numerical approximation for the H-MD simulation method and prove the mathematical expressions required for that approach. The speed of a H-MD simulation increases by a factor of up 3 compared to previous derivations with improved accuracy. Some numerical examples are calculated and compared in order to assess the applicability of the method.
机译：超分子动力学（H-MD）是一种新的仿真方法，旨在增加可进行分子动力学仿真的时间尺度。将偏电势加到原子间电势上，可以将模拟时间增加一个取决于系统温度的因素。可以将产生实质性“增强”的偏置电势定义为相对于原子坐标的总原子间电势的黑森州矩阵的最低特征值和电势梯度在本征矢量上的投影。为了在不对Hessian矩阵进行对角化的情况下获得这些数量的数值近似值，提出了数值最小化方法。超分子动力学模拟的性能取决于这种最小化方法的准确性和速度。在这里，我们给出了H-MD仿真方法的数值近似值，并证明了该方法所需的数学表达式。与以前的派生相比，H-MD仿真的速度提高了三倍，并且精度更高。计算并比较了一些数值示例，以评估该方法的适用性。

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