Can classical equations simulate quantum‐mechanical behavior? a molecular dynamics investigation of a diatomic molecule with a morse potential
Can classical equations simulate quantum‐mechanical behavior? a molecular dynamics investigation of a diatomic molecule with a morse potential
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经典方程可以模拟具有莫尔斯势的双原子分子的量子力学行为吗？
DOI：
10.1002/cpa.3160420807
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发表时间：
1989
影响因子：
3
通讯作者：
C. Peskin
中科院分区：
文献类型：
--
作者：
T. Schlick;C. Peskin
在最近的一篇论文中，我们提出了一种新的分子动力学计算方法，它使用反向欧拉格式来求解经典的朗之万动力学方程。模拟参数包括目标温度T、时间步长Δt和截止频率ωc。对于谐振子系统，为了模拟量子力学行为，可以将截止频率设置为ωc=kT/h。我们现在继续对一个非线性情况进行研究：一个受莫尔斯键势支配的双原子分子。由于该模型的近似量子力学能级是明确已知的，因此可以将能量与分子动力学结果进行比较。通过在很宽的温度范围内进行动力学运行并计算平均能量，我们发现这些能量与量子力学预测之间有很好的一致性。振动激发开始于800K左右的温度，在更高的温度下，两种能量曲线(分子动力学和量子力学)都接近经典预测的每个分子7/2KT的能量。未来的研究将集中在核酸和蛋白质力场中应用的更一般的非线性势函数。
In a recent paper, we presented a new computational method for molecular dynamics which uses the Backward-Euler scheme to solve the classical Langevin dynamics equations. Parameters for the simulation include a target temperature T, a time step Δt, and a cutoff frequency ωc. We showed for a harmonic oscillator system that the cutoff frequency can be set as ωc = kT/h in order to mimic quantum-mechanical behavior. We now continue this investigation for a nonlinear case: a diatomic molecule governed by a Morse bond potential. Since approximate quantum-mechanical energy levels are explicitly known for this model, a comparison of energies can be made with molecular dynamics results. By performing dynamics runs for a wide range of temperatures and calculating mean energies, we find a very good agreement between these energies and quantum mechanical predictions. Vibrational excitation begins at temperatures around 800 K, and for higher temperatures both energy curves (molecular dynamics and quantum mechanics) approach the classical prediction of 7/2kT energy per molecule. Future investigations will focus on more general nonlinear potential functions employed in force fields of nucleic acids and proteins.