The analytical expression for the matrix elements between Morse’s wavefunctions is shown. These results are computationally inexpensive and fast. The developed formulae show that the anharmonicity is responsible for a non-null displacement with respect to the equilibrium position at 0 K, that we call Zero Point Position. The theoretical model is implemented into the development of a simple atomic-level model for the estimation of temperature-dependent thermal expansion coefficients of bulk metals, which is presented in this study. This model provides an efficient and rapid way for evaluating material mechanic properties. Furthermore, a temperature-dependent modified Morse potential is also developed and validated. These models are analytical and are successfully tested on a series of metals.

给出了莫尔斯波函数之间的矩阵元素的解析表达式。这些结果在计算上便宜且快速。发达的公式表明，相对于0 K处的平衡位置，我们称零点为非零位移。该理论模型被应用到一个简单的原子级模型的开发中，该模型用于估算散装金属的温度相关的热膨胀系数，该研究已在此进行了介绍。该模型为评估材料力学性能提供了一种有效而快速的方法。此外，还开发并验证了随温度变化的莫尔斯电势。这些模型具有分析性，并已在一系列金属上成功进行了测试。