耦合聚类方法的自动微分
Automatic differentiation for coupled cluster methods
摘要：
自动微分是一种工具，用于数值计算给定函数的导数，直到机器精度。该工具对于量子化学方法是有用的，该方法需要计算梯度以用于相对于波函数参数的能量的最小化或用于计算分子对外部扰动的响应。在此，我们将自动微分应用于耦合团簇的双精度方法，其中波函数参数通过最小化能量拉格朗日函数来获得。这种方法的好处是可以在不实现通常的L-方程的情况下获得l个幅度，从而将编码工作减少大约二分之一。我们还表明，在耦合团簇水平的激发能可以contained只有几行代码使用自动微分。我们进一步将自动微分应用于多组分耦合团簇的双元方法，该方法以量子力学的方式处理电子和质子等多种粒子。这种方法对于多组分量子化学方法的原型设计、调试和测试特别有用，因为在这个新兴领域，参考和基准数据是有限的。
英文摘要：
Automatic differentiation is a tool for numerically calculating derivatives of a given function up to machine precision. This tool is useful for quantum chemistry methods, which require the calculation of gradients either for the minimization of the energy with respect to wave function parameters or for the calculation of molecular responses to external perturbations. Herein, we apply automatic differentiation to the coupled cluster with doubles method, in which the wave function parameters are obtained by minimizing the energy Lagrangian. The benefit of this approach is that the l amplitudes can be obtained without implementation of the usual L-equations, thereby reducing the coding effort by approximately a factor of two. We also show that the excitation energies at the coupled cluster level can be ontained with only a few lines of the code using automatic differentiation. We further apply automatic differentiation to the multicomponent coupled cluster with doubles method, which treats more than one type of particle, such as electrons and protons, quantum mechanically. This approach will be especially useful for prototyping, debugging, and testing multicomponent quantum chemistry methods because reference and benchmark data are limited in this emerging field.
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