空间群不可约导数的广义拟调和逼近
The generalized quasiharmonic approximation via space group irreducible derivatives
摘要：
准谐近似（QHA）是常压下相互作用声子的最简单的非平凡近似，它将非谐性的影响引入到与温度有关的观测量中。尽管如此，QHA通常是实现额外的近似，由于任意应变下计算声子的复杂性，和广义QHA，采用恒定应力边界条件，还没有完全开发。在这里，我们制定了广义QHA，提供了一个实用的算法计算的应变状态和其他可观的温度和真实应力的函数。我们规避计算声子的复杂性，在任意应变下，采用不可约的二阶位移导数的Born-Oppenheimer势和它们的应变依赖性，这是有效和精确地计算使用孤独的不可约导数的方法。我们制定了两个互补的应变参数化：离散应变网格插值和泰勒级数展开对称应变。我们说明了我们的方法，通过评估的弹性常数张量的温度和压力的依赖性和热膨胀在氧化钍（钍$_2$）使用密度泛函理论与三个交换相关泛函。QHA的结果相比，我们的测量的弹性常数张量使用时域布里渊散射和非弹性中子散射。我们的不可约衍生物的方法简化了广义QHA，这将有利于可重复的，数据驱动的应用程序的实现。
英文摘要：
The quasiharmonic approximation (QHA) is the simplest nontrivial approximation for interacting phonons under constant pressure, bringing the effects of anharmonicity into temperature dependent observables. Nonetheless, the QHA is often implemented with additional approximations due to the complexity of computing phonons under arbitrary strains, and the generalized QHA, which employs constant stress boundary conditions, has not been completely developed. Here we formulate the generalized QHA, providing a practical algorithm for computing the strain state and other observables as a function of temperature and true stress. We circumvent the complexity of computing phonons under arbitrary strains by employing irreducible second order displacement derivatives of the Born-Oppenheimer potential and their strain dependence, which are efficiently and precisely computed using the lone irreducible derivative approach. We formulate two complementary strain parametrizations: a discretized strain grid interpolation and a Taylor series expansion in symmetrized strain. We illustrate our approach by evaluating the temperature and pressure dependence of the elastic constant tensor and the thermal expansion in thoria (ThO$_2$) using density functional theory with three exchange-correlation functionals. The QHA results are compared to our measurements of the elastic constant tensor using time domain Brillouin scattering and inelastic neutron scattering. Our irreducible derivative approach simplifies the implementation of the generalized QHA, which will facilitate reproducible, data driven applications.
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