Abstract We introduce a new Python package ( pyHMA ) that interfaces with VASP to compute (classical) anharmonic properties of crystalline systems by post-processing data from NVT Born–Oppenheimer ab initio molecular dynamics (AIMD) simulation. It is based on the recently developed harmonically mapped averaging (HMA) method, which leverages the analytically known harmonic behavior to reformulate the direct/conventional ensemble averages in order to significantly improve precision, for a given CPU time. The package consists of two stages: reading AIMD data from vasprun.xml file(s) and then computing anharmonic properties. While the first stage is MD package-dependent, the second one is universal, given that it receives data in the required format. To demonstrate the usage of pyHMA , we compute anharmonic energy and pressure of aluminum fcc crystal at high pressure ( ≈ 115 GPa ) and up to 4000 K (near melting). We further compute anharmonic free energy as a function of temperature, using thermodynamic integration of the HMA anharmonic energy. Although pyHMA currently interfaces with VASP to compute HMA anharmonic energy and pressure, it is moduled in such a way to allow for interfacing with other codes (e.g., LAMMPS) by adding a new reader and can compute other HMA anharmonic properties (e.g., heat capacity) by adding a new method, once relevant data are available. Program summary Program title: pyHMA CPC Library link to program files: http://dx.doi.org/10.17632/bzgfk52msk.1 Licensing provisions: MPL-2.0 Programming language: Python 3.7 Nature of problem: Theormodynamic properties (e.g., energy, pressure, and heat capacity) of crystalline systems can be decomposed into: lattice (or, property at 0 K), quasiharmonic, and anharmonic contributions. Although the first two are feasible to compute using only a few single-point density functional theory (DFT) calculations, measuring anharmonic contribution requires running ab initio molecular dynamics (AIMD) simulation, which is computationally very demanding using direct ensemble averaging. Solution method: In pyHMA , we are adopting the harmonically mapped averaging (HMA) technique that provides order(s) of magnitude higher precision, in comparison to direct/conventional (Conv) averaging. The package works as a post-processor to VASP AIMD output to provide very precise (and accurate) estimate of anharmonic properties, for a given DFT model, with application to energy and pressure (at this time). Additional comments: The term anharmonicity is commonly used in literature to qualitatively describe a system with no equilibrium configuration at 0 K (i.e., imaginary frequencies); in other words, it refers to a “non-harmonic” potential-energy surface. Here, however, we define anharmonic contribution of some property X as the residual in excess of the harmonic approximation; X ah ≡ X − ( X lat + X qh ) . Therefore, this specific definition is meaningless if the system does not have equilibrium lattice configuration at 0 K. For this reason, pyHMA checks forces on the first configuration to make sure the system has an equilibrium configuration (i.e., zero forces). In addition, when using pyHMA to measure anharmonic free energy using thermodynamic integration from 0 K (Sec. 3.3), only ground-state DFT must be used; using finite-temperature DFT (i.e., Fermi–Dirac smearing; ISMEAR=-1 and SIGMA= k B T ), as often done with metals, cannot be used as the PES in this case is temperature-dependent, which is not accounted for in the integration. This contribution, however, can still be included using free-energy perturbation methods as described elsewhere [1]. On the other hand, for properties that do not require temperature integration (e.g., energy and pressure), pyHMA reads the electronic free-energy surface (F), rather than the ground-state energy (E0); hence, electronic contribution is accounted for.

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pyHMA：VASP 后处理器，用于使用谐波映射平均精确测量晶体非谐波特性

摘要 我们引入了一个新的 Python 包 (pyHMA)，它与 ​​VASP 接口，通过后处理来自 NVT Born-Oppenheimer ab initio 分子动力学 (AIMD) 模拟的数据来计算晶体系统的（经典）非谐特性。它基于最近开发的谐波映射平均 (HMA) 方法，该方法利用分析上已知的谐波行为来重新制定直接/常规集合平均值，以便在给定的 CPU 时间内显着提高精度。该包由两个阶段组成：从 vasprun.xml 文件中读取 AIMD 数据，然后计算非谐波属性。虽然第一阶段依赖于 MD 包，但第二阶段是通用的，因为它接收所需格式的数据。为了演示 pyHMA 的用法，我们计算了铝 fcc 晶体在高压 (≈ 115 GPa ) 和高达 4000 K（接近熔化）下的非谐波能量和压力。我们使用 HMA 非谐能的热力学积分进一步计算作为温度函数的非谐自由能。尽管 pyHMA 当前与 VASP 连接以计算 HMA 非谐波能量和压力，但它的模块化方式允许通过添加新读取器与其他代码（例如 LAMMPS）连接，并且可以计算其他 HMA 非谐波属性（例如，热容） ) 通过添加新方法，一旦相关数据可用。程序摘要 程序名称：pyHMA CPC 库程序文件链接：http://dx.doi.org/10.17632/bzgfk52msk.1 许可条款：MPL-2.0 编程语言：Python 3.7 问题性质：热力学性质（例如，能量、压力，和热容量）可以分解为：晶格（或 0 K 时的性质）、准谐波和非谐波贡献。尽管前两个可以仅使用一些单点密度泛函理论 (DFT) 计算进行计算，但测量非谐波贡献需要运行从头算分子动力学 (AIMD) 模拟，这在使用直接集成平均的计算上非常苛刻。解决方法：在 pyHMA 中，我们采用调和映射平均 (HMA) 技术，与直接/常规 (Conv) 平均相比，该技术提供了更高数量级的精度。该包作为 VASP AIMD 输出的后处理器，为给定的 DFT 模型提供非常精确（和准确）的非谐特性估计，并应用于能量和压力（此时）。附加评论：术语非谐性在文献中常用来定性描述在 0 K（即虚频率）下没有平衡配置的系统；换句话说，它指的是“非谐波”势能面。然而，在这里，我们将某些属性 X 的非调和贡献定义为超过调和近似的残差；X ah ≡ X − ( X lat + X qh ) 。因此，如果系统在 0 K 时没有平衡晶格配置，那么这个特定的定义是没有意义的。出于这个原因，pyHMA 检查第一个配置上的力以确保系统具有平衡配置（即零力）。此外，当使用 pyHMA 使用 0 K 的热力学积分测量非谐自由能时（第 3.3 节），必须仅使用基态 DFT；使用有限温度 DFT（即 , 费米-狄拉克涂抹；ISMEAR=-1 和 SIGMA= k BT )，正如通常对金属所做的那样，不能被使用，因为在这种情况下 PES 是温度相关的，这在积分中没有考虑在内。但是，仍然可以使用其他地方所述的自由能扰动方法来包括这种贡献 [1]。另一方面，对于不需要温度积分的性质（例如能量和压力），pyHMA 读取的是电子自由能面（F），而不是基态能量（E0）；因此，电子贡献被计算在内。仍然可以使用其他地方所述的自由能扰动方法 [1] 包括在内。另一方面，对于不需要温度积分的性质（例如能量和压力），pyHMA 读取的是电子自由能面（F），而不是基态能量（E0）；因此，电子贡献被计算在内。仍然可以使用其他地方所述的自由能扰动方法 [1] 包括在内。另一方面，对于不需要温度积分的性质（例如能量和压力），pyHMA 读取的是电子自由能面（F），而不是基态能量（E0）；因此，电子贡献被计算在内。