Department of Chemical and Biological Engineering , University of Colorado Boulder , Boulder , Colorado 80309 , United States.
J Chem Theory Comput. 2018 Nov 13;14(11):5904-5919. doi: 10.1021/acs.jctc.8b00460. Epub 2018 Oct 26.
We present a novel approach to efficiently implement thermal expansion in the quasi-harmonic approximation (QHA) for both isotropic and more importantly, anisotropic expansion. In this approach, we rapidly determine a crystal's equilibrium volume and shape at a given temperature by integrating along the gradient of expansion from 0 Kelvin up to the desired temperature. We compare our approach to previous isotropic methods that rely on a brute-force grid search to determine the free energy minimum, which is infeasible to carry out for anisotropic expansion, as well as quasi-anisotropic approaches that take into account the contributions to anisotropic expansion from the lattice energy. We compare these methods for experimentally known polymorphs of piracetam and resorcinol and show that both isotropic methods agree to within error up to 300 K. Using the Grüneisen parameter causes up to 0.04 kcal/mol deviation in the Gibbs free energy, but for polymorph free energy differences there is a cancellation in error with all isotropic methods within 0.025 kcal/mol at 300 K. Anisotropic expansion allows the crystals to relax into lattice geometries 0.01-0.23 kcal/mol lower in energy at 300 K relative to isotropic expansion. For polymorph free energy differences all QHA methods produced results within 0.02 kcal/mol of each other for resorcinol and 0.12 kcal/mol for piracetam, the two molecules tested here, demonstrating a cancellation of error for isotropic methods. We also find that with expansion in more than a single volume variable, there is a non-negligible rate of failure of the basic approximations of QHA. Specifically, while expanding into new harmonic modes as the box vectors are increased, the system often falls into alternate, structurally distinct harmonic modes unrelated by continuous deformation from the original harmonic mode.
我们提出了一种新颖的方法，可在各向同性和更重要的各向异性扩展的准谐近似（QHA）中有效地实现热膨胀。在这种方法中，我们通过从 0 开尔文沿扩展梯度积分到所需温度，快速确定给定温度下晶体的平衡体积和形状。我们将我们的方法与以前的各向同性方法进行了比较，这些方法依赖于暴力网格搜索来确定自由能最小值，这对于各向异性扩展是不可行的，也与准各向异性方法进行了比较，这些方法考虑了晶格能对各向异性扩展的贡献。我们比较了这些方法对已知实验性吡拉西坦和间苯二酚多晶型物的应用，并表明两种各向同性方法在 300 K 以内的误差范围内均一致。使用格林艾森参数会导致吉布斯自由能的偏差高达 0.04 kcal/mol，但对于多晶型物自由能差，在 300 K 时，所有各向同性方法的误差都会相互抵消，误差在 0.025 kcal/mol 以内。各向异性扩展允许晶体在 300 K 时相对于各向同性扩展松弛到晶格几何形状，能量降低 0.01-0.23 kcal/mol。对于多晶型物自由能差，所有 QHA 方法对于间苯二酚的结果在 0.02 kcal/mol 以内，对于吡拉西坦的结果在 0.12 kcal/mol 以内，这是这里测试的两种分子，表明各向同性方法的误差相互抵消。我们还发现，在扩展到多个体积变量时，QHA 的基本近似值会出现不可忽略的失败率。具体来说，当增加盒子向量以扩展到新的调和模式时，系统经常会陷入与原始调和模式无关的交替、结构上不同的调和模式。
