Dipartimento di Chimica IFM and Centre of Excellence NIS (Nanostructured Interfaces and Surfaces), Università di Torino, via P. Giuria 5, I-10125 Torino, Italy.
J Chem Phys. 2012 Jul 28;137(4):044114. doi: 10.1063/1.4737419.
In the frame of the Born-Oppenheimer approximation, nuclear motions in crystals can be simulated rather accurately using a harmonic model. In turn, the electronic first-order density matrix (DM) can be expressed as the statistically weighted average over all its determinations each resulting from an instantaneous nuclear configuration. This model has been implemented in a computational scheme which adopts an ab initio one-electron (Hartree-Fock or Kohn-Sham) Hamiltonian in the CRYSTAL program. After selecting a supercell of reasonable size and solving the corresponding vibrational problem in the harmonic approximation, a Metropolis algorithm is adopted for generating a sample of nuclear configurations which reflects their probability distribution at a given temperature. For each configuration in the sample the "instantaneous" DM is calculated, and its contribution to the observables of interest is extracted. Translational and point symmetry of the crystal as reflected in its average DM are fully exploited. The influence of zero-point and thermal motion of nuclei on such important first-order observables as x-ray structure factors and Compton profiles can thus be estimated.
在玻恩-奥本海默近似框架下，可以使用谐波模型相当准确地模拟晶体中的核运动。反过来，电子一阶密度矩阵（DM）可以表示为所有确定的统计加权平均值，每个确定结果都来自于瞬时核构型。该模型已在计算方案中实现，该方案在 CRYSTAL 程序中采用了从头算单电子（哈特ree-fock 或 Kohn-Sham）哈密顿量。选择合理大小的超胞并在谐波近似下求解相应的振动问题后，采用 Metropolis 算法生成核构型的样本，该样本反映了在给定温度下的概率分布。对于样本中的每个构型，计算“瞬时”DM，并提取其对感兴趣的观测值的贡献。晶体的平移和点对称性在其平均 DM 中得到了充分体现。因此，可以估计原子核的零点能和热运动对 x 射线结构因子和康普顿轮廓等重要一阶观测值的影响。
