Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. The resulting energy conservation in micro-canonical AIMD demonstrates that the implementation provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.

中文翻译：

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张量超收缩MP2和SOS-MP2在图形处理单元上的分析梯度

张量超收缩（THC）的解析能量梯度是针对二阶Møller-Plesset微扰理论（MP2）导出并实现的，其中有和没有按比例缩放的自旋（SOS）-MP2近似。通过利用THC分解，相对于系统大小，MP2和SOS-MP2梯度计算的形式缩放分别减少为四次和三次。已经开发出一种有效的实施方式，其利用图形处理单元和利用原子轨道的空间稀疏性的稀疏张量技术。THC-MP2已应用于几何优化和从头算起分子动力学（AIMD）模拟。在微规范AIMD中产生的能量守恒证明，该实现相对于THC-MP2势能面提供了准确的核梯度。