We propose an exact algorithm for computing the analytical gradient within the framework of the orbital-specific-virtual (OSV) second-order Møller-Plesset (MP2) theory in resolution-of-identity (RI) approximation. We implement the exact relaxation of perturbed OSVs through the explicit constraints of the perturbed orthonormality, the perturbed diagonality and the perturbed singular value condition. We explicitly show that the rotation of OSVs within the retained OSV subspace makes no contribution to gradients, as long as the iterative solution of the unperturbed Hylleraas residual equation is well converged. The OSV relaxation is solved as the perturbed non-degenerate singular value problem between the retained and discarded OSV subspaces. The detailed derivation and preliminary implementations for gradient working equations are discussed. The coupled-perturbed localization method is implemented for meta-Löwdin localization function. The numerical accuracy of computed OSV-MP2 gradients is demonstrated for the geometries of selected molecules that are often discussed in other theories. Moreover, the OSV-MP2 analytical gradients can generate atomic forces that are utilized to drive the Born-Oppenheimer molecular dynamics (BOMD) simulation for studying structural and vibrational properties with respect to OSV selections. By performing the OSV-MP2 NVE BOMD calculation using the normal OSV selection, the structural and vibrational details of protonated water cations are well reproduced. The 200 picoseconds NVT well-tempered metadynamics at 300 K has been simulated to compute the OSV-MP2 rotational free energy surface of coupled hydroxyl and methyl rotors for ethanol molecule.
Third-order many-body expansion of OSV-MP2 wavefunction for low-order scaling analytical gradient computation
我们提出了一种多体展开（MBE）公式和实现，用于基于我们早期的工作（Zhou等人，J. Chem. Theory Comput. 2020，16，196-210）。OSV-MP2波函数的三阶MBE（3）展开采用了轨道特定的成簇和长程终止方案，避免了MBE能体的逐项微分。我们实现了更好的效率，利用算法的稀疏性，允许修剪出无关紧要的拟合积分和OSV松弛。利用这些近似，本实施方式在一系列分子上进行基准测试，这些分子分别在用于计算MBE（3）-OSV-MP2振幅和梯度方程的线性和二次方案中显示经济缩放，并且产生与原始OSV-MP2结果相当的正常精度。通过共享存储器单侧通信的基于MPI-3的并行性被进一步开发，以通过将MBE（3）轨道簇分类为分布在跨许多节点的多个进程上的独立任务来改善并行可扩展性和存储器可访问性，支持全局和局部数据位置，其中区分并相应地放置不同大小的所选MBE（3）-OSV-MP2中间体。我们的MBE（3）-OSV-MP2分析梯度实现的准确性和效率水平最终在两个应用中得到了说明：我们表明，当调节配体长度时，可以区分机械互锁的Cu-索烃络合物的细微配位结构差异;并且卟啉分子动力学揭示了由与氢转移相关的软化N-H伸缩引起的振动特征的出现，第一次使用MP2水平的电子相关和经典核。
Analytical evaluation of relativistic molecular integrals. III. Computation and results for molecular auxiliary functions
本文给出了计算非整数主量子数的Slater型轨道上分子积分的全解析方法。这些积分是通过我们以前的论文中导出的相对论分子辅助函数表示的[Phys. Rev. E 91，023303（2015）]。详细介绍了分子辅助函数的计算过程。它适用于相对论和非相对论电子结构理论。它能够产生高度精确的分子积分的轨道参数和量子数的所有范围。
Analytical evaluation of relativistic molecular integrals. I. Auxiliary functions
辅助功能提供了有效的计算积分产生的自洽场（SCF）水平的分子使用斯莱特型基地。这适用于相对论和非相对论电子结构理论。本文详细讨论了在我们以前的论文[Phys. Rev. E 91，023303（2015）]中推导出的相对论分子辅助函数。在本研究中提出了两种解决方法。首先用不完全Beta函数的收敛级数表示代替病态的二项式级数表示公式，然后通过引入一个额外的参数来扩展收敛域，从而改进了病态的二项式级数表示公式。通过本研究中讨论的程序可以实现高度精确的积分结果，该程序在所有轨道参数范围内对量子数也没有限制。因此，在r=0的复分析意义上的非解析的非整数Slater型轨道获得解析关系的困难被消除了。
The Truncated Conjugate Gradient (TCG), a Non-iterative/Fixed-cost Strategy for Computing Polarization in Molecular Dynamics: Fast Evaluation of Analytical Forces
Sorbonne Universités, UPMC Univ. Paris 06（索邦大学，巴黎第六大学）
Can tunneling current in molecular junctions be so strongly temperature dependent to challenge a hopping mechanism? Analytical formulas answer this question and provide important insight into large area junctions
On the divergence of time-dependent perturbation theory applied to laser-induced molecular transitions: Analytical calculations for the simple algorithm
