Development of a linear-scaling MP2 method for large molecules by rigorous integral criteria

电子相关效应，特别是色散效应对于许多分子体系的量子化学计算是至关重要的。然而，即使是最简单的从头计算方法——二阶Møller-Plesset微扰理论（MP2）——的计算量也是分子大小的五次方，这使得传统方法无法应用于50-100个以上的原子。因此，减少缩放是至关重要的。虽然有几个小组在这方面取得了令人印象深刻的进展，但到目前为止，还没有严格的方法来预先选择对相关能有重大贡献的数字，因此，影响精度的特殊假设是必要的，或者计算工作的前因子太大。在我们的工作中，我们引入了第一个严格的上界（多极积分估计；MBIE），它允许预先选择对MP2能量的重要贡献，而无需进一步的假设。通过这种方式，保证了与传统方法相同的准确性和可靠性，并结合了获得线性缩放计算行为的可能性。基于这一想法，本研究计划的主要目标是开发一种线性缩放MP2方法，该方法可以可靠地计算具有500-1000个及更多原子（不对称）的分子的MP2能量，从而可以在大分子系统中解释色散型相互作用。

Electron-correlation and in particular dispersion-type effects are crucial for the quantum-chemical calculation of many molecular systems. However, the computational effort of even the simplest ab initio approach accounting for these effects —second-order Møller-Plesset perturbation theory (MP2) — scales with the fifth power of molecular size, which prohibits the application of conventional approaches to more than 50–100 atoms. Therefore, the reduction of the scaling is crucial. Although impressive progress has been made by several groups towards this goal, there has been so far no rigorous way of preselecting numerically significant contributions to the correlation energy, so that either ad-hoc assumptions influencing the accuracy were necessary or the prefactors of the computational effort have been too large. In our work, we have introduced the first rigorous upper bounds (multipole-based integral estimates; MBIE) which allow to preselect the significant contributions to the MP2 energy without further assumptions. In this way, the same accuracy and reliability as in conventional approaches is guaranteed, combined with the possibility to attain a linear-scaling computational behavior. Based on this idea, the main goal of the present research proposal is the development of a linear-scaling MP2 method, which allows for the reliable computation of MP2 energetics for molecules with 500-1000 and more atoms (without symmetry), so that dispersion-type interactions can be accounted for in large molecular systems.