The particle-particle random phase approximation (pp-RPA) has been shown tobe capable of describing double, Rydberg, and charge transfer excitations, forwhich the conventional time-dependent density functional theory (TDDFT) mightnot be suitable. It is thus desirable to reduce the computational cost ofpp-RPA so that it can be efficiently applied to larger molecules and evensolids. This paper introduces an $O(N^3)$ algorithm, where $N$ is the number oforbitals, based on an interpolative separable density fitting technique and theJacobi-Davidson eigensolver to calculate a few low-lying excitations in thepp-RPA framework. The size of the pp-RPA matrix can also be reduced by keepingonly a small portion of orbitals with orbital energy close to the Fermi energy.This reduced system leads to a smaller prefactor of the cubic scalingalgorithm, while keeping the accuracy for the low-lying excitation energies.
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机译：粒子-粒子随机相位近似（pp-RPA）已被证明能够描述双重，里德堡和电荷转移激发，而常规的时变密度泛函理论（TDDFT）可能不适合。因此，希望降低pp-RPA的计算成本，以便可以将其有效地应用于较大的分子甚至固体。本文介绍了一种$ O（N ^ 3）$算法，其中$ N $是轨道数，它基于插值可分离密度拟合技术和Jacobi-Davidson特征求解器来计算pp-RPA框架中的一些低地激发。 pp-RPA矩阵的大小也可以通过只保留一小部分轨道能量接近费米能量的方法来减小，这种减小的系统导致三次定标算法的较小因数，同时保持低地势的精度激发能。
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