Frozen Natural Orbitals for the State-Averaged Driven Similarity Renormalization Group

We present a reduced-cost implementation of the state-averaged driven similarity renormalization group (SA-DSRG) based on the frozen natural orbital (FNO) approach. The natural orbitals (NOs) are obtained by diagonalizing the one-body reduced density matrix from SA-DSRG second-order perturbation theory (SA-DSRG-PT2). We consider three criteria to truncate the virtual NOs for the subsequent electron correlation treatment beyond SA-DSRG-PT2. An additive second-order correction is applied to the SA-DSRG Hamiltonian to reintroduce correlation effects from the discarded orbitals. The FNO SA-DSRG method is benchmarked on 35 small organic molecules in the QUEST database. When keeping 98–99% of the cumulative occupation numbers, the mean absolute error in the vertical transition energies due to FNO is less than 0.01 eV. Using the same FNO threshold, we observe a speedup of 9 times compared to the conventional SA-DSRG implementation for nickel carbonyl with a quadruple-ζ basis set. The FNO approach enables nonperturbative SA-DSRG computations on chloroiron corrole [FeCl(C19H11N4)] with more than 1000 basis functions, surpassing the current limit of a conventional implementation.

本研究提出了一种基于冻结自然轨道（Frozen Natural Orbital, FNO）方法的降本实现方案，用于态平均驱动相似性重整化群（State-Averaged Driven Similarity Renormalization Group, SA-DSRG）。自然轨道（Natural Orbitals, NOs）通过对角化源自SA-DSRG二阶微扰理论（SA-DSRG-PT2）的一体约化密度矩阵得到。针对SA-DSRG-PT2之后的电子关联校正步骤，我们采用三项判据截断虚空间自然轨道。我们向SA-DSRG哈密顿量引入附加二阶校正项，以重新引入被截断轨道所携带的电子关联效应。本研究基于QUEST数据库中的35种小型有机分子对FNO-SA-DSRG方法进行了基准测试。当保留98%~99%的累积占据数时，由FNO近似导致的垂直跃迁能平均绝对误差小于0.01 eV。采用相同的FNO截断阈值时，针对使用四重ζ基组的羰基镍体系，本方案相较传统SA-DSRG实现方案获得了9倍的加速比。FNO方法使得针对拥有超过1000个基函数的氯铁咔咯[FeCl(C19H11N4)]的非微扰SA-DSRG计算成为可能，突破了传统实现方案的计算极限。