We derive analytic energy gradients of the driven similarity renormalization group (DSRG) multireference second-order perturbation theory (MRPT2) using the method of Lagrange multipliers. In the Lagrangian, we impose constraints for a complete-active-space self-consistent-field reference wave function and the semicanonical orthonormal molecular orbitals. Solving the associated Lagrange multipliers is found to share the same asymptotic scaling of a single DSRG-MRPT2 energy computation. A pilot implementation of the DSRG-MRPT2 analytic gradients is used to optimize the geometry of the singlet and triplet states of p-benzyne. The equilibrium bond lengths and angles are similar to those computed via other MRPT2s and Mukherjee's multireference coupled cluster theory. An approximate DSRG-MRPT2 method that neglects the contributions of three-body density cumulant is found to introduce negligible errors in the geometry of p-benzyne, lending itself to a promising low-cost approach for molecular geometry optimizations using large active spaces.
Improving the efficiency of the multireference driven similarity renormalization group via sequential transformation, density fitting, and the non-interacting virtual orbital approximation
Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics
Analytical Gradient Theory for Spin-Free State-Averaged Second-Order Driven Similarity Renormalization Group Perturbation Theory (SA-DSRG-MRPT2) and Its Applications for Conical Intersection Optimizations
A driven similarity renormalization group approach to quantum many-body problems
相似重整化群（SRG）方法的应用[F. Wegner，Ann.Phys.506，77（1994），S. D. Gadhazek和K. G. Wilson，Phys.Rev.D49，4214（1994）]对建立有用的电子关联多体理论的重要作用。除了提出一个生产级实现的SRG的基础上的单参考形式主义，一个新的积分版本的SRG的报告，其中的流动的哈密顿是由一个源操作。结果表明，这种驱动SRG（DSRG）产生的哈密顿流是类似的SRG。与需要传播一组常微分方程的SRG相比，DSRG在计算上是有利的，因为它由一组多项式方程组成。用一体和二体正规有序算符近似的SRG和DSRG计算了一系列双原子分子的平衡距离、谐波振动频率和振动非谐性，与单重、双重和微扰三重耦合团簇的基准值[CCSD（T）]吻合得很好.当SRG和DSRG方法应用于C $_2$和F $_2$时，发现了特别令人惊讶的结果。在前一种情况下，两种方法都不能收敛，而在后一种情况下，得到的是一条未结合的势能曲线。一个修改的换向器近似示出的DSRG方法的情况下，以纠正这些问题。
Renormalization group approach to second-order Green's function theory
University of Münster（明斯特大学）；Center for Multiscale Theory and Computation, University of Münster（明斯特大学多尺度理论与计算中心）；University of Hamburg（汉堡大学）；The Hamburg Centre for Ultrafast Imaging (CUI)（汉堡超快成像中心）
