Active-space two-electron reduced-density-matrix method: Complete active-space calculations without diagonalization of the N-electron Hamiltonian
Active-space two-electron reduced-density-matrix method: Complete active-space calculations without diagonalization of the N-electron Hamiltonian
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DOI：
10.1063/1.2983652
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发表时间：
2008-10-07
影响因子：
4.4
通讯作者：
Mazziotti, David A.
中科院分区：
文献类型：
--
作者：
Gidofalvi, Gergely;Mazziotti, David A.
化学中的分子系统通常具有波函数，其实质贡献来自两个或两个以上的电子构型。由于传统的完全激活空间自洽场(CASSCF)方法与激活电子数N成指数关系，其适用范围仅限于小的激活空间。本文发展了一种活动空间变分双电子约化密度矩阵(2-RDM)方法，其中昂贵的对角化用变分2-RDM计算代替，其中2-RDM受近似N-表示条件的约束。约束2-RDM的优化是通过大规模半定规划[Mazziotti，Phys.莱特牧师。93,213001(2004年)]。由于活动空间2-RDM方法的计算量为r(A)(6)的多项式，其中r(A)是活动轨道的个数，因此该方法可用于处理对传统CASSCF来说太大的活动空间。活动空间2-RDM方法包括两个步骤：(1)活动空间2-RDM的变分计算；(2)通过雅可比旋转优化活动轨道。对于大的基集，这种两步2-RDM方法比一步、低阶变分2-RDM方法更有效[Gidofalvi和Mazziotti，J.Chem。太棒了。127、244105(2007年)]。将其应用于HF、H2O和N-2以及n=2-8的n-苯链。当n>；4时，不能用传统的CASSCF方法处理烯；例如，当n=8时，CASSCF需要对大约1.47x10(17)个配置状态函数进行优化。随着链长的增加，正戊二烯的自然占位数呈现出双自由基和多自由基特征。(C)2008年美国物理研究所。
Molecular systems in chemistry often have wave functions with substantial contributions from two-or-more electronic configurations. Because traditional complete-active-space self-consistent-field (CASSCF) methods scale exponentially with the number N of active electrons, their applicability is limited to small active spaces. In this paper we develop an active-space variational two-electron reduced-density-matrix (2-RDM) method in which the expensive diagonalization is replaced by a variational 2-RDM calculation where the 2-RDM is constrained by approximate N-representability conditions. Optimization of the constrained 2-RDM is accomplished by large-scale semidefinite programming [Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)]. Because the computational cost of the active-space 2-RDM method scales polynomially as r(a)(6) where r(a) is the number of active orbitals, the method can be applied to treat active spaces that are too large for conventional CASSCF. The active-space 2-RDM method performs two steps: (i) variational calculation of the 2-RDM in the active space and (ii) optimization of the active orbitals by Jacobi rotations. For large basis sets this two-step 2-RDM method is more efficient than the one-step, low-rank variational 2-RDM method [Gidofalvi and Mazziotti, J. Chem. Phys. 127, 244105 (2007)]. Applications are made to HF, H2O, and N-2 as well as n-acene chains for n=2-8. When n>4, the acenes cannot be treated by conventional CASSCF methods; for example, when n=8, CASSCF requires optimization over approximately 1.47x10(17) configuration state functions. The natural occupation numbers of the n-acenes show the emergence of bi- and polyradical character with increasing chain length. (C) 2008 American Institute of Physics.