Complete-graph tensor network states: a new fermionic wave function ansatz for molecules
Complete-graph tensor network states: a new fermionic wave function ansatz for molecules
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DOI：
10.1088/1367-2630/12/10/103008
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发表时间：
2010-10-05
影响因子：
3.3
通讯作者：
Verstraete, Frank
中科院分区：
文献类型：
--
作者：
Marti, Konrad H.;Bauer, Bela;Verstraete, Frank
我们提出了一类张量网络状态，专门用于捕获任意结构分子内的电子相关性。在这个分析中，电子波函数用一个完全图张量网络（CGTN）分析来表示，该分析通过分解全构型相互作用（FCI）波函数的高维系数张量的复杂性，实现了变分参数数量的有效减少。这种应用于分子的分析方法是一种新的方法，它基于最近在晶格问题中研究的张量网络波函数。我们通过比较CGTN和FCI的膨胀系数证明了CGTN状态与分子基态的近似性。与许多标准量子化学方法相比，CGTN参数化不偏向于任何参考构型。这一特性使人们能够获得CGTN状态之间精确的相对能量，这是分子物理和化学的核心。我们讨论了量子化学的意义，并重点讨论了自旋态问题。我们的CGTN方法应用于亚甲基和强相关臭氧分子在过渡态结构上的不同自旋态的能量分裂。采用并行回火蒙特卡罗算法对张量网络分析参数进行变分优化。
We present a class of tensor network states specifically designed to capture the electron correlation within a molecule of arbitrary structure. In this ansatz, the electronic wave function is represented by a complete-graph tensor network (CGTN) ansatz, which implements an efficient reduction of the number of variational parameters by breaking down the complexity of the high-dimensional coefficient tensor of a full-configuration-interaction (FCI) wave function. This ansatz applied to molecules is new and based on a tensor network wave function recently studied in lattice problems. We demonstrate that CGTN states approximate ground states of molecules accurately by comparison of the CGTN and FCI expansion coefficients. The CGTN parametrization is not biased towards any reference configuration, in contrast to many standard quantum chemical methods. This feature allows one to obtain accurate relative energies between CGTN states, which is central to molecular physics and chemistry. We discuss the implications for quantum chemistry and focus on the spin-state problem. Our CGTN approach is applied to the energy splitting of states of different spins for methylene and the strongly correlated ozone molecule at a transition state structure. The parameters of the tensor network ansatz are variationally optimized by means of a parallel-tempering Monte Carlo algorithm.