Encoding the electronic structure of molecules using 2-electron reduced density matrices (2RDMs) as opposed to many-body wave functions has been a decades-long quest as the 2RDM contains sufficient information to compute the exact molecular energy but requires only polynomial storage. We focus on linear polymers with varying conformations and numbers of monomers and show that we can use machine learning to predict both the 1-electron and the 2-electron reduced density matrices. Moreover, by applying the Hamiltonian operator to the predicted reduced density matrices we show that we can recover the molecular energy. Thus, we demonstrate the feasibility of a machine learning approach to predicting electronic structure that is generalizable both to new conformations as well as new molecules. At the same time our work circumvents the N-representability problem that has stymied the adaption of 2RDM methods, by directly machine-learning valid Reduced Density Matrices.
翻译:利用2-电子降低密度矩阵(2RDMs)而不是多体波函数对分子的电子结构进行编码是一项长达数十年的探索,因为2RDM包含足够的信息来计算精确的分子能量,但只需要多分子存储。我们侧重于线性聚合物,其单质体的分质和数量各不相同,并表明我们可以利用机器学习来预测1-电子和2-电子降低密度矩阵。此外,通过将汉密尔顿操作员应用到预测的降低密度矩阵,我们证明我们可以恢复分子能量。因此,我们展示了一种机器学习方法的可行性,用以预测电子结构,既可以适用于新的相容性,也可以适用于新的分子。与此同时,我们的工作通过直接学习有效的降低密度矩阵,避免了对2RDM方法的调适性。