We present a new nonlinear variational framework for simultaneously computing ground and excited states of quantum systems. Our approach is based on approximating wavefunctions in the linear span of basis functions that are augmented and optimized \emph{via} composition with normalizing flows. The accuracy and efficiency of our approach are demonstrated in the calculations of a large number of vibrational states of the triatomic H$_2$S molecule as well as ground and several excited electronic states of prototypical one-electron systems including the hydrogen atom, the molecular hydrogen ion, and a carbon atom in a single-active-electron approximation. The results demonstrate significant improvements in the accuracy of energy predictions and accelerated basis-set convergence even when using normalizing flows with a small number of parameters. The present approach can be also seen as the optimization of a set of intrinsic coordinates that best capture the underlying physics within the given basis set.

翻译：我们提出了一种新的非线性变分框架，用于同时计算量子系统的基态和激发态。该方法基于在基函数的线性张成空间中近似波函数，这些基函数通过与归一化流的复合运算进行增强和优化。通过在多个体系上的计算验证了该方法的准确性和效率，包括：三原子H₂S分子的大量振动能级，以及典型单电子系统（氢原子、氢分子离子和单活性电子近似下的碳原子）的基态和若干激发电子态。结果表明，即使是使用少量参数的归一化流，能量预测的准确性也得到显著提升，且加快了基组收敛速度。该方法亦可视为对一组内禀坐标的优化，这些坐标能够在给定基组框架下最佳地捕捉底层物理特性。