Consider the problem of determining the optimal applied electric field to drive a molecule from an initial state to a desired target state. For even moderately sized molecules, solving this problem directly using the exact equations of motion -- the time-dependent Schr\"odinger equation (TDSE) -- is numerically intractable. We present a solution of this problem within time-dependent Hartree-Fock (TDHF) theory, a mean field approximation of the TDSE. Optimality is defined in terms of minimizing the total control effort while maximizing the overlap between desired and achieved target states. We frame this problem as an optimization problem constrained by the nonlinear TDHF equations; we solve it using trust region optimization with gradients computed via a custom-built adjoint state method. For three molecular systems, we show that with very small neural network parametrizations of the control, our method yields solutions that achieve desired targets within acceptable constraints and tolerances.

翻译：考虑确定最优外加电场以驱动分子从初始态演化至期望目标态的问题。对于中等尺寸的分子体系，直接使用时变薛定谔方程（TDSE）精确运动方程求解该问题在数值计算上是不可行的。我们基于时变哈特里-福克（TDHF）理论——即TDSE的平均场近似——提出了该问题的解决方案。最优性定义为在最大化期望目标态与实现态之间重叠度的同时最小化总控制能耗。我们将该问题构建为受非线性TDHF方程约束的优化问题，采用信赖域优化算法并结合基于自定义伴随状态法计算的梯度进行求解。针对三个分子体系的研究表明，即使采用极小规模的神经网络参数化控制场，我们的方法仍能在可接受的约束条件和容差范围内实现期望目标。