Exploiting the machinery of Constrained Density Functional Theory (CDFT), we propose a variational method for calculating low-lying excited states of molecular systems. We dub this method eXcited CDFT (XCDFT). Excited states are obtained by self-consistently constraining a user-defined population of electrons, N_c, in the virtual space of a reference set of occupied orbitals. By imposing this population to be N_c = 1.0, we computed the first excited state of 15 molecules from a test set. Our results show that XCDFT achieves an accuracy in the predicted excitation energy only slightly worse than linear-response time-dependent DFT (TDDFT), but without incurring into problems of variational collapse typical of the more commonly adopted ΔSCF method. In addition, we selected a few challenging processes to test the limits of applicability of XCDFT. We find that in contrast to TDDFT, XCDFT is capable of reproducing energy surfaces featuring conical intersections (azobenzene and H₃) with correct topology and correct overall energetics also away from the intersection. Venturing to condensed-phase systems, XCDFT reproduces the TDDFT solvatochromic shift of benzaldehyde when it is embedded by a cluster of water molecules. Thus, we find XCDFT to be a competitive method among single-reference methods for computations of excited states in terms of time to solution, rate of convergence, and accuracy of the result.

中文翻译：

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受约束DFT的低激发态

利用约束密度泛函理论（CDFT）的机制，我们提出了一种变分方法来计算分子系统的低激发态。我们将这种方法称为CDFT（XCDFT）。激发态是通过在被占领的轨道参考集中的虚拟空间中自洽地约束用户定义的电子团N _c来获得的。通过将此人口强加为N _c= 1.0，我们从测试集中计算了15个分子的第一个激发态。我们的结果表明，XCDFT在预测的激发能量上实现的精度仅稍差于线性响应时间相关的DFT（TDDFT），但不会引起更常用的ΔSCF方法典型的变化崩溃的问题。此外，我们选择了一些具有挑战性的过程来测试XCDFT的适用范围。我们发现，与TDDFT相比，XCDFT能够重现具有圆锥形相交点（偶氮苯和H ₃），并确保正确的拓扑结构和正确的整体能量学也远离交叉点。对于冷凝相系统而言，当XCDFT被一群水分子嵌入时，它会重现TDDFT苯甲醛的溶剂化变色。因此，在求解时间，收敛速度和结果的准确性方面，我们发现XCDFT是计算激发态的单参考方法中的一种竞争方法。