Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA.
J Chem Phys. 2018 Apr 14;148(14):144103. doi: 10.1063/1.5018615.
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, in the virtual space of a reference set of occupied orbitals. By imposing this population to be N = 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 H) 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.
我们利用约束密度泛函理论（CDFT）的原理，提出了一种计算分子体系低激发态的变分方法。我们将这种方法称为激发 CDFT（XCDFT）。通过在参考占据轨道的虚拟空间中自洽地约束用户定义的电子数 N，可以得到激发态。通过将这个电子数限制为 N = 1.0，我们计算了测试集中 15 个分子的第一激发态。结果表明，XCDFT 在预测激发能方面的准确性仅略逊于线性响应时间依赖密度泛函理论（TDDFT），但不会出现更常用的ΔSCF 方法中常见的变分崩溃问题。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 能够重现具有正确拓扑结构和正确整体能量的锥形交叉（偶氮苯和 H）的能面，即使在交叉点之外也是如此。在进入凝聚相体系时，XCDFT 能够重现苯甲醛在被水分子簇嵌入时的 TDDFT 溶剂化变色。因此，我们发现 XCDFT 在激发态计算方面，无论是求解时间、收敛速度还是结果的准确性，都是一种具有竞争力的单参考方法。
