Department of Chemistry and Supercomputing Institute, University of Minnesota, 207 Pleasant Street S.E., Minneapolis, MN 55455-0431, USA.
J Chem Phys. 2011 Jul 28;135(4):044118. doi: 10.1063/1.3607312.
A database containing 17 multiplicity-changing valence and Rydberg excitation energies of p-block elements is used to test the performance of density functional theory (DFT) with approximate density functionals for calculating relative energies of spin states. We consider only systems where both the low-spin and high-spin state are well described by a single Slater determinant, thereby avoiding complications due to broken-symmetry solutions. Because the excitations studied involve a spin change, they require a balanced treatment of exchange and correlation, thus providing a hard test for approximate density functionals. We test three formalisms for predicting the multiplicity-changing transition energies. First is the ΔSCF method; we also test time-dependent density functional theory (TDDFT), both in its conventional form starting from the low-spin state and in its collinear spin-flip form starting from the high-spin state. Very diffuse basis functions are needed to give a qualitatively correct description of the Rydberg excitations. The scalar relativistic effect needs to be considered when quantitative results are desired, and we include it in the comparisons. With the ΔSCF method, most of the tested functionals give mean unsigned errors (MUEs) larger than 6 kcal/mol for valence excitations and MUEs larger than 3 kcal/mol for Rydberg excitations, but the performance for the Rydberg states is much better than can be obtained with time-dependent DFT. It is surprising to see that the long-range corrected functionals, which have 100% Hartree-Fock exchange at large inter-electronic distance, do not improve the performance for Rydberg excitations. Among all tested density functionals, ΔSCF calculations with the O3LYP, M08-HX, and OLYP functionals give the best overall performance for both valence and Rydberg excitations, with MUEs of 2.1, 2.6, and 2.7 kcal/mol, respectively. This is very encouraging since the MUE of the CCSD(T) coupled cluster method with quintuple zeta basis sets is 2.0 kcal/mol; however, caution is advised since many popular density functionals give poor results, and there can be very significant differences between the ΔSCF predictions and those from TDDFT.
使用包含 17 个 p 区元素多重态变化价态和里德堡激发能的数据库来测试密度泛函理论（DFT）使用近似密度泛函计算自旋态相对能量的性能。我们仅考虑低自旋态和高自旋态都可以用单个斯莱特行列式很好地描述的系统，从而避免由于对称破缺解引起的复杂性。由于所研究的激发涉及自旋变化，因此需要对交换和相关进行平衡处理，从而为近似密度泛函提供了严格的测试。我们测试了三种用于预测多重态变化跃迁能的理论方法。首先是ΔSCF 方法；我们还测试了时变密度泛函理论（TDDFT），包括从低自旋态开始的传统形式和从高自旋态开始的共线自旋翻转形式。为了对里德堡激发进行定性正确的描述，需要使用非常弥散的基函数。当需要定量结果时，需要考虑相对论效应，我们将其包含在比较中。使用ΔSCF 方法，对于价态激发，大多数测试的泛函的平均未签名误差（MUE）大于 6 kcal/mol，对于里德堡激发，MUE 大于 3 kcal/mol，但对于里德堡态的性能要好得多，这比时变密度泛函要好。令人惊讶的是，在长程校正泛函中，在大电子距离处具有 100% Hartree-Fock 交换，并没有改善里德堡激发的性能。在所测试的所有密度泛函中，使用 O3LYP、M08-HX 和 OLYP 泛函的 ΔSCF 计算对价态和里德堡激发都具有最佳的整体性能，MUE 分别为 2.1、2.6 和 2.7 kcal/mol。这非常令人鼓舞，因为使用 quintuple zeta 基组的 CCSD(T)耦合簇方法的 MUE 为 2.0 kcal/mol；然而，需要谨慎，因为许多流行的密度泛函给出了较差的结果，并且 ΔSCF 预测和 TDDFT 预测之间可能存在非常显著的差异。
