Department of Chemistry and Biochemistry, Brigham Young University, Provo, Utah 84602, USA.
J Phys Chem A. 2012 May 24;116(20):4922-9. doi: 10.1021/jp300633j. Epub 2012 May 11.
Here we present and test several computational prescriptions for calculating singlet-triplet (ST) gap energies and bond dissociation curves for open-shell singlet diradicals using economical unrestricted single reference type calculations. For ST gap energies from Slipchenko and Krylov's atom and molecule test set (C, O, Si, NH, NF, OH(+), O(2), CH(2), and NH(2)(+)) spin unrestricted Hartree-Fock and MP2 energies result in errors greater than 15 kcal/mol. However, spin-projected (SP) Hartree-Fock theory in combination with spin-component-scaled (SCS) or scaled-opposite-spin (SOS) second-order perturbation theory gives ST gap energies with a mean unsigned error (MUE) of less than 2 kcal/mol. Density functionals generally give poor results for unrestricted energies and only the ωB97X-D, the M06, and the M06-2X functionals provide reasonable accuracy after spin-projection with MUE values of 4.7, 4.3, and 3.0 kcal/mol, respectively, with the 6-311++G(2d,2p) basis set. We also present a new one parameter hybrid density functional, diradical-1 (DR-1), based on Adamo and Barone's modified PW exchange functional with the PW91 correlation functional. This DR-1 method gives a mean error (ME) of 0.0 kcal/mol and a MUE value of 1.3 kcal/mol for ST gap energies. As another test of unrestricted methods the bond dissociation curves for methane (CH(4)) and hydrofluoric acid (H-F) were calculated with the M06-2X, DR-1, and ωB97X-D density functionals. All three of these functionals give reasonable results for the methane C-H bond but result in errors greater than 50 kcal/mol for the H-F bond dissociation. Spin-projection is found to significantly degrade bond dissociation curves past ~2.2 Å. Although unrestricted Hartree-Fock theory provides a very poor description of H-F bond dissociation, unrestricted SCS-MP2 and SOS-MP2 methods give accurate results.
在这里，我们提出并测试了几种使用经济的非限制单参考类型计算来计算开壳单重态二自由基的单线态-三重态（ST）能隙和键离解曲线的计算方法。对于来自 Slipchenko 和 Krylov 的原子和分子测试集（C、O、Si、NH、NF、OH(+)、O(2)、CH(2)和 NH(2)(+)）的 ST 能隙能量，非限制哈特ree-fock 和 MP2 能量的误差大于 15 kcal/mol。然而，自旋投影（SP）哈特ree-fock 理论与自旋分量缩放（SCS）或缩放相反自旋（SOS）二阶微扰理论相结合，可以得到 ST 能隙能量，其平均未签名误差（MUE）小于 2 kcal/mol。密度泛函通常对非限制能量的结果很差，只有 ωB97X-D、M06 和 M06-2X 函数在自旋投影后提供合理的精度，MUE 值分别为 4.7、4.3 和 3.0 kcal/mol，使用 6-311++G(2d,2p)基组。我们还提出了一种新的基于 Adamo 和 Barone 修改后的 PW 交换函数与 PW91 相关函数的单参数混合密度泛函，即双自由基-1（DR-1）。该 DR-1 方法对于 ST 能隙能量的平均误差（ME）为 0.0 kcal/mol，MUE 值为 1.3 kcal/mol。作为非限制方法的另一个测试，使用 M06-2X、DR-1 和 ωB97X-D 密度泛函计算了甲烷（CH(4)）和氢氟酸（HF）的键离解曲线。这三种函数都对甲烷 C-H 键给出了合理的结果，但对 HF 键离解的误差大于 50 kcal/mol。自旋投影发现，在超过~2.2 Å 时，键离解曲线会显著恶化。尽管非限制哈特ree-fock 理论对 HF 键离解的描述非常差，但非限制 SCS-MP2 和 SOS-MP2 方法给出了准确的结果。
