Semiempirical hybrid density functional with perturbative second-order correlation
Semiempirical hybrid density functional with perturbative second-order correlation
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DOI：
10.1063/1.2148954
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发表时间：
2006-01-21
影响因子：
4.4
通讯作者：
Grimme, S
中科院分区：
文献类型：
--
作者：
Grimme, S
提出了一种新的适用于一般化学的杂化密度泛函。它是基于一个混合的标准广义梯度近似（GGA）的交换由贝克（B）和相关的李，杨，和帕尔（LYP）与Hartree-Fock（HF）交换和微扰的二阶相关部分（PT 2），从科恩-沙姆（GGA）轨道和本征值。该虚轨道依赖泛函仅包含两个全局参数，分别描述HF和GGA交换的混合物（a（x））和PT 2和GGA相关性的混合物（c）。这些参数是通过G2/97地层热集的最小二乘拟合程序获得的。与传统的杂化泛函相反，发现最佳a（x）相当大（53%，c=27%），这至少部分解释了与传统方法相比许多有问题的分子系统的成功。新的功能称为B2-PLYP的性能进行评估的G2/97标准基准集，第二个测试套件的原子，分子和反应，被认为是电子上非常困难的（包括过渡金属化合物，弱键合配合物，反应障碍）和比较与其他混合功能的GGA和元GGA类型。根据许多实际测试，B2-PLYP可以被认为是分子的最佳通用密度泛函（例如，两个测试组的平均绝对偏差仅为1.8和3.2千卡/摩尔，相比之下，最佳的其它密度泛函分别为约3和5千卡/摩尔）。非常重要的是，最大和最小误差（异常值）也大大减少（约10-20 kcal/mol）。此外，对于过渡态势垒获得了非常好的结果，但与以前在这样一个良好的描述中的尝试不同，这肯定不是以牺牲平衡性质为代价的。对双原子分子和过渡金属配合物的平衡键长和谐波振动频率的初步计算也显示出很有希望的结果。B2-PLYP的均匀性提高了广泛的化学系统强调需要（虚拟）轨道相关的条款，描述非本地电子相关的准确交换相关泛函。从实用的角度来看，新的功能似乎是非常强大的，因此建议作为一个有效的量子化学方法的通用。
A new hybrid density functional for general chemistry applications is proposed. It is based on a mixing of standard generalized gradient approximations (GGAs) for exchange by Becke (B) and for correlation by Lee, Yang, and Parr (LYP) with Hartree-Fock (HF) exchange and a perturbative second-order correlation part (PT2) that is obtained from the Kohn-Sham (GGA) orbitals and eigenvalues. This virtual orbital-dependent functional contains only two global parameters that describe the mixture of HF and GGA exchange (a(x)) and of the PT2 and GGA correlation (c), respectively. The parameters are obtained in a least-squares-fit procedure to the G2/97 set of heat of formations. Opposed to conventional hybrid functionals, the optimum a(x) is found to be quite large (53% with c=27%) which at least in part explains the success for many problematic molecular systems compared to conventional approaches. The performance of the new functional termed B2-PLYP is assessed by the G2/97 standard benchmark set, a second test suite of atoms, molecules, and reactions that are considered as electronically very difficult (including transition-metal compounds, weakly bonded complexes, and reaction barriers) and comparisons with other hybrid functionals of GGA and meta-GGA types. According to many realistic tests, B2-PLYP can be regarded as the best general purpose density functional for molecules (e.g., a mean absolute deviation for the two test sets of only 1.8 and 3.2 kcal/mol compared to about 3 and 5 kcal/mol, respectively, for the best other density functionals). Very importantly, also the maximum and minium errors (outliers) are strongly reduced (by about 10-20 kcal/mol). Furthermore, very good results are obtained for transition state barriers but unlike previous attempts at such a good description, this definitely comes not at the expense of equilibrium properties. Preliminary calculations of the equilibrium bond lengths and harmonic vibrational frequencies for diatomic molecules and transition-metal complexes also show very promising results. The uniformity with which B2-PLYP improves for a wide range of chemical systems emphasizes the need of (virtual) orbital-dependent terms that describe nonlocal electron correlation in accurate exchange-correlation functionals. From a practical point of view, the new functional seems to be very robust and it is thus suggested as an efficient quantum chemical method of general purpose.