Hybrid DFT,

The Onsager model describes the system as a molecule with a multipole moment inside of a spherical cavity surrounded by a continuum dielectric. In some programs, only a dipole moment is used so the calculation fails for molecules with a zero dipole moment. Results with the Onsager model and HF calculations are usually qualitatively correct. The accuracy increases significantly with the use of MP2 or hybrid DFT functionals. This is not the most accurate method available, but it is stable and fast. This makes the Onsager model a viable alternative when PCM calculations fail. 

Alkorta, I., Elguero, J., 1998, Ab Initio Hybrid DFT-GIAO Calculations of the Shielding Produced by Carbon-Carbon Bonds and Aromatic Rings in H NMR Spectroscopy , New J. Chem., 381. 

Ujaque G, Maseras F (2004) Applications of Hybrid DFT/Molecular Mechanics to Homogeneous Catalysis 112 117-149 Umemoto K, see Saito S (2004) 109 41-57... 

Since a systematic study of this point is still missing, we investigated the performances of different computational approaches through geometry optimizations of the H2Si(Cp)2ZrCH3+ species with different pure and hybrid DFT functionals, and at the HF and MP2 level of theory. The main geometrical parameters are reported in Table 1. 

On the other hand, high-level computational methods are limited, for obvious reasons, to very simple systems.122 Calculations are likely to have limited accuracy due to basis set effects, relativistic contributions, and spin orbit corrections, especially in the case of tin hydrides, but these concerns can be addressed. Given the computational economy of density functional theories and the excellent behavior of the hybrid-DFT B3LYP123 already demonstrated for calculations of radical energies,124 we anticipate good progress in the theoretical approach. We hope that this collection serves as a reference for computational work that we are certain will be forthcoming. 

The hybrid DFT methods used here are B3LYP (35,36), PBEIPBE 39,40,47), mPWlPW91 37), and MPWIK 38). The ab initio methods discussed in this article include HF, MP4SDQ 44), and QCISD(T) (27). We consider only one pure DFT method, namely BLYP 48,49). 

Table 5 gives the errors for a DFT method, four hybrid DFT methods, and AMI. Although hybrid DFT is very affordable, it lacks the accuracy of multicoefficient semi-empirical methods based on explicitly correlated wave fiinctions. Nevertheless the mPWlPW91/MG3S and AMI methods have performance/cost characteristics that put them near the envelope of best performance in Figure 1. AMI is valuable for larger systems where the other methods in the figure are not affordable. 

Publication Date March 13, 2007 doi 10.1021/bk-2007-0958.ch009 Table 5. Mean Unsigned Errors (kcal/mol), Root-Mean-Square Errors, and Times for hybrid DFT and DPT Methods and AMI at QCISD/MG3 Geometries ... 

Figure /. A/eaAi unsigned error over all 202 data vs. gradient cost for AMI (m), ab initio (U), CBS (k), G3 (O), MCCM (m), DFT (V), and hybrid DFT (A) methods. The figure includes all the methods that are included in Tables 3-5.

Figure 2. (a) PSDs for 3.88 nm MCM-41 [22] calculated from nitrogen adsorption data at 77 K using i) the KJS approach with the BJH algorithm, ii) the hybrid DFT method, iii) the HK-based method with the relation between pore size and condensation pressure described by Eq. 2, and iv) the HK-based Saito-Foley method, (b) Comparison of PSDs for octyldimethylsilyl-bonded MCM-41 calculated from nitrogen adsorption using the KJS-calibrated BJH algorithm with t-curves for reference ODMS-modified silica and unmodified silica. 

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