Gradient-corrected DFT

OPW (orthogonalized plane wave) a band-structure computation method P89 (Perdew 1986) a gradient corrected DFT method parallel computer a computer with more than one CPU Pariser-Parr-Pople (PPP) a simple semiempirical method PCM (polarized continuum method) method for including solvation effects in ah initio calculations... 

PW91 (Perdew, Wang 1991) a gradient corrected DFT method QCI (quadratic conhguration interaction) a correlated ah initio method QMC (quantum Monte Carlo) an explicitly correlated ah initio method QM/MM a technique in which orbital-based calculations and molecular mechanics calculations are combined into one calculation QSAR (quantitative structure-activity relationship) a technique for computing chemical properties, particularly as applied to biological activity QSPR (quantitative structure-property relationship) a technique for computing chemical properties... 

Currently, the density functional theory (DFT) method has become the method of choice for the study of reaction mechanism with transition-metals involved. Gradient corrected DFT methods are of particular value for the computational modeling of catalytic cycles. They have been demonstrated in numerous applications for several elementary processes, to be able to provide quantitative information of high accuracy concerning structural and energetic properties of the involved key species and also to be capable of treating large model systems.30... 

Gradient corrected DFT methods, 177-178 Group 13 elements in 13/15 organometallic compounds, 225-316... 

The activity of CMe2-bridged Zr(II) and Hf(II) boratabenzene cationic complexes toward ethylene trimerization has been explored computationally using a gradient-corrected DFT approach the Zr species was calculated to be a highly efficient catalyst, exceeding the efficiency of the corresponding Cp system.108... 

Summarizing, the reliable electrostatics of gradient-corrected DFT methods provides a good basis for CSMs. Nevertheless, advanced CSMs such as C-PCM or COSMO have achieved an accuracy that is mainly limited by the electrostatic accuracy of DFT, but the next better quantum chemical levels are presently much too expensive for most practical applications. Therefore, we will have to live with the acceptable DFT accuracy for the next years, and no big improvements of the CSMs beyond the present accuracy should be expected, until more accurate quantum levels as CC become practically useful. 

Table 7.8 compares with experiment dipole moments calculated by B3LYP/6-31G, M06/6-31G, AMI (as a check on this fast method), and MP2(fc)/6-31G, for ten molecules. The two DFT methods give the same mean unsigned error, 0.11 D, three times smaller than the error of 0.31 D from the slowest method, MP2 (at least for this small selection of molecules), and the very fast AMI moments lie in-between, 0.22 D. None of these methods consistently gives values accurate to within 0.1 D. Very accurate dipole moments (mean absolute deviation 0.06-0.07 D) can be obtained with gradient-corrected DFT and very large basis sets [74]. 

TABLE 5. Calculated bond distances Re(A), total bond dissociation energies Do (kcalmol-1) which include ZPE corrections and force constants of the totally symmetric mode ke (Ncm-1) of the molecules EH4 and ECI4, using relativistic gradient-corrected DFT ... 

Currently, research in our laboratory continues on real-space models of exchange and correlation hole functions in inhomogeneous systems. We anticipate that this work will ultimately generate completely non-empirical parameter-free beyond-LDA density functional theories. The quality of molecular dissociation energies and related properties obtainable with existing semi-empirical gradient-corrected DFTs approaches chemical accuracy, and we hope these future theoretical developments will continue this trend. 

This apparent contradiction has stimulated a considerable amount of theoretical work from the early 90 s until very recently. A number of more and more refined calculations has been performed by several groups using various methods [72], from simple HF [73,74] to HF with extended inclusion of correlation [75,76], from LDA [77] to gradient corrected DFT [78,79]. However, the most sophisticated methods and calculations lead to the same conclusion CO is bound to the terrace sites of the MgO surface through electrostatic forces, with a very weak binding energy of less then 0.1 eV, and a very small vibrational shift, of -I-IO cm" or less [67,72]. Eventually, the discrepancy between the ab initio calculations and the results on MgO thin films lead to the suggestion that surface defects could be responsible for the observed chemisorption properties of CO/MgO/Mo(l 10). 

The results we will report here were obtained using gradient-corrected DFT methods with appropriate relativistic corrections. It is our experience, and that of others, that this approach has several distinct advantages for studies of the electronic structure of actinide complexes ... 

The DFT methods achieve their good quantitative accuracy with a computational cost that is much lower than that of traditional ab initio correlated methods because of their better scaling with respect to the size of the atomic basis set (31). For example, one recent study compared the CPU time used in the calculation of the energy hypersurface of organotransition metal systems, by using gradient-corrected DFT, and various correlated ab initio methods. The DFT calculations were found to be 66, 78, and 83 times faster than the ab initio QCISD, CCSD, and QCISD(T) methods, respectively (32). 

For most semiempirical MO methods or uncorrelated ab initio methods, the demand for basis sets is drastically increased, while the accuracy is usually reduced when going from light- to heavy-element systems. However, as we will show, the gradient-corrected DFT methods seem to have smaller basis set truncation error, so they are quite reliable for systems as heavy as those of actinides, and the results seem, at least qualitatively, to be less dependent on the choice of basis sets with high-angular-momentum components (40). 

Recently, Becke has derived theoretically the need to include part of the Hartree-Fock exact exchange (i.e. non-local effects) in the exchange functional to improve the predictions of the gradient-corrected DFT methods (16,17). Becke (17) proposed the functional... 

Gradient corrected DFT methods, specially the ACM versions, have been very successful in the prediction of different molecular properties. In the following we will give some examples of this behavior. One interesting study has been... 

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