Gradient-Dependent Density Functionals

The DMol methodology is reviewed with special emphasis on recent developments such as gradient dependent, or so-called nonlocal, density functionals. Applications to crystalline silicon structures in the nanometer size imply a discussion of excited states. This is also a first application using periodic boundary conditions. The application to carbonyl complexes is a case study of the effect of some recent gradient dependent density functionals on the energy surface. 

The term non-local is used sometimes in die literature in association with gradient-dependent (GGA) functionals. This nomenclature is not applied in this work. The LDA-, GGA-, and meta-GGA functionals are referred to as semi-local as they do not account for any long-range non-locality of the exchange-correlation energy density excseim local(r) = exc(p(r), Vp(r), V2p(r), r(r)) whereas... 

Figure 5. Enhancement factors F(s) of the gradient dependent exchange functionals with respect to the cxp4/3 local exchange in function of the normalized density gradient s = Vp p-

Time-dependent density functional theory (TDDFT) using different gradient-corrected density functionals, the BLYP and B3LYP functionals, and a hybrid DFT/HF approach based on the Perdew-Burke-Ernzenhofer exchange correlation functional (PBEIPBE) were recently applied to calculate vertical transitions to low-lying excited states of... 

Minezawa, N., Silva, N. D., Zahariev, F, Gordon, M. S. (2011). Implementation of the Anal5d ic Energy Gradient for the Combined Time-Dependent Density Functional Theory/Effective Fragment Potential Method Application to Excited-State Molecular D5mamics Simulations, / Chem. Phys., 134, 054111. 

Table 12 Vertical excitation energies (in eV) for N2- TDLDA and TDGGA represent results from time-dependent density-functional calculations with either a local-density (LDA) or a generalized-gradient (GGA) approximation, whereas TDHF are similar results from time-dependent Hartree-Fock calculations. MRCCSD, SOPPA, MRTDHF are results from sophisticated configuration-interaction calculations, and CIS are less sophisticated configuration-interaction calculations. The final state and the electronic excitation are also shown and the results are compared with experimental values (Exp.). The results are from ref. 89...

Quantum Chemistry in Multiwavelet Bases Time-Dependent Density Functional Theory with Asymptotically Corrected Potentials in Local Density and Generalized Gradient Approximations. 

M. Chiba, T. Tsuneda, and K. Hirao,/. Ghem. Phys., 124, 144106 1-11 (2006). Excited State Geometry Optimizations by Analytical Energy Gradient of Long-Range Corrected Time-Dependent Density Functional Theory. 

In addition to conventional ab initio methods, techniques based on the density functional theory (DFT) have also been used to study the Diels-Alder reaction between butadiene and ethylene97-99. With these kinds of methods, a concerted mechanism through a symmetric transition state is also predicted. Several kinds of density functionals have been used. The simplest one is based on the Local Density Approach (LDA), in which all the potentials depend only on the density. More sophisticated functionals include a dependence on the gradient of the density, such as that of Becke, Lee, Yang and Parr (BLYP). 

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