Density functional theory orbital-based

The definite positive kinetic energy density has received a considerable attention in order to build approximate kinetic energy functionals to be used in a density functional theory not based on orbitals (for a review of such functionals see Lacks and Gordon[33]). Among the most promising routes to this goal, we can mention the approximation proposed by Lee, Lee and Parr[34] ... 

Accordingly, the main goal of this work is to compare systematically the electronic properties of several member of a family of polymers, by using a parameter-free method. We will employ a Density Functional Theory (DFT) based-on method that uses the Linear Muffin Tin Orbitals (LMTO) considering full potential in the interstitial region. This method has been specifically adapted to calculate the electronic properties of helical polymers [4,22,23]. This method has proven to be an accurate tool for calculating the electronic properties of quasi-unidimensional periodical systems [24-26]. We also, will compare our results with previously reported ones... 

Fattebert J-L and Bernholc J 2000 Towards grid-based 0(N) density-functional theory methods optimized nonorthogonal orbitals and multigrid acceleration Phys. Rev. B 62 1713-22... 

This technique has been applied occasionally to orbital-based methods, where it is called seam searching. The rest of the techniques mentioned in this chapter are applicable to semiempirical, density functional theory (DFT), and ah initio techniques. 

Ab initio molecular orbital theory is concerned with predicting the properties of atomic and molecular systems. It is based upon the fundamental laws of quantum mechanics and uses a variety of mathematical transformation and approximation techniques to solve the fundamental equations. This appendix provides an introductory overview of the theory underlying ab initio electronic structure methods. The final section provides a similar overview of the theory underlying Density Functional Theory methods. 

If we except the Density Functional Theory and Coupled Clusters treatments (see, for example, reference [1] and references therein), the Configuration Interaction (Cl) and the Many-Body-Perturbation-Theory (MBPT) [2] approaches are the most widely-used methods to deal with the correlation problem in computational chemistry. The MBPT approach based on an HF-SCF (Hartree-Fock Self-Consistent Field) single reference taking RHF (Restricted Hartree-Fock) [3] or UHF (Unrestricted Hartree-Fock ) orbitals [4-6] has been particularly developed, at various order of perturbation n, leading to the widespread MPw or UMPw treatments when a Moller-Plesset (MP) partition of the electronic Hamiltonian is considered [7]. The implementation of such methods in various codes and the large distribution of some of them as black boxes make the MPn theories a common way for the non-specialist to tentatively include, with more or less relevancy, correlation effects in the calculations. 

It is a truism that in the past decade density functional theory has made its way from a peripheral position in quantum chemistry to center stage. Of course the often excellent accuracy of the DFT based methods has provided the primary driving force of this development. When one adds to this the computational economy of the calculations, the choice for DFT appears natural and practical. So DFT has conquered the rational minds of the quantum chemists and computational chemists, but has it also won their hearts To many, the success of DFT appeared somewhat miraculous, and maybe even unjust and unjustified. Unjust in view of the easy achievement of accuracy that was so hard to come by in the wave function based methods. And unjustified it appeared to those who doubted the soundness of the theoretical foundations. There has been misunderstanding concerning the status of the one-determinantal approach of Kohn and Sham, which superficially appeared to preclude the incorporation of correlation effects. There has been uneasiness about the molecular orbitals of the Kohn-Sham model, which chemists used qualitatively as they always have used orbitals but which in the physics literature were sometimes denoted as mathematical constructs devoid of physical (let alone chemical) meaning. 

The protocol developed by Jacobsen and Katsuki for the salen-Mn catalyzed asymmetric epoxidation of unfunctionalized alkenes continues to dominate the field. The mechanism of the oxygen transfer has not yet been fully elucidated, although recent molecular orbital calculations based on density functional theory suggest a radical intermediate (2), whose stability and lifetime dictate the degree of cis/trans isomerization during the epoxidation <00AG(E)589>. 

All calculations presented here are based on density-functional theory [37] (DFT) within the LDA and LSD approximations. The Kohn-Sham orbitals [38] are expanded in a plane wave (PW) basis set, with a kinetic energy cutoff of 70 Ry. The Ceperley-Alder expression for correlation and gradient corrections of the Becke-Perdew type are used [39]. We employ ah initio pseudopotentials, generated by use of the Troullier-Martins scheme [40], The coreradii used, in au, were 1.23 for the s, p atomic orbitals of carbon, 1.12 for s, p of N, 0.5 for the s of H, and 1.9, 2.0, 1.5, 1.97,... 

Hqm is the Hamiltonian of the QM region and might be based on semiempirical, ah initio molecular orbital or density functional theory (DFT) methods. Hqm/mm represents the interactions between the QM and MM regions, Hmm is the Hamiltonian of the purely MM region, and Hboundary is Hamiltonian for the boundary of the system, if this contribution is included. The corresponding total energy ( tot) of the QM/MM system is ... 

Quantum mechanics provide many approaches to the description of molecular structure, namely valence bond (VB) theory (8-10), molecular orbital (MO) theory (11,12), and density functional theory (DFT) (13). The former two theories were developed at about the same time, but diverged as competing methods for describing the electronic structure of chemical systems (14). The MO-based methods of calculation have enjoyed great popularity, mainly due to the availability of efficient computer codes. Together with geometry optimization routines for minima and transition states, the MO methods (DFT included) have become prevalent in applications to molecular structure and reactivity. 

This mechanistic question is one of the examples of the success of density functional theory methods in organometallic chemistry. Earlier work on the reaction mechanism could not discriminate between the two alternatives. Analysis of the different orbitals based on extended Hiickel calculations came to the result that the [3+2] pathway is more likely, but could not exclude the possibility of a [2+2] pathway [13]. Similar conclusions where obtained from the results of Hartree-Fock calculations in combination with QCISD(T) single point calculations [21], Attempts to use Ru04 as a model for osmium tetraoxide indicated that the formation of an oxetane is less favorable compared to the [3+2] pathway, but still possible [22, 23],... 

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