Density functional theory quantum mechanical description

The usual way chemistry handles electrons is through a quantum-mechanical treatment in the frozen-nuclei approximation, often incorrectly referred to as the Born-Oppenheimer approximation. A description of the electrons involves either a wavefunction ( traditional quantum chemistry) or an electron density representation (density functional theory, DFT). Relativistic quantum chemistry has remained a specialist field and in most calculations of practical... 

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. 

In the previous section we presented the semi-classical electron-electron interaction we treated the electrons quantum mechanically but assumed that they interact via classical electromagnetic fields. The Breit retardation is only an approximate treatment of retardation and we shall now consider a more consistent treatment of the electron-electron interaction operator that also provides a bridge to relativistic DFT, which is current-density functional theory. For the correct description we have to take the quantization of electromagnetic fields into account (however, we will discuss only old, i.e., pre-1940 quantum electrodynamics). This means the two moving electrons interact via exchanged virtual photons with a specific angular frequency u>... 

The quantum mechanical description of DNMR spectra runs back over several decades.16 In the widespread theory based on the average density matrix, the quantum mechanical state functions are time dependent ... 

Quantum-mechanical calculations have been successfully applied to the study of the carcinogenic pathways of PAH and aza-PAH derivatives, and very good correlations have been shown with the available experimental reactivities of these compounds (23-28). Furthermore, modeling studies of biological electrophiles from PAHs by density functional theory (DFT) methods have given proper descriptions of the charge delocalization modes and NMR characteristics of their resulting carbocations (29-33). 

First principles approaches are important as they avoid many of the pitfalls associated with using parameterized descriptions of the interatomic interactions. Additionally, simulation of chemical reactivity, reactions and reaction kinetics really requires electronic structure calculations [108]. However, such calculations were traditionally limited in applicability to rather simplistic models. Developments in density functional theory are now broadening the scope of what is viable. Car-Parrinello first principles molecular dynamics are now being applied to real zeolite models [109,110], and the combined use of classical and quantum mechanical methods allows quantum chemical methods to be applied to cluster models embedded in a simpler description of the zeoUte cluster environment [105,111]. 

The objective of this article is to expose the chemical engineering community to Car-Parrinello methods, what they have accomplished, and what their potential is for chemical engineering. Consistent with this objective, in Section IV, I give an overview of the most widely used quantum mechanical method for solving the many-body electronic problem, density-functional theory, but describe other methods only cursorily. I also describe the practical solution of the equations of density-functional theory for molecular and extended systems via the plane-wave pseudopotential method, mentioning other methods only cursorily. Finally, I end this section with a description of the Car-Parrinello method itself. 

By far the major computational quantum mechanical method used to compute the electronic state in Car-Parrinello simulations is density-functional theory (DFT) (Hohenberg and Kohn, 1964 Kohn and Sham, 1965 Parr and Yang, 1989). It is the method used originally by Roberto Car and Michele Parrinello in 1985, and it provides the highest level of accuracy for the computational cost. For these reasons, in this section the only computational quantum mechanical method discussed is DFT. Section A consists of a brief review of classical molecular dynamics methods. Following this is a description of DFT in general (Section B) and then a description of practical DFT computations of chemical systems using the plane-wave pseudopotential method (Section C). The section ends with a description of the Car-Parrinello method and some basic issues involved in its use (Section D). 

In order to improve the model further we are currently taking quantum effects in the lattice into account, i.e. treating the CH units not classically but on quantum mechanical basis. To this end we use an ansatz state similar to Davydov s so-called ID,> state [96] developed for the description of solitons in proteins. However, there vibrations are coupled to lattice phonons, while in tPA fermions (electrons) are coupled to the lattice phonons. The results of this study will be the subject of a forthcoming paper. Further we want to improve the description of the electrons by going to semiempirical all valence electron methods or even to density functional theories. Further we introduce temperature effects into the theory which can be done with the help of a Langevin equation (random force and dissipation terms) or by a thermal population of the lattice phonons. Starting then the simulations with an optimized soliton geometry in the center of the chain (equilibrium position) one can study the soliton mobility as function of temperature. Further in the same way the mobility of polarons can be... 

For the quantum-mechanical description of Kohn-Sham density-functional theory, we define in this section properties within the context of Schrodinger theory relevant to the interpretation. We also give a brief description of... 

The EBO concept rehes on a multi-configurational wavefunction and takes into account the effect of electron correlation involving the antibonding orbitals. There are various ways of quantifying bond orders [12-14]. The Natural Bond Orbital (NBO) valence and bonding concepts are also extensively used in the analysis of multiple bonds. NBO, like EBO, is based on a quantum mechanical wavefunction. The NBO description of a bond can be derived by variational, perturbative, or density functional theory (DFT) approximations of arbitrary form and accuracy [15]. 

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