Electronic structure methods density functional theory

Finite Element Method in Density Functional Theory Electronic Structure Calculations... 

Numerous H-bonded homodimers and heterodimers have been investigated using ab initio electronic structure calculations and density functional theory (DFT)-based methods [1-4]. Various aspects of H-bonding starting from classical definition to H-bonded dimers have been discussed in one of the earlier reviews by Kollman and Allen [47]. Water dimer is a typical example used to explain the H-bonding interaction. The structure of the water dimer was analyzed by a molecular beam electric resonance experiment [48, 49]. Almost all theoretical methods developed so far have been employed to predict the... 

In principle, any electronic structure method that can produce a gradient and Hessian can be used in quasi-classical dynamics. However, density functional theory (DFT)-based methods are, in general (at the time of writing), limited to ground-state surfaces. CASSCF-based dynamics calculations can be used for excited-state computations, and we will focus our discussion on this method. In this case, the size of the molecule that can be studied is limited by the size of the active space (Section 2.2.1) at present, no more than 10 active elec-... 

The spin Hamiltonian parameters of a complex or a model system can in principle be determined from a quantum chemical calculation of the electronic structure. The Density Functional Theory (DFT) [13] method is at present popular for this purpose, since it allows fairly large systems ( 200 atoms) to be investigated. By comparing the calculated and experimental spin Hamiltonian parameters it is often possible to distinguish between different proposed models and to gain further insight into the electronic and geometric structure of the sample. 

Recently, a third class of electronic structure methods have come into wide use density functional methods. These DFT methods are similar to ab initio methods in many ways. DFT calculations require about the same amount of computation resources as Hartree-Fock theory, the least expensive ab initio method. 

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. 

The ab initio methods used by most investigators include Hartree-Fock (FFF) and Density Functional Theory (DFT) [6, 7]. An ab initio method typically uses one of many basis sets for the solution of a particular problem. These basis sets are discussed in considerable detail in references [1] and [8]. DFT is based on the proof that the ground state electronic energy is determined completely by the electron density [9]. Thus, there is a direct relationship between electron density and the energy of a system. DFT calculations are extremely popular, as they provide reliable molecular structures and are considerably faster than FFF methods where correlation corrections (MP2) are included. Although intermolecular interactions in ion-pairs are dominated by dispersion interactions, DFT (B3LYP) theory lacks this term [10-14]. FFowever, DFT theory is quite successful in representing molecular structure, which is usually a primary concern. 

The basis set is 6-31G(d,p), and electron correlation at the MP2 level is included. A similar structure is obtained with the AMI and PM3 semi-empirical methods. Density functional theory at the B3LYP/6-31G(dp,p) level also produced the same structure for this ion-pair. The only observed differences between the semi-empiri-cal and the ab initio structures were slightly shorter hydrogen bonds (PM3 and AMI) between FI, F2, and F5 and the G2-F1 (H18) on the imidazolium ring. 

The determination of the electronic structure of lanthanide-doped materials and the prediction of the optical properties are not trivial tasks. The standard ligand field models lack predictive power and undergoes parametric uncertainty at low symmetry, while customary computation methods, such as DFT, cannot be used in a routine manner for ligand field on lanthanide accounts. The ligand field density functional theory (LFDFT) algorithm23-30 consists of a customized conduct of nonempirical DFT calculations, extracting reliable parameters that can be used in further numeric experiments, relevant for the prediction in luminescent materials science.31 These series of parameters, which have to be determined in order to analyze the problem of two-open-shell 4f and 5d electrons in lanthanide materials, are as follows. 

Efforts to tame the unfavorable scaling of electronic structure methods are not limited to density functional theory. For a general summary of the current state of the art see the review by Goedecker, 1999. 

From the early advances in the quantum-chemical description of molecular electron densities [1-9] to modem approaches to the fundamental connections between experimental electron density analysis, such as crystallography [10-13] and density functional theories of electron densities [14-43], patterns of electron densities based on the theory of catastrophes and related methods [44-52], and to advances in combining theoretical and experimental conditions on electron densities [53-68], local approximations have played an important role. Considering either the formal charges in atomic regions or the representation of local electron densities in the structure refinement process, some degree of approximate transferability of at least some of the local structural features has been assumed. 

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