Ab initio density functional theory

Hybrid density functional theory ab initio calculation method Cluster (molecular connectivity)... 

Cheeseman, J. R. Frisch, M. J. Devlin, F. J. Stephens, P. J. Hartree-Fock and density functional theory ab initio calculation of optical rotation using GIAOs basis set dependence, 7. Phys. Chem. A, 2000,104, 1039-1046. 

Computation completes more and more experimental results to explain, interpret, and predict structures, reactivities, and to contribute to the better understanding of reaction mechanisms. The powerful computers and software now available (density functional theory, ab-initio and molecular dynamic calculations, etc.) give calculated parameters closer and closer to the experimental values. 

Explicitly correlated methods Density functional theory Ab initio... 

His research interests are in both theoretical developments and applications of Quantum Chemistry. The range of the theoretical developments is wide, including non-Born Oppenheimer theory, linear-scaling technique, density functional theory, ab initio molecular dynamics, and relativistic quantum chemistry. He also contributed in discovering novel chemical concepts, such as hyperconjugation of methyl group in the excited state and symmetry rules for degenerate excitations. 

In addition to the chemistry that may be addressed, ab-initio calculations are needed to provide important guidance on which to develop semi-empirical and empirical schemes that use, in fact, the same formalism. There is an important interplay between all methods, and the information that we gain from ab-initio calculations is not only used to examine the chemistry of the model systems, but also used to help develop semi-empirical methods. The numbers obtained are often used to guide parameter choices where these are not available from experiment. Most importantly, discoveries in the underlying theory that we use are made in semi- empirical, density functional and ab-initio studies, and these improvements are adopted, perhaps in modified form, to affect all theories used in computational chemistry. 

The electron affinities of the aromatic hydrocarbons have been calculated using Huckel theory and MINDO/3 procedures. The electron affinities of benzene, naphthalene, anthracene, and tetracene have been calculated by density functional and ab initio procedures [8]. The relationship between the experimental and calculated values is examined. The electron affinities of other organic compounds have been calculated using MNDO, density functional, and ab initio procedures [9]. A more thorough discussion of these experimental and theoretical methods can be found in Electron and Molecule Interactions and Their Applications, Volume 2, Chapter 6. The experimental and theoretical electron affinities of atoms, molecules, and radicals up to 1984 are listed but not evaluated [10]. The NIST site briefly discusses the various methods for determining electron affinities and gives an... 

In 1985 Car and Parrinello invented a method [111-113] in which molecular dynamics (MD) methods are combined with first-principles computations such that the interatomic forces due to the electronic degrees of freedom are computed by density functional theory [114-116] and the statistical properties by the MD method. This method and related ab initio simulations have been successfully applied to carbon [117], silicon [118-120], copper [121], surface reconstruction [122-128], atomic clusters [129-133], molecular crystals [134], the epitaxial growth of metals [135-140], and many other systems for a review see Ref. 113. 

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. 

Ab initio Hartree-Fock and density functional theory calculations were performed to study the transition state geometry in intramolecular Diels-Alder cycloaddition of azoalkenes 55 to give 2-substituted 3,4,4u,5,6,7-hexahydro-8//-pyrido[l,2-ft]pyridazin-8-ones 56 (01MI7). 

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 precursor of such atomistic studies is a description of atomic interactions or, generally, knowledge of the dependence of the total energy of the system on the positions of the atoms. In principle, this is available in ab-initio total energy calculations based on the loc density functional theory (see, for example, Pettifor and Cottrell 1992). However, for extended defects, such as dislocations and interfaces, such calculations are only feasible when the number of atoms included into the calculation is well below one hundred. Hence, only very special cases can be treated in this framework and, indeed, the bulk of the dislocation and interfacial... 

Only the structures of di- and trisulfane have been determined experimentally. For a number of other sulfanes structural information is available from theoretical calculations using either density functional theory or ab initio molecular orbital theory. In all cases the unbranched chain has been confirmed as the most stable structure but these chains can exist as different ro-tamers and, in some cases, as enantiomers. However, by theoretical methods information about the structures and stabilities of additional isomeric sul-fane molecules with branched sulfur chains and cluster-like structures was obtained which were identified as local minima on the potential energy hypersurface (see later). 

These observations are supported by the calculations of Estreicher et al. [9], using the the PRDDO method and density functional theory, the semi-empirical calculations of Percival and Wlodek [10] and ab initio ROHF calculations [11]. They confirm that the most stable state of CeoMu results from the muon bonding itself to one of the carbon atoms from outside the cage. 

Ab initio methods allow the nature of active sites to be elucidated and the influence of supports or solvents on the catalytic kinetics to be predicted. Neurock and coworkers have successfully coupled theory with atomic-scale simulations and have tracked the molecular transformations that occur over different surfaces to assess their catalytic activity and selectivity [95-98]. Relevant examples are the Pt-catalyzed NO decomposition and methanol oxidation. In case of NO decomposition, density functional theory calculations and kinetic Monte Carlo simulations substantially helped to optimize the composition of the nanocatalyst by alloying Pt with Au and creating a specific structure of the PtgAu7 particles. In catalytic methanol decomposition the elementary pathways were identified... 

While in previous ab initio smdies the reconstructed surface was mostly simulated as Au(lll), Feng et al. [2005] have recently performed periodic density functional theory (DFT) calculations on a realistic system in which they used a (5 x 1) unit cell and added an additional atom to the first surface layer. In their calculations, the electrode potential was included by charging the slab and placing a reference electrode (with the counter charge) in the middle of the vacuum region. From the surface free energy curves, which were evaluated on the basis of experimentally measured capacities, they concluded that there is no necessity for specific ion adsorption [Bohnen and Kolb, 1998] and that the positive surface charge alone would be sufficient to lift the reconstmction. 

However, even the best experimental technique typically does not provide a detailed mechanistic picture of a chemical reaction. Computational quantum chemical methods such as the ab initio molecular orbital and density functional theory (DFT) " methods allow chemists to obtain a detailed picture of reaction potential energy surfaces and to elucidate important reaction-driving forces. Moreover, these methods can provide valuable kinetic and thermodynamic information (i.e., heats of formation, enthalpies, and free energies) for reactions and species for which reactivity and conditions make experiments difficult, thereby providing a powerful means to complement experimental data. 

Lev, D. A. Grotjahn, D. B. Amouri, H. Reversal of reactivity in diene-complexed o-quinone methide complexes insights and explanations from ab initio density functional theory calculations. Organometallics 2005, 24, 4232 -240. 

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