Hartree-Fock density functional

Hybrid Hartree-Fock/Density Functional Methods... 

Chapter 6, Selecting an Appropriate Theoretical Method, discusses the model chemistry concept introduced in Chapter 1 in detail. It covers the strengths, computational cost and limitations of a variety of popular methods, beginning with semi-empirical models and continuing through Hartree-Fock, Density Functional Theory, and electron correlation methods. 

Niu, S., Hall, M. B., 1997, Comparison of Hartree-Fock, Density Functional, Mpller-Plesset Perturbation, Coupled Cluster, and Configuration Interaction Methods for the Migratory Insertion of Nitric Oxide into a Cobalt-Carbon Bond , J. Phys. Chem. A, 101, 1360. 

Raymond, K. S., Wheeler, R. A., 1999, Compatibility of Correlation-Consistent Basis Sets With a Hybrid Hartree-Fock/Density Functional Method , J. Comput. Chem., 20, 207. 

Key words Hartree-Fock, Density functional theory, Extended Hiickel, Molecular mechanics, Quantum mechanics/molecular mechanics... 

Figure 5. Normal modes for vibration of tetrahedral [Cr04] (chromate). There are four distinct vibrational frequencies, including one doubly-degenerate vibration (E symmetry) and two triply-degenerate vibrations (F2 symmetry), for a total of nine vibrational modes. Arrows show the characteristic motions of each atom during vibration, and the length of each arrow is proportional to the magnitude of atomic motion. Only F2 modes involve motion of the central chromium atom, and as a result their vibrational frequencies are affected by Cr-isotope substitution. The normal modes shown here were calculated with an ab initio quantum mechanical model, using hybrid Hartree-Fock/Density Functional Theory (B3LYP) and the 6-31G(d) basis set—other ab initio and empirical force-field models give very similar results.

Basis sets for use in practical Hartree-Fock, density functional, Moller-Plesset and configuration interaction calculations make use of Gaussian-type functions. Gaussian functions are closely related to exponential functions, which are of the form of exact solutions to the one-electron hydrogen atom, and comprise a polynomial in the Cartesian coordinates (x, y, z) followed by an exponential in r. Several series of Gaussian basis sets now have received widespread use and are thoroughly documented. A summary of all electron basis sets available in Spartan is provided in Table 3-1. Except for STO-3G and 3 -21G, any of these basis sets can be supplemented with additional polarization functions and/or with diffuse functions. It should be noted that minimal (STO-3G) and split-valence (3-2IG) basis sets, which lack polarization functions, are unsuitable for use with correlated models, in particular density functional, configuration interaction and Moller-Plesset models. Discussion is provided in Section II. 

There are actually very few. Modern optimization techniques practically guarantee location of a minimum energy structure, and only where the initial geometry provided is too symmetric will this not be the outcome. With a few notable exceptions (Hartree-Fock models applied to molecules with transition metals), Hartree-Fock, density functional and MP2 models provide a remarkably good account of equilibrium structure. Semi-empirical quantum chemical models and molecular mechanics models, generally fare well where they have been explicitly parameterized. Only outside the bounds of their parameterization is extra caution warranted. Be on the alert for surprises. While the majority of molecules assume the structures expected of them, some will not. Treat "unexpected" results with skepticism, but be willing to alter preconceived beliefs. 

Except for very low values (< 600 cm ), frequencies can normally be measured to high precision (< 5 cm ) using infrared or Raman spectroscopy. Similar or better precision is available for frequencies calculated analytically (Hartree-Fock, density functional and semi-empirical models), but somewhat lower precision results where numerical differentiation is required (MP2 models). 

It has previously been documented (Chapter 6) that Hartree-Fock, density functional and MP2 models generally provide excellent descriptions of the energetics of bond separation energies, while semi-empirical models are not successful in this regard (Tables 6-10 and A6-36 to A6-43). Use of bond separation energies from these models (but not from semi-empirical models) together with... 

Gaussian. A function of the form x y z" exp (ar ) where 1, m, n are integers (0,1,2. . .) and a is a constant. Used in the construction of Basis Sets for Hartree-Fock, Density Functional, MP2 and other Correlated Models. 

SCF. Self Consistent Field. An iterative procedure whereby a one-electron orbital is determined under the influence of a potential made up of all the other electrons. Iteration continues until self consistency. Hartree-Fock, Density Functional and MP2 Models all employ SCF procedures. 

Restrepo-Cossio, A. A., Gonzalez, C. A., Mari, F. Comparative ab Initio Treatment (Hartree-Fock, Density Functional Theory, MP2, and Quadratic Configuration Interactions) of the Cycloaddition of Phosphorus Ylides with Formaldehyde in the Gas Phase. J. Phys. Chem. A 1998, 102, 6993-7000. 

Hartree-Fock, Density Functional and Perturbation Theory. 218... 

Outline This review concentrates on work which mainly treats ILs from theoretical considerations and not from an experimental point of view. If calculations play only a supportive role in them, articles may have been neglected on principle. We also refrain from an introduction to methodological aspects and rather refer the reader to good textbooks on the subjects. The review is organized as follows Static QC calculations are discussed in detail in the next section including Hartree-Fock, density functional theory (Sect. 2.2) and correlated (i.e., more sophisticated) methods (Sect. 2.4) as well as semiempirical methods (Sect. 2.1). We start with these kinds of small system calculations because they can be considered as a basis for the other calculations, i.e., an insight into the intermolecular forces is obtained. 

The electron affinities of a series of substituted quinones have been calculated using the hybrid Hartree Fock/density functional B3LYP method with a 6-311G(3d,p) basis set. The precision and accuracy plot for the Ea obtained from... 

Boesch, S. E. Wheeler, R. A. Structures and Properties of Ubiquinone-1 and Its Radical Anion from Hybrid Hartree-Fock/Density Functional Studies,"/ Phys. Chem. A1997,101,5799-5804. 

Grafton, A. K. Wheeler, R. A. "Structures and Properties of Vitamin K and its Radical Anion Predicted by a Hybrid Hartree-Fock/Density Functional Method,"/ Mol. Struc. (Theochem) 1997,392,1-11. 

Scheme for hybrid Hartree-Fock/density functional theory introduced by Becke... 

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