Density functional calculation calculations

Floizwarth N A W, Matthews G E, Dunning R B, Tackett A R and Zeng Y 1997 Comparison of the pro]ector augmented-wave, pseudopotentlal and linearized augmented-plane-wave formalisms for density-functional calculations of solids Phys. Rev. B 55 2005... 

Duarte H A and Salahub D R 1998 Embedded cluster model for chemisorption using density functional calculations oxygen adsorption on the AI(IOO) surface J. Chem. Phys. 108 743... 

Maurits, N.M., Altevogt, P., Evers, O.A., Fraaije, J.G.E.M. Simple numerical quadrature rules for Gaussian Chain polymer density functional calculations in 3D and implementation on parallel platforms. Comput. Theor. Polymer Sci. 6 (1996) 1-8. 

F, St-Amant A, I Papai and D R Salahub 1992. Gaussian Density Functional Calculations on Hydrogen-Bonded Systems, journal of the American Chemical Society 114 4391-4400. ter J C1974. Quantum Theory of Molecules and Solids Volume 4 The Self-Consistent Field for Molecules and Solids. New York, McGraw-Hill. 

Free surface density functions calculated at step 8 are used as the initial conditions to update the current position of the surface using the following integration... 

A basis set is a set of functions used to describe the shape of the orbitals in an atom. Molecular orbitals and entire wave functions are created by taking linear combinations of basis functions and angular functions. Most semiempirical methods use a predehned basis set. When ah initio or density functional theory calculations are done, a basis set must be specihed. Although it is possible to create a basis set from scratch, most calculations are done using existing basis sets. The type of calculation performed and basis set chosen are the two biggest factors in determining the accuracy of results. This chapter discusses these standard basis sets and how to choose an appropriate one. 

Density functional theory calculations have shown promise in recent studies. Gradient-corrected or hybrid functionals must be used. Usually, it is necessary to employ a moderately large basis set with polarization and diffuse functions along with these functionals. 

A number of types of calculations can be performed. These include optimization of geometry, transition structure optimization, frequency calculation, and IRC calculation. It is also possible to compute electronic excited states using the TDDFT method. Solvation effects can be included using the COSMO method. Electric fields and point charges may be included in the calculation. Relativistic density functional calculations can be run using the ZORA method or the Pauli Hamiltonian. The program authors recommend using the ZORA method. 

Kohn-Sham orbitals functions for describing the electron density in density functional theory calculations... 

Table I.IS gives total bonding energies in kilocalories per mole for some simple molecules. The B3iyP results are comparable in accuracy to G1 and G2 results. Another comparison was done with a series of cyclic hydrocarbons as the test case. The calculations were done using an isodesmic reaction scheme. The results are given in Table 1.19. Density functional calculations have also been successfully extended to functionalized molecules. ...

Density functional theory calculations on model diazenes of the type... 

Perform a low-level geometry optimization with a medium-sized basis set, for example, a Hartree-Fock or B3LYP Density Functional Theory calculation with the 6-31G(d) basis set. (For very large systems, a smaller basis set might be necessary.)... 

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 hetero-Diels-Alder reaction of aldehydes 12 with 2-azabutadienes 13 (Scheme 8.5) has been studied using high-level ab-initio multiconfigurational molecular orbital and density functionality calculation methods [28]. 

Calculations were done with a full-potential version of the LMTO method with nonoverlapping spheres. The contributions from the interstitial region were accounted for by expanding the products of Hankel functions in a series of atom-ce- -ered Hankels of three different kinetic energies. The corrected tetrahedron method was used for Brillouin zone integration. Electronic exchange and correlation contributions to the total energy were obtained from the local-density functional calculated by Ceperley and Alder " and parametrized by Vosko, Wilk, and Nusair. ... 

Extensive quantum chemical calculations have been reported for sulfur-rich compounds in the past two decades. These calculations were used to investigate molecular structures and spectroscopic properties, as well as to understand the nature chemical bonding and reaction mechanism. Many high-level ab initio calculations were used for interpretation of experimental data and for providing accurate predictions of molecular structures and thermochemical data where no reliable experimental values are available. In recent years, density functional calculations have been extensively tested and used on many first- and second-row compounds. These proven DFT methods look promising for larger systems because for their computational efficiency. 

This isomer was first obtained by density functional calculations R.O. Jones, D. Hohl, Int. J. Quantum Chem. Quantum Chem. Symp. 1990, 110, 4703... 

The molecular structures of the isolated polysulfide monoanions 8 with n=2-9 have been studied by density functional calculations and those of the smaller ions also by ab initio MO calculations. Compared to the neutral 8 molecules the extra electron occupies an antibonding orbital resulting in longer 88 bonds. The species 83 is bent and of C2V symmetry (a=115°) [140, 141]. 84 was calculated to be a planar ion of C2V symmetry (similar to the neutral molecule 84) but the planar C2h structure is only slightly less stable [140, 141]. The most stable isomer of 85 is a chain of Q symmetry sim-... 

Ab initio MO calculations at a high level of theory [28] support the open-chain structure for the ground state of S2O while density functional calculations predicted a cyclic ground-state structure [29]. 

Hartree-Fock as well as density functional calculations on hypothetical cyclic oligomers (SO) with =2-4 have been published [56] these species are all more stable than the corresponding number of monomeric SO mole-... 

The local density approximation is highly successful and has been used in density functional calculations for many years now. There were several difficulties in implementing better approximations, but in 1991 Perdew et al. successfully parametrised a potential known as the generalised gradient approximation (GGA) which expresses the exchange and correlation potential as a function of both the local density and its gradient ... 

An alternative stream came from the valence bond (VB) theory. Ovchinnikov judged the ground-state spin for the alternant diradicals by half the difference between the number of starred and unstarred ir-sites, i.e., S = (n -n)l2 [72]. It is the simplest way to predict the spin preference of ground states just on the basis of the molecular graph theory, and in many cases its results are parallel to those obtained from the NBMO analysis and from the sophisticated MO or DFT (density functional theory) calculations. However, this simple VB rule cannot be applied to the non-alternate diradicals. The exact solutions of semi-empirical VB, Hubbard, and PPP models shed light on the nature of spin correlation [37, 73-77]. 

Thiourea Ugands can be bounded to the metal centre through one nitrogen atom, the sulfur atom, or the C = S double bond. These coordination modes were studied by density functional theory calculations for Rh-thiourea complexes (Scheme 13). No stable structure was attained by optimisation of the nitrogen coordination mode I but optimised geometries as trigonal-bipyramidal complexes were obtained for modes II and III. An coordination is determined for the latter complex through both S and C atoms. As this... 

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