Density function method

Mineva T, Russo N and Sicilia E 1998 Solvation effects on reaction profiles by the polarizable continuum model coupled with Gaussian density functional method J. Oomp. Ohem. 19 290-9... 

Labanowski J K and Andzelm J W (eds) 1991 Density Functional Methods in Chemistry (New York Springer)... 

Weinert M, Wimmer E and Freeman A J 1982 Total-energy all-electron density functional method for bulk solids and surfaces Phys. Rev. B 26 4571-8... 

Fraaije, J.G.E.M., Van Vlimmeren, B.A.C., Maurits, N.M., Postma, M., Evers, O.A., Hoffmann, C., Altevogt, P., Goldbeck-Wood, G. The dynamic mean-field density functional method and its application to the mesoscopic dynamics of quenched block copolymer melts. J. Chem. Phys. 106 (1997) 4260-4269. 

Chapter 2 we worked through the two most commonly used quantum mechanical models r performing calculations on ground-state organic -like molecules, the ab initio and semi-ipirical approaches. We also considered some of the properties that can be calculated ing these techniques. In this chapter we will consider various advanced features of the ab Itio approach and also examine the use of density functional methods. Finally, we will amine the important topic of how quantum mechanics can be used to study the solid state. 

Hybrid Hartree-Fock/Density Functional Methods... 

Density Functional Methods for Studying the Solid State ... 

Johnson B G, P M W Gill and J A Pople 1993. The performance of a family of density functional methods. Journal of Chemical Physics 98 5612-5626. 

Density Functional Methods in Chemistry J. K. Labanowski, J. W. Andzelm, Eds., Springer-Verlag, New York (1991). 

Density Functional Methods in Physics R. M. Dreizler, J. du Providencia, Eds., Plenum, New York (1985). 

DYNAMIC MEAN-FIELD DENSITY FUNCTIONAL METHOD... 

The dynamic mean-field density functional method is similar to DPD in practice, but not in its mathematical formulation. This method is built around the density functional theory of coarse-grained systems. The actual simulation is a... 

To overcome these limitations, the hybrid QM-MM potential can employ ad initio or density function methods in the quantum region. Both of these methods can ensure a higher quantitative accuracy, and the density function methods offer a computaitonally less expensive procedure for including electron correlation [5]. Several groups have reported the development of QM-MM programs that employ ab initio [8,10,13,16] or density functional methods [10,41-43]. 

To date the majority of QM-MM applications have employed density functional methods ab initio or semiempirical methods in the quantum region. The energy tenns evaluated in these methods are generally similar, but there are specific differences. The relevant equations for the density functional based methods are described first, and this is followed by a description of the specific differences associated with the other methods. 

The use of QM-MD as opposed to QM-MM minimization techniques is computationally intensive and thus precluded the use of an ab initio or density functional method for the quantum region. This study was performed with an AMi Hamiltonian, and the first step of the dephosphorylation reaction was studied (see Fig. 4). Because of the important role that phosphorus has in biological systems [62], phosphatase reactions have been studied extensively [63]. From experimental data it is believed that Cys-i2 and Asp-i29 residues are involved in the first step of the dephosphorylation reaction of BPTP [64,65]. Alaliambra et al. [30] included the side chains of the phosphorylated tyrosine, Cys-i2, and Asp-i 29 in the quantum region, with link atoms used at the quantum/classical boundaries. In this study the protein was not truncated and was surrounded with a 24 A radius sphere of water molecules. Stochastic boundary methods were applied [66]. 

J Li, L Noodleman, DA Case. Electronic structure calculations Density functional methods with applications to transition metal complexes. In EIS Lever, ABP Lever, eds. Inorganic Electronic Structure and Spectroscopy, Vol. 1. Methodology. New York Wiley, 1999, pp 661-724. 

Freezing transitions have been examined in recent years by density functional methods [306-313]. Here we review the results [298] of a modification of the Ramakrishnan-Yussouff theory to the model fluid with Hamiltonian (Eq. (25)) a related study of phase transitions in a system of hard discs in two dimensions with Ising internal states which couple anti-ferromagnetically to their neighbors is shown in Ref. 304. First, a combined... 

Sec. Ill is concerned with the description of models with directional associative forces, introduced by Wertheim. Singlet and pair theories for these models are presented. However, the main part of this section describes the density functional methodology and shows its application in the studies of adsorption of associating fluids on partially permeable walls. In addition, the application of the density functional method in investigations of wettability of associating fluids on solid surfaces and of capillary condensation in slit-like pores is presented. 

Here r is the distance between the centers of two atoms in dimensionless units r = R/a, where R is the actual distance and a defines the effective range of the potential. Uq sets the energy scale of the pair-interaction. A number of crystal growth processes have been investigated by this type of potential, for example [28-31]. An alternative way of calculating solid-liquid interface structures on an atomic level is via classical density-functional methods [32,33]. 

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. 

Whether density functional methods are ab initio methods or not is a controversial question which we will not attempt to address. 

Barone also introduces two new basis sets, EPR-Il and EPR-llI. These are optimized for the calculation of hyperfine coupling constants by density functional methods. EPR-Il is a double zeta basis set with a single set of polarization functions and an enhanced s part. EPR-III is a triple zeta set including diffuse functions, double d polarization functions and a single set off functions. 

Barone, V. (1996) in Recent Advances in Density Functional Methods, ed. D. P. Chong, World Scientific, Singapore. 

Density-Functional Methods in Chemistry and Materials Science Edited by Michael Springborg Published 1997, ISBN 0 471 96759 9... 

An important conceptual, or even philosophical, difference between the orbital/wavefunction methods and the density functional methods is that, at least in principle, the density functional methods do not appeal to orbitals. In the former case the theoretical entities are completely unobservable whereas electron density invoked by density functional theories is a genuine observable. Experiments to observe electron densities have been routinely conducted since the development of X-ray and other diffraction techniques (Coppens, 2001).18... 

Meanwhile orbitals cannot be observed either directly, indirectly since they have no physical reality contrary to the recent claims in Nature magazine and other journals to the effect that some d orbitals in copper oxide had been directly imaged (Scerri, 2000). Orbitals as used in ab initio calculations are mathematical figments that exist, if anything, in a multi-dimensional Hilbert space.19 Electron density is altogether different since it is a well-defined observable and exists in real three-dimensional space, a feature which some theorists point to as a virtue of density functional methods. 

In addition most of the more tractable approaches in density functional theory also involve a return to the use of atomic orbitals in carrying out quantum mechanical calculations since there is no known means of directly obtaining the functional that captures electron density exactly. The work almost invariably falls back on using basis sets of atomic orbitals which means that conceptually we are back to square one and that the promise of density functional methods to work with observable electron density, has not materialized. 

As readers of this volume are also aware, the best of both approaches have been blended together with the result that many computations are now performed by a careful mixture of wavefunction and density approaches within the same computations (Hehre et al., 1986). But the unfortunate fact is that, as yet, there is really no such thing as a pure density functional method for performing calculations. The philosophical appeal of a universal solution for all the atoms in the periodic table based on observable electron density, rather than fictional orbitals, has not yet borne fruit.21,22... 

Interestingly, the energy difference is smallest for S7O which as a heterocycle forms a crown-shaped eight-membered ring similar to and isoelec-tronic with the well known 8 structure of 04a symmetry. The transformation of the heterocycle S7O into the homocyclic isomer 7=0 was studied by the molecular dynamics/density functional method but the unrealistically high barrier of 5 eV calculated for this transformation indicates that the system was far from equilibrium during most of the simulation [66]. 

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