Density gradient theory

The use of SAFT within theories for inhomogeneous fluids such as the square-gradient theory (usually called density-gradient theory, DGT) and density-functional theory" (DFT), provides a route towards the... 

Tractable models may be used to test approximations whose effect on the calculation of the properties of realistic systems is difficult to assess. We illustrate this point by using the results of the last section to test several versions of the van der Waals or density-gradient theory of Chapters 3 and 4. This theory, even in its most general form, is to be thought of as a set of approximations (smallness of p (z), constancy of the... 

A generalized density gradient theory of interfaces has been combined with a compressible lattice theory of polymers. This yields a unified theory of bulk and surface thermodynamic properties. A unique feature of this theory is that it is parameterless. The only parameters required to calculate a surface tension are obtained from pure component thermodynamic properties. Since the theory is a mean field theory, it is only applicable to non-polar and slightly polar liquids. For such systems, surface tensions can be accurately calculated. 

Recently we proposed a weight and poljrmer liquids. Thig theory was developed by com-bininggt j lattice fluid (LF) model with the density gradient theory of inhomogeneous fluids. The main objective of this paper is to illustrate that this method of estimating polymer melt surface tensions is superior to existing empirical or semi-empirical methods. 

Figure 1 illustrates that the lattice fluid/density gradient theory of interfaces adequately describes the molecular weight (MW) and temperature dependence of the surface tension of the n-alkanes. The inherent property of the theory responsible for this excellent agreement originates with the ability of the LF model to describe the variation of liquid density with MW and temperature. 

Duque, D. P mies, J.C. Vega, L.F. (2004). Interfacial properties of Lennard-Jones chains by direct simulation and density gradient theory. J. Chem. Phys. 121,11395-11401. 

Kahl, H. Enders, S. (2000). Calculation of surface properties of pure fluids using density gradient theory and SAFT-EOS. Fluid Phase Equilib. 172, 27-42. 

Massobrio C, Pasquarello A and Corso A D 1998 Structural and electronic properties of small Cu clusters using generalized-gradient approximations within density functional theory J. Chem. Phys. 109 6626... 

The application of density functional theory to isolated, organic molecules is still in relative infancy compared with the use of Hartree-Fock methods. There continues to be a steady stream of publications designed to assess the performance of the various approaches to DFT. As we have discussed there is a plethora of ways in which density functional theory can be implemented with different functional forms for the basis set (Gaussians, Slater type orbitals, or numerical), different expressions for the exchange and correlation contributions within the local density approximation, different expressions for the gradient corrections and different ways to solve the Kohn-Sham equations to achieve self-consistency. This contrasts with the situation for Hartree-Fock calculations, wlrich mostly use one of a series of tried and tested Gaussian basis sets and where there is a substantial body of literature to help choose the most appropriate method for incorporating post-Hartree-Fock methods, should that be desired. 

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. 

The pseudopotential density-functional technique is used to calculate total energies, forces on atoms and stress tensors as described in Ref. 13 and implemented in the computer code CASTEP. CASTEP uses a plane-wave basis set to expand wave-functions and a preconditioned conjugate gradient scheme to solve the density-functional theory (DFT) equations iteratively. Brillouin zone integration is carried out via the special points scheme by Monkhorst and Pack. The nonlocal pseudopotentials in Kleynman-Bylander form were optimized in order to achieve the best convergence with respect to the basis set size. 5... 

Schwerdtfeger, P., Bast, R., Gerry, M.C.L., Jacob, C.R., Jansen, M., Kelld, V., Mudring, A.V., Sadlej, A.J., Saue, T, Sdhnel, T. and Wagner, F.E. (2005) The quadrupole moment of the 3 /2 nuclear groimd state of Au from electric field gradient relativistic coupled cluster and density functional theory of small molecules and the solid slide. Journal of Chemical Physics, 122,124317-1-124317-9. 

Becke, A. D., 1999, Exploring the Limits of Gradient Corrections in Density Functional Theory , J. Comput. 

Bray, M. R., Deeth, R. J., Paget, V. J., Sheen, P. D., 1996, The Relative Performance of the Local Density Approximation and Gradient Corrected Density Functional Theory for Computing Metal-Ligand Distances in Werner-Type and Organometallic Complexes , Int. J. Quant. Chem., 61, 85. 

Burke, K., Perdew, J. R, Wang, Y., 1998, Derivation of a Generahzed Gradient Approximation The PW91 Density Functional , in Electronic Density Functional Theory. Recent Progress and New Directions, Dobson, J. F., Vignale, G., Das, M. P. (eds.), Plenum Press, New York. 

Gritsenko, O. V., Schipper, P. R. T., Baerends, E. J., 1997, Exchange and Correlation Energy in Density Functional Theory. Comparison of Accurate DFT Quantities With Traditional Hartree-Fock Based Ones and Generalized Gradient Approximations for the Molecules Li2, N2, F2 , J. Chem. Phys., 107, 5007. 

Helgaker, T., Watson, M., Handy, N. C., 2000, Analytical Calculation of Nuclear Magnetic Resonance Indirect Spin-Spin Coupling Constants at the Generalized Gradient Aproximation and Hybrid Levels of Density Functional Theory , J. Chem. Phys., 113, 9402. 

Laasonen, K., Parrinello, M., Car, R., Lee, C., Vanderbilt, D., 1993, Structures of Small Water Clusters Using Gradient-Corrected Density Functional Theory , Chem. Phys. Lett., 207, 208. 

Versluis, F., Ziegler, T., 1988, The Determination of Molecular Structures by Density Functional Theory. The Evaluation of Analytical Energy Gradients by Numerical Integration , J. Chem. Phys., 88, 322. 

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