Density functional description

Rushton PP, Tozer DJ, Clark SJ (2002) Nonlocal density-functional description of exchange and correlation in silicon, Phys Rev B, 65 235203... 

Misquitta, A.J. and Szalewicz, K. (2002). Intermolecular forces from asymptotically corrected density functional description of monomers. Chem, Phys. Lett., 357, 301-6. 

The relativistic variant of the HK theorem guarantees the formal existence of a density functional description of relativistic systems but does not give any hint how to construct the crucial functional [j]. Explicit approximations to E(oi [y]... 

Thus, for example, in the HF description of the helium atom as two electrons of opposite spin with the same spatial distribution, the two electrons may occupy the same point in space notwithstanding their mutual repulsion. Attempts at the physical interpretation of these phenomena are important in the density-functional description of electronic structure which we discuss in Chapter 33. 

Misquitta A, Jeziorski B, Szalewicz K (2003) Dispersion energy from density-functional description of monomers. Phys Rev Lett 91 033201... 

Salahub, D. R. Castro, M. Fournier, R. Calaminici, P. Godbout, N. Goursot, A. Jamorski, C. Kobayashi, H. Martinez, A. Papai, I. Proynov, E. Russo, N. Sirois, S. Ushio, J. Vela, A. Density Functional Description of Metal-Metal and Metal-Ligand Bonds. In Theoretical and Computational Approaches to Interface Phenomena, Sellers, H. L., Golab, J. T., Eds. Plenum New York, 1994 pp 187-218. 

P. B. Paramonov and S. F. Lyuks5mtov, Density-functional description of water condensation in proximity of nanoscale aperity, J. Chem. Phys., 123,084705 [2005],... 

Bukowski, R., Szalewicz, K., Groenenboom, G., 8c van der Avoird, A. (2006). Interaction potential for water dimer from symmetry-adapted perturbation theory based on density functional description of monomers. Journal of Chemical Physics, 125, 044301. 

F. Ortmann, F. Bechstedt, W.G. Schmidt, Semiempirical van der Waals correction to the density functional description of solids and molecular structures. Phys. Rev. B 73(20) (2006)... 

R. M. Richard and J. M. Herbert, /. Ghem. Theory Gomput., 7, 1296-1306 (2011). Time-Dependent Density-Functional Description of the L State in Polycyclic Aromatic Hydrocarbons Charge-Transfer Character in Disguise ... 

Liu S, Parr RG (1997) Second-order density-functional description of molecules and chemical changes. J Chem Phys 106(13) 5578-5586... 

The statistical mechanical approach, density functional theory, allows description of the solid-liquid interface based on knowledge of the liquid properties [60, 61], This approach has been applied to the solid-liquid interface for hard spheres where experimental data on colloidal suspensions and theory [62] both indicate 0.6 this... 

A1.3.3 DENSITY FUNCTIONAL APPROACHES TO QUANTUM DESCRIPTIONS OF CONDENSED PHASES... 

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. 

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. 

Let us proceed with the description of the results from theory and simulation. First, consider the case of a narrow barrier, w = 0.5, and discuss the pair distribution functions (pdfs) of fluid species with respect to a matrix particle, gfm r). This pdf has been a main focus of previous statistical mechanical investigations of simple fluids in contact with an individual permeable barrier via integral equations and density functional methodology [49-52]. 

It is important to realize that whenever qualitative or frontier molecular orbital theory is invoked, the description is within the orbital (Hartree-Fock or Density Functional) model for the electronic wave function. In other words, rationalizing a trend in computational results by qualitative MO theory is only valid if the effect is present at the HF or DFT level. If the majority of the variation is due to electron correlation, an explanation in terms of interacting orbitals is not appropriate. 

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... 

State vector, specification of, 493 Stationarity property of probability density functions, 136 Stationary methods, 60 Statistical independence, 148 Statistical matrix, 419 including description of "mixtures, 423... 

These limitations, most urgently felt in solid state theory, have stimulated the search for alternative approaches to the many-body problem of an interacting electron system as found in solids, surfaces, interfaces, and molecular systems. Today, local density functional (LDF) theory (3-4) and its generalization to spin polarized systems (5-6) are known to provide accurate descriptions of the electronic and magnetic structures as well as other ground state properties such as bond distances and force constants in bulk solids and surfaces. 

Density functions can be obtained up to any order from the manipulation of the Slater determinant functions alone as defined in section 5.1 or from any of the linear combinations defined in section 5.2. Density functions of any order can be constructed by means of Lowdin or McWeeny descriptions [17], being the diagonal elements of the so called m-th order density matrix, as was named by Lowdin the whole set of possible density functions. For a system of n electrons the n-th order density function is constructed from the square modulus of any n-electron wavefunction attached to the n-electron system somehow. 

The usual way chemistry handles electrons is through a quantum-mechanical treatment in the frozen-nuclei approximation, often incorrectly referred to as the Born-Oppenheimer approximation. A description of the electrons involves either a wavefunction ( traditional quantum chemistry) or an electron density representation (density functional theory, DFT). Relativistic quantum chemistry has remained a specialist field and in most calculations of practical... 

---