Local density function approach

We have extended the linear combination of Gaussian-type orbitals local-density functional approach to calculate the total energies and electronic structures of helical chain polymers[35]. This method was originally developed for molecular systems[36-40], and extended to two-dimensionally periodic sys-tems[41,42] and chain polymers[34j. The one-electron wavefunctions here are constructed from a linear combination of Bloch functions c>>, which are in turn constructed from a linear combination of nuclear-centered Gaussian-type orbitals Xylr) (in ihis case, products of Gaussians and the real solid spherical harmonics). The one-electron density matrix is given by... 

Murray, J. S., J. M. Seminario, M. C. Concha, and P. Politzer. 1992. An Analysis of Molecular Electrostatic Potentials Obtained by a Local Density Functional Approach. Int. J. Quant. Chem. 44,113. 

Table 3 Optimized regular interatomic distance (in A) and gain in energy per C2H2 unit (in eV) of regular polyacetylene by report to the alternating ground state, with the Neel state based higher order and the RVB ansatze. Results from Local-density-functional approach of Mintmire and White [48], Hartree-Fock and Mpller-Plesset perturbation Theory of Suhai [50], or Ashkenazi [49] are included.

An LCAO (linear combination of atomic orbitals) local-density functional approach was used to calculate the band structures of a series of polymer chain conformations unsubstituted polysilane in the all-trans conformation and in a 411 helical conformation, and all-trans poly(dimethylsilane). Calculated absorption spectra predict a highly anisotropic absorption for the all-trans conformation of polysilane, with the threshold absorption peak arising strictly from polarizations parallel to the chain axis. The absorption spectrum for the helical conformation is much more isotropic. Results for the dimethyl-substituted polysilane chain suggest that the states immediately surrounding the Fermi level retain their silicon-backbone a character upon alkyl-group substitution, although the band gap decreases by I eV because of contributions from alkyl substituent states both below the valence band and above the conduction band to the frontier states. 

The local-density functional approach was used to compare the band structures of the sW-trans conformation of unsubstituted polysilane with a 4/1 helical conformation and with an dll-trans conformation of dimethyl-substituted poly silane. In line with previous theoretical studies, the electronic wave functions in the vicinity of the Fermi level are primarily silicon-back-bone states, with the major effect of methyl substitution being a decrease in the gap. The predicted absorption spectra for the dll-trans conformations of unsubstituted and dimethyl-substituted polysilane are similar for nearthreshold absorption. Given this similarity, we believe that the shift in energy and strong anisotropy of threshold absorption that we predict for the two extremes of the dll-trans conformation and the dll-gauche model will also occur in alkyl-substituted systems, which are currently under investigation. 

One-electron calculations were carried out self-consistently based on the local density functional approach using the Slater s Xa potential (7). In the present calculation, a was fixed at 0.7, which was found to be the most appropriate value in many cases (8). The molecular orbitals were constructed as Hnear combination of the atomic orbitals (LCAO). The most remarkable feature of our program is that the atomic orbitals are created numerically in each iteration and flexible to the chemical environment. The details of this program have been described by Adachi et al. (9). 

Murray JS, Seminario JM, Concha MC, Politzer P. An analysis of molecular electrostatic potentials obtained by a local density functional approach. Int J Quantum Chem 1992 44 113-122. 

J.W. Mintmire, An LCAO Local Density Functional Approach to Sur ce Electronic Stmc-ture Calculations, Ph.D. Thesis, University of Florida, 1980 (unpublished). 

Delley B (1991) Analytic energy derivatives in the numerical local-density-functional approach. J Chem Phys 94(11) 7245— 7250... 

Local Density from a Density Functional Approach... 

FIG. 6 A comparison of the Monte Carlo (points), HHNCl, HNCl, and PYl density profiles. The results are for bulk density 0.403 (lower group of curves) and 0.741 (upper group of curves). The curves at z — 0, are, from the bottom, from HHNCl and HNCl approximations. (Reprinted from A. Trokhymchuk, D. Henderson, S. Sokolowski. Local density of overlapping spheres near a hard wall A density functional approach. Physics Letters A 209, 317-320. 1995, with permission from Elsevier Science.)... 

In this contribution it is shown that local density functional (LDF) theory accurately predicts structural and electronic properties of metallic systems (such as W and its (001) surface) and covalently bonded systems (such as graphite and the ethylene and fluorine molecules). Furthermore, electron density related quantities such as the spin density compare excellently with experiment as illustrated for the di-phenyl-picryl-hydrazyl (DPPH) radical. Finally, the capabilities of this approach are demonstrated for the bonding of Cu and Ag on a Si(lll) surface as related to their catalytic activities. Thus, LDF theory provides a unified approach to the electronic structures of metals, covalendy bonded molecules, as well as semiconductor surfaces. 

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. 

In addition to these studies, the DHFR catalytic mechanism has been studied using the local density function (LDF) approach.22 A detailed understanding of the catalytic mechanism is often very useful in the design of high affinity enzyme inhibitors since it can shed light on the transition state structure and the key interactions used by the enzyme to stabilize it. 

The Hartree-Fock (HF) and local density functional theory (local DFT) methods provide a first level of accurate quantitative approach to a number of problems in chemistry. Unfortunately, this is seldom the case in... 

Density functional approaches to molecular electronic structure rely on the existence theorem [10] of a universal functional of the electron density. Since this theorem does not provide any direction as to how such a functional should be constructed, the functionals in existence are obtained by relying on various physical models, such as the uniform electron gas and others. In particular, the construction of an exchange-correlation potential that depends on the electron density only locally seems impossible without some approximations. Such approximate exchange-correlation potentials have been derived and applied with some success for the description of molecular electronic ground states and their properties. However, there is no credible evidence that such simple constructions can lead to either systematic approximate treatments, or an exact description of molecular electronic properties. The exact functional that seems to... 

Another viable method to compare experiments and theories are simulations of either the cell model with one or more infinite rods present or to take a solution of finite semi-flexible polyelectrolytes. These will of course capture all correlations and ionic finite size effects on the basis of the RPM, and are therefore a good method to check how far simple potentials will suffice to reproduce experimental results. In Sect. 4.2, we shall in particular compare simulations and results obtained with the DHHC local density functional theory to osmotic pressure data. This comparison will demonstrate to what extent the PB cell model, and furthermore the whole coarse grained RPM approach can be expected to hold, and on which level one starts to see solvation effects and other molecular details present under experimental conditions. 

Combined local-density-functional molecular dynamics approach... 

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