Biomedical subjects

Aron J Cohen

Publications and source records attributed to Aron J Cohen.

5 recordsLinked to original sources

PubMed2006

Many-electron self-interaction error in approximate density functionals.

One of the most important challenges in density functional theory (DFT) is the proper description of fractional charge systems relating to the self-interaction error (SIE). Traditionally, the SIE has been formulated as a one-electron problem, which has been addressed in several recent functionals. However, these recent one-electron SIE-free functionals, while greatly improving the description of thermochemistry and reaction barriers in general, still exhibit many of the difficulties associated with SIE. Thus we emphasize the need to surpass this limit and shed light on the many-electron SIE. After identifying the sufficient condition for functionals to be free from SIE, we focus on the symptoms and investigate the performance of most popular functionals. We show that these functionals suffer from many-electron SIE. Finally, we give a SIE classification of density functionals.

Journal Article↗

PubMed2006

Influence of Coulomb-attenuation on exchange-correlation functional quality.

The dependence of functional quality on the attenuation parameters--which control the limiting (r12-->0, infinity) values and the rate of attenuation--is investigated for a Coulomb-attenuated exchange-correlation functional. For the attenuation and functional form considered, satisfaction of an exact long-range condition is detrimental for properties such as atomisation energies and bond lengths, but does improve classical reaction barriers and small molecule electronic excitation energies. The functionals considered can provide high quality valence, Rydberg, intramolecular and asymptotic intermolecular charge transfer (CT) excitations, but none are able to provide a simultaneously optimal description of all classes; CT excitations are not necessarily improved compared to those from conventional functionals. The study highlights the need for further development of Coulomb-attenuated functionals.

Journal Article↗

PubMed2006

Self-interaction-free exchange-correlation functional for thermochemistry and kinetics.

We develop a self-interaction-free exchange-correlation functional which is very accurate for thermochemistry and kinetics. This is achieved by theoretical construction of the functional form and nonlinear fitting. We define a simple interpolation of the adiabatic connection that uses exact exchange, generalized gradient approximation (GGA) and meta-GGA functionals. The performance is optimized by fitting a small number of empirical parameters. Overall the new functional improves significantly upon hybrids and meta-GGAs while correctly describing one-electron systems. The mean absolute error on a large set of reaction barriers is reduced to 1.99 kcal/mol.

Kinetics↗

PubMed2005

Analytic energy gradients of the optimized effective potential method.

The analytic energy gradients of the optimized effective potential (OEP) method in density-functional theory are developed. Their implementation in the direct optimization approach of Yang and Wu [Phys. Rev. Lett. 89, 143002 (2002)] and Wu and Yang [J. Theor. Comput. Chem. 2, 627 (2003)] are carried out and the validity is confirmed by comparison with corresponding gradients calculated via numerical finite difference. These gradients are then used to perform geometry optimizations on a test set of molecules. It is found that exchange-only OEP (EXX) molecular geometries are very close to the Hartree-Fock results and that the difference between the B3LYP and OEP-B3LYP results is negligible. When the energy is expressed in terms of a functional of Kohn-Sham orbitals, or in terms of a Kohn-Sham potential, the OEP becomes the only way to perform density-functional calculations and the present development in the OEP method should play an important role in the applications of orbital or potential functionals.

Journal Article↗

PubMed2004

Density-functional generalized-gradient and hybrid calculations of electromagnetic properties using Slater basis sets.

In this paper we extend our density-functional theory calculations, with generalized gradient approximation and hybrid functionals, using Slater-type orbitals (STOs), to the determination of second-order molecular properties. The key to the entire methodology involves the fitting of all STO basis function products to an auxiliary STO basis, through the minimization of electron-repulsion integrals. The selected properties are (i) dipole polarizabilities, (ii) nuclear magnetic shielding constants, and (iii) nuclear spin-spin coupling constants. In all cases the one-electron integrals involving STOs were evaluated by quadrature. The implementation for (ii) involved some complexity because we used gauge-including atomic orbitals. The presence of two-electron integrals on the right-hand side of the coupled equations meant that the fitting procedure had to be implemented. For (iii) in the hybrid case, fitting procedures were again required for the exchange contributions. For each property we studied a number of small molecules. We first obtained an estimate of the basis set limit using Gaussian-type orbitals (GTOs). We then showed how it is possible to reproduce these values using a STO basis set. For (ii) a regular TZ2P quality STO basis was adequate; for (i) the addition of one set of diffuse functions (determined by Slater's rules) gave the required accuracy; for (iii) it was necessary to add a set of 1s functions, including one very tight function, to give the desired result. In summary, we show that it is possible to predict second-order molecular properties using STO basis sets with an accuracy comparable with large GTO basis sets. We did not encounter any major difficulties with either the selection of the bases or the implementation of the procedures. Although the energy code (especially in the hybrid case) may not be competitive with a regular GTO code, for properties we find that STOs are more attractive.

Journal Article↗