On-top Pair Density Research Articles

Momentum Distribution of the Uniform Electron Gas and Its Proper Parametrization

The momentum distribution of the unpolarized uniform electron gas in its Fermi liquid regime, n(k, rs), with the momenta k measured in units of the Fermi wave number and with the density parameter rs, is constructed assuming that n(0, rs), n(1±, rs), and the on-top pair density as well as the kinetic correlation energy are known. Preliminary results for rs = 1 to 6 are presented.

An Accurate Description of the Bergman Reaction Using Restricted and Unrestricted DFT: Stability Test, Spin Density, and On-Top Pair Density

DFT calculations provide a reliable description of the Bergman reaction of (Z)-hex-3-ene-1,5-diyne 1 provided the following are considered. (a) Restricted DFT (RDFT) calculations along the reaction path have to be replaced by unrestricted DFT (UDFT) calculations at those locations where the former description becomes unstable. This is the case in the region of the p-didehydrobenzene biradical 2, which possesses significant multireference character. (b) LSD and pure GGA functionals are more stable than hybrid functionals, which can be directly related to the composition of these functionals. With increasing instability, RDFT calculations lead to increasing errors in the S−T splitting and the geometry of 2 as well as in the energetics of the Bergman reaction. (c) LSD and GGA functionals underestimate the energy barrier of the Bergman reaction of 1. This becomes obvious when the correct experimental barrier is considered, which was not done in previous DFT investigations. (d) The best description of the Berg...

Thepara-didehydropyridine,para-didehydropyridinium, and related biradicals?a contribution to the chemistry of enediyne antitumor drugs

Structure and stability of seven singlet (S) biradicals formed by Bergman cyclization from enediynes are investigated with unrestricted DFT using B3LYP/6-31G(d,p) and B3LYP/6-311+G(3df,3pd). The corresponding triplets (T) are also calculated and compared with their S states utilizing the on-top pair density and the S-T difference on-top pair density. A relationship between the geometry of a S biradical, its stability, and its biradical character is established using the on-top pair density and calculated S-T splittings. Through-bond coupling between the single electrons of the S biradical can be enhanced by the incorporation of a N atom into para-didehydrobenzene 1 due to lowering of antibonding orbitals, shortening of ring bonds by anomeric effect, and increased overlap between the interacting orbitals. Strong through-bond interactions lead to a stabilization of the S state and an increase of the S-T splitting. Because through-bond interactions also determine the degree of coupling between the single electrons, stabilization of the S biradical, and an increase of the S-T splitting always means a lowering of the biradical character and the H abstraction ability, which is relevant for the use of N-containing enediynes and their biradicals in connection with the design of new antitumor drugs. The S para-didehydropyridine biradical 2 is strongly stabilized and, therefore, has only reduced biradical character. However, the latter can be enhanced by protonation, because this always leads to a lengthening of ring bonds and a reduction of the overlap between interacting orbitals. In the weakly acidic medium of a tumor cell, S biradicals containing an amidine group can be protonated to yield S biradicals with high biradical character (low S-T splittings, small changes in bond alternation relative to the T state), which will abstract H atoms from the DNA of a tumor cell. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 216–229, 2001

Why semilocal functionals work: Accuracy of the on-top pair density and importance of system averaging

Gradient-corrected density functionals provide a common tool for electronic structure calculations in quantum chemistry and condensed matter physics. This article explains why local and semilocal approximations work for the exchange-correlation energy. We demonstrate the high accuracy of the local spin-density (LSD) approximation for the on-top pair density, which provides the missing link between real atoms and molecules and the uniform electron gas. Special attention is devoted to the leading correction to exchange in the high-density (or weakly correlated) limit. We give an improved analytic expression for the on-top pair density in the uniform electron gas, calculating its spin-polarization dependence exactly in the high-density limit. We find the exact form of the gradient expansion for the on-top pair density, using Levy’s scaling of the interacting wave function. We also discuss the importance of system averaging, which unweights spatial regions where the density varies most rapidly. We show how the depth of the on-top hole correlates with the degree of locality of the exchange-correlation energy. Finally, we discuss how well fully nonlocal approximations (weighted-density, self-interaction correction, and hybrid-exchange) reproduce the on-top hole.

On-top pair-density interpretation of spin density functional theory, with applications to magnetism

The on-top pair density P(r, r) gives the probability that one electron will be found on top of another at position r. We find that the local spin density (LSD) and generalized gradient (GGA) approximations for exchange and correlation predict this quantity with remarkable accuracy. We show how this fact and the usual sum-rule arguments explain the success of these approximations for real atoms, molecules, and solids, where the electron spin densities do not vary slowly over space. Self-consistent LSD or GGA calculations make realistic predictions for the total energy E, the total density n(r), and the on-top pair density P(r,r), even in those strongly “abnormal” systems (such as stretched H2) where these approximations break symmetries and yield unrealistic spin magnetization densities m(r). We then suggest that ground-state ferromagnetic iron is a “normal” system, for which for LSD or GGA m(r) and the related local spin moment are trustworthy, but that iron above the Curie temperature and antiferromagnetic clusters at all temperatures are abnormal system for which the on-top pair density interpretation is more viable than the standard physical interpretation. As an example of a weakly abnormal system, we consider the four-electron ion with nuclear charge Z → ∞ © 1997 John Wiley & Sons, Inc.

Escaping the symmetry dilemma through a pair-density interpretation of spin-density functional theory.

In the standard interpretation of spin-density functional theory, a self-consistent Kohn-Sham calculation within the local spin density (LSD) or generalized gradient approximation (GGA) leads to a prediction of the total energy E, total electron density n(r)=${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$(r)+${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$(r), and spin magnetization density m(r)=${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$(r)-${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$(r). This interpretation encounters a serious ``symmetry dilemma'' for ${\mathrm{H}}_{2}$, ${\mathrm{Cr}}_{2}$, and many other molecules. Without changing LSD or GGA calculational methods and results, we escape this dilemma through an alternative interpretation in which the third physical prediction is not m(r) but the on-top electron pair density P(r,r), a quantity more directly related to the total energy in the absence of an external magnetic field. This alternative interpretation is also relevant to antiferromagnetic solids. We argue that the nonlocal exchange-correlation energy functional, which must be approximated, is most nearly local in the alternative spin-density functional theory presented here, less so in the standard theory, and far less so in total-density functional theory. Thus, in LSD or GGA, predictions of spin magnetization densities and moments are not so robust as predictions of total density and energy. The alternative theory helps to explain the surprising accuracy of LSD and GGA energies, and suggests that the correct solution of the Kohn-Sham equations in LSD or GGA is the fully self-consistent broken-symmetry single determinant of lowest total energy.