Minhhuy Hô

A numerical study of molecular information entropies

Abstract Molecular information entropies are computed by means of a three-dimensional numerical integration from wavefunctions expanded in a variety of Gaussian basis sets at different levels. The results substantiate the use of the entropy sum as a measure of basis set quality. This sum is also shown to be sensitive to electron correlation. The previously observed trends for atomic systems computed from Slater-type orbitals are seen to be present in the results from wavefunctions expanded in Gaussian-type orbitals.

The He isoelectronic series and the Hooke’s law model: Correlation measures and modifications of Collins’ conjecture

The recently developed concept of a correlation entropy, S, as a quantitative measure of the correlation strength present in a correlated quantum many-body state is applied to the ground states of the He isoelectronic series He(Z) with varying nuclear charge Z and of the Hooke’s law model HLM(ω) with varying oscillator frequency ω. S is constructed from the natural orbital occupation numbers. It vanishes for weak correlation (large coupling constants Z or ω), and increases monotonically with decreasing Z or ω (strengthening correlation). A reduced correlation energy per particle Δecorr and a dimensionless ratio e=|Ecorr/E| are introduced which vanish asymptotically in the weak correlation limit in contrast to Ecorr and ecorr=Ecorr/N. These two intensive quantities, Δecorr and e, are compared with s=S/N. For both model systems, dΔecorr/ds⩾0 and de/ds⩾0 (which modifies Collins’ conjecture that |Ecorr|∼S).

Atomic information entropies beyond the Hartree-Fock limit

Atomic information entropies are computed from configuration interaction wavefunctions for members of the lithium isoelectronic series. For each member of the series, a sequence of wavefunctions built from increasingly larger basis sets is generated which satisfies a density convergence criterion, and exhibits a monotonic behaviour with respect to the density generated from the wavefunctions. Studies of the behaviour of the entropies along a sequence for a particular atom includes trends which have been shown to be present at the Hartree-Fock level. Results suggest that the position and momentum entropies are sensitive to small changes in density and thus can be useful indicators of the quality of the density. The sum of the entropies is also shown to be a useful indicator when density differences are larger. The nature of the information entropy-energy relationship is examined.

Relationships between Jaynes entropy of the one-particle density matrix and Shannon entropy of the electron densities

Relationships between the Jaynes and Shannon information entropies, both of which are related to the correlation energy, are given and the physical implications are explored. Evidence is provided from a study of the Be and Ne isoelectronic sequences that the Shannon entropy is more sensitive to the effects of the nuclear charge than is the Jaynes entropy. It is shown that the Jaynes entropy may be considered as the difference between the mean orbital Shannon entropy per electron and the mean orbital Shannon entropy of one electron. These mean orbital entropies display the same functional behavior as the total Shannon entropy throughout the isoelectronic sequence. We demonstrate that the Jaynes entropy may be considered as the sum of the Kullback–Leibler distance entropies occurring between natural spin orbital densities and a reference point whose occupation number is one. The large Z asymptotic behavior of the Jaynes and Shannon entropies is discussed. From a study of a Ne isonuclear sequence, it is show...

Interaction of anticonvulsant drugs with metals: a semi-empirical molecular orbital study of phenytoin–zinc(II) complexation

Abstract The interaction of Zn(II) cation with the anticonvulsant phenytoin (PHT) was investigated using semi-empirical AM1 molecular orbital calculations. All possible modes of PHT–Zn(II) complexation were systematically studied by aligning Zn(II) along the three amide faces of PHT’s imidazoline-2,4-dione ring. The AM1 calculations indicated that Zn(II) bridges two PHT molecules; six Zn(PHT) 2 2+ complexes were evaluated. In more stable structures, Zn(II) coordinates with two PHT through amide oxygens. These structures were hydrated, further optimized, and evaluated.

Hirshfeld-I charges in linear combination of atomic orbitals periodic calculations

Hirshfeld-I charges were implemented in the Crystal code, for periodic calculations with localized atomic basis sets. Some particular features of the present periodic implementation are detailed and discussed by means of selected illustrating examples. In these examples, the Hirshfeld-I charges are somewhere between the Bader and the Mulliken values and closer to the former. The implementation exploits heavily symmetry aspects and is shown to scale linearly with the unit cell dimension.

Theoretical studies of unusually short bond lengths in oxirane and derivatives

Abstract The π-Complex-Back-Donation model (π-cbd) has been used together with the topological analysis of the ab initio and semi-empirical densities to investigate bond lengths in the oxirane molecule and derivatives. Both models offer similar conclusions. The shortenings of the C–C bond in the oxirane ring and of the neighbouring C–C bond arise mainly from the substituent groups. However, neither the π-cbd model nor the atoms in molecules model offers a satisfactory explanation for the elongation of one of the C–O bonds.

Characterizing off-diagonal regions of one-electron density matrix

The off-diagonal regions of the one-electron density matrix (ODM) are characterized according to their contributions to the chemical bond. In particular, these regions of the ODM difference maps were used to characterize the chemical bond in various diatomic molecules. The nature of a critical point, core interaction critical point, in the off-diagonal part of ODM reveals the chemical bond type: maximum for covalent bond, minimum for closed-shell interaction, and saddle point for a charge-shift bond.

Electronic Charge Density Analysis of Li-Doped Polyacetylene: Molecular vs Periodic Descriptions and Nature of Li-to-Chain Bonding

A detailed analysis of the electronic structure and charge distribution around the trigonal site of Li-doped polyacetylene is reported using finite chain and periodic descriptions of the polymer. Atoms-in-molecules (AIM) analysis is done to characterize the nature of the bond between Li and the polymer backbone through the location of the bond critical points and computation of the total charge on the atomic basins around the doping site. We find that the Li atom donates practically one electron to the π-system, in accordance with the classical Su-Schriffer-Heeger model. However, despite that the Li atom is equidistant from the three closest C atoms in the geometric soliton, a single Li-C bond critical point is found. The AIM quantitative analysis of the electronic density reveals that the Li(+) ion is immersed into the polymer π-cloud in a way that resembles a metallic bonding interaction.

Asymptotic behaviour of the ratio of density gradient to electron density for atomic systems

The asymptotic behaviour of the negative ratio of the density gradient to the electron density, q(r), for neutral and singly charged atoms has been investigated. The results show that, for large r, q(r) can approach its limit √8ε, where ε is the first ionization potential, from either above or below depending on the specific system considered.