Effects of electron–electron interaction on the band structure in polydiacetylenes

The ground‐state band structure of polydiacetylenes is theoretically studied with the extensional Su–Schriffer–Heeger model supplemented by electron–electron interactions. The results show the following. First, the interval of valence bands (conduction bands) increases because of the electron–electron interactions. Second, the effect of the on‐site Coulomb energy (U) is different from that of the nearest neighbor Coulomb repulsion (V); the competition between U and V shows that U makes the bandwidth narrower and the gap broader, whereas V makes the bandwidth broader and the gap narrower. There is a critical value of U/V. Third, the whole band width (E_w) decreases when the U/V ratio is less than 1.0 and increases when the U/V ratio is greater than 1.0 at V = 2.0 eV. Thus, the ground‐state band structure is sensitive to the U/V ratio. The results also show that electron–electron interactions can play an important role in the band structure of polydiacetylenes. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1656–1661, 2000     

Role of electron–electron coalescence density in density functional theory

An expression for the evaluation of electron–electron coalescence density as a functional of the density for any electron system is proposed. The formula, clarifies previously advanced upper bounds for this quantity and provides a method to independently estimate the system‐averaged on‐top exchange–correlation hole. The relationship with the on‐top pair density shows that producing the true electron–electron coalescense should be considered as a leading physical requirement for trial wave functions in any energy minimization scheme. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Modeling exact exchange potential in spherically confined atoms

In this work, local exchange potentials corresponding to the Hartree–Fock (HF) electron density have been obtained using the Zhao–Morrison–Parr method for a number of closed‐shell confined atoms and ions. The exchange potentials obtained and the resulting density were compared with those given by the Becke–Johnson (BJ) model potential. It is demonstrated that introducing a scaling factor to the BJ potential allows improving the quality of the resulting density. The optimum scaling factor increases with decreasing confinement radius. The performance of Karasiev and Ludeña's SCα‐LDA method as well as of the Becke‐88 exchange potential for reproducing the HF electron densities in confined atoms has been also examined. © 2015 Wiley Periodicals, Inc.     

Improved partition–expansion of two‐center distributions involving slater functions

The calculation of the electronic structure of large systems is facilitated by the substitution of the two‐center distributions by their projections on auxiliary basis sets of one‐center functions. An alternative is the partition–expansion method in which one first decides what part of the distribution is assigned to each center, and next expands each part in spherical harmonics times radial factors. The method is exact, requires neither auxiliary basis sets nor projections, and can be applied to Gaussian and Slater basis sets. Two improvements in the partition–expansion method for Slater functions are reported: general expressions valid for arbitrary quantum numbers are derived and the efficiency of the procedure is increased giving analytical solutions to integrals previously computed by numerical quadrature. The efficiency of the new version is assessed in several molecules and the advantages over the projection methods are pointed out. © 2013 Wiley Periodicals, Inc.     

Interesting properties of Thomas–Fermi kinetic and Parr electron–electron‐repulsion DFT energy functional generated compact one‐electron density approximation for ground‐state electronic energy of molecular systems

The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N‐dimensions to a (nonlinear, approximate) density functional of three spatial dimension one‐electron density for an N‐electron system, which is tractable in the practice, is a long desired goal in electronic structure calculation. If the Thomas‐Fermi kinetic energy (～∫ρ^5/3d r ₁) and Parr electron–electron repulsion energy (～∫ρ^4/3d r ₁) main‐term functionals are accepted, and they should, the later described, compact one‐electron density approximation for calculating ground state electronic energy from the 2nd Hohenberg–Kohn theorem is also noticeable, because it is a certain consequence of the aforementioned two basic functionals. Its two parameters have been fitted to neutral and ionic atoms, which are transferable to molecules when one uses it for estimating ground‐state electronic energy. The convergence is proportional to the number of nuclei (M) needing low disc space usage and numerical integration. Its properties are discussed and compared with known ab initio methods, and for energy differences (here atomic ionization potentials) it is comparable or sometimes gives better result than those. It does not reach the chemical accuracy for total electronic energy, but beside its amusing simplicity, it is interesting in theoretical point of view, and can serve as generator function for more accurate one‐electron density models. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009     

Electron‐density delocalization in many‐electron atoms confined by penetrable walls: A Hartree–Fock study

The electronic structure of several many‐electron atoms, confined within a penetrable spherical box, was studied using the Hartree–Fock (HF) method, coupling the Roothaan's approach with a new basis set to solve the corresponding one‐electron equations. The resulting HF wave‐function was employed to evaluate the Shannon entropy, , in configuration space. Confinements imposed by impenetrable walls induce decrements on when the confinement radius, R_c, is reduced and the electron‐density is localized. For confinements commanded by penetrable walls, exhibits an entirely different behavior, because when an atom starts to be confined, delivers values less than those observed for the free system, in the same way that the results presented by impenetrable walls. However, from a confinement radius, shows increments, and precisely in these regions, the spatial restrictions spread to the electron density. Thus, from results presented in this work, the Shannon entropy can be used as a tool to measure the electron density delocalization for many‐electron atoms, as the hydrogen atom confined in similar conditions.     

On the original proof by reductio ad absurdum of the Hohenberg–Kohn theorem for many‐electron Coulomb systems

It is shown that, for isolated many‐electron Coulomb systems with Coulombic external potentials, the usual reductio ad absurdum proof of the Hohenberg–Kohn theorem is unsatisfactory since the to‐be‐refuted assumption made about the one‐electron densities and the assumption about the external potentials are not compatible with the Kato cusp condition. The theorem is, however, provable by more sophisticated means, and it is shown here that the Kato cusp condition actually leads to a satisfactory proof. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Seminumerical calculation of the Hartree-Fock exchange matrix: application to two-component procedures and efficient evaluation of local hybrid density functionals

A two-component extension of the seminumerical procedure for the calculation of the Hartree-Fock (HF) exchange matrix recently presented by Neese et al. (Chem Phys 2009, 356, 98) was implemented into the program system TURBOMOLE. It is demonstrated that this allows for efficient self-consistent treatment of spin-orbit coupling at HF and hybrid density functional theory level. One-component HF calculations were performed to study the accuracy of integration grids and the exploitation of the molecular point group symmetry. The efficiency was tested, and for one-component calculations compared to the implementation realized by Neese. It was further demonstrated that local hybrid density functionals can be evaluated with this technique. The "prototype" of this class of functionals, Lh-BLYP, was applied to an organic molecule with more than 150 atoms.     

An instability condition for the Hartree–Fock solution of the infinite one‐dimensional system with two‐crossing bands. I. Singlet‐instability check of metallic carbon nanotube

An instability condition is derived for the Hartree–Fock solution so that it can be applied to the system in which the highest occupied and the lowest unoccupied bands cross at the in‐between point in the Brillouin zone. The instability check developed here is further applied to a metallic single‐walled carbon nanotube having the two‐crossing bands toward prediction of its instability. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 574–582, 2000     

Complete one‐ and two‐center partitioning scheme for the total energy in the Hartree–Fock theory

We proposed a complete calculation scheme for attributing the total energy by the Hartree–Fock theory to atoms (E_A) and the region between two atoms (E_AB). It was pointed out that the conventional method using the Fock matrix includes a large amount of mutual contamination in both E_A and E_AB. The new scheme was derived from the basic expression of the total energy. Calculated results by the new scheme satisfy the theoretical requirements. The scaling effect on partitioned energies was also examined. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 35–46, 1999     

van der Waals interactions are critical in Car–Parrinello molecular dynamics simulations of porphyrin–fullerene dyads

The interplay between electrostatic and van der Waals (vdW) interactions in porphyrin‐C₆₀ dyads is still under debate despite its importance in influencing the structural characteristics of such complexes considered for various applications in molecular photovoltaics. In this article, we sample the conformational space of a porphyrin‐C₆₀ dyad using Car–Parrinello molecular dynamics simulations with and without empirical vdW corrections. Long‐range vdW interactions, which are poorly described by the commonly used density functional theory functionals, prove to be essential for a proper dynamics of the dyad moieties. Inclusion of vdW corrections brings porphyrin and C₆₀ close together in an orientation that is in agreement with experimental observations. The structural differences arising from the vdW corrections are shown to be significant for several properties and potentially less important for others. Additionally, our Mulliken population analysis reveals that contrary to the common belief, porphyrin is not the primary electron donating moiety for C₆₀. In the considered dyad, fullerene's affinity for electrons is primarily satisfied by charge transfer from the amide group of the linker. However, we show that in the absence of another suitable bound donor, C₆₀ can withdraw electrons from porphyrin if it is sufficiently close. © 2015 Wiley Periodicals, Inc.     

Development of spin‐dependent relativistic open‐shell Hartree–Fock theory with time‐reversal symmetry (I): The unrestricted approach

An open‐shell Hartree–Fock (HF) theory for spin‐dependent, two‐component relativistic calculations, termed the Kramers‐unrestricted HF (KUHF) method, is developed. The present KUHF method, which is formulated as a relativistic counterpart of nonrelativistic UHF, is based on quaternion algebra and partly uses time‐reversal symmetry. The fundamental characteristics of KUHF are discussed in this study. From numerical assessments, it was revealed that KUHF gives a corresponding solution to nonrelativistic UHF; furthermore, KUHF properly describes spin‐orbit interactions. In addition, KUHF can improve the self‐consistent field convergence behavior in spin‐dependent calculations, for example, for f‐block elements.     

Experimental and theoretical investigation of the molecular and electronic structure of N′‐benzylidene‐N‐[4‐(3‐methyl‐3‐phenyl‐cyclobutyl)‐thiazol‐2‐yl]‐chloro‐acetic acid hydrazide

The title compound, N′‐benzylidene‐N‐[4‐(3‐methyl‐3‐phenyl‐cyclobutyl)‐thiazol‐2‐yl]‐chloro‐acetic acid hydrazide, has been synthesized and characterized by elemental analysis, IR, ¹H and ¹³C NMR, and X‐ray single crystal diffraction. The compound crystallizes in the orthorhombic space group P 21 21 21 with a = 5.8671 (3) Å, b = 17.7182 (9) Å, and c = 20.6373 (8) Å. Moreover, the molecular geometry from X‐ray experiment, the molecular geometry, vibrational frequencies, and gauge‐including atomic orbital ¹H and ¹³C chemical shift values of the title compound in the ground state have been calculated by using the Hartree–Fock and density functional methods (B3LYP) with 6‐31G(d) and 6‐31G(d,p) basis sets. The results of the optimized molecular structure are exhibited and compared with the experimental X‐ray diffraction. Besides, molecular electrostatic potential, Frontier molecular orbitals, and thermodynamic properties of the title compound were determined at B3LYP/6‐31G(d) levels of theory. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Development of spin‐dependent relativistic open‐shell Hartree–Fock theory with time‐reversal symmetry (II): The restricted open‐shell approach

An open‐shell Hartree–Fock (HF) theory for spin‐dependent two‐component relativistic calculations, termed the Kramers‐restricted open‐shell HF (KROHF) method, is developed. The present KROHF method is defined as a relativistic analogue of ROHF using time‐reversal symmetry and quaternion algebra, based on the Kramers‐unrestricted HF (KUHF) theory reported in our previous study (Int. J. Quantum Chem., doi: 10.1002/qua.25356 ). As seen in the nonrelativistic ROHF theory, the ambiguity of the KROHF Fock operator gives physically meaningless spinor energies. To avoid this problem, the canonical parametrization of KROHF to satisfy Koopmans' theorem is also discussed based on the procedure proposed by Plakhutin et al. (J. Chem. Phys. 2006 , 125, 204110). Numerical assessments confirmed that KROHF using Plakhutin's canonicalization procedure correctly gives physical spinor energies within the frozen‐orbital approximation under spin–orbit interactions.     

Experimental and Quantum‐Chemical Studies on the Thermochemical Stabilities of Mercury Carbodiimide and Mercury Cyanamide

Calorimetric dissolution measurements of the solid compounds mercury carbodiimide HgNCN(I ) and mercury cyanamide HgNCN(II ) in aqueous HCl that targeted at their thermochemical stabilities show the cyanamide species HgNCN(II ) to be the more stable phase in terms of both enthalpy and Gibbs energy with an enthalpy difference of 2–3 kJ mol^?1. While the stability ranking of HgNCN(I ) and HgNCN(II ) thus perfectly matches Pearson's HSAB concept, quantum‐chemical stability predictions using common parametrizations of density functional theory appear to be fundamentally flawed. An analysis of the error is attempted on the basis of correlated wave functions for related molecules.     

Conditions for accurate description of the electron density of atoms and molecules

Based on the Kato's cusp condition of the electron density and our recent relations for local strongly decaying properties in an electronic system, necessary conditions for trial electron densities of atomic and molecular systems are derived. These conditions take the form of integral‐differential equations, and their validity is verified numerically. The relevance of these conditions to the Thomas–Fermi problem in the orbital‐less density functional approach is discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006