A study of excited states in trans-polyacetylene in the Hartree–Fock,Tamm–Dancoff,and random-phase approximation

We report calculations of the excitonic spectra for trans-polyacetylene obtained in the Hartree–Fock, Tamm–Dancoff, and random-phase approximations. In the first case, in terms of two-particle propagator theory, the interaction between the excited electron and the hole is neglected. In the latter two cases, this interaction is considered in the first order. In this framework, the interaction between excitations of different bands and k-vectors has been included. We discuss the bandwidths and density of states for π–π*, σ–π*, π–σ*, and σ–σ* excitons. © 1993 John Wiley & Sons, Inc.     

Self-consistent Thomas–Fermi–Dirac theory,extended by Gell-Mann and Brueckner correlation,in terms of density n and its two reduced gradients ∇2n/n and ∇n/n

We prove the following results, relevant for the density functional theory: the Thomas–Fermi–Dirac theory, generalized to include the contribution due to the high electron density result of Gell-Mann and Brueckner for the correlation energy, is shown to lead to a differential equation for the self-consistent ground-state density n( r ) in atoms and molecules in the form F(n, { ∇ n/n}², ∇²n/n)=1, where the function F is given explicitly. A straightforward extension yields a similar result for the equation determining the Pauli plus exchange–correlation potential and for the divergence of the many-electron force. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 145–149, 1998     

N‐band Hubbard models. III. Boson–fermion and interaction–boson models for high‐Tc superconductivity

In this series of articles (I, II), N‐band Hubbard models have been considered for strongly correlated electron systems, which are realized in d–p, π–d, π–R, and σ–R conjugated systems. The magnetism and superconductivity of these systems have been elucidated in terms of effective exchange integrals (J), which are calculated by first‐principle methods. In part III of this series, the BCS–BEC crossover theory, has been introduced to elucidate the physical foundation of our J and JP model for the high‐T_c superconductivity (HTSC). The boson–fermion (BF) model for this theory is found useful for a reasonable explanation of the experimental phase diagrams of HTSC. The underlying physics of the BF model is different from that of the slave boson field‐theoretical model assuming spinon–holon condensations in the low dimension. The interaction boson model (IBM) for nuclear matter is also employed to describe the cooperative mechanisms of electron–phonon (EP), spin fluctuation (SF), charge fluctuation (CF), and many‐bands (MB) effects. This phenomenological model is useful for pictorial understanding and for the theoretical explanation of the cooperative mechanisms: (EP + SF), (SF + CF), (EP + SF + MB), etc. These are also investigated in analogy to BF model of fermionic gases, where the Feshbach resonance between boson and fermion is responsible for their coupling. The implications of these theoretical results are discussed in relation to recent ALPES and STM experiments for HTSC, which suggest the contributions of SF (J) and EP (P) interactions. The recently discovered superconductivity of boron‐doped diamond is examined as an example of two‐band sigma‐radical (σ–R) conjugated systems. Finally, the bipolaron model is briefly discussed in relation to boson–fermion model via EP interaction to superconductivity. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Thomas–Fermi approximation for the quasi‐two‐dimensional electron gas

To take into account static correlation effects in the quasi‐two‐dimensional electron gas a screened Coulombic interaction between particles is studied. The Thomas–Fermi approximation is used and the potential screening appears as a function of the Wigner–Seitz density parameter r_s and the effective width t of the system. With the self‐consistent field theory applied to the modified deformable jellium, the ground‐state energy per particle and the conditions for electron localization are obtained in terms of the interparticle distance and the screening parameter μ. A critical minimum characteristic width t_c is obtained; below t_c no long‐range order is obtained. For larger widths a stable localized state is predicted at finite densities. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 269–276, 2001     

Ab initio calculation of the Dzyaloshinskii–Moriya parameters: Spin–orbit GSO‐HF,DFT, and CI approaches

We present ab initio methods to determine the Dzyaloshinskii–Moriya (DM) parameter, which provides the anisotropic effects of noncollinear spin systems. For this purpose, we explore various general spin orbital (GSO) approaches, such as Hartree–Fock (HF), density functional theory (DFT), and configuration interaction (CI), with one‐electron spin–orbit coupling (SOC1). As examples, two simple D_3h‐symmetric models, H₃ and B(CH₂)₃, are examined. Implications of the computational results are discussed in relation to as isotropic and anisotropic interactions of molecular‐based magnets. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Nonadiabatic sudden increase of the cooperative kinetic effect at lattice energy stabilization—Microscopic mechanism of superconducting state transition: Model study of MgB2

The theory of the nonadiabatic electron–vibration interactions has been applied to the study of MgB₂ superconducting state transition. It has been shown that at nonadiabatic conditions in which the Born–Oppenheimer approximation is not valid and electronic motion is dependent not only on the nuclear coordinates but also on the nuclear momenta, the fermionic ground‐state energy of the studied system can be stabilized by nonadiabatic electron–phonon interactions at broken translation symmetry. Moreover, the new arising state is geometrically degenerate; i.e., there are an infinite number of different nuclear configurations with the same fermionic ground‐state energy. The model study of MgB₂ yields results that are in a good agreement with the experimental data. For distorted lattice, with 0.016 Å/atom of in‐plane out‐of‐phase B? B atoms displacements out of the equilibrium (E_2g phonon mode) when the nonadiabatic interactions are most effective, it has been calculated that the new arising state is 87 meV/unit cell more stable than the equilibrium–high symmetry clumped nuclear structure at the level of the Born–Oppenheimer approximation. The calculated T_c is 39.5 K. The resulting density of states exhibits two‐peak character, in full agreement with the tunneling spectra. The peaks are at ±4 meV, corresponding to the change of the π band density of states, and at ±7.6 meV, corresponding to the σ band. The superconducting state transition can be characterized as a nonadiabatic sudden increase of the cooperative kinetic effect at lattice energy stabilization (NASICKELES). © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Electron localizability indicators ELI–D and ELIA for highly correlated wavefunctions of homonuclear dimers. I. Li2, Be2, B2, and C2

Electron localizability indicators based on the parallel‐spin electron pair density (ELI–D) and the antiparallel‐spin electron pair density (ELIA) are studied for the correlated ground‐state wavefunctions of Li₂, Be₂, B₂, and C₂ diatomic molecules. Different basis sets and reference spaces are used for the multireference configuration interaction method following the complete active space calculations to investigate the local effect of electron correlation on the extent of electron localizability in position space determined by the two functionals. The results are complemented by calculations of effective bond order, vibrational frequency, and Laplacian of the electron density at the bond midpoint. It turns out that for Li₂, B₂, and C₂ the reliable topology of ELI–D is obtained only at the correlated level of theory. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Accuracy and limitations of the pseudopotential method

Molecular model potential calculations have been performed within the SCF approximation on nine di- and triatomic molecules from the first row of the periodic table. We compare the molecular constants with ab initio SCF values and with model potential results obtained by other authors. Our results are accurate to a few per cent. The three most significant approximations in molecular model potential theory are: 1) The molecular model potential is the sum of atomic model potentials; 2) The atomic model potential is energy-independent; 3) The electron interaction model operator is l/r ₁₂. We arrive at the following general conclusions concerning these approximations: 1) The first approximation does not hold for strongly ionic molecules and for some highly excited molecular states. 2) Approximations 2 and 3 cancel to a large extent in molecules as they do in atoms, except in the case where approximation 1 breaks down. 3) Although various model- and pseudo-potentials yield reasonable results for atoms, not all of them are suitable for molecular calculations.     

Electron localizability indicators ELI–D and ELIA for highly correlated wavefunctions of homonuclear dimers. II. N2, O2, F2, and Ne2

Electron localizability indicators based on the electron pair density ELI–D and ELIA Electron localizability indicators ELI‐D and ELIA based on the electron pair density are studied for the correlated ground‐state wavefunctions of N₂, O₂, F₂, and Ne₂ diatomics. Different basis sets and reference spaces are used for the multireference configuration interaction method following the complete active space calculations to investigate the local effect of electron correlation on the extent of electron localizability in position space determined by the two indicators. The results are complemented by calculations of effective bond order, vibrational frequency, and Laplacian of the electron density at the bond midpoint. It turns out that for O₂ and F₂, the reliable topology of ELI–D is obtained only at the correlated level of theory. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

Quantum-chemical modeling of photoelectron spectra and electronic structure of <Emphasis Type="Italic">tris</Emphasis>-β-diketonates of 3<Emphasis Type="Italic">d</Emphasis>-metals Sc,Ti, V

The electronic structure and ionization energies of chelate complexes were calculated for transition metals Sc, Ti, and V using the Hartree-Fock (HF)SCF ab initio approximations. As the number of d electrons increases in the series of these compounds, the sequence of HF orbitals does not agree any longer with the PES bands and with the data obtained in the density functional theory approximation. Using the configuration interaction (CI) method considerably improves agreement with experiment. For the vanadium complex containing an odd d electron in the ionized state, the HF orbitals become a rough approximation for the CI decomposition, hindering the interpretation of the ionic states.Original Russian Text Copyright © 2004 by V. I. Vovna and I. S. OsmushkoTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 4, pp. 651–659, July–August, 2004.This revised version was published online in April 2005 with a corrected cover date.     

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     

Carbon-13 spin–lattice relaxation times as a probe for the study of electron donor–acceptor complexes

¹³C spin–lattice relaxation times (T₁'s) are reported for C-3 of 2-methylindole (methyl,3-¹³C₂) as a function of the concentration of added 1,3,5-trinitrobenzene at 35°C in 1,2-dichloroethane. The observed decreases in T₁, with increasing concentrations of 1,3,5-trinitrobenzene, are interpreted in terms of longer time-averaged correlation times which result from (a) the formation of increasing amounts of electron donor–acceptor complex and (b) increases in viscosity. An equation is derived which makes it possible to obtain estimates of the equilibrium constant for complex formation, and the spin–lattice relaxation time of the complex, from the observed T₁'s and viscosity measurements. From the data obtained, values of 6.4 × 10^?12 and 14.1 × 10^?12 s rad^?1 were calculated for the effective correlation times (at 35°C and 0.686 centipoise) and 0.21 and 0.28 nm for the effective radii of free and complexed donor respectively.     

Rouse–Bueche theory and the calculation of the monomeric friction coefficient in a filled system

Direct experimental access to the monomeric friction coefficient (ζ₀) relies on the availability of a suitable polymer dynamics model. Thus far, no method has been suggested that is applicable to filled systems, such as filled rubbers or microphase‐segregated A–B–A thermoplastic elastomers (TPEs) at T_g,B < T < T_g,A. Building upon the procedure proposed by Ferry for entangled and unfilled polymer melts, the Rouse–Bueche theory is applied to an undiluted triblock copolymer to extract ζ₀ from the linear behavior in the rubber‐glass transition region, and to estimate the size of Gaussian submolecules. When compared at constant T – T_g, the matrix monomeric friction factor is consistent with the corresponding value for the homopolymer melt. In addition, the characteristic Rouse dimensions are in good agreement with independent estimates based on the Kratky–Porod worm‐like chain model. These results seem to validate the proposed approach for estimating ζ₀ in filled systems. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1437–1442     

A model for the helix–coil transition of DNA

The helix–coil phase transition of DNA is studied through a model equivalent to the one used in the theory of superconductivity. A distribution function for the excitations analogous to the usual Fermi function is obtained which depends on the parameter T₀, the maximum temperature at which all pairs of bases are bonded. The expression for the number of unbonded pairs of bases depends only on the two parameters, T₀ and T_c (critical temperature).     

Ab initio copper–water interaction potential for the simulation of aqueous solutions

A new ab initio effective two-body potential that aims at mimicking the average copper–water interaction energy of the first solvation shell was developed. This new potential, together with the MCY water–water potential and a three-body ion–water–water induction potential, is tested in simulations of gas-phase clusters [Cu²⁺? (H₂O)₂₀] and diluted solutions [Cu²⁺? (H₂O)₂₀₀] at T = 298 K. The results of simulations with conventional ab initio pair potentials, with and without three-body induction corrections, are also presented. The different types of copper–water interaction potentials are evaluated comparatively and the efficiency of the newly proposed effective pair potential is discussed. © 1993 John Wiley & Sons, Inc.     

Electron–Electron interaction energy in homonuclear diatomic molecules

The derivative of the electron–electron potential energy U_ee with respect to internuclear separation R is studied for light homonuclear diatomic molecules at equilibrium. It is readily related to nuclear–nuclear potential energy U_nn, the force constant K, and the electron–nuclear potential energy U_en. An approximate expression, based on the simplest form of density functional theory, is then used to eliminate dU_en/dR|_Re. The result thus obtained for dU_ee/dR|_Re transcends an earlier proposal of Kryachko by including a term 2/3R_eK, with K the force constant. Numerical tests at SCF–RHF level are presented for nine homonuclear diatomic molecules.     

Theoretical study in [C2H4–Tl]+ and [C2H2–Tl]+ complexes

We studied the attraction between [C₂H_n] and Tl(I) in the hypothetical [C₂H_n–Tl]⁺ complexes (n = 2,4) using ab initio methodology. We found that the changes around the equilibrium distance C–Tl and in the interaction energies are sensitive to the electron correlation potential. We evaluated these effects using several levels of theory, including Hartree–Fock (HF), second‐order Møller–Plesset (MP2), MP4, coupled cluster singles and doubles CCSD(T), and local density approximation augmented by nonlocal corrections for exchange and correlation due to Becke and Perdew (LDA/BP). The obtained interaction energies differences at the equilibrium distance R_e (C–Tl) range from 33 and 46 kJ/mol at the different levels used. These results indicate that the interaction between olefinic systems and Tl(I) are a real minimum on the potential energy surfaces (PES). We can predict that these new complexes are viable for synthesizing. At long distances, the behavior of the [C₂H_n]–Tl⁺ interaction may be related mainly to charge‐induced dipole and dispersion terms, both involving the individual properties of the olefinic π‐system and thallium ion. However, the charge‐induced dipole term (R^?4) is found as the principal contribution in the stability at long and short distances. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Novel method of self‐interaction corrections in density functional calculations

It is demonstrated that the commonly applied self‐interaction correction (SIC) used in density functional theory does not remove all self‐interaction. We present as an alternative a novel method that, by construction, is totally free from self‐interaction. The method has the correct asymptotic 1/r dependence. We apply the new theory to localized f electrons in praseodymium and compare with the old version of SIC, the local density approximation (LDA) and with an atomic Hartree–Fock calculation. The results show a lowering of the f level, a contraction of the f electron cloud and a lowering of the total energy by 13 eV per 4 f electron compared to LDA. The equilibrium volume of the new SIC method is close to the ones given by LDA and the older SIC method and is in good agreement with experiment. The experimental cohesive energy is in better agreement using the new SIC method, both compared to LDA and another SIC method. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 247–252, 2001