Theory of strongly correlated electron systems. II. Including correlation effects into electronic structure calculations

We have previously shown that a division of the f‐shell into two subsystems gives a better understanding of the cohesive properties as well the general behavior of lanthanide systems. In this article, we present numerical computations, using the suggested method. We show that the picture is consistent with most experimental data, e.g., the equilibrium volume and electronic structure in general. Compared with standard energy band calculations and calculations based on the self‐interaction correction and LDA + U, the f‐(non‐f)‐mixing interaction is decreased by spectral weights of the many‐body states of the f‐ion. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Calculation of quasiparticle energy of molecular systems by the GW method

The quasiparticle energy of the H₂ molecule is calculated by using the GW method, in which the self‐energy operator fully depends on the frequency. The initial Green function G₀ is constructed from the wave function obtained by the Hartree–Fock approximation (HFA) and local density approximation (LDA) in the framework of the density functional theory (DFT). From the results obtained we have shown that the wave function from the DFT–LDA is more effective than that from the HFA for G₀. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 348–353, 2001     

All‐electron relativistic computations on the low‐lying electronic states,bond length,and vibrational frequency of CeF diatomic molecule with spin–orbit coupling effects

Ab initio all‐electron computations have been carried out for Ce⁺ and CeF, including the electron correlation, scalar relativistic, and spin–orbit coupling effects in a quantitative manner. First, the n‐electron valence state second‐order multireference perturbation theory (NEVPT2) and spin–orbit configuration interaction (SOCI) based on the state‐averaged restricted active space multiconfigurational self‐consistent field (SA‐RASSCF) and state‐averaged complete active space multiconfigurational self‐consistent field (SA‐CASSCF) wavefunctions have been applied to evaluations of the low‐lying energy levels of Ce⁺ with [Xe]4f¹5d¹6s¹ and [Xe]4f¹5d² configurations, to test the accuracy of several all‐electron relativistic basis sets. It is shown that the mixing of quartet and doublet states is essential to reproduce the excitation energies. Then, SA‐RASSCF(CASSCF)/NEVPT2 + SOCI computations with the Sapporo(‐DKH3)‐2012‐QZP basis set were carried out to determine the energy levels of the low‐lying electronic states of CeF. The calculated excitation energies, bond length, and vibrational frequency are shown to be in good agreement with the available experimental data. © 2018 Wiley Periodicals, Inc.     

Analysis of self‐interaction correction for describing core excited states

Core‐excitation energies are calculated by the self‐interaction‐corrected time‐dependent density functional theory (SIC‐TDDFT) and SIC‐delta‐self‐consistent field (SIC‐ΔSCF) methods. For carbon monoxide, SIC‐TDDFT severely overestimates core‐excitation energies, while the SIC‐ΔSCF method using Kohn–Sham density functional theory (KS‐DFT) slightly overestimates. These behaviors are attributed to the fact that the self‐interaction errors in the total and orbital energies considerably differ. We evaluate the difference of the self‐interaction errors for the Slater exchange functional. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

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     

Exact electronic properties in the classically forbidden region of a metal surface

We derive exact properties of the inhomogeneous electron gas in the asymptotic classically forbidden region at a metal–vacuum interface within the framework of local effective potential energy theory. We derive a new expression for the asymptotic structure of the Kohn–Sham density functional theory (KS‐DFT) exchange‐correlation potential energy v_xc(r) in terms of the irreducible electron self‐energy. We also derive the exact asymptotic structure of the orbitals, density, the Dirac density matrix, the kinetic energy density, and KS exchange energy density. We further obtain the exact expression for the Fermi hole and demonstrate its structure in this asymptotic limit. The exchange‐correlation potential energy is derived to be v_xc(z → ∞) = ?α_KS,xc/z, and its exchange and correlation components to be v_x(z → ∞) = ?α_KS,x/z and v_c(z → ∞) = ?α_KS,c/z, respectively. The analytical expressions for the coefficients α_KS,xc and α_KS,x show them to be dependent on the bulk‐metal Wigner–Seitz radius and the barrier height at the surface. The coefficient α_KS,c = 1/4 is determined in the plasmon‐pole approximation and is independent of these metal parameters. Thus, the asymptotic structure of v_xc(z) in the vacuum region is image‐potential‐like but not the commonly accepted one of ?1/4z. Furthermore, this structure depends on the properties of the metal. Additionally, an analysis of these results via quantal density functional theory (Q‐DFT) shows that both the Pauli W_x(z → ∞) and lowest‐order correlation‐kinetic W(z → ∞) components of the exchange potential energy v_x(z → ∞), and the Coulomb W_c(z → ∞) and higher‐order correlation‐kinetic components of the correlation potential energy v_c(z → ∞), all contribute terms of O(1/z) to the structure. Hence correlations attributable to the Pauli exclusion principle, Coulomb repulsion, and correlation‐kinetic effects all contribute to the asymptotic structure of the effective potential energy at a metal surface. The relevance of the results derived to the theory of image states and to KS‐DFT is also discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Magnetic ordering and metal‐atom site preference in tetragonal CrMnAs: Electronic correlation effects

The electronic and magnetic structures of tetragonal, Cu₂Sb‐type CrMnAs were examined using density functional theory. To obtain reasonable agreement with reported atomic and low‐temperature magnetic ordering in this compound, the intra‐atomic electron–electron correlation in term of Hubbard U on Mn atoms are necessary. Using GGA + U, calculations identify four low‐energy antiferromagnetically ordered structures, all of which adopt a magnetic unit cell that contains the same direct Cr Cr and Cr Mn magnetic interaction, as well as the same indirect Mn⋅⋅⋅Mn magnetic interaction across the Cr planes. One of these low‐energy configurations corresponds to the reported case. Effective exchange parameters for metal–metal contacts obtained from SPRKKR calculations indicate both direct and indirect exchange couplings play important roles in tetragonal CrMnAs. © 2018 Wiley Periodicals, Inc.     

Experimental and Theoretical Charge Density Study on Di‐2‐pyrazylamine (Hdpza) Molecule in Crystal

Electron density distribution of Di‐2‐pyrazylamine ( Hdpza ) is studied both by single‐crystal X‐ray diffraction method at 100K and theoretical calculation. Structural determination reveals that Hdpza molecules crystalize in a syn‐anti conformation with an intramolecular C? H?N hydrogen bond between two pyrazine rings and then gather together via two intermolecular N? H?N and C? H?N hydrogen interaction and π? π stacking interaction between pyrazine rings. Charge density analysis is made in terms of deformation density (Δπ), Laplacian distribution and topological analysis of total electron density based on multipole model and theoretical calculation. The agreement between experiment and theory is good. The topological properties at bond critical points of C? C and C? N bonds reveal a covalent bond character, and those of intermolecular interactions, such as hydrogen bonds and π? π stacking interactions, reveal a closed‐shell interaction. The potential energy curve of Hdpza molecule shows that the syn‐anti conformation is the most stable one (global minima) than the other two of syn‐syn and anti‐anti conformations.     

Correlation energy,correlated electron density,and exchange‐correlation potential in some spherically confined atoms

We report correlation energies, electron densities, and exchange‐correlation potentials obtained from configuration interaction and density functional calculations on spherically confined He, Be, Be²⁺, and Ne atoms. The variation of the correlation energy with the confinement radius R_c is relatively small for the He, Be²⁺, and Ne systems. Curiously, the Lee–Yang–Parr (LYP) functional works well for weak confinements but fails completely for small R_c. However, in the neutral beryllium atom the CI correlation energy increases markedly with decreasing R_c. This effect is less pronounced at the density‐functional theory level. The LYP functional performs very well for the unconfined Be atom, but fails badly for small R_c. The standard exchange‐correlation potentials exhibit significant deviation from the “exact” potential obtained by inversion of Kohn–Sham equation. The LYP correlation potential behaves erratically at strong confinements. © 2016 Wiley Periodicals, Inc.     

Theoretical studies of structural and electronic properties of AlnAsn clusters

We present theoretical results of size dependent structural, electronic, and optical properties of ligand‐free stoichiometric Al_nAs_n clusters of zinc‐blende modification. The investigation is done using a simplified parametrized linear combination of atomic orbital–density functional theory‐local density approximation–tight‐binding (LCAO–DFT–LDA–TB) method and consider clusters with n up to around 100. Initial structures have assumed as spherical parts of infinite zinc‐blende structure and then allowed to relax to the closest local‐energy‐minimum structure. We analyze the radial distributions of atoms, Mulliken populations, electronic energy levels (in particular, HOMO and LUMO), bandgap, and stability as a function of size and composition. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Synthesis and characterization of a novel ambipolar polymer semiconductor based on a fumaronitrile core as an electron‐withdrawing group

Two conjugated polymers containing stilbene and fumaronitrile moieties were synthesized to investigate their electronic properties by the existence of electron‐withdrawing cyano groups on a vinylene backbone. The cyclic voltammetry investigation and time‐dependent density functional theory calculations indicated that the cyano substituents lowered the lowest unoccupied molecular orbital (LUMO) energy level by about 0.65 and 0.63 eV, respectively. The lowering of the LUMO energy levels due to the electron‐withdrawing properties of the cyano substituents could enhance electron injection capability. Furthermore, bithiophene‐fumaronitrile (donor‐acceptor) intermolecular interaction facilitates the self‐assembly of the polymer chains. Organic field‐effect transistors (OFETs) based on PBTSB without the electron‐withdrawing group only exhibit hole transport, while OFETs based on PBTFN with cyano substituents exhibit ambipolar characteristics. The growth of PBTFN crystalline fibrils was observed with increasing annealing temperature, which enhanced hole and electron mobility. A complementary‐like inverter using PBTFN with ambipolar properties exhibited good symmetry with an inverting voltage nearly half that of the power supply with a gain of 9 at V_DD = 100 V. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Photo absorption of ‐coumaric acid in aqueous solution: RISM‐SCF‐SEDD theory approach

Photo absorption properties of p‐coumaric acid, the chromophore of photoactive yellow protein, in aqueous solution were investigated by means of reference interaction site model self‐consistent field with spatial electron density distribution (RISM‐SCF‐SEDD) method. RISM‐SCF‐SEDD is a combination methodology of electronic structure theory and statistical mechanics for molecular liquids. Here, time‐dependent density functional theory was coupled with RISM equation to study the electronic structure of p‐coumaric acid in aqueous system. Excitation energies of the chromophore in its neutral, two monoanionic and dianionic forms were computed to elucidate the effect of the deprotonation and solvation on the spectroscopic properties. We found that solvation strongly affects the excitation character of the chromophore, especially for phenolate anion and dianion. The free energy difference among the four protonation states is also discussed. © 2017 Wiley Periodicals, Inc.     

Three‐dimensional reference interaction site model self‐consistent field analysis of solvent and substituent effects on the absorption spectra of Brooker's merocyanine

Solvent and substituent effects on the absorption spectra of Brooker's merocyanine (BM) are investigated using the three‐dimensional reference interaction site model self‐consistent field method and time‐dependent density functional theory. The π–π* excitation energies are computed for BM and its derivative 2,6‐di‐tert‐butyl (di‐t‐Bu) BM. The behaviors of the computed excitation energies with increasing solvent polarity are in good agreement with those of the corresponding experimental measurements. In addition, analysis of the solute–solvent interaction energies and spatial distribution functions reveals that the effects of the solvent on the absorption spectra are reduced by the steric hindrance of the t‐Bu groups. Furthermore, from the difference in the solute–solvent interaction energies of BM and di‐t‐Bu BM, it is shown that the effect of the t‐Bu substituents on the absorption spectrum is greater in high‐polarity solvents. © 2015 Wiley Periodicals, Inc.     

Interaction of acetonitrile with alkaline metal cations: A density functional,coupled‐cluster,and quadratic configuration interaction study

A systematic quantum chemical study of CH₃CN and its CH₃CN?M⁺ 1:1 model adducts (M⁺∈{Li⁺, Na⁺}) is presented, with respect to binding energetics, structural and vibrational force field changes. Several gradient‐corrected density functional levels of theory were employed (of both “pure” and “hybrid” character), together with the coupled cluster including double substitutions from the Hartree–Fock determinant (CCD) and quadratic configuration interaction including single and double substitutions (QCISD) methods [with the rather large 6‐311G(d,p) basis set], and their performances compared. The binding energy decompositions according to the Kitaura–Morokuma scheme and the reduced variational space self‐consistent field (RVS‐SCF) method have shown that the electrostatic plus polarization interaction terms are primarily responsible for overall stabilization, while the charge‐transfer term is negligibly small and virtually identical for both adducts. The computed harmonic vibrational frequencies for acetonitrile correlate excellently with the experimental ones (r²>0.9998 for almost all cases, while for the BLYP level, r²=1). It is shown for the first time that the experimentally observed blue shifts of the ν_CN mode are caused even by formation of 1:1 adducts, contrary to the previously accepted opinions. The CCD and QCISD, as well as the BPW91 and BP86 levels of theory predict almost excellently the ν_CN mode blue shift upon adduct formation, while the BLYP and B3LYP levels perform significantly poorer. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Scaling relations,virial theorem,and energy densities for long‐range and short‐range density functionals

Decomposition of the Coulomb electron–electron interaction into a long‐range and a short‐range part is described within the framework of density functional theory, deriving some scaling relations and the corresponding virial theorem. We study the behavior of the local density approximation in the high‐density limit for the long‐range and the short‐range functionals by carrying out a detailed analysis of the correlation energy of a uniform electron gas interacting via a long‐range‐only electron–electron repulsion. Possible definitions of exchange and correlation energy densities are discussed and clarified with some examples. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

1,2,3-三氮杂苯－(水)3复合物多体相互作用

The interaction between 1,2,3-triazine and three water molecules was studied using density functional theory B3LYP method at 6-31-t＋＋G^＊＊ basis set. Various structures for 1,2,3-triazine-（water）n （n= 1, 2, 3） complex were investigated and the different lower energy structures were reported. Many-body analysis was also carded out to obtain relaxation energy and many-body interaction energy （two, three, and four-body）, and the most stable conformer has the basis set superposition error corrected interaction energy of -- 102.61 kJ/mol. The relaxation energy, two- and three-body interactions have significant contribution to the total interaction energy whereas four-body interaction was very small for 1,2,3-triazine-（water）3 complex.     

Intermolecular Interactions in Weak Donor–Acceptor Complexes from Symmetry‐Adapted Perturbation and Coupled‐Cluster Theory: Tetracyanoethylene–Benzene and Tetracyanoethylene–p‐Xylene

The interactions in the complexes of tetracyanothylene (TCNE) with benzene and p‐xylene, often classified as weak electron donor–acceptor (EDA) complexes, are investigated by a range of quantum chemical methods including intermolecular perturbation theory at the DFT‐SAPT (symmetry‐adapted perturbation theory combined with density functional theory) level and explicitly correlated coupled‐cluster theory at the CCSD(T)‐F12 level. The DFT‐SAPT interaction energies for TCNE–benzene and TCNE–p‐xylene are estimated to be ?35.7 and ?44.9 kJ mol^?1, respectively, at the complete basis set limit. The best estimates for the CCSD(T) interaction energy are ?37.5 and ?46.0 kJ mol^?1, respectively. It is shown that the second‐order dispersion term provides the most important attractive contribution to the interaction energy, followed by the first‐order electrostatic term. The sum of second‐ and higher‐order induction and exchange–induction energies is found to provide nearly 40 % of the total interaction energy. After addition of vibrational, rigid‐rotor, and translational contributions, the computed internal energy changes on complex formation approach results from gas‐phase spectrophotometry at elevated temperatures within experimental uncertainties, while the corresponding entropy changes differ substantially.