Terms Of Density Functional Theory Research Articles

Construction of Copper Halide-Triiron Selenide Carbonyl Complexes: Synthetic, Electrochemical, and Theoretical Studies

A new family of CuX-, Cu(2)X(2)-, and Cu(4)X(2)-incorporated mono- or di-SeFe(3)-based carbonyl clusters were constructed and structurally characterized. When the selenium-capped triiron carbonyl cluster [Et(4)N](2)[SeFe(3)(CO)(9)] was treated with 1-3 equiv of CuX in tetrahydrofuran (THF) at low or room temperatures, CuX-incorporated SeFe(3) complexes [Et(4)N](2)[SeFe(3)(CO)(9)CuX] (X = Cl, [Et(4)N](2)[1a]; Br, [Et(4)N](2)[1b]; I, [Et(4)N](2)[1c]), Cu(2)X(2)-incorporated SeFe(3) clusters [Et(4)N](2)[SeFe(3)(CO)(9)Cu(2)X(2)] (X = Cl, [Et(4)N](2)[2a]; Br, [Et(4)N](2)[2b]), and Cu(4)X(2)-linked di-SeFe(3) clusters [Et(4)N](2)[{SeFe(3)(CO)(9)}(2)Cu(4)X(2)] (X = Cl, [Et(4)N](2)[3a]; Br, [PPh(4)](2)[3b]) were obtained, respectively, in good yields. SeFe(3)CuX complexes 1a and 1b were found to undergo cluster expansion to form SeFe(3)Cu(2)X(2) complexes 2a and 2b, respectively, upon the addition of 1 equiv of CuX (X = Cl, Br). Furthermore, complexes 2a and 2b can expand further to form Cu(4)X(2)-linked di-SeFe(3) clusters 3a and 3b, upon treatment with 1 equiv of CuX (X = Cl, Br). [Et(4)N](4)[{SeFe(3)(CO)(9)(CuCl)(2)}(2)] ([Et(4)N](4)[4a]) was produced when the reaction of [Et(4)N](2)[SeFe(3)(CO)(9)] with 2 equiv of CuCl was conducted in THF at 40 degrees C. The Cu(2)Cl(2)-linked di-SeFe(3)CuCl cluster 4a is a dimerization product derived from complex 2a. Further, it is found that complex 4a can convert to the Cu(4)Cl(2)-linked di-SeFe(3) cluster 3a upon treatment with CuCl. The nature, formation, stepwise cluster expansion, and electrochemical properties of these CuX-, Cu(2)X(2)-, and Cu(4)X(2)-incorporated mono- or di-SeFe(3)-based clusters are elucidated in detail by molecular calculations at the B3LYP level of the density functional theory in terms of the effects of selenium, iron, copper halides, and the size of the metal skeleton.

Differential virial theorem in density-functional theory in terms of the Pauli potential for spherically symmetric electron densities: Illustrative example for the family of Be-like atomic ions

The differential virial theorem relates the force $\ensuremath{-}\ensuremath{\partial}V∕\ensuremath{\partial}\mathbf{r}$ associated with the one-body potential $V(\mathbf{r})$ of density-functional theory to the Laplacian ${\ensuremath{\nabla}}^{2}n$ of the ground-state density $n(\mathbf{r})$ and to a quantity ${\mathbf{z}}_{s}(\mathbf{r})$ involving the kinetic energy density tensor ${t}_{\ensuremath{\alpha}\ensuremath{\beta}}(\mathbf{r})$. Having the concept of the Pauli potential ${V}_{P}(\mathbf{r})$, ${z}_{s}$ is derived for spherically symmetric ground-state densities $n(r)$ in terms of the von Weizs\"acker kinetic energy density and the first derivative of ${V}_{P}(r)$. ${\mathbf{z}}_{s}$ is related solely to the gradient kinetic energy density ${t}_{G}(r)$ for Be-like atomic ions.

Strictly correlated electrons in density-functional theory: A general formulation with applications to spherical densities

We reformulate the strong-interaction limit of electronic density functional theory in terms of a classical problem with a degenerate minimum. This allows us to clarify many aspects of this limit, and to write a general solution, which is explicitly calculated for spherical densities. We then compare our results with previous approximate solutions and discuss the implications for density functional theory.

AlGaInN metal-organic-chemical-vapor-deposition gas-phase chemistry in hydrogen and nitrogen diluents: First-principles calculations

Direct impact of H 2 and N 2 diluents on the metal-organic-chemical-vapor-deposition gas-phase chemistry in M(CH 3) 3/NH 3 (M = Al, Ga, In) systems is identified in the framework of Density Functional Theory in terms of cohesive energy differences. While both diluents destabilize model reaction species, i.e. adducts, transition states and chain complexes, the effect is particularly strong with respect to N 2 in the Al(CH 3) 3/NH 3 system, and can be a factor to restrain the expansion of chain complexes that deplete the gas-phase from precursors. Theoretical results are supported by experimental evidences of higher growth rate and superior optical properties of AlN grown in N 2 vs. H 2 diluent.

Density functional theory in terms of a Legendre transformation for beginners

The derivation of the Hohenberg–Kohn (HK) theorem by means of a simplified version of Lieb's Legendre transformation is presented, with the stress on physically problematic aspects, and caring about the definition of the domains of the respective functionals only to the extent, that this is absolutely necessary. The take-home lesson consists in a critical analysis of some statements often found in the DFT literature. As a simple illustration for a Legendre transformation we discuss that in parameter space for the family of n-electron isoelectronic atomic ions, with the nuclear charge as parameter.

Fast algorithm for bandstructure calculation in silicon nanowires using supercell approach

Energy bandstructure in silicon nanowires with [100] crystal orientation is calculated using the Tight-Binding (TB) model with supercell approach. Numerical methods are designed according to the physical model to reach an optimal computational performance. Computation results show that the bandstructures of silicon nanowires deviate from that of bulk silicon. The efficiency and accuracy of the TB algorithm are analysed and compared to its counterpart the Density Functional Theory (DFT). Test examples show that TB delivers a good accuracy while far superior over DFT in terms of computational cost.

Absorption, resonance, and near‐resonance Raman studies of the tetracyanoquinodimethane neutral and its monoanion in terms of density functional theory and complete active space self‐consistent field methods

AbstractThe electronic structure of the 11B1u and 12B3u excited electronic states of the tetracyanoquinodimethane (TCNQ) neutral and its charged derivative are studied within the framework of complete active space self‐consistent field (CASSCF) and Becke's three‐parameter hybrid method with Lee–Yang–Parr correlation functional (B3LYP) methods applied to the level aug‐cc‐p‐VDZ basis set. Both CASSCF/aug‐cc‐p‐VDZ and B3LYP/aug‐cc‐p‐VDZ treatments provide the ground‐state and the excited state geometries; these are then used to assess the Franck–Condon (FC) parameters in the 11B1u state of the neutral TCNQ and in the 12B3u state of the TCNQ monoanion. The quality of numerical results is then tested on the base of available experimental near‐resonance and resonance Raman data. The studies are performed in terms of the vibronic model, which takes both FC and mode‐mixing (Dushinsky) effects into account. This somewhat simplified vibronic model leads to very good agreement between the theory and the Raman experiments concerning both neutral TCNQ and its monoanion. In particular, the calculated excitation profiles of the ν2 = 2215 cm−1, ν4 = 1389 cm−1, ν5 = 1195 cm−1, and ν9 = 336 cm−1 fundamentals are shown to be in excellent agreement with those for the TCNQ monoanion. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Differential virial theorem in relation to a sum rule for the exchange-correlation force in density-functional theory

Holas and March [Phys. Rev. A. 51, 2040 (1995)] gave a formally exact theory for the exchange-correlation (xc) force F(xc)(r)= -inverted Deltaupsilon(xc)(r) associated with the xc potential upsilon(xc)(r) of the density-functional theory in terms of low-order density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule nF(xc)=0 relating the xc force with the ground-state density n(r). Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A. 32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys. 119, 1916 (2003)] relating to the separation of the exchange and correlation contributions.

Quantal Density Functional Theory (Sahni, Viraht)

This book describes quantum chemistry in terms of classical force fields, gives a new physical understanding of density functional theory in terms of the various classical fields present in a quantum chemical system, and provides a new computational scheme for electronic structure calculations.

Quantum-Chemical Investigation of Keto-enol-enethiol Tautomerism in 3-oxo-3-R1-N-R2-propanethioamides

The keto-enol-enethiol tautomerism in 3-oxo-3-R1-N-R2-propanethioamides under vacuum and in acetone was studied in terms of density functional theory. It was established that the equilibrium depends on the structure of the 3-oxo-3-R1-N-R2-propanethioamides and on the nature of the solvent, but the most stable form is as a rule the keto form stabilized by an intramolecular hydrogen bond.

Minimal coupling model of the biaxial nematic phase

A minimal coupling model exhibiting isotropic, uniaxial, and biaxial nematic phases is analyzed in detail and its relation to existing models known in the literature is clarified. Its intrinsic symmetry properties are exploited to restrict the relevant ranges of coupling constants. Further on, properties of the model are thoroughly investigated by means of bifurcation theory as proposed by Kayser and Raveché [Phys. Rev. A 17, 2067 (1978)] and Mulder [Phys. Rev. A 39, 360 (1989)]. As a first step toward this goal, the bifurcation theory is applied to a general formulation of density functional theory in terms of direct correlation functions. On a general formal level, the theory is then analyzed to show that the bifurcation points from the reference, high-symmetry equilibrium phase to a low-symmetry structure depend only on the properties of the one-particle distribution function and the direct pair correlation function of the reference phase. The character of the bifurcation (whether spinodal, critical, tricritical, isolated Landau point, etc.) depends, in addition, on a few higher-order direct correlation functions. Explicit analytical results are derived for the case when only the leading L=2 terms of the potential (mean-field analysis) or of the direct pair correlation function expansion in the symmetry-adapted basis are retained. Formulas are compared with the numerical calculations for the mean-field, momentum L=2 potential model, in which case they are exact. In particular, bifurcations from the isotropic and uniaxial nematic to the biaxial nematic phases are discussed. The possibility of the recently reported nematic uniaxial-nematic biaxial tricritical point [A. M. Sonnet, E. G. Virga, and G. E. Durand, Phys. Rev. E 67, 061701 (2003)] is analyzed as well.

Low-temperature biligand complexes of europium and samarium with mesogenic alkylcyanobiphenyls

For low-temperature cocondensates of europium and samarium (M) with a mesogenic ligand 4-pentyl-4′-cyanobiphenyl (L), IR and UV spectroscopy studies have revealed the formation of two ML complexes (M/L = 1:2 and 1:1). Model calculations have been carried out in terms of density functional theory using the B3LYP exchange correlation potential. Biligand structures with an antiparallel arrangement of two ligand molecules including one and two metal atoms, respectively, are suggested. The values of the spectral shifts and the relative thermal stability of the complexes are discussed.

Density matrix force‐balance equation applied to He, Be, and Ne atoms and to almost‐spherical methane‐like molecules

AbstractHolas and March (Phys Rev A 1995, 51, 2040) expressed the force −∇Vxc(r) associated with the exchange correlation potential Vxc(r) of density functional theory in terms of low‐order density matrices. Their result utilizes a many‐electron force balance equation for −∇Vext(r), where Vext(r) denotes the external potential. Here, insight is sought into this force‐balance equation by using both Hartree–Fock results and correlated electron calculations. Examples of two‐electron systems, including the exactly solvable model Hookean atom, are first set out, followed by treatments of the Be and Ne atoms. As a final, molecular, example, methane‐like systems are also more briefly studied, but now restricted solely to the Hartree–Fock level of approximation. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

The electronic and vibrational structures of the vis–UV transitions in the 1,3-dicyanomethylene croconate anion in terms of CASSCF and DFT theory. The Franck–Condon analysis of [formula omitted] and [formula omitted] transitions

The visible and near UV absorption spectra of the 1,3-dicyanomethylene croconate anion radical are discussed in terms of density functional theory (DFT) and the complete active space (CASSCF) method employed with augmented cc-pVDZ basis set. It is shown that the three transitions 1 2 B 1→2 2 A 2 , 1 2 B 1→2 2 B 1 and 1 2 B 1→3 2 B 1 shape the absorption in the near UV region. The FC activity in the most intense 1 2 B 1→2 2 A 2 near UV transition was shown to be quite modest. On the other hand the near visible absorption of the croconate derivative is shown to be due to 1 2 B 1→1 2 A 2 transition accompanied by a short progression of v 5( a 1)=1567 cm −1 mode.

Spin-density inversion symmetry driven first-order magnetic phase transition inGaCMn3

The first-order magnetic phase transtion of the metallic perovskite ${\mathrm{GaCMn}}_{3}$ has been investigated in terms of density-functional theory using the all-electron total-energy full-potential linearized augmented plane-wave method. We found that the antiferromagnetic (AFM) state is more stable energetically than the ferromagnetic (FM) state at the low-temperature lattice constant. Total-energy calculations yield a critical lattice constant of $7.3411\mathrm{a}.\mathrm{u}.,$ which is remarkably close to the experimental one $(7.34\mathrm{a}.\mathrm{u}.)$ The calculated magnetic moments of Mn in each magnetic state are almost constant with lattice-constant variation, $\ensuremath{\sim}1.58{\ensuremath{\mu}}_{\mathrm{B}}$ for the FM and $\ensuremath{\sim}1.80{\ensuremath{\mu}}_{\mathrm{B}}$ for the AFM states, which are very close to experiment. The FM spin density is found to have even inversion symmetry, while the AFM one has odd, which restricts the direction of the AFM ordering vector along the [111] direction via tilting of the orbital orientation axis. Hence, the spin-density parity about the spin-inversion symmetry may be a key for understanding the first-order phase transition in ${\mathrm{GaCMn}}_{3}.$ We also found that the oddness of the spin-density-inversion symmetry in the AFM state brings about the wave-function sign dependent spin polarization and changes the bonding character. From the calculated density of states, the hybridization between the $\mathrm{Ga}\ensuremath{-}4p$ and $\mathrm{Mn}\ensuremath{-}3d$ states is important for determining the magnetism of ${\mathrm{GaCMn}}_{3}.$

NQR parameters: Electric field gradient tensor and asymmetry parameter studied in terms of density functional theory

AbstractThe calculations of the electric field gradients were performed in the different basis sets at the selected ab initio, density functional theory (DFT), and ECP levels of the theory. The most reliable QCC and η values were obtained within the DFT and with the use of B3LYP functional and middle 6‐31G* or extended 6‐311G* basis sets. The universality of the B3LYP/6‐31G* method was checked by comparing the experimental and calculated Up values as only such a comparison enables assessment of the quality of the results obtained for different (heavy and light) nuclei. The NQR parameters obtained with the use of all‐electrons (AE) and pseudopotential (ECP) methods for a group of halogens or nitrogen‐containing compounds were compared and the former were found to be close to the experimental values. The explanation of so extremely small values of EFG calculated with the use of pseudopotential was proposed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Studies of thiazide compounds in terms of density functional theory

AbstractA systematic study on the impact of hydrogen addition at positions N2 and C3, as well as the role of a substituent at position C3 of the benzothiadiazine ring, on the electronic structure of the chlorothiazide (CTZ) and hydrochlorothiazide (HCTZ) was carried out by the density functional theory (DFT) method. The results have shown the lowering of total energies with the addition of hydrogen atoms at positions N2 and C3. The HOMO and LUMO orbitals were located similarly in the unsaturated ring, along the C9C10 double bond with a delocalization on C5, on the C7C8 double bond, and on the nitrogen atoms N2 (only in CTZ analogs) and N4, regardless of the functional group at C3. The greatest contribution to HOMO in all thiazides comes from the atomic orbitals pz of nitrogen atoms N4; moreover, in the case of HCTZ analogs, in contrast to CTZ ones, the contribution of N2 nitrogen atom orbitals to HOMO is zero. For BTZ, there is a degeneracy in the HOMO orbitals, i.e., there are two orbitals with almost the same energy, one at C9C10 and the other at C7C8, opening the two reactive paths at HOMO and HOMO‐1. The greatest contributions to the LUMO orbitals comes from the atomic orbitals pz of the carbon atom C6 and only the LUMO orbital in BTZ is mostly localized on the carbon atoms C7 and C10. A comparison of the effective charge proves that the positions N2 and N4 can easily accept protons and of them N2 is more favored for HCTZ and CTZ whereas N4 is for the remaining thiazides. The higher charge density and electrostatic potentials are located in the NCN zone, especially on the N4 nitrogen atom. According to increasing electron–donor properties, the substituents can be ordered as CHCl2 < CH2SCH2CHCH2 < CH2SCH2Ph. Of key importance for stabilization of CTZ‐type compounds is the interaction of the free electron pair localized on N4 with antibonding π orbitals of the double bonds (nN4π and nN4π). The HCTZ type compounds are also stabilized by the interaction of a free electron pair localized on N4 with the antibonding π orbital of the double bond (nN4π) and by that of the bonding π with the antibonding π* orbitals (πC7C8π). A complementary objective was to gain some insight into the relationship between the physical and chemical properties and biologic activity of thiazides. The results of DFT calculations were confronted with experimental data from different spectroscopic and physical and chemical studies. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Crystal-field levels and magnetic susceptibility inPuO2

Ground-state electronic structure and crystal-field levels of ${\mathrm{PuO}}_{2}$ have been calculated by means of a symmetry constrained local density approximation to density-functional theory in terms of total energy differences. The calculated ${\ensuremath{\Gamma}}_{1}$ (ground state) to ${\ensuremath{\Gamma}}_{4}$ (first excited state) excitation energy of 99 meV is in reasonable agreement with the measured value 123 meV from inelastic-neutron-scattering experiments. The measured magnetic susceptibility has been analyzed and its discrepancy with neutron-scattering results is partially removed by the introduction of antiferromagnetic exchange enhancement.

Cluster Models of Co2+ at the Cation Sites of Zeolite ZSM-5

The local structure of Co2+ at the \(\alpha \)-, \(\beta \), and \(\gamma \)-cation sites of zeolite ZSM-5 was calculated in terms of density functional theory using the cluster approach. The local geometry of the oxygen environment of Co2+ is characterized; it is found that the ion stabilization energy increases in the series \(\alpha \to \beta \to \gamma \).

Study of the reactivity of radical-molecular addition reaction using density functional theory

The reactivity of radical-molecular addition reaction was studied in terms of density-functional theory (DFT) and Hartree-Fock theory (HFT). It was found that the DFT method can give more accurate estimated result than the HFT method. The reason might be that the energy of the highest occupied molecular orbital (HOMO) in DFT is not the ionization energy, but rather represents the change in the total energy with respect to the change in occupation number of electrons in the HOMO, consistent with the concept of the transition state. The energy of HOMO in HFT is the ionization energy, which may represent more properly the property of the products and reactants themselves.