Using the local density approximation and the LYP,BLYP and B3LYP functionals within reference-state one-particle density-matrix theory

For closed-shell systems, the local density approximation (LDA) and the LYP, BLYP and B3LYP functionals are shown to be compatible with reference-state one-particle density-matrix theory, where this recently introduced formalism is based on Brueckner-orbital theory and an energy functional that includes exact exchange and a non-universal correlation-energy functional. The method is demonstrated to reduce to a density functional theory when the exchange-correlation energy-functional has a simplified form, i.e. its integrand contains only the coordinates of two electrons, say r ₁ and r ₂, and it has a Dirac delta function δ(r ₁ - r ₂ as a factor. Since Brueckner and Hartree–Fock orbitals are often very similar, any local exchange functional that works well with Hartree–Fock theory is a reasonable approximation with reference-state one-particle density-matrix theory. The LDA approximation is also a reasonable approximation. However, the Colle–Salvetti correlation-energy functional and the LYP variant are not ideal for the method, since these are universal functionals. Nevertheless, they appear to provide reasonable approximations. The B3LYP functional is derived using a linear combination of two functionals: one is the BLYP functional; the other uses exact exchange and a correlation-energy functional from the LDA.     

Density functional theory predictions for small radicals containing boron and aluminium: broken symmetry problems and solutions

Selected exchange-correlation functionals were employed to study certain radicals for which unrestricted (U) Hartree–Fock and post-Hartree–Fock methods showed spatial symmetry breakings. For AlO, BO₂ and BS₂ all functionals produced symmetry adapted solutions and predicted geometries and vibrational spectra in good accord with experiment. The USVWN and UB3LYP solutions for the D_∞h O–Al–O structure break spin symmetry. Mixing of these spin-unrestricted Kohn–Sham orbitals yielded stable solutions with reasonable geometries and energetics but with large errors for the vibrational spectra. Only UBHandHLYP results in a broken spatial symmetry solution and yields an anomalous vibrational spectrum. The UBLYP solution does not show a tendency to instability and predicts a D_infin;h O–Al–O species with a ²Π_g electronic state.     

Theoretical study on the mechanism of the gas-phase elimination kinetics of alkyl chloroformates

The theoretical calculations on the mechanism of the homogeneous and unimolecular gas-phase elimination kinetics of alkyl chloroformates– ethyl chloroformate (ECF), isopropyl chloroformate (ICF), and sec-butyl chloroformate (SCF) – have been carried out by using CBS-QB3 level of theory and density functional theory (DFT) functionals CAM-B3LYP, M06, MPW1PW91, and PBE1PBE with the basis sets 6-311++G(d,p) and 6-311++G(2d,2p). The chlorofomate compounds with alkyl ester C_β–H bond undergo thermal decomposition producing the corresponding olefin, HCl and CO₂. These homogeneous eliminations are proposed to undergo two different types of mechanisms: a concerted process, or via the formation of an unstable intermediate chloroformic acid (ClCOOH), which rapidly decomposes to HCl and CO₂ gas. Since both elimination mechanisms may occur through a six-membered cyclic transition state structure, it is difficult to elucidate experimentally which is the most reasonable reaction mechanism. Theoretical calculations show that the stepwise mechanism with the formation of the unstable intermediate chloroformic acid from ECF, ICF, and SCF is favoured over one-step elimination. Reasonable agreements were found between theoretical and experimental values at the CAM-B3LYP/6-311++G(d,p) level.     

A comparison of finite basis set and finite difference Hartree—Fock calculations for the open-shell (X 2Σ+) molecules BaF and YbF

A comparison is made of the accuracy with which the total electronic energy can be calculated by using the finite basis set approach (the algebraic approximation) and the finite difference method in calculations employing the Hartree—Fock model for the open shell ground (X ²Σ⁺) states of the fluorides BaF and YbF. The convergence of the calculations carried out within the algebraic approximation is monitored by employing systematically constructed basis sets of increasing size. The difference between the finite basis set and finite difference Hartree—Fock energies is 2.6μE _h for BaF and 2.8μE _h for YbF. Dipole moments determined within the algebraic approximation are also compared with the corresponding finite difference expectation values.     

Density functional study of the half-metallic ferromagnetism in Co-based Heusler alloys Co2MSn (M = Ti, Zr, Hf) using LSDA and GGA

The half-metallic state in the Heusler alloys Co₂MSn (M = Ti, Zr, Hf) was studied by means of first principles calculation, using both, the Local Spin Density Approximation (LSDA) and the Generalized Gradient Approximation (GGA) to the exchange-correlation energy. While the GGA calculation shows that the three alloys are half-metallic ferromagnets, the LSDA results show that they are ferromagnetic but not half-metallic systems. The difference between the exchange-correlation functionals is analyzed through the electronic structure of the alloys. The origin of the gap in the minority spin channel for GGA calculations is discussed.     

Multiplet splittings and other properties from density functional theory: an assessment in iron–porphyrin systems

In transition metal compounds with spin states close in energy, the magnitude and sign of the energy splitting calculated with density functional theory depends strongly on the functional used. Therefore we must turn to additional criteria to assess the level of accuracy and reliability of predictions based on this level of theory. We report optimized geometries, total energies, and Mössbauer quadrupole splitting values for low-spin and high-spin, ferric and ferrous model hemes using a variety of gradient-corrected and hybrid functionals. In one model, the iron–porphyrin is axially ligated by two strong-field imidazole ligands [FeP(Im)₂] and has a low-spin ground state. In the other model complex the axial ligands are two weak-field, water molecules [FeP(H₂O)₂], and have a high-spin ground state. Among all the functionals used (UHF, B3LYP, B3LYP*, BLYP, half-and-half, LSDA), the B3LYP hybrid functional most consistently reproduced the experimental geometry, Mössbauer, and spin state data for the two model hemes. Simply gradient-corrected functionals exhibit strong biases towards low spin states, while Hartree–Fock favours strongly high spin states. These findings suggest that for systems with similar characteristics of several accessible electronic spin configurations, it is imperative to include properties other than just the energy in the assessment of the DFT predictions.     

Synthesis,structure, spectroscopic (FT-IR) and density functional modelling studies of 1-[(4-ethoxyphenylimino)methyl]napthalene-2-ol

Synthesis, crystallographic characterisation, spectroscopic (Fourier transform infrared spectroscopy [FT-IR]) and density functional modelling studies of the Schiff base 1-[(4-ethoxyphenylimino)methyl]napthalene-2-ol (C₁₉H₁₇NO₂) have been reported. The molecular structure obtained from X-ray single-crystal analysis of the investigated compound in the ground state has been compared using Hartree–Fock and density functional theory (DFT) with the 6-311++G(d,p) basis set. In addition to the optimised geometrical structures, atomic charges, molecular electrostatic potential, natural bond orbital, non-linear optical (NLO) effects and thermodynamic properties of the compound have been investigated by using DFT. The experimental (FT-IR) and calculated vibrational frequencies (using DFT) of the title compound have been compared. The solvent effect was also investigated for obtained molecular energies and the atomic charge distributions of the compound. There exists a good correlation between experimental and theoretical data for enol-imine form of the compound. The total molecular dipole moment (µ), linear polarisability (α), and the first-order hyperpolarisability (β) were predicted by the B3LYP method with different basis sets 6-31G(d), 6-31+G(d,p), 6-31++G(d,p), 6-311+G(d) 150 and 6-311++G(d,p) for investigating the effects of basis sets on the NLO properties. Our computational results yield that β_tot for the title compound is greater than those of urea.     

Visualization of deficiencies in approximate molecular wave functions: the orbital amplitude difference function for the matrix Hartree-Fock description of the ground state of the boron fluoride molecule

The orbital amplitude difference function is used to assess the quality of Hartree–Fock orbitals obtained by invoking the algebraic approximation for the BF ground-state. Systematic sequences of even-tempered, spherical-harmonic Gaussian-type basis functions are used to generate orbitals for which the corresponding total Hartree–Fock energy approaches the 1 μE _h level of accuracy. Exact orbitals are obtained from finite difference calculations using a grid based on spheroidal coordinates. The finite basis set approximations for the orbital are discretized. The accuracy of the discretization is assessed. For each occupied orbital a discretized representation of the orbital amplitude difference function is generated and analysed.     

Density functionals for nondynamical correlation constructed from an upper bound to the exact exchange energy density

ABSTRACT

Hyper-generalised-gradient approximations (hGGAs) for the exact exchange-correlation functional are increasingly popular in density functional theory. HGGAs model nondynamical correlation using a flexible local combination of exact (Hartree–Fock, HF) exchange and approximate exchange. We present a simplified ‘Rung 3.5’ upper bound to the HF exchange energy density, the essential ingredient of hGGAs. We also present a nonempirical generalised gradient approximation for this upper bound. Both upper bounds go to zero in the high-density and density tail limits, facilitating the construction of hGGAs that recover HF exchange in these limits. The ‘Rung 3.5’ construction enables facile evaluation of analytic derivatives and calculations in periodic boundary conditions. Extensive numerical tests show that the upper bounds capture the critical difference between HF and approximate exchange, showing these ingredients' promise for building simple hGGAs. The tests also indicate a need for more sophisticated semi-local upper bounds.     

Use of ab initio methods to classify four existing energy density functionals according to their possible variational validity

Density functional theory is, of course, fundamentally a variational method. Therefore, in this Letter we suggest a classification of available energy density functionals into two groups, which we term (i) heuristic (H) and (ii) possibly variationally valid (PV). Quantum-chemical ab initio methods are employed on some selected neutral and anionic atomic systems and the molecules H₂O and LiOB to make this separation into H and PV groups in the case of the exchange-correlation functionals LDA, PBE, PW91 and B3LYP. This study shows that while the PBE is a potential candidate for being variationally valid, the B3LYP, today's other most widely used density functional, shows its strongly heuristic character. The investigation of variational validity can be an important part of systematic functional development, which is today's biggest challenge in DFT.     

Structural phase transition and elastic properties of Curium and Uranium monobismuthides under pressure effect

A density functional (DFT) calculations of the structural, elastic and high pressure properties of the cubic XBi (X=U,Cm) compounds, has been reported using the full potential linear muffin-tin orbital (FP-LMTO) method. In this approach the local density approximation (LDA) is used for the exchange-correlation (XC) potential. Results are given for lattice constant, bulk modulus and its pressure derivatives. The pressure transitions at which these compounds undergo structural phase transition from NaCl-type (B1) to CsCl-type (B2) phase were found to be in good agreement with the available theoretical results. We have determined the elastic constants C₁₁, C₁₂, C₄₄ and their pressure dependence which have not been established experimentally or theoretically.     

First-principles linear muffin-tin orbital investigations in the electronic and magnetic structures of double perovskites Ba2TMoO6 (T=V,Cr, Mn,Fe and Co)

The electronic and magnetic structures of ordered double perovskites Ba₂TMoO₆ (T=V, Cr, Mn, Fe and Co) are systematically investigated by means of the first-principle linear muffin-tin orbitals with the atomic-sphere approximation (LMTO-ASA) method. The calculations are performed by using the both local spin density approximation (LSDA) and the LSDA+U Coulomb interaction schemes. The results show a half-metallic ferrimagnetic ground states for T=Cr, Fe and Co in LSDA+U treatment, whereas half-metallic ferromagnetic character is observed for T=V. For T=Mn, insulating ground state is obtained, stabilized in the antiferromagnetic state. The LSDA+U calculations yield better agreement with the theoretical and the experimental results than do the LSDA.     

Electronic Structure of RCo2 (R = Y, Nd, Ho, Er)

The results of electronic structure studies of the YCo₂ performed in the framework of the density functional theory (DFT) are reported. We have applied both local spin density approximation (LSDA) and generalized gradient approximation (GGA) for the treatment of exchange and correlation effects. We have found the stable paramagnetic ground state (a _min/a _exp = 0.962) using LSDA. In addition, we have investigated the influence of the local R-4f moments in RCo₂ (R = Nd, Ho, Er) on the ferrimagnetic solution using a self-interaction corrected LSDA method.     

Calculation of vibrational spectra for dioxouranium monochloride monomer and dimers

Structural models were built and spectral characteristics were calculated based on ab initio calculations for the monomer and dimers of dioxouranium monochoride UO₂Cl. The calculations were carried out in the effective core potential LANL2DZ approximation for the uranium atom and all-electron basis sets using DFT methods for oxygen and chlorine atoms (B3LYP/cc-pVDZ). The monomer UO₂Cl was found to possess an equilibrium planar (close to T-shaped) configuration with C_2v symmetry. The obtained spectral characteristics were analyzed and compared with experimental data. The adequacy of the proposed models and the qualitative agreement between calculation and experiment were demonstrated.     

Excess polarizabilities upon the first dipole‐allowed excitation of some conjugated oligomers

This paper presents theoretical predictions for the excess polarizabilities upon excitation from the ground state to the first dipole‐allowed excited state (1¹B_u) of some conjugated oligomers. The excess polarizability was obtained by simulating the Stark shift, which was predicted by the time‐dependent density functional theory (TDDFT) with the hybrid Becke‐3 Lee–Yang–Parr (B3LYP) potential. The Stark shift in solution was simulated by employing the non‐equilibrium integral equation formalism polarizable continuum model (IEFPCM). All the model molecules considered in this study were fully optimized by the Hartree–Fock (HF) method and the density functional theory (DFT) with the B3LYP potential, respectively. For diphenylpolyenes, the excess polarizabilities displayed by the DFT/B3LYP‐optimized geometries are more reasonable than those displayed by the HF‐optimized geometries when compared with the experimental results. However, this feature is not clearly demonstrated by our results in the cases of oligo(phenylenevinylene)s (OPVs). Copyright © 2008 John Wiley & Sons, Ltd.     

On the performance of density functional schemes for computing the static dipole polarizability of 4d transition-metal monohalides

This article presents the static dipole polarizabilities of 4d transition-metal monohalides in the framework of density functional theory. The behavior of a large number of density functionals, including various types of the local spin density approximation (LSDA), the generalized gradient approximation (GGA), meta GGA (MGGA), hybrid GGA (HGGA), and hybrid meta GGA (HMGGA), has been assessed in polarizability calculations. The highly accurate CCSD(T) methodology is used to benchmark a variety of functionals. Our results indicate that there is a large variation in performance of the various functionals of each type in the calculation of the dipole polarizability. It turned out that, in the LSDA class, SVWN5 gives better results than SVWN3 for the reference values. Of the GGA methods, BP86 and BPW91 give the best results for our data set, followed by G96LYP. The TPSS functional is the best method of the MGGA class, followed by the VSXC and BB95 functionals. Moreover, the B98 and mPW1PW91 functionals are the best methods of the HGGA lineage, predicting the most accurate static dipole polarizabilities. Finally, TPSS1KCIS and PBE1KCIS are the best methods of the HMGGA functionals for that purpose. In general, it was found that the HGGA and HMGGA functionals provide the best performance.     

FP-LMTO calculations of elastic and electronic properties of the filled skutterudite CeRu4P12

First-principles calculations have been used to investigate the structural, electronic and elastic properties of the filled skutterudite CeRu₄P₁₂, using the full-potential linear muffin-tin orbital (FP-LMTO) method. The exchange-correlation energy is described in the local spin density approximation (LSDA) using the Perdew–Wang parameterization. The results of the electronic properties show that this compound is an indirect band gap material. A special interest has been made to the determination of the elastic constants since there have been no available experimental and theoretical data. The energy band gaps and their volume and pressure dependence are investigated. Our results of the ground-state electronic properties are found to agree with experimental results.