Assessing the performance of density functional theory for the electronic structure of metal-salens: the M06 suite of functionals and the d⁴-metals

We have systematically investigated the electronic structure of the d? metal-salen complexes including the Cr(II)-, Mn(III)-, Fe(IV)-, Mo(II)-, Tc(III)-, and Ru(IV)-salen complexes. Density functional theory (DFT) has been employed, using the BP86 and B3LYP functionals, and the entire M05 and M06 suites of meta-generalized gradient functionals. These results are compared to robust complete active-space self-consistent field (CASSCF) optimized geometries and complete active-space third-order perturbation theory (CASPT3) energies for the lowest singlet, triplet, and quintet states. Although the M06 and M06-L DFT functionals have been generally recommended for computations on complexes that contain main group and transition metals, none of the M0-functionals appear statistically better than the B3LYP functional for the computation of spin-state energy gaps. DFT- and CASSCF-optimized geometries normally agree to within 0.3 ? least root mean squared deviation (LRMSD) for the singlet and triplet structures and less than 0.1 ? LRMSD for the quintet structures. It can be concluded that no DFT functional tested here can be considered reliable over all metal-salen complexes and it is highly recommended that the accuracy of any given DFT functional should be assessed on a case-by-case basis.     

Ab initio density functional theory: the best of both worlds?

Density functional theory (DFT), in its current local, gradient corrected, and hybrid implementations and their extensions, is approaching an impasse. To continue to progress toward the quality of results demanded by today's ab initio quantum chemistry encourages a new direction. We believe ab initio DFT is a promising route to pursue. Whereas conventional DFT cannot describe weak interactions, photoelectron spectra, or many potential energy surfaces, ab initio DFT, even in its initial, optimized effective potential, second-order many-body perturbation theory form [OEP (2)-semi canonical], is shown to do all well. In fact, we obtain accuracy that frequently exceeds MP2, being competitive with coupled-cluster theory in some cases. Furthermore, this is accomplished within a relatively fast computational procedure that scales like iterative second order. We illustrate our results with several molecular examples including Ne2,Be2,F2, and benzene.     

Assessment of the Van Voorhis–Scuseria exchange–correlation functional for predicting excitation energies using time-dependent density functional theory

We assess the performance of the Van Voorhis–Scuseria exchange–correlation functional (VSXC), a kinetic-energy-density-dependent exchange–correlation functional recently developed in our group, for calculating vertical excitation energies using time-dependent density functional theory in a benchmark set of molecules. Overall, VSXC performs very well, with accuracy similar to that of hybrid functionals such as the hybrid Perdew–Burke–Ernzerhof functional and Becke's three parameter hybrid method with the Lee, Yang, and Parr correlation functional, which contain a portion of Hartree–Fock exchange. Received: 29 December 1999 / Accepted: 5 June 2000 / Published online: 11 September 2000     

The importance of Colle–Salvetti for computational density functional theory

The purpose of this presentation is to show the importance of the Colle–Salvetti (Theor Chim Acta 37:329, 1975) paper in the development of modern computational density functional theory. To do this we cover the following topics (1) the Bright Wilson understanding (2) the Kohn–Sham equations (3) local density exchange (4) the exchange-hole (5) generalised gradient approximation for exchange (Becke and Cohen) (6) left–right correlation and dynamic correlation (7) the development of the Lee–Yang–Parr dynamic correlation functional from the Colle–Salvetti paper (8) the early success of GGA DFT. Finally we observe that the the BLYP and OLYP exchange-correlation functionals are not semi-empirical; this may explain their great success.     

Application of density functional theory and optical spectroscopy for the prediction of the photophysical properties of Р-pyridylphospholanes

Russian Chemical Bulletin - The spatial and electronic structure of a series of pyridyl-containing phospholanes, which are potential ligands for the synthesis of luminescent transition metal...     

The prediction of Fe Mössbauer parameters by the density functional theory: a benchmark study

We report the performance of eight density functionals (B3LYP, BPW91, OLYP, O3LYP, M06, M06-2X, PBE, and SVWN5) in two Gaussian basis sets (Wachters and Partridge-1 on iron atoms; cc-pVDZ on the rest of atoms) for the prediction of the isomer shift (IS) and the quadrupole splitting (QS) parameters of M?ssbauer spectroscopy. Two sources of geometry (density functional theory-optimized and X-ray) are used. Our data set consists of 31 iron-containing compounds (35 signals), the M?ssbauer spectra of which were determined at liquid helium temperature and where the X-ray geometries are known. Our results indicate that the larger and uncontracted Partridge-1 basis set produces slightly more accurate linear correlations of electronic density used for the prediction of IS and noticeably more accurate results for the QS parameter. We confirm and discuss the earlier observation of Noodleman and co-workers that different oxidation states of iron produce different IS calibration lines. The B3LYP and O3LYP functionals have the lowest errors for either IS or QS. BPW91, OLYP, PBE, and M06 have a mixed success whereas SVWN5 and M06-2X demonstrate the worst performance. Finally, our calibrations and conclusions regarding the best functional to compute the M?ssbauer characteristics are applied to candidate structures for the peroxo and Q intermediates of the enzyme methane monooxygenase hydroxylase (MMOH), and compared to experimental data in the literature.     

New model for a theoretical density functional theory investigation of the mechanism of the carbonic anhydrase: how does the internal bicarbonate rearrangement occur?

A theoretical density functional theory (DFT, B3LYP) investigation has been carried out on the catalytic cycle of the carbonic anhydrase. A model system including the Glu106 and Thr199 residues and the "deep" water molecule has been used. It has been found that the nucleophilic attack of the zinc-bound OH on the CO(2) molecule has a negligible barrier (only 1.2 kcal mol(-1)). This small value is due to a hydrogen-bond network involving Glu106, Thr199, and the deep water molecule. The two usually proposed mechanisms for the internal bicarbonate rearrangement have been carefully examined. In the presence of the two Glu106 and Thr199 residues, the direct proton transfer (Lipscomb mechanism) is a two-step process, which proceeds via a proton relay network characterized by two activation barriers of 4.4 and 9.0 kcal mol(-1). This pathway can effectively compete with a rotational mechanism (Lindskog mechanism), which has a barrier of 13.2 kcal mol(-1). The fast proton transfer found here is basically due to the effect of the Glu106 residue, which stabilizes an intermediate situation where the Glu106 fragment is protonated. In the absence of Glu106, the barrier for the proton transfer is much larger (32.3 kcal mol(-1)) and the Lindskog mechanism becomes favored.     

Concurrent cyclopropanation by carbenes and carbanions? A density functional theory study on the reaction pathways

The mechanisms for the addition reactions of phenylhalocarbenes and phenyldihalomethide carbanions with acrylonitrile (ACN) and trimethylethylene (TME) have been investigated using an ab initio BH and HLYP/6-31G (d, p) level of theory. Solvent effects on these reactions have been explored by calculations that included a polarizable continuum model (PCM) for the solvent (THF). These model calculations show that for the addition of phenylhalocarbenes, a TME species may readily undergo addition reactions with carbenes while ACN has a high-energy barrier to overcome. It was also found that phenyldihalomethide carbanions do not readily add to the electron-rich TME. The cyclopropane yields only appear to occur via addition of PhCBr to TME. However, the cyclopropanation proceeds not only via slow addition of phenylhalocarbenes to ACN but also forms through the stepwise reaction of phenyldihalomethide carbanions with ACN. Our calculation results are in good agreement with experimental observations (Moss, R.A.; Tian, J.-Z. J. Am. Chem. Soc. 2005, 127, 8960) that indicate that the cyclopropanation of phenylhalocarbenes and phenyldihalomethide carbanions with ACN are concurrent in THF.     

Excitation energies expressed as orbital energies of Kohn–Sham density functional theory with long-range corrected functionals

A new simple and conceptual theoretical scheme is proposed for estimating one-electron excitation energies using Kohn–Sham (KS) solutions. One-electron transitions that are dominated by the promotion from one initially occupied orbital to one unoccupied orbital of a molecular system can be expressed in a two-step process, ionization, and electron attachment. KS with long-range corrected (LC) functionals satisfies Janak's theorem and LC total energy varies almost linearly as a function of its fractional occupation number between the integer electron points. Thus, LC reproduces ionization energies (IPs) and electron affinities (EAs) with high accuracy and one-electron excitation energies are expressed as the difference between the occupied orbital energy of a neutral molecule and the corresponding unoccupied orbital energy of its cation. Two such expressions can be used, with one employing the orbital energies for the neutral and cationic systems, while the other utilizes orbital energies of just the cation. Because the EA of a molecule is the IP of its anion, if we utilize this identity, the two expressions coincide and give the same excitation energies. Reasonable results are obtained for valence and core excitations using only orbital energies.     

Camphor-based α-bromoketones for the asymmetric darzens reaction: Insights into the mechanism using density functional theory

Density functional theory (DFT) calculations at B3LYP/6-31G(d,p) level were carried out to investigate the mechanism of the reaction of benzaldehyde (BA) or acetaldehyde (AD) with (1R)-2-endo-bromoacetyl-1,7,7-trimethylbicyclo[2.2.1]heptan-2-ol (endo-2-bromoacetylisoborneol) 1 (Scheme 1). The calculations indicate that the reactions are diastereoselective, in good agreement with the experimental results [1]. Moreover, the calculations show that these reactions proceed via two steps: (1) an aldol-like reaction and (2) the formation of an epoxide. Our calculation study of the transition states demonstrates that the terminal hydroxyl group in compound 1 is vital for the stereoselectivity of the reactions.     

Comparison of the site occupancies determined by combined Rietveld refinement and density functional theory calculations: example of the ternary Mo-Ni-Re σ phase

The site occupancies of the Mo-Ni-Re σ phase have been studied as a function of the composition in the ternary homogeneity domain by both experimental measurements and calculations. Because of the possible simultaneous occupancy of three elements on the five sites of the crystal structure, the experimental determination of the site occupancies was achieved by using combined Rietveld refinement of X-ray and neutron diffraction data, whereas calculation of the site occupancies was carried out by using the density functional theory results of every ordered (i.e., 3(5) = 243) configuration appearing in the ternary system. A comparison of the experimental and calculation results showed good agreement, which suggests that the topologically close-packed phases, such as the σ phase, could be described by the Bragg-Williams approximation (i.e., ignoring the short-range-order contributions). On the other hand, the atomic distribution on different crystallographic sites of the Mo-Ni-Re σ phase was found to be governed by the atomic sizes. Ni, having the smallest atomic size, showed a preference for low-coordination-number (CN) sites, whereas Mo, being the largest in atomic size, preferred occupying high-CN sites. However, the preference of Re, having intermediate atomic size, varied depending on the composition, and a clear reversal in the preference of Re as a function of the composition was evidenced in both the calculated and experimental site-occupancy results.     

Magnetically active Ag–Zn nanoferrites synthesized by solution combustion route: physical chemical studies and density functional theory analysis

Nanoparticles with mixed compositions, particularly spinel ferrites with magnetic activity, have arisen as contrast agents for magnetic resonance imaging, magnetic hyperthermia. For such applications, it is desirable to possess specific particle size and physicochemical properties, i.e., magnetic response, porosity, crystallinity, and so on. It is well known that controlling specific variables in the synthetic process has a dramatic effect on final product properties and behavior. Amid preparation techniques reported in the literature, low-temperature solution combustion method has shown the ability to control and direct synthesis simply and efficiently. We are presenting a study about controlling and tuning the magnetic properties and the effect of particle size modified in Ag–Zn nanoferrites with different amounts of Co and Ni as doping metals. Different combinations of Co and Ni within Ag–Zn (Ag_0.25Zn_0.5-xM_xFe_2.25O₄) nanoferrites have been synthesized using the low-temperature solution combustion technique, and this method proved to be efficient and reliable for developing homogenous, fine structured materials. X-ray diffraction confirmed that the atomic structure of prepared nanoferrites is pure and cubic, whereas electron microscopy confirmed a semispherical and monodisperse morphology with particle diameter around 20 nm. The magnetic behavior of bred materials has been explained by analyzing magnetic factors such as saturation magnetization, coercivity, and retentivity, and all experimental findings are matched with theoretical density functional theory (DFT) studies to understand the effect of each material within A and B sites in ferrite crystal cell. The observed magnetic properties highlight the superparamagnetic behavior and the effect of doping metals which is an asset in developing new materials for diagnostic and therapeutic applications. DFT modeling was achieved in an attempt to understand the effect of metal substitution in cubic ferrite cells.     

How are the ready and unready states of nickel-iron hydrogenase activated by H2? A density functional theory study

We have explored possible mechanisms for the formation of the catalytically active Ni(a)-S state of the enzyme, nickel iron hydrogenase, from the Ni*(r) (ready) or Ni*(u) (unready) state, by reaction with H(2), using density functional theory calculations with the BP86 functional in conjunction with a DZVP basis set. We find that for the reaction of the ready state, which is taken to have an -OH bridge, the rate determining step is the cleavage of H(2) at the Ni(3+) centre with a barrier of approximately 15 kcal mol(-1). We take the unready state to have a -OOH bridge, and find that reaction with H(2) to form the Ni(r)-S state can proceed by two possible routes. One such path has a number of steps involving electron transfer, which is consistent with experiment, as is the calculated barrier of approximately 19 kcal mol(-1). The alternative pathway, with a lower barrier, may not be rate determining. Overall, our predictions give barriers in line with experiment, and allow details of the mechanism to be explored which are inaccessible from experiment.     

Influence of impurity elements on the corrosion of α-uranium surface: a density functional theory study

Journal of Radioanalytical and Nuclear Chemistry - Influence of substitutional Fe, Al and Mg atoms on the corrosion of α-U(110) surface was studied by DFT?+?U method. The...     

Conventional strain energies of azetidine and phosphetane: Can density functional theory yield reliable results?

The conventional strain energies for azetidine and phosphetane are determined within the isodesmic, homodesmotic, and hyperhomodesmotic models. Optimum equilibrium geometries, harmonic vibrational frequencies, and corresponding electronic energies and zero‐point vibrational energies are computed for all pertinent molecular systems using self‐consistent field theory, second‐order perturbation theory, and density functional theory and using the correlation consistent basis sets cc‐pVDZ, cc‐pVTZ, and cc‐pVQZ. Single point fourth‐order perturbation theory, CCSD, and CCSD(T) calculations using the cc‐pVTZ and the cc‐pVQZ basis sets are computed using the MP2/cc‐pVTZ and MP2/cc‐pVQZ optimized geometries, respectively, to ascertain the contribution of higher order correlation effects and to determine if the quadruple‐zeta valence basis set is needed when higher order correlation is included. In the density functional theory study, eight different functionals are used including B3LYP, wB97XD, and M06‐2X to determine if any functional can yield results similar to those obtained at the CCSD(T) level. © 2012 Wiley Periodicals, Inc.