Linear free energy relations and the hammett equation for substituted pyridine 1-oxides

It is recommended that a self-consistent set of sigma constants be used to obtain linear free energy relations with pyridine 1-oxides rather than using adjusted benzoic acid sigma constants. These recommended constants are derived from the literature values of the acid dissociated constants of the protonated substituted pyridine 1-oxides. A survey and discussion of linear free energy relations using these new constants (σP_yNO) is given. Comparisons of correlations using adjusted benzoic acid sigma constants and (σP_yNO) are presented.     

Linear free-energy relationships in the reduction of alkenes by hydrogen transfer

In this work we studied the relationship between the structure of alkene substrates and the rate of reduction of their double bond by hydrogen transfer over a Pd/sepiolite catalyst using cyclohexene as donor.

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Rapidly convergent procedure to solve the density profile equation in the classical density functional theory

An efficient recursive procedure to solve the density profile equation in the classical density functional theory (DFT) using an inverse Broyden method is described. The present iterative procedure is free of calculation of the Jacobian matrix, and its inversion unavoidable for the well-known Newton-Raphson (NR) method and its variants. Numerical calculation indicates that only the approximate solution and iterative matrix of the lower bulk density case are employed as the corresponding initial guesses of the higher bulk density case, the present recursive procedure can converge quickly to the physical solution with an accuracy of epsilon = 10(-14); therefore, the procedure provides an efficient numerical algorithm for the theory in which acquirement of a density profile of high accuracy is a key step. Extensive numerical calculation shows the advantage of the present inverse Broyden method over Broyles' mixing procedure and a modified Powell hybrid algorithm (a variation of the NR method).     

Tight-binding density functional theory: an approximate Kohn-Sham DFT scheme

The DFTB method is an approximate KS-DFT scheme with an LCAO representation of the KS orbitals, which can be derived within a variational treatment of an approximate KS energy functional. But it may also be related to cellular Wigner-Seitz methods and to the Harris functional. It is an approximate method, but it avoids any empirical parametrization by calculating the Hamiltonian and overlap matrices out of DFT-derived local orbitals (atomic orbitals, AO's). The method includes ab initio concepts in relating the Kohn-Sham orbitals of the atomic configuration to a minimal basis of the localized atomic valence orbitals of the atoms. Consistent with this approximation, the Hamiltonian matrix elements can strictly be restricted to a two-center representation. Taking advantage of the compensation of the so-called "double counting terms" and the nuclear repulsion energy in the DFT total energy expression, the energy may be approximated as a sum of the occupied KS single-particle energies and a repulsive energy, which can be obtained from DFT calculations in properly chosen reference systems. This relates the method to common standard "tight-binding" (TB) schemes, as they are well-known in solid-state physics. This approach defines the density-functional tight-binding (DFTB) method in its original (non-self-consistent) version.     

Linear response time-dependent density functional theory for van der Waals coefficients

A linear response time-dependent density functional theory is described and used to calculate the dynamic polarizabilities and van der Waals C(6) coefficients of complex atom pairs. We present values of C(6) for dimers of main group atoms and the first row of transition metal atoms.     

Density functional theory: Approximating quasiparticle density functional

A constructive approach for deriving the approximating quasiparticle energy density functional is proposed. As a matter of fact, the proposed approach is the direct development of the Kohn–Sham quasiparticle concept and the Levy–Valone approach. The approach presented takes into account a pseudopotential character of the exchange-correlation part of the density functional and results in a system of functional equations to obtain ground-state energies of many-electron systems.     

Ionization potentials of tantalum-carbide clusters: an experimental and density functional theory study

We have used photoionization efficiency spectroscopy to determine the ionization potentials (IP) of the tantalum-carbide clusters, Ta3Cn (n = 1-3) and Ta4Cn (n = 1-4). The ionization potentials follow an overall reduction as the number of carbon atoms increases; however, the trend is not steady as expected from a simple electrostatic argument. Instead, an oscillatory behavior is observed such that clusters with an odd number of carbon atoms have higher IPs and clusters with an even number of carbon atoms have lower IPs, with the Ta4C4 cluster exhibiting the lowest IP. Excellent agreement is found with relative IPs calculated using density functional theory for the lowest energy structures, which are consistent with the development of a 2 x 2 x 2 face-centered nanocrystal. This work shows that IPs may be used as a reliable validation for the geometries of metal-carbide clusters calculated by theory. The variation in IP can also be interpreted qualitatively with application of a simple model based upon isolobal frontier orbitals.     

Linear optical response of current-carrying molecular junction: a nonequilibrium Green's function-time-dependent density functional theory approach

We propose a scheme for calculation of linear optical response of current-carrying molecular junctions for the case when electronic tunneling through the junction is much faster than characteristic time of external laser field. We discuss relationships between nonequilibrium Green's function (NEGF) and time-dependent density functional theory (TDDFT) approaches and derive expressions for optical response and linear polarizability within NEGF-TDDFT scheme. Corresponding results for isolated molecule, derived within TDDFT approach previously, are reproduced when coupling to contacts is neglected.     

Equation for the direct determination of the density matrix: Time-dependent density equation and perturbation theory

The density equation proposed previously for the direct determination of the density matrix, i.e. for the wave mechanics without wave, is extended to a time-dependent case. The time-dependent density equation has been shown to be equivalent to the time-dependent Schr?dinger equation so long as the density matrix, included as a self-contained variable, is N-representable. Formally, it is obtainable from the previous time-independent equation by replacing the energy E with . The perturbation theory formulas for the density equation have also been given for both the time-dependent and time-independent cases. Received: 16 June 1998 / Accepted: 2 September 1998 / Published online: 8 February 1999     

Stability conditions for density functional reactivity theory: an interpretation of the total local hardness

The second-order Taylor series expansions commonly used in the density functional chemical reactivity theory are used to define local stability conditions for electronic states. Systems which satisfy these conditions are stable to infinitesimal perturbations due to approaching chemical reagents. The basic formalism considered here supersedes previous variational approaches to chemical reactivity theory like the electrophilicity, potentialphilicity, and chargephilicity. The total local hardness emerges naturally in this analysis, and can be clearly interpreted. When the total local hardness is small, the system is relatively insensitive to perturbations. Furthermore, minus the total local hardness is an energetically favorable perturbation of the external potential.     

Time-dependent density functional theory gradients in the Amsterdam density functional package: geometry optimizations of spin-flip excitations

An implementation of time-dependent density functional theory (TDDFT) energy gradients into the Amsterdam density functional theory program package (ADF) is described. The special challenges presented by Slater-type orbitals in quantum chemical calculation are outlined with particular emphasis on details that are important for TDDFT gradients. Equations for the gradients of spin-flip TDDFT excitation energies are derived. Example calculations utilizing the new implementation are presented. The results of standard calculations agree well with previous results. It is shown that starting from a triplet reference, spin-flip TDDFT can successfully optimize the geometry of the four lowest singlet states of CH₂ and three other isovalent species. Spin-flip TDDFT is used to calculate the potential energy curve of the breaking of the C?CC bond of ethane. The curve obtained is superior to that from a restricted density functional theory calculation, while at the same time the problems with spin contamination exhibited by unrestricted density functional theory calculations are avoided.     

Tuning nonlinear optical and optoelectronic properties of vinyl coupled triazene chromophores: a density functional theory and time-dependent density functional theory investigation

Triazenes are a unique class of polyazo compounds containing three consecutive nitrogen atoms in an acyclic arrangement and are promising NLO candidates. In the present work, a series of 15 donor-π-acceptor type vinyl coupled triazene derivatives (VCTDs) with different acceptors (-NO(2), -CN, and -COOH) have been designed, and their structure, nonlinear response, and optoelectronic properties have been studied using density functional theory and time-dependent density functional theory methods. B3LYP/6-311g(d,p) optimized geometries of the designed candidates show delocalization from the acceptor to donor through a π-bridge. Molecular orbital composition analysis reveals that HOMO is stabilized by the π-bridge, whereas acceptors play a major role in the stabilization of LUMO. Among the three acceptors, nitro derivatives are found to be efficient NLO candidates, and tri- and di-substituted cyano and carboxylic acid derivatives also show reasonably good NLO response. The effect of solvation on these properties has been studied using PCM calculations. From TDDFT calculations, the computed absorption spectra of these candidates lie in the range of 350-480 nm in the gas phase and have positive solvatochromism. The ground-state stabilization interactions are accounted from NBO calculations. In an effort to substantiate the thermal stability of the designed candidates, computations have been done to identify the weak interactions in the systems through NCI and AIM analysis. In summary, 10 out of 15 designed candidates are found to have excellent NLO and optoelectronic properties.     

Structure, spectroscopy, and reactivity properties of porphyrin pincers: a conceptual density functional theory and time-dependent density functional theory study

Porphyrin and pincer complexes are both important categories of compounds in biological and catalytic systems. The idea to combine them is computationally investigated in this work. By employment of density functional theory (DFT), conceptual DFT, and time-dependent DFT approaches, structure, spectroscopy, and reactivity properties of porphyrin pincers are systematically studied for a selection of divalent metal ions. We found that the porphyrin pincers are structurally and spectroscopically different from their precursors and are more reactive in electrophilic and nucleophilic reactions. A few quantitative linear/exponential relationships have been discovered between bonding interactions, charge distributions, and DFT chemical reactivity indices. These results are implicative in chemical modification of hemoproteins and understanding chemical reactivity in heme-containing and other biologically important complexes and cofactors.     

Molecular energies and properties from density functional theory: Exploring basis set dependence of Kohn—Sham equation using several density functionals

The performance of four commonly used density functionals (VWN, BLYP, BP91, and Becke's original three-parameter approximation to the adiabatic connection formula, referred to herein as the adiabatic connection method or ACM) was studied with a series of six Gaussian-type atomic basis sets [DZP, 6–31G**, DZVP, TZVP, TZ2P, and uncontracted aug-cc-pVTZ (UCC)]. The geometries and dipole moments of over 100 first-row and second-row molecules and reaction energies of over 300 chemical reactions involving such molecules were computed using each of the four density functionals in combination with each of the six basis sets. The results were compared to experimentally determined values. Based on overall mean absolute theory versus experiment errors, it was found that ACM is the best choice for predictions of both energies of reaction [overall mean absolute theory versus experiment error (MATvEE) of 4.7 kcal/mol with our most complete (UCC) basis set] and molecular geometries (overall MATvEE of 0.92 pm for bond distances and 0.88° for bond angles with the UCC basis set). For routine calculations with moderate basis sets (those of double-ζ type: DZP, 6–31G**, and DZVP) the DZVP basis set was, on average, the best choice. There were, however, examples of reactions where significantly larger basis sets were required to achieve reasonable accuracy (errors ≤ 5 kcal/mol). For dipole moments, ACM, BP91, and BLYP performed comparably (overall MATvEE of 0.071, 0.067, and 0.059 debye, respectively, with the UCC basis set). Basis sets that include additional polarization functions and diffuse functions were found to be important for accurate density functional theory predictions of dipole moments. © 1997 by John Wiley & Sons, Inc.     

Dissolution of oxygen reduction electrocatalysts in an acidic environment: density functional theory study

Density functional theory is employed to determine the reaction thermodynamics of a group of chemical and electrochemical reactions chosen to investigate the dissolution of metal atoms from oxygen reduction reaction catalysts in an acid medium. Once a set of thermodynamically allowed reactions is established, those reactions are selected to investigate the relative stabilities of Pt atoms and of other transition metal atoms (Ir, Pd, Rh, Ni, and Co) toward the dissolution reactions. The dissolution reactions that are found thermodynamically favorable are electrochemical and involve adsorbed oxygenated compounds that are intermediate species of the oxygen reduction reaction. Iridium is found to be the most stable among the various pure metals in comparison to Pt. Most of the metals alloyed with Pt cause a decrease of the Pt stability against dissolution, except for Ni, which does not affect it. On the other hand, the influence of Pt on the stability of the second metal in the alloy follows the same trend as in pure metal catalysts, with Ir being the most stable. When both atoms in a PtM alloy are involved in dissolution reactions, alloyed Ir is also found more stable than Pt in a given dissolution reaction, and the same behavior is found in alloyed Co for most of the reactions studied.