Ab initio calculations with effective core potentials on trivalent lanthanide–terpyridine complexes

 The electronic structures of complexes of terpyridine (tpy) with trivalent lanthanides (Ln) were calculated using ab initio methods with effective core potentials at Hartree–Fock and post-Hartree–Fock levels of theory. The quasirelativistic large-core (with 4f electrons included in the core) pseudopotentials of the Stuttgart group were chosen for the Ln atoms. The variation of several properties of the Ln(tpy)³⁺ complexes was studied for the whole Ln series. It was shown that there was a monotonous variation for all properties (geometrical and energetic) along the Ln series, except for Mulliken charges on the metal atom. Calculations were performed on three complexes of known solid-state structure. The difference between experimental and calculated geometries is discussed; for all structures, it is found to be lower than 0.2 ?. In all cases, the relative order from one complex to another is conserved. Received: 13 September 1999 / Accepted: 3 February 2000 / Published online: 19 April 2000     

Fully relativistic correlated benchmark results for uranyl and a critical look at relativistic effective core potentials for uranium

 A complete set of fully-relativistic benchmark results for the bond lengths and vibrational frequencies of uranyl at various levels of correlation treatment are presented. It is shown that the relativistic and correlation effects are of the same magnitude and should be treated on an equal footing. Results of uranyl calculations using various relativistic effective core potentials (RECP) are presented. Appropriate choices for RECPs for use in density functional theory (DFT) calculations in the local density approximation (LDA) and with the gradient-corrected B3LYP exchange-correlation functional are discussed. The conclusion is reached that small-core RECPs need to be used and that the best results as compared to the benchmark values are obtained by using a DFT functional that includes some fraction of Hartree-Fock Exchange. Received: 18 May 2001 / Accepted: 25 July 2001 / Published online: 30 October 2001     

Excitation energies, electron affinities and ionization potentials of the transition metals V, Cr and Mn

 Configuration interaction calculations were carried out for neutral ground and excited states and positively and negatively ionized states of the V, Cr and Mn atoms. Energy convergence with respect to systematic expansion of both the one-electron and configuration bases was investigated for valence correlation. Contributions from core electrons to the differential correlation energies and relativistic effects were evaluated separately. Assuming additivity of these contributions, excitation energies, electron affinities and ionization potentials of the atoms were obtained. All calculated values were in excellent agreement with the observed values within a deviation of 0.056 eV except for the electron affinity of the V atom, which had a calculated value 0.110 eV larger than the experimental value. Received: 9 August 2000 / Accepted: 26 October 2000 / Published online: 3 April 2001     

Electron affinities, excitation energies and ionization potentials of the transition metals (I) Sc and Ti

The electron affinities of the Sc and Ti atoms have been obtained by configuration interaction calculations. Energy convergence with respect to the systematic expansion of both the one-electron basis set and the configuration space was investigated for valence electrons, and the inclusion of correlation contributions from core electrons and relativistic effects gave the electron affinities of 0.181 eV and 0.163 eV for Sc and Ti, respectively. These are in excellent agreement with the observed values of 0.189 ± 0.020 eV and 0.080 eV. The same approach was applied for the first excited states and positive ions of both atoms. Excellent agreement with the experimental results was also obtained for these states. Received: 16 February 1998 / Accepted: 2 April 1998 / Published online: 23 June 1998     

Model studies of the chemisorption of hydrogen and oxygen on the Au (1 0 0) surface

 The convergence of chemisorption energy for hydrogen and oxygen on gold clusters is studied. Two theoretical approaches have been employed; wavefunction methods at the self-consistent-field second–order M?ller–Plesset level and density functional theory and the two methods are compared. Relativistic effective core potentials exploited in the former approach were developed in this work. Received: 25 October 1999 / Accepted: 21 February 2001 / Published online: 11 October 2001     

Inexpensive and accurate predictions of optical excitations in transition-metal complexes: the TDDFT/PBE0 route

Time-dependent density functional theory (TDDFT) is applied to calculate vertical excitation energies of three representative transition metal complexes. The computational model (PBE0) is obtained by combining the Perdew-Burke-Erzenrhof (PBE) generalized gradient functional with a predetermined amount of exact exchange. Our results show that the TDDFT/PBE0 model represents a cheap and reliable tool for the computation of optical excitations for transition metal complexes. Received: 8 August 2000 / Accepted: 7 September 2000 / Published online: 23 November 2000     

Solid-State nuclear magnetic resonance: performance of point-charge distributions to model intermolecular effects in 19F chemical shifts

This contribution presents results from applying two different charge models to take into account intermolecular interactions to model the solid-state effects on the ¹⁹F NMR chemical-shift tensors. The density functional theory approach with the B3LYP gradient-corrected exchange correlation functional has been used because it includes electron correlation effects at a reasonable cost and is able to reproduce chemical shifts for a great variety of nuclei with reasonable accuracy. The results obtained with the charge models are compared with experimental data and with results obtained from employing the cluster model, which explicitly includes neighboring molecular fragments. The results show that the point-charge models offer similar accuracy to the cluster model with a lower cost. Received: 3 October 1999 / Accepted: 3 February 2000 / Published online: 5 June 2000     

Energy decomposition in the topological theory of atoms in molecules and in the linear combination of atomic orbitals formalism: a note

 It is shown that the molecular energy calculated at the self-consistent-field level can be strictly expressed as a sum of one- and two-atom energy components in the framework of Bader's topological theory of atoms in molecules (AIM). The expressions of our recent “chemical energy component analysis” can be obtained from the AIM ones as some linear combination of atomic orbitals mappings of the integrations over the atomic basins. Received: 15 June 2000 / Accepted: 4 October 2000 / Published online: 19 January 2001     

Core-valence correlation effects for molecules containing first-row atoms. Accurate results using effective core polarization potentials

The accuracy of employing effective core polarization potentials (CPPs) to account for the effects of core-valence correlation on the spectroscopic constants and dissociation energies of the molecules B₂, C₂, N₂, O₂, F₂, CO, CN, CH, HF, and C₂H₂ has been investigated by comparison to accurate all-electron benchmark calculations. The results obtained from the calculations employing CPPs were surprisingly accurate in every case studied, reducing the errors in the calculated valence D _e values from a maximum of nearly 2.5 kcal/mol to just 0.3 kcal/mol. The effects of enlarging the basis set and using higher-order valence electron correlation treatments were found to have only a small influence on the core-valence correlation effect predicted by the CPPs. Thus, to accurately recover the effects of intershell correlation, effective core polarization potentials such as the ones used in the present work provide an attractive alternative to carrying out computationally demanding calculations where the core electrons are explicitly included in the correlation treatment. Received: 11 May 1998 / Accepted: 27 July 1998 / Published online: 28 October 1998     

A theoretical investigation of (−)-deprenyl (selegiline) as a radical scavenger

The chemical reactions between (−)-deprenyl and ·OH or ·OOH were studied using molecular orbital theory, with N,N-dimethylpropargylamine as a model. (−)-Deprenyl was confirmed to be a good radical scavenger. The active site was the acetylenic part and ·OH- or ·OOH was trapped on either acetylenic carbon. The activation energies were about 10–20 kcal/mol. The resulting ·OH- or ·OOH-adducts, still radicals, trapped further radicals on the remaining carbon of the acetylenic part. The final double trapping products were at extraordinarily lower energy levels than the original reactants by 50–70 kcal/mol. The secondary transition states were not detected, suggesting that the reactions occurred at once or in a cascade. Some results with the model system were verified by the results with the real (−)-deprenyl system. Received: 6 October 1999 / Accepted: 5 March 2000 / Published online: 21 June 2000     

A density functional theory study of the chemoselectivity and regioselectivity of the domino cycloaddition reactions of nitroalkenes with substituted alkenes

The chemoselectivity and regioselectivity of the domino intermolecular [4 + 2]/[3 + 2] cycloaddition reactions of nitroalkenes with substituted alkenes, vinyl ethers as electron-rich alkenes and vinyl ketones as electron-poor alkenes, have been studied using density functional theory (DFT) methods with the B3LYP functional and the 6-31G^* basis set. These domino processes comprise two consecutive cycloaddition reactions: the first one is an intermolecular [4 + 2] cycloaddition of the vinyl ether to the nitroalkene to give a nitronate intermediate, which then affords the final nitroso acetal adduct through an intermolecular [3 + 2] cycloaddition reaction with the vinyl ketone. The two consecutive cycloadditions present total chemoselectivity and ortho regioselectivity. While first [4 + 2] cycloaddition reaction takes place along the attack of the electron-rich alkene to nitroalkene, the [3 + 2] one takes place along the attack of the electron-poor alkene to the corresponding nitronate intermediate. This DFT study is in complete agreement with the experimental results. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Auxiliary basis sets for main row atoms and transition metals and their use to approximate Coulomb potentials

We present auxilliary basis sets for the atoms H to At – excluding the Lanthanides – optimized for an efficient treatment of molecular electronic Coulomb interactions. For atoms beyond Kr our approach is based on effective core potentials to describe core electrons. The approximate representation of the electron density in terms of the auxilliary basis has virtually no effect on computed structures and affects the energy by less than 10⁻⁴ a.u. per atom. Efficiency is demonstrated in applications for molecules with up to 300 atoms and 2500 basis functions. Received: 17 December 1996 / Accepted: 8 May 1997     

The unrestricted natural orbital-restricted active space method: methodology and implementation

The full configuration interaction method in the space of fractionally occupied unrestricted natural orbitals (UNO-CAS method) is extended to excited states as well as to strongly correlated and reactive systems with large active spaces. This is accomplished by␣using restricted active space (RAS) wave functions introduced by Olsen et al. [(1988) J Chem Phys 89: 2185] and using the UNOs without the expensive orbital optimization step. In RAS, the space of active orbitals is subdivided into three groups: a group with essentially doubly occupied orbitals (RAS1), the usual CAS space (RAS2), and a space with weakly occupied active orbitals (RAS3). We select these spaces on the basis of the occupation numbers of the UNOs. All possible electron distributions are allowed in the usual CAS space, but the number of vacancies is limited in RAS1 and the number of electrons is limited in RAS3. We discuss an efficient algorithm for generating a RAS wave function. This is based on the Handy-Knowles determinantal expansion with an addressing scheme adopted for the restricted expansion. Results for both ground and excited states of azulene and free base porphyrin are presented. Received: 16 July 1998 / Accepted: 7 August 1998 / Published online: 19 October 1998     

The mechanism of spin polarization in aromatic free radicals

 The spin-polarization mechanism in aromatic systems is analyzed with reference to the prototypical phenoxyl, cyclohexadienyl and benzyl radicals. In particular, a decomposition into “first-order” and “second-order” contributions is proposed, which helps to rationalize the different nature of the spin density for atoms in α or in β positions with respect to the radical center. The different weights of the two contributions are discussed on the basis of Hartree–Fock and density functional computations. Received: 17 September 1999 / Accepted: 3 February 2000 / Published online: 29 June 2000     

Dual propagation inversion of truncated signals

Fourier transforms occur in a variety of chemical systems and processes. A few examples include obtaining spectral information from correlation functions, energy relaxation processes, spectral densities obtained from force autocorrelation functions, etc. In this article, a new functional transform, named the dual propagation inversion (DPI) is introduced. The DPI functional transform can be applied to a variety of problems in chemistry, such as Fourier transforms of time correlation functions, energy relaxation processes, rate theory, etc. The present illustrative application is to generating the frequency representation of a discrete, truncated time-domain signal. The DPI result is compared with the traditional Fourier transform applied to the same truncated time signal. For both noise-free and noise-corrupted time-truncated signals, the DPI spectrum is found to be more accurate, particularly as the signal is more severely truncated. In the DPI, the distributed-approximating-functional free propagator is used to propagate and denoise the signal simultaneously. Received: 30 January 2000 / Accepted: 6 July 2000 / Published online: 23 November 2000     

Transition state for intramolecular C–H bond cleavage in [(LCu)2(μ-O)2]2+ (L = 1,4,7-tribenzyl-1,4,7-triazacyclononane)

Hybrid quantum mechanical/molecular mechanical electronic structure calculations reveal the transition state for C–H bond cleavage in [(LCu)₂ (μ-O)₂]²⁺ (L=1,4,7-tribenzyl-1,4,7-triazacyclononane) to be consistent with a hydrogen-atom-transfer mechanism from carbon to oxygen. At the MPW1K/double-zeta effective core potential(+)|univeral force field level, 0 K activation enthalpies for the parent, p-CF3, and p-OH substituted benzyl systems are predicted to be 8.8, 9.5, and 7.8 kcal/mol. Using a one-dimensional Eckart potential to estimate quantum effects on the reaction coordinate, reaction in the unsubstituted system is predicted to proceed with a primary kinetic isotope effect of 22 at 233 K. Structural parameters associated with the hydrogen-atom transfer are consistent with the Hammond postulate. Received: 10 October 2000 / Accepted: 3 November 2000 / Published online: 3 April 2001     

The hierarchy of localization basins: a tool for the understanding of chemical bonding exemplified by the analysis of the VOx and VOx+ (x=1–4) systems

The hierarchy of the electron localization basins is a powerful tool of analysis of the bonding in molecules and solids within the “elfological” framework. It is a generalization of the molecular isodensity contour analysis originally proposed by Mezey. In this approach the basins are ordered with respect to the electron localization function values at the critical points which determine the reduction of the reducible localization domains. The procedure enabling the corresponding tree diagrams to be built is described and it is shown how the method can be used as a generator of mathematical definitions of chemical concepts. The possibility offered by this simple tool is illustrated by a study of the VO _x and VO _x ⁺ (x=1–4) oxides in their ground state and in some excited states. Received: 20 July 2000 / Accepted: 20 October 2000 / Published online: 23 January 2001     

A density functional theory test study on the N2··· He dimer

 In the present contribution we report a study of the weakly bound van der Waals N₂–He molecule in the framework of the supermolecule approach by means of the PWPW and mPW1PW exchange–correlation functionals, using density functional theory local-spin-optimized atom-centered basis sets complemented with bond functions optimized at the mPW1PW level of theory. Calculations show that the mPW1PW functional using bond functions gives a realistic representation of the interaction-energy potentials for this van der Waals dimer, comparable to reference M?ller–Plesset perturbation theory calculations. In contrast, the PWPW functional is unable to describe the bonding properties of this system and all values of the bonding properties obtained at different geometries with this functional are considered out-of-scale compared with the rest of the calculations presented in this study. Received: 30 October 2000 / Accepted: 3 January 2001 / Published online: 3 April 2001     

Electric response properties of a confined gas of independent particles acted upon by a direct current electric field

Exact results for linear and nonlinear electric response properties of a non-interacting ensemble of charged particles, confined within an impenetrable box and subjected to a static, homogeneous electric field, are derived and discussed. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 5 June 2000