Effective Core Potential Basis Sets Research Articles

A theoretical analysis of the molecular events involved in hydrocarbons reactivity on palladium clusters

Abstract Palladium clusters have been chosen to represent a nanosized catalyst apt for a theoretical study on some fundamental aspects of surface molecular events. The investigation has been focused on hydrocarbon transformations to give dehydrogenation and hydrogenolysis products. The energetic details of the involved elementary processes have been calculated through density functional theory (DFT). The Becke Lee–Yang–Parr hybrid (B3LYP) functional was adopted to calculate exchange and correlation energy. An effective core potential basis set (ECP on core electrons and Dunning/Huzinaga on outer electrons) was found sufficiently accurate to reproduce experimental data. Clusters containing up to seven Pd atoms were considered and their interaction with hydrogen, methane and ethane and their fragments was analyzed and a kinetic study of the system was performed. Transition states structures and energies were calculated through quantum mechanics and the corresponding kinetic constants were derived from a statistic thermodynamic approach. On the basis of such information, a kinetic model that accounts for ethane transformations has been formulated. The scaling of such an atomic scale information to reactor scale is also considered.

Ab initio calculations on the Ground and Low‐Lying Excited States of InH.

Using multiconfiguration quasi-degenerate perturbation theory (MCQDPT), the ground and the low-lying excited states of InH are studied, and the potential energy curves and the spectroscopic constants of the , a 3Π0−,0+,1,2 and A 1Π1 states are obtained. By comparing the result of all-electron basis sets with that of relativistic effective core potential (RECP) basis sets, it is found that the former is better than the latter, especially in describing the A 1Π1 state. The transition properties of the excited states, including the transition dipole moments, the radiative lifetimes and the Franck–Condon factors, are predicted. It is shown that a 3Π0+ and a 3Π1 are long-lived states, while A 1Π1 is a short-lived state.

Theoretical Aspects of Compounds Containing Si, Ge, Sn and Pb

AbstractFor Abstract see ChemInform Abstract in Full Text.

Quantum Chemical Characterization of Methane Metathesis in L2MCH3 (L = H, Cl, Cp, Cp*; M = Sc, Y, Lu)

The dimerization, unimolecular methane ejection, and bimolecular methane metathesis reactions of L2MCH3 species where L = H, Cl, Cp, and Cp* and M = Sc, Y, and Lu are modeled at the density functional level (B3LYP) using a relativistic effective core potential basis set. Results for cases with H or Cl ligands are in poor quantitative agreement with analogous results for cases with Cp* ligands; in some instances, Cp ligands provide results in good agreement with those for Cp*, but in the case of methane metathesis, activation enthalpies are underestimated by 3−4 kcal mol-1 with the unmethylated ligand. Unimolecular methane ejection via formation of a tuck-in complex versus bimolecular methane metathesis is predicted potentially to be a competitive process for Sc, but to be comparatively too high in energy for Y and Lu to be thermodynamically significant under typical sets of reaction conditions. The difference is ascribable to the shorter metal−ligand distances observed for Sc. For (Cp*)2LuCH3, quantum mec...

Ab initio calculations on the ground and low-lying excited states of InH

Using multiconfiguration quasi-degenerate perturbation theory (MCQDPT), the ground and the low-lying excited states of InH are studied, and the potential energy curves and the spectroscopic constants of the , a 3Π0−,0+,1,2 and A 1Π1 states are obtained. By comparing the result of all-electron basis sets with that of relativistic effective core potential (RECP) basis sets, it is found that the former is better than the latter, especially in describing the A 1Π1 state. The transition properties of the excited states, including the transition dipole moments, the radiative lifetimes and the Franck–Condon factors, are predicted. It is shown that a 3Π0+ and a 3Π1 are long-lived states, while A 1Π1 is a short-lived state.

Computational Probes into the Basis of Silver Ion Chromatography. II. Silver(I)−Olefin Complexes

Alkene complexes of silver(I) are studied by four computational methodologies: ab initio RHF, MP2, and MP4 computations, and density functional B3LYP computations, with a variety of all-electron and effective core potential basis sets. Methodological studies indicate that MP2/SBK(d) computations can adequately represent Ag(I)−alkene complexes, and this method is used to study Ag(I) complexes with one to six ethene ligands as well as with methyl-substituted ethene derivatives. The first two alkene ligands enter the coordination sphere of Ag(I) with approximately the same energy, in line with ICR experiments. The association enthalpies of additional complexing ethene ligands diminish progressively. Computations on methyl-substituted alkenes show that the observed trends in argentation chromatography are opposite to those observed and computed for the gas phase, and suggest strong medium effects in Ag(I) chromatography.

DFT Calculations of 99Ru Chemical Shifts with All-Electron and Effective Core Potential Basis Sets

DFT Calculations of 99Ru Chemical Shifts with All-Electron and Effective Core Potential Basis Sets

Theoretical studies on the structure of the endohedral CoGe 10− cluster anion

Theoretical studies have been carried out on the structure of the endohedral CoGe 10 − cluster anion using ab initio (HF) and density functional theory (DFT-B3LYP) methods in conjunction with effective core potential basis sets (LanL2DZ and LanL2DZ*). For the important structures, all-electron basis sets plus polarization and diffuse functions (6-31+G*) are also used. At the levels of calculations employed, the bicapped tetragonal antiprism structure with D 4d symmetry is found to be most stable. Compared with the small fragments [Co+Ge 10 −(D 4d)], this structure is 97.7 kcal/mol more stable at the B3LYP/LanL2DZ level. Other low-energy structures have also been optimized on the potential energy surface of the endohedral CoGe 10 − cluster anion.

DFT Calculations of99Ru Chemical Shifts with All-Electron and Effective Core Potential Basis Sets

The nuclear shielding of 99Ru in several complexes has been investigated computationally by DFT methods with effective core potential and all-electron basis sets. Shieldings calculated with ECP bases correlate very satisfactorily with available experimental data, although they are ca. one order of magnitude lower than the experimental values. The influence of molecular geometry (semiempirical vs. DFT) on the nuclear shielding is also examined and discussed, particularly in the case of species containing Ru−S bonds {[RuCl2(DMSO)4] and α-[PW11RuO39(DMSO)]5−}. It is shown that such calculations may help the assignment of signals in 99Ru NMR spectra of mono- and polynuclear complexes. (© Wiley-VCH Verlag GmbH, 69451 Weinheim, Germany, 2002)

An Ab Initio Investigation of the Ground and Excited Electronic State Properties of a Series of Bromine- and Iodine-Containing Singlet Carbenes

Ab initio calculations have been performed to determine the structure and energies of the ground and first excited electronic states of bromine- and iodine-containing singlet carbenes. Effective core potential basis sets augmented with polarization functions were utilized at the CASSCF, CASPT2, and CISD levels of theory. Validation of the effective core potential basis sets for the ground and excited states of the singlet carbenes was carried out by comparison with previous results from all-electron basis set calculations. As was the case in previous studies of chlorine- and fluorine-containing halocarbenes, the bromine- and iodine-containing singlet carbenes are characterized by small bond angles in their ground states, ranging from 100° to 112°, and dramatically larger bond angles in their first excited states, ranging from 125° to 132°. This increase is due to the promotion of an electron from a carbon lone pair orbital coplanar with the carbon−halogen bonds to a carbon p-type orbital perpendicular to the bonds. Adiabatic transition energies for transitions from the ground to first excited state for the singlet carbenes determined at the CASPT2(18,12) and CISD levels range from 21 277 to 10 870 cm-1 and are in excellent agreement with experimental measurements where comparisons are available.

Dissociation Potential Curves of Low-Lying States in Transition Metal Hydrides. I. Hydrides of Group 4

The dissociation energy curves of low-lying spin-mixed states for Group 4 hydrides, TiH, ZrH, and HfH, have been calculated using both effective core potential and all-electron approaches. A comprehensive set of theoretical results including the dissociation energies, equilibrium distances, harmonic frequencies, anharmonicities, rotational constants, and dipole moments are reported for these molecules. We present results for both ground and a few excited states, filling a considerable gap in available data for these molecules. Absorption spectra are also predicted on the basis of the results. The present study uses three methods, all based on the multiconfigurational self-consistent field (MCSCF) method, augmented by second-order configuration interaction (SOCI), with either an effective core potential basis set (SBKJC) or a double-ζ basis set (MIDI): (i) MCSCF+SOCI/SBKJC(f,p) with a one-electron approximation using effective nuclear charges, (ii) MCSCF+SOCI/MIDI(3p,3p) with the full Breit−Pauli Hamiltonian, and (iii) MCSCF +SOCI/MIDI(3p,3p) with the relativistic elimination of the small component scheme and full Breit−Pauli Hamiltonian. The results are compared with previous theoretical studies and available experimental data reported previously. Good agreement is obtained between the results obtained when the first and third methods are used.

Force field scale factors of effective core potential basis sets of some selenium and tellurium heterocyclic molecules, selenophene, 1,2,5-selenadiazole, tellurophene and 1,2,5-telluradiazole

Vibrational frequencies were calculated for selenophene, SO, 1,2,5-selenadiazole, SA, tellurophene, TO, and 1,2,5-telluradiazole, TA, at the B3LYP, MP2 and HF levels of theory. The basis sets used are the CEP-121G, CEP-31G, LanL2DZ, SDDALL and SDD basis sets in addition to the 6-31G(p) and 6-311G(d,p) basis sets for SO and SA. The resulting internal coordinate force fields were scaled using one-scale-factor scaling. The scale factors were varied to minimize the difference between the calculated and experimental vibrational frequencies. Good agreement between the calculated and experimental geometries was obtained. Although the size of the effective core potential (ECF) basis sets is about half or less than those of the non-ECP basis sets, 6-31G(p) and 6-311G(d,p), the obtained average errors and scale factors were comparable to those obtained using the non-ECP basis sets. The lowest average errors were obtained by the SDDALL basis set. The average errors using the MP2 method were unusually high.

Calculation of the structural and NMR properties of the tridecameric AlO4Al12(OH)24(H2O)127+ polycation

The aluminum tridecameric polyoxocation, AlO4Al12(OH)24(H2O)127+ is a major component in partially hydrolyzed Al+3(aq) solutions and has been extensively studied experimentally, mainly using NMR techniques. I have calculated the equilbrium geometry of this cation using the Hartree-Fock method and a polarized double-zeta effective core potential basis set, obtaining bond distances which agree well with X-ray crystallographic studies of selenate and sulfate salts of the polycation (Al[4]: 4 × 1.85 Å calc, 4 × 1.84 Å exp: Al[6]: 4 × 1.85, 2 × 2.05 Å calc, 2 × 1.84, 2 × 1.88, 1.91, 2.04 Å exp [where the numbers in brackets indicate the coordination numbers]). I have also calculated electric field gradients and NMR shielding constants at all the atoms using the standard 6-31G∗ basis set and Hartree-Fock and hybrid Hartree-Fock-density functional (B3LYP) techniques. Using the Hartree-Fock method, the central four-coordinate Al is calculated to be deshielded by ∼56 ppm, and the six-coordinate Al atoms by ∼16 ppm, vs. the Al(OH2)6+3 reference, compared to experimental shifts of 63 and 12 ppm, respectively. The central Al[4] is thus shielded by ∼20 ppm with respect to the tetrahedral monomer Al(OH)4−1. Al-NMR shifts obtained from the B3LYP calculations are very similar. The calculated O-NMR shifts, vs. free gas-phase H2O, are 17 ppm for the η-OH2 groups, 30 ppm for the μ-OH and μOH′ groups, and 55 ppm for the μ4-O group, which match well with the experimentally assigned shifts of 20, 30, and 55 ppm, respectively (vs. liquid H2O). The B3LYP method yields O shifts, which are systematically about 40 to 50% larger. It is not clear whether the discrepancies in the calculated O shifts vs. liquid water are a result of deficiencies in the model (neglect of the aqueous environment) or in the method (lack of correlation in the Hartree-Fock method). Studies on the Al2(OH)2(OH2)8+4 cation with small numbers of explicit waters hydrogen-bonded to it indicate that O shifts can be perturbed strongly by the presence of solvent. The calculated 17O nuclear quadrupole coupling constants, NQCC (using the 6–31G∗ Hartree-Fock calibration factor of Ludwig et al., 1996 to relate electric field gradients to NQCC values) are 1.7 MHz for μ4-O, 7.8 to 8.0 MHz for the μOH and μOH′ groups and 10.7 MHz for the ηOH2 group. The μOH values are substantially higher than experimental values of 5 to 6 MHz observed for Al2OH groups in Al oxyhydroxides. B3LYP values are very similar. However, hydrogen bonding to water in simple model compounds like Al2(OH)2(OH2)8+4 reduces the -OH NQCC values to ∼6 MHz.

Ionic liquids based on FeCl(3) and FeCl(2). Raman scattering and ab initio calculations.

We have prepared ionic liquids by mixing either iron(II) chloride or iron(III) chloride with 1-butyl-3-methylimidazolium chloride (BMIC). Iron(II) chloride forms ionic liquids from a mole ratio of 1 FeCl(2)/3 BMIC to almost 1 FeCl(2)/1 BMIC. Both Raman scattering and ab initio calculations indicate that FeCl(4)(2-) is the predominant iron-containing species in these liquids. Iron(III) chloride forms ionic liquids from a mole ratio of 1 FeCl(3)/1.9 BMIC to 1.7 FeCl(3)/1 BMIC. When BMIC is in excess, Raman scattering indicates the presence of FeCl(4-). When FeCl(3) is in excess, Fe(2)Cl(7-) begins to appear and the amount of Fe(2)Cl(7-) increases with increasing amounts of FeCl(3). Ionic liquids were also prepared from a mixture of FeCl(2) and FeCl(3) and are discussed. Finally, we have used both Hartree-Fock and density functional theory methods to compute the optimized structures and vibrational spectra for these species. An analysis of the results using an all-electron basis set, 6-31G, as well as two different effective core potential basis sets, LANL2DZ and CEP-31G is presented.

A Kinetic Study of Hydrocarbons Reactivity on Palladium Catalysts through a DFT Approach

ABSTRACTPalladium clusters have been chosen to represent a typical supported heterogeneous catalyst and their interaction with hydrocarbons has been investigated theoretically. The calculations were performed through density functional theory and the Becke-Lee-Yang-Parr hybrid (B3LYP) functional was adopted to calculate exchange and correlation energy. An effective core potential basis set (ECP on core electrons and Dunning/Huzinaga on outer electrons) was found sufficiently accurate to reproduce experimental data. Clusters containing up to seven Pd atoms were considered and their interaction with hydrogen, methane and ethane and their fragments was analyzed and a kinetic study of the system was performed. Transition states structures and energies were calculated through quantum mechanics and kinetic constants were derived from a statistic thermodynamic approach. On the basis of such information, a kinetic model that accounts for ethane transformations. Finally the kinetic scheme was embedded in a plug flow reactor model and simulations were performed to test the validity of the developed mechanism. In this way information obtained at the atomic scale were adopted to study phenomena occurring on the much higher reactor scale.

Comparison of the non-linear optical properties of a dimethylaminostilbene derivative containing a molybdenum mononitrosyl redox centre and of p,p′-dimethylaminonitrostilbene, calculated by ab-initio methods

Dipole moments, linear and non-linear polarizabilities of [Mo(NO){HB(dmpz)3}Cl{OC6H4[CHCHC6H4N(CH3)2-4]-4} (dmpz = 3,5-dimethylpyrazolyl) (DMAMoS) and p,p′-dimethylaminonitrostilbene (DMANS) calculated at the SCF and second-order Moller–Plesset correlation (MP2) level with an effective core potential (ECP) basis set are reported. It is shown for DMANS that the ECPs are as accurate as calculations using all-electron basis sets of comparable quality. The effect of diffuse functions on the dominant components of the hyperpolarizabilities of DMANS is small. The dipole moment and linear polarisabilities of DMANS are in very good agreement with experimental values. The calculated hyperpolarisabilities are much smaller than the reported experimental values, but there are large uncertainties among the latter concerning calibration factors, concentration dependence and permanent local field effects, which render direct comparison difficult. Electronic correlation effects on the hyperpolarisabilities are large, especially for DMAMoS, for which the dominant component of the first hyperpolarisability increases by a factor of 5. Generally, the hyperpolarisabilities of DMANS are found to be larger than those of DMAMoS, in spite of the highly polarisable electronic charge-transfer character of the latter.

Density Functional Study of the Interaction of Palladium Clusters with Hydrogen and CHx Species

Structures and energies of Pdn clusters, with n ranging from 2 to 7, were determined through density functional theory. The calculations were performed adopting the B3LYP functionals to calculate the exchange and correlation energy, the effective core potential basis set of Hay and Wadt for the core electrons of palladium (double-ζ on the valence electrons), and the Dunning/Huzinaga full double-ζ basis set for the other atoms. It was found that Pdn optimized structures are almost regular polyhedrons, all stable as triplets. The calculated geometries were an isosceles triangle for Pd3, a distorted tetrahedron for Pd4, a bipyramid with triangular base for Pd5, a distorted octahedron for Pd6, and a bipyramid with pentagonal base for Pd7. The interaction of these clusters with atomic hydrogen in terms of structure and energy was also considered. All structures are stable with the hydrogen lying outside of the cluster, preferably 3-fold coordinated. A maximum of the hydrogen bond energy was found for a cluster...

The lowest singlet–triplet gap in CCl 2, CBr 2 and CI 2

High-level ab initio calculations are performed to determine the lowest singlet–triplet (S–T) gap in CCl 2, CBr 2 and CI 2. For CCl 2 all-electron basis sets are used. For CBr 2 all-electron and effective core potential (ECP) basis sets are used, whilst for CI 2 only ECP basis sets are used. Methods up to CCSD(T) are employed, as well as the B3LYP method. The conclusions are that for CCl 2 the S–T gap is 20±1 kcal mol −1 and that the gaps for CBr 2 and CI 2 are 17±2 kcal mol −1 and 9±2 kcal mol −1, respectively. Some comments are made regarding the disagreement with recent photodetachment studies.

Spin uncoupling in molecular hydrogen activation by platinum clusters

Complete active space multiconfiguration self-consistent field (CAS-MCSCF) and multireference configuration interaction (MRCI) calculations for H 2 reactions with platinum atom and small clusters (Pt 2, Pt 3) have been performed with account of spin-orbit coupling (SOC). Relativistic effective core potential basis sets are used. It is shown that the 3D 2 state of the Pt atom, which is only 2.2 kcal/mol higher in energy than the ground state component, 3D 3 , is reactive in hydrogen insertion reactions. The activation barrier (about 2 kcal/mol) is formed by a very efficient singlet–triplet ( 1S– 3D 2 ) avoided crossing determined by SOC in the 5 d shell of the metal, and a very stable singlet 1A 1 ground state product PtH 2 is produced by Pt( 3D 2 ) atom insertion into the hydrogen. Despite of the fact that asymptotic states in the entrance channel differ by 2 in angular momentum quantum number, a small mixing between the 1S and 1D states obtained at the MRCI level at the beginning of the reaction leads to a drastic change in the j– j coupling scheme and finally produces the S–T intersystem crossing. Other states are nonreactive, since they have a barrier higher than 15 kcal/mol. A simple concerted insertion of platinum dimer into H 2 molecule is studied in order to simulate spin uncoupling produced by CI between the ground singlet state of the reactants and the double–triplet state 1[ Pt 2( 3Σ − g)+ H 2(Σ + u)] . This type of spin uncoupling is typical for all studied reactions even when they do not follow the concerted mode. The triplet–singlet intersystem crossing occurs at the tight chemical interaction stage for cluster reactions in contrast to activation by a bare atom.

Structure and reactivity of four-membered titanacycles—theoretical studies

The equilibrium geometries of a series of four-membered titanacycles with exocyclic methylene group Cl 2 Ti–X–Y–C CH 2 (X: CH 2, CH, O, S, N, P; Y: CH 2, CH, CO, CCH 2, N–CH 3) and two derivatives without exocyclic methylene group Cl 2 Ti–X–CH 2–C H 2 (X: CH 2, O) have been calculated at the HF level of theory by using an effective core potential basis set. The geometries were compared with data from X-ray structures for the corresponding compound Cp* 2 Ti–X–Y–C CH 2. The structures of the planar four-membered titanacycles are well represented by the model complexes. The chloride ligands are good theoretical substitutes for the bent metallocene system with cyclic ligand systems in the intersecting plane between the Cp* ligands. The calculated metal–carbon bond distances are found to be shorter than in the X-ray structures of the real molecules. Total energies are calculated at the MP2 level and are used to predict the reactivity of the compounds. Titanacyclobutanes with an exocyclic methylene group are more stable than titanacyclobutanes without this group. Oxatitanacyclobutanes are subject to cycloreversion under formation of Cl 2TiO and allene. Azatitanacyclobutenes undergo spontaneous ring opening reactions. These statements are further supported by the analysis of the molecular orbitals of some selected derivatives.