Core Model Potential Research Articles

Relativistic correlating basis functions for the Ga–Kr, In–Xe, and Tl–Rn atoms

Generally contracted Gaussian-type function sets were developed for relativistic correlating functions of the Ga–Kr, In–Xe, and Tl–Rn atoms using an atomic natural orbital (ANO) approach. The ANOs were constructed based on configuration interaction calculations of the ground states of respective atoms including the major relativistic effects through model core potentials (MCPs). Both atomic and molecular applications are presented. The use of the present basis sets in conjunction with the MCPs gave the excitation energies, ionization potentials, and electron affinities in good agreement with the observed values for several atoms. The spectroscopic constants of the TlH molecule yielded by relativistic MCP calculations including spin–orbit effects were in excellent agreement with the experimental results.

Spin–orbit coupling with model core potentials

A method has been proposed to compute one- and two-electron spin–orbit coupling using model core potentials generated with spin-free Hamiltonian without any need for separately producing either spin-dependent model core potentials or use of some fitted parameters, such as effective charges. The use of approximations (one-centre spin–orbit integrals and partial two-electron contribution) is verified to work within 2% accuracy compared to much costlier full results. The new method has been tested on atoms, hydrides, and homonuclear diatomic cations of P, As, and Sb. The accuracy has been found to be 3% or better within the tested set.

Theoretical study of interactions between the Si [formula omitted] surface and metal atoms

We investigated the interactions between the Si(1 1 1) surface and the Na and Mg atoms using cluster model calculations. Calculations were performed at levels of the complete-active-space self-consistent-field and multi-reference single and double excited configuration interaction calculations using the model core potential method. Our calculations revealed that the most favorable sites of Na and Mg adsorption on Si(1 1 1) are on-top (T 1) and bridge (B 2) sites, respectively. The nature of chemical bonds between these metal atoms and the dangling bonds of the surface Si atoms are found to be essentially covalent.

Improved model core potentials: Application to the thermochemistry of organoxenon complexes

AbstractWe recently developed new pseudopotentials for the main group elements, incorporating the L‐shell structure in the basis sets and reoptimizing the parameters. These improved model core potentials were used to study the energetics of reactions leading to compounds with XeIIC bonds. We found that many compounds are thermodynamically stable with respect to the reactants, and consequently they could possibly be formed under the right kinetic conditions. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

Basic data of polyatomic ion-molecule systems for flue gas discharge modelling

In the presence of an external electric field, ion transportcoefficients (ion mobility and diffusion coefficients) are closelyrelated to the ion-neutral interaction potential. A new generalizedpotential model, coupled to an optimized Monte Carlo technique, has beendeveloped for the determination of the transport coefficients ofpolyatomic ions in weakly ionized gases. This corresponds to thepolyatomic ion-molecule systems which can affect the electricalbehaviour of the flue gas discharges used for the non-thermal plasmareactor for pollution control. The ion-molecule interaction has beendescribed by a rigid core potential model which is adapted for bothpolar and non-polar systems and also symmetric and asymmetric systems.Momentum transfer cross sections are then determined using asemi-classical approach. The corresponding sets of cross sectionsincluding the dominant processes in our intermediate ion energy range(elastic and mainly charge transfer in certain cases) are used in theMonte Carlo code to calculate the ion transport coefficients over a widerange of reduced electric field E/N. These ion transport data fitquite well the drift tube measurements available in the literature forthe CO2+/CO2 system, and also for certain weakly polarcases. The case of the H2O+/H2O system isthen considered thus giving in this highly polar system the ion swarmdata for the first time in the literature. Finally, we have consideredwith quite good reliability some asymmetric systems such as CO2+/N2 and N2+/CO2 whose ion data are alsoneeded for flue gas discharge modelling.

On the interaction of Mo and Mo2 with NH3, C2H4, and C3H6

The reactivity of Mo and Mo2 with ammonia, ethene, and propene molecules has been investigated by using Density Functional Theory. Different gradient-corrected and hybrid exchange-correlation functionals have been employed. Coordination modes, binding energies, geometrical structures, vibrational frequencies have been computed and compared with the available experimental counterparts. The results obtained show that the molybdenum atom is able to react with C2H4 and C3H6, and binds weakly with NH3. The dimer Mo2 gives a stable complexes with ammonia, ethene, and propene. For the Mo2NH3 complex, all the employed levels of theory give binding energies in good agreement with the experimental value, while in the case of the MoC2H4 system, the use of model core potentials coupled with gradient-corrected exchange-correlation functionals overestimates the binding energies. For MoC3H6, Mo2C2H4, and Mo2C3H6 we predict a binding energy of 14–15, 20–24, and 18–20 kcal/mol, respectively. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1557–1564, 2001

On the interaction of Mo and Mo2 with NH3, C2H4, and C3H6

AbstractThe reactivity of Mo and Mo2 with ammonia, ethene, and propene molecules has been investigated by using Density Functional Theory. Different gradient‐corrected and hybrid exchange‐correlation functionals have been employed. Coordination modes, binding energies, geometrical structures, vibrational frequencies have been computed and compared with the available experimental counterparts. The results obtained show that the molybdenum atom is able to react with C2H4 and C3H6, and binds weakly with NH3. The dimer Mo2 gives a stable complexes with ammonia, ethene, and propene. For the Mo2NH3 complex, all the employed levels of theory give binding energies in good agreement with the experimental value, while in the case of the MoC2H4 system, the use of model core potentials coupled with gradient‐corrected exchange‐correlation functionals overestimates the binding energies. For MoC3H6, Mo2C2H4, and Mo2C3H6 we predict a binding energy of 14–15, 20–24, and 18–20 kcal/mol, respectively. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1557–1564, 2001

Well-tempered model core potentials for groups 17 and 18

New family of model core potentials (MCPs) based on the well-tempered basis set expansions was introduced for the elements of groups 17 and 18. Both small- and large-core potentials were developed. The new potentials were tested in RHF calculations for the diatomic halogen and polyatomic interhalogen compounds, and for noble-gas fluorides. For the small-core potentials, the agreement with the results of all-electron calculations using the well-tempered basis sets is excellent.

Theoretical study on electronic excitation spectra of Mo and Re cluster complexes: [(Mo6Cl8)Cl6]2− and [(Re6S8)Cl6]4−

We report here on the electronic structures of [(Mo6Cl8)Cl6]2− and [(Re6S8)Cl6]4− obtained by the Tamm–Dankoff configuration interaction approximation, where Darwin and mass-velocity terms are taken into account through the model core potentials, and the spin–orbit interaction term is included in a semiempirical manner. These complexes have absorption spectra ranging from the visible to the near-ultraviolet energy region and have the long-lived luminescence. The calculated results of the transition moments roughly reproduce the experimental absorption and emission spectra. Especially for the absorption spectra, the theoretical strong intensity for the region higher than 4.5 eV in the two complexes is in good agreement with the experimental results. The obtained intense peak at 3.9 eV may correspond to the experimental broad peak at approximately 3.6 eV for the Mo complex. For the Re complex, the calculated intensity distribution gives one broad peak at around 3.1 eV. This peak may correspond to the experimental peak at 2.9 eV. In the experimental emission spectra, the maxima are located at 1.62 eV for the Mo complex and approximately 1.8 eV for the Re complex. Theoretically, 12 and eight states are found in the energy range between 1.5 and 2.0 eV for the Mo and Re complexes, respectively. At least one, if not more, of these states would be responsible for each emission maximum. To determine the character of the above transitions, the absorption and emission transitions were experimentally shown to be ligand-to-metal charge-transfer transitions and metal-localized transitions, respectively. Theoretically, absorption transitions were characterized as a mixture of metal-localized transitions and ligand-to-metal charge-transfer transitions, and emission transitions a mixture of metal-localized transitions and metal-to-ligand charge-transfer transitions.

ChemInform Abstract: Benchmarking of Model Core Potentials: Application to the Halogen Complexes of Group 4 Metals.

AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

Model potential density functional study of small cobalt clusters, Con,n?3

Small clusters of cobalt atoms, Con (n≤3), were studied with the aid of the program deMon-KS module release 3.2, which is a density functional theory based method. Self-consistent-field model core potential (MCP) calculations, which describe the core electrons of the cobalt atom, were done in concert with the generalized gradient approximation (GGA) and local spin density approximation for the treatment of the exchange–correlation (XC) effects, MCP and all-electron (AE) calculations, at the same level of theory for XC, are compared and discussed. The obtained GGA-MCP results show a dramatical improvement in the calculated binding energies (BE), which is due to the accurate description of the XC energy, through GGA, and to a substantial reduction of the basis set superposition errors (BSSE). Finally, the present calculations are compared with other theoretical and experimental results obtained for these systems. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 422–430, 2001

Benchmarking of model core potentials: application to the halogen complexes of group 4 metals.

The reliability of the model core potential (MCP) method was probed in a systematic RHF and MP2 study of the geometries of the group 4 metal halogen complexes (MX4; M = Ti, Zr, Hf and X = F, Cl, Br, I). The computed bond lengths were compared with experimental values, as well as those predicted using effective core potentials. Provided that electrons from the outermost core shell of the metal atom are treated explicitly in the calculation, both the MCP and ECP methods predict M-X bond lengths within 0.02-0.03 A of experiment. The reaction energies for a simple set of halogen substitution reactions of the MX4 complexes leading to the mixed halogen complex, MX2Y2, were also studied. Although no experimental values are available for these reactions, comparison was made with the values computed using effective core potentials. The predictability of the different pseudopotential techniques and the importance of the metal atom valence basis set contraction scheme and polarization space are discussed.

Theoretical study of low-lying electronic states of TiCl and ZrCl

Low-lying electronic states of TiCl and ZrCl were investigated by the complete active space SCF (CASSCF), multi-reference singly and doubly excited configuration interaction (MRSDCI), and multi-reference coupled pair approximation (MRCPA) calculations using the model core potential (MCP) method. Relativistic effects were incorporated in the MCP and basis sets for Zr at the level of Cowan and Griffin’s quasi-relativistic Hartree–Fock method. The 4Φ state was found to be the ground state of TiCl, whereas the 2Δ state was the ground state of ZrCl at all levels of calculation. Two low-lying excited states were very close in energy to the ground state. The excited 4Σ−and 2Δ states of TiCl were higher than the ground state by 0.102 eV and 0.458 eV, respectively, and the excited 4Φ and 4Σ− states of ZrCl were higher by 0.094 eV and 0.110 eV, respectively, at the MRCPA level. The calculated values of re(2.319 Å) and ωe(382 cm−1) for the ground 4Φ state of TiCl are quite close to the values of re(2.351 Å) and ωe(383 cm−1) for the ground 2Δ state of ZrCl. The values of re, ωe, Be, and αe are reasonably comparable to the observed values for both TiCl and ZrCl.

Multi-reference coupled pair approximation (MRCPA) calculations for the ground state of the ArI 2 complex

We performed multi-reference coupled pair approximation (MRCPA) calculations as well as single-reference CPA (SRCPA) calculations for the ground state of the ArI 2 complex using relativistic model core potentials which included major relativistic effects. The localized natural orbital (LNO) set approach was used to calculate the correlation energy. The T-shaped and linear isomers had almost the same binding energies. MRCPA calculations gave a potential surface on which the T-shaped minimum was lower than the linear minimum by 9 cm −1, while SRCPA calculations predicted that the linear and the T-shaped isomers were almost degenerate within 2 cm −1. The MR approach preferred the T-shaped geometry. The vibrational frequencies for the van der Waals stretch mode in the T-shaped and linear isomers were calculated to be 64 and 46 cm −1, respectively.

Spin-free relativistic no-pair ab initio core model potentials and valence basis sets for the transition metal elements Sc to Hg. II

This is the second part of a report on spin-free relativistic no-pair ab initio core model potentials for the transition elements Sc to Hg. In the first part [J. Chem. Phys. 110, 3678 (1999)], we introduced the no-pair ab initio model potential method and supplied model potentials for [Mg], [Zn], and [Cd,4f] cores of first-, second-, and third-row transition metals, respectively. At the Hartree–Fock level excellent agreement between all-electron and model potential results was observed for late transition metal oxides, whereas the performance of the model potentials was slightly less satisfactory for early transition metal oxides. In this paper we will present small-core model potentials corresponding to [Ne], [Ar,3d], and [Kr,4d,4f] cores, respectively. The performance of the model potentials is tested extensively in calculations on the diatomic oxides VO, NbO, TaO, NiO, PdO, and PtO, both at the Hartree–Fock level and when electron correlation is included by means of coupled-pair functional methods. Further we investigate the requirements on valence and intermediate basis sets used to represent the exchange and no-pair operators.

Spin-free relativistic no-pair ab initio core model potentials and valence basis sets for the transition metal elements Sc to Hg. Part I

Relativistic one-component ab initio core model potentials are presented for first-, second-, and third-row transition elements; corresponding valence spaces comprise the ns, (n−1)d, and (n−1)p shells. Direct relativistic effects on the valence electrons are explicitly taken into account by using one-component relativistic kinetic energy and Douglas–Kroll transformed no-pair nuclear attraction interaction operators. The Coulombic part of the atomic core–valence interaction has been fitted to the corresponding all-electron mean-field operators whereas a matrix representation has been chosen for the exchange part. While not involved in the fitting process, all-electron orbital energies and radial expectation values of the valence orbitals are very well reproduced in atomic model potential calculations. Molecular test calculations have been performed on selected transition metal oxides. Employing a [4s,4p,4d] contraction of the valence basis, excellent agreement between core model potential and all-electron no-pair results is achieved for bond distances, harmonic frequencies, and dissociation energies.

NO adsorption on Pd clusters. A density functional study

The interaction of NO with Pd clusters has been studied by means of the LCGTO-DF method. Metal cluster models (up to 13 atoms) with different size and geometry have been used to describe the atop, bridge and three-fold sites. The use of different model core potentials to increase the size of the cluster model treated and to save computational time has been discussed. The binding energies of N(1s), 4σ, 5σ and 1π electrons are calculated and compared directly to the experimental XPS and UPS data available. The NO is tilted with respect to the surface normal axis when adsorbed on top and bridge sites by about 52.6 and 46.7 degrees, respectively. On the two types of three-fold sites (hcp and fcc) the NO remains upright. The bending angle is very sensitive to the cluster size and affects the binding energies of N(1s), 4σ, 5σ and 1π orbitals. The NO adsorption energies on the different adsorption sites have been estimated using different cluster models. The vibrational frequencies have been calculated in the harmonic approximation and they are in reasonable agreement with the available experimental values. The cluster model approach is discussed in terms of its reliability to determine the adsorption energies and the favored site of adsorption.

THE ELECTRONIC STRUCTURE AND STABILITY OF M@C28 (M=Ti,Zr,Hf) ENDOHEDRAL COMPLEXES

We have studied the electronic structure of M@C28(M=Ti,Zr,Hf) endohedral complexes with ab initio method in B3-LYP effective core potential model and density functional theory.The computations were carried out for the geometry optimizations,which determined the structure constants of atoms in ground states,and the analysis of natural bond orbital.The interaction of Ti atom and C28 cluster was very different from that of Zr (or Hf) atom and C28 cluster. It occurred on the atomic configuration,the bonding character and the distribution of electronic states etc.According to the estimation of binding energy,three complexes could exist stably,and Zr@C28 and Hf@C28 were more stable than Ti@C28.The results have been analyzed and discussed,also compared with those in the literatare.

Model core potentials for the lanthanides

Model core potential (MCP) parameters and valence basis sets are determined for the lanthanides La through Lu. The 46 (1s–4d) electrons are replaced by the MCP and the 5s, 5p, 4f, 5d, and 6s are treated explicitly as valence electrons. The major relativistic effects at the level of Gowan and Griffin's quasi-relativistic Hartree–Fock method (QRHF) are incorporated into the MCPs. The valence orbitals thus obtained have inner nodal structure. The MCP is tested for various states of Pr, Pr +, Pr 2 + and Pr 3 + at the SCF level, and it is confirmed that the MCP determined for neutral atom works very well even for Pr 3 +. The CASSCF and SDCI calculations are performed for the ground state ( 3Φ) of CeO. The spectroscopic constants given by the SDCI including Davidson's correction ( r e=1.816 Å, ω e=866 cm − 1, and D e=7.89 eV) are in good agreement with the experimental values ( r e=1.820 Å, ω e=862 cm − 1, and D 0=8.18 eV).

Calibration and benchmarking of model core potentials: applications to systems containing main-group elements

The recently developed model core potentials for the main-group elements were used in a systematic investigation of their reliability and predictive power in the studies of the prospective ligand building blocks for organometallic complexes. The molecules studied include: homonuclear diatomics (Group VB: N 2, P 2, As 2, Sb 2 and the halogens: F 2, Cl 2, Br 2, I 2); heteronuclear diatomics (CO analogues XY, where X=C, Si, Ge, Sn, and Y=O, S, Se, Te; and interhalogen compounds); triatomic hydrides AH 2 (OH 2, SH 2, SeH 2, TeH 2), triatomic oxides (CO 2 and SO 2), tetra-atomic hydrides AH 3 (NH 3, PH 3, AsH 3, SbH 3), tetra-atomic analogues of NF 3, and small hydrocarbons (C 2H 2, C 2H 4, CH 2). Molecular geometries were optimized using a modified Powell method of searches along conjugate directions and the results compared with experimental data. Electron correlation effects were studied at the MP2 and CISD levels.