Hydrogen-bonded and van der Waals complexes studied by a Gaussian density functional method. The case of (HF)2, ArHCl and Ar2HCl systems

Summary Linear combination of Gaussian-type orbitals local spin density calculations (LCGTO-LSD) have been performed to further test the applicability to the method of hydrogen-bonded and van der Waals systems. The calculated minimum energy structures and binding energies for the (HF)₂, ArHCl and Ar₂HCl complexes are presented. In addition, the harmonic vibrational frequencies are reported for (HF)₂. The results show that by using nonlocal corrections and increasing the number of radial points in the grid, the calculated parameters are close to experimental ones and provide some encouraging evidence for the reliable use of density functional theory for these complex systems.     

The error due to neglecting the core spin–orbit splitting in valence ZORA calculations with frozen core approximation and its elimination

In valence zeroth-order regular approximation (ZORA) calculations with frozen core approximation, when the basis set optimized to the related scalar relativistic ZORA calculations is used, neglecting the core spin–orbit splitting may result in additional basis set truncation errors. It is found that the error is negligible for most elements except the 6p-block elements. When the basis set is extended by a p-type STO function put on the 6p element atoms with the ζ value proper to 5p_1/2 orbitals, the error can be reduced to be negligible. The calculated atomic properties related to valence orbitals can be improved greatly by use of this extended basis set. The frozen core approximation calculations of some molecules containing Tl, Pb and Bi with closed shells show that neglecting the core spin–orbit splitting only slightly affects the calculated bond lengths and bond energies, and the calculated molecular property can also be improved slightly by use of the extended basis sets.     

A non-local pseudopotential in the FSGO model: Study of some organometallic systems

A non-local core pseudopotential has been used in the framework of floating spherical Gaussian orbital (FSGO ) model to study the equilibrium geometries and valence electronic structures of some organolithium and organoberyllium systems. The calculated equilibrium geometries, heats of hydrogenation, average electric polarizabilities, and magnetic susceptibilities are in good agreement with the results of the all-electron FSGO model calculations. Valence electron wave functions obtained here have been used to predict the valence electron Compton profiles (CP ) and electron momentum distributions (EMD ) of the systems studied. A good correlation has been shown among the peak height of the CP (J(0)), valence electron energy (E_v), and number of valence electrons (N_v).     

On the use of common effective core potentials in density functional calculations. I. Test calculations on transition-metal carbonyls

The performance of effective core potentials adjusted at the Hartree-Fock level but applied in density functional calculations has been tested in a set of calculations using various basis sets and/or core potentials. Test molecules have been the first-row transition-metal carbonyls Cr(CO)₆, Fe(CO)₅, and Ni(CO)₄ and the second-row carbonyls Mo(CO)₆, Ru(CO)₅, and Pd(CO)₄. Only “small-core” potentials have been used, and these are able to reproduce molecular structures and bond energies from all-electron calculations. Relativistic effects have been estimated for the second-row carbonyls by using quasi-relativistic core potentials. © 1996 John Wiley & Sons, Inc.     

Applications of the MBPT in the localized representation

Diagrammatic formulation of the MBPT is applied when the occupied and the virtual canonical orbitals are separately localized by unitary transformations. In this localized representation, due to the off-diagonal Fock matrix elements, the perturbation operator contains extra terms generating the so-called localization corrections. These corrections enter the perturbation energy in third and higher orders. Their magnitude depends on the type of localization, but they represent only a small fraction of the canonical corrections. The calculation of the localization corrections, however, does not need a significant amount of extra computer time. It is shown that by introducing an “order of neighborhood” local and nonlocal effects of the electron correlation can be separated and the contribution of the nonlocal effects can be neglected to a good approximation. Ab initio calculations have been carried out for the normal saturated hydrocarbons: C_2n+1H_4n+4 and for the all-trans conjugated polyenes C_2n+2H_2n+4. As to the ratio of the local and nonlocal corrections, it is shown that there is only a quantitative difference for these two kinds of systems (strongly or weakly localizable). Neglecting nonlocal effects, considerable amount of computer time can be saved.     

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     

On the nature of the first excited states of the uranyl ion

Results of calculations on the uranylion using the LCAO MO Hartree—Fock—Slater method including relativistic effects are reported. The highest occupied molecular orbital is calculated to be σ_u, consisting predominantly of U 5f character. The σ_u orbital is the HOMO partly because of “pushing-from-below” by the U 6p orbital, but also as a result of the change in potential of the U 5f electrons with the uranium core elections brought about by relativistic contraction of the core electrons. This effect also determines the character of the first virtual levels (δ_u and Φ_u, respectively) in equatorial ligand fields.     

Spin coupling in shake-up processes

The treatment of spin coupling in calculations of shake-up states in core photoelectron processes is reviewed and the problems arising when the equivalent core approximation is used to model the core hole are discussed. A method for approximating the intensity of the triplet-coupled doublet state in semiempirical calculations is proposed. The intensities of the triplet-coupled doublet states in N₂, formaldehyde, and aniline core ionization spectra are calculated. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 189–196, 1997     

Effective-core-potential calculations of sulphur,selenium and tellurium dioxides and dihydrides

The ground-state electronic structures of SO₂, SeO₂, TeO₂, SH₂, SeH₂ and TeH₂ have been calculated with effective core potentials. Satisfactory agreement with experimental molecular geometries was achieved in the dioxides only after d-functions were included in the basis sets for S, Se and Te; however, these d-functions were not essential for the dihydrides. The importance of electron correlation to the determination of dissociation energy is also evident from these calculations.     

Electrostatic bonding models: A test on group 1 and 2 metal complexes with H2O,NH3, H2S,PH3, and related ligands

Electrostatic models frequently proposed to describe ion–molecule interactions have been tested on the adducts formed by Group 1 and 2 cations with H₂O, NH₃, H₂S, PH₃, their methyl analogs, and their anions. The results from the model calculations were compared with all-electron calculations (geometry optimized, MP2, TZP basis sets) carried out on adducts formed with Li⁺, Na⁺, K⁺, Ca²⁺, and Mg²⁺. The electrostatic potential model was utilized in two ways: The attraction of the point charge was calculated with and without relaxation of the ligand. A third model allowed relaxation of the ligand but treated the cation as a frozen core. The final model was the crude point charge/point dipole approximation. At long range, the models satisfactorily track the effects on energy of gross changes in the ion–ligand interaction (monovalent versus divalent ions, neutral ligands versus anions, parent ligands versus methyl derivatives), but correlation at close range is poor, especially for binding by divalent cations. The hypothesis that the calculated strength of cation–dipole binding is dependent on calculated dipole moment could not be verified. © 1995 by John Wiley & Sons, Inc.     

Achieving reliability of calculations for flat potential surfaces in density functional theory: The case of Al4 and Al4+1

Harmonic frequencies obtained by finite-differences from nonlocal density functional calculations are presented for the ground states of Al₄ (neutral and cationic). The effect of varying the step size used in the finite-difference evaluation and the influence of the density convergence threshold are discussed. Potential energy curves along the most important normal coordinates are shown. With these results, we found that for Al₄ the square and the rhombus minima are almost degenerate with each other, while for Al₄⁺¹, the rhombus is more stable and the square is a transition state. © 1997 John Wiley & Sons, Inc.     

Modification of dipole-length and dipole-velocity matrix elements: Application to 1sσg-2pσu transitions of H2+

A procedure, based on approximate variational improvement of the wavefunctions, is developed for modifying electric dipole matrix elements calculated in the length and velocity forms. Its relationship to the recently proposed method of Roginsky et al. is investigated and test calculations are carried out for 1sσ_g-2pσ_u, transitions of H₂⁺. The results indicate that it may be an effective procedure in molecular calculations.     

Comparative study of DFT methods applied to small titanium/oxygen compounds

The performance of a number of different local and nonlocal density functional theory (DFT) methods has been investigated for some small titanium—oxygen systems. Equilibrium geometries, ionization potentials, dipole moments, atomization energies, and harmonic vibrational frequencies have been calculated for the TiO, TiO₂, and Ti₂ molecules, and the results are compared with experimental data and ab initio calculations. It is shown that most DFT methods perform much better than the ab initio Hartree—Fock (HF), second-order perturbation theory (MP2), and configuration interaction including single and double excitations (CISD) treatments. For good agreement with experimental data, gradient corrections to the exchange part of the DFT functional are needed, as well as some type of correction for the errors in the calculated energy splittings between different atomic states of titanium. Hybrid methods including a mixture of HF exchange with DFT exchange correlation do not perform as well as “pure” DFT methods for the studied systems. © 1996 John Wiley & Sons, Inc.     

Quantum-chemical study of the structure of copper(I) acetate and trifluoroacetate oligomers

The results of B3LYP quantum-chemical calculations of the equilibrium structures of [(CX₃COOCu)₂]₃, [(CX₃COOCu)₂]₂, and (CX₃COOCu)₂ oligomers (X = H, F) using the cc-pVTZ correlation-consistent basis for C, O, and F atoms and the Stuttgart 1997 RSC basis and relativistic effective core potential for Cu(I) atoms are presented. The differences in the structures of the free dimer and dimer units in oligomers were studied. The hexamer structure was chosen as the model of a fragment of the crystalline phase. Good agreement was obtained between the experimental and calculated differences between the geometrical parameters of the structures in the “gas phase-crystal” and “acetate-trifluoroacetate” series. Based on the calculated data, the increase in the Cu(I)-Cu(I) bond length in the silver acetate crystal compared with the gas phase can be explained by the effect of the neighboring dimer units of the polymer ribbon, while the increase in the Cu(I)-Cu(I) bond length in gaseous trifluoroacetate compared with acetate, by the acceptor effect of fluorine atoms.     

Density functional Gaussian-type orbital approach in theoretical study of S2F2 isomerization

The structures of two isomers, difluorodisulfane (FSSF) and thiothionylfluoride (SSF₂), and the corresponding transition structure were generated with density functional theory (DFT) methods. Three groups of DFT methods were used: local (Local Spin Density Approximation, LSDA), nonlocal (local with gradient corrections; BLYP and BP86), and hybrid methods that include a mixture of Hartree-Fock (HF) exchange with nonlocal correlation (Becke3BLYP, Becke3P86). An extended basis set [6-311 + + G(3df)] was used for all calculations, although satisfactory results can be obtained with the 6-311G(d) basis set. The geometries obtained were compared with both restricted Hartree-Fock (RHF) calculated and experimentally obtained values. The energy outcome and the activation barrier for the isomerization were evaluated. It was determined that excellent geometries can be obtained with the Becke3B86 hybrid method, whereas for reasonable energies MP2 single-point calculations on these geometries are necessary. © 1996 by John Wiley & Sons, Inc.     

Differences Between Gas-Phase and Solid-State Molecular Structures of the Simplest Phosphonium Ylide,Me3P=CH2

Clearly different from local C ₃ symmetric is the heavy-atom core of Me₃P=CH₂, the simplest phosphonium ylide. The geometry obtained by reanalysis of gas-electron-diffraction data from 1977 is now consistent with theoretical calculations, but different from the molecular structure in the solid state. The picture shows the structure of Me₃P=CH₂ in the gas phase (a) and in the crystal (c) together with the calculated transition state (b) (viewed along the P=C bond).     

Calculated electron densities and experimental isomer shifts of Fe57 in the deoxy- and CO-compounds of myoglobin and hemoglobin

Relativistic calculations of various electronic configurations of the iron atom were used in conjunction with Hückel-type self consistent field molecular orbital calculations for CO-myoglobin and CO-hemoglobin (mbCO, hbCO) and with limited configuration interaction calculations for deoxymyoglobin and deoxy-hemoglobin (mb, hb) to determine electron densities at the iron nucleus, ?(0). The calculations included all effects of overlap of iron core and next nearest neighbour (ligand) orbitals, and the effect of potential distortion of iron core orbitals due to molecular configurations 3d ^m4s ⁿ. From the calculated electron densities we found that the change in the experimental Mössbauer isomer shift, Δδ =δ_{mbCO, mbCO} ?δ_mb,hb, was mainly due to changes in the so-called overlap distortion of iron cores orbitals. The considerably higher electron density ?(0) in mbCO, hbCO than in mb, hb corresponds to the stronger interaction between iron and ligands in mbCO, hbCO compared to mb, hb. From the calculated values for ?(0) and the experimental isomer shifts we derived an isomer shift calibration constant, α = Δδ/Δ?(0), of the value ?0.242 ± 0.039a ₀ ³ mm sec^?1, which agrees reasonably well with the work of other investigators.     

Applications of spectral-Representation model as a potential method for Cu clusters

We applied the spectral-representation technique developed by Katsuki and Huzinaga as a model potential in calculating the electronic structure of Cu clusters. The characteristics of this potential were closely investigated in Cu and Cu₂. For Cu, Cu₂, Cu₅, Cu₉, and Cu₁₃, we performed all-electron ab initio self-consistent field calculations and model-potential calculations where 3p, 3d, and 4s electrons, and 3d and 4s electrons are treated as valence electrons. The ionization potentials (IPs) given by the all-electron calculations were 6.26, 5.55, 4.52, 4.02, and 4.08 eV for Cu, Cu₂, Cu₅, Cu₉, and Cu₁₃, respectively. The IPs given by the model-potential calculations were 6.25, 5.56, 4.62, 4.09, and 4.23 eV for the 3p-, 3d-, and 4s-valence electrons, and 6.26, 5.68, 4.71, 4.07, and 4.19 eV for the 3d- and 4s-valence electrons. The IPs given by the model-potential calculations agree well with those of the all-electron calculations. We also performed model-potential calculations where only the 4s electrons were treated as valence electrons. The calculated IPs were 6.47, 5.98, 5.38, 4.63, and 4.88 eV for Cu, Cu₂, Cu₅, Cu₉, and Cu₁₃, respectively. These are ca. 0.8 eV higher than the IPs by the all-electron calculation for the larger clusters of Cu₅, Cu₉, and Cu₁₃. The higher IPs originate from the expulsion of the 3d electrons from the valence electrons. We also performed model-potential calculations with 4s electrons for Cu₇₄. The calculated IP is 4.61 eV, which is estimated to be 0.8 eV larger than that obtained by the all-electron calculation. The IPs with correlation corrections are 7.7, 7.4, 6.3, 5.8, 5.9, and 5.6 eV for Cu, Cu₂, Cu₅, Cu₉, Cu₁₃, and Cu₇₄, respectively. Experimental values are 7.73, 7.37, 6.30, 5.37, 5.67, and 5.26 eV. The agreement between the two is fairly good. The electron affinities are also discussed. © 1996 by John Wiley & Sons, Inc.     

Two‐component calculations of spin–orbit effects for a van der Waals molecule Rn2

Electronic structures of the weakly bound Rn₂ were calculated by the two‐component Møller–Plesset second‐order perturbation and coupled‐cluster methods with relativistic effective core potentials including spin–orbit operators. The calculated spin–orbit effects are small, but depend strongly on the size of basis sets and the amount of electron correlations. Magnitudes of spin–orbit effects on D_e (0.7–3.0 meV) and R_e (−0.4∼−2.2 Å) of Rn₂ are comparable to previously reported values based on configuration interaction calculations. A two‐component approach seems to be a promising tool to investigate spin–orbit effects for the weak‐bonded systems containing heavy elements. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 139–143, 1999