Kramers' restricted hartree—fock method for polyatomic molecules using ab initio relativistic effective core potentials with spin—orbit operators

A two-component Kramers' restricted Hartree–Fock method (KRHF) has been developed for the polyatomic molecules with closed shell configurations. The present KRHF program utilizes the relativistic effective core potentials with spin–orbit operators at the Hartree–Fock (HF) level and produces molecular spinors obeying the double group symmetry. The KRHF program enables the variational calculation of spin–orbit interactions at the HF level. KRHF calculations have been performed for the HX, X₂, XY(X, Y = I, Br), and CH₃I molecules. It is demonstrated that the orbital energies from KRHF calculations are useful for the interpretation of spin-orbit splittings in photoelectron spectra. In all molecules studied, bond lengths are only slightly expanded, harmonic vibrational frequencies are reduced, and bond energies are significantly decreased by the spin–orbit interactions.     

Spin-orbit effects on structures of closed-shell polyatomic molecules containing heavy atoms calculated by two-component Hartree–Fock method

We have implemented geometry optimization using an analytic gradient to a two-component Kramers' restricted Hartree–Fock (KRHF) method for polyatomic molecules with closed-shell configurations. The KRHF method is a Hartree–Fock method based on relativistic effective core potentials with effective spin-orbit operators. The derivatives of spin-orbit integrals are obtained by numerical differentiation. Geometries for the various forms of polyatomic hydrides containing row 6 p-block elements are optimized with and without spin-orbit interactions. The structural changes due to spin-orbit interactions are small, but show definite trends, which correlate well with the p_1/2 spinor population. Atomization energies are reduced significantly by incorporating spin-orbit interactions for all molecules considered. The KRHF calculations of several methylhalides demonstrate that the spinor energies from the KRHF method can be useful for the interpretation of experimental photoelectron spectra of molecules exhibiting spin-orbit splittings. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1526–1533, 1998     

Intermediate neglect of differential overlap spectroscopic studies on lanthanide complexes

Summary The Intermediate Nelgect of Differential Overlap model for spectroscopy has been extended to lanthanide complexes by including spin-orbit coupling. The method uses atomic spectroscopy and model Dirac-Fock calculations on the lanthanide atoms and ions to obtain ionization potentials, Slater-Condon factors and basis sets. The spin-orbit interaction strength, (nl), is acquired from atomic spectroscopy, and only one-center terms are formally included. Calculation then proceeds using one open-shell operator for all sevenf-orbitals initially assumed degenerate to generate starting non-relativistic molecular orbitals for the subsequent configuration-interaction and spin-orbit calculation.Calculations are performed on the monoxides La, Ce, Gd, and Lu where there are ample experimental assignments. In general, the results are quite good, suggesting that the calculated energies, oscillator strengths and spin-orbit splittings can be used with success in assigning spectra, even in those cases wherejj-coupling is of intermediate strength.     

Inclusion of relativistic effects into ZDO methods. IV. Relativistic CNDO/1

A relativistic, four-component version of the CNDO (complete neglect of differential overlap) method is introduced. This method spans the class of zero-differential-overlap approximation and it utilizes a nonempirical parametrization based on results of atomic Dirac-Fock calculations. The spin-orbit splitting is included implicitly using the relativistic basis set which distinguishes Slater-type functions of the lower and higher component spinors. The method is applicable to closed-shell as well as to open-shell systems. The actual version used is the R -CNDO /1_χ with a variable scaling approach. Applications to molecular geometries, ionization potentials, and energies of spin-orbit splitting are demonstrated for AH, AH₂, AH₃, MH, InX, and HgI₂ molecules at the self-consistent-field level as well as in the second order of the many-body perturbation theory.     

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.     

Optimization of Gaussian basis sets for Dirac-Hartree-Fock calculations

We investigate the optimization of Gaussian basis sets for relativistic calculations within the framework of the restricted Dirac-Hartree-Fock (DHF) method for atoms. We compare results for Rn of nonrelativistic and relativistic basis set optimizations with a finite nuclear-size. Optimization of separate sets for each spin-orbit component shows that the basis set demands for the lower j component are greater than for the higher j component. In particular, the p _1/2 set requires almost as many functions as the s _1/2 set. This implies that for the development of basis sets for heavy atoms, the symmetry type for which a given number of functions is selected should be based on j, not on l, as has been the case in most molecular calculations performed to date.     

The influence of the effective potential on the strong collision limiting low–pressure rate coefficients

The influence of the effective potential energy curves on the calculation of the strong collision limiting low-pressure rate coefficients of thermal dissociation-recombination reactions was analyzed in terms of the factorized formalism of Troe. An analysis of 26 reactions employing a Morse potential coupled with a quasitriatomic molecular model and an explicit account of the adiabatic zero-point barriers, as originallyproposed by Troe, was performed. A comparison between calculations realizedwith an exactly fitted looseness parameter, α, and with a standard value of α = 1.0 Å^?1, indicates that the use of this last value is satisfactorily justified in the evaluation of thestrong collision limiting low-pressure rate coefficients. A study interms of restrictive relationships between the looseness and Morse parameters and ab initio, radial potentials (for CH₄, CH₃O₂, and HO₂) was also realized. The uncertainties in the evaluation of termolecular rate coefficients due to the lack of a complete knowledge of the long-range potentials are also briefly discussed.     

Anab initio potential energy surface and dynamics calculations for vibrational excitation of I2 by He

We present newab initio calculations of the interaction potential and the elastic and inelastic cross sections for He scattering by I₂. The electronic structure calculations of the interaction potential are based on an extensive one-electron basis set (triple zeta plus ad set on each I, ans function plus ap set at the I₂ bond center, and quadruple zeta plus twop sets on He), a two-configuration-SCF orbital set, and a configuration interaction calculation based on all single and double excitations out of the two-configuration reference space. The calculations are performed at 16He-I₂ distances for nine combinations of I₂ vibrational displacement and orientation. A new form of analytic representation is presented that is particularly well suited to efficient and accurate fitting ofab initio interaction potentials that include vibrational displacements. Scattering calculations are performed by the vibrational close-coupling, rotational-infinite-order-sudden approximation with a converged vibrational basis.     

Calculation of Vertical Ionization Potentials of Oxygen Difluoride,Difluoramine, and Difluoromethane by Local Density Approximation

The vertical ionization potentials of OF₂, HNF₂, and CH₂F₂ were computed by the deMon density functional program. The results are compared with earlier calculations and with experiment. The average absolute deviation of the 21 computed ionization potentials of the outer valence electrons from experiment is 0.44 eV, which compares well with 0.37 eV for frozen-orbital configuration-interaction calculations. Although this performance is not as good as perturbation corrections to Koopmans' theorem, the computation requirements are much less demanding.     

Spin-orbit corrections to the indirect nuclear spin-spin coupling constants in XH4 (X = C, Si, Ge, and Sn)

Summary Using the quadratic response function at theab initio SCF level of approximation we have calculated the relativistic corrections from the spin-orbit Hamiltonian,H ^SO, to the indirect nuclear spin-spin coupling constants of XH₄ (X = C, Si, Ge, and Sn). We find that the spin-orbit contributions toJ _X-H are small, amounting only to about 1% forJ _Sn-H. For the geminal H-H coupling constants the relativistic corrections are numerically smaller than forJ _X-H, but in some cases relatively larger compared to the actual magnitude ofJ _H-H. We also investigate the use of an effective one-electron spin-orbit Hamiltonian rather than the fullH ^SO in the calculation of these corrections.     

Investigation of 205Tl NMR shielding,structural, and electronical properties in thallium halides by applying PBE-GGA,YS-PBE0 and mBJ functionals

We report the structural, electronical, and heavy nuclear ²⁰⁵Tl Nuclear Magnetic Resonance (NMR) shielding properties of thallium halides TlX (X = F, Cl, Br, and I) by the first principles calculation. The Perdew–Burke–Ernzerhof Generalized Gradient Approximation, Yukawa Screened-PBE0 hybrid functional, and modified Becke–Johnson (mBJ) functionals including the relativistic and spin-orbit coupling effects are applied for calculation of the exchange-correlation potentials. Calculated PDOS spectra display that the valence band is composed of the X-s, Tl-5d, X-p, and Tl-6s states, and these states play an important role in ²⁰⁵Tl NMR shielding. Our findings indicate that the nuclear magnetic shielding parameters depend on the electronic properties. Obtained results by mBJ show that there is a close agreement between the experimental and the calculated NMR parameters.     

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     

Substituent effects on the redox potentials of dihydroxybenzenes: theoretical and experimental study

The redox reactions of p-hydroquinone and pyrocatechol undergo a two-proton-two-electron process in aqueous solution. We calculated their redox potentials at the B3LYP/6-311+G(d,p) level, and verified the values by employing cyclic voltammetry experiments. Then we selected seven substituent groups (–F, –Cl, –OH, –COOH, –CN, –NH₂, and –NO₂ groups) to systematically investigate the substituent effect, including the sort, position, and number of the substituent, on the redox potentials of p-hydroquinone and pyrocatechol. The calculated results show that –NH₂ and –OH groups can decrease the redox potentials, while –F, –Cl, –COOH, –CN, and –NO₂ groups increase the potential values of p-hydroquinone and pyrocatechol. The calculations can accurately predict the substituent effects on the redox potentials of pyrocatechol and p-hydroquinone. We would expect that the accurate calculation results for the model systems could be applied in the prediction of electrode potentials of other molecules.     

Picture change error correction in the radial distributions of canonical orbital densities and total electron density of radon atom: the effect of the size of nucleus and the basis set limit

The 2nd order Douglas-Kroll-Hess (DKH2) and the Infinite Order Two Component (IOTC) radial distributions of electron density of canonical Hartree-Fock (HF) orbitals of radon atom are presented. Furthermore, the total electron density is revisited. The picture change error (PCE) correction is investigated by analytical means. The point charge model of nucleus and the Gaussian nucleus model are employed. The basis set is extrapolated by means of including tight s and also p Gaussians within the original triple zeta basis set. It is found that the DKH1 PCE corrected DKH2 total electron and s orbital contact densities are negative for the point charge model of nucleus if tight enough s Gaussians are included in the basis set. It is shown that this failure is caused due to the missing terms of the second order Douglas-Kroll transformation for the DKH2 electron density. PCE is found the most striking in the DKH2/IOTC electron density of s orbitals close to the nucleus. The radial distributions of the 2-component p _1/2 orbital densities are considerably affected by PCE at the nucleus as well. Furthermore, the PCE corrected DKH2/IOTC scalar p orbital densities have a non-zero value of electron density at nucleus and can be considered as an spin-orbit (SO) average of the p _1/2 and p _3/2 orbitals. The d and f orbitals are affected by PCE in the vicinity of the nucleus only little. The PCE corrected DKH2 and IOTC radial distributions of orbital densities are nodeless, which is completely in agreement with the radial distribution of the analytic or numeric DCH orbital densities.     

Potential Functions of Internal Rotation around the Csp2-S Bond and Intramolecular Interactions in Thioanisoles p-RC6H4SCH3

The potential functions of internal rotation around the Csp²-S bond in the compounds p-RC6H4S· CH3 (R = NH₂, OCH₃, CH₃, H, F, Cl, CN, NO₂) are studied by ab initio quantum-chemical calculations taking into account the correlation energy for all the electrons (MP2/6-31G*) and in the approximation of the density functional theory (B3LYP/6-31G*). As the electron-donor power of the p-substituents decreases and their electron-acceptor power grows, the molecular conformation changes in the sequence orthogonal-free rotation-planar. The interaction of the sulfur lone electron pairs with the aromatic ring is studied by the natural bond orbital method. The effect that the conformational changes occurring upon replacement of p-substituents exert on the electron density redistribution is demonstrated. The first Koopmans ionization potentials and the geometric parameters of the molecule are reported.     

Self consistent modified extended Hückel (SC-MEH) calculations on heavy metal systems. I. Platinum(II) tetragonal planar complexes with and without relativistic effects

The Self Consistent Modified Extended Hückel molecular orbital method had been applied to several square planar complexes of platinum (II). Calculations including both the limited 5d, 6s, 6p and extended 5s, 5p, 5d, 6s, 6p starting bases for platinum were made. It is shown that in PtCl ₄ ^2– both the nuclear quadrupole moment and minimum total energy vs. bond distance are calculated to be in good agreement with experiment, only with the extended platinum AO basis.Specific inclusion of relativistic parameters via a pseudo-relativistic approximation are shown to have a significant effect on the energy molecular energy levels, however no meaningful rationalization can be made without the simultaneous inclusion of ligand field parameters as well.Supported in part by a grant made available through the Cancer Association of Greater New Orleans. Use of the facilities of the Computer Research Center of the University of New Orleans is gratefully acknowledged.     

Full spin-orbit configuration interaction calculations on electronic states of LiBe

Ab initio calculations are reported for the simplest heteronuclear metal cluster, LiBe. Full spin-orbit configuration interaction calculations in the context of relativistic effective core potentials lead to accurate potential energy curves for low-lying states. Results are compared with recent experimental observations and with all electron multi-reference configuration interaction calculations.     

Application de la réduction polarographique des sulfones aromatiques et des p-toluènesulfonates d'alkyle à des problèmes de structure

The polarographic reduction potentials of a series of aromatic sulfones and homologous alkyl tosylates in anhydrous NN-dimethylformamide have been measured. The relation between reduction potential and structure is discussed on the basis of HMO. calculations, under the assumption that compounds PhSO₂X (X = NR¹R², OR, halogens) are sulfone derivatives A critical approach is made of the use of the Taft-Hammett relation for correlating half-wave potentials. The different reduction mechanisms at the electrode observed in aprotic and protic media for the above compounds are satisfactorily accounted for by simple MO. calculations.     

Density functional theory calculation of 2p spectra of SiH4, PH3, H2S,HCl, and Ar

The method developed recently for prediction of 1s electron spectra is now extended to the 2p spectra of SiH₄, PH₃, H₂S, HCl, and Ar. The method for X‐ray absorption spectra involves the use of ΔE for the excitation and ionization energies, and application of time‐dependent density functional theory using the exchange‐correlation potential known as statistical average of orbital potentials for the intensities. Additional assumptions and approximations are also made. The best exchange‐correlation functional E_xc for the earlier calculation of ΔE in 1s spectra of C to Ne (namely Perdew–Wang 1986 exchange, combined with Perdew–Wang 1991 correlation) is no longer used in this work on 2p spectra of Si to Ar. Instead, recently tested E_xc good for 2p core‐electron binding energies (known as OPTX) for exchange and LYP for correlation, plus scalar zeroth‐order regular approximation is adopted here for the ΔE calculations. Our calculated X‐ray absorption spectra are generally in good agreement with experiment. Although the predictions for the higher excitations suffer from basis set difficulties, our procedure should be helpful in the interpretation of absorption spectra of 2p electrons of Si to Ar. In addition, we report calculated results for other kinds of electron spectra for SiH₄, PH₃, H₂S, HCl, and Ar, including valence electron ionizations and excitations as well as X‐ray emission. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008