A no-pair formalism employing external-field projection operators correct to second order in the potential is used to calculate the 1s energies of one-electron atoms and ground-state properties of the bromine and silver atoms in the framework of the multireference double-excitation configurationinteraction (MRD-CI) method. It is found that the relativistic two-component method that has been used reproduces the one-particle energies of the Dirac equation to order (Za)'. The operator is bounded from below and can be used variationally in relativistic electron-structure calculations of many-electron atoms and molecules. The relativistic correction to the total energy recovers 97% of the relativistic correction of the Dirac-Hartree-Fock (DHF) result in the case of the bromine atom and more than 99%%uo in the case of the silver atom. The relativistic correction of the ionization potential of silver has been calculated to be 0.47 eV at the CI level, in good agreement with DHF results, the correlation contribution in the relativistic case being 0.42 eV. The remaining discrepancy of the absolute value of 6.85 eV (DHF 6.34 eV) to experiment (7.57 eV) is attributed to basis-set deficiencies. The corresponding CI value of the electron affinity (relativistic CI value 1.05 eV, nonrelativistic 0.90 eV) is in much better agreement with experiment (1.30 eV). It is found that correlation contribution and relativistic effects are nonadditive.
The exact exchange part in hybrid density functionals is analyzed with respect to the prediction of ground state multiplicities. It has been found [M. Reiher, O. Salomon, and B. A. Hess, Theor. Chem. Acc., 107, 48 (2001)] that pure and hybrid density functionals yield energy splittings between high-spin and low-spin states of Fe–sulfur complexes that differ by more than 100 kJ/mol and thus fail to reliably predict the correct multiplicity of the ground state. This deviation can lead to meaningless reaction energetics for metal-catalyzed reactions. The finding that the energy splitting depends linearly on the exact exchange admixture parameter led to a new parametrization of the B3LYP functional which was dubbed B3LYP⋆. In the present paper we investigate the generality and transferability of this functional. We study the extent to which the exact exchange admixture affects the thermochemistry validated with respect to the reference data set of molecules from the G2 test set. Metallocenes and bis(benzene) metal complexes of the first transition metal period are chosen to test the transferability of the findings for Fe–sulfur complexes. Moreover, the slope of the linear dependence of the energy splitting of high-spin and low-spin states on the amount of admixture of exact exchange is studied in detail.
Abstract:In this work we demonstrate how different modern quantum chemical methods can be efficiently combined and applied for the calculation of the vibrational modes and spectra of large molecules. We are aiming at harmonic force fields, and infrared as well as Raman intensities within the double harmonic approximation, because consideration of higher order terms is only feasible for small molecules. In particular, density functional methods have evolved to a powerful quantum chemical tool for the determination of the electronic structure of molecules in the last decade. Underlying theoretical concepts for the calculation of intensities are reviewed, emphasizing necessary approximations and formal aspects of the introduced quantities, which are often not explicated in detail in elementary treatments of this topic. It is shown how complex quantum chemistry program packages can be interfaced to new programs in order to calculate IR and Raman spectra. The advantages of numerical differentiation of analytical gradients, dipole moments, and static, as well as dynamic polarizabilities, are pointed out. We carefully investigate the influence of the basis set size on polarizabilities and their spatial derivatives. This leads us to the construction of a hybrid basis set, which is equally well suited for the calculation of vibrational frequencies and Raman intensities. The efficiency is demonstrated for the highly symmetric C 60 , for which we present the first all-electron density functional calculation of its Raman spectrum.
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