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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 1995-2003 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Relativistic effects and electron correlation effects on the dipole moments of the coinage metal hydrides are investigated and compared employing one-component (scalar) relativistic approximations based on the mass–velocity and Darwin operator and, alternatively, the Douglas–Kroll-transformed spin-averaged no-pair Hamiltonian. The former of the two operators is found to perform quite accurately for CuH and AgH. For AuH the limits of the Pauli approximation seem to be reached, as can be inferred from a comparison with the values obtained within the spin-averaged Douglas–Kroll no-pair formalism. The coupled cluster calculations in the Douglas–Kroll no-pair approximation for relativistic effects establish the dipole moment values of the coinage metal hydrides as equal to 1.05 a.u. for CuH, 1.14 a.u. for AgH and 0.52 for AuH. The corresponding non-relativistic results are 1.14 a.u., 1.36 a.u., and 1.22 a.u., respectively. Some formal problems arising in applications of the Douglas–Kroll no-pair approximation are discussed. It is shown that the Hellmann–Feynman theorem leads to a rather complicated form of the first-order energy change due to external perturbation. The usual expectation value formula is, however, valid through terms proportional to 1/c4 and can be used in most applications. The invariance property with respect to a shift in the external potential is addressed for the Douglas–Kroll no-pair approximation in a finite basis set. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 2991-2999 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Electric properties of heteronuclear dimers of the coinage metals are calculated at the level of the CCSD(T) approximation applied to 38 electrons of the valence and next-to-valence atomic shells. The relativistic effects are accounted for by using the scalar approximation to the Pauli hamiltonian. Both the pure relativistic and mixed relativistic-correlation contributions to energies and electric properties are computed. All calculations have been carried out by using the recently developed first-order polarized basis sets of the coinage metal atoms. In the non-relativistic approximation all studied dimers show only a moderate degree of polarity; the non-relativistic CuAg turns out to be the most polar dimer with the Cu(−)Ag(+) polarity. The relativistic effects considerably reduce the negative value of the CuAg dipole moment, change the sign of the CuAu dipole moment, and make the AgAu molecule the most polar species in the series. Simultaneously, the parallel component of the dipole polarizability shows only a small relativistic contraction. The calculated quasirelativistic interaction potentials have a correct behavior in the vicinity of their minima and give the Re and ωe values in complete agreement with experiment. Much less satisfactory are the dissociation energy data which seem to suffer from the single reference configuration approximation. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 9692-9704 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Dipole moments and dipole polarizabilities of a series of the alkali metal atom dimers involving Li, Na, K, and Rb are calculated at the level of different coupled cluster approximations as well as the complete active space self-consistent-field approach followed by the perturbation treatment of the dynamical correlation effects. All reported calculations have been carried out with recently developed polarized basis sets. The electron correlation effects on these electric properties are studied within the valence and valence plus next-to-valence shell approximations. Also the relativistic contribution is calculated by using the quasirelativistic scalar (mass–velocity+Darwin terms) approximation. A comparison of results of different methods indicates that the values calculated by the coupled clusters method in which one- and two-electron clusters are treated iteratively and the three-body terms perturbatively [as defined in the CCSD(T) method] are well saturated in terms of the electron correlation contribution to molecular electric properties of the dimers. The achieved agreement with available experimental data is for most molecules fairly good. The interpretation of the electric property data is based on the analysis of the valence and core-polarization contributions and the observed regularities are elucidated in terms of simple molecular orbital ideas. The dipole moments of the heteronuclear dimers follow the pattern predicted by electronegativities of the two atoms. The perpendicular component of the electric dipole polarizability has been found to mostly reflect its atomlike origin, while the parallel one is intimately related to the electronic structure of the week bonding in the dimers. The relativistic effect becomes of certain importance only for the rubidium compounds. The results of our calculations are compared with ab initio and empirical pseudopotential data and with more recent calculations using the density functional theory methods. Our results indicate that the density functional methods lead to fairly reliable polarizability data, though they depend on the choice of the exchange and exchange-correlation potentials. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1432-2234
    Keywords: Polarized basis sets ; Relativistic effects ; Douglas-Kroll no-pair approximation ; Dipole polarizabilities of Zn, Cd, Hg — Dipole moments of CuH, AgH, and AuH ; Polarizabilities of atomic ions: Cu+, Ag+, Zn2+, Cd2+, Hg2+
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The technique developed earlier for the generation of the so-called first-order polarized basis sets for accurate non-relativistic calculations of molecular electric properties is used to obtain similar basis sets suitable for calculations in the Douglas-Kroll no-pair approximation. The corresponding (relativistic) basis sets are devised for atoms of the Groups Ib and IIb of the periodic table and tested in calculations of atomic polarizabilities and dipole moments of the coinage metal hydrides. Excellent performance of these basis sets has been found in the case of molecular calculations.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 97 (1997), S. 260-270 
    ISSN: 1432-2234
    Keywords: Key words: Relativistic quantum chemistry ; Expectation values ; Direct perturbation theory ; Two-component relativistic Hamiltonians ; Regular relativistic Hamiltonians
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. Two methods for the evaluation of expectation values with approximate two-component relativistic functions are analysed. The first of them is based on the change of picture for the operator whose expectation value is to be calculated and associated with approximations leading to the given two-component relativistic wave function. This method, though hardly used in numerical calculations, gives the expectation values that directly reflect the accuracy of the wave function used for their calculation. The second method, most commonly used in calculations, neglects the picture change and is shown always to introduce an error of the order of α2, where α is the fine structure constant. This error is present independently of the accuracy of the approximate two-component wave function. The perturbation formalism developed in this paper is illustrated by calculations of relativistic corrections to the expectation values of r −1 for arbitrary states of hydrogenic ions.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 91 (1995), S. 353-371 
    ISSN: 1432-2234
    Keywords: Polarized basis sets ; Electric dipole polarizabilities of Zn, Cd, Hg, and their positive ions ; Electron correlation effects on atomic properties ; Relativistic effects on atomic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The first-order polarized basis sets are generated for Zn, Cd, and Hg and their performance is tested in high-level-correlated calculations of electric dipole polarizabilities of these atoms. The present results calculated at the level of the non-relativistic CCSD(T) approximation with 12 explicitly correlated electrons are: 40.4 a.u. for Zn, 56.3 a.u. for Cd, and 58.0 a.u. for Hg. Upon including the relativistic and electron correlation-relativistic corrections within the quasirelativistic scheme based on the mass-velocity and Darwin terms these values are reduced to 37.9 a.u., 47.6 and 31.8 a.u., respectively. The derived polarized basis sets have been also used for the evaluation of the dipole polarizability of singly and doubly positive ions of the group IIb elements and are recommended for calculations of interaction energies and interaction-induced electric properties in both neutral and charged systems.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 92 (1995), S. 253-267 
    ISSN: 1432-2234
    Keywords: Dipole moments of CuH, AgH, AuH ; Electron correlation effects ; Relativistic effects ; Polarized basis sets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The first-order polarized basis sets of the coinage metal atoms have been used to perform high-level-correlated calculations of the dipole moment in the series of the MeH (Me=Cu, Ag, Au) molecules. The relativistic effects were accounted for by using the quasirelativistic approach based on the mass-velocity and Darwin terms in both the SCF HF and correlated level approximations. The non-relativistic coupled cluster calculations with complete treatment of one- and two-body clusters and perturbative correction for the three-body terms (CCSD(T) predict the following sequence of the dipole moment data: 1.13 a.u. for CuH, 1.35 a.u. for AgH, and 1.21 a.u. for AuH. Upon including the relativistic correction the calculated dipole moments turn out to be 1.05 a.u. for CuH, 1.14 for AgH, and 0.64 a.u. for AuH. The influence of the electron correlation and relativistic effects on the electronic distribution in the MeH molecules is discussed. A comparison of calculations with different number of explicitly correlated electrons gives an approximate scheme for the estimation of the core polarization/correlation contribution.
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 1432-2234
    Keywords: Polarized basis sets ; Dipole polarizabilities of Cu, Ag, and Au ; Dipole polarizabilities of Cu+, Ag+, and Au+ ; Relativistic effects on atomic electric properties ; Electron correlation effects on atomic electric properties ; Relativistic ; correlation corrections ; SA CCSD(T) method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The first-order polarized basis sets PolMe are generated for elements (Me=Cu, Ag, Au) of group Ib of the periodic table by using the basis set polarization method developed in earlier papers. The performance of these basis sets is extensively tested in calculations of atomic dipole polarizabilities with particular attention given to the evaluation of the electron correlation and relativistic contributions. The extension by theg-type polarization functions (PolMe-g sets) is devised for use in accurate calculations of atomic and molecular electric properties. The (negative) electron correlation contribution to dipole polarizabilities of all elements of group Ib, as calculated at the level of the spin adapted coupled cluster method with single and double excitations and non-iterative corrections for the contribution of the T3 clusters (SA CCSD(T)), remains at the same level relative to the ROHF data. The pure relativistic correction to the ROHF results, evaluated within the quasirelativistic approximation involving the mass-velocity and Darwin corrections, is negative and rapidly increases with increase of the nuclear charge. Its large negative value is, for heavier systems, partly compensated by a positive contribution from the mixed relativistic-correlation terms. Our relativistically corrected SA CCSD(T) calculations predict the following values of the dipole polarizability in the coinage metal series: 46, 51, and 29 a.u., for Cu, Ag, and Au. The present results for Cu and Ag agree well with recent pseudopotential calculations by Schwerdtfeger and Bowmaker. However, for Au our result is by about 6 a.u. lower than that obtained by using 19-electron relativistic potentials. Several possible reasons for this discrepancy are discussed. The PolMe and PolMe-g basis sets are also used to calculate electric dipole polarizabilities of the singly positive ions of group Ib elements. The results obtained in the quasirelativistic CCSD(T) approximation are 6.6, 9.2, and 11.8 a.u. for Cu+, Ag+, and Au+, respectively. These values follow the pattern expected for the series of ions whose polarizability is dominated by the next-to-valenced shell.
    Type of Medium: Electronic Resource
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  • 9
    ISSN: 1432-2234
    Keywords: Electric properties of excited states ; Dipole moments ; Dipole polarizabilities ; Excitation energies ; H2O ; CASSCF ; CASPT2
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The dipole moments and dipole polarizabilities of the 1A1, 1B1, and 3B1 electronic states of the water molecule have been calculated by using the CASSCF approach followed by the evaluation of the dynamic electron correlation contribution by the second-order perturbation scheme CASPT2. All calculations have been carried out in a specifically extended ANO basis set which accounts for the Rydberg character of the two excited states. In order to estimate the correctness and accuracy of the present data a scan over a variety of different active spaces for the CASSCF wave function has been made. The present results are superior to earlier CASSCF calculations, although their qualitative features remain essentially the same. The dipole moments in 1B1 and 3B1 states are predicted to be about 0.49 a.u. and 0.33 a.u., respectively, and have the opposite orientation with respect to the ground state dipole moment. The dipole polarizability tensors of the excited states are characterized by high anisotropy and are dominated by the in-plane component perpendicular to the symmetry axis. All their components are found to be about an order of magnitude larger than those of the ground state polarizability tensor. The excitation energy dependence on the choice of the active orbital space in the CASSCF reference function is also considered and the analysis of the present data concludes in the concept of what is called the mutually compatible active spaces for the two states involved in excitation. All CASPT2 results are in good agreement with the results of recent calculations carried out in the framework of the open-shell coupled cluster formalism. This agreement confirms the high efficiency of the CASSCF/CASPT2 approach to the treatment of the electron correlation effects.
    Type of Medium: Electronic Resource
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  • 10
    ISSN: 1432-2234
    Keywords: Key words: Polarized basis sets ; Relativistic effects ; Douglas-Kroll approximation ; Ionization potentials of group Ia and IIa metals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. The technique previously developed for the generation of the so-called first-order polarized basis sets for accurate non-relativistic calculations of molecular electric properties is used to obtain similar basis sets suitable for calculations in the Douglas-Kroll no-pair approximation. The corresponding (relativistic) basis sets are constructed for atoms of groups Ia and IIa of the Periodic Table and tested in calculations of atomic and ionic polarizabilities. Also the first ionization potential of the group Ia and the first and second ionization potential of the group IIa metals have been evaluated to provide additional qualification of the generated basis sets. The present results are compared with earlier non-relativistic and quasirelativistic data and the role of the relativistic effect is discussed.
    Type of Medium: Electronic Resource
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