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The analytical gradient for the two-component Normalized Elimination of the Small Component (2c-NESC) method is presented. The 2c-NESC is a Dirac-exact method that employs the exact two-component one-electron Hamiltonian and thus leads to exact Dirac spin-orbit (SO) splittings for one-electron atoms. For many-electron atoms and molecules, the effect of the two-electron SO interaction is modeled by a screened nucleus potential using effective nuclear charges as proposed by Boettger [Phys. Rev. B 62, 7809 (2000)]. The effect of spin-orbit coupling (SOC) on molecular geometries is analyzed utilizing the properties of the frontier orbitals and calculated SO couplings. It is shown that bond lengths can either be lengthened or shortened under the impact of SOC where in the first case the influence of low lying excited states with occupied antibonding orbitals plays a role and in the second case the j j-coupling between occupied antibonding and unoccupied bonding orbitals dominates. In general, the effect of SOC on bond lengths is relatively small (=5% of the scalar relativistic changes in the bond length). However, large effects are found for van der Waals complexes Hg2 and Cn2, which are due to the admixture of more bonding character to the highest occupied spinors. [ABSTRACT FROM AUTHOR]

The analytical energy gradient of the normalized elimination of the small component (NESC) method is derived for the first time and implemented for the routine calculation of NESC geometries and other first order molecular properties. Essential for the derivation is the correct calculation of the transformation matrix U relating the small component to the pseudolarge component of the wavefunction. The exact form of ∂U/∂λ is derived and its contribution to the analytical energy gradient is investigated. The influence of a finite nucleus model and that of the picture change is determined. Different ways of speeding up the calculation of the NESC gradient are tested. It is shown that first order properties can routinely be calculated in combination with Hartree-Fock, density functional theory (DFT), coupled cluster theory, or any electron correlation corrected quantum chemical method, provided the NESC Hamiltonian is determined in an efficient, but nevertheless accurate way. The general applicability of the analytical NESC gradient is demonstrated by benchmark calculations for NESC/CCSD (coupled cluster with all single and double excitation) and NESC/DFT involving up to 800 basis functions. [ABSTRACT FROM AUTHOR]

A new method for calculating the indirect nuclear spin–spin coupling constant within the regular approximation to the exact relativistic Hamiltonian is presented. The method is completely analytic in the sense that it does not employ numeric integration for the evaluation of relativistic corrections to the molecular Hamiltonian. It can be applied at the level of conventional wave function theory or density functional theory. In the latter case, both pure and hybrid density functionals can be used for the calculation of the quasirelativistic spin–spin coupling constants. The new method is used in connection with the infinite-order regular approximation with modified metric (IORAmm) to calculate the spin–spin coupling constants for molecules containing heavy elements. The importance of including exact exchange into the density functional calculations is demonstrated. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The exact relativistic Hamiltonian for electronic states is expanded in terms of energy-independent linear operators within the regular approximation. An effective relativistic Hamiltonian has been obtained, which yields in lowest order directly the infinite-order regular approximation (IORA) rather than the zeroth-order regular approximation method. Further perturbational expansion of the exact relativistic electronic energy utilizing the effective Hamiltonian leads to new methods based on ordinary (IORAn) or double [IORAn(2)] perturbation theory (n: order of expansion), which provide improved energies in atomic calculations. Energies calculated with IORA4 and IORA3(2) are accurate up to c[sup -20]. Furthermore, IORA is improved by using the IORA wave function to calculate the Rayleigh quotient, which, if minimized, leads to the exact relativistic energy. The outstanding performance of this new IORA method coined scaled IORA is documented in atomic and molecular calculations. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Analytic expressions for the derivatives of the total molecular energy with respect to external electric field are derived within the regular approximation to the full four-component relativistic Hamiltonian and presented in matrix form suitable for implementation in standard quantum-chemical codes. Results of benchmark calculations using the infinite-order regular approximation with modified metric method are presented and discussed. The static electric dipole polarizabilities of group VIII metal tetroxides MO[SUB4] for M = Ru, Os, Hs (Z5108) are studied with the help of second-order Møller-Plesset perturbation theory using the infinite-order regular approximation with modified metric Hamiltonian. The polarizabilities obtained vary in the sequence RuO[SUB4] > OsO[SUB4] > HsO[SUB4], which is different from those obtained in other studies. However, it is in line with calculated [SUP1]T[SUB2] ← [SUP1]A[SUB1] excitation energies of the group VIII tetroxides, which provide a measure for the magnitude of their polarizabilities. [ABSTRACT FROM AUTHOR]

Analytic expressions are derived for the evaluation of derivatives of the total molecular energy with respect to external parameters (nuclear coordinates, external electric fields, etc.) within the relativistic regular approximation. The presented formalism employs the spectral resolution of the identity avoiding, however, the explicit use of an auxiliary basis set in the calculation of the matrix elements of the regular relativistic Hamiltonian. The final formulas for the total energy and energy derivatives are presented in matrix form suitable for implementation into standard quantum chemical packages. Results of benchmark calculations for gold containing diatomic molecules and for xenone hexafluoride performed at the Hartree-Fock and various correlation corrected levels of theory are presented and discussed. [ABSTRACT FROM AUTHOR]

The convergence behavior of the iterative solution of the normalized elimination of the small component (NESC) method is investigated. A simple and efficient computational protocol for obtaining the exact positive-energy eigenvalues of the relativistic Hamiltonian starting from the energies obtained within the regular approximation is suggested. The protocol is based on the analysis of the relationship between the eigenvalues of the quasi-relativistic Hamiltonian in the regular approximation and the positive-energy eigenvalues of the exact relativistic Hamiltonian which was derived in the course of this work. [ABSTRACT FROM AUTHOR]

With the help of resolution of the identity (RI) a compact representation for the zeroth-order (ZORA) and infinite-order (IORA) regular approximation Hamiltonians in matrix form is developed. The new representation does not require calculation of any additional molecular integrals, which involve an auxiliary basis set used in the RI. The IORA computational scheme is modified in such a way that the erroneous gauge dependence of the total energy is reduced by an order of magnitude. The new quasi-relativistic method, dubbed IORAmm, is tested along with the ZORA and IORA methods in atomic and molecular calculations performed at the SCF and MP2 level. [Copyright &y& Elsevier]