Analytic energy derivatives for regular approximations of relativistic effects applicable to methods with and without correlation corrections

Efficient J-oriented tin basis sets for the correlated calculations of indirect nuclear spin-spin coupling constants

New J-oriented tin basis sets, acvXz-J (X = 2, 3, 4), have been developed at the level of the second-order polarization propagator approximation with the coupled-cluster single and double amplitudes, SOPPA (CCSD), for the purpose of correlated calculations of indirect nuclear spin-spin coupling constants involving tin nucleus. High-quality coupled-cluster calculations of several tin-proton and tin-carbon spin-spin coupling constants, performed with one of the newly developed basis sets, namely, the acv3z-J, taking into account relativistic, solvent, and vibrational corrections showed that the acv3z-J basis set is capable to provide reliable results, as compared with the experimental data.

Quantum chemical calculations of 77 Se and 125 Te nuclear magnetic resonance spectral parameters and their structural applications

An accurate quantum chemical (QC) modeling of ⁷⁷ Se and ¹²⁵ Te nuclear magnetic resonance (NMR) spectra is deeply involved in the NMR structural assignment for selenium and tellurium compounds that are of utmost importance both in organic and inorganic chemistry nowadays due to their huge application potential in many fields, like biology, medicine, and metallurgy. The main interest of this review is focused on the progress in QC computations of ⁷⁷ Se and ¹²⁵ Te NMR chemical shifts and indirect spin-spin coupling constants involving these nuclei. Different computational methodologies that have been used to simulate the NMR spectra of selenium and tellurium compounds since the middle of the 1990s are discussed with a strong emphasis on their accuracy. A special accent is placed on the calculations resorting to the relativistic methodologies, because taking into account the relativistic effects appreciably influences the precision of NMR calculations of selenium and, especially, tellurium compounds. Stereochemical applications of quantum chemical calculations of ⁷⁷ Se and ¹²⁵ Te NMR parameters are discussed so as to exemplify the importance of integrated approach of experimental and computational NMR techniques.

Implementation of Analytical Energy Gradient of Spin-Dependent General Hartree-Fock Method Based on the Infinite-Order Douglas-Kroll-Hess Relativistic Hamiltonian with Local Unitary Transformation

An analytical energy gradient for the spin-dependent general Hartree-Fock method based on the infinite-order Douglas-Kroll-Hess (IODKH) method was developed. To treat realistic systems, the local unitary transformation (LUT) scheme was employed both in energy and energy gradient calculations. The present energy gradient method was numerically assessed to investigate the accuracy in several diatomic molecules containing fifth- and sixth-period elements and to examine the efficiency in one-, two-, and three-dimensional silver clusters. To arrive at a practical calculation, we also determined the geometrical parameters of fac-tris(2-phenylpyridine)iridium and investigated the efficiency. The numerical results confirmed that the present method describes a highly accurate relativistic effect with high efficiency. The present method can be a powerful scheme for determining geometries of large molecules, including heavy-element atoms.

Development and application of the analytical energy gradient for the normalized elimination of the small component method

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.

Perturbative treatment of scalar-relativistic effects in coupled-cluster calculations of equilibrium geometries and harmonic vibrational frequencies using analytic second-derivative techniques

An analytic scheme for the computation of scalar-relativistic corrections to nuclear forces is presented. Relativistic corrections are included via a perturbative treatment involving the mass-velocity and the one-electron and two-electron Darwin terms. Such a scheme requires mixed second derivatives of the nonrelativistic energy with respect to the relativistic perturbation and the nuclear coordinates and can be implemented using available second-derivative techniques. Our implementation for Hartree-Fock self-consistent field, second-order Moller-Plesset perturbation theory, as well as the coupled-cluster level is used to investigate the relativistic effects on the geometrical parameters and harmonic vibrational frequencies for a set of molecules containing light elements (HX, X=F, Cl, Br; H2X, X=O, S; HXY, X=O, S and Y=F, Cl, Br). The focus of our calculations is the basis-set dependence of the corresponding relativistic effects, additivity of electron correlation and relativistic effects, and the importance of core correlation on relativistic effects.

Quasirelativistic theory equivalent to fully relativistic theory

The Dirac operator in a matrix representation in a kinetically balanced basis is transformed to a quasirelativistic Hamiltonian matrix, that has the same electronic eigenstates as the original Dirac matrix. This transformation involves a matrix X, for which an exact identity is derived, and which can be constructed either in a noniterative way or by various iteration schemes, without requiring an expansion parameter. The convergence behavior of five different iteration schemes is studied numerically, with very promising results.

Calculation of spin-densities within the context of density functional theory. The crucial role of the correlation functional

It is demonstrated that the LYP correlation functional is not suited to be used for the calculation of electron spin resonance hyperfine structure (HFS) constants, nuclear magnetic resonance spin-spin coupling constants, magnetic, shieldings and other properties that require a balanced account of opposite- and equal-spin correlation, especially in the core region. In the case of the HFS constants of alkali atoms, LYP exaggerates opposite-spin correlation effects thus invoking too strong in-out correlation effects, an exaggerated spin-polarization pattern in the core shells of the atoms, and, consequently, too large HFS constants. Any correlation functional that provides a balanced account of opposite- and equal-spin correlation leads to improved HFS constants, which is proven by comparing results obtained with the LYP and the PW91 correlation functional. It is suggested that specific response properties are calculated with the PW91 rather than the LYP correlation functional.

Connection between the regular approximation and the normalized elimination of the small component in relativistic quantum theory

The regular approximation to the normalized elimination of the small component (NESC) in the modified Dirac equation has been developed and presented in matrix form. The matrix form of the infinite-order regular approximation (IORA) expressions, obtained in [Filatov and Cremer, J. Chem. Phys. 118, 6741 (2003)] using the resolution of the identity, is the exact matrix representation and corresponds to the zeroth-order regular approximation to NESC (NESC-ZORA). Because IORA (=NESC-ZORA) is a variationally stable method, it was used as a suitable starting point for the development of the second-order regular approximation to NESC (NESC-SORA). As shown for hydrogenlike ions, NESC-SORA energies are closer to the exact Dirac energies than the energies from the fifth-order Douglas-Kroll approximation, which is much more computationally demanding than NESC-SORA. For the application of IORA (=NESC-ZORA) and NESC-SORA to many-electron systems, the number of the two-electron integrals that need to be evaluated (identical to the number of the two-electron integrals of a full Dirac-Hartree-Fock calculation) was drastically reduced by using the resolution of the identity technique. An approximation was derived, which requires only the two-electron integrals of a nonrelativistic calculation. The accuracy of this approach was demonstrated for heliumlike ions. The total energy based on the approximate integrals deviates from the energy calculated with the exact integrals by less than 5 x 10(-9) hartree units. NESC-ZORA and NESC-SORA can easily be implemented in any nonrelativistic quantum chemical program. Their application is comparable in cost with that of nonrelativistic methods. The methods can be run with density functional theory and any wave function method. NESC-SORA has the advantage that it does not imply a picture change.

A gauge-independent zeroth-order regular approximation to the exact relativistic Hamiltonian—Formulation and applications

A simple modification of the zeroth-order regular approximation (ZORA) in relativistic theory is suggested to suppress its erroneous gauge dependence to a high level of approximation. The method, coined gauge-independent ZORA (ZORA-GI), can be easily installed in any existing nonrelativistic quantum chemical package by programming simple one-electron matrix elements for the quasirelativistic Hamiltonian. Results of benchmark calculations obtained with ZORA-GI at the Hartree-Fock (HF) and second-order Moller-Plesset perturbation theory (MP2) level for dihalogens X(2) (X=F,Cl,Br,I,At) are in good agreement with the results of four-component relativistic calculations (HF level) and experimental data (MP2 level). ZORA-GI calculations based on MP2 or coupled-cluster theory with single and double perturbations and a perturbative inclusion of triple excitations [CCSD(T)] lead to accurate atomization energies and molecular geometries for the tetroxides of group VIII elements. With ZORA-GI/CCSD(T), an improved estimate for the atomization energy of hassium (Z=108) tetroxide is obtained.

Revision of the Dissociation Energies of Mercury Chalcogenides?Unusual Types of Mercury Bonding

Mercury chalcogenides HgE (E=O, S, Se, etc.) are described in the literature to possess rather stable bonds with bond dissociation energies between 53 and 30 kcal mol(-1), which is actually difficult to understand in view of the closed-shell electron configuration of the Hg atom in its ground state (...4f(14)5d(10)6s(2)). Based on relativistically corrected many body perturbation theory and coupled-cluster theory [IORAmm/MP4, Feenberg-scaled IORAmm/MP4, IORAmm/CCSD(T)] in connection with IORAmm/B3LYP theory and a [17s14p9d5f]/aug-cc-pVTZ basis set, it is shown that the covalent HgE bond is rather weak (2-7 kcal mol(-1)), the ground state of HgE is a triplet rather than a singlet state, and that the experimental bond dissociation energies have been obtained for dimers (or mixtures of monomers, dimers, and even trimers) Hg2E2 rather than true monomers. The dimers possess association energies of more than 100 kcal mol(-1) due to electrostatic forces between the monomer units. The covalent bond between Hg and E is in so far peculiar as it requires a charge transfer from Hg to E (depending on the electronegativity of E) for the creation of a single bond, which is supported by electrostatic forces. However, a bonding between Hg and E is reduced by strong lone pair-lone pair repulsion to a couple of kcal mol(-1). Since a triplet configuration possesses somewhat lower destabilizing lone pair energies, the triplet state is more stable. In the dimer, there is a Hg-Hg pi bond of bond order 0.66 without any a support. Weak covalent Hg-O interactions are supported by electrostatic bonding. The results for the mercury chalcogenides suggests that all experimental dissociation energies for group-12 chalcogenides have to be revised because of erroneous measurements.

Relativistically corrected hyperfine structure constants calculated with the regular approximation applied to correlation corrected ab initio theory

The infinite-order regular approximation (IORA) and IORA with modified metric (IORAmm) is used to develop an algorithm for calculating relativistically corrected isotropic hyperfine structure (HFS) constants. The new method is applied to the calculation of alkali atoms Li-Fr, coinage metal atoms Cu, Ag, and Au, the Hg(+) radical ion, and the mercury containing radicals HgH, HgCH(3), HgCN, and HgF. By stepwise improvement of the level of theory from Hartree-Fock to second-order Møller-Plesset theory and to quadratic configuration interaction theory with single and double excitations, isotropic HFS constants of high accuracy were obtained for atoms and for molecular radicals. The importance of relativistic corrections is demonstrated.

Calculation of indirect nuclear spin–spin coupling constants within the regular approximation for relativistic effects

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.