Methods Of Relativistic Quantum Chemistry Research Articles

Spectroscopic/Bond Property Relationship in Group 11 Dihydrides via Relativistic Four-Component Methods.

Group 11 dihydrides MH2– (M = Cu, Ag, Au, Rg) have been much less studied than the corresponding MH compounds, despite having potentially several interesting applications in chemical research. In this work, their main spectroscopic constants (bond lengths, dissociation energies, and force constants) have been evaluated by means of highly accurate relativistic four-component coupled cluster (4c-CCSD(T)) calculations in combination with large basis sets. Periodic trends have been quantitatively explained by the charge-displacement/natural orbitals for chemical valence (CD-NOCV) analysis based on the four-component relativistic Dirac–Kohn–Sham method, which allows a consistent picture of the nature of the M–H bond to be obtained on going down the periodic table in terms of Dewar–Chatt–Duncanson bonding components. A strong ligand-to-metal donation drives the M–H bond and it is responsible for the heterolytic (HM···H–) dissociation energies to increase monotonically from Cu to Rg, with RgH2– showing the strongest and most covalent M–H bond. The “V”-shaped trend observed for the bond lengths, dissociation energies, and stretching frequencies can be explained in terms of relativistic effects and, in particular, of the relativistically enhanced sd hybridization occurring at the metal, which affects the metal–ligand distances in heavy transition-metal complexes. The sd hybridization is very small for Cu and Ag, whereas it becomes increasingly important for Au and Rg, being responsible for the increasing covalent character of the bond, the sizable contraction of the Au–H and Rg–H bonds, and the observed trend. This work rationalizes the spectroscopic/bond property relationship in group 11 dihydrides within highly accurate relativistic quantum chemistry methods, paving the way for their applications in chemical bond investigations involving heavy and superheavy elements.

Strong electron correlation in UO2−: A photoelectron spectroscopy and relativistic quantum chemistry study

The electronic structures of actinide systems are extremely complicated and pose considerable challenges both experimentally and theoretically because of significant electron correlation and relativistic effects. Here we report an investigation of the electronic structure and chemical bonding of uranium dioxides, UO2(-) and UO2, using photoelectron spectroscopy and relativistic quantum chemistry. The electron affinity of UO2 is measured to be 1.159(20) eV. Intense detachment bands are observed from the UO2(-) low-lying (7sσg)(2)(5fϕu)(1) orbitals and the more deeply bound O2p-based molecular orbitals which are separated by a large energy gap from the U-based orbitals. Surprisingly, numerous weak photodetachment transitions are observed in the gap region due to extensive two-electron transitions, suggesting strong electron correlations among the (7sσg)(2)(5fϕu)(1) electrons in UO2(-) and the (7sσg)(1)(5fϕu)(1) electrons in UO2. These observations are interpreted using multi-reference ab initio calculations with inclusion of spin-orbit coupling. The strong electron correlations and spin-orbit couplings generate orders-of-magnitude more detachment transitions from UO2(-) than expected on the basis of the Koopmans' theorem. The current experimental data on UO2(-) provide a long-sought opportunity to arbitrating various relativistic quantum chemistry methods aimed at handling systems with strong electron correlations.

Perspective: Relativistic effects

This perspective article discusses some broadly-known and some less broadly-known consequences of Einstein's special relativity in quantum chemistry, and provides a brief outline of the theoretical methods currently in use, along with a discussion of recent developments and selected applications. The treatment of the electron correlation problem in relativistic quantum chemistry methods, and expanding the reach of the available relativistic methods to calculate all kinds of energy derivative properties, in particular spectroscopic and magnetic properties, requires on-going efforts.

Explaining the derivation and functioning of the exact infinite-order two-component Dirac theory in terms of the Hückel model

The transition from the four-component Dirac theory to the exact two-component formalism is considered by using a simple algebraic model of the Dirac hamiltonian. This model is found to correspond to the four-center Huckel matrix and permits to replace the complex operator algebra by very easy matrix operations. This mapping of operators onto number matrices shows how the exact two-component relativistic hamiltonians are derived. It also explains certain conceptual aspects of the relation between four-component and two-component hamiltonians and their eigenfunctions. The generalized Huckel model of a four-center heteroatomic π-electron system can be used to analytically analyze the essential features of a variety of different exact and approximate two-component methods of relativistic quantum chemistry.

Two-component methods of relativistic quantum chemistry: from the Douglas–Kroll approximation to the exact two-component formalism

The two-component methods of relativistic quantum chemistry based on the Foldy–Wouthuysen (FW) transformations of the Dirac hamiltonian are reviewed. Following the strategy designed by Douglas and Kroll, the FW transformation is carried out in two steps. The first amounts to performing the exact free-particle FW transformation. At variance with other approaches, the second step is written in the form, which results in a nonlinear operator equation. This equation can be solved iteratively, leading to two-component hamiltonians of arbitrarily high accuracy in even powers of the fine structure constant. All these hamiltonians can be classified according to their completeness with respect to the leading order in the fine structure constant. On passing to the basis set representation one obtains the usual Douglas–Kroll hamiltonian and all possible higher-order approximations. By a simple modification of the operator equation which determines the block-diagonalizing transformation one can obtain numerical infinite-order solutions, i.e. one can obtain the exact numerical solution for the separation of the pure electronic part of the Dirac spectrum. This gives the exact two-component method for the use in relativistic quantum chemistry. The computational aspects of this approach are discussed as well. The transition from the Dirac formalism to any two-component approximation is accompanied by the change of all operators, including those which correspond to external perturbations and lead to properties of different orders. This so-called change of picture problem is given particular attention and its importance for certain operators is identified.

The change of picture of the Hellmann–Feynman force operator in approximate relativistic methods

The calculation of energy gradients in one- and two-component approximate methods of relativistic quantum chemistry which follow from the block-diagonalisation of the Dirac hamiltonian, is considered. It is indicated that the transition to these approximate methods involves the so-called change of picture for all operators. In particular this applies to the Hellmann–Feynman force operator. To avoid explicit transformation of this operator to the new picture two schemes for its modelling in terms of the usual Coulomb attraction operators are proposed. One of them is based on the point charge nuclear dipole moment model. The other one, the so-called shifted nucleus model, involves a parametrised shift of the nucleus. Both these models lead to a semianalytical method for the evaluation of energy gradients in approximate relativistic calculations, in which the relaxation terms is obtained analytically whereas the matrix elements of the Hellmann–Feynman force are calculated by using the finite difference method. The accuracy and relative merits of the two models are analysed. The two models are tested within the one-component Douglas–Kroll method. A large change of picture contribution is found in calculations of intramolecular forces in the coinage metal hydrides. This shows that any approximate relativistic technique for calculations of the energy gradients and for the relativistic geometry optimisation must take into account the change of picture contribution to the evaluated Hellmann–Feynman force.

Nonsingular two/one-component relativistic Hamiltonians accurate through arbitrary high order in ?2

A series of nonsingular two-component relativistic Hamiltonians is derived from the Dirac Hamiltonian by first performing the free-particle Foldy–Wouthuysen transformation and then a block-diagonalizing transformation. The latter is defined in terms of operators which can be determined iteratively through arbitrary order in α, leading to transformed Hamiltonians with the two-component block accurate through α2k, k=1, 2, 3,… . These Hamiltonians give relativistic energies which differ from Dirac's energies only in terms higher than α2k. Their relation to other nonsingular methods of relativistic quantum chemistry (the Douglas–Kroll method, the regular Hamiltonian schemes) is discussed. By removing the spin-dependent operators, the derived Hamiltonians can be written in spin-free one-component form. The computational effort involved is essentially the same as in the case of the Douglas–Kroll scheme and amounts to relatively easy modification of the core Hamiltonian. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 225–239, 1997