Harry M. Quiney

Foundations of the relativistic theory of atomic and molecular structure

Publisher Summary This chapter discusses the basics of the relativistic theory of atomic and molecular structure. The dominant role of the atomic nucleus in the isolated atom means that the directional dependence of the wave function can be handled algebraically, so that only the dependence on the radial coordinate need can be treated by numerical methods. An understanding of the analytic behavior of Eigen solutions of the Dirac operator is fundamental to the construction of a rigorous description of the relativistic quantum mechanics of atoms and molecules. One-particle models provide a remarkably good first approximation for many processes in atoms and it is no coincidence that most many-body theories are built from one-body wave functions. In quantum electrodynamics textbooks, plane wave solutions of Diracs equation for non-interacting free electrons are the commonest building blocks. Because the theory only conserves total charge, but not the individual numbers of electrons and positrons, excitations producing electron-positron pairs will appear only as intermediate states in perturbation expansions in low energy processes. At higher energies, real pairs may be produced.

Anatomy of relativistic energy corrections in light molecular systems

Relativistic energy corrections which arise from the use of the Dirac-Coulomb Hamiltonian, and the Gaunt and Breit interaction operators, plus Lamb-shift effects have been determined for the global minima of the ground electronic states of C2H6, NH3, H2O, [H,C,N], HNCO, HCOOH, SiC2, SiH− 3, and H2S, and for barrier characteristics for these molecular systems (inversion barrier of NH3 and SiH− 3, barrier to linearity of H2O, H2S, and HNCO, rotational barrier of C2H6, difference between conformations of HCOOH (Z/E) and SiC2 (linear/T-shaped), and isomerization barrier of HCN/HNC). The relativistic calculations performed at the Hartree-Fock and the highly correlated CCSD(T) levels employed a wide variety of basis sets. Comparison of the perturbational and the four-component fully variational results indicate that the Coulomb-Pauli Hamiltonian and the lowest order Hamiltonian of direct perturbation theory (DPT(2)) are highly successful for treating the relativistic energy effects in light molecular systems both at a single point on the potential energy hypersurface and along the surface. Electron correlation contributions to the relativistic corrections are relatively small for the systems studied, and are comparable with the 2-electron Darwin correction. Corrections beyond the Dirac-Coulomb treatment are usually rather small, but may become important for high accuracy ab initio calculations.

The Dirac equation in the algebraic approximation

The construction of variational approximations to the solutions of the Dirac equation is discussed. The importance of imposing the physical boundary conditions for both the point- and finite-nuclear models on the set of trial functions is emphasised. The low-frequency Breit interaction is shown to cause no variational failure when included in the iterative solutions of the Dirac-Hartree-Fock equations. The practical advantages of calculations which variationally include the Breit interaction over conventional treatments which employ only the Coulomb interaction are discussed. Manybody perturbation theory calculations of the radial correlation energy of helium- and beryllium-like systems are reported

Ab initio relativistic quantum chemistry: four-components good, two-components bad!*

In view of the debate which resulted from the introductory lecture at this meeting, this article has been submitted to address the issues raised concerning the validity and implementation of relativistic theories of many-electron systems. We present the formulation and construction of BERTHA, our relativistic molecular structure program, and illustrate features of relativistic electronic structure theory with examples. These include magnetic and hyperfine interactions in small molecules, the use of spinor basis functions which include a dependence on a magnetic field strength, NMR shielding constants, P-odd interactions in chiral molecules, and computational details of a relativistic ab initio treatment of germanocene.

Reflections on spontaneous asymmetric synthesis by amplifying autocatalysis

Spontaneous generation of chirality was observed in the course of studying the mechanism of asymmetric autocatalysis by NMR in ZnR2 alkylation of pyrimidin-5-aldehydes. A systematic study was carried out in order to discover its origins. Even in clean fresh non-glass reaction vessels spontaneous ee was clearly observed, and was not dependent on any single reaction parameter. For comparison it was demonstrated that enantiomerically pure Zn alkoxide catalyst could control the configuration of the reaction product even when present at below micromolar concentrations. The high propensity of the Soai reaction system to produce an enantiomerically enriched product without initial bias is suggested to result from stochastic effects. These are especially important in autocatalysis because all the final products can be derived by breeding from a small number of initial events. The statistical excess of one enantiomer in that set is sufficient to generate a measurable ee in the product. The process is aided by the requirement for dimerisation before the product is an active catalyst. An enumeration that rationalises these observations is provided.

Application of relativistic theories and quantum electrodynamics to chemical problems

The BERTHA program embodies a new formulation of relativistic molecular structure theory within the framework of relativistic quantum electrodynamics (QED). This leads to a simple and transparent formulation of Dirac–Hartree–Fock–Breit (DHFB) self-consistent field equations along with algorithms for molecular properties, electron correlation, and higher order QED effects. The DHFB equations are solved by a direct method based on a relativistic generalization of the McMurchie–Davidson algorithm for molecular integrals that economizes memory requirements and is not significantly more expensive computationally than comparable nonrelativistic calculations. Some noteworthy features of this approach include the ease with which relativistic point-group symmetry can be analyzed and the ease of calculation of electromagnetic properties, for example, g factors, nuclear hyperfine interactions, nuclear magnetic resonance (NMR) shielding parameters and molecular effects of parity-violating weak interactions. The “negative energy” states, which are often regarded as a dangerous nuisance in other treatments of relativistic effects, make a vital contribution. As well as outlining the main ideas underlying our development, this study presents results for small molecules, some of which involve heavy elements.

The Dirac equation in the algebraic approximation. V. Self-consistent field studies including the Breit interaction

It is argued that the Breit interaction can be included in the self-consistent-field procedure of Dirac-Hartree-Fock calculations, and need not necessarily be treated as a first-order perturbation, as is widely believed. The matrix Dirac-Hartree-Fock equations including the frequency-independent Breit interaction are presented and discussed. Prototype calculations for helium-like and beryllium-like ions are presented.

Biomolecular imaging and electronic damage using X-ray free-electron lasers

A potentially critical limiting factor in the use of free-electron lasers to determine the structure of organic molecules is the damage the procedure may cause. A model based on coherence theory and quantum electrodynamics suggests that it should be possible to reconstruct a molecule’s structure from the X-ray data obtained as it undergoes damage.

Relativistic, quantum electrodynamic and many-body effects in the water molecule

Abstract Ab initio calculations are reported of the electronic structure of the water molecule, based on the Dirac theory of the electron using correlation consistent basis sets. We calculate electron correlation corrections by second-order many-body perturbation theory, NMR shielding constants in the four-component relativistic interaction Hamiltonian formulation of QED, and report the first calculation of the electronic structure of a molecular system in which the Breit interaction is included both perturbatively and variationally in the calculation of the total energy.

Hematin-hematin self-association states involved in the formation and reactivity of the malaria parasite pigment, hemozoin.

The malaria parasite pigment, hemozoin, is a crystal of ferriprotoporphyrin IX (FP-Fe(III)), a product of hemoglobin digestion. Hemozoin formation is essential for FP-Fe(III) detoxification in the parasite; it is the main target of quinoline antimalarials and can modulate immune and inflammation responses. To gain further insight into the likely mechanisms of crystal formation and hemozoin reactivity, we have reanalyzed the crystal structure data for beta-hematin and solved the crystal structure of Plasmodium falciparum hemozoin. The analysis reveals that the structures are very similar and highlights two previously unexplored modes of FP-Fe(III) self-association involving pi-pi interactions that may initiate crystal formation and help to stabilize the extended structure. Hemozoin can be considered to be a crystal composed of pi-pi dimers stabilized by iron-carboxylate linkages. As a result, it is predicted that two surfaces of the crystal would consist of pi-pi dimers with Fe(III) partly exposed to solvent and capable of undergoing redox reactions. Accordingly, we demonstrate that the crystal possesses both general peroxidase activity and the ability to cause lipid oxidation.