New Generation Relativistic Quantum Chemical Methods And Application

The dissertation is composed of three major parts, viz. relativistic electronic structuretheory, time-dependent relativistic density functional theory, and group symmetries. Goodprogresses have been made along each of the directions.(1) New generation relativistic quantum chemical methodsWhile the importance of relativistic e?ects for the chemistry and physics of heavy ele-ments has widely been recognized, there is little consensus on how to account for such e?ectsin the actual calculations. That is, which of the two sets of methods, four-component andtwo-component, is superior has long been controversial, and one often hears statements like"four-component good, two-component bad!"or"two-component good, four-component bad!".In the present dissertation we will show that four- and two-component methods can actuallybe made fully equivalent in all aspects of simplicity, accuracy, and e?ciency, which then allowsus to speak of"four- and two-component equally good!". Note that this has been achievedbased solely on physical arguments but not on mathematical tricks. One of the essential ideasis"from atoms to molecule"employing the spatial locality of relativistic e?ects and the knowl-edge about the atoms. The other is to formulate two-component theories at matrix level ratherthan at operator level, by one-step block-diagonalization of the matrix representation of theDirac operator in a restricted kinetically balanced basis. The resulting matrix two-componenttheories are far simpler than the operator counterparts and exact in that they can reproduce theelectronic (and positronic) eigenstates of the original Dirac matrix. The SESC (symmetrizedelimination of the small component) variant is particularly attractive because it requires onlynonrelativistic-type molecular ERI integrals and outperforms all previous quasirelativistic the-ories, whether finite- or infinite-order. In addition, SESC furnishes a seamless bridge betweenthe Dirac and Schro¨dinger equations allowing for hybrid treatments of heavy and light elements in the system. This is indeed a conceptual breakthrough. These findings allow us to claim thatrelativity in chemistry (and ordinary physics) has been solved!(2)Further development of time-dependent relativistic density functional theory for excitedstatesSince relativistic density functional theory is so far the only first principles method fordescribing large and complex systems containing heavy elements, it is of great value to extendit to the time-dependent domain in order to describe excited states and dynamical propertiesof heavy elements. This is actually done for the first time by Prof. W. Liu's group. Inthe present work we have further extended the theory by using a noncollinear form for theexchange-correlation kernel. We have thus obtained a general matrix formalism and a highlyaccurate simplified formulation, by which four-, two-, and one-component relativistic as wellas nonrelativistic time-dependent density functional methods can be expressed with the sameequations.(3)A novel method and routines for generating double group and time-reversal symmetriesBy analyzing the characteristics of the Boson and Fermion irreducible representations ofmolecular point groups we have developed a novel method and corresponding routines forgenerating arbitrary single and double point group symmetries as well as time-reversal sym-metry. Full use of such symmetries greatly enhances the e?ciency of density functional andtime-dependent density functional calculations.All the works have been accomplished on top of the BDF (Beijing Density Functional)package.