Relativistic effects in atomic and molecular properties

2010 ◽  
Vol 60 (3) ◽  
Author(s):  
Miroslav Iliaš ◽  
Vladimír Kellö ◽  
Miroslav Urban
Keyword(s):  
Heavy Metal ◽  
Relativistic Quantum ◽  
Relativistic Effects ◽  
Molecular Properties ◽  
Quadrupole Moments ◽  
Basic Principles ◽  
Dissociation Energies ◽  
Heavy Metal Element ◽  
The Many ◽  
Nuclear Quadrupole Moments

Relativistic effects in atomic and molecular propertiesWe present an overview of basic principles and methods of the relativistic quantum chemistry. Practical aspects of different methods will be discussed stressing their capability of providing accurate predictions of molecular properties, particularly in species containing a heavy metal element. We will present a series of examples showing the importance of relativistic effects in a variety of molecular properties including electron affinities, ionization potentials, reaction and dissociation energies, electric, spectroscopic and other properties. It is possible to recognize a link between these properties and behaviour of materials in some cases. Particular attention is paid to relativistic calculations of the nuclear quadrupole moments for which accurate theoretical electric field gradient is combined with data from the microwave spectra. Important aspect of the present paper is understanding of trends in electronically related atoms throughout the Mendeleev Periodic Table rather than focusing on highly accurate numbers. We will show that relativistic effects represent an unavoidable instrument for explaining some unexpected properties of heavy metal containing compounds. We will also discuss an interplay between the many-electron correlation and relativistic effects.

A Comprehensive Computational Study on OCH+-Rg (Rg = He, Ne, Ar, Kr, Xe) Complexes

2003 ◽  
Vol 68 (3) ◽  
pp. 489-508 ◽  
Author(s):  
Yinghong Sheng ◽  
Jerzy Leszczynski
Keyword(s):  
Computational Study ◽  
Relativistic Effects ◽  
Dft Method ◽  
Basis Set ◽  
Rare Gas ◽  
Geometrical Parameters ◽  
Minor Effect ◽  
Dissociation Energies ◽  
Equilibrium Geometries

The equilibrium geometries, harmonic vibrational frenquencies, and the dissociation energies of the OCH+-Rg (Rg = He, Ne, Ar, Kr, and Xe) complexes were calculated at the DFT, MP2, MP4, CCSD, and CCSD(T) levels of theory. In the lighter OCH+-Rg (Rg = He, Ne, Ar) rare gas complexes, the DFT and MP4 methods tend to produce longer Rg-H+ distance than the CCSD(T) level value, and the CCSD-calculated Rg-H+ bond lengths are slightly shorter. DFT method is not reliable to study weak interaction in the OCH+-He and OCH+-Ne complexes. A qualitative result can be obtained for OCH+-Ar complex by using the DFT method; however, a higher-level method using a larger basis set is required for the quantitative predictions. For heavier atom (Kr, Xe)-containing complexes, only the CCSD method predicted longer Rg-H+ distance than that obtained at the CCSD(T) level. The DFT method can be applied to obtain the semiquantitative results. The relativistic effects are expected to have minor effect on the geometrical parameters, the H+-C stretching mode, and the dissociation energy. However, the dissociation energies are sensitive to the quality of the basis set. The nature of interaction between the OCH+ ion and Rg atoms was also analyzed in terms of the interaction energy components.

Introduction to Relativistic Quantum Chemistry

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Dirac Equation ◽  
Quantum Chemistry ◽  
Relativistic Theory ◽  
Density Functional ◽  
Relativistic Quantum ◽  
Relativistic Effects ◽  
Basis Sets ◽  
Spin Orbit ◽  
Approximate Methods ◽  
Nonrelativistic Theory

This book provides an introduction to the essentials of relativistic effects in quantum chemistry, and a reference work that collects all the major developments in this field. It is designed for the graduate student and the computational chemist with a good background in nonrelativistic theory. In addition to explaining the necessary theory in detail, at a level that the non-expert and the student should readily be able to follow, the book discusses the implementation of the theory and practicalities of its use in calculations. After a brief introduction to classical relativity and electromagnetism, the Dirac equation is presented, and its symmetry, atomic solutions, and interpretation are explored. Four-component molecular methods are then developed: self-consistent field theory and the use of basis sets, double-group and time-reversal symmetry, correlation methods, molecular properties, and an overview of relativistic density functional theory. The emphases in this section are on the basics of relativistic theory and how relativistic theory differs from nonrelativistic theory. Approximate methods are treated next, starting with spin separation in the Dirac equation, and proceeding to the Foldy-Wouthuysen, Douglas-Kroll, and related transformations, Breit-Pauli and direct perturbation theory, regular approximations, matrix approximations, and pseudopotential and model potential methods. For each of these approximations, one-electron operators and many-electron methods are developed, spin-free and spin-orbit operators are presented, and the calculation of electric and magnetic properties is discussed. The treatment of spin-orbit effects with correlation rounds off the presentation of approximate methods. The book concludes with a discussion of the qualitative changes in the picture of structure and bonding that arise from the inclusion of relativity.

Relativistic Multiple Scattering Theory

1991 ◽  
Vol 253 ◽  
Author(s):  
B. L. Gyorffy
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Schr6dinger Equation ◽  
Relativistic Effects ◽  
Relativistic Quantum Mechanics ◽  
Absolute Minimum ◽  
Crystalline Anisotropy ◽  
Symmetry Properties ◽  
Finite Set

The symmetry properties of the Dirac equation, which describes electrons in relativistic quantum mechanics, is rather different from that of the corresponding Schr6dinger equation. Consequently, even when the velocity of light, c, is much larger than the velocity of an electron Vk, with wave vector, k, relativistic effects may be important. For instance, while the exchange interaction is isotropic in non-relativistic quantum mechanics the coupling between spin and orbital degrees of freedom in relativistic quantum mechanics implies that the band structure of a spin polarized metal depends on the orientation of its magnetization with respect to the crystal axis. As a consequence there is a finite set of degenerate directions for which the total energy of the electrons is an absolute minimum. Evidently, the above effect is the principle mechanism of the magneto crystalline anisotropy [1]. The following session will focus on this and other qualitatively new relativistic effects, such as dichroism at x-ray frequencies [2] or Fano effects in photo-emission from non-polarized solids [3].

scholarly journals PROBABILITY IN RELATIVISTIC QUANTUM MECHANICS AND FOLIATION OF SPACE–TIME

2007 ◽  
Vol 22 (32) ◽  
pp. 6243-6251 ◽  
Author(s):  
HRVOJE NIKOLIĆ
Keyword(s):  
Quantum Mechanics ◽  
Wave Equations ◽  
Integral Curve ◽  
Relativistic Quantum ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Relativistic Wave ◽  
Probability Densities ◽  
The Many ◽  
Conserved Currents

The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be nonnegative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of space–time must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.

Basis Set Superposition Errors in the Many-Body Expansion of Molecular Properties

2019 ◽  
Vol 123 (20) ◽  
pp. 4500-4511 ◽  
Author(s):  
Benjamin G. Peyton ◽  
T. Daniel Crawford
Keyword(s):  
Molecular Properties ◽  
Basis Set ◽  
Many Body ◽  
The Many
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