Relativistic Quantum Chemistry

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Relativistic Quantum Chemistry

• Presented by Boris Averkiev

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Relativistic Mechanics
Quantum Mechanics
Relativistic Quantum Mechanics
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Relativity
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Classical Mechanics
y
y
v
Time is constant
x
x
z
z
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Relativistic Mechanics
Speed of light is constant
Time and space are homogeneous
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Lorenz Group
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Schrödinger Equation
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Approaches

• Square Equation
• Linearization

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Klein-Gordon Equation

• Initial values at t0
• Problem

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Dirac Equation
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Dirac Matrices
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Dirac Equation
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Angular Momentum and Spin
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Free Particle
Particle
Large component
Small component
Anti-Particle
Particle, s1/2 Particle, s-1/2 Anti-Particle,
s1/2 Anti-Particle, s-1/2
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Spinor
y
x
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Dirac construction
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Hydrogen-like Atom
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Hydrogen-like Atom
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Hydrogen-like Atom
2p
1s
3s
2s
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Relativistic Effects

• Radial contraction of the s and p shells
• Spin-orbit splitting
• Radial expansion of the d and f shells

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Many-electron System
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Dirac-Fock Method
Slater determinant
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Relativistic Effects

• Bond Lengths
• Electronic Configuration
• Color
• Melting Point

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Bond Lengths
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Electronic Configuration
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Ag versus Au
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Why Mercury is Liquid?
inert pair effect
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Literature

• Levich V. G. Theoretical Physics, 1970
• Pyykko P. Introduction to Relativistic Quantum
  Chemistry, Lecture Notes, 2001
• Pyykko P. Relativistic Effects in Structural
  Chemistry, Chem Rev. 1988, 88, 563-594
• Norrby L. J. Why is Mercury Liquid? J. Chem.
  Educ. 1991, 68, 110-113

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Acknowledgments

• Dr. Alexander Boldyrev
• Alina Sergeeva