5210-chap1

# 5210-chap1 - Chapter 1 Introduction and Background to...

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Chapter 1: Slide 1 Chapter 1 Introduction and Background to Quantum Mechanics

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Chapter 1: Slide 2 The Need for Quantum Mechanics in Chemistry Without Quantum Mechanics, how would you explain: Periodic trends in properties of the elements Structure of compounds e.g. Tetrahedral carbon in ethane, planar ethylene, etc. Discrete spectral lines (IR, NMR, Atomic Absorption, etc.) Electron Microscopy Bond lengths/strengths Without Quantum Mechanics, chemistry would be a purely empirical science. PLUS: In recent years, a rapidly increasing percentage of experimental chemists are performing quantum mechanical calculations as an essential complement to interpreting their experimental results.
Chapter 1: Slide 3 Outline The failure of Classical Physics Concepts in Quantum Mechanics • Wave Properties of Particles • Heisenberg Uncertainty Principle Some Classical Physics

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Chapter 1: Slide 4 Classical Physics On the basis of experiments, in particular those performed by Galileo, Newton came up with his laws of motion: 1. A body moves with a constant velocity (possibly zero) unless it is acted upon by a force. 1. The “rate of change of motion”, i.e. the rate of change of momentum, is proportional to the impressed force and occurs in the direction of the applied force. 1. To every action there is an equal and opposite reaction. 1. The gravitational force of attraction between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. × = 2 2 1 r m m G F
Chapter 1: Slide 5 Classical Physics Consider a volume, τ , through which fluid flows. The amount of fluid in τ is: τ ρ d Where ρ is the density which is a function of x , y , z and t . The velocity of the flow (a vector) has cartesian components u , in the x -direction, v , in the y -direction and w in the z -direction. The law of conservation of matter leads us to the equation of continuity : 0 1 = + + + z w y v x u dt d ρ ρ

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Chapter 1: Slide 6 Classical Physics We have successfully related velocity and density for our system. We have not however considered pressures or forces. We may relate the density to the pressure. We may also relate the forces and the velocities. Moving volume element with dimensions dx dy dz whose coordinates are x , y and z , and whose velocity components, u , v and w are functions of the time, t . Let the components of the external force acting on the volume element be X , Y , Z . With some rearrangement we get the hydrodynamic equations of motion : dt du dxdydz x ρ is direction in the change of rate The - dz p dt dw dy p dt dv dx p dt du - = - = - = ρ ρ ρ 1 ; 1 ; 1
Chapter 1: Slide 7 Classical Physics There is a second way of relating the density and the pressure using an equation of state (EOS), pV=nRT etc.

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