Introduction to Quantum Chemistry - csus.edu

1 1140 BDr. Mack1 Chem. 140 BDr. MackIntroduction to Quantum ChemistryWhy as a chemist, do you need to learn this material? Why as a chemist, do you need to learn this material? 140 BDr. Mack2 Without Quantum mechanics , how would you explain: Periodic trends in properties of the elements Structure of Tetrahedral carbon in ethane, planar ethylene, etc. Discrete spectral lines (IR, NMR, Atomic Absorption, etc.) Electron Microscopy & surface science Bond lengths/strengthsWithout Quantum mechanics , Chemistry would be a purely empiricalWithout Quantum mechanics , Chemistry would be a purely (We would be no better than ) (We would be no better than ) 2140 BDr.

2 Mack3 Classical PhysicsOn the basis of experiments, in particular those performed by Galileo, Newton came up with his laws of body moves with a constant velocity (possibly zero) unless it is acted upon by a rate of change of motion , the rate of change of momentum, is proportional to the impressed force and occurs in the direction of the applied every action there is an equal and opposite 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.

3 =221rmmGF140 BDr. Mack4 The Failures of Classical MechanicsThe Failures of Classical Mechanics1. Black Body Radiation: The Ultraviolet CatastropheThe Ultraviolet Catastrophe2. The Photoelectric Effect: Einstein's belt buckleEinstein's belt buckle3. The de Broglie relationship: Dude you have a wavelength!Dude you have a wavelength!4. The double-slit experiment: More wave/particle dualityMore wave/particle duality5. Atomic Line Spectra: The 1 The 1ststobservation of Quantum levelsobservation of Quantum levels3140 BDr.

4 Mack5 Black Body RadiationBlack Body RadiationLight Waves:Electromagnetic RadiationElectromagnetic RadiationLight is composed of two perpendicular oscillating vectors waves:A magnetic field & an electric fieldAs the light wave passes through a substance, the oscillating fields can stimulate the movement of electrons in a substance. (m) (s 1) = c(m s 1)c = 140 BDr. Mack6 The Electromagnetic Spectrum:The Electromagnetic Spectrum:4140 BDr. Mack7As the frequency of light increases, the energy the wavelength of light increases, the energy h = = Red Light (650 nm)photonhcE == 10 Js 10s 650 nm91 m 10 nm 10 photon= This doesn t seem like much, but when you consider a mole of kJ/molNow that s what I m talkin about!

5 140 BDr. Mack8 Quantized Energy and PhotonsQuantized Energy and Photons1900:Max Planck explained the phenomenon Black Body Radiation by concluding that light must be quantizedquantized. Cavity with a small openingWhen light enters the cavity it is reflected throughout the internal surface. The light that escapes is representative of the internal temperature of the the cavity. Classical theory predicts that the intensity of the light that escapes increases with the frequency of the leads to Ultraviolet CatastropheUltraviolet Catastrophe.

6 5140 BDr. Mack9 Classically, the intensity of the light increases to infinity as the temperature increases. Experimentally, the maximum intensity shifts to the blue as temperature )(/33 = Plank s equation corrected for classical failure by stating thatenergy can only be transferred ina finite minimum Mack10In 1905 Albert Einstein used Planck s Law to explain the Photoelectric EffectPhotoelectric Effect. When light strikes the surface of certain metals, electrons are ejected electrons produce a current that proportional to their is found that the current produced follows the light there is a frequency dependence, below which, no electros are ejected.

7 6140 BDr. Mack111905 Einstein: oscillators in light source can only have quantized energies nh (n = 0,1,2,3,..). As oscillators change their energy from nh to (n-1)h emit radiation of frequencyv and energyhv(photon). If the photons energy is more than then an electron is ejected:KE (electron) = E (photon) = mev2140 BDr. Mack12 The Wave-like Nature of a ParticleLouis de Broglie in response to Planck & Einstein s assertion that light was particle-like (photon) stated that small particles moving fast could exhibit a characteristic wavelength.

8 2E mc=2h mc =h mc p (momentum)c ==1since c =hh p or p= = Conclusion:Light waves have mass,particles have a , you gotta wavelength!!7140 BDr. Mack13 What is the de Broglie wavelength of an electron travelingat c (c=speed of light)?c= = = (insignificant) = = (on the order of atomic dimensions)What is the de Broglie wavelength of a 1 gram marble travelingat 10 cm/sh = s140 BDr. Mack14x xThe particle and the wave:The electron looks like a wave superimposed on a particle: The electron appears as a build up of amplitude in the wave at position x: Uncertainty arises because of the width at Mack15 The DoubleThe Double--slit experimentslit experimentWhen light waves impinge upon a single slit, they may pass such that those incident clear with no destructive interference (a), whereas those at acute angles pass with interference that is related to the angle of incidence.

9 (b) and (c)140 BDr. Mack16 The result of wave transmission amplitude build up is a diffraction Mack17A source of electronsare directed toward either slit closed, we see the expected build up of both slits open, we see a diffraction pattern that is fits wavelike characteristics!140 BDr. Mack18 Such a pattern can only occur if the particle passes through both slitssimultaneously!The particleThe particlemust have wavelikemust have wavelikeproperties to do to do Mack19 Pre-1900 Numerous researchers produced atomic spectra by heating up atoms of a material to high temperature and collecting the emitted energy in the form of an atomic Rutherford proposes model of the atom.

10 Positive central nucleus surrounded by many electrons. 1913 Bohr s laws of the Hydrogen atom orbits nucleus (like a planet around the sun) the possible orbits only those for which the orbital angular momentum of the electron is an integral multiple of h/2 are in these orbits don t radiate an electron changes its orbit a Quantum of energy (photon) is emitted with energy E = hv,where E is the energy difference between the two Line Spectra:Atomic Line Spectra:140 BDr. Mack20 When an electron jumps form a lower state to a higher state, Energy (light) is an electron jumps form a higher state to a lower state, Energy is (light) Bohr Atom:2Hn2-Z RE n=The Energy Levels:The Bohr Model:rn= n2aon = 1, 2, 3, Mack21 Emission of Light:Electrons move from a higher level (state) to a lower level (state)Absorption of Light:Electrons move from a lower level (state) to a higher level (state)140 BDr.