Quantum Chemistry

1. Quantum Chemistry Dr. Ron Rusay

2. Atomic Structure and Periodicity • Electromagnetic Radiation • The Nature of Matter • The Atomic Spectrum of Hydrogen • The Bohr Model • The Quantum Mechanical Model of the Atom • Quantum Numbers • Orbital Shapes and Energies • Electron Spin and the Pauli Principle • PolyelectronicAtoms • The History of the Periodic Table • The Aufbau Principles and the Periodic Table • Periodic Trends in Atomic Properties • The Properties of a Group: The Alkali Metals

3. Quantum Theory • Based on experimental observations of light and particles • Development progressed through rigorous mathematical computations • It bridges physics and chemistry • It is described generally as quantum mechanics

4. Electromagnetic Radiation(“Light”) • Energy that exhibits wave-like behavior. • In a vacuum, electromagnetic energy travels through space at the speed of light. • It is described by the Electromagnetic Spectrum.

5. Nature of EM Energy

6. Demonstrating Light’sWave Nature

7. Frequency & Wave length

9. Waveshttp://chemistry.beloit.edu/BlueLight/waves/index.html • Waves have 4 primary characteristics: • 1. Wavelength: distance between two peaks in a wave. • 2. Frequency: number of waves per second that pass a given point in space. • 3. Amplitude: the height of the wave. • 4. Speed: speed of light is 2.9979  108m/s.

10. Waveshttp://chemistry.beloit.edu/BlueLight/waves/index.html • Focus on 2 of the primary characteristics: • 1. Wavelength: distance between two peaks in a wave. • 2. Frequency: number of waves per second that pass a given point in space. • 3. Amplitude: the height of the wave. • 4. Speed: speed of light is 2.9979  108 m/s.

11. Wavelength and frequency  = c /  •  = frequency (s1) •  = wavelength (m) • c = speed of light (m s1)

12. QUESTION

13. Planck’s Constant Transfer of energy is quantized, and can only occur in discrete units, called quanta. • E = change in energy, in J • h = Planck’s constant, 6.626  1034 J s •  = frequency, in s1 •  = wavelength, in m • c = speed of light

15. Planck’s Equation (Interactive)

16. Electromagnetic Energy • EM Spectrum : Chem Connections http://chemistry.beloit.edu/Stars/EMSpectrum/index.html

17. Energy and Mass • Energy has mass • E = mc2 • E = energy • m = mass • c = speed of light

18. Energy and Mass”Duality” (Hence the dual nature of light.)

19. Wavelength and Mass de Broglie’s Equation •  = wavelength, in m • h = Planck’s constant, 6.626  1034J .s = kg m2 s1 • m = mass, in kg •  = frequency, in s1

20. Atomic Spectrum of Hydrogen http://chemistry.beloit.edu/BlueLight/pages/color.html • Continuous spectrum: Contains all the wavelengths of light. • Absorbtion vs.Emission • http://chemistry.beloit.edu/BlueLight/pages/elements.html • Line (discrete) spectrum: Contains only some of the wavelengths of light.

22. Absorption & Emission

23. Emissions: Flame Tests

25. Electromagnetic Energy • Visible Light / Color : ChemConnections • http://chemistry.beloit.edu/Stars/applets/emission/index.html • The Perception of Colors • http://chemconnections.org/organicchem227/227assign-06.html#vision

26. Atomic Emission Spectrum of H2

29. The Bohr Model • E = energy of the levels in the H-atom • z = nuclear charge (for H, z = 1) • n = an integer “The electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits.” X

30. The Bohr Model • Ground State: The lowest possible energy state for an atom (n = 1).

31. Energy Changes in the Hydrogen Atom • E = Efinal state Einitial state

33. Heisenberg Uncertainty Principle Quantum Entanglement/SuperpositionSchrödinger’s Cat: Alive or Dead?Can something be in two places at the same time? • The more accurately we know a particle’s position, the less accurately we can know its momentum or vice versa. In quantum microstates, YES. Science, 272, 1132 (1996)

34. Quantum Numbers (QN) for Electrons(Solutions for the Schrödinger Equation:  =) Where:  = Wave function • 1. Principal QN ( integer n = 1, 2, 3, . . .) : relates to size and energy of the orbital. • 2. Angular Momentum QN ( integer lor)= 0 to n  1) : relates to shape of the orbital. • 3. Magnetic QN (integer m l orm= + l to  l) : relates to orientation of the orbital in space relative to other orbitals. • 4. Electron Spin QN : (ms = +1/2, 1/2) : relates to the spin state of the electron.

35. “ORBITAL”: Electron Probability = ||2 ||2 =  (double integral of wave function  )

36. Periodic Table ClassificationsElectron Configurations & Quantum Numbers • Representative Elements (A Groups): s (l=0) and p (l=1) (N, C, Al, Ne, F, O) • Transition Elements: d (l=2) orbitals (Fe, Co, Ni, etc.) • Lanthanide and Actinide Series (inner transition elements): f (l=3) orbitals (Eu, Am, Es)

37. Valence Electrons Valence electrons are the outermost electrons in the highest principal quantum level of an atom. They are found in the s- and p- orbitals and are the bonding electrons. Inner electrons are called core electrons.

39. QUESTION

40. QUESTION

41. Quantum Numbers : l, mlOrbital Shape & Orientation

42. Magnetic Spin ms

43. Electron Probability = ||2 ||2 =  (double integral of wave function  )

48. Atomic Orbitals • See the following Web page: Identify the unknown orbitals by comparing their shapes to the known orbitals and assign quantum numbers to each orbital. http://chemconnections.org/general/chem120/atomic-orbitals/orbitals.html

50. Multi-electron AtomsElectron Configuration