Chemistry 356

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Chemistry 356

• Atomic structure
• Symmetry

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Schrödinger equation(time-independent)
Where H Hamiltonian operator E total energy
of the system (Eigenvalue) Y wavefunction
(Eigenfunction) V potential energy of the
system m mass of electron h Plancks
constant x, y, z Cartesian coordinates
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Wavefunction

• Contains all measurable information about the
  particle
• yy 1 summed over all space
• If particle exists, probability of finding it
  must be equal to one
• Establishes probability distribution in 3D
• Allows energy calculation
• Permits calculation of most probable value

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Solutions/approximations to Schrödinger

• Give us detailed info regarding behavior of
  electron in a mathematical formula
• Model (we attach meaning)
• Useful info comes from squaring the wavefunction
• Results represent the probability of finding the
  electron at any point in the region surround the
  nucleus
• Many solutions to the wave equation
• Each describes a different orbital
• Probability distribution for an electron
• Defined by set of 3 integers

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Polar and Cartesian coordinates
Radial (R) functionvariation of wavefunction
with distance from nucleus
Angular (A) functionangular shape and
orientation in space
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Radial wavefunction for s orbitals
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Radial wavefunctions for p orbitals
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Radial probability functions
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RDFs for s-, p-, and d-orbitals
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s orbitals
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p orbitals
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d orbitals
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f orbitals
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Depictions of orbitals
2pz orbital
2s orbital
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Energies of atomic orbitals by atomic number
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Atomic radius
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Atomic radius
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Ionic radius
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Ionization energy
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Electron affinity
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Electronegativity
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Symmetry
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Reflection
Symmetry operation reflectionSymmetry element
mirror plane, s
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Rotation
180
Symmetry operation rotation Symmetry operation
n-fold axis, Cn
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Rotation
180
180, n2
45, n8, Principal rotation axis
Symmetry operation rotation Symmetry operation
n-fold axis, Cn
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Mirror planes
sd
sv
sh
Vertical mirror planecontains the principal
rotation axis Horizontal mirror planeplane
perpendicular to the principal rotation
axis Dihedral mirror planebisects the angle
between two adjacent 2-fold axes
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Inversion
Symmetry operation Reflection through a center
of symmetry Symmetry element inversion center, i
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Improper rotation (rotate and reflect)
45 turn
Symmetry operation Rotation of 360/n followed
by perpendicular reflection Symmetry element
n-fold axis of improper rotation, Sn
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Identity
Symmetry operation Identity Symmetry element
molecule, object, E
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Character tables
Point group
Basis functions having the same symmetry as the
IR
Classes of symmetry operations
Totally symmetric representation of the group
Symmetry or Mulliken labels, each corresponding
to a different irreducible representation
cubic functions
Characters (of the IRs of the group)
quadratic functions
linear functions translations along specified
axis R, rotation about specified axis
Symmetries of the s, p, d, and f orbitals can be
found here (by their labels). Ex the dxy
orbital shares the same symmetry as the B2
IR. The s orbital always belongs to the totally
symmetric representation (the first listed IR of
any point group).
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More on Mulliken labels