Part 1:Properties of Atom

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Part 1Properties of Atom
? Schrödingers Equation
? Description of Eigenfunctions
-- Angular Function Yl,ml(?,?) lts, p, d, gt,
Angular Nodes
-- Radial Function Rn,l(r) , Radial Nodes
? Orbital Energy (Eigenvalues)
-- H-like Atom Emission Spectrum of H Atom
-- Aufbau Process Pauli Exclusion Principle
Hunds Rule
-- Ionization Potential (IP) Electron Affinity
(EA)
Part 2Molecular orbitals (MO) from Atomic
orbitals (AO)
? Linear Combination of Atomic Orbitals (LCAO)
? Dinuclear Molecules
-- Homo-nuclearH2 A2
-- Hetero-nuclearAH AB
-- Poly-nuclearHn AHn AXn
Part 3Chemical Bonding of 3d Transition Metal
Complexes
? Lewis Structure VSEPR Hybridization
? Crystal Field Theory (CFT)
? Ligand Field Theory (LFT)
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Properties of Atom
? Schrödingers Equation
H? ? E?
HHamiltonian (H?K.E.?P.E.) ?Eigenfunctions EEig
envalues (Total Energy)
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? Description of the Eigenfunctions
x ? r sin? cos? r ? 0, ? y ? r sin? sin?
? ? 0, ? z ? r cos? ? ? 0, 2?
Analytical Form
Quantum Numbers nPrincipal lAngular
Momentum mlMagnetic
?n,l,m(r, ?, ?) ? Rn,l(r)Yl,ml(?, ?)
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Angular Functions, Yl,ml(?,?)
? The s function (l ? 0, ml ? 0)
Symbols Angular Nodes ? l ? 0
Angular ? Y0,0(?, ?) ? 1 Spherical shape
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ml ? 0
? The p function (l ? 1, ml ? ?1, 0, ?1)
Symbolp Angular Nodes ? l ? 1
xy plane
pzYl,ml(?, ?) ? cos?
Y1,0(?, ?) ? 0 when ? ? 90? i.e. xy plane
ml ? ?1
pxYl,ml(?, ?) ? sin? cos?
pyYl,ml(?, ?) ? sin? sin?
Yl,ml(?, ?) ? 0
Yl,ml(?, ?) ? 0
? ? 0?, ? ? 0?
? ? 0?, ? ? 90?
yz plane
xz plane
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? The d function (l ? 2, ml ? ?2, ?1, 0, ?1, ?2)
ml ? 0
Symbold Angular Nodes ? l ? 2
Yl,ml(?, ?) ? 3cos2? ? 1
when
ml ? ?2
ml ? ?1
Yl,ml(?, ?) ? sin2? cos2?
Yl,ml(?, ?) ? sin2? sin2?
Yl,ml(?, ?) ? sin? cos? sin?
Yl,ml(?, ?) ? sin? cos? cos?
Y 0 when ? ? 0?, ? ? ?45?
? ? 0?, ? ? 0? or 90?
? ? 0? or 90?, ? ? 0?
? ? 0? or 90?, ? ? 90?
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Radial Functions, Rn,l(r)
Radial Nodes ? n ? l ? 1 Total Nodes ? n ? 1
Combine angular and radial nodes
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Nomenclature for the Eigenfunctions, ?i
The Principal Quantum Number n The Angular Quantum Number l The Magnetic Quantum Number Ml
n ? 1, 2, 3, 0 ? l ? n ?l ? ml ? ?l
n ? 1 l ? 0 ml ? 0 1s
n ? 2 l ? 0 ml ? 0 2s
n ? 2 l ? 1 ml ? ?1 ml ? 0 ml ? ?1 2p?1 2p0 2p?1
n ? 3 l ? 0 ml ? 0 3s
n ? 3 l ? 1 ml ? ?1 ml ? 0 ml ? ?1 3p?1 3p0 3p?1
n ? 3 l ? 2 ml ? ?2 ml ? ?1 ml ? 0 ml ? ?1 ml ? ?2 3d?2 3d?1 3d0 3d?1 3d?2
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? Orbital Energy (Eigenvalues)
For H En - Ry / n2
Degeneracy n2 e.g. 2s
2px,2py,2pz Degenerate states different
orbitals. Have same eigenvalue
Hydrogen-like Atoms
He? (Z ? 2), Li2? (Z ? 3), and Be3? (Z ? 4)
Slaters Rules for The Calculation of The
Screening Constant
n ? n ? 1 n ? n ? 1 n ? n n ? n
1s ? ? 0.30 0
ns, np 1 0.85 0.35 0
nd, nf 1 ? 0.35 0
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Emission Spectrum of H Atom
E1 ? ?Ry (n ? 1) ground state
E2 ? ?Ry/4 (n ? 2) first excited state
E3 ? ?Ry/9 (n ? 3) second excited state
etc.
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The Aufbau Process Klechkowskys Rule
1s ? 2s ? 2p ? 3s ? 3p ? 4s ? 3d ? 4p
n ? l 1 2 3 3 4 4 5 5
n / l 0 1 2 3
1 1s
2 2s 2p
3 3s 3p 3d
4 4s 4p 4d 4f
5 5s 5p 5d 5f
6 6s 6p 6d
7 7s
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Pauli Exclusion Principle
Hunds Rule
For degenerate states, the electron is filled in
with the same spin to set the maximum total spin
quantum S.
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Ionization Potential (IP)
A ? A? ? e? ?H ? IP -orbital energy
Element I1 I2 I3 I4 I5 I6 I7
Na 495 4560
Mg 735 1445 7730
Al 580 1815 2740 11,600
Si 780 1575 3220 4350 16,100
P 1060 1890 2905 4950 6270 21,200
S 1005 2260 3375 4565 6950 8490 27,000
Cl 1255 2295 3850 5160 6560 9360 11,000
Ar 1527 2665 3945 5770 7230 8780 12,000
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Electron Affinity (EA)
X(g) ? e? ? X?(g) ?H ? ?B.E.
Electron Affinities of the Halogens
Atom Electron Affinity (kJ/mol)
F ? 327.8
Cl ? 348.7
Br ? 324.5
I ? 295.2