23): Chemical Bonding in Diatomic Molecules Chapter 12...
Transcript of 23): Chemical Bonding in Diatomic Molecules Chapter 12...
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Section 1. H2
+
Chapter 12 (23): Chemical Bonding in Diatomic Molecules
H2+ exact
electronic energies
Ground state:Re = 2.00 Bohr
De = (-0.500 - -0.603) EhDe = 0.103 Eh = 2.79 eV
source: Ira Levine, Quantum Chemistry, 5th ed., Prentice Hall, 20002
H2+ electronic wave functions
source: unrestricted Hartree-Fock 6-31G(d,p) plus {s,p,d}with ζ=0.55.
Chapter 12 (23): Chemical Bonding in Diatomic Molecules
Orbital angular momentun:λ is the quantum number for z-axis angular momentum(like ml).
λ = 0, 1, 2, … and <Lz > = ±λħ.
Wave functions of diatomic molecules are labeled according to λ.
λ: 0 1 2ψ: σ π δ
Subscript "g" or "u" (gerade or ungerade)tells inversion symmetry.
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Chapter 12 (23): Chemical Bonding in Diatomic Molecules
Section 2: minimum-basis LCAO theory of H2+
ϕ1 sa =1√π (
ζ
a0 )3/2
e−ζ|r−rA|/a0
MO ψ = ca ϕ1 sa+cbϕ1 sb
ψg and ψu are graphed along z with x=0 and y=0.
ψg = (2+2 Sab )−1/2(ϕ1 sa + ϕ1 sb)
ψu = (2−2 S ab)−1 /2(ϕ1 sa − ϕ1 sb)
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Chapter 12 (23): Chemical Bonding in Diatomic Molecules
Section 2: LCAO H2+ energy
E g =H aa+H ab1 + S ab
E u =H aa−H ab1 − S ab
Results graphed are for ζ=1. Optimization gives
ζ = 1.24Re=2.00 BohrDe=0.087 Hartree
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E g =H aa+H ab
1 + S abE 1 s =−
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Hartree (ζ=1)
Chapter 12 (23): Chemical Bonding in Diatomic Molecules
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E u =H 11−H 121 − S12
ψu = (2−2 S12)−1/2
(ϕ1 − ϕ2)
E g =H 11+H 121 + S12
ψg = (2+2 S1 2)−1 /2 (ϕ1 + ϕ2)
Chapter 12 (23): Chemical Bonding in Diatomic Molecules
Summary of homonuclear solutions:
ψu
ψg
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Section 5. Homonuclear Diatomic Molecular OrbitalsSigma Orbitals
source: http://www.mpcfaculty.net/mark_bishop/molecular_orbital_theory.htm
Chapter 12 (23): Chemical Bonding in Diatomic Molecules
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Section 5. Homonuclear Diatomic Molecular OrbitalsPi Orbitals
source: http://www.mpcfaculty.net/mark_bishop/molecular_orbital_theory.htm
Chapter 12 (23): Chemical Bonding in Diatomic Molecules
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Homonuclear Diatomic Molecular Orbital Energiespairwise LCAO energy levels secondary sigma(s) - sigma(p
z) mixing
Chapter 12 (23): Chemical Bonding in Diatomic Molecules
secondary σ-σ interactiongreater for smaller Z
E(3σg) > E(1πu) before O2
All Es ↓ as Z ↑
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Section 6. Homonuclear Diatomic Molecular Orbital EnergiesEngel and Reid's Figure 12.19 (23.19)
Chapter 12 (23): Chemical Bonding in Diatomic Molecules
Notable predictions: N2 triple bond O2 triplet ground state
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E (Eh): -1.685 -1.327 -0.641 -0.641 -0.596 -0.454 -0.454 +0.446
MO: 2σg
2σu* 1π
u(x) 1π
u(y) 3σ
g1π
g*(x) 1π
g*(y) 3σ
u*
F1 2s 0.648 0.768 0.000 0.000 0.225 0.000 0.000 -0.283
F1 2pz -0.107 0.086 0.000 0.000 0.639 0.000 0.000 0.825
F1 2px 0.000 0.000 0.683 0.000 0.000 0.734 0.000 0.000
F1 2py 0.000 0.000 0.000 0.683 0.000 0.000 0.734 0.000
F2 2s 0.648 -0.768 0.000 0.000 0.225 0.000 0.000 0.283
F2 2pz 0.107 0.086 0.000 0.000 -0.639 0.000 0.000 0.825
F2 2px 0.000 0.000 0.683 0.000 0.000 -0.734 0.000 0.000
F2 2py 0.000 0.000 0.000 0.683 0.000 0.000 -0.734 0.000
F2RHF using STO-3G minimum basisSCF eigenvalues (Hartree) and eigenvectorsF-F is on the z axis. R = 1.315 Angstroms
Chapter 12 (23): Chemical Bonding in Diatomic Molecules
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F2RHF using STO-3G minimum basis
LCAO-MO valence orbitals
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Section 8. Heteronuclear bondingHF LCAO-MO with H1s and F2pz AOs
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Chapter 12 (23): Chemical Bonding in Diatomic Molecules
Section 8. Heteronuclear bondingHF LCAO-MO with H1s and F2pz and F 2s AOs, 4 electrons
ψ = c1ϕH 1 s + c2ϕF 2 pz+ c3ϕF 2 s
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Section 9. electrostatic potential of hydrogen fluoride
Chapter 12 (23): Chemical Bonding in Diatomic Molecules
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Section 9. electrostatic potential of hydrogen fluoride
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electrostatic potential of ethyltrifluoracetate
electrostatic potentialon electron density surface
DFT B3LYP 6-31G*
Chapter 12 (23): Chemical Bonding in Diatomic Molecules