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Hydrogen Molecule Valence Bond Model Atomic Hybridization

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Presentation on theme: "Hydrogen Molecule Valence Bond Model Atomic Hybridization"— Presentation transcript:

1 Chapter 6. Orbitals and Chemical Bonding I: The Valence Bond Model and Molecular Geometry
Hydrogen Molecule Valence Bond Model Atomic Hybridization Electron-Pair Repulsion: Molecular Shapes Electric Dipole Moment σ and π Bond Types Shortcomings of the Valence Bond Model How to make Lewis electron-dot structures somehow consistent with quantum mechanics?

2 6.1 Hydrogen Molecule: The Simplest Electron-Pair Bond
• H2: simplest covalent bond • When the neutral atoms are very far apart, two electron- nuclear attractions are vanishingly small. • Then, the system can be approximated to a system of two independent H-atoms. • The wave function for the ground state becomes the product of the 1s orbitals on the two atoms: (6.1) Nevertheless, QM solution for the exact ψ is impossible.

3 • Substituting Eq.(6.1) into the Schrødinger equation, the output:
Fig.6.2 Bond potential energy curve & orbital overlaps Eq(6.1) Heitler-London Treatment of H2 • Allowing nuclei a and b to share electrons 1 and 2 (or, the electrons exchange between a and b), we should consider both 1sa(r1)1sb(r2) and 1sa(r2)1sb(r1). Therefore, Eq(6.2) (Spectroscopy) (6.2) a normalization const. Importance of orbital overlap Electrons → can only be exchanged between atoms if their orbitals have an overlap ← overlap integral ψa= valence orbital of atom a S ≠ 0 for exchange

4 Exchange energy: Non-classical – it cannot be described as an electrostatic interaction among charges. Formation of a covalent chemical bond is a fundamentally quantum-mechanical phenomenan. These orbital products allow for swapping or exchange of the electrons What about Pauli’s exclusion principle?: Electron spins had to be paired just as in an atomic orbital. Lewis’ ideas fit nicely with this => The electron pair bond is justified from the orbital analysis. This is not an orbital (wave function) for one electron case, but a two-electron wave function !

5 6.2 Polyatomic Molecules: Pauling’s Valence Bond Model
• Pauling: all electron sharing within a Lewis molecular structure ~ can be accounted for by valence-bond wave functions like the Hitler-London treatment • covalent bond electron pair of F (1s22s22p5) (6.4) Fluorine uses valence 2p orbital for the overlap bond. All other F electrons remain paired in their filled AOs

6 Fig. 6.3 Valence bond model for H2O
• A VB for H2O employs two mutually perpendi- cular 2px and 2py of O in making overlaps with the 1s orbital of H. • Two identical VB wave functions obtained from Eq.(6.4) replacing pF by 2pO are the two covalent bonds pointing at a right angle. • The lone pairs on O then occupy the remaining 2pZ and the 2s. • It may be thought that, due to the polar covalent bonding, each H bears a partial positive charge +δ, and the two H’s therefore repel each other by Coulomb’s law. Correct? No! Why?

7 Encountered Problems of VB Model
• Methane, CH4: Tetrahedral (109.5°) • C (1s22s22p2)  How? • 4 bonds from VB model  breakup of 2s2 but, 3 at 90° angles (2p) 1 with no direction (2s) • Directional 2p orbitals  more effective at overlapping the H 1s than 2s of C  expects stronger and shorter bonds than 2s How adjust the reality ? What is the Next ??

8 Pauling (1931) propsed ‘Hybrid Orbital ’
A new set of orbitals • 4 orbitals  identical except for spatial orientation, • hybrid orbitals  formed by linear combinations of the original 2s and 2p orbitals • one of these hybrid orbitals: sp3 orbital h2 = ½(2s -2px-2py+2pz) h3 = ½(2s -2px+2py-2pz) h4 = ½(2s +2px-2py-2pz) • sp3 hybridization can be extended further ← VB model: sp3 hybridization for 2 C

9 BeH2 is a linear molecule (sp hybrid)
* 2 equivalent Be-H bonds from Be(1s22s2)  2 linear hybrid orbitals  contributed from 2s and 2px of Be Boundary surfaces for 2s and 2px sp hybrids Overlaps of the hybrids

10 The hybrids: (6.6) Overlapping each sp hybrids with H 1s then produces the requisite bonding characteristics.

11 BF3 (sp2 hybrid) • B (1s22s22p1) • hybridization (sp2)  Planar structure (x-y plane)  usable orbitals are 2s, 2px, and 2py * A trigonal-planar structure, with a central boron and the fluorines located at the vertices of an equilateral triangle, yielding bond angles of 120°. The usable orbitals are 2s, 2px, and 2py . Since these orbitals are not adapted to 120°, the VB model requires hybridization, sp2. (Fig. 6.6) The boron lacks an octet but is relatively electronegative, making BF3 a strong Lewis acid and an important catalyst for many organic reactions.

12 Fig. 6.6

13 • N (1s22s22p3)  expects 3 H-N-H bonds at 90o
Trigonal pyramidal, with one lone pair electrons on N NH3 • N (1s22s22p3)  expects 3 H-N-H bonds at 90o • In reality, it is 107.5o  needs alternative view: hybridization • Orbitals of N  sp3 hybrid • One lone pair of N  occupying an sp3 orbital • by making sp3 hybrid orbitals  roughly tetrahedral

14 • O (1s22s22p4)  expects 2 H-O-H bonds at 90o
V-shaped, with two lone pairs on O H2O • O (1s22s22p4)  expects 2 H-O-H bonds at 90o • In reality, it is 104.5o  needs alternative view: hybridization • Orbitals of O  sp3 hybrid • Two lone pairs of O  occupying an sp3 orbital • by making sp3 hybrid orbitals  roughly tetrahedral

15 6.3 Double and Triple Bonds: σ and π Bond Types
The valence bond model for multiple bonding: Ethylene (C2H4) – planar • angles of C-C-H and H-C-H: ~ 120° trigonal planar  suggests sp2 hybrid of each C • C: 1s22s22p2 • if sp2  each C has one extra 2p orbital (not used for hybrids) • leftover 2p  perpendicular to the bonding plane • each leftover 2p orbital of each C  overlap and form π-bond

16 Valence bond σ-π picture
Cylindrically symmetric about the bond axis (σ-bond) Overlapped orbitals form π-bond two nonequivalent types of bonds (σ and π bonds) C2H4 is relatively more reactive than C2H6 C2H4 is readily attacked by electrophiles: C2H4 + Br2 → C2H4Br2 C2H6 + Br2 → no reaction

17 Acetylene (C2H2) • C2H2  more reactive than C2H4
• C2H2  Lewis structure H-C≡C-H (linear) • C  sp hybridization • C-C s bond  sp-sp overlap • Two unused p orbitals on each C  perpendicular to molecular axis • each parallel pair of p’s  overlap to form π bond • C≡C  one σ and two π bonds

18 EXAMPLE 6.1 Give a valence bond description of and sketch the bonding in the NO2-, given an ONO bond angle of 118°, and two equal bond lengths. Solution: Lewis structure •Since both resonance forms are identical in bonding characteristics, only one of them is considered. • Bond angle and double bond suggest sp2 hybridization of N. • The bonding consists of a pair of N-O σ-bonds involving sp2 hybrids on N, and either unhybridized 2p or sp3 hybrids on O. • The unused 2p on N pointing perpendicular to the molecular plane and corresponding 2pπ orbital on O’s form a π bonding.

19 6.4 Electron-Pair Repulsion: Predicting Molecular Shapes
• Two VB electron pairs repel each other due to Coulomb repulsion • Repulsion makes the orbitals swing away to give lowest potential energy  valence-shell electron-pair repulsion (VSEPR) σ-Bonded Molecules potential energy three-pair case four-pair case Department of Chemistry, KAIST

20 Bond angles and Geometries
• The bond angles, HXH, of CH4, NH3, OH2  109°, 107°, 105° • Lone pair electrons  more repulsive than bonding pair, because ??? equatorial position? axial position? the arrangement of electron pairs  atomic geometry

21 Expanded Octet Molecules
S atom accommodates 5 electron pairs Trigonal-bipyramidal structure • lone pair electron  equatorial (experimentally known)  Sawhorse geometry

22 Molecules with π Bonds • C2H4 ~ trigonal planar about each C atom
with σ and π valence bonds between the carbons • C=C p-electron density is concentrated above and below the molecular plane  π bond exerts smaller effect than σ-bond for molecular geometry • In the VSEPR scheme, π bonds are minor perturbations  ignore them in classifying the geometry types Molecules with π Bonds CO2 is linear SO2 is bent (O-S=O angle, 119°)

23 Heteroatom Effect (p 193-194)
We will skip this part !!!

24 Overall Assessment of VSEPR (p 195)
We will skip this part !!!

25 6.5 Asymmetric Electron Sharing: Electric Dipole Moment
• Unbalanced electron sharing in pair bond between atoms with different electronegativity (χ)  constitute an electric dipole  the molecules possess a dipole moment (m) 6.5 Asymmetric Electron Sharing: Electric Dipole Moment μ = q r distance between charges magnitude of the charge separation

26 HF a heteronuclear diatomic molecule with ΔΧ ≠ 0
μcal = δere = (δ)(4.8 x 10-10esu)(1x10-8cm) = (δ)4.8 Debye (D) μexp = 1.82 D a heteronuclear diatomic molecule with ΔΧ ≠ 0 δe: charge separation (q), re: bond length bond distance of HF 41% of the full electronic charge is transferred from H to F or 41% of HF is ionic

27 measuring dipole moments by capacitance
no E, polar molecules are randomly oriented E, dipolar molecules are lined up • total dipole moment  vector sum of individual bond dipole

28

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30 Effect of Heteroatoms VSEPR rules predict a bent molecule, making μ non-zero

31 Example 6.4 Predict whether or not the following molecules
will have nonzero dipole moments: in VB-VSEPR model, start with Lewis structures ! 1 of 3 isomers trans-1,2-difluoroethylene μ = 0 2-electron pair linear, μ = 0 4-pair case bent, μ≠0 3-pair case m ≠ 0

32 Valence Bond Description of Partial Ionic Character (p 199)
We will skip this part !!!

33 6.6 Shortcomings of the Valence Bond Model
Inadequate treatment of odd-electron molecules and resonances 2) Magnetism of molecules O2 N2 • Paramagnetic: molecules with unpaired electrons • Diamagnetic: weakly repelled by a magnetic field both are expected to be diamagnetic !!

34 then, what would be the alternative ??
3) Reaction Mechanisms and Molecular Energy Levels • not suitable to describe the reaction in σ-bonded molecules • not giving a model for electron transferring to a molecule of filled valance orbitals and all of its electrons already paired • not giving a description of molecular energy levels that can be excited by UV. then, what would be the alternative ??

35 Department of Chemistry, KAIST
Fig Molecular Orbitals Department of Chemistry, KAIST


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