Bonding Theories: Valence Bond Theory Molecular Orbital Theory

Lewis Theory: Electron Groups and Molecular Shapes There are Regions of electrons in an atom: Some from placing shared pairs of valence electrons between bonding nuclei; Other from placing lone pairs valence electrons on a single nuclei Regions of electron groups should repel each other (VSEPR) and determines the molecular shape and molecular polarity Tro: Chemistry: A Molecular Approach, 2/e

Tro: Chemistry: A Molecular Approach, 2/e

Problems with Lewis Theory Useful predicting trends, but not quantitative e.g. bond angles, bond strength, bond length Can not give one correct structure for many molecules where resonance is important Often does not predict the correct magnetic behavior of molecules e.g. O2 is paramagnetic, though the Lewis structure predicts it is diamagnetic Tro: Chemistry: A Molecular Approach, 2/e

Valence Bond Theory. I Linus Pauling et al: Chemical bonds form when the orbitals (wave functions of electrons in the atoms) on those atoms interact (overlap) The kind of interaction depends on whether the orbitals align along the axis between the nuclei, or outside the axis Tro: Chemistry: A Molecular Approach, 2/e

Orbital Interaction As two atoms approach, the half-filled valence atomic orbitals on each atom would interact and become more stable: covalent bonds Covalent bonds are regions of high probability of finding the shared electrons in the molecule Tro: Chemistry: A Molecular Approach, 2/e

Orbital interaction Stabilizes the molecule Forming covalent bond would stabilize the molecule because they would contain paired electrons shared by both atoms Attraction between the shared electrons and the nuclei > Repulsion between the nuclei Tro: Chemistry: A Molecular Approach, 2/e

Atomic Orbital in the Bonding of H2S ↑ H 1s ↑↓ H─S bond + S ↑ ↑↓ 3s 3p ↑ H 1s ↑↓ H─S bond Predicts bond angle = 90° Actual bond angle = 92° Tro: Chemistry: A Molecular Approach, 2/e

Valence Bond Theory I – Problem Many molecules such as methane (tetrahedral, bond angle = 109.5°) can not be explained by half-filled atomic orbitals C = 2s22px12py12pz0 would predict two or three bonds that are 90° apart Tro: Chemistry: A Molecular Approach, 2/e

Valence Bond Theory II: Orbital Hybridization When forming covalent bonds, each valence electron can reside in either standard s, p, d, and f orbitals, or in hybridized orbitals of these atomic orbitals. Covalent bond forms via half-filled atomic orbitals interacting, ONE pair of electrons (↑↓) in the new bonding orbital Shape of the molecule determined by the geometry of the interacting orbitals Tro: Chemistry: A Molecular Approach, 2/e

Hybridization + = Some atoms hybridize their orbitals to maximize bonding Hybridization: mixing different types of orbitals in the valence shell to make a new set of degenerate (equal energy) orbitals 1 x s orbital + 2 x p orbital = 3 x sp2 hybrid orbital Same type of atom can have different types of hybridization C = sp, sp2, sp3 Tro: Chemistry: A Molecular Approach, 2/e

Hybrid Orbitals The number of standard atomic orbitals combined = the number of hybrid orbitals formed combining a 2s with a 2p gives 2 x sp hybrid orbitals H cannot hybridize!! its valence shell only has one orbital The number and type of standard atomic orbitals combined determines the shape of the hybrid orbitals

Orbital Diagram of sp3 Hybridization in C

Orientation of sp3 Hybridized Orbitals Tro: Chemistry: A Molecular Approach, 2/e

Methane: Hydrogen bonded with sp3-hybridized Carbon Tro: Chemistry: A Molecular Approach, 2/e

Various Carbon Hybridizations Unhybridized    2s 2p sp hybridized     2sp 2p sp2 hybridized     2sp2 2p sp3 hybridized     2sp3 Tro: Chemistry: A Molecular Approach, 2/e

sp3 Hybridization Atom with _____ electron groups around it tetrahedral geometry 109.5° angles between hybrid orbitals Atom uses hybrid orbitals for all bonds and lone pairs Tro: Chemistry: A Molecular Approach, 2/e

sp3 Hybridized Atoms Orbital Diagrams Place electrons into hybrid and unhybridized valence orbitals as if all the orbitals have equal energy Lone pairs generally occupy hybrid orbitals Unhybridized atom sp3 hybridized atom C        2s 2p 2sp3 N         2s 2p 2sp3 Tro: Chemistry: A Molecular Approach, 2/e

Bonding with Valence Bond Theory According to valence bond theory, bonding takes place between atoms when their atomic or hybrid orbitals interact (“overlap”). To interact, The orbitals must either be aligned along the axis between the atoms. or The orbitals must be parallel to each other and perpendicular to the interatomic axis Tro: Chemistry: A Molecular Approach, 2/e

Ammonia Formation with sp3 N Tro: Chemistry: A Molecular Approach, 2/e

Sigma (s) bond The interacting atomic orbitals point along the axis connecting the two bonding nuclei either standard atomic orbitals or hybrids s–to–s, p–to–p, hybrid–to–hybrid, s–to–hybrid, etc. Tro: Chemistry: A Molecular Approach, 2/e

pi (p) bond Definition: The bonding atomic orbitals are parallel to each other and perpendicular to the axis connecting the two bonding nuclei between unhybridized parallel p orbitals Double bond = one s bond + one p bond Triple bond = one s bond + two p bonds Strength of orbital overlap: s bonds > p bonds Tro: Chemistry: A Molecular Approach, 2/e

sp2 Atom with _____ electron groups around it trigonal planar system C = trigonal planar N = trigonal bent O = “linear” 120° bond angles flat Atom uses hybrid orbitals for s bonds and lone pairs, uses nonhybridized p orbital for p bond Tro: Chemistry: A Molecular Approach, 2/e

sp2 Hybridized Atoms Orbital Diagrams Unhybridized atom sp2 hybridized atom C 3 s 1 p        2s 2p 2sp2 2p N 2 s 1 p         2s 2p 2sp2 2p Tro: Chemistry: A Molecular Approach, 2/e

Tro: Chemistry: A Molecular Approach, 2/e

Formaldehyde, CH2O Orbital Diagram p   p C p O s sp2 C       sp2 O s s   1s H 1s H Tro: Chemistry: A Molecular Approach, 2/e

Hybrid orbitals overlap to form a s bond. Unhybridized p orbitals overlap to form a p bond. Tro: Chemistry: A Molecular Approach, 2/e

CH2NH Orbital Diagram ･ p   p C p N s sp2 C       sp2 N s s s 1s H 1s H 1s H Tro: Chemistry: A Molecular Approach, 2/e

Does Bond Rotation Affect Bonding? s bond forms along the internuclear axis, rotation around that bond does not affect the interaction between the orbitals. p bond interacts above and below the internuclear axis, so rotation around the axis requires the breaking of the interaction between the orbitals Tro: Chemistry: A Molecular Approach, 2/e

Bond Rotation: s bond vs. p bond Tro: Chemistry: A Molecular Approach, 2/e

Rigidity of double bonds leads to TWO different compounds Different Polarity (dipole moment), Density, melting points, boilding points: Tro: Chemistry: A Molecular Approach, 2/e

sp hybridization Atom with _____ electron groups linear shape 180° bond angle Atom uses hybrid orbitals for s bonds or lone pairs, uses nonhybridized p orbitals for p bonds p s Tro: Chemistry: A Molecular Approach, 2/e

Tro: Chemistry: A Molecular Approach, 2/e

Tro: Chemistry: A Molecular Approach, 2/e

HCN Orbital Diagram 2p     p C p N s sp C     sp N s  1s H Tro: Chemistry: A Molecular Approach, 2/e

sp Hybridized Atoms Orbital Diagrams Unhybridized atom sp hybridized atom C 2s 2p        2s 2p 2sp 2p N 1s 2p         2s 2p 2sp 2p Tro: Chemistry: A Molecular Approach, 2/e

sp3d Atom with five electron groups trigonal bipyramid electron geometry Seesaw, T–Shape, Linear 120° & 90° bond angles Use empty d orbitals from valence shell d orbitals can be used to make p bonds Tro: Chemistry: A Molecular Approach, 2/e

Tro: Chemistry: A Molecular Approach, 2/e

sp3d Hybridized Atoms Orbital Diagrams Unhybridized atom sp3d hybridized atom     P      3s 3p 3sp3d 3d     S      3s 3p 3d 3sp3d (non-hybridizing d orbitals not shown) Tro: Chemistry: A Molecular Approach, 2/e

SOF4 Orbital Diagram p   d S p O s sp3d S         sp2 O s 2p F 2p F 2p F 2p F Tro: Chemistry: A Molecular Approach, 2/e

sp3d2 Atom with six electron groups around it octahedral electron geometry Square Pyramid, Square Planar 90° bond angles Use empty d orbitals from valence shell to form hybrid d orbitals can be used to make p bonds Tro: Chemistry: A Molecular Approach, 2/e

Tro: Chemistry: A Molecular Approach, 2/e

sp3d2 Hybridized Atoms Orbital Diagrams Unhybridized atom sp3d2 hybridized atom ↑↓ ↑↓ ↑ ↑ S ↑ ↑ ↑ ↑ ↑ ↑ 3s 3p 3d 3sp3d2 5s 5p ↑↓ 5d ↑ I ↑↓ ↑ ↑ ↑ ↑ ↑ 5sp3d2 (non-hybridizing d orbitals not shown) Tro: Chemistry: A Molecular Approach, 2/e

Tro: Chemistry: A Molecular Approach, 2/e

Predicting Hybridization and Bonding Scheme 1. Start by drawing the Lewis structure 2. Use VSEPR Theory to predict the electron group geometry around each central atom 3. Select the hybridization scheme based on the electron group geometry 4. Sketch the atomic and hybrid orbitals on the atoms in the molecule, showing overlap of the appropriate orbitals 5. Label the bonds as s or p Tro: Chemistry: A Molecular Approach, 2/e

Example: Predict the hybridization and bonding scheme for CH3CHO Draw the Lewis structure Predict the electron group geometry around inside atoms C1 = 4 electron areas  C1= tetrahedral C2 = 3 electron areas  C2 = trigonal planar Tro: Chemistry: A Molecular Approach, 2/e

Predict the hybridization and bonding scheme for CH3CHO Determine the hybridization of the interior atoms C1 = tetrahedral  C1 = sp3 C2 = trigonal planar  C2 = sp2 Sketch the molecule and orbitals Tro: Chemistry: A Molecular Approach, 2/e

Predict the hybridization and bonding scheme for CH3CHO Label the bonds Tro: Chemistry: A Molecular Approach, 2/e

Practice – Predict the hybridization of all the atoms in H3BO3 H = can’t hybridize B = 3 electron groups = sp2 O = 4 electron groups = sp3 Tro: Chemistry: A Molecular Approach, 2/e

Practice – Predict the hybridization and bonding scheme of all the atoms in NClO • • • • • • • O N C l • • • • s:Osp2─Nsp2 ↑↓ ↑↓ ↑↓ N = 3 electron groups = sp2 O = 3 electron groups = sp2 Cl = 4 electron groups = sp3 ↑↓ s:Nsp2─Clp ↑↓ ↑↓ p:Op─Np Tro: Chemistry: A Molecular Approach, 2/e

Problems with Valence Bond Theory VB theory predicts many properties better than Lewis theory bonding schemes, bond strengths, bond lengths, bond rigidity However, VB theory doesn’t predict many other properties magnetic behavior of O2 In addition, VB theory treats the electrons as localized in orbitals on the atoms in the molecule Tro: Chemistry: A Molecular Approach, 2/e

Molecular Orbital Theory In MO theory, solving Schrödinger’s wave equation to calculate a set of molecular orbitals In this treatment, the electrons belong to the whole molecule – so the orbitals belong to the whole molecule delocalization Tro: Chemistry: A Molecular Approach, 2/e

LCAO The simplest guess starts with the atomic orbitals of the atoms adding together to make molecular orbitals – this is called the Linear Combination of Atomic Orbitals method weighted sum Because the orbitals are wave functions, the waves can combine either constructively or destructively Tro: Chemistry: A Molecular Approach, 2/e

Molecular Orbitals Wave functions combine constructively forms molecular orbital _____ energy than the original atomic orbitals  Bonding Molecular Orbital s, p most of the electron density between the nuclei Wave functions combine destructively forms molecular orbital ______ energy than the original atomic orbitals Antibonding Molecular Orbital s*, p* most of the electron density outside the nuclei nodes between nuclei Tro: Chemistry: A Molecular Approach, 2/e

Interaction of 1s Orbitals: Bonding vs. Antibonding Tro: Chemistry: A Molecular Approach, 2/e

Molecular Orbital Theory Electrons in bonding MOs are stabilizing lower energy than the atomic orbitals Electrons in antibonding MOs are destabilizing higher in energy than atomic orbitals electron density located outside the internuclear axis electrons in antibonding orbitals cancel stability gained by electrons in bonding orbitals Tro: Chemistry: A Molecular Approach, 2/e

Energy Comparisons of Atomic Orbitals to Molecular Orbitals Tro: Chemistry: A Molecular Approach, 2/e

MO and Properties Bond Order = difference between number of electrons in bonding and antibonding orbitals only need to consider valence electrons may be a fraction higher bond order = stronger and shorter bonds if bond order = 0, then bond is unstable compared to individual atoms and no bond will form Paramagnetic: unpaired electrons in MO if all electrons paired it is diamagnetic Tro: Chemistry: A Molecular Approach, 2/e

Because more electrons are in Dihydrogen, H2 Molecular Orbitals Hydrogen Atomic Orbital Hydrogen Atomic Orbital s* 1s 1s s Because more electrons are in bonding orbitals than are in antibonding orbitals, net bonding interaction Tro: Chemistry: A Molecular Approach, 2/e

H2 s* Antibonding MO LUMO s bonding MO HOMO Tro: Chemistry: A Molecular Approach, 2/e

Because there are as many electrons in Dihelium, He2 Molecular Orbitals Helium Atomic Orbital Helium Atomic Orbital s* 1s 1s s BO = ½(2-2) = 0 Because there are as many electrons in antibonding orbitals as in bonding orbitals, there is no net bonding interaction Tro: Chemistry: A Molecular Approach, 2/e

therefore only need to consider valence shell Dilithium, Li2 Molecular Orbitals Lithium Atomic Orbitals Lithium Atomic Orbitals s* 2s 2s s Any fill energy level will generate filled bonding and antibonding MO’s; therefore only need to consider valence shell s* BO = ½(4-2) = 1 1s 1s s Because more electrons are in bonding orbitals than are in antibonding orbitals, there is a net bonding interaction Tro: Chemistry: A Molecular Approach, 2/e

Li2 s* Antibonding MO LUMO s bonding MO HOMO Tro: Chemistry: A Molecular Approach, 2/e

Interaction of p Orbitals Tro: Chemistry: A Molecular Approach, 2/e

Interaction of p Orbitals Tro: Chemistry: A Molecular Approach, 2/e

Tro: Chemistry: A Molecular Approach, 2/e

O2 Dioxygen is paramagnetic Paramagnetic material has unpaired electrons Neither Lewis theory nor valence bond theory predict this result Tro: Chemistry: A Molecular Approach, 2/e

O2 as Described by Lewis and VB Theory Tro: Chemistry: A Molecular Approach, 2/e

2 x unpaired electrons in the Oxygen Atomic Orbitals Oxygen Atomic Orbitals p* 2p O2 MO’s 2p more electrons are in bonding orbitals than are in antibonding orbitals: net bonding interaction p s 2 x unpaired electrons in the antibonding orbitals, O2 as paramagnetic s* BO = ½(8 be – 4 abe) BO = 2 2s 2s s Tro: Chemistry: A Molecular Approach, 2/e

Example: N2− : bond order and magnetic properties Bond order = (#bonding electrons - #antibonding electrons) ÷ 2 Presence of unpaired electrons  paramagnetic BO = ½(8 be – 3 abe) BO = 2.5 This is lower than BO of N2 (3), the bond should be weaker s2s s*2s p2p s2p p*2p s*2p ↑ ↑ ↓ ↑ ↓ ↑ ↓ Unpaired electrons: paramagnetic ↑ ↓ ↑ ↓ Tro: Chemistry: A Molecular Approach, 2/e

Heteronuclear Diatomic Molecules & Ions When the combining atomic orbitals are identical and equal energy, the contribution of each atomic orbital to the molecular orbital is equal When the combining atomic orbitals are different types and energies, the atomic orbital closest in energy to the molecular orbital contributes more to the molecular orbital Tro: Chemistry: A Molecular Approach, 2/e

Heteronuclear Diatomic Molecules & Ions The more electronegative an atom is, the lower in energy are its orbitals Lower energy atomic orbitals contribute more to the bonding MOs Higher energy atomic orbitals contribute more to the antibonding MOs Nonbonding MOs remain localized on the atom donating its atomic orbitals Tro: Chemistry: A Molecular Approach, 2/e

Example: Draw a molecular orbital diagram of N2− ion and predict its bond order and magnetic properties Write a MO diagram for N2− using N2 as a base Count the number of valence electrons and assign these to the MOs following the aufbau principle, Pauli principle & Hund’s rule s2s s*2s p2p s2p p*2p s*2p N has 5 valence electrons 2 N = 10e− (−) = 1e− total = 11e− ↑ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ Tro: Chemistry: A Molecular Approach, 2/e

NO a free radical s2s Bonding MO shows more electron density near O because it is mostly O’s 2s atomic orbital BO = ½(6 be – 1 abe) BO = 2.5 Tro: Chemistry: A Molecular Approach, 2/e

Practice – Draw a molecular orbital diagram of C2+ and predict its bond order and magnetic properties Tro: Chemistry: A Molecular Approach, 2/e

Practice – Draw a molecular orbital diagram of C2+ and predict its bond order and magnetic properties C has 4 valence electrons 2 C = 8e− (+) = −1e− total = 7e− s2s s*2s p2p s2p p*2p s*2p BO = ½(5 be – 2 abe) BO = 1.5 ↑ ↓ ↑ Because there are unpaired electrons, this ion is paramagnetic ↑ ↓ ↑ ↓ Tro: Chemistry: A Molecular Approach, 2/e

HF Tro: Chemistry: A Molecular Approach, 2/e

Polyatomic Molecules When many atoms are combined together, the atomic orbitals of all the atoms are combined to make a set of molecular orbitals, which are delocalized over the entire molecule Gives results that better match real molecule properties than either Lewis or valence bond theories Tro: Chemistry: A Molecular Approach, 2/e

Ozone, O3 MO Theory: Delocalized p bonding orbital of O3 Tro: Chemistry: A Molecular Approach, 2/e