Molecular Geometry and

Bonding TheoriesBrown, LeMay Ch 9

AP ChemistryMonta Vista High School

•Lewis structure is a flat drawing showing the relative placement of atoms, bonds etc. in a molecule, but does not tell anything about the shape of the molecule.

•VSEPR theory helps construct molecular shape (3-D) from the Lewis structures, which are 2-D structures.

Rationale for VSEPR Theory

Valence Shell Electron Pair Repulsion Theroy• The basis principal of VSEPR is that each group of valence

electrons (electron domains) around a central atom tend to be as far as possible from each other to minimize repulsions. These electron domain repulsions around the central atom determine the molecular geometry of a molecule.

• Electron domains: areas of valence e- density around the central atom;

Includes bonding e- pairs and nonbonding (lone) e- pairs A single, double, or triple bond counts as one domain

• Repulsions between two e domains are : lone pair-lonepair >lone pair-bond pair> bond pair-bond pair

Valence-shell electron-pair repulsion theory– Why is lone pair- lone pair repulsion greater than bond

pair-bond pair repulsion?– Good Links:

Good Power point on VSEPR, Shapes of sp3, sp2, sp Carbon, VSEPR Lecture

http://mageechemistry11.blogspot.com/2012/05/vsepr.html

Limitations of VSEPR TheoryEven though the VSEPR model is useful in predicting the shapes of molecules, it does not differentiate between single, double and triple bonds and does not account for bond strengths.

Molecular Dipole Moments

• In complex molecules that contain polar covalent bonds, the three-dimensional geometry and the compound’s symmetry determine if there is a net dipole moment

• Mathematically, dipole moments are vectors; they possess both a magnitude and a direction

• Dipole moment of a molecule is the vector sum of the dipole moments of the individual bonds in the molecule

• If the individual bond dipole moments cancel one another, there is no net dipole moment

• Molecular structures that are highly symmetrical (tetrahedral and square planar AB4, trigonal bipyramidal AB5, and octahedral AB6) have no net dipole moment; individual bond dipole moments completely cancel out

• In molecules and ions that have V-shaped, trigonal pyramidal, seesaw, T-shaped, and square pyramidal geometries, the bond dipole moments cannot cancel one another and they have a nonzero dipole moment

Molecular Dipole Moments Contd.Two factors must be considered in the polarity of a

molecule:1. Are the individual bonds (joining different atoms in a

molecule) polar? Ex. HCl vs. H2. HCl is polar while H2 is not.

H-Cl:

::

H-Cl:

::

+ -

• Bond polarity is most often represented by an arrow that points toward the -

(most EN atom), showing the shift in e-

density.

• The dipole moment () is a vector (i.e., has a specific direction) measuring the polarity of a bond which contains partial charges (Q) that are separated by a distance (r).

= Q r

2. If individual bonds are polar, then do individual dipole moments cancel out or not. A molecule is polar if its centers of (+) and (-) charge do not cancel out- generally happens in a distorted molecule (molecules with lone pairs of e on the central atom.)

How to determine if a molecule is polar?

The sum of the bond dipole moments in a molecule determines the overall polarity of the molecule.1. Draw the true molecular geometry (3D geometry).2. Draw each bond dipole as an arrow3. Add the vectors, and draw the overall dipole moment. If none, then = 0.4. Generally, a distorted molecule (with lone pairs on the central atom) will have a dipole. Exception: AB2E3

type

What is the big deal about polarity?• The polarity of a molecule will tell you a lot about

its solubility, boiling point, etc. when you compare it to other similar molecules. Water, for example, is a very light molecule (lighter than oxygen gas or nitrogen gas) and you might expect it would be a gas based on its molecular weight, however the polarity of water makes the molecules "stick together" very well. Hence water is present as liquid.

• Polar substances are soluble in water (which is polar) and non polar substances are soluble in non polar solvents such as benzene and oil.

PracticeDraw molecular geometires, bond dipole moments, and overall dipolemoments. Also, name the e- domain geometry and the moleculargeometry.

CO2 BF3 H2O

CCl4 NH3 PH3

Rationale For Valence Bond Theory

• VB theory provides a basis for covalent bond formation based upon overlapping of atomic orbitals to share electrons.

• This theory successfully predicts bond strengths based upon orbital overlap (such as H2 bond being weaker than N2 bond)- sigma vs. pi bond strength

Covalent Bonding and Orbital Overlap: Valence Bond Theory

The basic principle of VB theory is that a covalent bond forms when the orbitals of two atoms overlap. Three central themes of VB theory derive from this principle:1. Opposing spins of e pairs: In accordance with Pauli’s exclusion principle, an orbital can have max of two e with opposite spins.2. Maximum overlap of bonding orbitals: The bond strength depends upon the attraction of nuclei for the shared e, so the greater the overlap, the stronger the bond.3. End to end overlap of the atomic orbitals form a sigma bond and allows the free rotation of the parts of the molecule. Side-to-side overlap forms a pi bond, which restricts rotation. A multiple bond consists of one sigma bond and rest pi bonds.

Sigma and Pi bondsSigma () bond:• Covalent bond that results from axial overlap of orbitals between atoms in

a molecule• Lie directly on internuclear axis• “Single” bonds, could form between s-s orbital or s-p orbital or p-p orbital

by axial overlappingEx: F2

Pi () bond:• Covalent bond that results from side-by-side overlap of orbitals between

atoms in a molecule.• Are “above & below” and “left & right” of the inter nuclear axis and

therefore have less total orbital overlap, so they are weaker than bonds. Forms between two p orbitals (py or pz)

• Make up the 2nd and 3rd bonds in double & triple bonds.Ex: O2 N2

Covalent Bonding and Orbital Overlap

• Valence-bond theory: overlap of orbitals between atoms results in a shared valence e- pair (i.e., bonding pair)

Energy

(kJ/mol)0

  -436

0.74 ÅH-H distance

Figure : Formation of bond in H2 a. As 2 H atoms approach, the 2 valence e- in the 1s orbitals begin to overlap, becoming more stable.

b. As H-H distance approaches 0.74 Å, energy lowers b/c of electrostatic attraction between the nuclei & the incoming e-.

c. When H-H distance = 0.74 Å, energy is at its lowest because electrostatic attractions & repulsions are balanced. (This is the actual H-H bond distance.

d. When H-H distance < 0.74 Å, energy increases b/c of electrostatic repulsion between 2 nuclei & between the 2 e-.

ab

c

d

Covalent Bonding and Orbital Overlap

Limitations of VB Theory• Valence bond (VB) theory assumes that all

bonds formed between two atoms are localized bonds and are formed by the donation of an electron from each atom. This is actually an invalid assumption because many atoms bond using delocalized electrons.

Rationale for Hybrid Orbital TheoryGood youtube video

• Hybrid orbital theory is seen as an extension of VB theory, where atomic orbitals “hybridize” to form new hybrid orbitals. This hybrid orbital theory helps explains the bonding in terms of quantum mechanical model of atom (s,p,d,f orbitals).

9.5: Hybrid Orbital TheoryMovie on Hybrid Orbitals

• Explains the molecular geometries in terms of s,p,d,f orbitals.

• VSEPR explains that e domains must be farthest from each other around central atom, but fails to explain these in terms of orbitals as defined in wave mechanical model of atom.

• Hybrid orbital theory of Linus Pauling proposed that the valence atomic orbitals in the molecule are very different from those in the isolated atoms.

• The process of orbital mixing is called hybridization, and the new atomic orbitals are called hybrid orbitals. Animation on Hybrid Orbitals, Hybridization Movie

Hybrid Orbital Theory

• Two key points about the number and types of hybrid orbitals are that

1. The number of hybrid orbitals obtained equals the number of atomic orbitals mixed.

2. The type of hybrid orbitals obtained varies with the types of atomic orbitals mixed.

• The combination of an ns and an np orbital gives rise to two equivalent sp hybrids oriented at 180º.

Hybridization of s and p Orbitals

Hybrid Orbital Theory

Combination of an ns and two np orbitals produces three equivalent sp2 hybrid orbitals.

Hybrid Orbital TheoryHybridization of s and p Orbitals

Hybridization of s and p Orbitals

Hybrid Orbital Theory

Combination of an ns and three np orbitals produces four equivalent sp3 hybrid orbitals.

Molecular Orbital Theory

• Atomic orbitals other than ns orbitals can interact to form molecular orbitals

• p orbitals are not spherically symmetrical — need to define a coordinate system to know which lobes are interacting inthree-dimensional space

• For each np subshell, there are npx, npy, and npz orbitals

– All have the same energy and are degenerate but have different spatial orientations

• Just as with ns orbitals, molecular orbitals can be formed from np orbitals by taking their mathematical sum and difference

Molecular Orbital Diagrams for Homonuclear Diatomic Molecules

• With this approach, the electronic structures of homonuclear diatomic molecules (molecules with two identical atoms), can be understood.

• Most substances contain only paired electrons like F2.

• F2 has a total of 14 valence electrons; starting at the lowest energy level, the electrons are placed in the orbitals according to the Pauli’s principle and Hund’s rule.

– Ttwo electrons each fill the 2s and *2s orbitals, two fill the 2pz orbital, four fill two degenerate orbitals, and four fill two degenerate * orbitals.

– There are eight bonding and six antibonding electrons, giving a bond order of 1.

• The O2 molecule contains two unpaired electrons and is attracted into a magnetic field.

Molecular Orbital Diagrams for Homonuclear Diatomic Molecules

Molecular Orbitals for Heteronuclear Diatomic Molecules

• A similar procedure can be applied to molecules with two dissimilar atoms, called heteronuclear diatomic molecules.

• When two nonidentical atoms interact to form a chemical bond, the interacting atomic orbitals do not have the same energy.

• Use a molecular orbital energy-level diagram that is skewed or tilted toward the more electronegative element.

Molecular Orbitals for Heteronuclear Diatomic Molecules

• An odd number of valence electrons: NO – Nitric oxide (NO) is an example of a heteronuclear diatomic

molecule. – Molecular orbital theory is able to describe the bonding in

molecules with an odd number of electrons, such as NO, whereas Lewis electron structures cannot.

– The molecular orbital energy-level diagram for NO is similar to that for O2.

– Molecular orbital theory can also describe the chemistry of molecules, such as NO.

Molecular Orbitals for Heteronuclear Diatomic Molecules

• Nonbonding Molecular Orbitals

– Molecular orbital theory can explain the presence of lone pairs of electrons by determining the presence of nonbonding molecular orbitals (nb).

– A nonbonding molecular orbital occupied by a pair of electrons is the molecular orbital equivalent of a lone pair of electrons.

Combining the Valence Bond and Molecular Orbital Approaches

Multiple Bonds

• To describe the bonding in more complex molecules that contain multiple bonds, an approach that combines hybrid atomic orbitals to describe the bonding and molecular orbitals to describe the bonding is used.

• In this approach, unhybridized np orbitals on atoms bonded to one another are allowed to interact to produce bonding, antibonding, or nonbonding combinations.

Multiple Bonds

• For bonds between two atoms (as in ethylene or acetylene), the resulting molecular orbitals are virtually identical to the molecular orbitals in diatomic olecules.

Multiple BondsDraw Lewis structures. For C’s: label hybridization, molecular geometry, and unique bond

angles

C2H6

C2H4

C2H2

C6H6

Sigma () bonds in C2H4

Ex: ethene; C-C -bonds and C-H -bonds result from axial overlap of H s-orbitals and C sp2-orbitals

Pi () bonds in C2H4

• Each C has 4 valence e-:– 3 e- for 3 bonds– 1 e- for 1 bond, which results from side-by-side

overlap of one non-hybridized p-orbital from each C

2pC

2ssp2 hybrids bond

axially = bonds

p orbital bonds side-by-side = bond

Sigma () bonds in C2H2

Ex: ethyne (a.k.a. acetylene) C-C -bond and C-H -bonds result from axial overlap of H s-orbitals and C sp-orbital

Pi () bonds in C2H2

Each C has 4 valence e-:– 2 e- for 2 bonds– 2 e- for 2 bonds, which result from side-by-side overlap of two non-hybridized p-orbitals

from each carbon

sp hybrids bond axially = bonds

2pC

2s

p orbital bonds side-by-side = bonds

Sigma () bonds in C6H6

Ex: benzene; C-C -bonds and C-H -bonds result from axial overlap of H s-orbitals and C sp2-orbitals

http://www2.chemistry.msu.edu/faculty/reusch/VirtTxtJml/intro3.htm#strc8c

Localized v. Delocalized Bonds• Delocalized bonds are present in compounds

showing resonance structures, while electrons are localized in most other bonds.

Localized vs. Delocalized Bonds

(localized) (delocalized – MINIMUM OF 4 c’S)

Delocalized bonds in C6H6

• C-C -bonds result from overlap of one non-hybridized p-orbitals from each C• Delocalization of e- in -bonds results in a “double-donut” shaped e- cloud above

and below the molecular carbon plane.

Limitations of Hybrid Orbital Theory

Hybrid orbital theory assumes that all bonds are formed with localized electrons, which is not true. MO (Molecular Orbital) theory explains bonding in terms of delocalized orbitals as well.

9.7: Molecular Orbital (MO) theory So far we have used valence-bond theory (covalent

bonds form from overlapping orbitals between atoms) with hybrid orbital theory and VSEPR theory to connect Lewis structures to observed molecular geometries. However, VB theory does not explain the magnetic or spectral properties of a molecule.

MO theory is similar to atomic orbital (AO) theory (s, p, d, f orbitals) and helps to further explain some observed phenomena, like unpredicted magnetic properties in molecules like those in O2.

AO are associated with the individual atoms, but MO are associated with the whole molecule.

*AO & MO in H2

Combination of two 1s AO from each H forms two MO in H2 molecule.

Bonding MO: form between nuclei and are stable Antibonding MO: marked with *; form “behind” nuclei

and are less stable.

1s 1s

Molecular orbitalsE

1s

*1s

Atomic orbitals

Bonding orbital

Anti-bonding orbital

*Types of MO

• Sigma () MO: form from combinations of:– Two 1s or 2s orbitals from different atoms; written as 1s

or 2s.– Two 2pz orbitals from different atoms (axial overlap);

written as 2pz.(Some sources say 2 px orbitals?)

• Pi () MO: form from combinations of:– Two 2px or 2py orbitals from different atoms; written as

2px or 2py

.

– Do not appear until B2 molecule

MO s from Atomic p-Orbital Combinations

P orbitals can interact with each other forming either sigma molecular orbitals, 2p , in a end-to-end overlap or pi molecular obrbitals, p, in a side-to-side overlap.

The order of energy for MO s derived from 2p orbitals is 2p < p < p*< 2p*

There are three perpendicular p orbitals, so two sigma p orbitals (one bonding and one antibonding) and four pi p orbitals (two bonding and two antibonding) are formed.

This energy order gives the expected MO diagram for most of the p-block elements for homonuclear diatomic molecules.

MO s for B, C and N The energy order of p orbitals results from the assumption that

since s and p orbitals have differences in energy, they do not interact with each other. (or mix)

However, when 2p atomic orbitals are half filled, such as in B, C and N, the repulsions between e are little and the energy of these p orbitals is not much different than the s atomic orbital, which leads to s and p orbital mixing. This mixing lowers the energy of the 2s bonding and antibonding orbitals and increases the energy of sigma 2p (bonding and antibonding) orbitals.The pi 2p orbitals are not affected. This mixing gives a different energy order:

2s < 2s*< p<2p < p*< 2p

*MO diagrams for “< O2”• Resulting MO for

diatomic molecules with < 16 e- (B2, C2, N2, etc.)

Bond order =½ (# bonding e-

- # antibonding e-)

B.O. (N2) = ½ (10 – 4) =6 / 2 = 3 (triple bond)

N2 has no unpaired electrons which makes it diamagnetic.

N atom N atom

*MO diagrams for “≥ O2” Resulting MO for diatomic molecules with ≥ 16 e- (like O2, F2, Ne2, etc.)

O atom O atom

Bond order =½ (# bonding e-

- # antibonding e-)

B.O. (O2) = ½ (10 – 6) == 2 (double bond)

O2 has unpaired electrons which makes it paramagnetic.

Liquid N2 and liquid O2

• From U. Illinois:http://www.chem.uiuc.edu/clcwebsite/liquido2.html

N2 O2

MagnetismIn an element or compound: Diamagnetism: all e-

paired; no magnetic properties Paramagnetism: at least 1 unpaired e-

– * Drawn into exterior magnetic field since spins of atoms become aligned; unlikely to retain alignment when field is removed

Ex: N OSc MnO2

* Ferromagnetism: occurs primarily in Fe, Co, Ni– Drawn into exterior magnetic field since spins of atoms become aligned;

very likely to retain alignment when field is removed (i.e., “a permanent magnet”)

– Nd2Fe14B is very ferromagnetic