MOLECULAR GEOMETRY AND BONDING THEORIES CH 9 By

MOLECULAR GEOMETRY AND BONDING THEORIES (CH. 9) By: Maggie Dang

9. 1 Molecular Shapes The overall shape of a molecule is determined by its bond angles, the angles made by the lines joining the nuclei of the atoms in the molecule Molecules with a central atom A surrounded by n atoms B, denoted ABn, adopt a number of different geometric shapes, depending o n the value of n and on the particular atoms involved

9. 2 The VSEPR Model Valence-shell electron-pair repulsion (VSEPR) model rationalizes molecular geometries in terms of the repulsions between electron domains, which are regions about a central atom in which electrons are likely to be found. Bonding pairs of electrons are involved in making bonds Nonbonding pairs of electrons, also called lone pairs, both create electron domains around an atom

Electron Domains Based on the VSEPR model, electron domains orient themselves to minimize electrostatic repulsions and to remain as far apart as possible Electron domains from nonbonding pairs exert slightly greater repulsions than those from bonding pairs Electron domains from multiple bonds exert greater repulsions than those from single bonds Electron-Domain Geometry: arrangement of electron domains around a central atom Molecular Geometry: arrangement of atoms

Steps to Predicting Molecular Geometries with the VSEPR Model Sketch the Lewis structure of the molecule or ion Count the total number of electron domains around the central atom, and arrange them in the way that minimizes the repulsions among them Describe the molecular geometry in terms of the angular arrangement of the bonded atoms A double or triple bond is counted as one electron domain when predicting geometry. 1. 2. 3. 4. Ex: CO 2 has C=O double bonds When we apply the VSEPR model to CO 2, each double bond counts as one electron domain. The VSEPR model predicts that CO 2 is linear. Because multiple bonds count as one electron domain, the number of electron domain can be counted as (# of electron domains)= (# of atoms bonded to the central atom) + (# of nonbonding pairs on the central atom) Refer to pgs 207 -209 for molecular geometry tables

Example Using the VSEPR model, predict the molecular geometries of O 3.

The Effect of Nonbonding Electrons and Multiple Bonds on Bond Angles Electron domains for non-bonding electron pairs exert greater repulsive forces on adjacent electron domains and thus tend to compress the bond angles Electron domains for multiple bonds exert a greater repulsive force on adjacent electron domains than do single bonds.

Molecules with Expanded Valence Shells These shapes generally contain axial and equatorial positions When pointing toward an axial position, an electron domain is situated 90° from three equatorial positions In equatorial position an electron domain is situated 120° from the other two equatorial positions and 90° from the two axial positions Repulsions between domains are much greater when they are situated 90° from each other than when they are at 120°. Variations of the trigonal bipyramidal shape show lone electron pairs in the equatorial position Variations of the octahedral shape show lone electron pairs in the axial positions

Molecules with More than One Central Atom The VSEPR theory can be used for molecules with more than one central atom

9. 3 Polarity of Polyatomic Molecules The dipole moment of a polyatomic molecule depends on the vector sum of the dipole moment due to each individual bond, called the bond dipole. Certain molecular shapes, such as linear AB 2 and trigonal planar AB 3, assure that the bond dipoles cancel, leading to a dipole moment of zero for the molecule. In other shapes such as bent AB 2 and trigonal pyramidal AB 3, the bond dipoles do not cancel and the molecule will have a nonzero dipole moment called a polar molecule One with a zero dipole moment is called nonpolar. Polarity is also used when talking about covalently bonded molecules. If the molecule has only 2 different atoms, such as, HF or CCl 4 you can calculate the electronegativity difference and determine the type of covalent bond (polar or non-polar).

Example Predict whether Br. Cl is polar or nonpolar. Chlorine is more electronegative than bromine. Consequently, Br. Cl will be polar with chlorine carrying the partial negative charge.

Polarity and Bond Type Electronegativity Difference Bonding Type <0. 5 Non-polar covalent 0. 5 – 1. 9 Polar covalent > 2. 0 ionic

9. 4 Covalent Bonding and Orbital Overlap Valence-bond theory is an extension of Lewis’s notion of electron-pair bonds. In valence-bond theory, covalent bonds are formed when atomic orbitals on neighboring atoms overlap one another. The overlap region is a favorable one for the two electrons because of their attraction to two nuclei. The greater the overlap between two orbitals, the stronger the bond that is formed.

9. 5 Hybrid Orbitals To extend the ideas of valence-bond theory to polyatomic molecules, it is useful to envision the mixing of s, p, and sometimes d orbitals to form hybrid orbitals. Hybrid orbitals can overlap with orbitals on other atoms to make bonds, or they can accommodate nonbonding pairs. The process of hybridization leads to hybrid orbitals that are directed along certain definite directions

sp, sp 2, and sp 3 Hybrid Orbitals One s orbital and one p orbital can hybridize to form two equivalent sp hybrid orbitals For sp 2, using BF₃ as an example, a 2 s electron on the B atom can be promoted to a vacant 2 p orbital. Mixing the 2 s and two of the 2 p orbitals yields three equivalent sp 2 hybrid orbitals For sp 3, using CH₄ as an example, it forms four equivalent bonds with the four hydrogen atoms. This process results from the mixing of the 2 s and all three 2 p atomic orbitals of carbon to creat four equivalent sp 3 hybrid orbitals. See pgs 318 -320 for diagrams

Hybridization Involving d Orbitals Atoms in the third period and beyond can use d orbitals to form hybrid orbitals. Mixing one s orbital, three p orbitals, and one d orbital leads to five sp 3 d hybrid orbitals. These hybrid orbitals are directed toward the vertices of a trigonal bipyramid. Similarly, mixing one s orbital, three p orbitals, and two d orbitals gives six sp 3 d 2 hybrid orbitals, which are directed toward the vertices of an octahedron. The use of d orbitals in constructing hybrid orbitals corresponds to the notion of an expanded valence shell.

Example Predict the hybridization of SF 4 There are five electron domains around S, giving rise to the trigonal bipyramidal electron-domain geometry. With an expanded octet of 10 electrons, the use of a d orbital on the sulfur is required. The trigonal bipyramidal electron-domain geometry corresponds to SP 3 d hybridization. One of the hybrid orbitals that points in an equatorial direction contains a nonbonding pair of electrons; the other four are used in forming the S-F bonds. -

Steps to Predict Hybrid Orbitals Draw the Lewis structure for the molecule or ion. 2. Determine the electron-domain geometry using the VSEPR model. 3. Specify the hybrid orbitals needed to accommodate the electron pairs based on their geometric arrangement. 1.

9. 6 Multiple Bonds Sigma bonds (σ): covalent bonds in which the electron density lies along the line connecting the atoms Pi bonds (π): formed from the overlap of p orbitals that are oriented perpendicular to the internuclear axis A double bond, such as that in C₂H₄, consists of one sigma bond and one pi bond. A triple bond, such as that in C₂H₂, is composed of one sigma bond and two pi bonds. Ex: H-H has one sigma bond, N₂ has one sigma plus two pi bond

Delocalized Pi Bonding Every pair of bonded atoms shares one or more pairs of electrons. In every bond at least one pair of electrons is localized in the space between the atoms, in a sigma bond. The electrons in sigma bonds are localized in the region between two bonded atoms and do not make a significant contribution to the bonding between any other two atoms. When atoms share more than one pair of electrons, the additional pairs are in pi bonds. The centers of charge density in a pi bond lie above and below the bond axis Molecules with two or more resonance structures can have pi bonds that extend over more than two bonded atoms. Electrons in pi bonds that extend over more than two atoms are said to be delocalized. Delocalized: Pi bonds are spread among several atoms

9. 7 Molecular Orbitals Molecular orbital theory: another model used to describe the bonding in molecules. In this model, the electrons exist in allowed energy states call molecular orbitals (MOs). A molecular orbital can be spread among all the atoms of a molecule, can have a definite energy, and can hold two electrons of opposite spin.

The Hydrogen Molecule Whenever two atomic orbitals overlap, two moleular orbitals form. Thus, the overlap of the 1 s orbitals of two hydrogen atoms to form H₂ produces two MOs. The lower-energy MO of H₂ concentrates electron density between the two hydrogen nuclei and is called the bonding molecular orbital. The higher-energy MO has very little electron density between the nuclei and is called the antibonding molecular orbital. The electron density in both the bonding and the antibonding molecular orbitals of H₂ is centered about the internuclear axis. MOs of this type are called sigma molecular orbitals. The bonding sigma molecular orbital of H₂ is labeled σ1 s, indicating that the MO is formed The antibonding sigma molecular orbital of H₂ is labeled σ1 s*, the asterisk denoting that MO is antibonding. The interaction between two 1 s orbitals to form σ1 s and σ1 s* molecular orbitals can be represented by an energy-level diagram(molecular orbital diagram). It shows the interacting atomic orbitals in the left and right columns and the MOs in the middle column. from two 1 s orbitals.

Bond Order The stability of a covalent bond is related to its bond order. Bond order= ½ (# of bonding electrons - # of antibonding electrons) A bond order of 1 represents a single bond, a bond order of 2 represents a double bond, and a bond order of 3 represents a triple bond. Because MO theory also treats molecules with an odd number of electrons, bond orders of ½, 3/2, or 5/2 are possible. Ex: H₂ has 2 bonding electrons and no antibonding ones. It has a bond order of ½(2 -0)=1.

Example What is the bond order of the O 2+ ion? The O 2+ ion has eight bonding electrons and three antibonding ones. Thus, its bond order is Bond order= ½ (8 -3) = 2. 5

9. 8 Second-Row Diatomic Molecules Second-row atoms have more than one atomic orbital The way we place electrons in the orbitals: 1. The number of Mos formed equals the number of atomic 2. 3. 4. 5. orbitals combined Atomic orbitals combine most effectively with other atomic orbitals of similar energy. The effectiveness with which 2 atomic orbitals combine is proportional to their overlap with one another. As the overlap increases, the bonding MO is lowered in energy, and the antibonding MO is raised in energy. Each molecular orbital can accommodate, at most, two electrons, with their spins paired (Pauli exclusion principle) When Mos have the same energy, one electron enters each orbital ( with the same spin) before spin pairing occurs (Hund’s rule)

Molecular Orbitals for Li₂ and Be₂ Core electrons usually do not contribute significantly to bonding in molecule formation.

Molecular Orbitals from 2 p Atomic Orbitals The p orbitals that point directly at one another can form sigma bonding and sigma antibonding MOs. The p orbitals that are oriented perpendicular to the internuclear axis combine to form pi molecular orbitals. In diatomic molecules, the pi molecular orbitals occur as pairs of degenerate (same energy) bonding and antibonding MOs. The σ2 p bonding MO is expected to be lower in energy (more stable) than the π2 p bonding Mos because of larger orbital overlap. This ordering is reversed in B₂, C₂, and N₂ because of interaction between the 2 s and 2 p atomic orbitals.

Electron Configurations for B₂ Through Ne₂ For B₂, C₂, and N₂, the σ2 p MO is above the π2 p molecular orbitals in energy. For O₂, F₂, and Ne₂, the σ2 p MO is below the π2 p molecular orbitals.

Electron Configurations and Molecular Properties Molecules with 1 or more unpaired electrons are attracted into a magnetic field. The more unpaired electrons in a species, the stronger the force of attraction. This type of magnetic behavior is called paramagnetism. Substances with no unpaired electrons are weakly repelled from a magnetic filed. This property is called diamagnetism. It is a much weaker effect than paramagnetism.