Chapter 10 Chemical Bonding II
Valence Bond Theory Valence Bond Theory: A quantum mechanical model which shows how electron pairs are shared in a covalent bond. Bond forms between two atoms when the following conditions are met: Covalent bonds are formed by overlap of atomic orbitals, each of which contains one electron of opposite spin. Each of the bonded atoms maintains its own atomic orbitals, but the electron pair in the overlapping orbitals is shared by both atoms. The greater the amount of overlap, the stronger the bond. 2
Orbital Interaction In some cases, atoms use simple atomic orbital (e.g., 1s, 2s, 2p, etc.) to form bonds. In other case, they use a mixture of simple atomic orbitals known as hybrid atomic orbitals. as two atoms approached, the partially filled or empty valence atomic orbitals on the atoms would interact to form molecular orbitals the molecular orbitals would be more stable than the separate atomic orbitals because they would contain paired electrons shared by both atoms 3
Valence Bond Theory - Hybridization one of the issues that arose was that the number of partially filled or empty atomic orbital did not predict the number of bonds or orientation of bonds C = 2s 2 2p x1 2p y1 2p z0 would predict 2 or 3 bonds that are 90 apart, rather than 4 bonds that are 109.5 apart to adjust for these inconsistencies, it was postulated that the valence atomic orbitals could hybridize before bonding took place one hybridization of C is to mix all the 2s and 2p orbitals to get 4 orbitals that point at the corners of a tetrahedron 4
Valence Bond Theory Main Concepts 1. the valence electrons in an atom reside in the quantum mechanical atomic orbitals or hybrid orbitals 2. a chemical bond results when these atomic orbitals overlap and there is a total of 2 electrons in the new molecular orbital a) the electrons must be spin paired 3. the shape of the molecule is determined by the geometry of the overlapping orbitals 5
The Phase of an Orbital Orbitals are determined from mathematical wave functions. A wave function can have positive or negative values. As well as nodes where the wave function = 0 The sign of the wave function is called its phase. When orbitals interact, their wave functions may be in phase (same sign) or out of phase (opposite signs). This is important in bonding as will be examined in a later chapter. 6
Types of Bonds a sigma (s) bond results when the bonding atomic orbitals point along the axis connecting the two bonding nuclei either standard atomic orbitals or hybrids s-to-s, p-to-p, hybrid-tohybrid, s-to-hybrid, etc. a pi (p) bond results when the bonding atomic orbitals are parallel to each other and perpendicular to the axis connecting the two bonding nuclei between unhybridized parallel p orbitals the interaction between parallel orbitals is not as strong as between orbitals that point at each other; therefore s bonds are stronger than p bonds 7
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Hybridization some atoms hybridize their orbitals to maximize bonding hybridizing is mixing different types of orbitals to make a new set of degenerate orbitals sp, sp 2, sp 3, sp 3 d, sp 3 d 2 more bonds = more full orbitals = more stability better explain observed shapes of molecules same type of atom can have different hybridization depending on the compound C = sp, sp 2, sp 3 9
Hybrid Orbitals H cannot hybridize!! the number of standard atomic orbitals combined = the number of hybrid orbitals formed the number and type of standard atomic orbitals combined determines the shape of the hybrid orbitals the particular kind of hybridization that occurs is the one that yields the lowest overall energy for the molecule in other words, you have to know the structure of the molecule beforehand in order to predict the hybridization 10
sp 3 Hybridization of C 11
sp 3 Hybridization atom with 4 areas of electrons tetrahedral geometry 109.5 angles between hybrid orbitals atom uses hybrid orbitals for all bonds and lone pairs Ammonia Formation with sp 3 N H sp 3 sp 3 H C N H s s H H 12
sp 2 atom with 3 areas of electrons 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 13
3-D representation of ethane (C 2 H 4 ) 14
Bond Rotation because orbitals that form the s bond point along the internuclear axis, rotation around that bond does not require breaking the interaction between the orbitals but the orbitals that form the p bond interact above and below the internuclear axis, so rotation around the axis requires the breaking of the interaction between the orbitals 15
sp atom with 2 areas of electrons linear shape 180 bond angle atom uses hybrid orbitals for s bonds or lone pairs, uses nonhybridized p orbitals for p bonds 16
sp 3 d atom with 5 areas of electrons around it trigonal bipyramid shape See-Saw, T-Shape, Linear 120 & 90 bond angles use empty d orbitals from valence shell d orbitals can be used to make p bonds 17
sp 3 d 2 atom with 6 areas of electrons around it octahedral shape Square Pyramid, Square Planar 90 bond angles use empty d orbitals from valence shell d orbitals can be used to make p bonds 18
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) Use Table 10.3 to select the hybridization scheme that matches 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 # of e- groups around Hybrid orbitals used central atom 2 sp 3 sp 2 4 sp 3 5 sp 3 d 6 sp 3 d 2 Orientation of Hybrid Orbitals 19
Examples: Predict the Hybridization and Bonding Scheme of All the Atoms in Then sketch a σ framework and a π framework O N Cl CH 3 CHO CH 2 NH H 3 BO 3 20
Problems with Valence Bond Theory VB theory predicts many properties better than Lewis Theory bonding schemes, bond strengths, bond lengths, bond rigidity however, there are still many properties of molecules it doesn t predict perfectly magnetic behavior of O 2 21
Molecular Orbital Theory in MO theory, we apply Schrödinger s wave equation to the molecule to calculate a set of molecular orbitals in practice, the equation solution is estimated we start with good guesses from our experience as to what the orbital should look like then test and tweak the estimate until the energy of the orbital is minimized in this treatment, the electrons belong to the whole molecule so the orbitals belong to the whole molecule unlike VB Theory where the atomic orbitals still exist in the molecule 22
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 23
Molecular Orbitals when the wave functions combine constructively, the resulting molecular orbital has less energy than the original atomic orbitals it is called a Bonding Molecular Orbital s, p most of the electron density between the nuclei when the wave functions combine destructively, the resulting molecular orbital has more energy than the original atomic orbitals it is called a Antibonding Molecular Orbital s*, p* most of the electron density outside the nuclei nodes between nuclei 24
Molecular Orbital Theory Electrons in bonding MOs are stabilizing Lower energy than the atomic orbitals Electrons in anti-bonding MOs are destabilizing Higher in energy than atomic orbitals Electron density located outside the internuclear axis Electrons in anti-bonding orbitals cancel stability gained by electrons in bonding orbitals H 2 s bonding MO HOMO s* Antibonding MO LUMO 25
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 - no bond will form. A substance will be paramagnetic if its MO diagram has unpaired electrons if all electrons paired it is diamagnetic Bond Order # Bond Elec. - # Antibond 2 Elec. 26
Molecular Orbital Theory: The Hydrogen Molecule Bond Order = 2-0 2 = 1
What would happen if two helium atoms tried to form a bond by overlapping their two 1s orbitals? The bonding picture is essentially the same as for the hydrogen molecule, except that each helium atom brings two electrons to the molecular orbitals. There would be four electrons to fill into our molecular orbital diagram and that would force us to fill in the bonding sigma MO and the anti-bonding sigma-star MO. The bond order calculation equals zero, as expected for a diatomic helium molecule. Bond order = 2-2 2 = 0 28
Lithium Atomic Orbitals Dilithium, Li 2 Molecular Orbitals s * Lithium Atomic Orbitals 2s BO = ½(4-2) = 1 s s * 2s Any fill energy level will generate filled bonding and antibonding MO s; therefore only need to consider valence shell 1s Since more electrons are in bonding orbitals than are in antibonding orbitals, net bonding interaction s 29 1s
Examples What would the MO pictures of H 2+, H 2-30