Chapter 10 Chemistry
Bond order
(#bonding electrons-#antibonding electrons)/2
Formation of SP hybrid orbitals
-1 s orbital and 1 p orbital combine to form two sp orbitals -sum of hybridized orbitals=sum of unhybridized orbitals.
configuration of the trigonal planar system (120 degree bond angles)
-1s orbital and 2 p orbitals combine to form three sp2 orbitals. -1 p orbital is left, perpendicular to the sp2 plane, and forms a pi bond.
table 10.3 electron geometry scheme
-2 electron groups=sp, linear -3 electron groups=sp2, trigonal planar (120 degrees) -4 electron groups=sp3, tetrahedral (109.5) -5 electron groups=sp4, trigonal bipyramidal (90/120)-sp3d -6 electron groups=sp3d2, octahedral (90 degrees)
Hybridization
-Some atoms hybridize their orbitals to maximize bonding -more bonds=more full orbitals=more stability -hybridizing=mixing different types of orbitals in the valence shell to make a new set of degenerate orbitals -sp, sp2, sp3, sp3d, sp3d2 -same type of atom can have different types of hybridization -C=sp, sp2, sp3
Hybrid orbitals
-The number of standard hybrid orbitals combined=the number of hybrid orbitals formed -combining a 2s and a 2p gives a 2sp orbital -H cannot hybridize because its valence shell has only one atomic orbital -number and type of atomic orbital determines the shape. -the particular kind of hybridization that occurs is the one that yields the lowest total energy.
3 ways of predicting how atoms combine to form molecules. Approximations are needed because solving Schrodingers equation is too complex.
-Valence Shell electron repulsion (VSEPR) -Valence Bond Theory -Molecular Orbital Theory
Molecular orbital (MO) theory
-apply schrodinger's wave equation to calculate a set of molecular orbitals. -in practice, the equation solution is estimated -we start with good guesses as to what the orbital should look like -test and tweak the estimate until the energy of the orbital is minimized. Lowest energy=best approximation of actual orbital . -in this treatment, the electron bonds belong to the whole molecule, so the orbitals belong to the whole molecules (delocalization)
Orbital interaction
-as two atoms approach, half-filled valence atomic orbitals interact to form molecular orbitals. -molecular orbitals=regions of high probability of finding shared electrons in the molecule. -molecular orbitals are more stable because they contain electrons shared by both atoms. -potential energy is lowered when molecular orbitals contain a total of two paired electrons compared to separate one electron atomic orbitals. -geometry of overlapping orbitals determines shape of molecule.
sp3d orbitals
-atom with 5 electron groups around it. -trigonal bipyramid electron geometry, which is see-saw, T-shape, or linear. -120 degree, and 90 degree bond angles -use empty d orbital from valence shell -d orbitals are used to make pi bonds
sp3d2 example
-atom with 6 electron groups around it. -octahedral electron geometry -square pyramid, square planar -90 degree bond angles -empty d orbitals from valence shell to form hybrid -d orbitals are used to make pi bond.
SP3 hybridization
-atoms with four electron groups around it -Tetrahedral geometry -109.5 degree angles between hybrid orbitals -atom uses hybrid orbitals for all bonds and lone pairs. -similar to VSEPR, shapes of orbitals and mathematical expressions for orbitals that are amenable to quantum mechanical calculations.
Molecular orbital and properties
-bond order=difference between number of electrons in bonding and anti bonding orbitals -only need to consider valence electrons -may be a fraction -higher bond order=stronger and shorter bond -if bond order is 0, then bond is unstable compared to individual atom and no bond will form. -substance is paramagnetic if MO diagram has unpaired electrons, it is diamagnetic if has paired electrons.
molecular orbital theory
-electrons in bonding molecular orbitals are stabilizing -they have less energy than atomic orbitals -electrons in anti bonding are destabilizing -higher energy than atomic orbitals -electron density located outside internuclear axis -electrons in antibonding orbitals cancel stability gained by electrons in bonding orbitals (node)
formation of sp3d orbitals
-five sp3d orbitals and uunhybridized d orbitals.
Problems with Lewis and VSEPR
-good for trends in properties, but not so good for numerical properties such as bond strength and bond length. -good approximations of bond angle, usually can't predict actual bond angle. -cannot write one correct structure for those that have resonance. -Cannot predict correct magnetic behavior -O2 is paramagnetic, but Lewis predicts it is diamagnetic.
problems with VSEPR
-good trends in properties, but not good with numerical trends, such as bond length and bond strength -good at approximations of angles, but not so good for actual angles. -cannot write one correct structure if resonance is important. -often does not predict the correct magnetic behavior. O2 is paramagnetic, but Lewis structure predicts it is diamagnetic.
sigma bond
-half-filled px orbital + half-filled px orbital. interacting orbitals point along the axis.
pi bond
-half-filled py or pz + half-filled py or pz -bonding orbitals are parallel to each other and perpendicular to the axis connecting the two bonding orbitals. formed between unhybridized parallel p orbitals.
orbital diagrams of bonding
-hybrid orbitals overlap to form a pi bond. -unhybridized orbitals overlap to form a sigma bond.
polyatomic molecules
-many atoms are combined together, atomic orbitals of all atoms are combined to make a set of molecular orbitals, which are delocalized over the entire molecule. -results that better match real molecular properties than either Lewis or valence bond theories.
Valence Bond Theory-Hybridization
-number of partially filled orbitals does not predict the number or the orientation of bonds. -VSEPR considers all valence electrons equivalent. -valence bond theory is more accurate because it says that orbitals can hybridize before the bonding takes place. -one hybridization of C is to mix all the 2s and 2p orbital s to get four orbitals that point to the corner of a tetrahedron (resembles VSEPR but gives more complete picture)
characteristics of PF3
-one unshared pair of electrons on p -polar molecule -polar bonds -tetrahedral, trigonal pyramidal -one unshared pair of electrons on the phosphorus -bonds are polar, dipole moments do not cancel -so the molecule is polar -sp3 hybridized
Bond rotation and reactivity
-orbitals that form sigma bond (hybrid orbital overlap), rotation around that bond does not require breaking the interaction between orbitals. -orbitals that form pi bond (unhybridized p orbitals)=are above and below internuclear axis, so rotation around it requires breaking interaction between orbitals. -pi bonds are weaker and more exposed, so more subject to chemical attack by reactants.
orbital diagrams of bonding orbital example: formaldehyde: CH20
-overlap of a hybrid with either a hybrid or a non hybrid results in a pi bond -overlap of unhybridized orbitals results in a pi bond.
Problems with valence bond (VB) theory
-predicts many properties better than Lewis theory, such as bond schemes, bond strength, bond length, bond rigidity. -many properties it does not predict perfectly, such as the magnetic behavior of O2 -VB presumes that electrons are localized on the atoms in the molecule, this does not account for delocalization, and does not consider the phases of the wave function.
Valence Shell Electron repulsion (VSEPR)
-qualitative approach. Treats all valence electrons the same, as belonging to a molecule as a whole without considering orbital shape.
C6H6 benzene molecular formula
-sigma bonds: sp2 hybrid orbitals -6 pz orbitals: delocalized pi system=benzene ring
LCAO
-simplest guess starts with the atomic orbitals of the atoms adding together to make molecular orbitals, this is the molecular orbital theory, using the Linear Combination of Atomic Orbital (LCAO) method. -orbitals are wave functions, so they can combine constructively or destructively.
Main concepts of the valence bond theory
-the valence electrons reside in quantum-mechanical atomic orbitals. They can be s,p,d, or f orbitals, or can be a combination of the two -a chemical bond results when the atomic orbitals interact and there is a total of two electrons in the molecular orbital. (must be opposite spins) -shape of the molecules is determined by the geometry of the interacting orbitals.
molecular orbitals
-when the wave functions combine constructively, the resulting molecular orbital has less (lower energy, more stable) energy than the original atomic orbital. it is called a bonding molecular orbital. -two types of molecular orbitals are sigma and pi -most electron density is between the nuclei -when the wave functions combine destructively, the resulting molecular orbital has more energy than the original atomic orbital; it is called an anti bonding molecular orbital. -sigma* or pi* -most of the electron density is outside the nuclei -nodes between nuclei
predicting hybridization and bonding scheme
1. start by drawing the lewis structure. 2. use VSEPR theory to predict electron group geometry around 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 the overlap of the appropriate orbitals. 5. label the bonds as sigma or pi. does not always work, but it is the best we can do without complex calculations.
interactions of 1s orbitals
1s-1s=destructive interference. (antibonding molecular orbital) 1s+1s=constructive interference (bonding molecular orbital)
Bonding with Valence Bond Theory
According to valence bond theory, bonding takes place between atoms when their atomic or hybrid orbitals interact (called overlap) -be aligned along the axis between orbitals, or -be parallel to each other and perpendicular to interatomic axis
Valence bond theory: hybridization
Linus Pauling: principles of quantum mechanics to molecules. -bonds occur in atoms when orbitals interact to make those bonds. -kind of interaction depends on whether orbital is along axis between nuclei, or outside the axis.
First, get the structure using VSEPR
SP -atom with two electron groups -linear shape -180 degree bond angle -atom uses hybrid orbitals for sigma bonds or lone pairs, and non hybridized p orbitals for pi bonds.
Valence Bond Theory
Semi-quantitative approach. uses quantum mechanics. Treats atoms as described by quantum mechanical orbitals. Predicts some properties better than VSEPR.
why are sigma bonds stronger than pi bonds
The interaction between parallel orbitals is not as strong as between orbitals that point at each other.
Heteronuclear diatomic molecules and 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. -more electronegative, lower energy orbital -lower energy orbitals contribute more to bonding molecular orbitals -higher energy atomic orbitals contribute more to anti bonding -nonbonding molecular orbitals remain localized on the atom donating its atomic orbitals.
Wave functions that accurately describe the locations of electrons
Valence Bond Theory and Molecular Orbital theory. Finding mathematical functions that describe space regions where valence electrons reside.
unhybridized C orbitals predict the wrong bonding and geometry.
Would predict CH2 H= 1s C=2s 2p VSEPR predicts the structure correctly but does not provide a formalism as to why we treat all valence electrons as belonging to the molecule as a whole.
equilibrium molecular separation
balance between attraction of electron to nuclei and repulsion of equally charged nuclei.
interaction of p orbitals
bond above and below inter nuclear axis, this is a pi bond
interaction of p orbitals
bond along the internuclear axis (between the nuclei , this is a sigma bond) -3 orientations, 2px, 2py, and 2pz
Valence bond theory of H2
bond formation=overlapping of two half-filled orbitals. Chemical bond exists in region of maximum overlap.
Molecular Orbital Theory
constructs orbitals for the molecule as a whole (Molecular orbitals). Construct trial molecular orbitals and select the one that minimizes energy. Predicts some properties better than valence bond theory.
oxygen
dioxygen is paramagnetic -nothing predicts this
number of atomic orbitals
equal to number of molecular orbitals. Hund's rule applies
rotations around doubles bonds are restricted
rotation about pi bonds=restricted
Bond rotation in pi and sigma bonds
sigma bond: hybrid orbital overlap, rotation around bond does not require breaking interaction between orbitals. -pi bonds: (unhybridized p orbitals): above and below internuclear axis, so rotation around it requires breaking interaction between orbitals -pi bonds are weaker, more exposed, so more subject to chemical attack by reactants.
Linus Pauling
valence bond theory of H2
Heteronuclear diatomic molecules and ions
when the combining atomic orbitals are identical and of 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.