CHEM 101 > Ch. 10 > Flashcards
Ch. 10 Flashcards
Valence shell electron pair repulsion (VSEPR) theory
A theory that allows prediction of the shapes of molecules based on the idea that electrons either as lone pairs or as bonding pairs repel one another.
•The main principle is that electron pairs(bond pairs or lone pairs) are arranged around a central atom to minimize repulsions. 
Electron groups
A general term for lone pairs, single bonds, multiple bands, or lone electrons in a molecule
Linear geometry
The molecular geometry of three atoms with a 180° bond angle due to the repulsion of 2 electron groups.
(2 groups around central atom)
Trigonal planar geometry
The molecular geometry of 4 atoms with 120° bond angles in a plane. (3 groups around central atom)
Tetrahedral geometry
The molecular geometry a 5 atoms with 109.5° bond angles.
(4 groups around central atom)
Trigonal bipyramindal geometry
The molecular geometry of 6 atoms with 120° bond angles between the three equatorial electron groups and 90° bond angles between the two axial electron groups and the trigonal plane.
(5 groups around central atom)
Octahedral geometry
The molecular geometry of 7 atoms with 90° bond angles.
(6 groups around central atom)
Electron geometry
The Geometrical arrangement of electron groups in a molecule
Molecular geometry
The geometrical arrangement of atoms in a molecule
Trigonal pyramidal
The molecular geometry of a molecule with a tetrahedral electron geometry and one lone pair.
Bent geometry
A local molecule geometry where the bond angle is less than 180° 
Seesaw
The molecular geometry of a molecule with the trigonal bypyramidal electron geometry and one lone pair in an axial position.
T-shaped
The molecular geometry of a molecule with the trigonal bipyramidal electron geometry and 2 lone pairs in an axial positions.
Square pyramidal
The molecular geometry of a molecule with octahedral electron geometry and one lone pair
Square planar
The molecular geometry of a molecule with octahedral electron geometry and 2 lone pairs
Valance bond theory
Advanced model of chemical bonding in which electrons reside in quantum mechanical orbitals localized on individual atoms that are a hybridized blend of standard atomic orbitals; chemical bonds results from an overlap of these orbitals. 
Hybridization
A mathematical procedure in which standard atomic orbitals are combined to form new, hybrid Orbitals
Hybrid atomic orbitals (Hybrid Orbitals)
Orbitals formed from the combination of standard atomic orbitals that correspond more closely to the actual distribution of electrons in a chemically bonded Atom. 
Pi bonds
The bond that forms between 2 p orbitals that overlap side to side
Sigma bonds
The resulting bond that forms between a combination of any 2 s, P, or hybridized Orbitals that overlap end to end. 
Molecular Orbital (MO) theory 
An advanced model of chemical bonding in which electrons reside in molecular orbitals delocalized over the entire molecule. In the simplest version, the molecular Orbitals are simply linear combinations of atomic orbitals. 
In general, when 2 atomic orbitals are added together to form molecular orbitals, one of the resultant molecular Orbitals will be lower in energy (the bonding orbital) then the atomic orbitals, and the other will be higher in energy (the anti-bonding Orbital).
Remember that electrons in orbitals behave like waves. The bonding molecular orbital arises out of constructive interference between the atomic orbitals because both orbitals have the same phase. The antibonding Orbital arises out of destructive interference between the atomic orbitals because subtracting one from the other means the two interacting orbitals have opposite phases.
For this reason, the bonding Orbital has an increased electron density in the inter-nuclear region, while the anti-bonding orbital has a node in the inter-nuclear region.
-Bonding orbitals have a greater electron density in the inter-nuclear region, thereby lowering their energy compared to the orbitals in non-bonded atoms.
-Anti-bonding orbitals have less electron density in their inter-nuclear region, and their energies are generally higher than in the orbitals of non-bonded atoms.

Bonding orbital
Molecular orbital that is lower in energy than any of the atomic orbitals from which it was formed. 
Anti-bonding Orbital
Molecular orbital that is higher in energy than any of the atomic orbitals from which it was formed. 
Bond order
For a molecule, the number of electrons in bonding orbitals minus the number of electrons in non-bonding orbitals divided by two; a positive bond order implies that the molecule is stable.
(# of e^- in bonding MOs) - (# of e^- in antibonding MOs) / 2
A positive bond order means that there are more electrons in bonding molecular orbitals then in anti-bonding molecular Orbitals. the electrons will therefore have lower energy than they did in the orbitals of isolated Atoms, and a chemical bond will form.
In general, the higher the bond order, the stronger the bond.
A negative or zero bond order indicates a bond will not form between the Atoms.
As the bond order increases, the bond gets stronger (greater bond energy) and shorter (smaller bond length)
B2 has 6 electrons, BO is 1.
C2 BO is 2
N2 BO reaches a maximum with a value of 3.
O2 BO is 2.
Molecular shapes
•Lewis structures portray the arrangement of electrons, but not the molecular shape. Molecular structure’s have important consequences on properties.
•Electron geometry shape ≠ Molecular shape.
-Electron group depends on the electrons around the central Atom.
-Molecular group depends on the bonds around the central Atom.
Molecular shape procedure:
1. Draw a possible Lewis structure.
-Use any resonance structure
-Count electron groups
-Multiple bonds count as one group
- Establish electron group arrangement
-A = Central Atom
-X = Terminal Atoms
-E = Lone pairs - Determine molecular shape
-The name depends on arrangement of Atoms - Predict deviations
-Repulsive forces: 1p-1p > 1p-bp > bp-bp - Polar or nonpolar?
-Take vector sum of bond dipoles

Molecular shapes: two groups
•bond angle is 180°
•shape is linear.
Molecular shapes: Three groups
•bond angle is 120°
•shapes can be Trigonal Planar or Angular/V-shapes/bent
Molecular shapes: four groups
•4 groups around a central Atom adopt a tetrahedral electron group arrangement.
•bond angles is 109.5°. 
•shapes can be tetrahedral, trigonal pyramidal, bent/angular/v-shaped
Molecular shapes: five groups
•Five groups around a Central Atom adopt a trigonal bipyramidal electron group arrangement, with two in axial and three in equatorial positions. Any lone pairs will be in equatorial positions. 
•bond angles are 90° and 120°
•shapes can be trigonal bipyramidal, see-saw, T-shaped, linear,
Molecular shapes: six groups
•Six groups around a Central Atom adopt an octahedral electron group arrangement, all in equivalent positions. •bond angles are 90°
•shapes can be octahedral, square pyramidal, square planar
Electron and molecular geometries table
Electron groups: 2
Bonding groups: 2
Lone pairs: 0
Electron geometry: linear
Molecular geometry: linear
Approximate bond angles: 180°
Electron-Group Arrangement: AX2
Polarity: non-polar
Electron groups: 3
Bonding groups: 3
Lone pairs: 0
Electron geometry: Trigonal planar
Molecular geometry: Trigonal Planar
Approximate bond angles: 120°
Electron-Group Arrangement:AX3
Polarity: non-polar
Electron groups: 3
Bonding groups: 2
Lone pairs: 1
Electron geometry: Trigonal planar
Molecular geometry: bent
Approximate bond angles: <120°
Electron-Group Arrangement:AX2E
Polarity:
Electron groups: 4
Bonding groups: 4
Lone pairs: 0
Electron geometry: Tetrahedral
Molecular geometry: Tetrahedral
Approximate bond angles: 109.5°
Electron-Group Arrangement:AX4
Polarity: non-polar
Electron groups: 4
Bonding groups: 3
Lone pairs: 1
Electron geometry: Tetrahedral
Molecular geometry: Trigonal pyramidal
Approximate bond angles: <109.5°
Electron-Group Arrangement:AX3E
Polarity: Polar
Electron groups: 4
Bonding groups: 2
Lone pairs: 2
Electron geometry: tetrahedral
Molecular geometry: bent
Approximate bond angles: <109.5°
Electron-Group Arrangement:AX2E2
Polarity: polar
Electron groups: 5
Bonding groups: 5
Lone pairs: 0
Electron geometry: Trigonal bipyramidal
Molecular geometry: Trigonal bipyramidal
Approximate bond angles: 120° (Equatorial) 90° (axial)
Electron-Group Arrangement:AX5
Polarity: non-polar
Electron groups: 5
Bonding groups: 4
Lone pairs: 1
Electron geometry: Trigonal bipyramidal
Molecular geometry: see-saw
Approximate bond angles: <120° (Equatorial) <90° (axial)
Electron-Group Arrangement:AX4E
Polarity: Polar
Electron groups: 5
Bonding groups: 3
Lone pairs: 2
Electron geometry: Trigonal bipyramidal
Molecular geometry: T-shaped
Approximate bond angles: <90°
Electron-Group Arrangement:AX3E2
Polarity: polar
Electron groups: 5
Bonding groups: 2
Lone pairs: 3
Electron geometry: Trigonal bipyramidal
Molecular geometry: linear
Approximate bond angles: 180°
Electron-Group Arrangement:AX2E 3
Polarity: non-polar
Electron groups: 6
Bonding groups: 6
Lone pairs: 0
Electron geometry: Octahedral
Molecular geometry: Octahedral
Approximate bond angles: 90°
Electron-Group Arrangement:AX6
Polarity: non-polar
Electron groups: 6
Bonding groups: 5
Lone pairs: 1
Electron geometry: Octahedral
Molecular geometry: square pyramidal
Approximate bond angles: <90°
Electron-Group Arrangement:AX5E
Polarity: polar
Electron groups: 6
Bonding groups: 4
Lone pairs: 2
Electron geometry: Octahedral
Molecular geometry: square planar
Approximate bond angles: 90°
Electron-Group Arrangement:AX4E2
Polarity: non-polar
EG BG LP EG MG ABA 2 2 0 Linear Linear 180° 3 3 0 TP TP 120° 3 2 1 TP Bent <120° 4 4 0 Tetra Tetra 109.5° 4 3 1 Tetra TPY <109.5° 4 2 2 Tetra Bent <109.5° 5 5 5 TBPY TBPY 120°&90 5 4 1 TBPY Seesaw <120&90 5 3 2 TBPY T-shaped <90° 5 2 3 TBPY Linear 180° 6 6 0 Octa Octa 90° 6 5 1 Octa SPY <90° 6 4 2 Octa SP 90°
Molecular Orbital (MO) Theory
An advanced theory of chemical bonding in which electrons reside in molecular Orbitals and delocalized over the entire molecule. In the simplest version, the molecular orbitals are simply Linear combinations of atomic orbitals. 
Is a specific application of a more general quantum mechanical approximation technique called the variational method. In the variational method, the energy of a trial function within the Schrödinger equation is minimized.
One important concept to get at the heart of molecular Orbital theory. In order to determine how well a trial function for an orbital works in molecular orbital theory, you calculate its energy. No matter how good your trial function, you will never do better then nature at minimizing the energy of the orbital.
In other words, devise any trial function that you like for an orbital in a molecule and calculate its energy. The energy you calculate for the devised Orbital will always be greater than or at best equal to the energy of the actual Orbital.
The best possible description of the orbital will therefore be the one with the minimum energy. Variation with the lowest energy is the best approximation for the actual molecular Orbital. 
The schrödinger equation Is solved(just like for H atom) for electrons in a molecule resulting in molecular Orbitals (MOs)(just a Approximation). These MOs represent electron delocalization over an entire molecule.
Hybrid orbitals ≠ Molecular Orbitals
HO-Combining two orbitals in one atom
MO-Combining two atomic orbitals on multiple atoms 
Linear combination of atomic orbitals (LCAO)
Is a weighted Linear sum—analogous to a weighted average— of the valance atomic orbitals of the atoms in the molecule.
In Valance bond theory, hybrid Orbitals, weighted linear sums of the valance atomic orbitals of a particular atom, and the hybrid Orbitals remain localized on that atom.
In molecular orbital theory, the molecular Orbitals are weighted Linear sums of the valance atomic orbitals of all the atoms in the molecule, and many of the molecular orbitals are the localized over the entire molecule.
When molecular orbitals are computed mathematically, it is actually the wave functions correspond to the orbitals that are combined.
When electrons occupy bonding molecular Orbitals, the energy of the electrons is lower than it would be if they were occupying atomic orbitals.
Constructive interference between two atomic orbitals gives rise to a molecular orbital that is lower in energy than the atomic orbitals. This is the bonding Orbital. When 2 atomic orbitals have opposite phases, destructive interference gives rise to a molecular Orbital that is higher in energy than the atomic orbitals. This is the anti-bonding Orbital.
We can think of a molecular Orbital in a molecule in much the same way that we think about an atomic orbitals in an Adam. Electrons will seek the lowest energy molecular Orbital available, but just as an atom has more than one atomic Orbital (and some may be empty), so a molecule has more than one molecular Orbital and (some may be empty).
LCAO example
Consider the H2 molecule. One of the molecular Orbitals for H2 is simply an equally weighted sum of the 1s orbital from one atom and the 1s Orbital from the other. The name of this molecular orbital is S 1s. The Sigma comes from the shape of the orbital, which looks like a Sigma bond in valance bond Theory, and the 1S comes from it’s formation by a linear sum of 1S orbitals. s1s Orbital is lower and energy than either of the 21S atomic orbitals from which it was formed.
For this reason, the orbital is called a bonding Orbital. When electrons occupying bonding Orbitals, the energy of the electron it is lower than it would be if they were occupying atomic orbitals. 
The next molecular orbital of H2 is approximated by subtracting the one S orbital from one hydrogen from the one at orbital on the other hydrogen atom. The different phases of the orbitals result in destructive interference between them. The resulting molecular Orbital therefore has a node between the two atoms. The name of this molecular orbital is Sigma*1s. the asterisk Indicates that this orbital is an anti-bonding Orbital. Electrons in anti-bonding orbitals have higher energy than they did in the representative atomic orbitals and therefore tend to raise the energy of the system (relative to the unbonded Atoms)
The molecular orbital diagram shows that to hydrogen atoms can lower their overall energy by forming H2 because the electrons can move from higher energy atomic orbitals into the lower energy S1S bonding molecular orbital. In molecular orbital theory, we defined the bond order of a diatomic molecule such as H2 as
BO = (# of Electrons in bonding MOs) - (# If electrons in anti-bonding MOs) / 2
So H2 BO = 2-0/2 = 1 
Bond order ex
He2. The two additional electrons must go into the higher energy anti-bonding Orbitals. There is no net stabilization by joining to helium Atoms to form helium molecule, as indicated by the pond order:
He2 BO = 2-2/2 = 0.
So, according to MO theory, He2 should not exist as a stable molecule, and indeed it does not. An interesting case is the helium helium ion, He2^+.
The bond order is 1/2, indicating that He2^+ should exist, and indeed it does.
Page 408. Reference
Summarizing LCAO-MO Theory
•Like atomic orbitals in multi electron Atoms, calculation of molecular Orbital wave functions requires iterative methods(but we don’t do this)
•We can approximate (Adding or subtracting AOs) molecular orbitals (MO’s) as a Linear combination of atomic orbitals (AOs). The total number of MO’s formed from a particular set of AO will always equal the number of AOs in the set. ( # MOs out = AOs in)
•When 2 AOs combine to form 2 MO’s, 1MO will be lower energy (the bonding MO) and the other will be higher energy (the anti-bonding MO)
•The square of the molecular orbital way function gifts the probability density.
• when assigning the electrons of a molecule to MOs, fill the lowest energy MOs first with a maximum of two spin pair of electrons per orbital.
-Pauli exclusion Principle
-Hund’s rule
•Bond strength can be measured by the calculated bond order. (higher bond order = stronger bond = shorter bond length
•The bond order in a diatomic molecule is the number of electrons in bonding MOs minus the number of anti-bonding MOs divided by two.
•Stable bonds require a positive bond order (more electrons in bonding MOs than in anti-bonding MOs)
-Notice the power of the molecular orbital approach. Every electron the enters a bonding MO stabilizes the molecule or polyatomic ion, and every electron that enters the anti-bonding MO destabilizes it. The emphasis on electron pairs has been removed. One electron in a bonding MO stabilizes half as much as two, so a bond order of 1/2 is nothing mysterious. 
Period 2 Homonuclear diatomic molecule’s
Molecules made up of two Atoms of the same kind formed from second period Elements have between 2 and 16 electron valances.
To explain bonding in these molecules, we must consider the next step of higher energy molecular Orbitals, which can be approximated by linear combinations of the valance atomic orbitals of the period two elements
-The core electrons can be ignored because, as with other models for bonding, these electrons do not contribute significantly to chemical bonding. 
In a more detailed treatment, the MOs Are formed from Linear combinations that include all of the AOs That are relatively close to each other in energy and of the correct symmetry. Specifically, the 2 2s Orbitals and the 2 2pz Orbitals should all be combined to form a total of four molecular orbitals. The extent to which this type of mixing affects the energy levels of the corresponding MOs depends somewhat on how close in energy The original atomic orbitals were. The energy separation of the 2S and 2p orbitals in B, C, and N are smaller than in O, F, and Ne. It is the larger nuclear charge O, F, and Ne That causes larger energy separation of the orbitals in these Atoms
The bottom line is that s-p mixing is significant in B2, C2, and N2, but not in O2, F2, and Ne2.
Examples:
Li2- Even though lithium is normally a metal, we can use MO theory to predict whether or not the molecules should exist in the gas phase. We approximate the molecular orbitals in lithium as linear combinations of the 2S atomic orbitals. The resulting molecular orbitals look much like those of the H2 molecule.
-To valence electrons of lithium occupy a bonding molecular orbital. We would predict that the molecule is stable with a bond order of one. Experiments confirm this prediction.
In contrast, consider the MO diagram for Be2- The four electrons of Be2 occupy one bonding MO and one bonding anti-bonding MO. The bond order is zero and we predict that Be2 should not be stable; again, this is consistent with experimental findings.
The next homonuclear a molecule composed of second row elements is B2 Which has six total balance electrons to accommodate. We can approximate the next higher energy molecular orbitals for B2 and the rest of the period to diatomic molecule as Linear combination of the 2P orbitals taken pairwise. 
Since the three 2P orbitals orient along three orthogonal axes, we must sign similar axes to the molecule. Then the LCAO-MOs The results from the combination of 2PZ Orbitals the ones that lie along the inter-nuclear axes.
The bonding MO from this pair of atomic orbitals has increased electron density in the inter nuclear region due to constructive interference between the two 2p atomic orbitals. It has the characteristics sigma shape (it is cylindrically symmetrical about the bond axis) And is therefore called the s2p Bonding Orbital. The anti-bonding Orbital, sigma*2p has a node Between the two nuclei (do you to destructive interference between the 2P orbitals) and is higher in energy than either of the 2pz Orbitals.
2px The P orbitals or added together in a side-by-side orientation in contrast to that of the 2pz Orbitals, Which are orientated end-to-end. The resultant molecular orbitals consequently have a different shape. The electron density of the bonding molecular orbital is above and below the inter-nuclear axis with a nodal plane that includes the Internuclear axis. This orbital resembles the electron density distribution of a pi bond in valance bond Theory. We call this orbital the pi2p Orbital. The corresponding anti-bonding Orbital has an additional node between the nuclei perpendicular to the inter-nuclear axis and is called the pi*2p. 
2py. The only difference between the 2py and 2px Atomic orbitals is a 90° rotation about the inter-nuclear axis. Consequently, the only difference between the resulting MO’s is a 90° rotation about the inter-nuclear axis. The energies and the names of the bonding and anti-bonding MO’s obtained from the combination of the 2PY AOs are identical to those obtained from the combination of the 2Px AOs.
The degree of mixing between two orbitals decreases with increasing energy difference between them. Mixing of the 2S and 2PZ orbitals is there for greater in B2, C2, and N2 than O, F, and Ne. Dismissing produces a change in energy ordering for the pi2p and sigma2p Molecular orbitals.
The reason for the Difference in energy ordering can only be explained by going back to our LCAO-MO model. We assumed that the MOs that result from second period AOs could be calculated pairwise. In other words, we took the linear combination of the 2S from one atom with the 2S from another, 2pz from one Adam with 2pz from the other, and so on.
Molecular Orbitals of H2:
Consider the simplest molecule, H2. We construct MOs as linear combinations of the 1S atomic orbitals on each H atom to form 2 new MOs
HA-HB
-The electron density is disposed with cylindrical symmetry about the bond axis, So these are Sigma MOs.
Both atomic orbitals are a circle with + phase.
H had 1 e- in 1s orbital = circle.
In phase —> Constructive, there’s a wave, Amplitude increases. Out of phase —> Destructive, no wave
Subtract: (Destructive interference)
1+ phase & 1- phase.
(Adding + and - = -)
Imagine two circles What’s the dotted line between them
|<— something between them. line is .|a node.
O O
|
-Nuclei No longer have electron density between them = the repel one another.
-Antibonding a Orbital MO = No electron density between the two Atom.
-No bond
-Electrons could be anywhere in the circles.
-1A — -1B
-sigma*1s
-Hire an energy compared to original atomic orbitals = unstable.
Add: (Constructive interference)
-A circle with two dots on each side.
-sigma1s
-Electron is between the two nuclei equalling Sigma bond, therefore Sigma molecular bond.
-Combination of 2 1S Orbitals
-Is a bonding molecular Orbital = Build up of electron density between atoms = form a bond
-Bonding MO Lower in energy compared to the original atomic orbitals = more stable. 
MOs Of second-period orbitals
•For diatomic molecule of the second-period Elements, we must now combined 2S and 2P orbitals.
-The 2S Orbitals combine to form Sigma2s and Sigma2s orbitals
-The 2B orbitals combine to form sigma2p and sigma2p Orbitals (from end to end overlap), and pi2p and pi2p orbitals (from side to side overlap)
•MOs for 2s orbitals are the same as 2p orbitals
•The more notes there are the more likely there’s going to be ABOs
BO = Bonding Orbital
ABO = Antibonding Orbital
Reference lecture slides 70 to see shapes.
All going to bond side to side = 4 MOs
Add them = 2 BOs
Subtract them = 2 ABOs
Sigma2s density between nuclei, no nodes
Sigma2s No electron density between nuclei = 1 node.
Pi2p no nodes
Pi2p 1 node
-End to end gives Sigma bonds
-Side to side gives Pi bonds
Sigma2p Lower than Pi2p. Because more stable because more electron density between nuclei. Because end to end is more efficient.
-Depending on how we combined Orbitals will change the amount of electron density between nuclei.
Why the splitting of energy between bonding and aunt Bonding Emmey Home is greater for Sigma 2P and Sigma* 2p vs. Pi2p and pi*2p?
-Related to end to end and side to side. How adding and subtracting (AOs)?
- pi- overlap is less effective (weaker side to side internuclear) then sigma overlap
-How are you can relate energy of M02 number of nodes?
-more nodes —> more depletion of electron density
The MO => less stable (higer in E)
-Interestingly, the Sigma 2P and pie 2p MOs Are reversed in energy for diatomic molecule of the early elements in this period
-The expected energy ordering is observed for the diatomic molecules of the later elements
Highest occupied molecular Orbital = HOMO. Highest MO that has electrons in it.
Lowest unoccupied molecular orbital = LUMO. Highest MO that doesn’t have electrons in it
Two different patterns for diatomic second-period Elements
|
|
|
E
____
Sigma2p
____ ____
Pi2p
__ __ __ __ __ __
2p 2p
____
Sigma2p
____ ____
Pi2p
____
Sigma*2s
__ __
2s 2s
____
Sigma2s
For B2, C2, N2, (Early in period)
E(pi2p < E sigma2p)
\
____
Sigma2p
____ ____
Pi2p
__ __ __ __ __ __
2p 2p
\
____ ____
Pi2p
____
Sigma2p
____
Sigma*2s
__ __
2s 2s
____
Sigma2s
For O2,F2 (late in period) E(sigma2p < E pi2p)
\
