doing my best to understand quantum wave functions without any advanced math knowledge
Quantum wave function:
Quantum = smallest piece of a physical property that can be used during a particle interaction. E.g. if particle interaction is electron in atom dropping down an energy level, it emits a photon, which is the smallest piece of the physical property of energy that could be used in this interaction.
Wave = disturbance that transmits energy through space or a material medium; anything with a back-and-forth shape
(Mathematical) Function = a "machine" that you put numbers into to get an output that depends on the input (function = a mathematical relationship showing that some measurements depend on other measurements)
Wave functions = function that looks wavy, so it's written using sin(x) or cos(x) because those look wavy
Quantum wave function is a wave function for quantum things; it shows a relationship (specifically, a dependence) between two measurements that has a wavy pattern and is about tiny particles.
Input = measurement about a particle (e.g. position, momentum, etc.)
We can't know anything with certainty in quantum mechanics but we can predict the probabilities of what those properties might be.
Output of other wave functions is usually something else that we can measure directly (like a distance or field strength). But the output of the quantum wave function doesn't have any physical meaning. However, the Born rule says the square of the quantum wave function gives us a probability distribution for the property we want to measure.
E.g. if we want to measure the position of a 1D particle in a box (the particle moves back and forth along a straight line within the box), the square of the quantum wave function gives us some idea of its position by telling us where it's likely to be (e.g. it might tell us that the particle has a better probability of being found in the center of the box than at the edges). It gives us a probability per unit length measured along the 1D box.
Height of each "bar" is the probability density at that location. There's so many possible locations for the particle that it looks like a completely shaded area equal to 1 or 100% because there's a 100% chance that we will find the particle somewhere in the box because we put it there.
If you want to find the probability of the particle being found between a specific range of positions, find the area between those two points:
Shaded area = probability. Some areas have higher probability than others.
If you're interested in other properties of the particle, change your quantum wave function's inputs to that property. E.g. instead of inputting position, input momentum if you want to find the probability of the particle having certain momentums. You can do this for energy, linear momentum, angular momentum, any property of the particle you want.
E.g. probability densities for electron in hydrogen atom. 1st image: input = distance of electron from nucleus, 2nd image: input = momentum of electron
today is a lazy day but i really need to clean up these notes for future me...so here i am, pt. 2 🙃
also tbh i don't understand MO theory as well as i'd like to because i don't understand the math of wave functions. but i don't need to for this course and i need to keep the pace so i'm gonna save that for later...
Ok, so this second, more accurate theory of how covalent bonding works says that orbitals aren't localized. They aren't fixed in position. So you could take any atomic orbital, combine their wave functions and get a bond. It doesn't have to be 2 atomic orbitals, 1 from each atom combining as was in VB theory. MO theory calls these bonds "bonding molecular orbitals". So you can have sigma molecular orbitals for single bonds and pi molecular orbitals for double or triple bonds, but more on that later in the post. There is no hybridization in MO theory.
Always always go back to the idea that the square of the electron wave function is a probability distribution telling us where electrons are most likely to be and the shape of the wave function is a spherical harmonic, which is the shape of orbitals. So orbitals are wave functions aka probability distributions aka NOT actually electrons.
With this in mind, MO theory says that molecular orbitals are probability distributions telling us the likelihood of bonds forming (...I think?). MO theory also says that we can combine orbital wave functions constructively and destructively. And when we do that, we get the same number of molecular orbitals as we had atomic orbitals. Half of those molecular orbitals experienced constructive interference, creating bonding molecular orbitals, and the other half of those molecular orbitals experienced destructive interference, creating antibonding molecular orbitals.
Hey, here's a piece of jargon from the textbook that you might need to know (idk really): we combine atomic orbital wave functions linearly to create molecular orbitals. So we can say molecular orbitals are created by taking linear combinations of atomic orbitals (LCAO). This is what we did in VB theory with just 2 atomic orbitals. And this is what we're doing in MO theory with more than just 2 atomic orbitals.
So when we combine atomic orbital wave functions, the probability of them destructively interfering with each other equals the probability of them constructively interfering with each other.
When atomic orbitals constructively interfere with each other, they create bonding molecular orbitals, which are lower in energy than the constituent atomic orbitals.
Another example with two 2p_z orbitals that are in phase → sigma 2p bonding molecular orbital (yeah the diagram's not precisely labelled can we ignore that for now):
When atomic orbitals destructively interfere with each other, they create antibonding molecular orbitals. Antibonding molecular orbitals are the bonding molecular orbitals except with a node in the middle of it. They are higher in energy than the constituent atomic orbitals because where electrons want to be (i.e. right in between the two nuclei), they can't be because of that middle node.
Another example with two 2p_z orbitals that are out of phase → sigma 2p antibonding molecular orbital aka sigma 2p star:
sigma MOs are bonding orbitals with electron density concentrated along internuclear axis (basically sigma bonds of VB theory)
sigma* MOs are antibonding orbitals along the internuclear axis with a planar node perpendicular to the internuclear axis b/t the 2 atoms
Here are some pi bonding and antibonding molecular orbitals. They're created from p_x orbital + p_x orbital or p_y orbital + p_y orbital. The diagrams show p_y:
pi MOs = bonding orbitals with electron densities above and below the internuclear axis, not on it (basically pi bonds from VB theory)
pi* MOs = antibonding orbitals with electron densities above and below the internuclear axis, not on it, WITH a planar node perpendicular to the internuclear axis
We call these molecular orbitals sigma and pi like in VB theory with sigma and pi bonds. But the difference is now we have sigma bonding molecular orbitals AND sigma antibonding molecular orbitals, and pi bonding molecular orbitals AND pi antibonding molecular orbitals. We denote the antibonding molecular orbitals with an asterisk *. Electrons can go in either the bonding molecular orbital and be lower energy than when they're in atomic orbitals or the antibonding molecular orbital and be higher energy than when they're in atomic orbitals.
Molecules wouldn't form if forming bonds raised the energy of the system (the atoms of the molecule), so when we say a "bond forms", we mean the bonding electrons are found in the bonding molecular orbitals and they aren't completely cancelled out by antibonding electrons in the antibonding molecular orbitals. When electrons don't contribute to bonding, it's because some of them are found in the antibonding molecular orbitals, which cancel out the energy decrease caused by electrons in the bonding molecular orbitals. When this happens for an entire orbital, it's called a nonbonding molecular orbital. This is easier visualized in molecular orbital diagrams. Btw, molecules only have molecular orbitals, no atomic orbitals. All the constituent atoms used their atomic orbitals to form molecular orbitals.
Here are some molecular orbital diagrams:
On the sides, we show the electrons b4 bonding in atomic orbitals (on 1 side is 1 atom and on the other side is the 2nd atom). In the middle, we show the electrons after bonding in molecular orbitals.
To fill in these diagrams, we follow the electron configuration rules: Aufbau process/principle (fill lowest energy orbitals first. this includes molecular orbitals: so first you fill the bonding molecular orbitals, then you fill the antibonding molecular orbitals if you have electrons left), Pauli exclusion principle, and Hund's rule.
^^ is MO diagram for H2 at ground-state. If you shine light of the right frequency on the H2 molecule and excite an electron up to the sigma 1s antibonding molecular orbital, the two cancel each other out and there's no net bonding because the energy difference for going up to the antibonding molecular orbital from the atomic orbital and the energy difference for going down to the bonding molecular orbital from the atomic orbital is about the same. Thus, the right frequency of EMR would split the H2 into individual H atoms.
From MO theory, we get the bond order formula:
More MO diagrams:
sigma p is higher energy than pi p because sigma p has unused electron densities that try to pull apart the bond. so sigma p is not as good a bond as pi p if "good" means lower energy.
MO theory can also tell us whether a molecule is paramagnetic or diamagnetic:
Paramagnetism - some electrons in a substance are unpaired so their spins don't cancel out and the substance is attracted in a magnetic field
Diamagnetism - all electrons in a substance are paired so their spins DO cancel out and the substance experiences a weak repulsion in a magnetic field
there's no sigma bonds in C dimer, which is held together only with pi bonds, which contradicts VB theory where hybridization always predicts the 1st bond in a multiple bond molecule is a sigma bond.
In O2's Lewis structure, O2's electrons all look paired, so we might think that it's diamagnetic, but it's actually paramagnetic and MO theory shows this as there's 2 unpaired electrons in the pi 2p antibonding molecular orbital.
MO diagrams have sigma p higher being higher energy than pi p for most molecules made of only n = 2 elements (e.g. N2, C2, B2, NO, etc. - single, double single, double single), but this is flipped for O2 and anything to the right of it. This is because as you move right on the periodic table, core charge increases. The higher positive charge of the nucleus pulls the orbitals closer and closer together. This causes s orbitals and p orbitals to mix a little better, creating more orbital overlap and smaller electron densities that counteract the bond, which lowers the energy of sigma p bonds below pi p.
Ok, so if you look at how we've been naming the MOs, it doesn't seem to add up with the idea behind MO theory that all atomic orbital in all atoms of the molecule contribute to MOs - it still looks like only 2 atomic orbitals are contributing. That's because the MO diagrams and the MO names are overly simplified. MOs are generally named by the predominant contributing orbitals, but there are also very small contributions from other orbitals that make the real MO. Because of this, computer programs determine the best combination of atomic orbitals (LCAO) to create each MO. So calculations using MO theory like calculations for bond energy require computer programs.
MO theory tells us that electrons are in a more stable arrangement when in bonding molecular orbitals aka bonds than when they're unpaired in atomic orbitals. From this, we know that when bonds form, energy is released. Chemical reactions are basically just reactant bonds breaking to form product bonds. This has to do with the kinetic energy of the atoms/molecules in the reaction aka thermal energy. Thus, there is a transfer of thermal energy aka heat in chemical reactions due to bonds forming and breaking. When this occurs at constant pressure, this heat is called enthalpy. (And since we live in a constant pressure world, not a constant volume world, heat at constant pressure aka enthalpy is more useful than heat at constant volume.) So we can use enthalpy of reaction to approximate bond energies in our constant pressure world.
So in summary, MO theory tells us:
Bonds = bonding molecular orbitals and antibonding molecular orbitals exist and destabilize bonds.
Molecular orbitals are a mixture of all orbitals in atoms contributing to the molecule, but we name the molecular orbitals after those atomic orbitals that contribute the most to it.
Whether a molecule is paramagnetic or diamagnetic
Accurate bond orders (sometimes they disagree with Lewis structures created according to Lewis theory)
Certain bonds are higher energy than others due to how big the electron densities that don't contribute to the bond are (e.g. sigma p is usually higher energy than pi p because sigma p has bigger electron densities that don't contribute to the bond compared to pi p. This is unless there's s-p mixing, which lowers sigma p's energy below pi p)
Useful video explaining MO theory here. The annotated screenshots came from there.
VSEPR stands for valence shell electron pair repulsion theory. The initial idea was that electron pair(s) in the valence shell repel each other, affecting the molecule's shape. But we now know this doesn't apply just to electron pairs. You could also be talking about a single electron if you have an odd number of electrons, double bonds where the bond = 2 pairs of electrons, or triple bonds where the bond = 3 pairs of electrons. This region of space occupied by the electrons causing repulsion = the domain, which is not necessarily the same thing as orbitals. Either way, we live in a 3D world, so VSEPR theory giving us 3D molecular shapes gives us more info than Lewis structures can.
What VSEPR tells us that Lewis structures cannot:
If two structures superimposable, they're the same molecule. Lewis structures don't show this (you may have different Lewis diagrams for the same molecule). Say you have this compound CH2ClF and you move the Cl and F in the Lewis structure. It's still the same molecule when you look at it in 3D because you can rotate the molecule in a certain way and see that the molecules represented by the two Lewis structures superimpose.
If two structures are NOT superimposable, they're not the same molecule. Lewis structures don't show this either (you may have 1 Lewis diagram for different molecules). Say you have the compound CHBrClF. From the Lewis structure, you can't tell that there are different ways you can structure this molecule in 3D space. If you were to look at it in 3D, you'll see there's no way to rotate the molecules and have the two structures be the same. (This is why VSEPR is really useful for organic chemistry because you have lots of isomers - stuff with the same chemical formula but different structure like this. This kind of isomer in particular is called an enantiomer.)
Radicals are atoms (no charge), molecules (no charge), or ions (has charge) that have at least one unpaired valence electron. This makes radicals generally very highly reactive.
This unpaired electron(s) means the radical has an odd number of electrons, so when it comes to drawing Lewis structures, you'll never be able to make the model match the real molecule no matter how many models you try where all the electrons are paired. You must have an electron(s) unpaired.
E.g. NO2, which is a neutral molecule.
In option 1, sum of F.C. = charge of molecule = 0.
In option 2, sum of F.C. = -1 + 1 = charge of molecule = 0.
Following the Lewis structure rules, option 1 should be the correct option because its F.C. = already 0. But experimental data says option 2 is the correct one. So our Lewis structure rules have broken down and we need a better model for molecular structure.
Resonance
Many molecules have electrons that are localized in simple orbitals as bonds or lone pairs, etc., and exist primarily in their ground-state electron configurations. These are well-represented by single Lewis structures.
Other molecules have delocalized electrons. These delocalized electrons are not associated with a single atom or covalent bond, so they're free to move around. Those delocalized electrons can form lone pairs or contribute to double or triple bonds. So you can have multiple possible ground-state Lewis structures where certain lone pairs turn into a double/triple bond, certain double/triple bonds turn into lone pairs, or where the double/triple bond seems to move around on the molecule. Each Lewis structure will still be the same molecule with the same structure, the same total valence electrons and overall charge. So each single Lewis structure is equally correct. So each of these single Lewis structures is a resonance structure of the molecule. This is one way you could create resonance structures.
pi bond = double or triple bond
And you can't say that the molecule was just rotated to create these different resonance structures because electrons, being much less massive than the atomic nucleus, move around MUCH faster than the nucleus, so it's as if the atoms of the molecule didn't move at all while the electrons have so much time to create these different configurations.
The molecule's actual structure is a resonance hybrid - "A weighted average of all significant resonance contributors depicting the true electronic structure of a molecule".
2 interesting thing about resonance structures:
different bond orders have different energies and these energies can be seen in absorption spectroscopy. Single bonds have different energies from double bonds and double bonds have different energies from triple bonds. If these bonds were fixed, you would see absorption lines appearing in different areas of the spectrum representing the different bond orders' energies. But you don't see that for molecules that display resonance. Instead, you see just one absorption line with an energy in between those of the typical bond orders. E.g. if your molecule looks like it has moveable single and double bonds according to the single Lewis structures, the absorption line observed would show a bond with energy in between that of single and double bonds. This means that a molecule displaying resonance doesn't actually have the bond orders described in the single Lewis structures but bonds with energies somewhere in between. So the more correct way to draw Lewis structures for molecules displaying resonance of this kind would be to draw their bonds with a dashed line to indicate its bond energy is somewhere in between those of the 3 typical bond orders. E.g. This is how you would draw the Lewis structure for the resonance hybrid of sulfate (SO4^2-)
Also, if you keep moving the bonds, you keep changing the formal charges on individual atoms (the sum of these formal charges always equals the overall charge of the molecule, but the atoms on which those formal charges occur keeps changing).
So you end up with this concept of average formal charge and average bond order:
avg BO = 1 and 1/2 means that there's always 1 bond joining the SO pair and 1/2 the time, there's a second bond joining the same pair:
Another way you could create resonance structures is if the molecule forms higher energy structures (you know they're higher energy because the formal charges are larger). These would also count as resonance structures. However, because high-energy configurations don't last long due to the first law of thermodynamics, they don't contribute as much to the overall structure, so we don't count them in the avg FC or avg BO calculations.
So molecules that display resonance either have multiple possible Lewis structures that are each equally correct or electrons that move to higher energy levels, creating Lewis structures with higher-energy configurations.
Electron-deficient resonant structures
We see in the sulfate example that average bond order of 1 and 1/2 is greater than the actual bond order of a particular bond in the resonance structure where the resonance is occurring. This is the case of most resonance structures because typically, 1 bond stays in place throughout and then a second or third bond moves from place to place.
But when there aren't enough electrons for normal bonding to occur, resonance structures can have a bond order that's less than 1. This happens because at least one of the resonance structures completely lack that bond. The missing bond means compounds that experience this are less stable than other molecules that display resonance.
E.g. B2H6 - each B can only form 3 bonds:
Bond order is a way of measuring bond intensity and stability. The higher the bond order, the more stable the bond is, the harder it is to break. Having a fractional bond order does NOT mean that the bond only exists for a fraction of the time, e.g. bond order = 1/2 doesn't mean the bond exists for only half the time. This is a wrong conclusion to gain from Lewis theory.
This particular bond bridging the 2 borons is an electron-deficient 3-center bond, particularly a three-center two-electron bond (3c-2e bond) because it involves 3 atoms (2 B's and 1 H) but only 2 electrons. Sometimes these 3c-2e bridge bonds are called a banana bond because it's shaped like a banana (bent), and you show this in the Lewis structure for the resonance hybrid.
There are other examples of this type of bond occurring in exact chemical analogues (i.e. __2H6) made of other column 3 elements like Al, Ga, etc., but they aren't as stable, sometimes so unstable that they quickly reform into other, more stable compounds.
There are stable analogues to B2H4 though, e.g. Al2Cl4 and it also uses electron-deficient three-center bonds.
Lewis bases and Lewis acids
So acids donate protons and bases accept them. Lewis acids ACCEPT electron pairs, while Lewis bases DONATE electron pairs. These are not mutually exclusive statements.
This donation and acceptance of an electron pair(s) creates a covalent bond between 1 species that has an extra electron pair and a species that lacks an electron pair.
Hydrogen bonding
Hydrogen bonding doesn't actually form chemical bonds, it's just a strong attraction.
It occurs when you have 1 molecule where H is bonded to a small, highly electronegative atom and another highly electronegative atom (may or may not be part of another molecule) that has lone pairs available.
When H is bonded to a highly electronegative atom, the highly electronegative atom pulls the bonding electrons towards itself, leaving the H with a partial positive charge and the highly electronegative atom with a partial negative charge. Expose the H with the partial positive charge to a highly electronegative atom with lone pairs and the two attract each other.
Draw the structure of the molecule to satisfy the normal or hypervalences of the elements. To do that:
a) Count total number of valence electrons in compound. If compound has a negative charge, add an electron to the total for every negative charge. If compound has a positive charge, subtract an electron from the total for every positive charge.
b) In general, put the least electronegative atom that is NOT hydrogen in the center of the diagram - more electronegative atoms or H are terminal atoms (atoms on the outside).
c) First, assume single bonds. Subtract the electrons used from the total.
d) Assign leftover electrons to the terminal atoms. Subtract the electrons used from the current total number of unused electrons.
e) If needed, assign any leftover electrons to the central atom. If the central atom has an octet or exceeds an octet, you're usually done. If the central atom does NOT have an octet, create multiple bonds until you do.
2. If you must use a valence that's not a normal or hypervalence for an atom, assign a formal charge to it by comparing its actual valence state with the valence state of atoms from neighboring columns in the periodic table. Assign formal charges on all other atoms by the same method.
In general, negative formal charges should appear on the more electronegative atom.
It's unlikely that formal charges of the same sign will appear on atoms directly adjacent to each other.
3. If the formal charge on any atom has a magnitude >1, try to rearrange pairs of electrons to lower the formal charges, keeping in mind valence and hypervalence states.
It's important to keep the formal charges as low as possible b/c real molecules aren't very stable if they have high localized charges.
4. Sum the formal charges. If the structure is right, the sum of the formal charges = the overall charge on the molecule.
5. Assign lone pairs as needed, following the lone pair numbers in the table of valences and hypervalences:
If you can create >1 valid Lewis structure for a molecule, the one with the smallest formal charges is the best one.
FINAL CHECK: count the electrons in the molecular structure. they should = total valence electrons of molecule that we calculated in step 1 + the overall charge on the molecule.
You can use all dots to represent lone pair electrons AND bonding pair electrons, lines to represent bonding pairs and dots for lone pairs, or use lines for both bonding pairs and lone pairs.
^^ total valence electrons + charge = 2 + 4 + 3(6) = -2 + 4 + 18 = 24 electrons, and there are.
^^ total valence electrons + charge = 0 + 2(6) = 12 electrons, and there are.
formal charges make it seem like C is more negative, when in reality, O, being more electronegative, pulls the bonding pairs closer to it, creating a polar covalent bond with most of the negative charge closer to O. and it's this that brings the actual atomic charge closer to 0 for each atom. this is a shortcoming of the Lewis dot model.
For all the examples ^^, we know these are not just valid Lewis structures but also the correct ones because the formal charges on each atom all have a magnitude of 1 at most.
More complex example:
How you'd draw Lewis structures for ionic compounds:
Normal valence and hypervalent states and why we need formal charge
Intro to bonding
Chemical bonds are strong forces of attraction, specifically electrostatic forces, between atoms - follows Coulomb's law. Like charges repelling and opposite charges attracting explains what makes a stable bond and what doesn't.
2 main kinds of bonds:
Ionic bonds: electrons are transferred from 1 atom to another to form ions → the oppositely charged ions (cation lost electron to what is now an anion) are electrostatically attracted to each other by Coulomb's law. No bonds are 100% ionic. Point of ions forming is to obtain a noble gas electron configuration, which is more stable.
Ionic bonds form because metals have low ionization energies and low electron affinities, so they tend to form cations to achieve a full octet.
Non-metals have high electron affinities and high ionization energies, so they tend to form anions to achieve a full octet. Down the group, atomic radius increases, so even if it's a non-metal, the big atomic radius means lower electron affinity, so it's less likely to want to gain electrons to form an anion. Compounds formed from such non-metals are probably not gonna be stable.
Covalent bonds: electrons = shared so each atom achieves a full octet. Usually covalent bonds follow the octet rule. Mostly happens between non-metal atoms.
Intro to Lewis structures & the normal valence state
Lewis dot structures are a simple model of how bonding works, explaining simple bond behaviors and simple molecular shapes and geometries. Lewis structures only contain valence electrons because we assume the inner core electrons aren't involved in chemical bonding since they're held tightly to the nucleus and not involved in electron sharing or transfer.
Valence is the number of bonds an atom can have in a molecule. Since Lewis structures deal with valence electrons, we need to know the valence of every atom in a molecule if we want to create a Lewis structure of it.
If we were to draw the ground-state Lewis dot structures of the n = 2 elements in groups 1A-8A, we'd get:
The ground-state Lewis structures correlate to the ground-state electron configurations for these elements (if we're just looking at the valence shells of those elements).
But in this table of normal valences, we see that elements in groups 1-4 have valences that match the group number, but elements in groups 5-8 have valences that go from 3 to 0. This is because when atoms form bonds, the electrons don't always stay in the ground-state configuration. Atoms move and bang around, get energized, and when the atom forms a bond with another, the electrons in some atoms like Be, B, and C (group 2, 3, and 4) are in a more stable configuration when they're unpaired. Which orbitals these unpaired electrons are found in is the topic of this post. So with this reality, we can say that the valence of an atom = the number of unpaired electrons in that atom. An atom can only form as many bonds as it has unpaired electrons. So the Lewis structures for these elements when they're in their normal valence state are:
We can split up the lone pairs in Be, B, and C because n = 2 has 4 orbitals (2s and 3 degenerate 2p orbitals) into which we can put electrons without spending too much energy. We can't split lone pairs in N, O, or F because we're already at the 4 orbital limit so the only option would be to move some electrons into orbitals in n = 3 which would cost too much energy. What counts as too much energy? The energy put into making bonds, into moving electrons around to form their normal valence state, must be returned by the bond forming. If too much energy is put into forming the valence state, not all of it may be returned by bond formation.
These n = 2 elements tend to follow the octet rule, which is the simplest view of bonding: all atoms tend to lose or gain electrons to achieve a valence (outermost) shell of 8 electrons. It was called a "rule" because most atoms in the n = 2 and n = 3 periods of the periodic table want to form a valence shell that had 8 electrons. But there are many ways of breaking the octet rule, so in reality it's more like a guideline than a rule.
Some ways to break the octet rule include:
Duet rule: atoms that only have 1s orbital occupied while higher energy orbitals aren't involved in the atom's chemistry, i.e. n = 1 elements H and He
Some boron compounds - boron has a normal valence of 3 with no lone pairs (e.g. BF3 is a very stable molecule in which boron has 6 electrons). Boron can't complete its octet and remain electrically neutral: in BF4, fluoride is attracted to the empty orbital in B → the fluoride shares one of its lone pairs with the boron → B and every F has a full octet and there's a net negative charge on the molecule. In other words, when B fills its octet in a compound, it becomes a polyatomic ion that can form ionic compounds like NaBF4
Expanded valence aka hypervalence → hypervalent states: while N, O, F, and Ne with valence shell n = 2 can't split their lone pairs further because it's too much energy to move the would-be unpaired electrons into the n = 3 energy level, elements in rows 3 and onwards have d orbitals. Having more orbitals in an energy level means more lone pairs can be split → more unpaired valence electrons and it won't necessarily be too much of an energy cost to do it.
Here's a more concise and complete version of the table of normal and hypervalent states. Hypervalent states only occur when atoms have extra electrons in lone pairs that can be split up to make extra bonding sites. This is why you don't see hypervalent states for groups 1A-4A in the table. Regardless of how far down you get in these groups, even though they have the extra unfilled orbitals in their valence shells, they don't have enough valence electrons to fill all of them. This table gives us a cheatsheet for drawing pretty much any Lewis structure.
That being said, these are the goals for drawing Lewis diagrams for covalent molecules and ionic compounds:
Goals for every Lewis diagram:
Have the correct number of total valence electrons (v.e.)
Each atom has the correct number of valence electrons for that atom
Ensure the way electrons are shared fulfills the octet rule for every atom unless it's an exception (see above for the exceptions)
To make sure we fulfill these goals, we need to keep track of the electrons and the easiest way to do that is to make assumptions about the nature of the bonds (even if they aren't true in reality). There's 2 ways to do this and both use the notion of core charge:
Formal charge (this is the one we use for Lewis structures) - assumes 100% covalent bonds → each element gets 1 electron of each bonding pair. Formal charge is the difference between the number of electrons in the isolated, neutral atom and the atom when it's bonded to the other atom(s).
There's 2 ways to figure out the formal charge on each element in a molecule: mathematically and intuitively (i.e. using the table of valences and hypervalences). Intuition is, ofc, much faster.
Intuitive method says that if the atom's valence and lone pair numbers match with a cell in their proper column of the table of valences and hypervalences, the atom has no charge. If the element isn't in its normal valence or hypervalence states, then you can assign a formal charge to the atom by comparing it with the valence states of neighboring atoms.
Number of bonds an atom forms is related to its formal charge. N with formal charge of +1 acts like a group 4 element in its normal valence state: instead of N's normal valence state of 3 bonds, it can actually form 4 bonds with F.C. of +1
You can think of it as:
If the sum of the formal charges = the overall charge on the species (i.e. the molecule), the Lewis structure is correct.
Oxidation number (this is used in redox chemistry) - assumes 100% ionic bonds → both electrons in the bond "go to" the more electronegative element in the bond.
to find the oxidation numbers for atoms in a compound:
figure out which atoms are more electronegative, so you can figure out which one gets the bonding electrons. (e.g. Cl is more electronegative than H, so the bonding electrons go to Cl and Cl becomes an "ion" [not really, but for the sake of oxidation numbers, that's what we assume])
calculate oxidation numbers
oxidation # for more electronegative atom = core charge aka # of v.e. in neutral, isolated atom - # of electrons in lone pairs - # of bonded electrons
oxidation # of Cl = 7 - 6 - 2 = -1
oxidation # for less electronegative atom = core charge aka # of v.e. in neutral, isolated atom - # of lone pairs
oxidation # of H = 1 - 0 = +1
Charges determined by oxidation number and formal charge don't reflect reality except in perfect diatomic molecular elements where the charge on each atom in the molecule is truly 0.
When an atom is in an excited state, its electrons move to a higher energy level.
When an atom is in the ground state, its electrons are in the lowest possible energy levels they could be in.
So the goal of ground-state electron configurations is to have all electrons in the lowest energy state possible (e.g. while 3s^1 is a valid electron configuration for an H atom, it's not the ground-state electron configuration because it's not the lowest possible energy level the electron could be in).
3 rules to follow for ground-state electron configurations (for the most part):
Pauli exclusion principle: 2e per orbital, and paired e have opposite spins because no 2 electrons in the same orbital can have the same set of quantum numbers
Aubfau process/principle: fill lowest energy subshells 1st (see pic below to help you remember w/c ones are lowest energy); always follow Aufbau w exception being: where Hund's rule stabilization occurs, it overrules Aufbau
energy of levels generally increases as n and l increase, and as n increases, the differences b/t levels becomes smaller so higher l levels of one n level are often almost the same or even a little higher than the lower l levels of the next higher n level (e.g. 3d and 4s, 4d and 5s, 5d and 6s and 4f)
To write electron configurations: first number = shell number (n), letter = subshell type, superscript is total number of electrons in the subshell
Noble gases have full subshells so to shorten electron configurations, you can use the nearest noble gas to "fill in" the full subshells you DO have and then write out the remaining electrons as normal
Hund's rule: the most stable (lowest energy) state for incompletely filled subshells is the one with the highest total spin (opposite spins cancel each other out). This means we want electrons to occupy degenerate orbitals one at a time with the electron spins parallel (all the same direction). Then, after all degenerate energy levels are half-filled, we add any additional electrons that occupy the same orbitals but with spins opposite from the first ones to follow Pauli exclusion. Hund's rule also means we want half-filled subshells where it's easy to have them and full subshells where it's easy to have them because such shells are spherically symmetrical which means they're more stable - "easy" meaning takes the least effort (i.e. lower energy so more stable). This is what we mean by Hund's rule stabilization.
Hund's rule stabilization means you move electrons to make d^4 into d^5 and to make d^9 into d^10. Aufbau overrules Hund's rule stabilization when dealing with s → p because there's a big energy difference between s and p. Hund's rule stabilization overrules Aufbau when dealing with subshells that have a small energy difference between them e.g. 3d and 4s
As you increase number of energy levels (increase n aka period number), the energy levels are more and more closely spaced (n = 5 and above), causing many slight deviations so there's no rule for them - there are more exceptions than rules in those cases...
Can also write electron configurations as box diagrams
arranging periodic table into blocks, we see that as you go left to right, top to bottom, it follows the increasing energies of subshells w/c occur due to increasing amounts of electron shielding (e.g. 4s → 3d)
n = row number
columns are grouped by l (b/c it indicates s, p, d, or f subshell)
s block elements have outermost electrons in s subshell
p block elements have outermost electrons in p subshell
d block elements have outermost electrons in d subshell
f block elements have outermost electrons in f subshell; f-block elements = lanthanides and actinides and they actually insert themselves here:
rows aka periods = principal quantum number n
Periodic table trends = based on Coulomb's law:
We can't calculate r exactly because of quantum mechanics, so we need to use a mean r value to calculate force of attraction between nucleus and an electron.
Core charge = change experienced by outermost electrons of an atom, assuming the inner electrons shield them 100% from the nucleus and outermost electrons don't shield each other at all.
Ignoring transition metals, core charge = group number (+1 to +8).
In reality, orbitals of outer electrons somewhat penetrate inner orbitals so effective shielding isn't 100% and electrons in the same shell can partially shield each other somewhat. So the actual amount of shielding and effective nuclear charge depends on interactions between different orbitals (e.g. s orbitals have more electron density near or on the nucleus than a p orbital with the same n, so s orbitals shield the nucleus better and is less affected by shielding from other orbitals than p). The actual amount of shielding isn't the same as the amount of shielding assumed in core charge calculations, and thus, the effective nuclear charge does not exactly equal core charge.
Atomic radii
Core charge increases as you go left to right w/c means 1 of the q's in Coulomb's law is increasing, assuming everything else is the same; core charge = one's place of group #. This means force of attraction between outer electron and nucleus increases as you go left to right because the higher the core charge, the more strongly the nucleus pulls the outer electrons towards itself. This means atomic radii decrease from left to right.
As you go down the periodic table, atomic radii increase because you increase in number of energy levels with each period (n ↑).
So largest atomic radii are at the bottom-left of the table.
Ionization energy
Ionization energy = amount of energy (ΔH) that must be absorbed to remove an electron from an atom, to turn the atom into an ion (M → M+ + e-)
We tend to measure energy in enthalpy, so energy = ΔH
The more loosely an atom holds its electrons, i.e. the more electron shielding there is, and therefore the larger the atomic radii, the lower the ionization energy because it's easier for an electron to be removed.
The more tightly an atom holds it's electrons, i.e. the less shielding their is, the smaller the atomic radii, the higher the ionization energy.
So the highest ionization energies are at the top-right of the table (except noble gases because they have full valence shells).
First ionization energy - an outermost electron is removed first
Second ionization energy - a 2nd electron is removed after the first, w/c is always higher than the first because there's greater attraction to nucleus with fewer electrons in the way
You can also have third, 4th, etc. ionization energies, it just depends how many electrons in the atom you have that you want to remove
Sometimes the difference b/t 1st and subsequent ionization energies is small, sometimes it's a really big difference. Difference is really big when you go from outer electrons to core electrons. Difference is small when you're just dealing with outer electrons
Electron affinity
Electron affinity is the amount of energy (ΔH) released when adding an electron to an atom (M + e- → M-)
All atoms have negative electron affinity except noble gases, so they all can take more electrons except for noble gases, but elements with the highest electron affinity are in the top-right of the periodic table (they tend to form anions)
Metals tend to have low ionization energy and low electron affinity, becoming cations
Non-metals tend to have high ionization energy and high electron affinity, becoming anions
So metals + non-metals → ionic compounds
Metalloids/semimetals can act metallic or non-metallic depending what they're paired with
Electronegativity
Electronegativity is how likely is an atom that shares an electron pair w/ another atom going to attract that pair to itself vs attracted away from it to the other atom and where the electrons spend most of their time? When high electron affinity elements form a covalent bond, they are more likely to hog electrons aka have high electronegativity.
Reactivity
group 1A / alkali metals → lose 1 electron, often form salts (react w/ halogens), reactivity increases as you go down the group
group 2A / alkali earth metals → lose 2 electrons, tends to react with atoms that gain 1 or 2 electrons
group 3A → tend to form 3+ ions except B b/c that would make it very unstable (instead, B forms covalent bonds)
group 4A → C and Si both form tetrahedral structures but Si can have more complex molecule geometries b/c it has d orbitals and tends to lose electrons like metals (hence, it's a metalloid), while C can lose or gain electrons
group 5A → N and P are non-metals forming 3- ions, As and Sb are metalloids so can go either way, Bi is a metal that tends to lose electrons b/c it's a large atom so low ionization energy
group 6A / chalcogens → O, S, and Se are non-metals that can form 2- anions, Te is a metalloid, Po is a metal that tends to lose electrons b/c it's a large atom so low ionization energy
group 7A / halogens → easily form 1- anions b/c they just need 1 more electron to fill their outer shell; F = the most electronegative and has the highest electron affinity of any atom in the table
group 8A / noble gases → least reactive b/c all their outer shells are filled
H can be classified as part of 1A or 7A because it can lose an electron → 1+ or gain an electron → 1-
