• chemical bonds are lasting attractions between two atoms
• chemical bonds can be established between two atoms which do not have their valnce electron shell completely filled
  • noble gasses (helium, neon and argon primarily) are thus very unreactive and form only a very small number of compounds
• chemical bonds form in three differnet ways:
  1. electron sharing - covalent bonds
  2. elecrostatic attraction - ionic bonds
  3. electron transfer - donor-acceptor bonds
  • in all of these cases, the atoms which constitute the bond are as close as possible to the most stable electron configuration of the noble gases
• bonds can be devided into two categories by force:
  • strong/primary - the bonds mentioned above and in detail explained below
  • weak/secondary - intermolecular forces

Intramolecular force

• intramolecular force is an attraction or any force in general that is formed between two atoms within a molecule
  • intramolecular forces include covalent and ionic bonds

Bond length and energy

• bond length is the distance of the two nuclei of the bonding partners
  • it is usually meassured in ångströms ($1Å=10^{-10}m$)
• bond energy is measures the bond’s strength and how much energy is needed to destroy it

Bond formation

• as the bonding partners are moving closer together, the potntial energy of the system changes
• when the atoms are distant, the attraction is practically non-existent
• with distance, the energy of the system decreases and thus the system becomes much more stable
• at a point when the attractve force is the same as the rpulsive force of the two atoms, the energy of the system reaches the smallest point and a bond is formed
  • the bond length is determined here also
• energy needed to seperate the atoms can be seen
• if the atoms were moved even closer together, the enrgy of the system increases rapidally

• the energy needed to dissociate the bond partners increases as the bond length gets shorter
  • triple bonds will thus be much stronger than single bonds
  • energy of the bonds with larger atomic readii will be smaller
• bonds get stronger in this order: metalic - non-polar covalent - polar covalent - ionic

Covalent bonds

• covalent bonds are created between atoms when it is most stable fo them to share electrons
• one, two, three or more electron pairs (one electron belonging to each bonding partner) can be shared to form single, double, triple or higher-multiplicity bonds respectively
  • the attraction between is stronger with more electron pairs shared
  • single, double and triple bonds are the most common in the nature
    • higher-multiplicity bonds occure only between lanthanides and actinides
• the bond is formed via an overlap or a strong attraction of orbitals of the bonding partners

$\sigma$ bonds

• $\sigma$ bodning occurs when orbitals overlap

• the orbitals overlap along the internuclear axis (nulceus-nucleus)
• electron density between the two bonding partners is symmetric
• they are the strongest bond between two atoms

$\pi$ bonds

• $\pi$ bonding occurs when orbital overlap on a parallel to the internuclear axis or when they are strongy attracted towards one another
• the electron density is highest above and below the plane of the intermolecular axis
• $\pi$ bonds are formed in double, triple and higher-multiplicity bonds, the single bond is always a $\sigma$ bond

The role of electronegativity

• electronegativity plays a part to the covalent bond as well
• the result of bonding of two atoms of different negativites is that the more electronegative bartner attracts the shared electrons more than the more electropositive bonding partner
• this means that some parts of the molecule are partially charged

Partial charge

• partial charge - $\delta$ - can be either positive - $\delta^+$ - or negative - $\delta^-$
  • the bonding partner with higher electronegativity will have a negative partial charge
  • the bonding partner with lower electronegativity will have a positive partial charge
• molecules with significant differences of partial charges are called polar
• molecules with insignificant or no partial charges are called non-polar
• if partial charges exist, the bonding partners form an electric dipole
  • this plays a massive role in the intermolcular forces between different electric dipoles and it influences the properties of the molecule
• in one molecule, there can be more electric dipoles influencind one another
  • the polarity of a molecule depends on where the electric dipoles are and the molecule’s geometry
  • if the the strenghts of the dipoles is equal and the dipoles are directly oposite to one another, the molecule is overall non-polar

Differences of electronegativites

• the difference in electronegativities of the bonding partners determines how polar the bond is
  • if the difference is low, the bond is less polar
    • this is when the difference is less than 0.4
  • if the difference is rather high, the bond is more polar
    • this is when the difference is in a range from 0.4 to 1.7
  • if the differnece is really high, the bond is probably not longer covalent but ionic
    • this is when the difference is higher than 1.7

Ionic bonds

• ionic bonds are created between atoms when it is most stable for them to give up electrons
• typically, ionic bonds are formed between metals and non-metals
• electrons of the bond partners are transfered
  • the transfer leads to creation of two oppositely charged particles
  • one partner loses one or more valence electrons and a cation is formed
  • on partner gains one or more valence electrons and a anion is formed
• the electron configurations of the bodning partners reach as close as possible to the electron configuration of noble gases
  • the octet rule states that an atom is most stable when all of its valence orbitals are filled (with eight electrons exactly)
  • the duet rule states that it is more stable for an atom to have to atoms in its valnce shell rather that more or less
• ionic compounds have a distinct structure and they form large crystals - for their description, we use the empirical formula
• hence, there are two conditions for an ionic compound to be formed:
  1. The stability rule - the atom must adhere to the octet or duet rule
  2. The neutrality rule - the created ionic compound must be neutral and the charges of the ions forming the bond must be balenced out

Structure of ionic solids

Crystaline structure

• the anions and cations of the ionic compound together create a lartger three-dimensional structure - crystaline structure
• the structure is highly regular and forms an ordinal latice
• one ionic compound can have more than one crystline structure

Lattice energy

• the ions together in this crystaline structre are minimazing the lattice energy
• it is the energy of the repulsion and attraction between individual ions
  • the attractive forces are at maximum whilst the repulsive forces are at minimum
• it influences many properties of the compound - solubility, hardness, volatility
  • ionic compounds are usually very hard but brittle
  • they also have very high melting points
• the smaller atomic radii and higher the charge, the higher the lattice energy
• the higher the melting point of an ionic solid, the higher the lattice energy

Valence shells

• electrons in the valence shells are localized (unlike in metalic bonds)
• ionic compounds show very low electric and heat conductivity
• when ionic compounds are heated, the valence shells don’t start to overlap, but the conductivity is still higher, because the ions themselves are able to carry the charge

Coulumb’s law

• the interaction between ions in a crystalline lattice can be described using the Coulumb’s law
• the interaction strength can be approximated using:

$$E=k\cfrac{Q_1Q_2}{d}$$

• where:
  • $E$ is the interaction strength
  • $k$ is the Coulumb’s constant ($=8.99\cdot{10^{-9}}\ Nm^2C^{-2}$)
  • $Q_1$ and $Q_2$ are the charges of the particles
  • $d$ is the distance between atomic nuclei
• the overall energy of the interactions is equal to the sum of the energies between all atoms and their combinations in the lattice
  • for $NaCl$ that is:

$$ E=E_{Na^+Cl^-}+E_{Na^+Na^+}+E_{Cl^-Cl^-}=\cfrac{-k}{d_{Na^+Cl^-}}+\cfrac{k}{d_{Na^+Na^+}}+\cfrac{k}{d_{Cl^-Cl^-}}$$

Metalic bond

• metalic bond is a special type of bond
• it is created in polymeraic structures of metal crystals
• the orbitals of these metals overlap a lot and all the electrons of these overlapping orbitals are shared in the whole crystal creating the electron gas

Structure of metals and alloys

Pure metals

• metals usually have a much higher number of electrons in the highest enrgy orbitals due to the electrons in d-orbitals and in f-orbitals
• electrons are delocalized in metals and can flow almost freely through the whole lattice
• metalic bond explains many characteristics of metals
  • ductility, melleability
    • the individual layers of the metalic lattice and theit delocalized electrons are able to easily slide when external force is applied
  • heat conductivity, electric conductivity
    • the free movement of electrons enables very easy transfer of charge, thus the trasnfer of heat and electricity
  • high melting and boiling points
    • the attraction of the ions and electrons together is very strong

Alloys

• alloys are mixtures (or combinations) of two or more metals
  • they sometimes have other elements added as well
• the metal that composes the majority of the alloy is called the base
• the metal that is added to the base metal is called the dopant
• these combinations of different elements change the properties of pure elements
  • the properties of the alloy can be changed by adjusting its composition
  • the properties resulting from alloying include strength, hardness, durability and resistence to corrosion

Substitutional alloys

• substitutional alloys are those alloys, where the atoms of the dopant are very similar in size to the atoms of the base metal
• the atoms of the dopant simply substitute the atoms of metal in the lattice
• the final structure can be very similar to that of a pure metal
• examples: bronze, brass

Interstitial alloys

• interstitial alloys are those alloys, where atoms of the dopant are rather different in size to the atoms of the base metal
• the dopant’s atoms are usually smaller
• the atoms of the dopant fill out the empty spaces (intersices) between the metalic cation of the crystaline latice
• the positions of the atoms of the dopant strongly influence the alloy’s properties

Lewis structures

• Lewis strctures (Lewis diagrams or Lewis electron dot diagrams) enable us to write the role of every valence electron in a chemical bond

Lewis symbols

• electrons are represented as dots on the sides of the symbol of an element
  • electron pairs are represented as a double dot or more commonly with a line
  • typically, it does not matter on which side the unpaired electrons end up, but if there are more than one, the should be on the oposite side
  • only valence electrons are included (the orbitals in which they are do not matter)
• ex. Lewis diagram of an oxygen atom - $\cdot\underline{\overline{O}}\cdot$
• the dots can be used to ilustrate ionistion reactions more easily
  • ex. Lithium loosing its electron - $Li\cdot\longrightarrow{Li^++e^-}$

Octet rule

• it is most stable for elements to have eight valence electrons in their valence shell
  • exceptions are the atoms closer to Helium, where it is most stable for them to have only two electrons in their valence shell (duet rule)
• atoms achive this usually via bonding
  • the shared electrons count to the number of electrons in both participants' valence shells
• these stable atoms can be written using the Lewis diagrams as $|\underline{\overline{X}}|$

Exceptions

• molecules with odd numbers of electrons
  • sometimes, it is natural for radicals (substances with one or more unpaired electrons) to occur naturally
  • no multiplicity of the bond enables them to have the electron octet
  • ex. $NO$ - $\cdot\overline{N}\equiv{O|}$
• over-filled octets
  • sometimes, central atoms have more than eight electrons in their valence shell after bonding
  • this occurs with elements that can create complex compounds with other types of bonds
• under-filled octets
  • sometimes, the central atom’s most stable arrengements are more simple and with less valence electrons than the octet rule suggests
  • in these compound, new interesting types of bonding occure

Ionic Lewis dot structures

• Lewis structures of ionic compounds can clearly show where electrons were transfered in a compound
• the ions are usually written in a square parathesis [] with their charges written
• ex. Lewis structure of sodium chloride - $[Na]^+\ [|\overline{\underline{Cl}}|]^-$

Covalent Lewis dot structure

• covalent Lewis structures include also the covalent bonds between elemnts besides their valence electrons
• ex. Lewis structure of carbon dioxide - $\overline{\underline{O}}=C=\overline{\underline{O}}$

Calculating Lewis dot structures

1. Writing the formula of the compound and structure analysis
2. Writing every known covlent bond 3, Add electron pairs to each atom to reach the octet
3. If the number of electron pairs is not in agreement with the octet rule:
   • in the case of too many electrons, the free electron pairs are converted to bonds
   • in the case of too few electrons, add some to the central atom

Formal charge

• formal charge is the actual charge an atom in a molecule has
  • while compounds are usually most stable in neutral states, individual atoms can be charged in the molecule
    • the overall charge of the molecule stays neutral

Calculating formal charge

• formal charge can be calculated using a Lewis diagram
• it is calculated as follows: $$Q_f=n_v-(n_n+\frac{1}{2}n_b)$$
• where:
  • $Q_f$ is the formal charge
  • $n_v$ is the number of valence electrons (in a free atom)
  • $n_n$ is the number of non-bonding electrons
  • $n_b$ is the number of bonding electrons

Resonant structures

• resonance structures are a set of at least two Lewis diagrams which collectively describe the electronic bonding in a molecule
  • this also accounts for fractional bonding
  • they can also be used to describe a system of delocalized electrons
• they are used whenever we do not know with certainty which lewis structre is correct
  • the propabilites of double bonds for example can be the same in two different cases
  • the existance of a resonant structure has been proven by meassuring the bond length of a molecule with multiple possible lewis diagrams
    • the bond lengths were quite far off the theoretical value
• ex. Resonance structure of $NO_3^-$

Structure of molecules

• the resonant structures, Lewis diagrmas and formulae are representing a two dimensional molecule, VSEPR and the theory of hybridization helps us explain the three dimensional structure
• bond length is the straight distance between the nuclei of two bonded atoms
  • it is usually measured in ånsgtröms or picometers
    • $1\ Å=10^{-10}m$
    • $1\ pm=10^{-12}m$
• bond angle is the angle between any two chosen bonds which intersect with one another in one common atom
  • it is usually measured in degrees or radians

Hybridization

• hybridization is a mathematical concept which describes the using of atomic orbitals to form new hybridized orbitals of the same energy
• the new orbitals have different energies nad shapes from the individual atomic orbitals
• these new orbitals are more sutable for the bonds in the molecule
• valence orbitals are most likely to hybridize
  • d-orbitals can also hybridize
• the number of new hybridized orbitals is equal to the number of originally involved atomic orbitals
• hybridization occurs when the participating orbitals have more or less similar energy and are suitably symmetric
• the type of hybridization depends on the atomic orbitals involved

sp hybridization

• the hybridization of one s-orbital and one p-orbital results in the creation of two hybridized sp-orbitals of the same energy

• the shape of the sp-orbitals is different

• sp hybridization results in linear geometrical structure
  • it usually involves two $\sigma$ bonds
  • the bond angles around the central atom are 180°

sp$^2$ hybridization

• the hybridization of one s-orbital and two p orbitals results in the creation of three hybridized sp$^2$-orbitals
• sp$^2$ hybridization results in trigonal planar geometrical structure
  • it usually involves three $\sigma$ bonds
  • the bond angles around the central atom are 120°

sp$^3$ hybridization

• the hybridization of one s-orbital and three p-orbitals results in the creation of four hybridized sp$^3$-orbitals
• sp$^3$ hybridization results in tetrahedral geometrical structure
  • it usually involves four $\sigma$ bonds
  • the bond angles around the central atom are approximatelly 109.5°

VSEPR - Valence Shell Electron Pair Repulsion

• some molecules do not follow the standard theory of hybridization because of their free electron pairs acting repulsing the other electrons of the bonds
• the bond angles are a little deformed as a result of the repulsion
• VSEPR predicts the shapes of molecules based on an order of repulsion
  • lone pairs occupy the least ammount of space and have the highest electron density
  • bonding pairs occupy the most ammount of space and have the lowest electron density
  • higher multiplicity bonds occupy less space than lower multiplicity bonds and have higher electron density
• oder of repulsion (from strongest to weakest)
  1. lone pair - lone pair
  2. lone pair - bonding pair
  3. bonding pair - bonding pair

Predicting the electorn pair geometry

1. Drawing the Lewis diagram
2. Identify the hybridization based on the number of $\sigma$ bonds
3. Place the lone electron pairs of the central atom accordng to the order of repulsion

VSEPR Shapes