Fundamentals

• principal quantum number (n) = describes the energy and size of the atomic orbital

  (the bigger the value, the higher the energy and the larger the orbital)

  *n = 1,2,3 intergers

  *orbitals of the same n belong to the same shell
• Angular momentum quantum number (l)

  *distinguishes orbits of given, n, having different shapes (also related to energy)

  *allowed values for l: 0 to (n-1)

  l name origin of name

  0 s sharp

  1 p principal

  2 d diffuse

  3 f fundamental
• magnetic quantum number (mₗ) = differentiates orbitals of given n and l by orientation in space

  *allowed mₗ values = -ve l to +ve l
• spin quantum number (mₛ) = represented by 'spin up' and 'spin down'

  *allowed values for mₛ = -1/2 and 1/2
• S Orbital (l=0, mₗ=0)

  *spherically symmetric

  *surface boundary is of constant phase (either positive or negative)

  *the larger the value of n, the bigger the orbital
• P Orbitals (l=1, mₗ=-1,0,+1)

  *shape is bi-lobed (dumbbell)

  *a change in phase of the surface boundary occurs, at a nodal plane ( zero probability at the node)

  *in p-orbitals, the nodal plane is at the nucleus

  *p-orbitals have 3 different orientations (called degenerate orbitals)
• D Orbitals (l=2, mₗ= -2,-1,0+1,+2)

  *5 degenerate orbitals

  *important for transition metal chemistry
• Orbital energies can be expressed as:

  $En =$$-R/n^2$

  R= Rydberg constant

  1. lowest E for n=1 and n=1 =1s orbital
  2. E closer together as n increases
• ground state atom = an isolated atom of an element that is in its lowest energy, or unexcited state

  (guiding principle is to keep the total energy of the atom as low as possible)
• Hund's rule = electrons occupy all of the orbitals of a given sub shell singly before pairing begins, the unpaired electrons have parallel spins
• pauli exclusiom principle = no two electrons in an atom can have identical sets of four quantum numbers

  1. two electrons in the same orbital must have different spins
  2. two electrons in one orbital are said to be spin-paired and one is unpaired
• valence electrons = from the above, same configuration down each group (hence similarity in reactivity)
• Van der Waals radii = vary across the periods (atoms get smaller as you move from left to tight due to stronger pull from the nucleus)
• electronegativity = the ability of an atom to attract an electron to itself

  *increases left to right across period (external electrons feel the positive charge of nucleus more for smaller atoms)

  *decreases down groups (increasing n= more layers of electrons and hence positive pull felt less strongly by external electrons)
• ionic bonding = an array of positively charged and negatively charged ions, held in a lattice by charge attraction (electron transfer occurs- formation of ions)
• covalent bonding = atoms share valence electrons to attain a filled set of outer orbitals
• central atom = all other groups/ atoms are attached to this
• terminal atom = each atom has one connection to the central atom
• lone pair = pair of electrons that are not shared with a second atom
• octet rule = during a chemical reaction, elements gain, lose, or share electrons in order to attain a noble gas configuration

  *hydrogen, lithium ad beryllium follow a duet rule (2 electrons in the outer shell) by trying to acquire the electron configuration of hellium
• Lewis structure of ions

  ANIONS: add an extra electron to the total count to account for the negative charge

  CATION: subtract an electron from the Toal count for the positive charge
• Formal charge (FC) = (number of valence electrons in uncombined atom) - (number of lone pair electrons on bound atom) - 1/2 (number of electrons in bonds to the atom)
• Valence shell electron pair repulsion (VSEPR)

  *the valence electrons in a molecule repel each other because of their charge

  ASSUMPTIONS:

  *atoms in a molecule are bonded together b electron pairs

  *atoms in a molecule can possess electron pairs that are nit involved in bonding

  RULES:

  *bonding pairs (bp) and lone pairs (lp) around an atom adopt positions in which their interactions with other electron pairs are minimised

  *a lone pair occupies more space than a bp

  *multiple bonds (i.e. double and triple bonds) occupy more space than a single bond
• Factors causing distortion of bond angles

  *where all bonds are single, a sequence of repulsion strength applies, which takes the following order

  1p-1p > 1p-bp . bp-bp

  *when multiple bonds are present, space occupied decreases according to

  triple bond > double bond > single bond
• Bonding pairs molecular geometry

  2 linear

  3 trigonal planar

  4 tetrahedral

  5 trigonal bipyramidal

  6 octahedral
• Bond polarity

  *a bond is polar if its centres of positive and negative charge do not coincide

  *the degree of polarity of a bond depends on the equality of the sharing of electrons between the 2 atoms

  -->this depends on the electronegatively's pf two atoms which

  share electron density

  -->electrons can be attracted closer to a more electronegative atom
• Molecular dipole

  *a net charge separation across a molecule-molecule dipole

  *the presence of a molecular dipole is dependent on bond polarity and shape

  *factors influencing the magnitude of a molecular dipole:

  --> relative electronegativity's of the atoms

  --> presence of lone pairs
• The hybrid orbital approach (HOA):

  *bonds from via overlap of atomic orbitals

  *electrons are assigned to 2-centre bonds

  *the shape and orientation of atomic orbitals is important and must account for then observed geometry of the molecule

  *consider the properties of orbitals:

  -->s-orbital: spherical e- density in all directions

  -->p-orbital: e- density greatest along x-axis
• *the hybridisation model is necessary as above the p orbitals have an unpaired electron each --> two bonds to carbon only

  *electron promotion is required:

  -->to form four bonds: 4 unpaired electrons are needed
• *s, p, d orbitals can mix (hybridise) to give hybrid orbitals

  -->sp hybrid - mix 1xs orbital + 1xp orbital

  -->sp² hybrid - mix 1xs orbital + 2xp orbitals

  --> sp³ hybrid - mix 1xs orbital + 3xp orbitals

  *ALL in some valence shell (i.e with same value of principle quantum number, n )

  *the number of hybrid orbitals formed equals the number of s, p, d etc. AOs that mix to form them

  *if hybridised, a given atom in a molecule has only one type of hybrid orbital. Orbitals of a type are equivalent in every respect (energy, electron density, shape and direction)
• Sigma σ bond

  The axial overlap of atomic orbitals (AOs) or hybrid AOs allows unpaired electrons to pair and a bond forms

  The axial overlap achieves maximum orbital overlap (maximum e- density overlap)
• Bonding in Alkanes

  *Each carbon atom uses four sp³ orbitals

  *tetrahedral geometry about each C atom

  *7 σ bonds ((6 x C-H) + (1 x C-C))

  *Rotation can occur about σ bonds ~ doesn't affect overlap

  *Generally carbon is sp³ hybridised when it is directly bound to 4 atoms
• Bonding in Alkenes

  *each C atom is bonded to 3 other atoms

  -->3 equivalent bonds could arise if the carbon s orbital

  hybridises with 2 of the p-orbitals

  *direct overlap (along axis) of 3sp² orbitals with orbitals of other atoms --> 3σ bonds

  *more s character than in sp³ orbitals

  *equidistant arrangement in plane of original p orbitals
• Axial overlap of the remaining p orbital cannot occur as they are out of plane and there is zero electron density along the C-C bond axis.
• Instead, overlap occurs above and below bond axis (side on), resulting in weaker overlap compared to a σ bond.
• π + σ = double bond.
• π bond only occurs where there is already a σ bond.
• The presence of a σ bond brings the remaining p-orbitals in close enough.
• Restriction in movement across the molecule along the double bond would destroy p orbital overlap.
• No rotation about C=C bond leads to isomers in substituted alkenes.