P-Chem Exam 2 Review: Atkins (11th ed) Ch. 8, 9, & 11
Heteronuclear diatomic MOs
Nonpolar bond: c1^2 = c2^2 Polar bond: c1^2 < c2^2 Ionic bond: c1^2 = 0 c2^2 = 1 lower energy orbital contributes to bonding orbital, higher energy orbital contributes to antibonding orbital
d orbitals
For exam: need to know mathematical format and how to graph n=3, l=2, m(l)=-2, -1, 0, 1, 2 d(xy) = xy f(r) d(yz) = yz f(r) d(xz) = xz f(r) d(x^2-y^2) = 0.5(x^2 - y^2) f(r) d(z^2) = sqrt(3) * 0.5 * (3z^2 - r^2) f(r) = sqrt(3) * 0.5 * (2z^2) f(r)
Emission spectrum
Frequency of emitted ratiation when electric charge passed through gas / element exposed to hot flame atoms are produced and absorb nrg to get into excited states atoms discard nrg by emitting EM radiation at discrete frequencies to return to ground state
Selection Rules: General
Gross selection rule = general feature Specific selection rule = in terms of quantum numbers
Understanding Radial Solutions
R depends on n & l as r --> inf, R --> 0 = boundary condition for l = 0, max at r = 0 (no angular momentum) If |l| > 0 then R and r = 0
Absorption spec in polyatomics
bonding, antibonding, and nonbonding orbitals most common transitions are pi to pi* and nonbonding to sigma* strongest transition is HOMO to LUMO chromophores = groups with well-defined absorptions (not always vis, sometimes UV) - exact transition position depends on whole molecule but generally have characteristic optical absorption
Spectrum linewidths
decrease lifetime = broader line/less defined energy doppler effect - moving molecules towards/away from detector, temperature dependent
Electronic structure
description of arrangement of e- around the nucleus
Effective nuclear charte (Zeff)
e- at distance r from nucleus experiences repulsions from all e- within sphere of radius r equivalent to a point negative charge located in nucleus s e- have greater penetration than p e- --> more likely to be closer to nucleus Order of shielding: s < p < d < f (shielding so weak for d and f that 4s are lower energy than 3d)
Valence electrons
e- in outermost shell
Hybridization
e- interact and create new wavefunctions by combining their atomic orbitals (sp^3 gives 4 new wavefunctions) N.B. resonance creates new wavefunctions also but decreases energy
Potential energy
electrostatic interaction between positive nucleus and negative e- at distance r, use reduced mass to treat 2 charges as 1 (nuclear model places nucleus at center with e- moving around)
Terms
energy can depend on all 4 quant #s of single e- each nrg level is called a term lines in spectra due to transitions between terms find terms, determine allowed transitions
Sigma Bond
enhanced e- density between 2 nuclei (spin pairing - 2 e- need opposite spins if in same orbital) wavefunct has cyllindrical symmetry around internuclear axis
Bonding Orbitals
gerarde (g) orbitals - "even" symmetry region of constructive interference in atomic orbital overlap / large probability of finding e- in that region (large value of wavefunction) inversion center = wavefunction values are same on each side (even function)
Bond Order (b)
greater bond order = shorter bond and stronger bond
HOMO
highest occupied molecular orbital
Ligand Field Theory
in some transition metals in solution, ligands can donate e- density to empty d-orbitals to give fun colors - unexpected b/c d-orbitals are degenerate/same nrg e- on ligand can change d-orbitals on molecule Octrahedral complexe d orbitals: z2 and x2-y2 increase to e(g) orbitals, xy/yz/xz decrease to t(2(g)) orbitals predict change in energy using symmetry of d-orbitals largely focus on # of ligands and molecular geometry energy difference = ligand field splitting parameter = different w/ diff ligands = diff colors Useful with Lambert-Beer law to find concentration Need to use wavelength where analyte has large absorption coefficient ε
Spectral Line Intensity
increase J (rotational quant number) = increase temperature
Radius trends
increase n = increase radius decreases with atomic number radius of H = 3/2 a(0) a(0) = about 59 pm (Bohr radius)
Raman Spec
intensity of scattered radiation, weak intensities, Rayleigh (frequency same as incident) Stokes = frequency smaller than incident Anti-Stokes = frequency larger than incident Specific selection rules: delta(J) = +/- 2 Gross selection: complex Diff selection rules = study molecules that are not active in "normal" spec (e.g. homonuclear diatomics)
Wavenumber
inverse wavelength
Orbital angular momentum quantum number
l = 0, 1, ... , n-1 determines magnitude of angular momentum subshells/"shape" of orbital 0 = s 1 = p 2 = d 3 = f etc.
UV-Vis Spec
larger energies to change e- distribution than needed for vibration/rotation (100s of kJ/mol) broad bands in liquids and solids decrease wavelength = increase frequency = larger energy changes Purple = high freq/low wavelength
LCAO (linear combo of atomic orbitals)
look for solutions based on H-atom solutions as functions of atomic orbitals solution found at overall minimum variational principle - vary c1 and c2 until energy is minimized
Building up principle
Aufbau principle, specific order in which orbitals are filled e- e- repulsion cause exceptions, if a d-orb can be completely or half filled it will be
Solutions to energy portion of Schroedinger equation
Dependent only upon n (speciifically 1/n^2) large spacing = small n, solutions are negative, larger atomic number nuclei have lower energies as n approaches infinity E --> 0
Valence Bond Theory
Descriptive > predictive, can interpret 90% of chem, introduced sigma and pi bonding
LUMO
lowest unoccupied molecular orbital excitation = HOMO / LUMO transition
Spin quantum number
m(s) = +/- 1/2 for an e- inherent e- property
MO Diagrams
Draw orbitals, populate with e- Lowest energy filled first Pauli - 2 e- per orbital with paired spins Hund - degenerate orbitals have parallel spins N.B. pz is a sigma orbital due to orientation general order of orbitals (low -> high nrg): 1 sigma 1 sigma * 2 sigma 1 pi (double degenerate) 1 pi * (double degenerate) 2 sigma * (flip 1 pi and 2 sigma at nitrogen) for pi orbitals, switch g and u If net S (spin angular momentum) (if unpaired e- remain) then the molecule is paramagnetic (if S = 0 then it is diamagnetic)
Conjugation
think particle in a box longer wavelengths when conjugated = can shift into visible which indicates extent of conjugation (more conjugation = greater wavelength)
Problems with VB Theory
too arbitrary hybridization resonances too many experimental factors to interpret
IR Spec
type of vibrational spec Most molecules at room temp have v=0, strongest transition is 1 <-- 0 visible to microwave wavelengths Polyatomic molecules have 3N-6 vibrations (3N-5 if linear) where N = number of atoms
Antibonding Orbitals
ungerarde (u) orbitals - "odd" symmetry Higher energy solution to wavefunction - nuclei repel each other Destructive interference & antisymmetric inversion point
Vibrational-Rotational Spec
vibrational nrg level (v) rotational nrg level (J) they correspond to each other, total energy is their sum Specific selection rules: delta(v) = +/- 1 delta(J) = 0, +/- 1 If dJ is -1 = P branch (2B spacing) If dJ is 0 = Q branch, change only in vibration, one line If dJ is +1 = R branch (2B spacing) Sometimes Q branch is missing, double lines indicate isotopes
Pi Bonds
side-by-side overlap of p-orbitals
1s orbital
spherical symmetrical, most likely to find e- in center and probability decays outwards n=1, l=0, m(l)=0
isodensity surface
surface of constant e- density / electrostatic potential surface total e- density = sum of squares of wavefunctions
Boundary surface
surface that captures high portion (~90%) of e- probability
p orbitals
2p is simplest +/- denotes sign of Ψ p(z): n=2, l=1, m(l)=0 p(z) is 0 in the x-y plane p(x) & p(y): n=2, l=1, m(l)=+/-1 exist as superposition of 2 states, solutions are usually complex
Hueckel Approximation
MO nrg diagrams for conjugated pi bonds Only considers pi orbitals (sigma bonds used as molecular frame, rigid) relies on experimental data = semiempirical
Rotational Spec
Molecular rotation quantized Energy depends on angular momentum around axis and moment of inertia corresponding to that rotation Determine l and use to predict bond angles and lengths Wavenumber usually 0.1 to 10 cm^-1 (for most molecules) Gross Selection: polar molecules Specific selection: delta(J) = +/- 1
Molecular Orbital Theory
Solve Schr eqn for 1 e- of molecule to get energies and orbitals and place e- on molecular orbitals (use 1 e- wavefunction/MO to spread thru whole molecule)
Oppenheimer Approximation
Solve Schro eqn for fixed nuclei, equilibrium bond length is minimum of curve with the minimum energy
Hund's Maximum Multiplicity Rule
an atom in its ground state adopts a configuration with greatest number of unpaired e-
Spectroscopy
analysis of EM radiation emitted, absorbed, or scattered by atoms and molecules, nrg of photons gives info about molecular nrg
Selection rules
angular momentum conserved in transition Δn = any Δl = +/- 1 Δm(l) = 0, +/- 1 ΔS = 0 ΔL = 0, +/- 1 ΔJ = 0, +/- 1 (but not 0 to 0) Grotian diagram shows all permitted transitions
Transition
atom changes nrg level from one to another, difference carried away by photon, emission spec gives info about these energies
Boltzmann Distribution
avg energy of molecules related to temperature (thermal motion nrg proportional to kT)
Ionization energy (I)
min nrg needed to remove e- completely from atom
Magnetic quantum number
ml = 0, +/- 1, ... , +/- l determines z-component of angular momentum, specifies the particular orbital within a subshell where an electron is likely to be found at a given moment in time/orientation of orbital
Vibrational Spec
model by harmonic oscillator Gross selection: molecule's dipole moment is disrupted Specific selection rule: delta(v) = +/- 1 (+1 absorption, -1 emission) homonuclear diatomics = IR inactive heteronuclear diatomics = IR active
Emission Spec
molecule undergoes transition from high energy state to low energy state and emits xs nrg as photon
Principal quantum number
n --> related to distance from nucleus = shell 1 = K 2 = L 3 = M 4 = N etc. 1 shell has n^2 orbitals (wavefunctions) with each energy level being n^2 fold degenerate
ⁿL₀
n = S, S is 1 & 3 if 2 e-, 2 if 1 e- L = 0 for s, 1 for p, 2 for d, 3 for f... L for 2 e-: L = l1+l2, l1+l2-1, ... , |l1-l2| 0 = J, J = L+S, L+S-1, ... , |L-S| Greater L = lower energy; in terms of J, 1 < 2 < 3 nrg
Absorption spec
net absorption of nearly monochromatic/single frequency incident radiation monitored as radiation swept over range of frequencies goal = obtain transmitted intensity as function of frequency
Pauli Exclusion Principle
no more than 2 e- may occupy any given orbital, and if 2 e- do occupy 1 orbital then their spins must be paired (opposite spins)
Nodes vs. radial nodes
node = wavefunction is zero radial node = R is zero ns orbitals have (n-1) nodes
Decay
non-radiative/internal conversion = molecule collides with others and xs nrg transferred into their motions (thermal motion, heat) radiative = molecule discards xs nrg as photon (can give photochemistry reactions), two types are fluorescence and phosphorescence Flourescence = spontaneous emission of radiation within a few ns after exciting radiation is extinguished (fast conversion); vertical transition to vibrational state from photon absorved, gives up nrg to surrounding molecules as returns to v=0, if they will accept it; spontaneous emission = vertical transition = radiation = lower nrg = lower frequency = longer wavelength than incident Fluorescence quenching = intensity depends on solvent molecules accepting energy, solvents with many nrg lvls can quench / decrease intensity based on # atoms in solvent Phosphorescence = spontaneous emission may persist for long time (but can still be relatively fast) - like a leak; intersystem crossing excites from singlet to triplet state and molecule gets stuck as triplet (triplet to singlet transition is forbidden) so emission is weak
Frank-Codon Principle
nuclei are so much bigger than e- and electronic transition occurs faster than nuclei can respond = vertical transition from ground state to turning point molecule can be in other vibrational states (absorption occurs at diff frequencies)
Hydrogenic atoms
one e- atoms of general atomic number Z (e.g. H, He+, Li2+, etc.) Can solve Schroedinger equn for them and then apply them to many e- atoms and molecules
