Lecture 1

Brooklyn College Inorganic Chemistry (Spring 2006) Prof. James M. Howell Room 359NE (718) ; Office hours: Mon. & Thu. 10:00 am-10:50 am & Wed. 5 pm-6 pm Textbook: Inorganic Chemistry, Miessler & Tarr, 3rd. Ed., Pearson-Prentice Hall (2004)

What is inorganic chemistry? Organic chemistry is: the chemistry of life the chemistry of hydrocarbon compounds C, H, N, O Inorganic chemistry is: The chemistry of everything else The chemistry of the whole periodic Table (including carbon)

Organic compounds Inorganic compounds Single bonds  Double bonds  Triple bonds  Quadruple bonds  Coordination number ConstantVariable GeometryFixedVariable

Single and multiple bonds in organic and inorganic compounds

Unusual coordination numbers for H, C

Typical geometries of inorganic compounds

Inorganic chemistry has always been relevant in human history Ancient gold, silver and copper objects, ceramics, glasses (3,000-1,500 BC) Alchemy (attempts to “transmute” base metals into gold led to many discoveries) Common acids (HCl, HNO 3, H 2 SO 4 ) were known by the 17th century By the end of the 19th Century the Periodic Table was proposed and the early atomic theories were laid out Coordination chemistry began to be developed at the beginning of the 20th century Great expansion during World War II and immediately after Crystal field and ligand field theories developed in the 1950’s Organometallic compounds are discovered and defined in the mid-1950’s (ferrocene) Ti-based polymerization catalysts are discovered in 1955, opening the “plastic era” Bio-inorganic chemistry is recognized as a major component of life

Nano-technology

Hemoglobin

The hole in the ozone layer (O 3 ) as seen in the Antarctica

Some examples of current important uses of inorganic compounds Catalysts: oxides, sulfides, zeolites, metal complexes, metal particles and colloids Semiconductors: Si, Ge, GaAs, InP Polymers: silicones, (SiR 2 ) n, polyphosphazenes, organometallic catalysts for polyolefins Superconductors: NbN, YBa 2 Cu 3 O 7-x, Bi 2 Sr 2 CaCu 2 O z Magnetic Materials: Fe, SmCo 5, Nd 2 Fe 14 B Lubricants: graphite, MoS 2 Nano-structured materials: nanoclusters, nanowires and nanotubes Fertilizers: NH 4 NO 3, (NH 4 ) 2 SO 4 Paints: TiO 2 Disinfectants/oxidants: Cl 2, Br 2, I 2, MnO 4 - Water treatment: Ca(OH) 2, Al 2 (SO 4 ) 3 Industrial chemicals: H 2 SO 4, NaOH, CO 2 Organic synthesis and pharmaceuticals: catalysts, Pt anti-cancer drugs Biology: Vitamin B 12 coenzyme, hemoglobin, Fe-S proteins, chlorophyll (Mg)

Atomic structure A revision of basic concepts

Atomic spectra of the hydrogen atom Lyman series (UV) Balmer series (vis) Paschen series (IR) Energy levels in the hydrogen atom Energy of transitions in the hydrogen atom Bohr’s theory of circular orbits fine for H but fails for larger atoms …elliptical orbits eventually also failed0

de Broglie wave-particle duality  = h/mv = wavelength h = Planck’s constant m = mass of particle v = velocity of particle Heisenberg uncertainty principle  x  p x  h/4   x uncertainty in position  p x uncertainty in momentum The fundamentals of quantum mechanics Schrödinger wave functions H: Hamiltonian operator  : wave function E : Energy Planck quantization of energy E = h h = Planck’s constant = frequency

Quantum mechanics provides explanations for many experimental observations From precise orbits to orbitals: mathematical functions describing the probable location and characteristics of electrons electron density: probability of finding the electron in a particular portion of space

Characteristics of a well behaved wave function Single valued at a particular point (x, y, z). Continuous, no sudden jumps. Normalizable. Given that the square of the absolute value of the eave function represents the probability of finding the electron then sum of probabilities over all space is unity. It is these requirements that introduce quantization.

Electron in One Dimensional Box Definition of the Potential, V(x) V(x) = 0 inside the box 0 <x< l V(x) = infinite outside box; x l

Q.M. solution in atomic units -½ d 2 /dx 2 X(x) = E X(x) Standard technique: assume a form of the solution. Assume X(x) = a e kx Where both a and k will be determined from auxiliary conditions. Recipe: substitute into the DE and see what you get.

Substitution yields -½ k 2 e kx = E e kx or k = +/- i (2E) 0.5 General solution becomes X (x) = a e i sqrt(2E)x + b e –i sqrt(2E)x where a and b are arbitrary consants Using the Cauchy equality e i z = cos(z) + i sin(z) Substsitution yields X(x) = a cos (sqrt(2E)x) + b (cos(-sqrt(2E)x) + i a sin (sqrt(2E)x) + i b(sin(-sqrt(2E)x)

Regrouping X(x) = (a + b) cos (sqrt(2E)x) + i (a - b) sin(sqrt(2E)x) Or X(x) = c cos (sqrt(2E)x) + d sin(sqrt(2E)x) We can verify the solution as follows ½ d 2 /dx 2 X(x) = E X(x) (??) - ½ d 2 /dx 2 (c cos (sqrt(2E)x) + d sin (sqrt(2E)x) ) = - ½ ((2E)(- c cos (sqrt(2E)x) – d sin (sqrt(2E)x) = E (c cos (sqrt(2E)x + d sin(sqrt(2E)x)) = E X(x)

We have simply solved the DE; no quantum effects have been introduced. Introduction of constraints: -Wave function must be continuous at x = 0 or x = l X(x) must equal 0 Thus c = 0, since cos (0) = 1 and second constraint requires that sin(sqrt(2E) l ) = 0 Which is achieved by (sqrt(2E) l ) = n  Or

In normalized form

Atomic problem, even for only one electron, is much more complex. Three dimensions, polar spherical coordinates: r,  Non-zero potential –Attraction to nucleus –For more than one electron, electron-electron repulsion. The solution of Schrödinger’s equations for a one electron atom in 3D produces 3 quantum numbers Relativistic corrections define a fourth quantum number

Quantum numbers Orbitals are named according to the l value: l orbitalspdfg... SymbolNameValuesRole nPrincipal1, 2, 3,...Determines most of the energy lAngular momentum 0, 1, 2,..., n-1Describes the angular dependence (shape) and contributes to the energy for multi-electron atoms mlml Magnetic0, ± 1, ± 2,..., ± l Describes the orientation in space msms Spin± 1/2Describes the orientation of the spin of the electron in space

Principal quantum number n = 1, 2, 3, 4 …. determines the energy of the electron in a one electron atom indicates approximately the orbital’s effective volume n = 12 3

Angular momentum quantum number l = 0, 1, 2, 3, 4, …, (n-1) s, p, d, f, g, ….. determines the shape of the orbital s

See: Magnetic quantum number Determines the spatial orientation of the orbital m l = -l,…, 0, …, +l l = 0 m l = 0 l = 1; m l = -1, 0, +1 l = 2 m l = -2, -1, 0, +1, +2

Electrons in polyelectronic atoms (the Aufbau principle) Electrons are placed in orbitals to give the minimum possible energy to the atom Orbitals are filled from lowest energy up Each electron has a different set of quantum numbers (Pauli’s exclusion principle) Since m s =  1/2, no more than 2 electrons may be accommodated in one orbital Electrons are placed in orbitals to give the maximum possible total spin (Hund’s Rule) Electrons within a subshell prefer to be unpaired in different orbitals, if possible

Placing electrons in orbitals

Approximate order of filling orbitals with electrons 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p E

1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p E