Lecture 1

Brooklyn College Inorganic Chemistry (Spring 2009) Prof. James M. Howell Room 359NE (718) ; Office hours: Mon. & Thu. 9:00 am-9:30 am & 5:30 – 6:30 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 chemistry Biochemistry Environmental science Materials science & nanotechnology Inorganic chemistry Organometallic chemistry Coordination chemistry Solid-state chemistry Bioinorganic chemistry

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 1 electron 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 failed!

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 Fundamental Equations 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 requires changes in our way of looking at measurements. 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 Quantization of certain observables occur Energies can only take on certain values.

By demanding that the wave function be well behaved. 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 wave function represents the probability of finding the electron then the sum of probabilities over all space is unity. It is these requirements that introduce quantization. How is quantization introduced?

Example of simple quantum mechanical problem. 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, particle constrained to be in box

Q.M. solution (in atomic units) to Schrodinger Equation -½ d 2 /dx 2 X(x) = E X(x) X(x) is the wave function; E is a constant interpreted as the energy. We seek both X and E. Standard technique: assume a form of the solution and see if it works. Standard Assumption: X(x) = a e kx Where both a and k will be determined from auxiliary conditions (“well behaved”). Recipe: substitute trial solution into the DE and see if we get X back multiplied by a constant.

Substitution of the trial solution into the equastion yields -½ k 2 e kx = E e kx or k = +/- i sqrt(2E) There are two solutions depending on the choice of sign. General solution becomes X (x) = a e i sqrt(2E)x + b e –i sqrt(2E)x where a and b are arbitrary constants 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 with c = a + b and d = i (a-b) 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, must be 0 at x = 0 and x = l X(x) must equal 0 at x = 0 or x = l 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  which is where sine produces 0 Or Quantized!!

In normalized form Where n = 1,2,3…

Atomic problem, even for only one electron, is much more complex. Three dimensions, polar spherical coordinates: r,  Non-zero potential –Attraction of electron 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 Atoms

Quantum numbers for atoms 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 relative to an applied external magnetic field. 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) and 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 number of nodal surfaces (where wave function = 0). s