Lecture 1 Brooklyn College Inorganic Chemistry Spring 2009

Lecture 1

Brooklyn College Inorganic Chemistry (Spring 2009) • Prof. James M. Howell • Room 359 NE (718) 951 5458; jhowell@brooklyn. cuny. edu Office hours: Mon. & Thu. 9: 00 am-9: 30 am & 5: 30 – 6: 30 • Textbook: Inorganic Chemistry, Miessler & Tarr, 3 rd. 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)

Inorganic chemistry Organometallic chemistry Organic chemistry Coordination chemistry Bioinorganic chemistry Environmental science Solid-state chemistry Materials science & nanotechnology

Organic compounds Inorganic compounds Single bonds Double bonds Triple bonds Quadruple bonds Coordination number Geometry Constant Variable Fixed Variable

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 17 th century • By the end of the 19 th 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 20 th 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 http: //www. atm. ch. cam. ac. uk/tour/

Some examples of current important uses of inorganic compounds Catalysts: oxides, sulfides, zeolites, metal complexes, metal particles and colloids Semiconductors: Si, Ge, Ga. As, In. P Polymers: silicones, (Si. R 2)n, polyphosphazenes, organometallic catalysts for polyolefins Superconductors: Nb. N, YBa 2 Cu 3 O 7 -x, Bi 2 Sr 2 Ca. Cu 2 Oz Magnetic Materials: Fe, Sm. Co 5, Nd 2 Fe 14 B Lubricants: graphite, Mo. S 2 Nano-structured materials: nanoclusters, nanowires and nanotubes Fertilizers: NH 4 NO 3, (NH 4)2 SO 4 Paints: Ti. O 2 Disinfectants/oxidants: Cl 2, Br 2, I 2, Mn. O 4 Water treatment: Ca(OH)2, Al 2(SO 4)3 Industrial chemicals: H 2 SO 4, Na. OH, 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 Energy levels in the hydrogen atom Paschen series (IR) Balmer series (vis) Lyman series (UV) 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!

Fundamental Equations of quantum mechanics Planck quantization of energy E = hn h = Planck’s constant n = frequency de Broglie wave-particle duality l = h/mv l = wavelength h = Planck’s constant m = mass of particle v = velocity of particle Heisenberg uncertainty principle Dx Dpx h/4 p Schrödinger wave functions Dx uncertainty in position Dpx uncertainty in momentum H: Hamiltonian operator Y: wave function E : Energy

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.

How is quantization introduced? 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 the sum of probabilities over all space is unity. It is these requirements that introduce quantization.

Example of simple quantum mechanical problem. Electron in One Dimensional Box Definition of the Potential, V(x) = 0 inside the box 0 <x<l V(x) = infinite outside box; x <0 or 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) 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 ekx 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 ekx = E ekx or k = +/- i sqrt(2 E) There are two solutions depending on the choice of sign. General solution becomes X (x) = a ei sqrt(2 E)x + b e –i sqrt(2 E)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(2 E)x) + b (cos(-sqrt(2 E)x) + i a sin (sqrt(2 E)x) + i b(sin(-sqrt(2 E)x)

Regrouping X(x) = (a + b) cos (sqrt(2 E)x) + i (a - b) sin(sqrt(2 E)x) Or with c = a + b and d = i (a-b) X(x) = c cos (sqrt(2 E)x) + d sin(sqrt(2 E)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(2 E)x) + d sin (sqrt(2 E)x) ) = - ½ ((2 E)(- c cos (sqrt(2 E)x) – d sin (sqrt(2 E)x) = E (c cos (sqrt(2 E)x + d sin(sqrt(2 E)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(2 E) l ) = 0 Which is achieved by (sqrt(2 E) l ) = np which is where sine produces 0 Or Quantized!!

In normalized form Where n = 1, 2, 3…

Atoms Atomic problem, even for only one electron, is much more complex. • Three dimensions, polar spherical coordinates: r, q, f • 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 3 D produces 3 quantum numbers Relativistic corrections define a fourth quantum number

Quantum numbers for atoms Symbol Name Values Role n Principal 1, 2, 3, . . . Determines most of the energy l Angular momentum 0, 1, 2, . . . , n-1 Describes the angular dependence (shape) and contributes to the energy for multi-electron atoms ml Magnetic 0, ± 1, ± 2, . . . , ± l Describes the orientation in space relative to an applied external magnetic field. ms Spin ± 1/2 Describes the orientation of the spin of the electron in space Orbitals are named according to the l value: l 0 1 2 3 4 5 orbital s p d f g . . .

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 = 1 2 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