TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Method: The method further comprises heat-treating the lithium transition metal composite oxide under an inert gas atmosphere prior to the heat-treating under the atmosphere of the gas mixture. Preferred Components: The gas mixture further comprises water vapor, and an inert gas consisting of nitrogen, helium, and/or argon. The lithium transition metal composite oxide: comprises a positive electrode active material for a rechargeable lithium battery; and is a nickel-cobalt-manganese oxide of formula (LiNia1Cob1Mnc1Med1O2) (V). The carbon coating is uniformly distributed on the composite metal oxide, and has uniform distribution of carbon atoms as confirmed by carbon mapping of an energy dispersive X-ray spectrum of the composite metal oxide. The carbon coating comprises a carbon material including a carbon-carbon covalent bond together with at least one carboxylic (COOH) moiety, a hydroxyl (-OH) moiety, and a carbonate moiety. The lithium transition metal composite oxide includes lithium nickel oxide, lithium cobalt oxide, lithium manganese oxide, a metal oxide compound of formulae (LiNixCo1-xO2) (VI), (LiNi1-x-yCoxMnyO2) (VII), (LiM3(1-aa)M4aXO4) (VIII), (Lix1Co1-y1-z1Niy1Mz1O2-abXab) (IX), and (Lix2Mn2-y2M5y2O4-abX1ab) (X), lithium manganese phosphate, lithium iron borate, lithium iron phosphate, lithium iron vanadate, lithium iron silicate, lithium iron titanate, and lithium iron germanate. The lithium transition metal composite oxide is an over-lithiated oxide compound of (Li1+a2M6b2M7c2N2d2Oe2) (XI), and has a lithium content of a mole ratio of greater than 1. (XI) is a lithium manganese oxide compound of formula (yLi(Li1/3Me2/3)O2.(1-y)LiMe3O2) (XII).Me = Al, Ti, or Si;a1-c1 = 0.01-0.9;d1, aa, z1 = 0-0.5, where the sum of a1, b1, c1 and d1 is 1;x, y, x+y = 0-1;M3 = Mn, Co, Cu, or Ge;M4 = transition metal other than Mo and Co;X = P, Si, V or Ti;x1, x2 = 0.9-1.6;y1, y2, ab, y = 0-1;M5 = Co, Mo, W, V, Ti, Al, Zr, Ru, Rh, Pd, Os, Ir or Pt;X1 = O, F, S or P;Me2 = Mn, Mo, W, V, Ti, Zr, Ru, Rh, Pd, Os, Ir or Pt;Me3 = Ni, Mn or Co, where one of Me2 and Me3 comprises Mn;a2 = 0-1.5;b2, c2, d2 = 0-2, where the sum of b2, c2, and d2 are not simultaneously equal to 0;e2 = 2-4; andM6, M7, N2 = Ni, Co, Mn, Mo, Cu, Fe, Cr, Ge, Al, Mg, Zr, W, Ru, Rh, Pd, Os, Ir, Pt, Sc, Ti, V, Ga, Nb, Ag, Hf, Au, Cs, B or Ba, where at least one of M6, M7 and N2 comprises Ni, Co, Mn, Mo, Cu or Fe.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: (I) and (II) comprise methane, ethylene, propylene, methanol, ethanol and/or propanol.