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A Principle of Linear Covariance is stated which follows from the "superposition principle" of quantum mechanics. Accordingly, quantum mechanical equations should be written in linearly covariant form which makes them look the same under non-unitary as well as unitary transformations. The principle leads to a non-unitary classification of all molecules (and clusters and solids) into distinct equivalence classes giving hitherto unknown relations between isomeric molecules. One also gets kinetic and thermic selection rules for chemical reactions. All these are independent of, and far more general than any unitary or point group symmetries. The invariants found for each class of molecules or clusters allow qualitative electronic deductions and are more generally applicable than symmetry based quantum numbers.

A Principal of Linear Covariance for Quantum Mechanics and Its Consequences Taking one Beyond Symmetry