A new ansatz for local electron correlation is introduced, which truncates double substitutions subject to a triatomics in molecules (TRIM) criterion. TRIM includes all double substitutions in which one occupied-virtual substitution is atomic while the other substitution can be nonlocal (a cubic number, before cutoffs). With an additional approximation, the TRIM second-order Moller-Plesset perturbation theory (MP2) model can be noniteratively solved; this is the model that is implemented. Results are shown for absolute energies of alkane and polyene chains, rotational barriers of substituted ethylenes and benzenes, and association energies of the water and neon dimers. Over 99.7% of the untruncated MP2 energy is recovered for the test cases, and the relative energies of small systems are in error by less than 0.1 kcal/mol. By contrast, a diatomics in molecules (DIM) truncation recovers about 95% of the full MP2 energy, and yields errors several times larger for relative energies. (C) 2000 American Institute of Physics. [S0021-9606(00)30505-0].