The paper presents the Gaussian-4 (G4) theory, an extension of the Gaussian-3 (G3) theory for calculating energies of molecular species containing first-, second-, and third-row main group elements. G4 theory modifies G3 in five key ways: (1) an extrapolation procedure to obtain the Hartree-Fock (HF) limit, (2) increased $d$-polarization sets for first- and second-row atoms, (3) replacement of QCISD(T) with CCSD(T) for higher correlation treatment, (4) use of B3LYP density functional for optimized geometries and zero-point energies, and (5) addition of two new higher-level correction parameters. The G4 theory is assessed on the G3/05 test set, which includes 454 experimental energies. The average absolute deviation from experiment is significantly improved from 1.13 kcal/mol for G3 to 0.83 kcal/mol for G4, with the largest improvement observed for nonhydrogen systems. The contributions of the new features to this improvement are analyzed, and the performance on different types of energies is discussed. The paper also includes a "complete" version of G4 theory based on a single calculation using the full basis set, which corrects issues with the G3 theory's additivity approximation.The paper presents the Gaussian-4 (G4) theory, an extension of the Gaussian-3 (G3) theory for calculating energies of molecular species containing first-, second-, and third-row main group elements. G4 theory modifies G3 in five key ways: (1) an extrapolation procedure to obtain the Hartree-Fock (HF) limit, (2) increased $d$-polarization sets for first- and second-row atoms, (3) replacement of QCISD(T) with CCSD(T) for higher correlation treatment, (4) use of B3LYP density functional for optimized geometries and zero-point energies, and (5) addition of two new higher-level correction parameters. The G4 theory is assessed on the G3/05 test set, which includes 454 experimental energies. The average absolute deviation from experiment is significantly improved from 1.13 kcal/mol for G3 to 0.83 kcal/mol for G4, with the largest improvement observed for nonhydrogen systems. The contributions of the new features to this improvement are analyzed, and the performance on different types of energies is discussed. The paper also includes a "complete" version of G4 theory based on a single calculation using the full basis set, which corrects issues with the G3 theory's additivity approximation.