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The spectroscopic identification of Bi 4 has been very elusive. Two constitutional Bi 4 isomers of T d and C 2v symmetry are investigated and each is found to be a local energetic minimum. The optimized geometries and vibrational frequencies of these two isomers are obtained at the CCSD(T)/cc-pVQZ-PP level of theory, utilizing the Stoll, Metz, and Dolg 60-electron effective core potential. The fundamental frequencies of the T d isomer are obtained at the same level of theory. The focal point analysis method, from a maximum basis set of cc-pV5Z-PP, and proceeding to a maximum correlation method of CCSDTQ, was employed to determine the dissociation energy of Bi 4 ( T d ) into two Bi 2 and the adiabatic energy difference between the C 2v and T d isomers of Bi 4 . These quantities are predicted to be +65 kcal mol −1 and +39 kcal mol −1 , respectively. Two electron vertical excitation energies between the T d and C 2v electronic configurations are computed to be 156 kcal mol −1 for the T d isomer and 9 kcal mol −1 for the C 2v isomer. The most probable approach to laboratory spectroscopic identification of Bi 4 is via an infrared spectrum. The predicted fundamentals (cm −1 ) with harmonic IR intensities in parentheses (km mol −1 ) are 94(0), 123(0.23), and 167(0) for the T d isomer. The moderate IR intensity for the only allowed fundamental may explain why Bi 4 has yet to be observed. Through natural bond orbital analysis, the C 2v isomer of Bi 4 was discovered to exhibit “long-bonding” between the furthest apart ‘wing’ atoms. This long-bonding is postulated to be facilitated by the σ-bonding orbital between the ‘spine’ atoms of the C 2v isomer.