The density functional theory (DFT) calculations in different approximations have been performed for the geometries and vibrational states of the tuans-glyoxal molecule in the ground state S-0 ((X) over tilde(1) A(g)) and in the lowest excited triplet state T-1 ((a) over tilde(3) A(u), n-pi* type). Eight typical combinations of exchange and correlation functionals have been used. Comparative Hartree-Fock (HF) calculations have also been performed. For the open shell (a) over tilde A(u) state the standard spin-unrestricted Hartree-Fock and Kohn-Sham approaches (UHF, UKS) as well as the restricted open-shell versions (ROHF, ROKS) have been applied. The calculated frequencies have been compared, among others, with the data resulting from the most recent phosphorescence exicitation spectra of glyoxal cooled in the supersonic molecular beam, recorded with the cooperation of one of us (JH) for the spin-forbidden S-0-T, transition. The most realistic description of the vibrational frequencies. within the unsealed harmonic approximation, can be obtained using the 3-parameter Becke-93 exchange functional (B3), whereas this description practically does not depend on the correlation functional used. Our calculations support the recently reexamined experimental energy of the symmetric CH-rocking fundamental for the T-1 state. (C) 2000 Elsevier Science Ltd. All rights reserved.