A new variational methodology for the treatment of the Renner-Teller effect in tetra-atomic molecules has been developed in valence coordinates. The kinetic-energy operator of Bramley et al. [Mol. Phys. 1991, 73, 1183] for any sequentially bonded four-atom molecule, A-B-C-D, in the singlet nondegenerate electronic state has been adapted to the Renner-Teller and spin couplings by modifying the expression of the nuclear angular momentum. The total Schrödinger equation is solved by diagonalizing the Hamiltonian matrix in a three-step contraction scheme. The main advantage of this new theoretical development is the possibility of studying different isotopomers using the same potential-energy surfaces. This procedure has been tested on HCCH(+) and its deuterated derivatives DCCD(+) and DCCH(+). The calculated rovibronic band origins were compared with previous data deduced from the Jacobi coordinates methodology, dimensionality reduced variational treatment, and photoelectron spectra with a good global agreement. Rotational structures for these systems are also tackled.
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