Files of the Supplementary Material: 1) The transitions_h2d.txt file contains the measured transitions of H2D+ in MARVEL format. 2) The transitions_d2h.txt file contains the measured transitions of D2H+ in MARVEL format. 3) The EnergyComparison.zip file contains the energy comparison of variational and MARVEL energy levels. After unzipping the file, double click on the index.html file (using any type of browser) and using the links you can see the dynamic figures of comparison. 4) The file D2H_VarEnergies.xlsx contains the variational energy levels of the D2H+ ion. Using the worksheets you can see the calculated energies up to J = 7. 5) The file H2D_VarEnergies.xlsx contains the variational energy levels of the H2D+ ion. Using the worksheets you can see the calculated energies up to J = 7. 6) The file PCCP_TI_0414_ESI.pdf contains footnotes to Tables 1 and 2, as well as four tables listing the MARVEL energy levels for the two isotopologues separated between ortho and para spin isomers. The tables within the files D2H_VarEnergies.xlsx and H2D_VarEnergies.xlsx contain the variationally computed (2J+1)*20 (ro)vibrational eigenvalues and their assignment for each J from 0 up to 7. For each J>0 eigenvalue, 4 sets of approximate quantum labels are shown, from which the top row contains the RRD assigned labels, while the other three rows show the quantum labels of the functions giving the three largest RRD overlaps for the given rovibrational state. Note that the RRD assignment might be different from the one given by the largest RRD overlap, this indicates the inapplicabillity of the RRD in that case. All energies are given in units of cm-1, J=0 eigenvalues contain the zero point vibrational energy. Notation: n1, n2, and n3 are normal mode quantum numbers; J, Ka, and Kc are rigid rotor quantum numbers; RRD^2 are the square of the RRD overlaps. FullVib shows the sum of the RRD^2 values for the given (n1 n2 n3) vibrational state.