These materials are provided as a supplement to the 2018 "Atoms" manuscript "Two-photon vibrational transitions in O$_2^+$ as probes of variation of the proton-to-electron mass ratio" by Ryan Carollo, Alexander Frenett, and David Hanneke.

Unless specified otherwise, all energies are relative to the ground state of the neutral molecule and specified as wavenumbers in inverse-centimeters and all lengths are in angstroms.

The calculated potentials are in "X state.csv" and "A state.csv". Units are cm^-1 vs. angstroms.

The calculated energy levels and rotational constants are in "O2+ X State Energy Levels and rotational constants.csv" and "O2+ A State Energy Levels and rotational constants.csv".

energy differences.csv: Energy of the state |A, v_A> minus energy of the state |X, v_X>. Units are cm^-1. Rows are vibrational levels in the A state, and columns are in the X state. The first element is v_A = 0, v_X = 0.

The wavefunctions in csv format are zipped in "X_state_wvfncts.zip" and "A_state_wvfncts.zip". The positions are in angstroms. The wavefunction amplitudes have units of angstrom^(-1/2) such that they are normalized when squared and integrated.

overlap integrals.csv: Overlap integral of the |A, v_A> and |X, v_X> wavefunctions (not squared). Unitless. Rows are vibrational levels in the A state, and columns are in the X state. The first element is v_A = 0, v_X = 0.

transition dipole moments.csv: Total transition dipole moment between the |A, v_A> and |X, v_X> states, including both electronic and vibrational contributions. Units are atomic units (e a_0). Rows are vibrational levels in the A state, and columns are in the X state. The first element is v_A = 0, v_X = 0.