A combined experimental and theoretical study of the intermolecular vibrations of 2,3-dimethylnaphthalene . Ar (2,3-DMN . Ar), for the first excited electronic state (S1), is reported. Methyl groups at C2 and C3 positions of naphthalene lower the symmetry of the complex, so that transitions involving excitation of the intermolecular long-axis in-plane x mode become allowed in electronic spectra, in addition to the out-of-plane z mode. Two-color resonant two-photon ionization (2C-R2PI) spectrum of the van der Waals (vdW)-mode region (0(0)0+70 cm-1) of 2,3-DMN . Ar exhibits six bands to the high-frequency side of the electronic origin 0(0)0, which arise from excitation of low-frequency intermolecular vibrations of the complex in the S1 state. Accurate quantum three-dimensional (3D) calculations of vdW vibrational (J=0) levels of S1 2,3-DMN - Ar have been performed, using a recently developed quantum method based on the 3D discrete variable representation. Since no approximation is made in the treatment of coupled, very anharmonic vdW vibrations, the calculated eigenstates are essentially exact for the intermolecular potential energy surface (PES) employed, thus enabling direct comparison between theory and experiment. The intermolecular PES was modeled as a sum of atom-atom Lennard-Jones (LJ) pair potentials. Some of the initial LJ parameters were modified until very good agreement was achieved between the calculated and measured vdW frequencies of S1 2,3-DMN . Ar. This allowed assignment of the vdW bands to the blue side of 0(0)0, and resulted in an improved intermolecular PES of the complex. In addition, the quantum 3D calculations provided a quantitative description of the vdW vibrational level structure and floppiness of S1 2,3-DMN . Ar up to approximately 60-70 cm-1 above the ground vdW state. The wave functions of all vdW states below approximately 49 cm-1 relative to the ground state, are sufficiently regular to allow assignment of vibrational quantum numbers. At higher excitation energies, mode coupling becomes stronger, and irregular vdW states whose assignment is uncertain, are common.