proach, and compared it with that computed using the ab initio TDDFT approach. The photoabsorption spectra computed using the two approaches are generally in good agreement with each other, with the published TDDFT spectrum[25] being slightly blue-shifted compared to our work. Therefore, it will be of considerable interest to per- form optical absorption experiments on Al 4 H 6 cluster, to determine the nature of its optical excitations, and shed further light on its electronic structure. Our results can then be used for optical characterization of this cluster. Table I: Excitation energies and many-particle wave functions of excited states corresponding to the peaks in the CNDO-CI linear absorption spectrum of Al 4 H 6 ( cf. Fig. 4), along with the squares of their dipole coupling ( µ $^{2}$= ∑$_{i}$ |〈 f | d i | G 〉| 2 ) to the ground state. | f 〉 denotes the excited state in question, | G $_{〉}$, the ground state, and d i is the i -th Cartesian component of the electric dipole operator. In the wave function column, the numbers in the parentheses are the CI coefficients of a given electronic configuration. Symbols H / L denote HOMO/LUMO orbitals. 5 [1] M. P. Stracke, G. Ebeling, R. Cataluña, and J. Dupont, J. Energy & Fuels 21 , 1695 (2007). [2] G. W. Crabtree, M. S. Dresselhaus and M. V. Buchanan, Physics Today 39 , (December-2004). [3] T. Ozturk, A. Demirbas, Energy Sources, Part A 29 , 1415 (2007). [4] R. Zidan, B. L. Garcia-Diaz, C. S. Fewox, A. C. Stowe, J. R. Gray, and A. G. Harter, Chem. Comm. 25 , 3717 (2009) [5] Aldridge, S.; Downs, A. J. Chem. Rev. 101 , 3305 (2001). [6] X. Li, A. Grubisic, S. T. Stokes, J. Cordes, G. F. Gan- teför, K. H. Bowen, B. Kiran, M. Willis, P. Jena, R. Burgert, and H. Schnöckel, Science 315 , 356 (2007). [7] A. Grubisic, X. Li, S. T. Stokes, J. Cordes, G. F. Gante- for, K. H. Bowen, B. Kiran, P. Jena, R. Burgert, and H. Schnockel, J. Am. Chem. Soc. 129 , 5969 (2007). [8] M. L. McKee, Z. Wang and P. v R. Schleyer, J. Am. Chem. Soc. 122 , 4781 (2000). [9] ´P. V. R. Schleyer, K. Najafian, and A. M. Mebel, Inorg. Chem. 37 , 6765 (1998). [10] W. N. Lipscomb, Boron Hydrides , W. A. Benjamin, Inc., NY, 1963. [11] K. Wade, Adv. Inorg. Chem. Radiochem. 18 , 1(1976). [12] D. M. P. Mingos, Nat. -Phys. Sci. 236 , 99 (1972). [13] K. Wade, J. Chem. Soc. D, 15 , 792 (1971). [14] M. Pelissier and J. P. Malrieu, J. Chem. Phys. 67 , 5963 (1977). [15] S. Kaur and K. L. Baluja, Phys. Rev. A 80 , 042701 (2009). [16] For a recent measurement and a review of previous works, see, e.g ., W. Szanja, and M. Zachwieja, Eur. Phys. J. D 55 , 549 (2009), and references therein. [17] C. W. Bauschlicher, Jr. and S. R. Langhoff, J. Chem. Phys. 89 , 2116 (1988). [18] F. Marinelli and A. Allouche, Theo. Chim. Act. 62 , 175 (1986). [19] C. Liang, R. D. Davy, and H. Schaefer, Chem. Phys. Lett. 159 , 393 (1989); B. J. Duke, C. Liang, and H. Schae- fer, J. Am. Chem. Soc. 113 , 2884 (1991); B. J. Duke, J. Mol. Struct. 208 , 197 (1990); K. Lammertsma and J. Leszczynski, J. Phys. Chem. 94 , 2806 (1990); C. W. Bock, M. Trachtman, C. Murphy, B. Muschert, and G. J. Mains, J. Phys. Chem. 95 , 2339 (1991). [20] X. Wang, L. Andrews, S. Tam, M. E. DeRose,| and M. E. Fajardo, J. Am. Chem. Soc., 125 , 9218 (2003). [21] M. Shen and H. Schaefer, J. Chem. Phys. 96 , 2868 (1992). [22] V. Barone, L. Orlandini, and C. Adamo, J. Phys. Chem. Peak Energy (eV) 〈 µ $^{2}$〉 Wave function I 2.98 0.08 | H → L 〉 (0.9425) II 3.28 0.09 | H − 1 → L 〉 (0.9423) III 4.93 0.02 | H − 1 → L + 2 〉 (0.9226) | H → L + 1 〉 (0.1531) IV 5.66 0.03 | H → L + 3 〉 (0.9313) V 6.24 0.07 | H − 1 → L + 3 〉 (0.9027) | H − 1 → L + 4 〉 (0.1609) | H → L + 4 〉 (0.1056) VI 6.93 0.11 | H → L + 5 〉 (0.9249) | H → L + 4 〉 (0.1242) VII 7.31 0.12 | H − 3 → L 〉 (0.8391) | H − 1 → L + 5 〉 (0.3062) | H − 2 → L + 2 〉 (0.1600) VIII 8.05 0.44 | H − 1 → L + 7 〉 (0.8590) | H → L + 9 〉 (0.2880) | H − 2 → L + 3 〉 (0.1812)