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would like to benchmark it against other calculations to ensure its correctness. Therefore, to ascertain the ac- curacy of our CNDO-CI calculations, we also performed ab initio TDDFT calculation of its lowest photoexcited state, at the B3LYP/6-311+g(d) level of theory using the Gaussian03 program package[37]. Our CNDO-CI value of 2.98 eV (peak I in Fig.4), compares excellently with the TDDFT value of 3.03 eV, which gives us confidence as to correctness of our calculation. Martinez and Alonso[25] used an ab initio TDDFT methodology to compute the photoabsorption spectrum of Al 4 H 6 all the way up to 12 eV ( cf. Fig. 7 of Ref.[25]). The first peak in the TDDFT spectrum of Martinez and Alonso[25] is at an energy slightly higher than 3 eV, and their highest peak occurs at an energy close to 9 eV, thus making their spec- trum slightly blue-shifted compared to ours. However, the qualitative nature of their spectrum[25] is quite sim- ilar to our spectrum discussed below. 

Next, we examine the nature of excited states corre- sponding to the peaks present in our calculated spec- trum ( cf. Fig. 4). The important peaks in the spectrum up to the excitation energy ≈ 8 eV have been labeled, and the many-particle wave functions of these excited states, along with their ground-state transition dipole moments, are presented in table I. The first peak in Fig. 4 occurs at 2.98 eV, and is a relatively weak peak corresponding to the across the gap H → L transition. The next peak (II) located at 3.28 eV is also similarly weak and corresponds to H − 1 → L excitation. When we examine the nature of the many-particle wave func- tions ( cf . Table I) of various excited states, we realize that: (a) the wave functions of all the states consist pre- dominantly of singly-exited CSFs, (b) all the states have 

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one dominant configuration with magnitude of its coef- ficient always greater than 0.8, with some configuration mixing with the increasing excitation energy. The high- est peak in the spectrum is located at 8.05 eV with the dominant CSF being | H − 1 → L + 7 $_{〉}$, with some con- tributions from | H → L + 9 〉 and | H − 2 → L + 3 $_{〉}$. Koutecký and coworkers[39] have formulated a criterion according to which if the many particle wave function of a given excited state is dominated by one singly-excited configuration, it is classified as a normal inter-band ab- sorption. On the other hand, if the wave function ex- hibits strong mixing of several CSFs with coefficients of almost equal magnitude, it is considered to be a plas- monic collective excitation[39]. In metallic clusters such as Al 4 H 6 , to know whether the excited states are plas- monic in nature or not, is always of interest. As per the Koutecký [39] criterion, the excited states correspond- ing to peaks I to VIII do not appear to be of plasmonic type. This is to be contrasted with the nature of optical absorption in the bare Al 4 rhombus cluster which were found to be of plasmonic type by Deshpande et al .[40] in an ab initio time-dependent local-density approximation (TDLDA) calculation. In their work, authors reported that low-intensity optical absorption in Al 4 begins close to 1 eV, and increases in intensity with energy peaking around 8 eV. This suggests that in Al 4 H 6 , it is the in- fluence of hydrogenation which increases the optical gap, as well as changes the nature of excited states from plas- monic to inter-band excitations. 

In conclusion, we have preseneted the linear optical ab- sorption spectrum of Al 4 H 6 calculated using a wave func- tion based methodology employing the CNDO-CI ap- 

## IV. CONCLUSIONS 

