Theoretical Study of Gallium Nitride Molecules, GaN 2 and GaN 4 . Demeter Tzeli,* Giannoula Theodorakopoulos, and Ioannis D. Petsalakis Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, 48 Vassileos Constantinou AVenue, Athens GR-116 35, Greece ReceiVed: March 5, 2008; ReVised Manuscript ReceiVed: May 29, 2008 The electronic and geometric structures of gallium dinitride GaN 2 , and gallium tetranitride molecules, GaN 4 , were systematically studied by employing density functional theory and perturbation theory (MP2, MP4) in conjunction with the aug-cc-pVTZ basis set. In addition, for the ground-state of GaN 4 ( 2 B 1 ) a density functional theory study was carried out combining different functionals with different basis sets. A total of 7 minima have been identified for GaN 2 , while 37 structures were identified for GaN 4 corresponding to minima, transition states, and saddle points. We report geometries and dissociation energies for all the above structures as well as potential energy profiles, potential energy surfaces and bonding mechanisms for some low-lying electronic states of GaN 4 . The dissociation energy of the ground-state GaN 2 (X ˜ 2 Π) is 1.1 kcal/mol with respect to Ga( 2 P) + N 2 (X 1 Σ g + ). The ground-state and the first two excited minima of GaN 4 are of 2 B 1 (C 2V ), 2 A 1 (C 2V , five member ring), and 4 Σ g - (D ∞h ) symmetry, respectively. The dissociation energy (D e ) of the ground-state of GaN 4 , X ˜ 2 B 1 , with respect to Ga( 2 P) + 2N 2 (X 1 Σ g + ), is 2.4 kcal/mol, whereas the D e of 4 Σ g - with respect to Ga( 4 P) + 2 N 2 (X 1 Σ g + ) is 17.6 kcal/mol. I. Introduction Gallium nitrides are semiconducting materials with promising technological applications in microelectronics, nanomaterials, and optics. 1–3 Consequently a significant number of experimental and theoretical studies of the electronic, structural, and optical properties of the solid phase material have been reported in the literature. 4 Information on the geometry and electronic structure of small GaN clusters is essential for applications in micro- electronics, yet work on such clusters either experimental or theoretical is less common, with publications of the latter kind being on the rise lately. Several theoretical studies on Ga x N y species have been reported, for example on symmetric molecules, Ga n N n (n ) 1-6 5–8 ), but not many for the systems of interest here. For GaN 2 three previous studies exist: Kandalam et al. 9 employing density functional theory (DFT) calculations found 3 isomers. Zhou et al. 10 presented the spectra of laser-ablated Ga atoms codeposited with pure nitrogen and some DFT calculations where two states of GaN 2 were determined but not the ground state. In 2004, Wang et al. 11 using DFT, Møller-Plesset Perturbation theory (MP2) and Coupled-Clusters methods (CCD) calculated four isomers of the GaN 2 molecule. For the case of GaN 4 , there is only one study, where Song et al. 12 using the full potential linear muffin tin orbital method calculated three isomers. Thus, a comprehensive and systematic theoretical study of the possible stable structures of GaN 2 and GaN 4 were not pursued in these previous reports. In the present work, which is a continuation of our previous work on the corresponding cations GaN 2 + and GaN 4 + , 13 gallium dinitride and tetranitride molecules, GaN 2 and GaN 4 , were systematically studied using both DFT and MP (MP2, MP4) techniques. In total, 7 minima for GaN 2 and 37 structures for GaN 4 were determined corresponding to minima, transition states, and saddle points. Total energies (E), binding energies (D e ), and geometries (r e , angles) are reported for all 7 structures of GaN 2 and for 17 of GaN 4 , while the corresponding data for the remaining 20 isomers (minima, transition states, and saddle points) calculated for GaN 4 are provided as Supporting Informa- tion. Moreover, vibrational frequencies, potential energy profiles (PEP), and two-dimensional sections of potential energy surfaces (PES) of some low-energy structures of GaN 2 and GaN 4 are plotted. Finally, the bonding process for selected structures is discussed. In Section II, we describe the computational procedure followed, in Section III we discuss our results on the GaN 2 molecule, in Section IV our results on GaN 4 , and, finally, in Section V we present some conclusions and comments. II. Computational Procedure For the GaN 2 molecule, the lowest lying, spin doublet and quartet, linear and bent (NNGa, NGaN) structures were calcu- lated giving seven distinct species. For GaN 4 , a preliminary sampling of the configuration space and bonding networks was performed using the electronic structures of the combining fragments N 4 + Ga, N 3 + Ga + N, N 2 + GaN 2 , GaN 3 + N, and GaN 2 + 2N. About 80 structures were examined for stability resulting in 37 spin doublet and quartet geometry optimized electronic structures of GaN 4 at the B3LYP/LANL2DZ level of theory. B3LYP is a DFT functional using Becke’s three parameter gradient corrected functional 14 with the gradient corrected correlation of Lee, Yang, and Parr. 15 The Hay-Wadt LANL2DZ ECP 16 basis set consists of a pseudopotential for the core electrons (up to 3d electrons) of Ga and a double- quality basis set, for the three outer electrons of Ga, (4s 2 4p 1 ) , and the seven electrons of N, i.e., (3s3p)f [2s2p] Ga and (10s5p)f[3s2p] N . Moreover, additional calculations have been carried out for the ground-state of GaN 4 ( 2 B 1 ), which is a van der Waals isomer, in order to test the limits of reliability of the different theoretical procedures. The DFT method was used with various combinations involving 4 functionals [B3LYP, 14,15 B3PW91, 17 PBEPBE, 18 and LSDA 19 ] and 10 basis sets [LANL2DZ, 16 DGDZVP, 20 cc-pVDZ, 21 SDD, 22 6-311, 23 * Corresponding author. E-mail: dtzeli@eie.gr. Fax: +30-210-7273-794. J. Phys. Chem. A 2008, 112, 8858–8867 8858 10.1021/jp8019396 CCC: $40.75  2008 American Chemical Society Published on Web 08/20/2008