9236
J. Phys. Chem. 1992,96,9236-9243
Electronic Structure and Potential Energy Surfaces of Positive Ions of Group I V Tetramers (Ge,+-Pb,+) Dingguo Dai and I(. Balasubramanian**f Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287- 1604 (Received: May 18, 1992)
We compute the geometries and energy separations of 17 electronic states of Ge4+,Sn4+,and Pb4+. The complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by multireference singles + doubles configuration interaction (MRSDCI)calculationsarc employed in this investigation. Spin-orbit effects are also included using the relativistic configuration interaction (RCI) method for Pb4+. The ground state of Ge4+is found to be a 2Blustate with an equilibrium geometry of a rhombus. For Sn4+we find two nearly-degenerate electronic states of 2Bluand 2A,symmetries as candidates for the ground state both with rhombus equilibrium geometries. We find three nearly-degenerate electronic states (2BlU, 2B3U,and 2A8)for Pb4+as candidates for the ground state in the absence of spin-orbit interaction. Upon introduction of spin-orbit coupling the E(I) ground state becomes a 88% 2Bluand 7% 2B3, mixture. Dissociation energies of Ge4+-Pb4+ as well as ionization potentials of Ge4-Pb4 are computed. The nature of the electronic states of Ge4+-Pb4+are analyzed. The energy separations of the excited electronic states of Ge4+-Pb4+are found to decrease, especially the splitting between the rhombus and tetrahedral structures, as one goes down the group.
Introduction Clusters of main group elements and especially the semiconductor group IV and group III-V clusters are being actively investigated both theoretically and ~xperimentaUy.~-~~ The interest in group IV clusters in particular is attributed in part to their technological importance since group IV materials (Si, Ge) are used in the fabrication of microelectronicdevices. Smalley and co-workers have studied the photofragmentation patterns of Si; and Gent cluster ions, as well as Si; and Ge; ions!*'* They found certain interesting trends in the photofragmentation patterns of these species. Martin and Schaber have obtained the mass spectra of both tin and germanium clusters.26 They too found several fascinating trends in the mass spectra of these species. In particular, they found that the mass spectra of tin clusters exhibit a gradual decrease in the intensity for up to 13-atom clusters. In dramatic contrast, the leatom cluster was absent in the mass spectrum while the intensities of the peaks which correspond to 15- and 16-atom clusters increase again. Magic numbers were also found for the 6- and 10-atom clusters of Si,+ and Gent. Lineberger and c o - ~ o r k e r shave ~ ~ recently obtained the photodetachment spectra of Si, and Pb; clusters. They have analyzed the spectra of dimers in considerable detail and found very good agreement with the results of previous theoretical calculations on Pbz and Snz (see ref 1 for a review of computed results on dimers and trimers). Experimental studies have also been made on positively charged Pb clusters.34 There are laser-inducedfluorescence studies on dimers of Pb and Sn. Neumark and ~o-workers~~ have obtained negative photodetachment spectra of Si4-. T h m are several recent experimental and theoretical on the excited states of Si3 as well as Ge3. Among the heavier group IV clusters, Si4 has been the most studied molecule theoretically.19P Pacchioni and K0ute42l@~have studied the ground-state properties of Ge4. There are theoretical studies on Sn3, Si4, Gq,and Ge4. Raghavachari and co-worke r ~have ~ studied ~ , ~Si,~ (n 3-10), excited states of Si3and Si4, among other related species. These studies have yielded a wealth of information on silicon clusters. While considerable information has been accumulated on silicon clusters, this is not the case for heavier group IV clusters. Spectroscopic studies on the positive ions are on the increase since the sizes of the charged clusters can be established unequivocally compared to the neutral clusters. For example, Duncan and -workersa are investigating positively charged clusters using laser spectroscopic methods. There is a real need to know the
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geometries and energy separations of both the ground and excited states of these species. The objective of the present theoretical study is the computation of geometries and energy separations of several electronic states of Ge4+,Sq+,and Pb4+. We consider several electronic states with many geometries. We employ complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by multireferenceconfiiration interaction (MRSDCI) and relativistic configuration interaction (RCI) calculations.
Metbod of C.lculations It is now well established that the ground state of S4 (and Ge,) is a lA (DZk)state with an equilibrium geometry of a rhombus.1932f39 The leading configuration is composed of la~2a23a~lb~,2b~,lb~lb~81b~u. Removal of an electron from the state for the positive ion while the 3a8 orbtal would lead to a 2Blustate can be formed by removing an electron from the 2bl, orbital. Since the lb, orbital is primarily composed of the valence s orbitals of two of the group IV atoms, this is not an attractive candidate for ionization. On the other hand, removal of an electron from 1b3*or 1b3, could lead to ZB38and 2BB,,states, respectively. consequently, in the present study on Gc4+-Pb4+, we &der 2 k 2 B 3 , , and ZB3,states with rhombus geometries. e tetrahedral geometry is somewhat more complex due to the degeneracy of the and e orbitals. The 'Al state of the neutral structure39 arises from the la:lt!2a:2t$ confiiations. Hence removal of an electron from the 2t2 orbital leads to the q2 state. On the other hand, the spin-exchange stabilization energy could favor the 6A1state arising from the la:lt$2a:2t:le2 configuration due to the near proximity of the 2t2 and l e orbitals as well as spin-stabilization energy. Consequently, in addition to these states we also considered electronic states of lT2,4E, and 'Tz symmetries for the tetrahedral structure. For the linear structure of neutral Si, the 32;state was found This state arises from the to be the lowest state. l u ~ 2 < 3 4 1 4 2 4 l r t l $ configuration. Hence a few possible low-lymg electronic states for the positive ion with linear geometry are "2: (3uu141a$, 42, (3u81rt1$),, 2118 (3
