Small elemental clusters. I. The structures of Be₂, Be₃, Be₄, and Be₅

Abstract

The geometries and energies of beryllium clusters up to Be5 are examined using ab initio molecular orbital theory. Allowances are made for electron correlation with MBller-Plesset perturbation theory to fourth order. Correlation is found to have a dramatic effect on the relative energies of the several structures examined for Be4 and Bes. Furthermore, the effect of d-type basis functions on the correlation energy results in an increased binding energy for the clusters. Be2 is only weakly bound. For Be:i, the best estimate of the binding energy is 6 kcal/mole for the singlet equilateral triangle. Be4 is tetrahedral in its ground state and the estimated binding is 56 kcal/mole. The best structure for Be5 is a singlet trigonal bipyramid, and the binding energy is 88 kcal/mole at the highest level of theory used.

Vibrational Frequencies of Small Metal Clusters. The Beryllium Tetramer

“…The bond distances and total energies are consistent with earlier theoretical studies [8][9][10][11][12][13][14][15][16][17][18][19]. The theoretical frequencies in Table 2 do not fit this formula well a result which is not surprising when one realizes that the CFA amounts to neglecting all off-diagonal elements in the internal coordinate force constant matrix.…”

“…Previous theoretical research has shown [14,17,19] that the reliable prediction or the dissociation energy of Be 4 , namely 6E(Be 4 + 4Be), requires a high level of theory. Specifically, d orbitals must be included in the basis set, and the effects of electron correlation must be carefully considered.…”

“…• Subsequent theoretical studies [9][10][11][12][13][14][15][16][17][18][19] Vibrational spectroscopy has in recent years become a powerful tool for the characterization of metal surfaces and of chemisorption on metal surfaces [22]. In light of the analogy between surfaces and gas-phase metal clusters [7], it is apparent that the vibrational spectroscopy of the latter will in time become an important area of research" Since experimental studies of the infrared and Raman spectra of naked metal clusters are e.ssentially nonexistent, theory is in a good position to provide some potentially helpful guidance to laboratory research.-In this vein, we report here a ·theoretical-study of the vibrational frequencies of Be 4 , a simple, relatively stable metal cluster.…”

Ab initio molecular orbital studies of the potential energy curves for the low lying triplet states of Be2 and Be3

“…Among the various metal clusters that have been investigated theoretically, probably beryllium clusters of varying size have been studied most extensively (14)(15)(16)(17)(18)(19)(20)(21). The, smallest system, Be2, has been used as a model in theoretical studies since 1931 (22,23).…”

“…The, smallest system, Be2, has been used as a model in theoretical studies since 1931 (22,23). The potential energy curve of the ground state of Be2 has been the subject of a number of theoretical investigations (14)(15)(16)(17)(18) but in spite of the large number of calculations with various degrees of sophistication, it was only recently that reliable calculations on the potential energy curve for the ground state of Be2 have Feen reporte$ (14,16,17). The calculated values of Re = 2.51 A (16), 2.50A (17) and D, = 2.23-2.34kcal/mol (14), 2.04 k 0.2kcal/mol (17) are in good agreement with the experimentally determined values of Re = 2.465 A, and D, = 2.29 kcal/mol (24)(25)(26).…”