An ab initio cluster study of the structure of the Si(001) surface

Ab initio calculations, employing double zeta plus polarization (DZP) basis sets and generalized valence bond (GVB) wave functions, have been performe d on clusters of varying size, to investigate the utility of such clusters as prototypes for the study of silicon surfaces, and to investigate the eff ect of the level of theory used on predicted results. This work builds on l andmark papers by Goddard in 1982 and Paulus in 1998 that demonstrate that a single reference wave function description of the silicon dimer bond is i ncorrect, and that a multireference description results in a symmetric dime r in a silicon cluster containing one dimer. In this work, it is shown that the imposition of arbitrary geometrical constraints (fixing subsurface ato ms at lattice positions) on cluster models of the Si(100) surface can also lead to nonphysical results. Calculations on the largest clusters, without geometrical constraints, reveal that surface rearrangement due to dimer bon d formation is "felt" several layers into the bulk. The predicted subsurfac e displacements compare favorably to experiment. Thus, small clusters, such as Si9H12, cannot adequately represent bulk behavior. Vibrational analysis shows that dimer buckling modes require minimal excitation energy, so the experimental observation of buckled dimers on silicon surfaces may reflect the ease with which a symmetric dimer can be perturbed from its minimum ene rgy structure. In the study of surface reconstruction and relaxation, and t he associated issue of the buckling of dimer surfaces, it is critical to us e adequate wave functions. As shown in this work and previously by Goddard and Paulus, this generally means that multireference treatments are needed to correctly treat the dangling bonds. (C) 2000 American Institute of Physi cs. [S0021-9606(00)30206-9].