An angular-force method for bcc transition-metals is obtained by generating a functional form via a quantum-mechanical analysis, and subsequently fitting the parameters in this form to experimental and ab-initio theoretical inputs. The quantummechanical analysis uses a four-moment treatment of the electronic density of states (DOS) in a d-band tight-binding model. Calibration of the method gives excellent results for the bcc-fcc energy difference and the vacancy-formation energy in W. The method is used to treat relaxation and c(2×2) reconstruction on the W (100) surface. The relaxation energy is primarily due to two-body terms, while the reconstruction requires the angular terms. Agreement with ab-initio results is obtained for reasonable values of the parameters in the model. However, the energy difference between the reconstructed surface and the optimally relaxed surface is quite sensitive to the details of the implementation of the method.
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Carlsson, A.E. Semiempirical Angular-Force Method for BCC Transition Metals. MRS Online Proceedings Library 209, 165–170 (1990). https://doi.org/10.1557/PROC-209-165