β-BaB2O4 crystal is a new-type ultraviolet SHG crystal as found in our Institute for the first time. In this paper, on the basis of our theoretical work of "An anionic group theory of non-linear optical effects of the crystals" and the theory of odd-ordered crystal field produced by A-site cation, we have calculated SHG coefficients of β-BaB2O4 crystal by using CNDO/S approximations. The calculated values agree satisfactorily with the experimental data, for both absolute values and relative sign of the above coefficients. The result shows that the conjugate π orbitals of anionic group (B3O6)3-give major contribution to the SHG coefficients. Moreover, it also shows that the CNDO/S-approximation is a suitable method for calculating molecular orbitals of cova-lent-bonded (B3O6)3- group in crystals.
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