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We have investigated the influence of the oxygen vacancy on the linear and nonlinear optical properties and the microscopic first hyperpol of asymmetric Pb7O(OH)3(CO3)3(BO3). The O-vacancy reduces the energy gap and changes the energy band gap from indirect to direct. The calculated indirect energy band gap of Pb7O(OH)3(CO3)3(BO3) (I) of 3.56 eV is in good agreement with the experimental gap of 3.65 eV. The direct gap in O-deficient Pb7(OH)3(CO3)3(BO3) (II) is 1.61 eV. The oxygen vacancy results in a red-shifted energy band gap, making the material useful in the visible region. Calculations show that I exhibits a negative uniaxial anisotropy and birefringence, whereas II exhibits positive uniaxial anisotropy and birefringence. This shows that the O-vacancy has a significant influence on the uniaxial anisotropy and birefringence. We have calculated the second harmonic generation (SHG) for I and II at zero energy limit and at wavelength λ = 1064 nm. The calculated SHG for I at λ = 1064 nm is close to the experimental value of the well known compound KTiOPO4 (KTP), whereas for II it is about a quarter of the experimental value of the KTP. In addition, the microscopic first hyperpolarizability for I and II is calculated at the static limit and at wavelength 1064 nm.

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The influence of oxygen vacancies on the linear and nonlinear optical properties of Pb7O(OH)3(CO3)3(BO3)