  B-spline functions have been widely used in computational atomic physics.
Different from the traditional B-spline basis (a simple product of two
B-splines), the recently developed correlated B-spline basis functions(C-BSBF),
in which the interelectronic coordinate $r_{12}$ is included explicitly, have
greatly improved the computational accuracy of polarizability [S. J. Yang
\textit{et al}., Phys. Rev. A \textbf{95}, 062505 (2017)] and bethe logarithm [
S. J. Yang \textit{et al}., Phys. Rev. A \textbf{100}, 042509 (2019)] for
singlet states of helium. Here, we report the extension of the C-BSBF to the
leading relativistic and QED correction calculations for energy levels of the
$1\,^1S$, $2\,^1S$, $2\,^3S$, and $3\,^3S$ states of helium. The relativistic
kinetic term $p_{1}^{4}$, contact potential $\delta^{3}(r_{1})$,
$\delta^{3}(r_{12})$ and Araki-Sucher correction $\langle 1/r_{12}^{3} \rangle$
are calculated by using the global operator method, in which $r_{12}^n$ and
$r_{12}^n\ln r_{12}$ involved are calculated with the generalization of
Laplace's expansions. The obtained values for the ground state are $\delta
E_{rel}/\alpha ^{2}=-$1.951 754 7(2) and $\delta E_{QED}/\alpha^{3}=$57.288
165(2), consistent with previous results, which opens the possibility of
calculating higher-order relativistic and QED effects using the C-BSBF.
