Let $V$ be a Kähler space with only log terminal singularities. $V$ is said to be $\mathbb{Q}$-CY, iff there is some multiple $N^{\prime}$ of $index(X)$ such that $H^{0}(V,\omega^{[N^{\prime}]}_{V})=\mathbb{C}\alpha$, where $\alpha$ is a global generator of $\omega^{[N^{\prime}]}_{V}$.