\begin{equation}
\begin{array}{lcl}
E_{v} & = & \hbar\omega(v+\frac{1}{2})+\frac{1}{16}V_{4}\left(\frac{\hbar}{\mu\omega}\right)^{2}(v^{2}+v+\frac{1}{2})-\frac{5V_{3}^{2}}{48\hbar\omega}\left(\frac{\hbar}{\mu\omega}\right)^{3}(v^{2}+v+\frac{11}{30})\\
 & = & \hbar\omega(v+\frac{1}{2})-\left[\frac{5V_{3}^{2}}{48\hbar\omega}\left(\frac{\hbar}{\mu\omega}\right)^{3}-\frac{V_{4}}{16}\left(\frac{\hbar}{\mu\omega}\right)^{2}\right](v+\frac{1}{2})^{2}+\frac{1}{64}V_{4}\left(\frac{\hbar}{\mu\omega}\right)^{2}-\frac{7V_{3}^{2}}{576\hbar\omega}\left(\frac{\hbar}{\mu\omega}\right)^{3}\end{array}
\end{equation}