Knowledge Bank

Since its inception in 1975 by Anderson,}, {\underline{63}}, 1499 (1975).} Diffusion Monte Carlo (DMC) has been successfully applied to a wide range of electronic and vibrational problems. In the latter case, it has been shown to be a powerful method for studying highly fluxional systems exhibiting large amplitude vibrational motions. We report here our recent work developing a new DMC algorithm capable of treating rotational excited states. We first develop the appropriate coordinates, nodal structures, and re-crossing corrections for this problem. Then, using H$3$O$+$ and D$3$O$+$ as model systems,}, {\underline{118}}, 5431 (2003).} we show that our method can successfully describe a range of rotational states from $\mid 0,0,0⟩$ to $12(\mid 10,10,0⟩+\mid 10,-10,0⟩)$. In particular, we examine the combined effects of rotational and zero-point vibrational motion on the geometric structure of the molecules. Finally, we find the $\mid 10,0,0⟩$ state to be somewhat problematic but show that the problem is straightforward to identify and has a well-defined solution.