Abstract
We present a new collocation method for computing the vibrational spectrum of a polyatomic molecule.
Some form of quadrature or collocation is necessary when the potential energy surface does not have a simple
form that simplifies the calculation of the potential matrix elements required to do a variational calculation.
With quadrature, better accuracy is obtained by using more points than basis functions. To achieve the
same advantage with collocation, we introduce a collocation method with more points than basis functions.
Critically important, the method can be used with a large basis because it is incorporated into an iterative
eigensolver. Previous collocation methods with more points than functions were incompatible with iterative
eigensolvers. We test the new ideas by computing energy levels of molecules with as many as 6 atoms. We
use pruned bases, but expect the new method to be advantageous whenever one uses a basis for which it is
not possible to find an accurate quadrature with about as many points as there are basis functions. For our
test molecules, accurate energy levels are obtained even using non-optimal, simple, equally spaced points.