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**Sergei Manzhos, Koichi Yamashita
Department of Chemical Systems Engineering, School of Engineering, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan**

Tucker Carrington

*Department of Chemistry, Queen's University, 90 Bader Lane, Chernoff Hall, Kingston, ON, K7L 3N6, Canada*

We address the problem of computing a vibrational spectrum using a small number of basis functions in the expansion of the wavefunction and a small number of samples of the potential energy surface (PES). While it is possible today to solve for hundreds of *v*-levels of a 5-6 atomic molecule (in vacuum) with high accuracy, the task is formidable due to the size of the Hamiltonial matrix and the need for a PES function.

In many applications, such as vibrations of molecules at surfaces, however, only several *v*-levels are desired, and the accuracy of ~1 cm-1 would suffice. A complex with an adsorbed molecule has a much higher dimensionality than the molecule in vacuum, which is why today, only normal mode, harmonic analysis of frequencies is feasible. However, the PES of adsorbate-containing systems deviates strongly from a (uncoupled) harmonic well. A method is desired to compute spectral signatures of molecule-surface/particle complexes taking into account the real shape of the PES.

We present a method that calculates several vibrational levels from a very small, flexible (parameterized) basis. It simplifies the solution of the Schrödinger equation in many dimensions, where basis size explosion (due mainly to the use of direct product bases) is the principal impediment to studying larger molecular and reactive systems. The approach combines non-linear optimization of parameters of the basis with a method to solve a rectangular matrix problem for linear parameters.

The algorithm [*Can. J. Chem.* **87**, 864 (2009), *Chem. Phys. Lett*., **474**, 217 (2009)] avoids the calculation of integrals and of the potential energy function. We demonstrate its application to a model problem in up to 6 dimensions, to the spectrum of H2O, and on-going application to a molecule-surface system.

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