Assuming that a (Born Oppenheimer) potential energy surface (PES) is known, one can compute a (ro-)vibrational spectrum from first principles. Spectra from first principles are useful when anharmonicity and coupling play an important role, e.g. in Van der Waals dimers. The calculation is often done using a variational method, which requires choosing coordinates and basis functions and then calculating eigenvalues of a matrix that represents the Hamiltonian operator in the chosen basis. In this talk, I shall review the key components of such variational calculations. The main difficulty arises due to the size of the basis required to obtain converged energy levels and wavefunctions. This necessitates using iterative eigensolvers. It is straightforward to use iterative eigensolvers with simple product bases, even when the PES has a complicated functional form. Using a product basis, however, limits the size of the molecule for which it is possible to compute a spectrum. It is better, but more difficult, to use contracted basis functions and I’ll discuss how to use them in conjunction with the Lanczos algorithm to calculate vibrational (or ro-vibrational) spectra. The basis functions are products of contracted functions that are themselves eigenfunctions of reduced-dimension Hamiltonians obtained by freezing coordinates. The basis functions represent the desired wavefunctions well, yet are simple enough that matrix-vector products, required to use an iterative eigensolver, may be evaluated efficiently.
Tucker Carrington Jr., “Computing (ro-)vibrational spectra of molecules with more than four atoms,” J. Chem. Phys. [Invited Perspective article] 146, 120902-1 – 120902-10 (2017).
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Financial Support
The Cooper Union for the Advancement of Science and Art is pleased to provide support for the 2024 VWSCC through a generous donation from Alan Fortier.
We thank Leibniz Institute for Catalysis (LIKAT) and CECAM for their support.
Virtual Winter School on Computational Chemistry