MOSCOW, November 29. /TASS/. Ivan Oseledets have put forward a novel approach for solving the famous Schr·dinger equation to calculate vibrionic spectra of molecules, Skoltech’s press service said. The new technique allows for calculating states of molecules with a high precision using even minimalistic computational facilities, an ordinary laptop.

To describe molecular vibrations, the Schrodinger equation (the main equation of quantum mechanics) is used, and during its numerical solution process, tensors, or multidimensional data structures appear. That said, the computational memory requirements for storing tensors quickly expand as the molecular size increases, which is dubbed "dimensionality damnation".

"For example, due to "dimensionality damnation" the calculation of properties of a relatively small molecule of acetonitrile would require hundreds of petabytes of computational memory," Rakhuba explained. "Hence, the results described in all recent articles, even for very small objects, took several days or weeks of computational time on a large computer cluster, otherwise one would have had to sacrifice accuracy. Our scheme allows an individual to avoid such limitations: anyone can perform calculations even with an ordinary laptop in a short time without losing accuracy."

To simplify the computational scheme, researchers utilized an approach of tensor decomposition, namely, the tensor-train decomposition, which is often capable of coping with the "dimensionality damnation." The study’s results have been recently published in the international scientific journal, The Journal of Chemical Physics.