Stochastic approach optimizes a system’s wavefunction to improve computational efficiency

Though solving the Schrodinger equation reveals all needed information for any problem, this is difficult to do a for an arbitrarily complicated system. In quantum chemistry, challenging systems are often treated using a class of techniques known as multireference methods. These methods cannot be applied to arbitrarily large and complicated systems due to the high-rank reduced density matrices involved. Mahajan et al. have formulated a technique to calculate energies without the need for the computationally expensive reduced density matrices.

“In multireference quantum chemistry, one often uses very accurate wavefunctions, such as the internally contracted multireference interaction,” said lead author Sandeep Sharma. “These wavefunctions happen to be at just the right level of difficulty that, although it is possible to perform polynomial-scaling deterministic calculations with them, the cost scales quite unfavorably with the size of the active space.”

The authors overcame this bottleneck using a stochastic approach. They estimated the energy of the system’s wavefunction by averaging the local energy for a number of different configurations of the system as determined by a random walk through its Hilbert space. By optimizing the wavefunction’s parameters to minimize its energy, they transformed a single, expensive calculation into a series of smaller and cheaper ones.

Testing this stochastic approach on several different diatomic molecules indicates its feasibility in treating larger, more complicated systems. It outperforms traditional deterministic methods, both in terms of computational time and memory cost, regardless of the type of wavefunction used, allowing for the exciting prospect of studying large systems previously inaccessible to computational techniques.

Looking ahead, the group plans to extend the work to the study of core electron correlations.

Source: “Multireference configuration interaction and perturbation theory without reduced density matrices,” by Ankit Mahajan, Nick S. Blunt, Iliya Sabzevari, and Sandeep Sharma, Journal of Chemical Physics (2020). The article can be accessed at https://doi.org/10.1063/1.5128115 .