A radically new approach to solving the electronic Schrödinger equation

  • Nov 30, 2017
  • Piotr Piecuch

Graph of the dataSolving the electronic Schrödinger equation in an accurate and computationally efficient manner has been a key challenge in quantum chemistry for decades. In ab initio wave function theories, which approach the problem using first principles of quantum mechanics without empirical parameters, one ends up with highly complex systems of algebraic equations, whose solution requires enormous computer power. An alternative to this deterministic approach is a stochastic wave function sampling using Quantum Monte Carlo ideas. Both approaches have pros and cons. The purely deterministic methodologies, such as those based on the coupled-cluster formalism, lead to numerically precise answers that can be systematically improved, but the computational cost of obtaining such answers is often prohibitive. The stochastic approach can be made computationally less demanding, but one ends up with numerical noise and long wave function propagation times to achieve convergence. In the recent paper, published in Physical Review Letters (Phys. Rev. Lett. 119, 223003 (2017)), MSU Chemistry Professor Piotr Piecuch and two members of his group, J. Emiliano Deustua and Dr. Jun Shen, propose a radically new approach to accurately solving the electronic Schrödinger equation addressing the above challenges by fusing the stochastic Monte Carlo and deterministic coupled-cluster ideas. Stochastic methods are used to identify the leading wave function components, whereas the subsequent deterministic coupled-cluster calculations, combined with suitable energy corrections, provide the rest of the information. As shown by Professor Piecuch and co-workers, the new methodology, abbreviated as CC(P;Q), displays rapid convergence toward target molecular electronic energetics based on the information extracted from the early stages of Monte Carlo wave function propagations, reducing computational costs by orders of magnitude and opening a new research paradigm in areas of quantum chemistry and many-body theory.