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A novel computational technique to solve the many-particle Schrödinger equation

One of the goals of electronic structure theory is to precisely describe increasingly complex polyatomic systems. The most difficult question in this kind of many-body problematic is to describe electron correlation. While 99% of the question is solved by the classical variation principle, lots of important physics is happening in the remaining 1%. To look into these 1%, there are three know methods and one of them is named the Coupled-Cluster Theory.

The basic assumption of coupled cluster theory is that the exact many-electron wavefunction may be generated by the operation of an exponential operator on a single determinant. The excitation operator can be written as a linear combination of single, double, triple, etc. excitations, up to N fold excitations for an N electron system. Interestingly, scientists recently discovered a new approach to solve this problem in a much more efficient way.

It's like playing chess and being able to predict the outcome of the game after the initial few moves.

Ψ is the exact wavefunction, T is an excitation operator and Φ0 is the reference determinant defining the Fermi vacuum, usually the Hartree-Fock determinant.

The team led by Piotr Piecuch just proposed a new approach to the determination of accurate electronic energies that are equivalent to the results of high-level coupled-cluster calculations. The approach is based on merging one formalism correcting energies with a stochastic configuration interaction. They showed that this combination allows to recover high-level energetics even when electronic quasi degeneracies become substantial. This new stochastic approach is opening up new possibilities in the way high-level coupled-cluster calculations are carried out.

In the case of nuclei, instead of being concerned with electrons, one would use our new approach to solve the Schrödinger equation for protons and neutrons. […] The mathematical and computational issues are similar. Just like chemists want to understand the electronic structure of a molecule, nuclear physicists want to unravel the structure of the atomic nucleus. Once again, solving the many-particle Schrödinger equation holds the key.

Piotr Piecuch, Department of Physics and Astronomy, Michigan State University

The advantages of the proposed methodology are illustrated by molecular examples, where the goal is to recover the energetics obtained in the coupled-cluster calculations with a full treatment of singly, doubly, and triply excited clusters.

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