# New tools for quantum chemistry at high energies and loose bindings - New tools for quantum chemistry at high energies and loose bindings

# New tools for quantum chemistry at high energies and loose bindings

Controlling radiation damage is a significant problem in the design and development of fusion reactors. Computational modeling of the radiation damage caused by the energetic particles generated by the fusion reactions hitting the walls of the reactor requires accurate knowledge of the highly repulsive part of the interatomic potential energy curve.

Although the potential energy at any internuclear distance can in principle be obtained in a straightforward manner from a diatomic electronic structure calculation, these calculations become numerically challenging at small distances (e.g. R=0.01 Å or 0,001 nm), as in contrast to chemistry in ambient conditions, also the core electrons may be significantly affected by the interactions between the two atoms; this effect is ignored in many computational approaches.

In addition, other types of electronic structure approaches tend to break down at small internuclear distances, because the problem is no longer well-defined due to significant linear dependencies caused by the closeness of the nuclei. Moreover, diatomic molecules may be tough to model even at the chemical equilibrium distance – for instance, the chromium dimer Cr_{2} is a textbook example of a molecule whose electronic structure is quantum mechanically entangled and continues to be a significant challenge to quantum chemical models.

## Modern techniques for highly accurate calculations

Fully numerical electronic structure calculations are flexible enough to be applied also at small internuclear distances. Although fully numerical calculations on diatomic molecules have been feasible since the 1970s, also their application to the repulsive problem at small R proves to be problematic.

However, Academy of Finland postdoctoral fellow, docent **Susi Lehtola** at the University of Helsinki has developed modern techniques for highly accurate fully numerical calculations on atoms and diatomic molecules, allowing routine self-consistent field calculations at the complete basis set limit - even at extremely small internuclear distances.

Lehtola’s review on fully numerical calculations and articles describing the new multipurpose tools for reaching higher accuracy in fundamental studies of quantum chemistry were recently published as cover articles in the International Journal of Quantum Chemistry, with cover graphics by Jyrki Hokkanen, CSC.

With the new HelFEM program he developed, Lehtola and coworkers have *e.g.* been able to carry out accurate calculations on H_{2}, HeH^{+}, LiH, BeH^{+}, BH, and CH^{+} in magnetic fields up to 2 million tesla with CSC’s supercomputers. The work has also yielded new insights into electronic structure calculations on larger molecules.

## Modeling loosely bound electrons

More recently, Lehtola has studied the modeling of loosely bound electrons in electronic structure calculations. For instance, dipole bound electrons are often only weakly attached to the system, and may be observed in *e.g.* anionic water clusters. Calculating the binding energy of the excess electron accurately is also a challenge to typical electronic structure calculations, because correct modeling of the diffuse character of the solvated electron often results in numerical instabilities in the electronic structure calculation.

Lehtola succeeded in removing these instabilities with a simple modification to pre-existing quantum chemistry software that removes redundant degrees of freedom, allowing accurate binding energy calculations on* e.g.* (H_{2}O)_{24}^{-} even while reducing the computational cost.

Lehtola has shown recently that the very same approach also affords accurate modeling of the strongly repulsive potential energy curve by studying a set of nuclear reactions between closed-shell atoms. This is demonstrated in the figure below for the He + Ne ↔ Mg nuclear reaction, where the solid line is computed using a linear combination of atomic orbitals (LCAO) approach, and the fully numerical reference values that are in excellent agreement with the LCAO results are shown with +.

Despite the recent successes, there still remain many challenges and open questions. Can the fully numerical approaches be extended to heavier atoms? What are the effects of relativity on the repulsive potentials? How should open shells be described in the calculations? Among others, these are issues Lehtola hopes to address in future work.

### Further information

S. Lehtola, Assessment of initial guesses for self-consistent field calculations. Superposition of Atomic Potentials: simple yet efficient, *J. Chem. Theory Comput.* 15, 1593 (2019).

S. Lehtola, Fully numerical Hartree–Fock and density functional calculations. I. Atoms, *Int. J. Quantum Chem.* 119, e25945 (2019).

S. Lehtola, Fully numerical Hartree–Fock and density functional calculations. II. Diatomic molecules, *Int. J. Quantum Chem.* 119, e25944 (2019).

S. Lehtola, A review on non-relativistic fully numerical electronic structure calculations on atoms and diatomic molecules, *Int. J. Quantum Chem.* 119, e25968 (2019).

S. Lehtola, M. Dimitrova, and D. Sundholm, Fully numerical electronic structure calculations on diatomic molecules in weak to strong magnetic fields, *Mol. Phys.* **118**, e1597989 (2020).

S. Lehtola, Curing basis set overcompleteness with pivoted Cholesky decompositions, *J. Chem. Phys.* 151, 241102 (2019).

S. Lehtola, Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals, *Phys. Rev. A* 101, 012516 (2020).

S. Lehtola, Accurate reproduction of strongly repulsive interatomic potentials, Phys. Rev. A **101**, 032504 (2020).

S. Lehtola, L. Visscher, E. Engel, Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets, *J. Chem. Phys.* 152, 144105 (2020).

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- Publish Date
- 4/30/20