Accurate reproduction of strongly repulsive interatomic potentials

Knowledge of the repulsive behavior of potential energy curves $V(R)$ at $R\to0$ is necessary for understanding and modeling irradiation processes of practical interest. $V(R)$ is in principle straightforward to obtain from electronic structure calculations; however, commonly-used numerical approaches for electronic structure calculations break down in the strongly repulsive region due to the closeness of the nuclei. In the present work, we show by comparison to fully numerical reference values that a recently developed procedure [S. Lehtola, J. Chem. Phys. 151, 241102 (2019)] can be employed to enable accurate linear combination of atomic orbitals calculations of $V(R)$ even at small $R$ by a study of the seven nuclear reactions He2 Be, HeNe Mg, Ne2 Ca, HeAr Ca, MgAr Zn, Ar2 Kr, and NeCa Zn.

[1]  F. Bloch,et al.  Bemerkung zur Elektronentheorie des Ferromagnetismus und der elektrischen Leitfähigkeit , 1929 .

[2]  M. A. Karolewski.  Repulsive potentials for low energy projectiles incident on copper surfaces , 2007 .

[3]  Man-Ching Wong,et al.  57 , 2015, Tao te Ching.

[4]  M. A. Karolewski.  Ab initio interatomic potentials for low-energy He ion/atom scattering , 2012 .

[5]  Yihan Shao,et al.  Curvy steps for density matrix-based energy minimization: Application to large-scale self-consistent-field calculations , 2003 .

[6]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[7]  Matt Challacombe,et al.  A simplified density matrix minimization for linear scaling self-consistent field theory , 1999 .

[8]  Susi Lehtola.  Curing basis set overcompleteness with pivoted Cholesky decompositions. , 2019, The Journal of chemical physics.

[9]  M. A. Karolewski.  Repulsive interatomic potentials for noble gas bombardment of Cu and Ni targets , 2006 .

[10]  Susi Lehtola,et al.  Assessment of Initial Guesses for Self-Consistent Field Calculations. Superposition of Atomic Potentials: Simple yet Efficient , 2018, Journal of chemical theory and computation.

[11]  Susi Lehtola,et al.  Fully numerical Hartree‐Fock and density functional calculations. II. Diatomic molecules , 2018, International Journal of Quantum Chemistry.

[12]  P. Sigmund.  Particle Penetration and Radiation Effects Volume 2: Penetration of Atomic and Molecular Ions , 2014 .

[13]  Frank Jensen,et al.  Polarization consistent basis sets: Principles , 2001 .

[14]  K. Nordlund,et al.  Pair potential for Fe-He , 2008 .

[15]  Susi Lehtola.  Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals , 2020 .

[16]  Short-range repulsive interatomic interactions in energetic processes in solids , 2004, cond-mat/0401265.

[17]  J. Keinonen,et al.  First-principles simulation of collision cascades in Si to test pair-potentials for Si-Si interaction at 10 eV–5 keV , 1994 .

[18]  Francesco Aquilante,et al.  Fast noniterative orbital localization for large molecules. , 2006, The Journal of chemical physics.

[19]  S. Lehtola.  A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules , 2019, International Journal of Quantum Chemistry.

[20]  K. Nordlund,et al.  Radiation damage production in massive cascades initiated by fusion neutrons in tungsten , 2014 .

[21]  Nora H. Sabelli,et al.  Ground-state potential curves forAl2andAl26+in the repulsive region , 1979 .

[22]  Gustavo E. Scuseria,et al.  Linear scaling conjugate gradient density matrix search as an alternative to diagonalization for first principles electronic structure calculations , 1997 .

[23]  S. Lehtola,et al.  Fully numerical electronic structure calculations on diatomic molecules in weak to strong magnetic fields , 2018, Molecular Physics.

[24]  H. Harbrecht,et al.  On the low-rank approximation by the pivoted Cholesky decomposition , 2012 .

[25]  Tikkanen,et al.  First-principles simulation of intrinsic collision cascades in KCl and NaCl to test interatomic potentials at energies between 5 and 350 eV. , 1991, Physical review letters.

[26]  S. Lehtola.  Fully numerical Hartree‐Fock and density functional calculations. I. Atoms , 2018, International Journal of Quantum Chemistry.

[27]  Keijo Hämäläinen,et al.  ERKALE—A flexible program package for X‐ray properties of atoms and molecules , 2012, J. Comput. Chem..

[28]  Andrew G. Glen,et al.  APPL , 2001 .

[29]  J. Almlöf,et al.  Integral approximations for LCAO-SCF calculations , 1993 .

[30]  J. Herbert.  The Quantum Chemistry of Loosely-Bound Electrons , 2015 .

[31]  Range parameters of heavy ions in carbon calculated with first-principles potentials , 2006 .

[32]  N. H. Beebe,et al.  Simplifications in the generation and transformation of two‐electron integrals in molecular calculations , 1977 .

[33]  J. Gauss,et al.  Implementation of analytic gradients for CCSD and EOM-CCSD using Cholesky decomposition of the electron-repulsion integrals and their derivatives: Theory and benchmarks. , 2019, The Journal of chemical physics.

[34]  Roland Lindh,et al.  Atomic Cholesky decompositions: a route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency. , 2009, The Journal of chemical physics.

[35]  K. Nordlund,et al.  Repulsive interatomic potentials calculated using Hartree-Fock and density-functional theory methods , 1997 .

[36]  Roland Lindh,et al.  Unbiased auxiliary basis sets for accurate two-electron integral approximations. , 2007, The Journal of chemical physics.

[37]  P. Pyykkö.  Relativistic effects in chemistry: more common than you thought. , 2012, Annual review of physical chemistry.

[38]  N. Sabelli,et al.  SCF potential curves for AlH and AlH+ in the attractive and repulsive regions , 1978 .

[39]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[40]  Henrik Koch,et al.  An efficient algorithm for Cholesky decomposition of electron repulsion integrals. , 2018, The Journal of chemical physics.

[41]  M. Barthe,et al.  Modelling radiation damage and He production in tungsten , 2011 .

[42]  F. E. Jorge,et al.  Accurate universal Gaussian basis set for all atoms of the Periodic Table , 1998 .

[43]  P. Pyykkö.  The physics behind chemistry and the periodic table. , 2012, Chemical reviews.

[44]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[45]  P. Dirac.  Note on Exchange Phenomena in the Thomas Atom , 1930, Mathematical Proceedings of the Cambridge Philosophical Society.

[46]  B. M. Fulk.  MATH , 1992 .

[47]  K. Nordlund,et al.  Comparison of repulsive interatomic potentials calculated with an all-electron DFT approach with experimental data , 2017 .

[48]  Calculations of range parameters for heavy ions in carbon using ab initio potentials , 2007 .

[49]  P. Löwdin.  Quantum theory of cohesive properties of solids , 2001 .

[50]  J. Ziegler,et al.  stopping and range of ions in solids , 1985 .

[51]  W. Marsden.  I and J , 2012 .