A GENERAL TRANSFORMATION TO CANONICAL FORM FOR POTENTIALS IN PAIRWISE INTERMOLECULAR INTERACTIONS

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1 1 A GENERAL TRANSFORMATION TO CANONICAL FORM FOR POTENTIALS IN PAIRWISE INTERMOLECULAR INTERACTIONS Jay R. Walton Department of Mathematics, Texas A & M University College Station, TX, USA Luis A. Rivera-Rivera, Robert R. Lucchese, and John W. Bevan Department of Chemistry, Texas A & M University College Station, TX, USA

2 2 Outline A general transformation to canonical form for potentials in pairwise interatomic interactions Canonical potentials and spectra investigated strictly within the Born-Oppenheimer approximation Application of canonical approach to multidimensional systems

3 3 Overview We introduced a generalized formulation of explicit transformations to investigate the concept of a canonical potential in both fundamental chemical and intermolecular bonding. Specifically, accurately determined potentials of the diatomic molecules H 2, H 2+, HF, LiH, argon dimer, and one-dimensional dissociative coordinates in Ar-HBr, OC-HF, and OC-Cl 2 are investigated throughout their bound potentials.

4 4 Advantages The canonical approach is not a universal or reduced method, it is a force-base approach related to the work of Feynman (Phys. Rev. 1939, 56, 340). We will demonstrate that this approach can give accurate prediction of equilibrium dissociation energies in weakly bound systems. This approach also gives different perspective on the fundamental nature of bonding. Specifically, it has relevance to previous assertions that there is no very fundamental distinction between van der Waals bonding and covalent bonding (J. C. Slater, JCP, 1972, 57, 2389) or for that matter hydrogen and halogen bonds.

5 5 Power-law distribution of the maximum attractive force, F m F (cm 1 /Å) F m 2 2 F m 2 3 F m 2 4 F m 3.0 F M F α = c 4.0 R e F m F α = E R α R α R e R m R 1 R 2 R 3 R ( ) E( R ) e R (Å)

6 6 Canonical Transformation, H 2 K. Pachucki, Phys. Rev. A, 82, (2010).!E ( α z):= E R E R α ( ) E( R ) e ( ) E( R ) e z = R R e R α R e Lucchese et al. J. Phys. Chem. A 118, 6287 (2014). Walton et al. Phys. Chem. Chem. Phys. 17, (2015).

7 7 Strongly Bound System (a) Weakly Bound System (b) Average absolute deviation of 14 parts in (a) Canonical potential for: H 2 (solid curve), HF (square), H 2 + (diamond), and LiH (circle). (b) Canonical potential for: H 2 (solid curve), Ar 2 (triangle), OC-HF (square), Ar-HBr (diamond), and OC-Cl 2 (circle).

8 8 Strongly Bound System H 2 H + 2 LiH HF D e (cm -1 ) true D e (cm -1 ) est % error R e (Å) F m (cm -1 /Å) R m (Å)

9 9 Weakly Bound System Ar 2 Ar-HBr OC-HF OC-Cl 2 D e (cm -1 ) true D e (cm -1 ) est % error R e (Å) F m (cm -1 /Å) R m (Å)

10 10 Conclusions for Topic 1 Within an average absolute deviation of 14 parts in there exists a canonical transformation for pairwise interatomic interactions considered. The transformation applies to: Intramolecular and intermolecular systems Pairwise interactions with D 0 covering the range 85 to 89,592 cm -1. Bonding categories from van der Waals, halogen and hydrogen bonds to covalent or ionic bonding.

11 11 Outline A general transformation to canonical form for potentials in pairwise interatomic interactions Canonical potentials and spectra investigated strictly within the Born-Oppenheimer approximation Application of canonical approach to multidimensional systems

12 Canonical Potentials and Spectra Investigated Strictly within the Born-Oppenheimer approximation Data for only the most accurate available ground electronic state pairwise interatomic potentials in H 2, HD, D 2, HeH +, and LiH are used. Pachucki, Phys. Rev. A 2010, 82, Pachucki and Komasa, J. Chem. Phys. 2012, 137, Holka et al. J. Chem. Phys. 2011, 134, The corresponding potentials are generated explicitly using parameters calculated with algebraic functions from that of the single canonical potential of the simplest molecule, H

13 13 Canonical transformation from H 2 + to H V (10 4 cm 1 ) H 2 R e R 1 (γ) V (10 4 cm 1 ) H 2 R 1 R e R (Å) R (Å)

14 Vibrational Eigenvalues for H 2 14 ν E ν (cm -1 ) acc E ν (cm -1 ) est acc-est (cm -1 )

15 Vibrational Eigenvalues for HeH + 15 ν E ν (cm -1 ) acc E ν (cm -1 ) est acc-est (cm -1 )

16 Vibrational Eigenvalues for LiH ν E ν (cm -1 ) acc E ν (cm -1 ) est acc-est (cm -1 )

17 17 Conclusion for Topic 2 Deviations are demonstrated to be less than 2 cm -1 for all vibrational states in H 2, HD, D 2, HeH +, and LiH with an average standard deviation of 0.27 cm -1 for the 87 states considered. This gives convincing evidence for the existence of the canonical approach.

18 18 Outline A general transformation to canonical form for potentials in pairwise interatomic interactions Canonical potentials and spectra investigated strictly within the Born-Oppenheimer approximation Application of canonical approach to multidimensional systems

19 19 Multidimensional Systems: Ar-HBr E(R) = 10 = 90 = Ẽ(x) Canonical Transformation = 10 = 90 = R θ

20 20 Multidimensional Systems: Ar-HBr Ẽ(x) H + 2 = 10 = = R θ

21 21 ArHBr 2-D Potential Surface: Canonical Approximation R ArHBr 2-D Potential Surface: True R Relative Error of ArHBr Surface Canonical Approximation R

22 22 Acknowledgments Robert A. Welch Foundation At Texas A&M University LST/ST The Laboratory for Molecular Simulation The Supercomputing Facility The Institute for Applied Mathematics and Computational Science