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Abstract The exact expressions for the dipole, quadrupole, and octupoles of a collection ofNpoint charges involve summations of corresponding tensors over theNsites weighted by their charge magnitudes. When the point charges are atoms (in a molecule) theN‐site formula is an approximation, and one must integrate over the electron density to recover the exact multipoles. In the present work we revisit theN(N + 1)/2‐site point charge density model of Hall (Chem. Phys. Lett.6, 501, 1973) for the purpose of fitting ab initio derived multipole moment hypersurfaces using permutationally invariant polynomials (PIP). We examine new approaches in PIP‐fitting procedures for the dipole, quadrupole, octupole moments, and polarizability tensor surfaces (DMS, QMS, OMS and PTS, respectively) for a non‐polar CCl4and a polar CHCl3and show that compared to the primitiveN‐site model theN(N + 1)/2‐site model appreciably improves the relative RMSE of the DMS and does much more substantially so, by an order of magnitude, for the corresponding ones of QMS and OMS. Training datasets are obtained by sampling potential energies up to 18 000 cm−1above the global minima, generated by molecular dynamics simulations at the DFT B3LYP/aug‐cc‐pVDZ level of theory.
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Permutationally invariant polynomial representation of polarizability tensor surfaces for linear regression analysis
Abstract A linearly parameterized functional form for a Cartesian representation of molecular dipole polarizability tensor surfaces (PTS) is described. The proposed expression for the PTS is a linearization of the recently reported power series ansatz of the original Applequist model, which by construction is non‐linear in parameter space. This new approach possesses (i) a unique solution to the least‐squares fitting problem; (ii) a low level of the computational complexity of the resulting linear regression procedure, comparable to those of the potential energy and dipole moment surfaces; and (iii) a competitive level of accuracy compared to the non‐linear PTS model. Calculations of CH4PTS, with polarizabilities fitted to 9000 training set points with the energies up to 14,000 cm−1show an impressive level of accuracy of the linear PTS model obtained with ~1600 parameters: ~1% versus 0.3% RMSE for the non‐linear vs. linear model on a test set of 1000 configurations.
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- Award ID(s):
- 1855583
- PAR ID:
- 10445946
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Journal of Computational Chemistry
- Volume:
- 43
- Issue:
- 22
- ISSN:
- 0192-8651
- Page Range / eLocation ID:
- p. 1495-1503
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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