Origin-Independent Decomposition of the Static Polarizability

Refinement of Atomic Polarizabilities for a Polarizable Gaussian Multipole Force Field with Simultaneous Considerations of Both Molecular Polarizability Tensors and In-Solution Electrostatic Potentials

Atomic polarizabilities are considered to be fundamental parameters in polarizable molecular mechanical force fields that play pivotal roles in determining model transferability across different electrostatic environments. In an earlier work, the atomic polarizabilities were obtained by fitting them to the B3LYP/aug-cc-pvtz molecular polarizability tensors of mainly small molecules. Taking advantage of the recent PCMRESPPOL method, we refine the atomic polarizabilities for condensed-phase simulations using a polarizable Gaussian Multipole (pGM) force field. Departing from earlier works, in this work, we incorporated polarizability tensors of a large number of dimers and electrostatic potentials (ESPs) in multiple solvents. We calculated 1565 × 4 ESPs of small molecule monomers and dimers of noble gas and small molecules and 4742 × 4 ESPs of small molecule dimers in four solvents (diethyl ether, ε = 4.24, dichloroethane, ε = 10.13, acetone, ε = 20.49, and water, ε = 78.36). For the gas-phase polarizability tensors, we supplemented the molecule set that was used in our earlier work by adding both the 4252 monomer and dimer sets studied by Shaw and co-workers and the 7211 small molecule monomers listed in the QM7b database to a combined total of 13,523 molecular polarizability tensors of monomers and dimers. The QM7b polarizability set was obtained from quantum-machine.org and was calculated at the LR-CCSD/d-aug-cc-pVDZ level of theory. All other polarizability tensors and all ESPs were calculated at the ωB97X-D/aug-cc-pVTZ level of theory. The atomic polarizabilities were developed using all polarizability tensors and the 1565 × 4 ESPs of small molecule monomers and were then assessed by comparing them to the 4742 × 4 ab initio ESPs of small molecule dimers. The predicted dimer ESPs had an average relative root-mean-square error (RRMSE) of 9.30%, which was only slightly larger than the average fitting RRMSE of 9.15% of the monomer ESPs. The transferability of the polarizability set was further evaluated by comparing the ESPs calculated using parameters developed in another dielectric environment for both tetrapeptide and DES monomer data sets. It was observed that the polarizabilities of this work retained or slightly improved the transferability over the one discussed in earlier work even though the number of parameters in the present set is about half of that in the earlier set. Excluding the gas-phase data, for the DES monomer set, the average transfer RRMSEs were 16.25% and 10.83% for pGM-ind and pGM-perm methods, respectively, comparable to the average fitting RRMSEs of 16.03% and 10.54%; for tetrapeptides, the average transfer RRMSEs were 5.62% and 3.95% for pGM-ind and pGM-perm methods, respectively, slightly larger than 5.41% and 3.61% of the fitting RRMSEs. Therefore, we conclude that the pGM methods with updated polarizabilities achieved remarkable transferability from monomer to dimer and from one solvent to another.

Why are information-theoretic descriptors powerful predictors of atomic and molecular polarizabilities

CONTEXT

We rationalize the excellent performance of information-theoretic descriptors for predicting atomic and molecular polarizabilities. It seems that descriptors which capture information about the change in valence-shell structure, especially the relative Fisher information measures, are particularly useful. Using this, we can rationalize why the G3 form of the relative Fisher information, which measures the deviation of effective nuclear charge between an atom-in-a-molecule and the reference pro-atom, is especially effective as a predictor of molecular polarizability.

METHODS

There are no methods used in this paper, which relies on mathematical derivation and analysis.

Ambiguities in Decomposing Molecular Polarizability into Atomic Charge Flow and Induced Dipole Contributions

The molecular dipole polarizability can be decomposed into components corresponding to the charge flow between atoms and changes in atomic dipole moments. Such decompositions are recognized to depend on how atoms are defined within a molecule, as, for example, by Hirshfeld, iterative Stockholder, or quantum topology partitioning of the electron density. For some of these, however, there are significant differences between the numerical results obtained by analytical response methods and finite field calculations. We show that this difference is due to analytical response methods accounting for (only) the change in electron density by a perturbation, while finite field methods may also include a component corresponding to a perturbation-dependent change in the definition of an atom within a molecule. For some atom-in-molecule definitions, such as the iterative Hirshfeld, iterative Stockholder, and quantum topology methods, the latter effect significantly increases the charge flow component. The decomposition of molecular polarizability into atomic charge flow and induced dipole components thus depends on whether the atom-in-molecule definition is taken to be perturbation-dependent.

Exact decompositions of the total KS-DFT exchange-correlation energy into one- and two-center terms

In the so-called Interacting Quantum Atoms (IQA) approach, the molecular energy is numerically decomposed as a sum of atomic and diatomic contributions. While proper formulations have been put forward for both Hartree-Fock and post-Hartree-Fock wavefunctions, this is not the case for the Kohn-Sham density functional theory (KS-DFT). In this work, we critically analyze the performance of two fully additive approaches for the IQA decomposition of the KS-DFT energy, namely, the one from Francisco et al., which uses atomic scaling factors, and that from Salvador and Mayer based upon the bond order density (SM-IQA). Atomic and diatomic exchange-correlation (xc) energy components are obtained for a molecular test set comprising different bond types and multiplicities and along the reaction coordinate of a Diels-Alder reaction. Both methodologies behave similarly for all systems considered. In general, the SM-IQA diatomic xc components are less negative than the Hartree-Fock ones, which is in good agreement with the known effect of electron correlation upon (most) covalent bonds. In addition, a new general scheme to minimize the numerical error of the sum of two-electron energy contributions (i.e., Coulomb and exact exchange) in the framework of overlapping atoms is described in detail.

Origin-Independent Densities of Static and Dynamic Molecular Polarizabilities

The notion of the electric dipole polarizability density function of atoms and molecules has been considered. The current density induced by the time derivative of the electric field of monochromatic light allows for a new definition of the electric dipole polarizability density, which is translationally invariant. This translational invariance provides the physical meaning that was lacking in previous defined polarizability densities. The new polarizability density has been implemented at the TD-DFT level of theory. The origin independence has been proven in silico to hold regardless of the basis set size. Two emblematic molecules, i.e., CO and N₂, which in many respects display similar electric response, have been studied in detail. The substantial differences, which have been highlighted in the topology of the parallel and perpendicular polarizability density tensor components of CO and N₂, are grossly hidden by compensation, when integration is carried out to get the molecular properties.