Prediction of polymer properties through electronic characterization of polymer fragments and QSPR

1. Prediction of polymer properties through electronic characterization of polymer fragments and QSPR Curt M. Breneman N. Sukumar Rensselaer Polytechnic Institute

2. Outline Functional group modification QSPR models for electronic polarizability Screening a large Functional Group library ab initiocomputations with different Functional Groups electronic & ionic polarizability dipole moment Identification of Functional Groups with High Ionic Polarizabilities Hydrophobicity estimation for functional groups for polymer backbones Design of QSPR enabling software

3. Modeling Electronic Polarizability:Functional group modifications • The goal is the identification of classes of polymers with an attractive set of dielectric properties. • In the “functional group alteration” approach, the underlying premise is to identify highly polar, highly polarizable and highly rotatable functional groups to manipulate the dielectric response. • Validated QSPR models were constructed for HOMO-LUMO gaps and the trace of the electronic component of the polarizability tensor employing constitutional and topological descriptors from MOE. • Models were trained on HOMO-LUMO gaps and polarizabilities computed from DFT (using Gaussian '03) for polymer fragments of varying length.

4. The functional group Data Set • The goal is the identification of classes of polymers with an attractive set of dielectric properties. • In the “functional group alteration” approach, the underlying premise is to identify highly polar, highly polarizable and highly rotatable functional groups to manipulate the dielectric response.

5. Modeling polarizability contributions of Functional Groups with sum of atomic polarizabilities (apol) Modeling the trace of the electronic component of the polarizability tensor (computed from Gaussian) with the MOE 2-D Descriptor, "apol" which is the sum of the atomic polarizabilities (taken from the CRC Handbook of Chemistry and Physics, CRC Press, 1994) for 84 functional group substitution of PE. Polymers containing Li, Na and K groups are not well modeled by apol. When molecules with Li, Na and K are removed, a correlation coefficient of 0.98 is obtained.

6. Screening a large Functional Group library A fragment library of 13,300 functional groups from the MOE® fragment library was screened for apol and other semi-empirical descriptors and functional groups with high apol per Van der Waals volume and high HOMO-LUMO gap (shown here as cyan circles) were selected for further analysis.

7. DFT Computation of Electronic and Ionic Polarizabilities and Dipole Moments of Functional Groups • DFT (PBE/6-31G* with full optimization) computations using Gaussian'03 on 151 top-ranked functional groups from the first pass. • The functional groups from the first pass were neutralized (deprotonated) wherever possible. • Using a C2 chain to represent the backbone • Dipole moments computed with Electric Field along +X, +Y & +Z directions and geometry optimized with C2 backbone held fixed in the same orientation. αT = ∂μX/∂EX + ∂μY/∂EY + ∂μZ/∂EZ

9. Functional Groups with High Ionic Polarizabilities Comparing the total versus electronic polarizabilities identifies the functional groups with high ionic polarizabilities (cyan circles in the previous page).

10. Hydrophobicity estimation for Functional Groups through Partial Equalization of Orbital Electronegativities • Partial Charge Descriptors depend on the partial charge of each atom in a chemical structure. • Sanderson’s postulate of electronegativity equalization (1976) asserts that when two or more different atoms combine to form a molecule, their electronegativities change to a common intermediate value. • This yields a formalism to calculate atomic charges, based on the change in electronegativity from the isolated atom value to its value after equalization in the molecule. • However, in this way, identical charges are obtained for all atoms of the same elemental type in a molecule. • In The Partial Equalization of Orbital Electronegativities (PEOE) method of calculating atomic partial charges (due to Gasteiger), charge is transferred between bonded atoms until equilibrium. • Atoms are characterized by their orbital electronegativities. • Only the connectivities of the atoms are considered. Thus, only the topology of a molecule is of importance and partial equalization of orbital electronegativity is obtained through an iterative procedure.

11. PEOE VSA Descriptors

12. Selected Functional Groups

13. Selected Functional Groups

14. The polymer backbone Data Set

15. Hydrophobicity estimation for Polymer Backbones through Surface Electrostatic & Ionization Potentials • Electrostatic Potential (EP): • Politzer's Local Average Ionization Potential (PIP): Both properties are computed from ab initiowavefunctions on the molecular Van der Waals surface (as approximated by the ρ(r)=0.002 e/Bohr3 electron density isosurface). • (We use an ab initio approach since Ge, for instance, is not well parameterized in the semi-empirical methods).

20. MQSPR enabling software:The ONR Materials Informatics Resource

21. QSPR enabling software A 4-descriptor model is able to produce a decent cross-validated MLR regression for the electronic component of the polarizability tensor.

22. Model validity verified through Y-scrambling tests

23. Descriptors importance is displayed through Sensitivity Analysis or as Star Plots

24. Summary • In an effort to design high dielectric constant polymers with moderately high band gaps, QSPR models were constructed for HOMO-LUMO gaps and electronic polarizabilities of polymer fragments with a variety of side-chain functionalization. • The models were trained on and validated with electronic polarizabilities from ab initio DFT computations and HOMO-LUMO gaps from ab initioHartree-Fock computation. • The apol descriptor (sum of the atomic polarizabilities) was found to provide a good approximation to determine functional group contributions to electronic polarizabilities. • Semi-empirical AM1 computations gave a reasonable estimate of Hartree-Fock HOMO-LUMO gaps. • These descriptors were then used to screen a large fragment library of 13,300 functional groups, and identify the 150 most promising functional groups for further analysis. • These were then ranked by their ionic polarizabilities, as determined from ab initio DFT computations, and by other criteria such as the total dipole moment and number of rotatable bonds. • Hydrophobicity estimation for functional groups was performed using the parametrized Partial Equalization of Orbital Electronegativitiesmethod. • Hydrophobicity was estimated forpolymerbackbones by studying the Electrostatic & Local Ionization Potentials on the Van der Waals surfaces.

25. Next Steps • Experimental tests on polymers with the functional groups identified herein will serve to validate our models and provide training data for construction of more refined models, as required. • Predicted and computed data on polarizabilities and hydrophobicities of polymer backbones will inform how alterations of backbone chemistry will affect the electronic properties of new block co-polymers.

26. RESERVE SLIDES

27. Validation Strategies Y-scrambling Randomization of the modeled property External validation Split ratio (training and test data sets) Bootstraps Leave-group-out Leave-one-out

28. Requirements of a good QSPR model All descriptors used in the model should be significant, None of the descriptors account for single peculiarities. No leverage or outlier compounds in the training set. Cross-validation performance should show: Significantly better performance than that of randomized tests Training set and external test set homogeneity.

29. The functional group Data Set • The goal is the identification of classes of polymers with an attractive set of dielectric properties. • In the “functional group alteration” approach, the underlying premise is to identify highly polar, highly polarizable and highly rotatable functional groups to manipulate the dielectric response.

30. Total Electronic Polarizabilities are seen to be only weakly dependent upon backbone conformation (as expected)

31. Total Dipole Moments are even less sensitive to backbone conformation(The outlier is a +1 charged species; all others are neutral)

32. Modeling the Total Polarizability contributions of Functional Groups by DFT • Of these, functional groups lacking conformational flexibility, i.e. where the fraction of rotatable bonds was less than 0.1, were discarded. • The remaining 150 functional groups were neutralized (deprotonated) and DFT (PBE/6-31G* with full optimization) computations were performed on polymer fragments with these 150 groups. • Since the computational bottleneck is geometry optimization (which grows with length of the backbone chain), a very short (C2) PE chain was employed to represent the polymer backbone in the ab initio computations.

33. Outliers on apol vs.αe plot are all alkali groups

34. Theory: Orbital Electronegativities • Hinze introduced the concept of orbital electronegativity. • Orbital electronegativities depend not only on the hybridization, but also on the occupation number of the orbital: An empty orbital has a higher electron attracting power than a singly-occupied orbital, which has a higher electron attracting power than a doubly-occupied orbital. • Parr used the Hohenberg-Kohn DFT to define electronegativity as the negative of the chemical potential. • They demonstrated that the orbital electronegativities are also equal in the ground state. • Politzer and Weinstein showed that at equilibrium, the electronegativities (or chemical potentials) of all arbitrary portions of a molecule with a given total number of electrons are the same.

35. Hydrophobicity/hydrophilicity of C-, Si- and Ge-containing backbones Saturated: (-CH2-)8 (-SiH2-)8 (GeH2-)8 (-SiF2-)8 [-Si(CN)2-]8 (-GeF2-)8 [-Ge(CN)2-]8 Unsaturated: (-CH=CH-)4 (-SiH=SiH-)4 (-GeH=GeH-)4 (-SiF=SiF-)4 (-SiCN=SiCN-)4 (-GeF=GeF-)4 (-GeCN=GeCN-)4 Ab initio DFT (PBE/6-31G*) computations on octamers:

39. Histograms

43. Histograms

44. The Eight Commandments of Successful QSPR/QSAR Modeling There should be a PLAUSIBLE (not necessarily known or well understood) mechanism or connection between the descriptors and response. Otherwise we could be doing numerology… Robustness: you cannot keep tweaking parameters until you find one that works just right for a particular problem or dataset and then apply it to another. A generalizable model should be applicable across a broad range of parameter space. Know the domain of applicability of the model and stay within it. What is sauce for the goose is sauce for the gander, but not necessarily for the alligator. Likewise, know the error bars of your data. No cheating... No looking at the answer. This is the minimum requirement for developing a predictive model or hypothesis. Not all datasets contain a useful QSAR/QSPR “signal”. Don’t look too hard for something that isn’t there… Consider the use of “filters” to scale and then remove correlated, invariant and “noise” descriptors from the data, and to remove outliers from consideration. Use your head and try to understand the chemistry of the problem that you are working on – modeling is meant to assist human intelligence – not to replace it…