July 16, 2004 Final Author’s Version Accurate Partial Atomic Charges for High-Energy Molecules Using Class IV Charge Models with the MIDI! Basis Set Casey P. Kelly, Christopher J. Cramer*, and Donald G. Truhlar* Department of Chemistry and Supercomputing Institute, 207 Pleasant St. SE, University of Minnesota, Minneapolis, MN 55455-0431 *[email protected], [email protected] Key words: basis set, MIDI! – dipole moments – materials, high-energy – nitramines, inversion barrier – partial charges, class IV Abstract. We have recently developed a new class IV charge model for calculating partial atomic charges in molecules. The new model, called Charge Model 3 (CM3), was parameterized for calculations on molecules containing H, Li, C, N, O, F, Si, S, P, Cl, and Br by Hartree-Fock theory and by hybrid density functional theory (HDFT) based on the modified Perdew-Wang density functional with several basis sets. In the present article, we extend CM3 for calculating partial atomic charges by Hartree-Fock theory with the economical but well balanced MIDI! basis set. Then, using a test set of accurate dipole moments for molecules containing nitramine functional groups (which include many high-energy materials), we demonstrate the utility of several parameters designed to improve the charges in molecules containing both N and O atoms. We also show that one of our most recently developed CM3 models that is designed for use with wave functions calculated at the mPWXPW91/MIDI! level of theory (where X denotes a variable percentage of Hartree-Fock exchange) gives accurate charge distributions in nitramines without additional parameters for N and O. To demonstrate the reliability of partial atomic charges calculated with CM3, we use these atomic charges to calculate polarization free energies for several nitramines, including the commonly used explosives 1,3,5-trinitro-s-triazine (RDX) and 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane (HNIW), in nitromethane. These polarization energies are large and negative, indicating that electrostatic interactions between the charge distribution of the molecule and the solvent make a large contribution to the free energy of solvation of nitramines. By extension, the same conclusion should apply to solid-state condensation. Also, in contrast to some other charge models, CM3 yields atomic charges that are relatively insensitive to the presence of buried atoms and small conformational changes in the molecule, as well as to the level of treatment of electron correlation. This type of charge model should be useful in the future development of solvation models and force fields designed to estimate intramolecular interactions of nitramines in the condensed phase. 1 Introduction Unlike many other electronic properties that can be extracted from a quantum mechanical wave function, such as electron density, permanent electrical moments, or the molecular electrostatic potential, the partial atomic charge on an atom in a molecule is not a quantum mechanical observable. As a result, the rules for determining partial atomic charges, which involves assigning quantitative values to the amount of electron density belonging to each atom in a molecule, are ambiguous, and many different methods have been developed and evaluated for accomplishing this [1-79]. We have assigned [73] these various methods to four broad categories, or classes. Class I includes all methods for which partial atomic charges can, in principle, be determined without first calculating a quantum mechanical wave function for the given molecule. Examples include assigning partial atomic charges based on X-ray diffraction data [3], IR stretching frequencies [2,4-8], or, for the case of a diatomic molecule, calculating them directly by dividing the dipole moment by the bond length. Some class I charge models have been proposed that use only the molecular topology of the given molecule to assign 2 its partial atomic charges [11-14], while other class I charge models [15-30] assign partial atomic charges based on the concept of electronegativity equalization [80,81]. Class II includes methods that use a population analysis of a molecular wave function to assign charges, and include Mulliken [31-33], Löwdin [34], and natural [47] population analyses, as well as Bader’s “atoms in molecules” (AIM) method [49]. Another class II charge model, called redistributed Löwdin population analysis [35] (RLPA), is designed to alleviate some of the sensitivity to the inclusion of diffuse functions when calculating partial atomic charges from a Löwdin population analysis. Class III charge models include those methods that assign partial atomic charges by a fit to a wave-function-dependent physical observable. Models that assign partial atomic charges from a least-squares fit to the electrostatic potential calculated at a number of points around the molecule of interest, such as ChElP [60], ChElPG [65], and the Merz-Singh-Kollman scheme [60,66], are examples of class III charge models. Class IV charge models, which include charge model 1 (CM1) [73] and CM2 [74,75], differ from class III charge models in that they map partial atomic charges obtained from some other charge-assigning scheme in order to reproduce experimental or converged theoretical charge-dependent observables. One of the major motivations behind the development of class IV charge models by our group [73- 79] was to remedy two major deficiencies of class III models. First, the partial atomic charges obtained from class III charge models are necessarily dependent on the quality of the wave function used to calculate the physical observable against which the partial atomic charges are fit. In many cases, such as for large molecules or for large libraries of molecules, this approach is not practical, since it is often the case that high-level wave functions are required in order to deliver relatively accurate physical observables. Second, for many class III charge models, some partial atomic charges in a given molecule are less well-determined than others (i.e. large fluctuations in the values of some charges may have only a small effect on the error function against which the atomic charges are fit). As a result of this second deficiency, class III charge models can in some cases deliver partial atomic charges that are less 3 transferable than those calculated with other models and that also depend too strongly on the conformation of the molecule. Recently, several molecular mechanics force fields that use partial atomic charges as quantum chemical descriptors have been developed in order to model the solid-state properties of various molecules containing nitramine functionality. For example, Sorescu and coworkers have used partial atomic charges obtained from the ChElPG fitting procedure to investigate the solid-state properties of several commonly used explosives, including 1,3,5-trinitro-s-triazine (RDX) [82], 2,4,6,8,10,12- hexanitrohexaazaisowurtzitane (HNIW) [83], and 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX) [84] in the solid phase, as well as a variety of other molecules containing nitro-group functionality [85,86]. Smith and coworkers have developed a similar type of force field for dimethylnitramine (DMNA) in the solid phase; these workers used partial atomic charges that were obtained from a modified electrostatic fitting procedure subject to the additional constraint that the partial atomic charges of equivalent atoms remain equal during the fit [87]. The charge model used by these workers is similar in spirit to Bayly et al.’s restrained electrostatic potential (RESP) charge fitting scheme [71], in which hyperbolic penalty functions are associated with each atom during the electrostatic fitting procedure. Recently, we developed a new class IV charge model called charge model 3 (CM3) [77]. This new model has several advantages compared to the models developed earlier within our group [73-76]. First, the functional form is less sensitive to unphysical fluctuations (when one changes the basis set or level of treatment of electron correlation) in calculated bond orders. Second, the model is based on RLPA charges, which [35] are more suitable for use with diffuse basis functions. This is important because the use of diffuse basis functions is often required for accurate calculations of conformational energies and barrier heights [88]. Third, the CM3 model is based on a larger and more diverse training set than used for previous models. Fourth, it includes an additional term that improves the charges on N and O when these atoms are in the same molecule. 4 We report in this article a new set of parameters that, when combined with wave functions calculated at the HF/MIDI! [89-91] level of theory, yield accurate partial atomic charges for molecules containing H, Li, C, N, O, F, Si, S, P, Cl, and Br, as judged by comparison of point-charge-derived molecular dipole moments to accurate values. We also show that this model, along with a previously developed CM3 model [76] that is based on wave functions calculated at the mPW1PW91/MIDI! level of theory, where mPW1PW91 is the hybrid density functional of Adamo and Barone [92], and the “1” denotes 25% Hartree-Fock exchange, can both be used to obtain accurate partial atomic charges for nitramines in the gas phase. Specifically, we show that the partial atomic charges for a test set of molecules containing nitramine functionality are invariant to the level of treatment of electron correlation relative to those atomic charges calculated using several other charge models. In addition, we also show that the partial atomic charges obtained with class IV charge models are less conformation dependent and are far more consistent for atoms sharing similar local molecular environments than are those partial atomic charges obtained using the ChElPG fitting procedure (a class III model). The models presented in this work, which are designed to use economical wave functions to give reliable partial atomic charges for molecules, should be useful in future force fields designed to investigate the solid-state properties and solubility of high-energy materials.