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J. Phys. Chem. A 2010, 114, 624–632
Modeling of Molecular Charge Distribution on the Basis of Experimental Infrared Intensities and First-Principles Calculations: The Case of CH Bonds Alberto Milani* and Chiara Castiglioni Politecnico di Milano - Dip. Chimica, Materiali e Ing. Chimica “G. Natta”, P.zza Leonardo da Vinci 32, I-20133 Milano, Italy ReceiVed: August 24, 2009; ReVised Manuscript ReceiVed: October 14, 2009
DFT calculations are used to predict CH stretching infrared (IR) intensities for about 50 small molecules. B3LYP and PBE1PBE functionals and different basis sets are tested to obtain the best agreement with the experimental absolute IR intensities available. PBE1PBE functional in particular predicts average CH stretching intensities very close to the experimental ones. On the basis of a simple analytical model, it is shown how it is possible to extract atomic charges directly from computed atomic polar tensors (APTs): these IR charges are very close in value to the experimentally derived ones and faithfully reproduce peculiar molecular phenomena. DFT-derived IR charges are also compared with the charges obtained by population schemes such as Mulliken population analysis, natural population analysis (NPA), and with charges obtained by fitting the electrostatic potential according to the Merz-Kollman (MK), CHELP, and CHELPG models. IR charges are found to be similar especially to the charges obtained by these last methods: therefore they can be used as an alternative scheme for the determination of the molecular charge distribution while being strictly connected to experimentally measurable properties. Moreover, the analytical model is further developed to obtain a method for the calculation of the charge fluxes, which take place along the chemical bonds during molecular vibrations. I. Introduction About 40 years ago, accurate spectroscopy studies, devoted to the determination and analysis of the absolute IR band intensities of simple organic molecules, started to appear in the literature.1 These experimental investigations were supported by many theoretical studies aimed at the interpretation of the intensity data; on this basis several models were developed for a description from IR intensity data of the molecular charge distribution and its mobility. In particular, the electro-optical parameters model (EOP) proposed by the Russian school,2 and the related equilibrium charges and charge fluxes (ECCF) model3 gave powerful but simple methods to describe the effect of the intramolecular chemical environment on the electrical features of bonds and atoms in molecules.4 Moreover, atomic polar tensors (APTs),5,6 which can be directly derived from IR intensities (and equilibrium electrical dipole moments), were used with the same purpose. A comprehensive discussion of these different models and of the performances of several IR intensity parameters is reported in a fairly recent review7 based on the experimental data relative to large series of molecules. In more recent years, a model named charge-charge flux-dipole flux (CCFDF)8 based on the atom-in-molecules theory9 appeared in the literature and has been successfully applied to the prediction of IR intensities of different molecules.10 Many applications of IR parameters (especially in the form of ECCF parameters) were proposed in the past for the description of several chemical-physical effects, such as: i) the charge polarization and charge backdonation from electronegative atoms, like N, O, F;11 ii) hyperconjugation, (e.g., in CH3 groups attached to a π electrons system);12,13 and iii) the * To whom correspondence
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occurrence of long-range charge fluxes due to the π-conjugation.14 Moreover, the simplified description given by ECCF has been successfully proposed as a tool for the identification of the molecular sites or atoms involved in the formation of intermolecular complexes.15,16 The atomic charges thus derived allowed an estimate of the stabilization energies and induced dipole moment16 of hydrogen bonded dimers and, recently, they provided an accurate interpretation of the aggregation effects on IR spectra.17 On the other hand, the need to accurately describe the electrostatic interactions between nonbonded atoms in molecular dynamics simulations18 requires reliable atomic charges. It is indeed well known that a good description of complex systems in different phases is largely dependent on the quality of force fields, where partial atomic charges play a fundamental role. On these grounds, experimentally and computationally derived IR charges could find a promising application. However, the determination of reliable ECCF from experimental IR intensities is partially hindered by the difficulty of obtaining accurate absolute intensity data and by intrinsic problems related to the derivation of the intensity parameters (good vibrational force fields required, a number of ECCF parameters, which largely exceeds that of the experimental data available, etc.7). Ab initio calculations have been recommended as a tool complementary to experimental IR intensity studies, to obtain some information, which cannot be directly determined experimentally (as for instance for sign assignment or for the direction of molecular dipole derivatives (∂M/∂Qk)19). More recently, computational predictions of IR spectra have shown such a level of accuracy that they can be routinely used in the comparison with their experimental counterpart in many different fields ranging from conformational analysis20 to polymer spectroscopy21 to nonlinear optics.22
10.1021/jp908146d 2010 American Chemical Society Published on Web 11/04/2009
The Case of CH Bonds In this article, we discuss the possible application of IR intensity parameters obtained by DFT calculations. Several organic molecules, for which accurate experimental intensity data (and often intensity parametrizations) are available, will be considered and computed IR intensities will be compared with their experimental counterpart. Moreover, an analytical model based on ECCF parameters will be used to obtain atomic charges and charge fluxes from the APTs. This work will be mainly devoted to the study of CH stretching intensities. Previous studies showed that these data can be successfully correlated to the physical features of CH bonds (first of all IR hydrogen equilibrium charges) in different intramolecular environments.4,7 In section III, we will compare the experimentally available data with CH stretching IR intensities computed by different DFT methods, whereas in section IV, following the early works by Ramos et al.23,24 we will illustrate a simple way to derive IR atomic charges from DFT-computed APTs. In addition, a general analytical model is worked out to obtain the full expressions that relate APT elements to ECCF parameters, namely IR charges but also charge fluxes occurring during vibrational displacements of the atoms. The obtained IR charges are compared with those resulting by the parametrization of the experimental intensities, showing the same ability in the description of intramolecular effects. Moreover, in section V they are compared to atomic charges obtained by means of other schemes, demonstrating how IR charges can be used as a valuable alternative to these methods while being strictly related to experimental observables (molecular dipole moment and IR intensities). II. Computational Details The computational study of IR spectra and molecular charge distribution is carried out on 47 molecules (Table S1 of the Supporting Information) on the basis of DFT calculations, as implemented in the Gaussian 03 package.25 Two popular hybrid functionals, namely B3LYP26 and PBE1PBE,27 have been used because they already showed a wide applicability for different kinds of molecular systems. Furthermore, for each functional four different basis sets have been chosen: 6-311G**, 6-311++G** and their correlation consistent counterpart cc-pVTZ, and augcc-pVTZ. Our choice is not dictated by the intention of an exhaustive investigation of the accuracy of DFT functionals nor of basis set effects;28 on the opposite, we focused on the performances in predicting IR intensities of two of the mostly used functionals. The use of the four basis sets indicated above is motivated by the fact that current computational facilities allow calculations with Pople’s basis sets on quite large systems. The comparison with much more onerous basis sets, expected to give more reliable results, provides a check of accuracy (in terms of IR intensities predictions), which can be obtained already by means of the standard Pople’s basis sets, thus assessing their validity for accurate investigations of large systems. Because our analysis is limited to the few choices here presented, we cannot exclude that a better agreement with experiments could be obtained if other combinations of functionals/basis sets are used out of the common choices, such as for example by choosing the novel M06-class functionals of Truhlar and Zhao29 recently proposed. Once verified that the level of the theory adopted allows satisfactory predictions of IR intensities, we will focus on the computed APTs. These tensors indeed collect the derivatives of the molecular dipole moment with respect to Cartesian atoms’ displacements ξk (which are the basic quantities of any prediction of IR intensities) according to the relationship:
J. Phys. Chem. A, Vol. 114, No. 1, 2010 625
b /∂Qi)0 | 2 ) C|Σk(∂M b /∂ξk)0Lki | 2 Ii ) C|(∂M
(1)
where the ‘0’ apex indicates values calculated at the minimum (equilibrium) geometry. Ii is the absolute IR intensity associated to the normal mode Qi, Li is the Cartesian eigenvector relative to Qi, and C is a constant whose value depends on the units used. As it will be illustrated in section IV, equilibrium atomic charges can be obtained from the calculated APTs. This will be done in the case of H atoms belonging to CH bonds, whose charges are then compared with Mulliken charges, charges from natural population analysis (NPA),30 and with three different types of charges obtained from the fitting of the molecular electrostatic potential that is MK,31 CHELP,32 and CHELPG33 schemes. All of these calculations have been carried out as implemented in the Gaussian 03 code. III. Absolute Infrared Intensities: Comparison between Computed and Experimental CH Stretching Absorption In Table S1 of the Supporting Information, we present CH stretching intensity data obtained by DFT calculations for several molecules for which absolute experimental IR intensities are available (Table S1 of the Supporting Information for references). Because the CH stretching frequency range usually shows overlapping bands, the integration of experimental bands can be often carried out only on the whole region. For this reason, we decide to compare average values, calculated as the sum of the intensities of the CH stretching transitions, normalized over the number of CH bonds of the molecule. The percentage error of DFT calculations with respect to the experimental data has been calculated. Moreover, for each choice of functional and basis set the mean error has been reported to judge the performance of the computations. In the calculation of this parameter, molecules that show absolute experimental intensities
