Wagner E. Richter

How Accessible Is Atomic Charge Information from Infrared Intensities? A QTAIM/CCFDF Interpretation

Infrared fundamental intensities calculated by the quantum theory of atoms in molecules/charge-charge flux-dipole flux (QTAIM/CCFDF) method have been partitioned into charge, charge flux, and dipole flux contributions as well as their charge-charge flux, charge-dipole flux, and charge flux-dipole flux interaction contributions. The interaction contributions can be positive or negative and do not depend on molecular orientations in coordinate systems or normal coordinate phase definitions, as do CCFDF dipole moment derivative contributions. If interactions are positive, their corresponding dipole moment derivative contributions have the same polarity reinforcing the total intensity estimates whereas negative contributions indicate opposite polarities and lower CCFDF intensities. Intensity partitioning is carried out for the normal coordinates of acetylene, ethylene, ethane, all the chlorofluoromethanes, the X(2)CY (X = F, Cl; Y = O, S) molecules, the difluoro- and dichloroethylenes and BF(3). QTAIM/CCFDF calculated intensities with optimized quantum levels agree within 11.3 km mol(-1) of the experimental values. The CH stretching and in-plane bending vibrations are characterized by significant charge flux, dipole flux, and charge flux-dipole flux interaction contributions with the negative interaction tending to cancel the individual contributions resulting in vary small intensity values. CF stretching and bending vibrations have large charge, charge-charge flux, and charge-dipole flux contributions for which the two interaction contributions tend to cancel one another. The experimental CF stretching intensities can be estimated to within 31.7 km mol(-1) or 16.3% by a sum of these three contributions. However, the charge contribution alone is not successful at quantitatively estimating these CF intensities. Although the CCl stretching vibrations have significant charge-charge flux and charge-dipole flux contributions, like those of the CF stretches, both of these interaction contributions have opposite signs for these two types of vibrations.

Quantum theory of atoms in molecules/charge-charge flux-dipole flux models for fundamental vibrational intensity changes on H-bond formation of water and hydrogen fluoride.

The Quantum Theory of Atoms In Molecules/Charge-Charge Flux-Dipole Flux (QTAIM/CCFDF) model has been used to investigate the electronic structure variations associated with intensity changes on dimerization for the vibrations of the water and hydrogen fluoride dimers as well as in the water-hydrogen fluoride complex. QCISD/cc-pVTZ wave functions applied in the QTAIM/CCFDF model accurately provide the fundamental band intensities of water and its dimer predicting symmetric and antisymmetric stretching intensity increases for the donor unit of 159 and 47 km mol(-1) on H-bond formation compared with the experimental values of 141 and 53 km mol(-1). The symmetric stretching of the proton donor water in the dimer has intensity contributions parallel and perpendicular to its C2v axis. The largest calculated increase of 107 km mol(-1) is perpendicular to this axis and owes to equilibrium atomic charge displacements on vibration. Charge flux decreases occurring parallel and perpendicular to this axis result in 42 and 40 km mol(-1) total intensity increases for the symmetric and antisymmetric stretches, respectively. These decreases in charge flux result in intensity enhancements because of the interaction contributions to the intensities between charge flux and the other quantities. Even though dipole flux contributions are much smaller than the charge and charge flux ones in both monomer and dimer water they are important for calculating the total intensity values for their stretching vibrations since the charge-charge flux interaction term cancels the charge and charge flux contributions. The QTAIM/CCFDF hydrogen-bonded stretching intensity strengthening of 321 km mol(-1) on HF dimerization and 592 km mol(-1) on HF:H2O complexation can essentially be explained by charge, charge flux and their interaction cross term. Atomic contributions to the intensities are also calculated. The bridge hydrogen atomic contributions alone explain 145, 237, and 574 km mol(-1) of the H-bond stretching intensity enhancements for the water and HF dimers and their heterodimer compared with total increments of 149, 321, and 592 km mol(-1), respectively.

Review of Experimental GAPT and Infrared Atomic Charges in Molecules

This review contains experimental values of polar tensors and generalized atomic polar tensor (GAPT) charges determined since the publication of the polar tensor formulism for infrared intensity interpretation in 1961. GAPT charges, also called mean dipole moment derivatives, for 167 atoms of 67 molecules are discussed and compared with infrared charges also determined completely from experimental intensities. The importance of the charge transfer and polarization dynamic contributions to the GAPT charge are emphasized as they differentiate this charge from most theoretically calculated charges. The inclusion of these dynamic contributions is shown to be necessary to provide adequate numerical descriptions of core electron ionization energy processes. These contributions are expected to be important in studies of chemical reactivity.

QTAIM charge–charge flux–dipole flux models for the fundamental infrared intensities of BF3 and BCl3

Quantum Theory of Atoms in Molecules Charge-Charge Flux-Dipole Flux (QTAIM/CCFDF) models have been determined for the BF3 and BCl3 molecules. Model parameters were obtained from MP2/6-31G(2d,2p) wave functions owing to their accurate estimations of the BF3 intensities and were found to be insensitive to changes in basis sets with polarization functions and to the level of electron correlation treatment, MP2, QCISD and DFT. The BF3 stretching intensity has a very dominant equilibrium charge contribution with small charge and dipole fluxes occurring in the opposite direction to the charge movement. Large equilibrium charge and small dynamic contributions are also characteristic of stretching vibrations in the ionic diatomic molecules, NaF, NaCl, LiF and LiCl. Furthermore the Laplacians of the electron density at the bond critical points of BF3 and these diatomics are all positive indicating electron depletion in their bonding regions relative to large electronic densities concentrated around their nuclei that is characteristic of ionic bonds. The MP2/6-31G(2d,2p) BCl3 stretching intensity can be accurately estimated by equilibrium charge movement since the charge and dipole fluxes almost exactly cancel one another. Both in-plane and out-of-plane BF3 and BCl3 bending deformations are described by equilibrium charge movements that are partially canceled by opposing dipole fluxes that measure the effect on the dipole moment change from electron densities polarized in the opposite direction. Charge fluxes are calculated to be small for the in-plane deformations and are zero by symmetry for the out-of-plane ones.

Dynamic atomic contributions to infrared intensities of fundamental bands

Dynamic atomic intensity contributions to fundamental infrared intensities are defined as the scalar products of dipole moment derivative vectors for atomic displacements and the total dipole derivative vector of the normal mode. Intensities of functional group vibrations of the fluorochloromethanes can be estimated within 6.5 km mol(-1) by displacing only the functional group atoms rather than all the atoms in the molecules. The asymmetric CF2 stretching intensity, calculated to be 126.5 km mol(-1) higher than the symmetric one, is accounted for by an 81.7 km mol(-1) difference owing to the carbon atom displacement and 40.6 km mol(-1) for both fluorine displacements. Within the Quantum Theory of Atoms in Molecules (QTAIM) model differences in atomic polarizations are found to be the most important for explaining the difference in these carbon dynamic intensity contributions. Carbon atom displacements almost completely account for the differences in the symmetric and asymmetric CCl2 stretching intensities of dichloromethane, 103.9 of the total calculated value of 105.2 km mol(-1). Contrary to that found for the CF2 vibrations intramolecular charge transfer provoked by the carbon atom displacement almost exclusively explains this difference. The very similar intensity values of the symmetric and asymmetric CH2 stretching intensities in CH2F2 arise from nearly equal carbon and hydrogen atom contributions for these vibrations. All atomic contributions to the intensities for these vibrations in CH2Cl2 are very small. Sums of dynamic contributions of the individual intensities for all vibrational modes of the molecule are shown to be equal to mass weighted atomic effective charges that can be determined from atomic polar tensors evaluated from experimental infrared intensities and frequencies. Dynamic contributions for individual intensities can also be determined solely from experimental data.

Quantum Theory of Atoms in Molecules Charge–Charge Transfer–Dipolar Polarization Classification of Infrared Intensities

Fundamental infrared vibrational transition intensities of gas-phase molecules are sensitive probes of changes in electronic structure accompanying small molecular distortions. Models containing charge, charge transfer, and dipolar polarization effects are necessary for a successful classification of the C-H, C-F, and C-Cl stretching and bending intensities. C-H stretching and in-plane bending vibrations involving sp3 carbon atoms have small equilibrium charge contributions and are accurately modeled by the charge transfer-counterpolarization contribution and its interaction with equilibrium charge movement. Large C-F and C═O stretching intensities have dominant equilibrium charge movement contributions compared to their charge transfer-dipolar polarization ones and are accurately estimated by equilibrium charge and the interaction contribution. The C-F and C-Cl bending modes have charge and charge transfer-dipolar polarization contribution sums that are of similar size but opposite sign to their interaction values resulting in small intensities. Experimental in-plane C-H bends have small average intensities of 12.6 ± 10.4 km mol-1 owing to negligible charge contributions and charge transfer-counterpolarization cancellations, whereas their average out-of-plane experimental intensities are much larger, 65.7 ± 20.0 km mol-1, as charge transfer is zero and only dipolar polarization takes place. The C-F bending intensities have large charge contributions but very small intensities. Their average experimental out-of-plane intensity of 9.9 ± 12.6 km mol-1 arises from the cancellation of large charge contributions by dipolar polarization contributions. The experimental average in-plane C-F bending intensity, 5.8 ± 7.3 km mol-1, is also small owing to charge and charge transfer-counterpolarization sums being canceled by their interaction contributions. Models containing only atomic charges and their fluxes are incapable of describing electronic structure changes for simple molecular distortions that are of interest in classifying infrared intensities. One can expect dipolar polarization effects to also be important for larger distortions of chemical interest.

Atomic polarizations necessary for coherent infrared intensity modeling with theoretical calculations

The inclusion of atomic polarizations for describing molecular electronic structure changes on vibration is shown to be necessary for coherent infrared intensity modeling. Atomic charges from the ChelpG partition scheme and atomic charges and dipoles from Quantum Theory of Atoms in Molecules (QTAIM) were employed within two different models to describe the stretching and bending vibrational intensities of the C-H, C-F, and C=O groups. The model employing the QTAIM parameters was the Charge-Charge Transfer and Dipolar Polarization model (QTAIM/CCTDP), and the model employing the ChelpG charges was the Equilibrium Charge-Charge Flux (ChelpG/ECCF). The QTAIM/CCTDP models result in characteristic proportions of the charge-charge transfer-dipolar polarization contributions even though their sums giving the total intensities do not discriminate between these vibrations. According to the QTAIM/CCTDP model, the carbon monoxide intensity has electronic structure changes similar to those of the carbonyl stretches whereas they resemble those of the CH stretches for the ChelpG/ECCF model.

Core–valence correlation effects on IR calculations: the BF3 and BCl3 cases

The first theoretical results of core–valence correlation effects are presented for the infrared wavenumbers and intensities of the BF3 and BCl3 molecules, using (double– and triple–zeta) Dunning core–valence basis sets at the CCSD(T) level. The results are compared with those calculated in the frozen core approximation with standard Dunning basis sets at the same correlation level and with the experimental values. The general conclusion is that the effect of core–valence correlation is, for infrared wavenumbers and intensities, smaller than the effect of adding augmented diffuse functions to the basis set, e.g., cc–pVTZ to aug–cc–pVTZ. Moreover, the trends observed in the data are mainly related to the augmented functions rather than the core–valence functions added to the basis set. The results obtained here confirm previous studies pointing out the large descrepancy between the theoretical and experimental intensities of the stretching mode for BCl3.

Revisiting the integrated infrared intensities and atomic polar tensors of the boron trihalides

Integrated infrared intensities obtained from spectra of the Pacific Northwest National Laboratory (PNNL) database are reported for BF3, BCl3 and BBr3. The BF3 and BCl3 intensities are compared with values reported much earlier whereas the asymmetric BBr3 stretching intensity is reported for the first time. Although agreement is good for the BF3 intensities, the result from the PNNL spectra for the asymmetric BCl3 stretching vibration is about three times larger than the one reported earlier. The intensities obtained from the PNNL spectra are in excellent agreement with results from QCISD/cc-pVTZ quantum chemical calculations having an rms error of only 32.9cm(-1) or 5.9% of the average intensity. Revised experimental atomic polar tensors and GAPT charges are reported for all these molecules.