Characteristic Substituent Effect Model for the Infrared Intensities of the X2CY (X = H, F, Cl, Br; Y = O, S) Molecules.

Many years ago, the gas-phase infrared fundamental intensities of Cl2CS were determined within experimental error from the experimental intensities and frequencies of F2CO, Cl2CO, and F2CS. An additive characteristic substituent shift relationship between atomic polar tensors of these molecules formed the basis for these calculations. Here, QCISD/cc-pVTZ-level Quantum Theory of Atoms In Molecules (QTAIM) individual charge, charge transfer, and polarization contributions to these atomic polar tensor elements are shown to obey the same basic relationship for the extended X2CY (Y = O, S; X = H, F, Cl, Br) family of molecules. QTAIM charge and polarization contributions, as well as the total equilibrium dipole moments of the X2CY molecules, also follow this characteristic substituent shift model. The root-mean-sqaure error for the 231 estimates of these parameters is 0.14 e or only about 1% of the total 10 e range of the Atomic Polar Tensor (APT) contributions determined from the wave functions. The substituent effect APT contribution estimates were used to calculate the infrared intensities of the X2CY molecules. Although one serious discrepancy was observed for one of the CH stretching vibrations of H2CS, accurate values were within 45 km·mol-1 or about 7% of the 656 km·mol-1 intensity range predicted by the QCISD/cc-pVTZ wave functions. Hirshfeld charge, charge transfer, and polarization contributions are also found to follow this model, although their charge parameters do not follow electronegativity expectations.

Energetic Origins of Force Constants: Adding a New Dimension to the Hessian Matrix via Interacting Quantum Atoms.

The Interacting Quantum Atoms (IQA) energy decomposition scheme divides the total energy of a molecule into intra- and interatomic contributions. While the former relates to the kinetic and potential energies of electrons inside a unique individual atomic basin, the latter contains the Coulomb and exchange-correlation potentials between electrons from two atomic basins. Considering that the molecular energy is a sum of IQA contributions, the Hessian matrix can also be written as a sum of "IQA Hessian" matrices, whose elements are second derivatives of IQA terms. Herein, we present a mathematical formalism for the IQA decomposition of force constants revealing their energetic origins. The method consists of adding a new dimension to the Hessian matrix, which becomes 3N × 3N × N2, with N being the number of atoms in the molecule and N2 the number of IQA terms. Since there is no analytical method that produces the IQA second derivatives, the three-dimensional IQA Hessian is numerically calculated. When studying molecular vibrations, force constants, providing information about the nature of chemical bond and related to infrared frequencies, can be obtained by Wilson's FG method, which involves detailed manipulations of the Hessian matrix. In this paper, the methodology is reported and validated for a set of 30 molecules and more than 200 force constants and their interactions. Energetic origins of force constants are presented for diatomics and small molecules containing carbon-carbon, oxygen-oxygen, and carbon-oxygen bonds with different bond orders. It is found that bond stability and stiffness can have strikingly different energetic origins.

Are "GAPT Charges" Really Just Charges?

Generalized atomic polar tensor (GAPT) has turned into a very popular charge model since it was proposed three decades ago. During this period, several works aiming to compare different partition schemes have included it among their tested models. Nonetheless, GAPT exhibits a set of unique features that prevent it from being directly comparable to "standard" partition schemes. We take this opportunity to explore some of these features, mainly related to the need of evaluating multiple geometries and the dynamic character of GAPT, and show how to obtain the static and dynamic parts of GAPT from any static charge model in the literature. We also present a conceptual evaluation of charge models that aims to explain, at least partially, why GAPT and quantum theory of atoms in molecules (QTAIM) charges are strongly correlated with one another, even though they seem to be constructed under very different frameworks. Similar to GAPT, infrared charges (also derived from atomic polar tensors of planar molecules) are also shown to provide an improved interpretation if they are described as a combination of static charges and changing atomic dipoles rather than just experimental static atomic charges.

AC/DC Analysis: Broad and Comprehensive Approach to Analyze Infrared Intensities at the Atomic Level.

We present a complete theoretical protocol to partition infrared intensities into terms owing to individual atoms by two different but related approaches: the atomic contributions (ACs) show how the entire molecular vibrational motion affects the electronic structure of a single atom and the total infrared intensity. On the other hand, the dynamic contributions (DCs) show how the displacement of a single atom alters the electronic structure of the entire molecule and the total intensity. The two analyses are complementary ways of partitioning the same total intensity and conserve most of the features of the total intensity itself. Combined, they are called the AC/DC analysis. These can be further partitioned following the CCTDP (or CCT) models according to the population analysis chosen by the researcher. The main conceptual features of the equations are highlighted, and representative numerical results are shown to support the interpretation of the equations. The results are invariant to rotation and translation and can readily be extended to molecules of any size, shape, or symmetry. Although the AC/DC analysis requires the choice of a charge model, all charge models that correctly reproduce the total molecular dipole moment can be used. A fully automated protocol managed by the Placzek program is made available, free of charge and with input examples.

Electrostatics Explains the Reverse Lewis Acidity of BH3 and Boron Trihalides: Infrared Intensities and a Relative Energy Gradient (REG) Analysis of IQA Energies.

The reaction path for the formation of BX3-NH3 (X = H, F, Cl, Br) complexes was divided into two processes: (i) rehybridization of the acid while adopting a pyramidal geometry, and (ii) the complex formation from the pyramidal geometries of the acid and base. The interacting quantum atom (IQA) method was used to investigate the Lewis acidity trend of these compounds. This topological analysis suggests that the boron-halogen bond exhibits a considerable degree of ionicity. A relative energy gradient (REG) analysis on IQA energies indicates that the acid-base complex formation is highly dependent on electrostatic energy. With increasing halogen electronegativity, a higher degree of ionicity of the B-X is observed, causing an increase in the absolute value of X and B charges. This increases not only the attractive electrostatic energy between the acid and base but also enhances the repulsive energy. The latter is the main factor behind the acidity trend exhibited by trihalides. Changes in geometry are relevant only for complexes where BH3 acts as an acid, where lower steric hindrance facilitates the adoption of the pyramidal geometry observed in the complex. The CCTDP analysis shows that infrared intensities of BX3-NH3 are determined mostly by the atomic charges and not by the charge transfer or polarization. The opposite is observed in covalent analogues.

QTAIM Atomic Charge and Polarization Parameters and Their Machine-Learning Transference among Boron-Halide Molecules.

Atomic charges are invariant for out-of-plane distortions, making their molecular vibrations enticing for electronic structure studies. Of planar molecules, the boron trihalides contain some of the most polar bonds known to chemistry, although their out-of-plane bending intensities are very small contrary to expectations from atomic charge models. Here, the out-of-plane infrared intensities of the BX(2)X(3)X(4) (X(2), X(3), X(4) = H, F, Cl, Br) molecules are investigated using quantum theory of atoms in molecules atomic charges and atomic dipoles within the formulism of the charge, charge transfer, dipolar polarization model at the QCISD/aug-cc-pVTZ quantum level. Dipole moments induced by equilibrium charge displacement of atoms perpendicular to the molecular plane are almost completely cancelled by their electronic density polarizations. The calculated boron trihalide intensities are small for molecules with such polar bonds ranging from 0.6 to 106.1 km mol-1. Even though the Cl atomic charge of -0.72 e in BCl3 is more negative than the hydrogen values of -0.67 e in BH3, the hydride out-of-plane intensity of 82.0 km mol-1 is an order of magnitude larger than that of the trichloride, 6.3 km mol-1. Owing to their diverse electronic structures, transference of atomic charges and dipole parameters among the boron trihalides is extremely challenging and does not result in accurate intensity values. For this reason, a machine-learning decision-tree algorithm was used to perform the transference procedure. Decision trees were optimized using quantum-level intensity values. Atomic charge and dipole parameters were estimated for a set of 12 test set molecules. These parameters provided intensity estimates with a root-mean-square error of 2.1 km mol-1 compared with QCISD/aug-cc-pVTZ reference values.

Infrared Intensification and Hydrogen Bond Stabilization: Beyond Point Charges.

Infrared band intensification of the A-H bond stretching mode of A-H···B acid-base systems has long been known to be the most spectacular spectral change occurring on hydrogen bonding. A QTAIM/CCTDP model is reported here to quantitatively explain the electronic structure origins of intensification and investigate the correlation between experimental enthalpies of formation and infrared hydrogen bond stretching intensifications amply reported in the literature. Augmented correlation-consistent polarized triple-zeta quantum calculations at the MP2 level were performed on complexes with HF and HCl electron acceptors and HF, HCl, NH3, H2O, HCN, acetonitrile, formic acid, acetaldehyde, and formaldehyde electron donor molecules. The A-H stretching band intensities are calculated to be 3 to 40 times larger than their monomer values. Although the acidic hydrogen atomic charge is important for determining the intensities of HF complexes relative to HCl complexes with the same electron donor, they are not important for infrared intensifications occurring on hydrogen bond formation for a series of bases with a common acid. Charge transfers are found to be the most important factor resulting in the intensifications, but dipolar polarization effects are also significant for each series of complexes. A mechanism involving intra-acid and intermolecular electron transfers as well as atomic polarizations is proposed for understanding the intensifications. The calculated sums of the intermolecular electron transfer and acid dipolar polarization contributions to the dipole moment derivatives for each series of complexes are highly correlated with their enthalpies of formation and H-bond intensifications. This could be related to increasing electron transfer from base to acid that correlates with the calculated hydrogen bonding energies and may be a consequence of the A-H bond elongation on complex formation having amplitudes similar to those expected for the A-H vibration.

Atomic Polarizations, Not Charges, Determine CH Out-of-Plane Bending Intensities of Benzene Molecules.

Infrared gas phase intensities are reported for the first time for 23 CH out-of-plane bending vibrations of eight substituted benzene molecules and naphthalene by integration of bands from the Pacific Northwest National Laboratory (PNNL) spectral library. These experimental values are found to have an rms difference of 8.7 km mol-1 with the B3LYP/6-311++G(d,p) values for intensities ranging from close to zero to 126.7 km mol-1. These intensities are found to have transferable electronic structure parameters, and their square roots are proportional to the amplitudes of the hydrogen atom displacements perpendicular to the benzene ring. Quantum Theory of Atom in Molecules (QTAIM)-Charge-Charge Transfer-Dipolar Polarization models were determined from the B3LYP/6-311++G(d,p) electronic densities. By far, the largest electronic contribution to these intensities is the dipolar polarization of the carbon atom of the displaced CH bond, 0.214 e. Smaller contributions are found for the polarizations of the displaced hydrogen atoms (-0.043 e) and nearest neighbor carbon atoms (-0.052 e), both having directions opposite to that of the carbon atom polarization of the displaced CH bond. The movements of static equilibrium hydrogen charges make the smallest contribution canceling most of the hydrogen polarization changes. In fact, the carbon atomic polarizations alone account for 96.9% of the dipole moment derivative vector norm for the CH out-of-plane bends. The polarization model is also found to be valid for seven CH out-of-plane bending vibrations of N-fused benzene ring molecules (N = 3, 4, 5).

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.

Characteristic infrared intensities of carbonyl stretching vibrations.

The experimental infrared fundamental intensities of gas phase carbonyl compounds obtained by the integration of spectral bands in the Pacific Northwest National Laboratory (PNNL) spectral database are in good agreement with the intensities reported by other laboratories having a root mean square error of 27 km mol(-1) or about 13% of the average intensity value. The Quantum Theory of Atoms in Molecules/Charge-Charge Transfer-Counterpolarization (QTAIM/CCTCP) model indicates that the large intensity variation from 61.7 to 415.4 km mol(-1) is largely due to static atomic charge contributions, whereas charge transfer and counterpolarization effects essentially cancel one another leaving only a small net effect. The Characteristic Substituent Shift Model estimates the atomic charge contributions to the carbonyl stretching intensities within 30 km mol(-1) or 10% of the average contribution. However, owing to the size of the 2 × C × CTCP interaction contribution, the total intensities cannot be estimated with this degree of accuracy. The dynamic intensity contributions of the carbon and oxygen atoms account for almost all of the total stretching intensities. These contributions vary over large ranges with the dynamic contributions of carbon being about twice the size of the oxygen ones for a large majority of carbonyls. Although the carbon monoxide molecule has an almost null dipole moment contrary to the very polar bond of the characteristic carbonyl group, its QTAIM/CCTCP model is very similar to those found for the carbonyl compounds.

QTAIM-Based Characteristic Group Infrared Intensities of Amino Acids and Their Transference to Peptides.

Dynamic atomic contributions (DACs) to the infrared intensities of 14 amino acids have been transferred to three peptide molecules, glycylglycine, trialanine, and the melanocyte-inhibiting factor MIF-1, to estimate the infrared intensities of the most strategic peptide bands. The DACs of the amino acids and infrared intensities of the peptides were determined at the DFT B3LYP/6-311+(d,p) level. The Quantum Theory of Atoms In Molecules (QTAIM) Charge-Charge Transfer-Dipolar Polarization (CCTDP) model at this Density Functional Theory (DFT) level was used to classify the O-H, NH2, N-H, and C═O stretching as well as the NH2 bending characteristic groups for use in the transference procedure. Contrary to the frequencies, the intensities within these groups can have very diverse values, although their electronic structure changes upon vibration have predictable QTAIM behaviors for each group. Compared to the DFT calculated values, the two transferred O-H stretching intensities of the peptides are estimated with a root-mean-square (rms) error of 19.1 km mol-1. Six NH2 symmetric and antisymmetric stretching intensities were determined with a 9.9 km mol-1 error. The eight estimated C═O stretching bands have a rms error of 78.0 km mol-1 or 23.6% of the average DFT peptide C═O intensity of 328.4 km mol-1. The proposed procedure is applicable to experimental infrared intensities if a calibration set of molecules with known atomic polar tensors and normal coordinate transformations is available.

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.

An atom in molecules study of infrared intensity enhancements in fundamental donor stretching bands in hydrogen bond formation.

Vibrational modes ascribed to the stretching of X-H bonds from donor monomers (HXdonor) in complexes presenting hydrogen bonds (HF···HF, HCl···HCl, HCN···HCN, HNC···HNC, HCN···HF, HF···HCl and H2O···HF) exhibit large (4 to 7 times) infrared intensity increments during complexation according to CCSD/cc-pVQZ-mod calculations. These intensity increases are explained by the charge-charge flux-dipole flux (CCFDF) model based on multipoles from the Quantum Theory of Atoms in Molecules (QTAIM) as resulting from a reinforcing interaction between two contributions to the dipole moment derivatives with respect to the vibrational displacements: charge and charge flux. As such, variations that occur in their intensity cross terms in hydrogen bond formation correlate nicely with the intensity enhancements. These stretching modes of HXdonor bonds can be approximately modeled by sole displacement of the positively charged hydrogens towards the acceptor terminal atom with concomitant electronic charge transfers in the opposite direction that are larger than those occurring for the H atom displacements of their isolated donor molecules. This analysis indicates that the charge-charge flux interaction reinforcement on H-bond complexation is associated with variations of atomic charge fluxes in both parent molecules and small electronic charge transfers between them. The QTAIM/CCFDF model also indicates that atomic dipole flux contributions do not play a significant role in these intensity enhancements.

Atomic charge transfer-counter polarization effects determine infrared CH intensities of hydrocarbons: a quantum theory of atoms in molecules model.

Atomic charge transfer-counter polarization effects determine most of the infrared fundamental CH intensities of simple hydrocarbons, methane, ethylene, ethane, propyne, cyclopropane and allene. The quantum theory of atoms in molecules/charge-charge flux-dipole flux model predicted the values of 30 CH intensities ranging from 0 to 123 km mol(-1) with a root mean square (rms) error of only 4.2 km mol(-1) without including a specific equilibrium atomic charge term. Sums of the contributions from terms involving charge flux and/or dipole flux averaged 20.3 km mol(-1), about ten times larger than the average charge contribution of 2.0 km mol(-1). The only notable exceptions are the CH stretching and bending intensities of acetylene and two of the propyne vibrations for hydrogens bound to sp hybridized carbon atoms. Calculations were carried out at four quantum levels, MP2/6-311++G(3d,3p), MP2/cc-pVTZ, QCISD/6-311++G(3d,3p) and QCISD/cc-pVTZ. The results calculated at the QCISD level are the most accurate among the four with root mean square errors of 4.7 and 5.0 km mol(-1) for the 6-311++G(3d,3p) and cc-pVTZ basis sets. These values are close to the estimated aggregate experimental error of the hydrocarbon intensities, 4.0 km mol(-1). The atomic charge transfer-counter polarization effect is much larger than the charge effect for the results of all four quantum levels. Charge transfer-counter polarization effects are expected to also be important in vibrations of more polar molecules for which equilibrium charge contributions can be large.

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.

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.

Electronic Distribution of SN2 IRC and TS Structures: Infrared Intensities of Imaginary Frequencies.

A novel IRC-TS-CCTDP method to investigate transition states (TS) is proposed in which changes in the molecular geometry follow atomic displacements corresponding to the imaginary frequency normal coordinate. Electronic charge structure changes can be analyzed using the charge-charge-transfer-dipolar polarization (CCTDP) model. An application is presented for the gas-phase SN2 reaction transition state structures for nine NuCX3LG- systems, with Nu and LG = H, F, Cl and X = H, F. Using quantum theory of atoms in molecules (QTAIM) at the QCISD/aug-cc-pVTZ level, atomic charges and atomic dipoles were obtained and applied to calculate the CCTDP contributions to their imaginary normal mode intensities. The results show that the imaginary bands are exceptionally strong, ranging from 1217 to 16 086 km·mol-1, much higher than the stretching intensities found in the methyl halides (that are all less than 100 km·mol-1). For all systems, the CT contributions are responsible for 63% of the total dipole moment derivatives. The charge contributions are slightly higher for transition states where X = F. Dipolar polarization contributions are always small and only reflect the molecular orientation change when the nucleophile displaces the leaving group and, therefore, can be neglected. The same occurs for contributions from the X atoms. Only atoms aligned with the reaction axis Nu--C-LG contribute to the total intensity. Almost all of the infrared intensities are determined by electron transfers from the nucleophile to carbon and subsequently from carbon to the leaving group. The mechanism of charge transfer revealed by the CCTDP model is consistent with the well-accepted reaction mechanism. Open-access codes for performing the IRC-TS-CCTDP analysis are described and provided for potential users in the Supporting Information.

Unavoidable failure of point charge descriptions of electronic density changes for out-of-plane distortions.

Population analyses based on point charge approximations accurately estimating the equilibrium dipole moment will systematically fail when predicting infrared intensities of out-of-plane vibrations of planar molecules, whereas models based on both charges and dipoles will always succeed. It is not a matter of how the model is devised but rather how many degrees of freedom are available for the calculation. Population analyses based on point charges are very limited in terms of the amount of meaningful chemical information they provide, whereas models employing both atomic charges and atomic dipoles should be preferred for molecular distortions. A good model should be able to correctly describe not only static, equilibrium structures but also distorted geometries in order to correctly assess information from vibrating molecules. The limitations of point charge models also hold for distortions much larger than those encountered vibrationally.

QTAIM charge-charge flux-dipole flux interpretation of electronegativity and potential models of the fluorochloromethane mean dipole moment derivatives.

Infrared fundamental vibrational intensities and quantum theory atoms in molecules (QTAIM) charge-charge flux-dipole flux (CCFDF) contributions to the polar tensors of the fluorochloromethanes have been calculated at the QCISD/cc-pVTZ level. A root-mean-square error of 20.0 km mol(-1) has been found compared to an experimental error estimate of 14.4 and 21.1 km mol(-1) for MP2/6-311++G(3d,3p) results. The errors in the QCISD polar tensor elements and mean dipole moment derivatives are 0.059 e when compared with the experimental values. Both theoretical levels provide results showing that the dynamical charge and dipole fluxes provide significant contributions to the mean dipole moment derivatives and tend to be of opposite signs canceling one another. Although the experimental mean dipole moment derivative values suggest that all the fluorochloromethane molecules have electronic structures consistent with a simple electronegativity model with transferable atomic charges for their terminal atoms, the QTAIM/CCFDF models confirm this only for the fluoromethanes. Whereas the fluorine atom does not suffer a saturation effect in its capacity to drain electronic charge from carbon atoms that are attached to other fluorine and chlorine atoms, the zero flux electronic charge of the chlorine atom depends on the number and kind of the other substituent atoms. Both the QTAIM carbon charges (r = 0.990) and mean dipole moment derivatives (r = 0.996) are found to obey Siegbahn's potential model for carbon 1s electron ionization energies at the QCISD/cc-pVTZ level. The latter is a consequence of the carbon mean derivatives obeying the electronegativity model and not necessarily to their similarities with atomic charges. Atomic dipole contributions to the neighboring atom electrostatic potentials of the fluorochloromethanes are found to be of comparable size to the atomic charge contributions and increase the accuracy of Siegbahn's model for the QTAIM charge model results. Substitution effects of the hydrogen, fluorine, and chlorine atoms on the charge and dipole flux QTAIM contributions are found to be additive for the mean dipole derivatives of the fluorochloromethanes.