Substituent effects on intramolecular Schmidt reactions: a theoretical study on the formation of bridged lactams.

The competitive formation of isomeric bridged lactams via acid-catalyzed intramolecular Schmidt reactions from 3-azidoethylcyclopentanones is explored using density functional theory (DFT) calculations, primarily performed at the M06-2X/6-311++G(d,p) level of theory. The results indicate that specific substituents installed at α-carbons can efficiently control the regioselectivity of the reaction by lone pair-cation interactions or steric hindrance reversing the main product preference, whereas cation-π interactions are not so effective.

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.

Infrared intensities of [Formula: see text]: a true challenge for DFT methods.

Absolute infrared intensities of [Formula: see text] were evaluated with a great variety of DFT and ab initio methods and basis sets. It is shown that the intensities calculated by different levels of theory may not agree with each other even in the qualitative (weak/strong) sense. Geometrical parameters, as well as net atomic charges evaluated from multiple partition schemes, did not vary as much as the intensities and thus cannot explain the tremendous differences found for the latter. As there are no experimental estimates for the intensities to guide the theoretical evaluation, deciding on the best level of theory is reduced to comparisons between the different DFT methods and QCISD or CCSD, believed to be the best theoretical estimates in the set. The differences found among the various DFT methods suggest the development of new methods, instead of converging to a focal point, is rather diverging.

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.

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.

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.

Atomic charge and atomic dipole modeling of gas-phase infrared intensities of fundamental bands for out-of-plane CH and CF bending vibrations.

Out-of-plane CH group bending vibrational bands have long been known to be more intense than those for CF groups in similar molecular environments. This contrasts with expectations derived from charge models for which equilibrium atomic charge displacements are considered dominant contributions to dipole moment change on vibration. For this reason, the Charge, Charge Transfer, Dipolar Polarization (CCTDP) model based on the Quantum Theory for Atoms in Molecules (QTAIM) has been applied to the ethylene, tetrafluoroethylene and difluoro- and dichloroethylene molecules. Atomic charges and atomic dipoles from QTAIM and infrared intensities were calculated at the M06-2X/aug-cc-pVTZ level. The CH out-of-plane bending vibrations with relatively high intensities between 48.0 and 82.1 km/mol are characterized by small atomic charge and large polarization contributions having the same sign resulting in large net dipole moment contributions. Large charge and polarization dipole moment derivative contributions with opposite signs cancel each other producing very small intensities between 0.3 and 12.7 km/mol for the CF bends. Intensity variations can be successfully modeled by only their carbon atomic contributions with smaller contributions from the terminal atoms. Both CH and CF bending vibrations have large polarization contributions. Their charge contributions are usually small except for carbon atoms bonded to two fluorine atoms. The terminal atoms as well as the carbons have charge and polarization contributions of opposite sign. Comparison to benzene and hexafluorobenzene reveals that changes in these molecules' electronic densities caused by the out-of-plane atomic displacements are characteristic for each bond. In conclusion, successful modeling of the ethylene intensities must include atomic dipole parameters.Models based only on charges are doomed to failure.

Quantum chemical intensity determinations of overlapped gas phase infrared bands.

The largest source of experimental error in determining gas phase fundamental infrared intensities arises from the separation of overlapped bands. Quantum chemical calculations at the QCISD/cc-pVTZ and QCISD/aug-cc-pVTZ levels were carried out on four simple hydrocarbons and the fluoro- and chloromethanes with the aim of accurate overlapped band separation. Fundamental vibrational intensity results were compared with individual empirical intensity estimates reported for overlapped band systems. Root mean square differences of 3.7 km mol-1 are found between the experimental and QCISD/cc-pVTZ values for nine overlapped bands of the hydrocarbons and 11.8 km mol-1 for the QCISD/aug-cc-pVTZ values for 12 overlapped bands of the fluoro- and chloromethanes. These values correspond to 14% and 18% of the average hydrocarbon and halomethane intensity values. Previous experimental separation errors were estimated to be quite larger, between 20% and 50%. As quantum calculations are continuously being refined one can expect more accurate band separation results in the future.

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.

FTIR and dispersive gas phase fundamental infrared intensities of the fluorochloromethanes: Comparison with QCISD/cc-pVTZ results.

New experimental values of the fundamental infrared gas phase intensities of the fluorochloromethanes have been determined by integrating the areas of vibrational bands contained in the PNNL spectral library using homemade software. The root mean square differences of these values and averages of experimental values determined at lower resolution during the latter part of the 20th century is 26.6 km mol-1. All but one of the low resolution intensities are smaller than the PNNL values. The exception is the ν1,ν4 overlapped band intensity of CF3Cl that has a standard deviation of the low resolution values of ±112.5 km mol-1, larger than the observed difference of 102.5 km mol-1. The use of an augmented triple zeta basis set at the QCISD level results in an rms difference of only 8.4 km mol-1 for the fluoro- and chloromethane PNNL intensities, whereas a comparison of these with results at the QCISD/cc-pVTZ level produces an error twice as large, 16.2 km mol-1. As such these results suggest that future comparisons of theoretical intensities with experimental values should take into account integrated intensities that can be obtained from hundreds of spectra in the PNNL library. Furthermore, the intensity values obtained from the PNNL spectra confirm electronegativity model results previously reported based on the low resolution intensities.

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.

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.

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.

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.

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.