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Sanjay Kumar. The overall reaction path is the resultant of the two previous processes. The REG analysis over the reaction path shows again that the intermolecular electrostatic contributions feature among the highest-ranked IQA terms in Segment 2, while Segment 1 continues to be dominated by the steric effect of the nitrogen atom, E intra N.
Table S2 presents the results for the REG analysis over the reaction path. Once again, the balance between the attractive and repulsive electrostatic potential is the key to understanding the Lewis acidity order of boron trihalides. Figure 6 displays two different plots.
In fact, it is difficult to spot any difference between the two plots. This suggests that the rehybridization process, although important for the acidity order among BH 3 and the trihalides, does not cause any significant change in the charge disposition, leaving the electrostatic potential energy largely unchanged. The high importance of the electrostatic terms is surprising because it indicates that the B—N bonds have a high degree of ionicity.
Within this approach, the B—N bond in all complexes is strongly ionic, expressed by the high magnitude of V cl B,N.
At the same time, the exchange-correlation terms for these bonds are small, confirming the results of the REG analysis, where the classical terms are more highly ranked compared to the exchange-correlation terms.
The ordinate reveals the magnitude of V cl A,B , which is associated with the degree of ionicity. The abscissa displays the magnitude of V xc A,B , which is associated with the degree of covalency. All quantities are displayed in Hartree.
Carbon monoxide is an example of a highly covalent molecule that also shows high polarity in its bonds, i. In contrast, HCl is an example of a single-bond covalent compound where the exchange-correlation contribution is 6 times larger than the classical electrostatic contribution. The B—F bond is high in ionicity and has only a small contribution from the exchange correlation. The other B—X bonds also display low covalency and their locations along the V xc -axis of the 2D plot are close to gas-phase NaCl.
This is evidence for the ionic character of the B—X bond according to Gillespie. As stated before, such changes can be interpreted in terms of the poor overlap of X orbitals with the empty p orbital of boron when the acid is rehybridized. Symmetry arguments show, and quantum calculations confirm, that infrared intensities of out-of-plane bending modes of planar molecules receive no contributions from charge transfer terms.
However, upon complex formation, the planar symmetry is broken and the BX 3 out-of-plane bending mode is modified. Not only is the wavenumber blue- or red-shifted but the intensities change drastically. Earlier work 27 demonstrates that the enhancement of the hydrogen stretching band that occurs when a hydrogen bond is formed relates to the hydrogen bond energy.
Moreover, that work showed that the CCTDP contributions provide useful information on changes in the electronic structure during the formation of the H-bond complex. In the H-bond case, comparisons between monomers and complex intensities were easier since the displacement vector of the hydrogen-bonded H atom and the not-hydrogen-bonded H were similar in magnitude. Now, we are not only comparing the out-of-plane vibration of BX 3 and the more complicated bending vibration in the BX 3 —NH 3 complex but also comparing vibrations of different molecules.
Note that displacement vectors play an important role in determining the infrared intensities. Table 3 shows the frequencies in cm —1 and intensities in km mol —1 of the B—X out-of-plane bending for the BX 3 monomers and the corresponding vibration in the BX 3 —NH 3 complexes. The most electron-deficient molecule BH 3 displays the greatest values of C 2 and DP 2 , which is explained by the mechanical weight depending on atomic mass of hydrogens: smaller atoms will show greater displacements, thereby enhancing their contributions.
Table 3. The electronic density in a covalent bond is easier to deform when the atoms move because it is concentrated between atoms. In ionic bonds, the electronic density is concentrated at the atoms so small displacements will result in a lower charge derivative. The systems that show greater contributions from charge transfer are the ones that present the greater degrees of covalency, as shown in Figure 7. To investigate this further, we have to look at the atomic displacements within the normal coordinate.
Figure 8 shows the atomic displacement vectors in red, out of scale. Note that for the BX 3 —NH 3 complex the movement of the atoms mimics the complex formation path, where the X atoms are displaced out of the BX 3 plane rehybridization as the base is approaching.
This means that the changes in the electronic density that occur during the vibrational movement are similar to those that occur in the reaction path. When the boron or carbon is displaced in the z direction, it moves closer or further from to the nitrogen atom. The charge transfer that occurs for this movement is measured by the term of the charge transfer atomic polar tensor Table 4. For the BX 3 monomers, these terms are zero. For BX 3 NH 3 complexes, the magnitude of the p zz term is the smallest of the three principal diagonal terms xx , yy , and zz presenting evidence of the small degree of covalency between B and N, which impedes electron exchange between nuclei.
The carbon counterparts exhibit a higher covalency degree between C and N or C—C. Hence, charge transfers between these nuclei are favored leading to higher values in magnitude for the p zz term relative to the p xx and p yy derivatives. Table 4. BH 3 —0. The complexation reactions were divided into two simpler processes: i the acid is allowed to deform i.
The IQA analysis on the acid rehybridization reveals that steric effects and classical electrostatics are acting against the adoption of the sp 3 geometry. The relative energy gradient REG analysis over the adduct formation highlighted the main energy components that drive the complexation process, allowing us to understand the energetics behind the formation of the B—N bond.
Finally, in the vibrational analysis of the out-of-plane B—X bending, the infrared intensities were decomposed into its atomic charge and dipole derivatives elucidating the electronic density changes with the formation of the adduct. Instead, a REG analysis shows that electrostatic energy terms, not exchange-correlation, explain the energy profile of the chemical path that leads to complex formation. The stabilization of the acid—base complex results from a balance between the attractive and repulsive electrostatic energy.
An increase in electronegativity of X will increase its charge and thus enhance the magnitudes of both attractive and repulsive energies, resulting in the observed acidity order. For the trihalides, differences in the rehybridization energies are small. The IR-CCTDP analysis, performed over the BX 3 Lewis acids and their adducts, shows that normal modes of vibration are useful to understand electronic structure changes when molecules react.
In fact, normal coordinates are obtained following the same procedure to determine reaction coordinates, that is, by finding the eigenvalues of the Hessian matrix. The normal coordinate of the B—X out-of-plane bending defines both the rehybridization process and the base approaching the acid. Since complex formation is dominated by electrostatics, the B—N bond also exhibits a high degree of ionicity. The ionic nature of trihalides and their complexes, accompanied by the equilibrium between attractive and repulsive electrostatics, is sufficient to explain the acidity trend in these compounds without an ad hoc explanation.
Supporting Information. Author Information. Paul L. Leonardo J. Wagner E. Roy E. The authors declare no competing financial interest. Google Scholar There is no corresponding record for this reference. Inorganic Chemistry ; Pearson Education Ltd. An Ab Initio Study. An ab initio study. An ab initio theor.
Lewis acidity scale of these mols. The increase in acidity when going from BF3 to BBr2can be understood in terms of the electron affinity and of the nature of the boron-halogen bond. The formation of H3N. BCl3 is favored by 4. BF3 at the MP2 level. This is in agreement with the exptl. Lewis Acidity of Boron Trihalides.
A , , — , DOI: American Chemical Society. We obtained the unoccupied reactive orbitals that show the max. The former is similar in magnitude for these boron halide compds. Contrary to common belief, the conjugation between the boron atom and the attached halogen atoms is not necessarily stronger in BF3 relative to others. BF3 and SiF4 are much more ionic than has hitherto generally been supposed. The fully ionic model is a much better description of the bonding than the fully covalent model, and it provides a simple explanation of the bond lengths and bond energies.
Contrary to common belief, predominately ionic mols. They do not necessarily condense to ionic solids because of size limitations on the max. A Ligand Close-Packing Model. JAI Press Inc. A review with many refs. A study of the exptl. From these inter-ligand distances a const. Inter-ligand distances in species with mixed ligands, such as chlorofluorides and oxofluorides, can be accurately predicted with these ligand radii. The ligand charges, although large, are smaller than the full ionic charges and decrease with increasing electronegativity of the central atom and it is the charge on the ligand that dets.
On the basis of these results it is proposed that in these mols. We call this the ligand close-packing LCP model. It is shown that this model provides simpler explanations for the bond lengths and bond angles in mols.
On this basis it is possible to understand why "lone pairs" are sometimes stereochem. Elsevier Science S. A review with 15 refs. Considerable improvements in our understanding of mol. These improvements have enabled several aspects of the VSEPR model to be better understood and explanations of exceptions to the model to be proposed.
The LCP model shows that particularly for the small atoms of the period 2 elements, ligand-ligand interactions are very important in detg.
Electron d. The unexpected greater Lewis acidity of BCl3 than BF3 with respect to strong bases such as NH3 has been the subject of much discussion. The halogen ligands remain close-packed throughout the formation of an adduct and the bond lengths increase accordingly.
In contrast, in the formation of a complex with a weak base such as CO, the BX3 is barely distorted from planarity and so the acidity of BF3 is greater than that of BCl3 because the charge on boron is greater in BF3 than BCl3. A spherical ion model is used to est.
The bond dipole moments are estd. An alternative set of net at. The exptl. It is proposed that BF3 and SiF4 would, if they were ionic substances, aggregate to dimeric or polymeric species.
Generalized at. 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 "std. 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 mols. QTAIM charges are strongly correlated with one another, even though they seem to be constructed under very different frameworks. Much chemical insight ultimately comes down to finding out which fragment of a total system behaves like the total system, in terms of an energy profile.
A simple example is that of the water dimer, where this system is regarded as held together by a hydrogen bond. However, from a quantum mechanical point of view, each atom in the total system interacts with any other atom. Thus, the view that the hydrogen bond by itself governs the energetic stability of the water dimer needs rigorous justification. In this work, we propose a method that provides such a justification, in general, but only illustrated on the water dimer here.
This method is based on the topological energy partitioning method called interacting quantum atoms IQA. The method is implemented in the program ANANKE, which calculates correlations between the energy profile of the total system and those of subsystems or fragments.
Although applied only for the water dimer in this work, the method is general and able to explain the gauche effect, the torsional barrier in biphenyl, the arrow-pushing scheme of an enzymatic reaction peptide hydrolysis in the HIV-1 Protease active site , and halogen-alkane nucleophilic substitution SN2 reactions.
Those applications will appear elsewhere as separate and elaborated case studies; here we focus on the details of the ANANKE method and its justification, using the water dimer as a concrete case. Theory Comput. We make use of the Quantum Theory of Atoms in Mols. QTAM to partition the total energy of a many-electron system into intra- and interat.
While the general scheme is formally equiv. The partition is ultimately performed within the d. It is intimately linked with the atomistic picture of the chem. Many qual. The mol. Root-mean-square rms errors of 0. Parallel polar tensor elements for the diat. These fluxes have a large neg. The classical model proposed here to calc. The utility of the AIM at. These results show that IR intensities do contain information relevant to the study of intermol.
ChemistryOpen , 8 , — , DOI: Symons, Benjamin C. We show that the mutual, through-space compression of at. This insight was obtained using the modern energy partitioning method called interacting quantum atoms IQA. This behavior is consistent for all atoms except hydrogen, which can behave differently depending on its environment.
While all atoms experience charge transfer when they interact, the intra-at. The difference in behavior is found to be due to hydrogen's lack of a core of electrons, which, in heavier atoms, consistently provide repulsion when compressed. As such, hydrogen atoms do not always provide steric hindrance.
In accounting for hydrogen's unusual behavior and demonstrating the exponential character of the intra-at. Quantifying Electron Correlation of the Chemical Bond. McDonagh, James L. Such an anal. Electron correlation lowers the energy of the atoms at either end of a bond, but for the bond itself, it can be stabilizing or destabilizing. Bonds are described in a two-dimensional world of exchange and charge transfer, where covalency is not the opposite of ionicity.
A review. The quantum topol. In the last three years we have enriched this anal. This work led to a new computational and interpretational tool to generate atomistic electron correlation and thus topol.
A series of papers published by us and other groups shows that the behavior of electron correlation is deeply ingrained in structural chem. Some concepts that were shown to be connected to bond correlation are bond order, multiplicity, aromaticity, and hydrogen bonding. Moreover, the concepts of covalency and ionicity were shown not to be mutually excluding but to both contribute to the stability of polar bonds.
The correlation energy is considerably easier to predict by machine learning kriging than other IQA terms. Regarding the nature of the hydrogen bond, correlation energy presents itself in an almost contradicting way: there is much localized correlation energy in a hydrogen bond system, but its overall effect is null due to internal cancelation.
We also explore the role of electron correlation in protobranching, which provides an explanation for the extra stabilization present in branched alkanes compared to their linear counterparts.
We hope to show the importance of understanding the true nature of the correlation energy as the foundation of a modern representation of dispersion forces for ab initio, DFT, and force field calcns. Quantum Chemical Topology. Py , Gaussian 09 , revision D1; Gaussian, Inc. Some Procedures with Reduced Errors. Some procedures with reduced errors.
A new direct difference method for the computation of mol. It appears that these new features can give a strong redn. It has been generally accepted that this problem is dominated by unresolved difficulties and the relation of the new methods of these apparent difficulties is analyzed here. Nova , 26 , — , DOI: Sociedade Brasileira de Quimica.
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