Is VSEPR valid?

Summary A chief tenet of VSEPR (valence shell electron pair repulsion theory) is that very electronegative atoms or groups attached to a central atom pull electrons toward themselves. These electron pairs, being farther apart, exert less repulsion, and consequently the bond angles involving them are decreased. A comparison of 37 pairs of common compounds shows that this rule holds only for hydrogen compounds. For other molecules, the size of the attached groups determines the bond angles.

---

VSEPR: ist es stichhaltig?

Zusammenfassung Ein Hauptgrundsatz der VSEPR (Valenzschalen-Elektronenpaar-Repulsion) Theorie heißt: hoch elektronegative, an einem Zentralatom angelagerte Atome oder Atomgruppen ziehen Elektronen an. Da sie weiter voneinander entfernt sind, üben diese Elektronenpaare weniger Repulsion aus. Daher werden die dazugehörigen Bindungswinkel vermindert. Ein Vergleich von 37 Paaren einfacher Verbindungen zeigt, daß diese Regel nur für Wasserstoffverbindungen gilt. In anderen Molekülen bestimmt die Größe der angelagerten Gruppen die Valenzwinkel.

     

Single electron densities: a new tool to analyze molecular wavefunctions

A new partitioning scheme for the electron density of a many-electron wavefunction into single electron densities is proposed. These densities are based on the most probable arrangement of the electrons in an atom or molecule. Therefore, they contain information about the electron-electron interaction and, most notably, the Fermi hole due to the antisymmetry of the many-electron wavefunction. The single electron densities overlap and can be combined to electron pair distributions close to the qualitative electron pairs that represent, for instance, the basis of the valence shell electron pair repulsion model. Single electron analyses are presented for the water, ethane, and ethene molecules. The effect of electron correlation on the single electron and pair densities is investigated for the water molecule.     

Chemical bonding in hypervalent molecules: is the octet rule relevant?

The bonding in a large number of hypervalent molecules of P, As, S, Se, Te, Cl, and Br with the ligands F, Cl, O, CH(3), and CH(2) has been studied using the topological analysis of the electron localization function ELF. This function partitions the electron density of a molecule into core and valence basins and further classifies valence basins according to the number of core basins with which they have a contact. The number and geometry of these basins is generally in accord with the VSEPR model. The population of each basin can be obtained by integration, and so, the total population of the valence shell of an atom can be obtained as the sum of the populations of all the valence basins which share a boundary with its core basin. It was found that the population of the V(A, X) disynaptic basin corresponding to the bond, where A is the central atom and X the ligand, varies with the electronegativity of the ligand from approximately 2.0 for a weakly electronegative ligand such as CH(3) to less than 1.0 for a ligand such as F. We find that the total population of the valence shell of a hypervalent atom may vary from close to 10 for a period 15 element and close to 12 for a group 16 element to considerably less than 8 for an electronegative ligand such as F. For example, the phosphorus atom in PF(5) has a population of 5.37 electrons in its valence shell, whereas the arsenic atom in AsMe5 has a population of 9.68 electrons in its valence shell. By definition, hypervalent atoms do not obey the Lewis octet rule. They may or may not obey a modified octet rule that has taken the place of the Lewis octet rule in many recent discussions and according to which an atom in a molecule always has fewer than 8 electrons in its valence shell. We show that the bonds in hypervalent molecules are very similar to those in corresponding nonhypervalent (Lewis octet) molecules. They are all polar bonds ranging from weakly to strongly polar depending on the electronegativity of the ligands. The term hypervalent therefore has little significance except to indicate that an atom in a molecule is forming more than four electron pair bonds.     

Valence-Shell Electron-Pair Repulsion Theory Revisited: An Explanation for Core Polarization

Valence-shell electron-pair repulsion (VSEPR) theory constitutes one of the pillars of theoretical predictive chemistry. It was proposed even before the advent of the concept of “spin”, and it is still a very useful tool in chemistry. In this article we propose an extension of VSEPR theory to understand the core structure and predict core polarization in the main-group elements. We show from first principles (Electron Localization Function analysis) how the inner- and outer-core shells are organized. In particular, electrons in these regions are structured following the shape of the dual polyhedron of the valence shell (3^rd period) or the equivalent polyhedron (4^th and 5^th periods). We interpret these results in terms of “hard” and “soft” core character. All the studied systems follow this trend, providing a framework for predicting electron distribution in the core. We also show that lone pairs behave as “standard ligands” in terms of core polarization. The predictive character of the model was tested by proposing the core polarization in different systems not included in the original set (such as XeF₄ and [Fe(CN)₆]³⁻) and checking the hypothesis by means of a posteriori calculations. From the experimental point of view, the extension of VSEPR to the core region has consequences for current crystallography research. In particular, it explains the core polarization revealed by high resolution X-ray experiments.     

A topological study of the geometry of AF6E molecules: weak and inactive lone pairs

The geometries of AF6E molecules, which may have either an O(h) or a C(3v) geometry, have been studied by means of the electron localization function. Our results show that when the molecule has a C(3v) geometry, there is a valence-shell monosynaptic V(A) basin corresponding to the presence of a lone pair in the valence shell of the central atom A. The population of this basin is, however, extensively delocalized so that the electron density has a core-valence basin character, which is consistent with an earlier suggestion of a weakly active lone pair that gives a C(3v) distorted octahedral molecule rather than the valence-shell electron-pair repulsion predicted pentagonal-pyramid geometry. In contrast, the molecules with O(h) geometry do not have a monosynaptic valence-shell basin, but they have a larger core. These results provide confirmation of a previous suggestion that in AX6E (X = Cl, Br, I) molecules with the O(h) geometry the ligands X are sufficiently closely packed around the central atom A so as to leave no space in the valence shell for the lone pair E, which remains part of the core. Among the corresponding fluorides, only BrF6- has the O(h) geometry, while the others have the C(3v) geometry because there is sufficient space in the valence shell to accommodate the lone pair, the presence of which distorts the O(h) geometry to C(3v). The energies of the O(h) and C(3v) geometries have been shown to be very similar so the observed geometries are a consequence of a very fine balance between ligand-ligand repulsions and the energy gained by the expansion of the two nonbonding electrons into the valence shell.     

Ligand close packing and the geometry of the fluorides of the nonmetals of periods 3, 4, and 5

This paper discusses the geometry of the fluorides of the nonmetals of periods 3, 4, and 5 in terms of the ligand close packing (LCP) model according to which molecular geometry is determined primarily by ligand-ligand repulsions (Pauli closed shell repulsions) rather than by the bonding and lone pair Pauli repulsions of the VSEPR model. The LCP model becomes the dominant factor in determing geometry when the ligands are sufficiently crowded that they may be regarded as essentially incompressible. Ligand close packing is a modification of the VSEPR model in which ligand-ligand repulsion (Pauli closed shell repulsion) is given more emphasis than bonding and nonbonding electron pair Pauli repulsion. The nonmetals of period 3 are large enough to form octahedral six coordinated molecules in which the ligands are close packed. The larger nonmetals of period 4 also have a maximum coordination number of six and an octahedral geometry although the ligands are not close packed. Ligand radii derived from the interligand distances in the molecules of period 3 depend only on the charge of the fluorine ligands and are consistent with the previously derived radii obtained from the fluorides of the close packed tetrahedral molecules of the period 2 elements. Although the ligands in the molecules of the period 4 nonmetals are not close packed, these elements are not large enough to form molecules with a higher coordination number. However, the larger period 5 nonmetals may have coordination numbers of seven and eight. The seven coordinated molecules have a pentagonal bipyramidal geometry in which the equatorial ligands are close packed. The eight coordinated molecules have a square antiprism geometry, which is not a close packed geometry although the fluorine interligand distances are only a little larger than expected for close packing. The difference between the axial and equatorial bond lengths in the trigonal bipyramidal pentafluorides and the pentagonal bipyramidal pentafluorides can be understood on the basis of ligand close packing. Ligand packing prevents the lone pair in AF(6)E molecules from fully entering the valence shell and thereby exerting its full stereochemical effect so that these molecules have a C(3)(v)() distorted octahedral geometry rather than a geometry based on pentagonal bipyramidal seven coordination.     

The Physical Basis of the VSEPR Model

The VSEPR model is a consequence of the correlation of same-spin electrons resulting from the operation of the Pauli exclusion principle. Although the VSEPR rules can be interpreted in terms of an orbital model they do not provide the physical basis for the model.     

Models of molecular geometry

Although the structure of almost any molecule can now be obtained by ab initio calculations chemists still look for simple answers to the question "What determines the geometry of a given molecule?" For this purpose they make use of various models such as the VSEPR model and qualitative quantum mechanical models such as those based on the valence bond theory. The present state of such models, and the support for them provided by recently developed methods for analyzing calculated electron densities, are reviewed and discussed in this tutorial review.     

Bonding analysis using localized relativistic orbitals: water, the ultrarelativistic case and the heavy homologues H2X (X = Te, Po, eka-Po)

We report the implementation of Pipek-Mezey [J. Chem. Phys. 90, 4916 (1989)] localization of molecular orbitals in the framework of a four-component relativistic molecular electronic structure theory. We have used an exponential parametrization of orbital rotations which allows the use of unconstrained optimization techniques. We demonstrate the strong basis set dependence of the Pipek-Mezey localization criterion and how it can be eliminated. We have employed localization in conjunction with projection analysis to study the bonding in the water molecule and its heavy homologues. We demonstrate that in localized orbitals the repulsion between hydrogens in the water molecule is dominated by electrostatic rather than exchange interactions and that freezing the oxygen 2s orbital blocks polarization of this orbital rather than hybridization. We also point out that the bond angle of the water molecule cannot be rationalized from the potential energy alone due to the force term of the molecular virial theorem that comes into play at nonequilibrium geometries and which turns out to be crucial in order to correctly reproduce the minimum of the total energy surface. In order to rapidly assess the possible relativistic effects we have carried out the geometry optimizations of the water molecule at various reduced speed of light with and without spin-orbit interaction. At intermediate speeds, the bond angle is reduced to around 90 degrees , as is known experimentally for H(2)S and heavier homologues, although our model of ultrarelativistic water by construction does not allow any contribution from d orbitals to bonding. At low speeds of light the water molecule becomes linear which is in apparent agreement with the valence shell electron pair repulsion (VSEPR) model since the oxygen 2s12 and 2p12 orbitals both become chemically inert. However, we show that linearity is brought about by the relativistic stabilization of the (n + 1)s orbital, the same mechanism that leads to an electron affinity for eka-radon. Actual calculations on the series H2X (X = Te, Po, eka-Po) show the spin-orbit effects for the heavier species that can be rationalized by the interplay between SO-induced bond lengthening and charge transfer. Finally, we demonstrate that although both the VSEPR and the more recent ligand close packing model are presented as orbital-free models, they are sensitive to orbital input. For the series H2X (X = O, S, Se, Te) the ligand radius of the hydrogen can be obtained from the covalent radius of the central atom by the simple relation r(lig)(H) = 0.67r(cov)(X) + 27 (in picometers).     

Electron and positron pair emission by low energy positron impact on surfaces

The emission of electron pairs from surfaces has the power to reveal details about the electron–electron interaction in condensed matter. This process, stimulated by a primary electron or photon beam, has been studied both in experiment and theory over the last two decades. An additional pathway, namely positron–electron pair emission, holds the promise to provide additional information. It is based on the notion that the Pauli exclusion principle does not need to be considered for this process.We have commissioned a laboratory based positron source and performed a systematic study on a variety of solid surfaces. In a symmetric emission geometry we can explore the fact that positron and electron are distinguishable particles. Following fundamental symmetry arguments we have to expect that the available energy is shared unequally among positron and electron. Experimentally we observe such a behavior for all materials studied. We find an universal feature for all materials in the sense that on average the positron carries a larger fraction of the available energy. This is qualitatively accounted for by a simplified scattering model. Numerical results, which we obtained by a microscopic theory of positron–electron emission from surfaces, reveal however that there are also cases in which the electron carries more energy. Whether the positron or the electron is more energetic depends on details of the bound electron state and of the emission geometry. The coincidence intensity is strongly material dependent and there exists an almost monotonic relation between the singles and coincidence intensity. These results resemble the findings obtained in electron and photon stimulated electron pair emission. An additional reaction channel is the emission of an electron pair upon positron impact. We will discuss the energy distributions and the material dependence of the coincidence signal which shows similar features as those for positron–electron pairs.     

Synthesis of the missing oxide of xenon, XeO2, and its implications for Earth's missing xenon

The missing Xe(IV) oxide, XeO(2), has been synthesized at 0 °C by hydrolysis of XeF(4) in water and 2.00 M H(2)SO(4(aq)). Raman spectroscopy and (16/18)O isotopic enrichment studies indicate that XeO(2) possesses an extended structure in which Xe(IV) is oxygen bridged to four neighboring oxygen atoms to give a local square-planar XeO(4) geometry based on an AX(4)E(2) valence shell electron pair repulsion (VSEPR) arrangement. The vibrational spectra of Xe(16)O(2) and Xe(18)O(2) amend prior vibrational assignments of xenon doped SiO(2) and are in accordance with prior speculation that xenon depletion from the Earth's atmosphere may occur by xenon insertion at high temperatures and high pressures into SiO(2) in the Earth's crust.     

The Nature of Chemical Bonds from PNOF5 Calculations

Natural orbital functional theory (NOFT) is used for the first time in the analysis of different types of chemical bonds. Concretely, the Piris natural orbital functional PNOF5 is used. It provides a localization scheme that yields an orbital picture which agrees very well with the empirical valence shell electron pair repulsion theory (VSEPR) and Bent’s rule, as well as with other theoretical pictures provided by valence bond (VB) or linear combination of atomic orbitals–molecular orbital (LCAO‐MO) methods. In this context, PNOF5 provides a novel tool for chemical bond analysis. In this work, PNOF5 is applied to selected molecules that have ionic, polar covalent, covalent, multiple (σ and π), 3c–2e, and 3c–4e bonds.     

Electron‐pair density decomposition for core–valence separable systems

The electron pair density of a core‐valence separable system can be decomposed into three parts: core‐core, core‐valence, and valence‐valence. The core‐core part has a Hartree‐Fock like structure. The core‐valence part can be written as Γ_cv (1,2) = γ_c (1,1)γ_v (2,2) ? γ_c (1,2)γ_v (2,1) + γ_c (2,2)γ_v (1,1) ? γ_c (2,1)γ_v (1,2), where only the 1‐matrices from the core and valence orbitals contribute. The valence‐valence part is left to be determined from the reduced frozen‐core type wave function, which often contains the essential information on the electron correlation and the chemical bond. We demonstrate the analysis to the ground state of negative ion Li^? and 2¹Σ_u⁺ excited state of the Li₂ molecule. © 2012 Wiley Periodicals, Inc.     

Core distortions in metal atoms and the use of effective core potentials

The recent experimental determination of the geometry of Ti(CH₃)₂Cl₂ shows it to be inconsistent with the VSEPR model, a result not uncommon for molecules containing transition metal atoms. The valence shell charge concentrations (CCs) that appear as maxima in L(r)=−²ρ(r), provide a physical basis for the VSEPR model of molecular geometry for main group molecules. The same model accounts for the geometry of transition metal molecules with the proviso that the CCs are formed within the outer shell of the core of the metal atom, as defined by the shell structure of L(r). This observation appears to be in conflict with calculations for Ti(CH₃)₂Cl₂ showing that its geometry can be predicted using an effective core potential for the metal atom, a procedure that would appear to preclude the presence of core distortions. The apparent contradiction is resolved by distinguishing between the definition of the core using L(r) and one based on the orbital model.     

Analyzing the electric response of molecular conductors using “electron deformation” orbitals and occupied‐virtual electron transfer

The concept of “electron deformation orbitals” (EDOs) is used to investigate the electric response of conducting metals and oligophenyl chains. These orbitals and their eigenvalues are obtained by diagonalization of the deformation density matrix (difference between the density matrices of the perturbed and unperturbed systems) and can be constructed as linear combinations of the unperturbed molecular orbitals within “frozen geometry” conditions. This form of the EDOs allows calculating the part of the electron deformation density associated to an effective electron transfer from occupied to virtual orbitals (valence to conduction band electron transfer in the band model of conductivity). It is found that the “electron deformation” orbitals pair off, displaying the same eigenvalue but opposite sign. Each pair represents an amount of accumulation/depletion of electron charge at different molecular regions. In the oligophenyl systems investigated only one pair contributes effectively to the charge flow between molecular ends, resulting from the promotion of electrons from occupied orbitals to close in energy virtual orbitals of appropriate symmetry and overlapping. Analysis of this pair along explains the differences in conductance of olygophenyl chains based on phenyl units. © 2014 Wiley Periodicals, Inc.     

次级键与晶体中锑(III)螯合物配位多面体研究

考虑立体活性孤对电子附近次级键配位原子的贡献, 对文献报道的三十个氨基多羧酸锑(III)螯合物的晶体结构中配位多面体描述进行了全面的修正. 配位多面体的几何构型指定采用了单位球内截多面体的两面角判据及其相关的ANVPDA程序. 所有配位多面体几何构型的修正均得到了键价计算的有力支持.     

次级键与晶体中锑(III)螯合物配位多面体研究

考虑立体活性孤对电子附近次级键配位原子的贡献,对文献报道的三十个氨基多羧酸锑(III)螯合物的晶体结构中配位多面体描述进行了全面的修正.配位多面体的几何构型指定采用了单位球内截多面体的两面角判据及其相关的ANVPDA程序.所有配位多面体几何构型的修正均得到了键价计算的有力支持.     

XeOF2, F2OXeN identical with CCH3, and XeOF2.nHF: rare examples of Xe(IV) oxide fluorides

The syntheses of XeOF2, F2OXeNCCH3, and XeOF2.nHF and their structural characterizations are described in this study. All three compounds are explosive at temperatures approaching 0 degrees C. Although XeOF2 had been previously reported, it had not been isolated as a pure compound. Xenon oxide difluoride has now been characterized in CH3CN solution by 19F, 17O, and 129Xe NMR spectroscopy. The solid-state Raman spectra of XeOF2, F2OXeNCCH3, and XeOF2.nHF have been assigned with the aid of 16O/18O and 1H/2H enrichment studies and electronic structure calculations. In the solid state, the structure of XeOF2 is a weakly associated, planar monomer, ruling out previous speculation that it may possess a polymeric chain structure. The geometry of XeOF2 is consistent with a trigonal bipyramidal, AX2YE2, VSEPR arrangement that gives rise to a T-shaped geometry in which the two free valence electron lone pairs and Xe-O bond domain occupy the trigonal plane and the Xe-F bond domains are trans to one another and perpendicular to the trigonal plane. Quantum mechanical calculations and the Raman spectra of XeOF2.nHF indicate that the structure likely contains a single HF molecule that is H-bonded to oxygen and also weakly F-coordinated to xenon. The low-temperature (-173 degrees C) X-ray crystal structure of F2OXeNCCH3 reveals a long Xe-N bond trans to the Xe-O bond and a geometrical arrangement about xenon in which the atoms directly bonded to xenon are coplanar and CH3CN acts as a fourth ligand in the equatorial plane. The two fluorine atoms are displaced away from the oxygen atom toward the Xe-N bond. The structure contains two sets of crystallographically distinct F2OXeNCCH3 molecules in which the bent Xe-N-C moiety lies either in or out of the XeOF2 plane. The geometry about xenon is consistent with an AX2YZE2 VSEPR arrangement of bond pairs and electron lone pairs and represents a rare example of a Xe(IV)-N bond.     

高中化学新教材中VSEPR模型的b值规定之刍议

新教材关于VSEPR模型中b值的计算,暂未考虑"与中心原子结合的原子"所处的位置环境,即只做了静态规定,是符合新课标要求的;但若拓展运用在CH3COOH这样常见的分子上,会出现与常识不相符的情况,使得VSEPR模型的适用范围受限.从拓展高中化学的教与学的角度出发,笔者认为,将"与中心原子结合的原子"所处的位置环境考虑在...