Ligand close packing, molecular compactness, the methyl tilt, molecular conformations, and a new model for the anomeric effect.

All the atoms in a molecule attract each other until they reach their equilibrium positions at which point the repulsive forces between the atoms just balance the attractive forces and there are no resultant forces acting on any of the atoms in the molecule. Thus, we can consider that in the equilibrium geometry the atoms in a molecule are arranged as compactly as possible. This is the basis of the ligand close packing (LCP) model according to which three or four monatomic ligands X, such as F, Cl or O (formally =O or O(-)) pack as closely as possible around a small central atom such as a boron or carbon atom giving a truly close-packed equilateral triangular AX(3) molecule or a tetrahedral AX(4) molecules. Such monatomic ligands can, to a good approximation, be described as having a spherical shape with a single ligand radius r(X). In contrast, ligands with donor atoms with lone pairs such as the oxygen atom in an OX group have a less symmetrical electron density requiring two ligand radii, r(O(lp)) in the lone pair direction, and r(O(b)) in the bonding direction, where r(O(lp)) < r(O(b)) for an approximate description. On this basis we propose an explanation for the "methyl tilt", in methanol and many related molecules, and in conjunction with the concept of compactness, a model for explaining the relative energies of the conformations of molecules containing OH and OMe ligands, including molecules that exhibit the anomeric effect. We compare our model for the anomeric effect with the widely accepted "hyperconjugation" model. We also discuss the relationship between the concept of compactness and the concept of hardness.

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.

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.

An electron localization function study of the geometry of d(0) molecules of the period 4 metals Ca to Mn.

We have studied the geometry of the formally d(0) MX(n)() (X = F, H, CH(3) and O; n = 2-6) molecules of the period 4 metals from Ca to Mn by studying the topology of the electron localization function (ELF) in order to try to understand why many of these molecules have non-VSEPR geometries. The quantitative analysis of the core basin population shows that it is always larger than its conventional value (18) because, in the LCAO-MO scheme, the 3d basis functions centered on the metal noticeably contribute to the electron density within the core region associated with the M shell. Therefore, the density available to form the bonds is less than Z(M) - 18, the value adopted in electron counts. Under the influence of the ligands, these electrons cause the core to lose its spherical symmetry by the formation of opposite-spin pair localization basins, which in turn influence the geometry of the ligands if the interaction of the ligands with the core is sufficiently strong. All of the ligands considered in this study, except F, interact with the core sufficiently strongly to give non-VSEPR geometries, which we have rationalized on the basis of the ELF topology.

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.

Ligand Close-Packing and the Lewis Acidity of BF(3) and BCl(3).

The unexpected greater Lewis acidity of BCl(3) than BF(3) with respect to strong bases such as NH(3) has been the subject of much discussion. A number of explanations have been proposed, among which the most popular and most widely quoted is that stronger back-donation from fluorine than from chlorine decreases the availability of the otherwise empty 2p orbital on boron from accepting an electron pair from a base. In contrast, toward weak bases such as CO, BF(3) is a stronger Lewis acid than BCl(3). We have reinvestigated the relative acid strengths of BF(3) and BCl(3) toward Lewis bases by calculating geometries and atomic charges for the following adducts: BF(3).NH(3), BF(3).N(CH(3))(3), BF(3).OH(2), BF(3).O(CH(3))(2), BCl(3).NH(3), BCl(3).N(CH(3))(3), BCl(3).OH(2), and BCl(3).O(CH(3))(2). Our results show that the halogen ligands remain close-packed throughout the formation of an adduct and that the bond lengths increase accordingly. It takes more energy to lengthen the short strong BF bonds than the longer weaker BCl bonds and it is for this reason that BCl(3) is a stronger Lewis acid than BF(3) toward a strong base such as NH(3). In contrast, in the formation of a complex with a weak base such as CO, the BX(3) is barely distorted from planarity and so the acidity of BF(3) is greater than that of BCl(3) because the charge on boron is greater in BF(3) than BCl(3).

Bond Lengths and Bond Angles in Oxo, Hydroxo, and Alkoxo Molecules of Be, B, and C: A Close-Packed Nearly Ionic Model.

We have surveyed the experimental data for oxo, hydroxo, and alkoxo molecules of Be, B, and C and have shown that the intramolecular interligand distances for a given central atom are remarkably constant and independent of coordination number and of the presence of other ligands. Atomic charges obtained from the analysis of the calculated electron densities for a large selection of molecules of this type have shown that these molecules are predominately ionic. On the basis of these results we suggest that the bond lengths and geometries of these molecules can be best understood in terms of a model in which anion-like ligands are close-packed around a cation-like central atom. Values of the interligand radius of each ligand obtained from the intramolecular interligand contact distances are smaller than the crystal ionic radii and decrease as expected with decreasing ligand charge. This model provides a simple quantitative explanation of the decrease in the bond lengths in these molecules with decrease in the coordination number from four to three and of the changes in bond length caused by the presence of other ligands with different ligand radii. With decreasing bond length the electron density at the bond critical point increases correspondingly for Be-O, B-O, and C-O bonds. The nontetrahedral angles found in all A(OX)(4) molecule are explained on the basis of a noncylindrically symmetrical charge distribution around oxygen.

Bonding and Geometry of OCF(3)(-), ONF(3), and Related Molecules in Terms of the Ligand Close Packing Model.

The nature of the bonding in OCF(3)(-) and the isoelectronic molecule ONF(3) has been the subject of much discussion for many years, because these species appear to have unusual bond lengths and angles. We have reinvestigated the nature of the bonding in these and some related molecules by analyzing their calculated electron density distributions. The results show that the bonding in the series OBF(3)(2)(-), OCF(3)(-), ONF(3) ranges from predominately ionic in OBF(3)(2)(-) to predominately covalent in ONF(3) and that the interligand distances are consistent with the close packing of the ligands around the central atom. The AO bonds (A = B, C, N) are double bonds ranging in nature from a very ionic B=O bond to a predominately covalent N=O double bond, but all three are strong and short so that, in accordance with the ligand close packing (LCP) model, the AF bonds are correspondingly long. Also consistent with this model the bonds in a three-coordinated AOF(2) molecule are shorter than those in the corresponding AOF(3) molecule. Protonation of the doubly bonded oxygen, which converts the A=O bond to a single A-OH bond in each case, considerably lengthens the A-O bond, and the bond angles accordingly adopt values much closer to the tetrahedral angle. The difficulties of trying to describe the bonding in these molecules in terms of Lewis structures are discussed.

Reinterpretation of the Lengths of Bonds to Fluorine in Terms of an Almost Ionic Model.

We have calculated the electron density distributions, electron densities at the bond critical point, and atomic charges in the period 2 and 3 fluorides and a number of their cations and anions. On the basis of this information and an analysis of X-F bond lengths, we have examined the factors that determine the lengths of these bonds. We have shown that all the molecules except NF(3), OF(2), and F(2) have considerable ionic character. The bond lengths of the fluorides reach a minimum value at BF(3) in period 2 and at SiF(4) in period 3 when the product of the charges on the central atom and a fluorine reaches a maximum, consistent with a predominately ionic model for these fluorides. The length of a given A-F bond decreases with decreasing coordination number, and we show that it is determined primarily by packing considerations. This provides an alternative to the previously proposed back-bonding model explanation, for which our work provides no convincing evidence. There is also no evidence to support the Schomaker-Stevenson equation which has been widely used to correct A-F bond lengths calculated from the sum of the covalent radii of A and F for the difference in the electronegativities of A and F. We propose a new value for the covalent radius of fluorine and point out the limitations of its use.

Study of Bond Angles and Bond Lengths in Disiloxane and Related Molecules in Terms of the Topology of the Electron Density and Its Laplacian.

We have calculated the electron density distributions for the series of molecules H(n)XOXH(n), X = Li to F and Na to Cl, and some related molecules. We have analyzed these distributions and their Laplacian to obtain atomic charges, electron densities at the bond critical point, and the charge concentrations revealed by the Laplacian. On the basis of this information and an analysis of the X-O bond lengths and angles, we have examined the factors that determine the lengths of the X-O bonds and the XOX bond angles. The XO bond length reaches a minimum value at boron in period 2 and at silicon in period 3 when the product of the charges on X and O reaches a maximum value, consistent with a predominately ionic model for the molecules X = Li, Be, B, Na, Mg, Al, and Si. In the remaining molecules of both series, the XO bonds have an increasing covalent character. The bond length and the bond angle in disiloxane are consistent with the ionic character of the molecule, and there is no evidence for the frequently quoted back-bonding model. In disiloxane and related molecules in which the ligand is considerably less electronegative than oxygen the electrons in the valence shell of oxygen are not well localized into pairs, so the bond angle is intermediate between the tetrahedral angle expected when the valence shell electrons of oxygen are strongly localized into four tetrahedral pairs and the 180 degrees bond angle expected on the basis of the electrostatic and/or steric repulsion between the positively charged X atoms. The effects on the bond lengths and angles of substituting oxygen by sulfur and hydrogen by fluorine are discussed.

Geometry of the Fluorides, Oxofluorides, Hydrides, and Methanides of Vanadium(V), Chromium(VI), and Molybdenum(VI): Understanding the Geometry of Non-VSEPR Molecules in Terms of Core Distortion.

This paper describes a study of the topology of the electron density and its Laplacian for the molecules VF(5), VMe(5), VH(5), CrF(6), CrMe(6), CrOF(4), MoOF(4), CrO(2)F(2,) CrO(2)F(4)(2)(-) and CrOF(5)(-) all of which, except VF(5,) CrF(6), and CrOF(5)(-) have a non-VSEPR geometry. It is shown that in each case the interaction of the ligands with the metal atom core causes it to distort to a nonspherical shape. In particular, the Laplacian of the electron density reveals the formation of local concentrations of electron density in the outer shell of the core, which have a definite geometrical arrangement such as four in a tetrahedral arrangement or five in a square pyramidal or trigonal bipyramidal and six in an octahedral arrangement. Ligands that are predominately covalently bonded are found opposite regions of charge depletion between these core charge concentrations. In VH(5), VMe(5), CrOF(4), and MoOF(4), these core charge concentrations have a square pyramidal arrangement, and the regions of charge depletions have the corresponding inverse square pyramidal arrangement so that these molecules have a square pyramidal geometry rather than a trigonal prism geometry. In CrMe(6), there are five core charge concentrations with a trigonal bipyramidal arrangement so that the regions of charge depletion have a trigonal prismatic arrangement and the molecule has the corresponding trigonal prism geometry rather than an octahedral geometry. In contrast, molecules in which the only ligand is the more ionically bound fluorine are less affected by core distortion and have VSEPR-predicted structures. The unexpected bond angles in CrO(2)F(2) and the preference of CrO(2)F(4)(2)(-) for a cis structure are also discussed in terms of the pattern of core charge concentrations.