AIM Bond Concepts. U A bond is defined along the bond line between two nuclei, called a bond path, along which electron density is concentrated.

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Duane Riley
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1 AIM Bond Concepts U A bond is defined along the bond line between two nuclei, called a bond path, along which electron density is concentrated. U The bond critical point, ρ b, is a point along the bond path at the interatomic surface, where the shared electron density reaches a minimum. U The value of ρ b is an approximate measure of the amount of electron density built up in the bonding region and as such may be taken as characteristic of the bond. Predominantly covalent bonds have high values of ρ b. Predominantly ionic bonds have low values of ρ b. The hypothetical pure ionic bond would have ρ b = 0.

2 Bond Character, Critical Point Density, and Charge U The concepts of covalent vs. ionic are poorly defined and not quantitatively related to AIM concepts. U Qualitatively, the amount of shared electron density, approximately measured by ρ b, represents a covalent contribution to bonding, and atomic charges represent an ionic contribution to bonding. U Bonds may be predominantly covalent (high value of ρ b ) and still have significant polarity (classical notion of ionic character ). L Bonds between atoms with large charges and small value of ρ b are describes as predominantly ionic. L Bonds between atoms with very small charges and a large value of ρ b are described as predominantly covalent. L Polar bonds fall between these extremes and may have both significant values of ρ b and significant charges.

3 Bond Strengths and Lengths U Bond strength increases with increased bond critical point density increased charge on the bonded atoms U Bond length decreases with increased bond critical point density increased charge on the bonded atoms decreased coordination number about A for the same A X pair U The bonding radius, r b, is a measure of the size of an atom, defined as the distance from the nucleus to the bond critical point. U Bond length is the sum of the bonding radii of the two bonded atoms. U Bond radii are not constant nor transferrable (unlike covalent radii), because they depend upon the molecule in which the atom is situated. 1 U Bonding radius increases with increasing negative charge decreases with increasing positive charge 1 This point is misstated in the opposite on p. 184 of Gillespie & Popelier.

4 Fluorides of Li, Be, B, C Contour Maps with BCP Gradients

5 Period 2 Fluorides Molecular and Atomic Data

6 Period 2 Fluorides - Bonding Trends U Atomic charges Always less than ideal ionic charge. Charge on A rises rapidly, then falls after CF 4. Negative charge on F declines steadily. U Electron density Nearly spherical around A in LiF and BeF 2, consistent with ionic character. Considerable transfer of electron density from A to F (cf. B contour for atom and in BF 3 ). From LiF to CF 4, more electron density transferred toward BCP, causing ρ b to rise. U Bond lengths and radii Size of A declines rapidly with charge increase, then rises as charge declines with increasing electronegativity. Size of F declines with continuous decline in negative charge. Bond length decreases from LiF through BF 3 as both radii decrease, then increase to an almost constant value for NF 3, OF 2, and F 2 as increase in r b (A) roughly balances decrease in r b (F). U Bond critical point density Values rise rapidly from LiF to CF 4, then remain roughly constant at 0.3 au, consistent with increasing covalent character High charges on F in BeF 2, BF 3, and CF 4 indicate highly polar bonds. As bond length increases with coordination number, ρ b values decline (cf. BeF 2, BeF 3, BeF 4 2 ; BF 3, BF 4 ; CF 3+, CF 4 ).

7 Strength of B F and C F Bonds U Among fluorides, the strongest bonds are B F (613 kj/mol) and C F (485 kj/mol), and the B F bond is the strongest of all single bonds. Bond Mean Bond Energy (kj/mol) ρ b (au) q(f) Bond length (pm), calc d Li F? Be F? B F C F N F O F F F U Except for LiF and BeF 2 (predominantly ionic), all period 2 A F bonds have relatively high values of ρ b, but only the B F and C F covalent bonds have high polarity. U The short length and high strength of the B F bond can be understood from its high ρ b and polarity, without invoking backbonding arguments.

8 Chlorides of Li, Be, B, C Contour Maps with BCP Gradients

9 Period 2 Chlorides Molecular and Atomic Data

10 Period 2 Chlorides - Bonding Trends U Atomic charges Negative charge on Cl declines from LiCl to almost zero at CCl 4, consistent with small electronegativity difference between C and Cl ( χ = χ Cl χ C = = 0.3). Charge on Cl becomes increasingly positive from NCl 3 through FCl as electronegativity and negative charge on A rises. Charge on A rises sharply from LiCl to BCl 3, then drops sharply at CCl 4, becoming increasingly negative from NCl 3 through FCl. Bond in CCl 4 is predominantly covalent with low polarity. U Electron density Nearly spherical density distributions in LiCl are consistent with ionic bonding. Increase in covalent bonding through the series is reflected in increasingly non-spherical density distributions from BeCl 2 through CCl 4 U Bond lengths and radii Bonding radius of Cl decreases with decreasing negative charge and increasing positive charge through the series. Bonding radius of A decreases with increasing positive charge from LiCl through BCl 3, rises abruptly with C s low positive charge (+0.35), then continues to rise slowly as negative charge increases on A through the rest of the series. As a result of trends in r Cl and r A, bond length declines from LiCl through BCl 3, increases slightly at CCl 4, then declines slowly through the rest of the series. U Bond critical point density BCP decreases from LiCl to CCl 4 and remains essentially constant for the rest of the series. BCP values are lower for chlorides than fluorides.

11 Laplacian Contours of LiCl, BeCl 2, BCl 3, CCl 4 U Laplacian contours show transition from predominantly ionic bonding in LiCl to increasingly covalent bonding in CCl 4. U Contours are nearly spherical for both Li and Cl. U Bonding charge concentrations (CCs) along the bond line are evident at BeCl 2. U Nonbonding CCs on chlorines in BCl 3 and CCl 4 are tori of electron density perpendicular to bond lines.

12 Comparing Period 2 Fluorides and Chlorides U The larger size of Cl results in longer bonds. U Longer bonds have lower critical point densities and are therefore weaker. Bond Mean Bond Energy (kj/mol) ρ b (au) q(x) Bond length (pm), calc d B F B Cl C F C Cl N F N Cl O F O Cl F F F Cl U Higher charge (polar bonds) compensates for lower ρ b in the cases of OCl 2 and FCl, making their bonds stronger than OF 2 and F 2. U Lower strength of BCl 3 bonds compared to BF 3 make a lower barrier to forming four coordination in Lewis acid-base reactions, making BCl 3 a stronger Lewis acid. BX 3 + NH 3 6 X 3 B:NH 3 X = F, Cl

13 Hydrides of Li, Be, B, C Contour Maps with BCP Gradients

14 Period 2 Hydrides Molecular and Atomic Data

15 Period 2 Hydrides Bonding Trends U Atomic charges Charges are high in LiH, BeH 2, and BH 3, indicating very polar bonds. C H bond has very little polarity. H is slightly negative ( 0.04) despite hydrogen s slightly lower electronegativity, suggesting χ H > χ C in CH 4 ; i.e., hydrogen s electronegativity is probably variable. Charge on H is increasingly positive from NH 3 to HF. U Electron density and bond critical density Spherical density distribution and ρ b = for LiH suggests predominantly ionic bonding. Less spherical density distributions and rising ρ b values indicate increasing covalent bonding through the rest of the series, reaching a roughly constant maximum value of ρ b for NH 3 to HF. U Bonding radii and bond lengths Hydrogen bonding radius decreases dramatically across the series (88.0 pm in LiH to 15.5 pm in HF) due to lack of core electrons. Large and continuous change in r H is principal cause of declining bond lengths across the series. Change in bonding radius parallels change in ligand radius, and suggests that hydrogen s van der Waals radius must change similarly.

Ligand Close-Packing Model

Ligand Close-Packing Model! VSEPR is an electronic model for explaining molecular geometry.! The Ligand Close-Packing (LCP) model is a steric model. L The geometry of an AX n molecule is that which allows