A Hybrid Valence Bond/Molecular Orbital Model of Bonding
The idea of valence bond theory (VBT), as originally put forth by Heitler and London (Z. Phys., 44, 455(1927)) and expanded by Pauling (J. Am. Chem. Soc., 53, 1367 (1931)), was that the binding energy between two atoms arises primarily from exchange (resonance, sharing) of electrons between the two atoms in a bond. The results of calculations on the hydrogen molecule showed that an energy minimum occurs at a certain internuclear distance if the electrons are free to associate with either nucleus. Electron density accumulates between the two nuclei.
Fig. Contour maps of (a) total electron density and (b) density difference relative to the spherical atoms for the H2 molecule.
(F. A. Carey and R. J. Sundberg, “Advanced Organic Chemistry, part A”, p.4, Fig1.1)
* Figure (b) shows that there is electron density depletion relative to spherical atoms outside of the hydrogen nuclei.
The area of space occupied by electrons is referred to as an orbital. The staring point of VBT is to assign electrons to individual orbitals on atoms. Bonding is, in effect, viewed as a perturbation of this arrangement; when two atoms are brought together, each electron interacts with either nucleus, and bonds consist of two electrons in the region between two atoms. The resulting electron pair is considered to be mostly localized between the two adjacent atoms. Localization of the electrons between two atoms would require the orbitals (occupied by the bonding electrons) point in the appropriate direction in space.
§6.1 Orbital overlap and hybridization
Orbital overlap
Pauling assumed that bonds arise from the overlap of atomic orbitals on adjacent atoms, and that the better the overlap the stronger the bond. In a qualitative sense, orbital overlap can be thought of as the extent to which the orbitals occupy the same space.
However, if there are regions of overlap with matched and mismatched phasing, the contributions to the overlap have opposite signs and will cancel. The more space occupied where the phasing reinforces, the larger the overlap. When the opposite phasing in the various areas completely cancels, there is no overlap.
Hybridization
It was known that CH3+ prefers bond angles of 120o, and methane prefers bond angles of 109.5o. To understand how s and p atomic orbitals can accommodate these experimentally determined bond angles, Pauling argued that orbitals with directionality would give stronger bonds because the overlap would be higher. Pauling suggested that to achieve orbitals with directionality, mixtures of atomic orbitals on the same atom are formed in a process known as hybridization.
/ ± / / à /2 sp hybrid orbitals
/ ± / / ± / / à /
3 sp2 hybrid orbitals
The geometries for acetylene, methyl cation and methane correspond to the bond angles for the different hybridization states sp, sp2, and sp3, respectively.
The prototypical hydrocarbon examples of sp2 and sp hybridization are ethene and ethyne, respectively. For ethene, the electron density is somewhat elliptical because the π component is not cylindrically symmetrical. For ethyne, the combination of two π bonds restores cylindrical symmetry.
Fig. (a) Contour map of electron density in the plane of ethane molecule. (b) Contour map of electron density perpendicular to the plane of ethane molecule at the midpoint of C=C bond.
(F. A. Carey and R. J. Sundberg, “Advanced Organic Chemistry, part A”, p.6, Fig1.2)
The idea that π bonds are formed by the overlap of p orbitals puts some geometrical constraints on molecular structure. Ethene, for example, is planar to maximize p-orbital overlap. Allene, on the other hand, must have the terminal CH2 groups rotated by 90o to accommodate two π bonds at the central sp carbon.
Hybridization index, spi
1 + i cosθ = 0; θ is the observed bond angle.
Hybridization provides an alternative “explanation” to VSEPR for the deviations from ideal angles－180o, 120o, 109.5o displayed in most organic molecules. In going from pure sp to sp2, sp3, and pure p, the angles go from 180o to 120o, 109.5o, and 90o. Thus, decreasing s character leads to decreasing bond angles. We could say that in ammonia the N-H bonds have lost s character from N relative to a pure sp3 N, because the angle is smaller than the perfect tetrahedral angle.
In ammonia, the N hybrids that bond to H are sp3.4, and in water the bonds to H are formed by sp4 hybrids (i.e., the orbitals that make up the O-H bond are 80% p in character and 20% s, versus the 75:25 mixture implied by sp3). The lone pairs must take on extra s character in NH3 and H2O.
* The magnitude of 13C-1H NMR coupling constants is expected to be proportional to the amount of carbon s character in the bond, because only s orbitals have density at the carbon nucleus and can affect neighboring nuclear spin states. For example,
In cyclic alkanes, the smaller the ring, the larger the p character in the hybrid orbitals used to form the C-C bonds. Correspondingly, the C-H bonds would have higher s character.
Ring system / JC-HCyclopropane / 161
Cyclobutane / 134
Cyclopentane / 128
Cyclohexane / 124
Cycloheptane / 123
Cyclooctane / 122
(L. N. Ferguson (1973) “Highlights of Alicyclic Chemistry”, part1.)
Creating localized σ and π bonds: σ bonds are defined as having their electron density along the bond axis, while π bonds have their electron density above and below the bond axis.
The combination of two orbitals on adjacent atoms that creates in-phase interactions between the two atoms is called the bonding orbitals; the combination that results in out-of-phase interactions is called the antibonding orbitals. A nodal plane exists in the antibonding orbital between the two atoms making the bond, which means that populating this orbital with electrons leads to a repulsive interaction between the atoms. (The mixing, or linear combination, of atomic orbitals to create bonding and antibonding orbitals is actually a molecular orbital theory notion.)
Empty σ* and π* orbitals are of importance in terms of reactivity, particularly with electron-donating nucleophilic reagents, since it is the empty antibonding orbitals that interact most strongly with approaching nucleophiles.
There are also nonbonding orbitals that contain lone pairs of electrons. In standard neutral organic compounds, only the bonding and nonbonding orbitals are occupied with electrons.
It is important to remember that hybridization is a description of the observed molecular geometry and electron density. Hybridization does not cause a molecule to have a particular shape. Rather, the molecule adopts a particular shape because it maximizes bonding interactions and minimizes electron-electron and other repulsive interactions.It is worth noting that a particular hybridization scheme does not provide a unique description of molecular structure. The same conclusions about geometry and electron density are reached if ethene and ethyne are described in terms of sp3 hybridization. In this approach, the double bond in ethene is thought of as arising from two overlapping sp3 orbitals. These two bonds equivalent and are called bent bonds. This bonding arrangement also predicts a planar geometry and elliptical electron distribution; in fact, this description is mathematically equivalent to the sp2 hybridization description. Similarly, ethyne can be thought of as arising by sharing of three sp3 hybrid orbitals.
The fundamental point is that there is a single real molecular structure defined by atomic positions and electron density. Orbitals partition the electron density in specific ways, and it is the sum of the orbital contributions that describes the structure.
Ethene Ethyne
§6.2 Polar covalent bonding
Once the geometry of a molecular has been established, the next crucial feature for predicting the reactivity is its charge distribution. Electronegativity is the primary determinant of the charge distribution in a molecule, with hybridization playing a secondary but still important role.
Whenever two different atoms form a bond, the sharing of electrons is unequal; a covalent bond that has an unequal sharing of the bonding pair of electrons is called polar covalent, and there is a positive end and a negative end to the bind.
Electronegativity
The electronegativity of a atom means the power of the atom in a molecule to attract electrons to itself. Pauling assigned values to various atom type by examining bond dissociation energies of molecules. As such, the Pauling electronegativity scale depends upon molecular properties. Mulliken defined an electronegativity scale that is derived from the average of the ionization potential and electron affinity of an atom, and therefore is solely an atomic property. Using the Pauling scale, a bond whose electronegativity difference is 1.7 is considered to be 50% ionic and 50% covalent.
The major factor influencing electronegativity is the energy of the orbitals that the atom uses to accept electrons.
* When rationalizing reactivity trends, electronegativity is not the whole story, but polarizability is also important. For example, the electronegativity difference between C and I in both scales is smaller than the difference between C and H; so a C-I bond is predicted to have a smaller charge polarization than a C-H bond. However, iodide is a good leaving group in SN2 reactions.
Electrostatic potential surfaces
Plots of electrostatic potential surfaces are useful to view the charge distribution in complex organic molecules. The surface is more typically an isodensity surface, meaning a surface with a constant electron density, such as 0.002 electron/A2. This is a very low level of electron density and such points are typically found near the outermost fringe of the molecule's electron cloud. Therefore, this surface approximately defines the size and shape of the molecule.
Imagine taking a small sphere with a charge of +1 and rolling it around the isodensity surface. At each point, we ask whether the sphere is attracted to or repulsed by the surface and what the energetic magnitude of the interaction is. The magnitude of the interaction is the electrostatic potential. In these plots, red represents negative electrostatic potential whereas blue represents positive electrostatic potential; a green color is a region that is essentially neutral.
* The electrostatic potential surfaces are usually plots for the ground states of the molecules. When a chemical reaction occurs, we expect a substantial reorganization of charge; it is risky to use the electrostatic potential surfaces of the ground states to predict or rationalize reactivity.
Inductive effects
The phenomenon of withdrawing electrons through σ bonds to the more electronegative atom or group is called an inductive effect. The inductive effect is what gives rise to bond polarizations, polarizations within molecules, and bond and molecular dipole moments. A similar but separate phenomenon is a field effect, which is a polarization in a molecule that results from charges interacting through space, and it can influence the structure and reactivity of other parts of the molecule.
例. 1-fluorobutane, an example for the danger of directly extrapolating ground state electronic structural features to reactivity patterns.
/ Bond polarization along a σ chain generally diminish as we move out from a strongly polarizing substituent－a very electronegative element, F.Advanced quantum chemical calculations reveal that C1 is δ+ with a charge of +0.36, C2 with -0.17, C3 with +0.09 and C4, -0.24. The result that the magnitude of the charge on C4 goes up is found even in computational studies of longer alkyl halides.
Inductive effects are often cited to explain trends in thermodynamics or reactivity of organic molecules. Experimental observations of inductive effects on thermodynamics and kinetics do not usually show an alternating pattern; for example, for a linear alkanoic acid (R-COOH), adding a strongly electronegative element like F to the alkyl chain always increases the acidity of the carboxylic acid functional group, and the effect is always stronger the closed the F is to the incipient carboxylate.
Group electronegativities
It is often convenient to consider groups that make up particular portions of a molecule as having their own electronegativity. The following table lists some group electronegativity values that were derived to be comparable to the Pauling scale for atoms:
Group / Electronegativity-CH3 / 2.3 / ~C
-CH2Cl / 2.8
-CHCl2 / 3
-CCl3 / 3
-CF3 / 3.4 / ~O
-Ph / 3
-CH＝CH2 / 3 / ~N
-C≡CH / 3.3
-C≡N / 3.3
-NH2 / 3.4
-NH3+ / 3.8
-NO2 / 3.4
-OH / 3.7
*A full positive charge, such as that associated with a protonated amine, has the highest group electronegativity.
(P. R. Wells (1968) Prog. Phys. Org. Chem. 6, 111.)
Hybridization effects
It is often said that s orbitals have better electron penetration to the nucleus than p orbitals, suggesting that it is harder to withdraw electrons from s orbitals. The cause of the discrepancy between the Pauling scale, which describes C as more electronegative than H, and the Mulliken scale, which gives the opposite ordering, is a hybridization effect. Because s orbitals have substantial density at the nucleus while p orbitals have a node at the nucleus, the more s character in a hybrid orbital, the closer to the nucleus the electrons in that hybrid tend to be. Since electronegativity describes an atom’s ability to attract electrons to itself, sp2 hybrids should be more electronegative than sp3 hybrids. In the above table, the electronegativities are
-C≡CH > -CH＝CH2 > -CH3, in consistent with sp > sp2 > sp3.
A good deal of evidence points to the conclusion that an sp2 C is more electronegative than H, while an sp3 C and H have very similar electronegativities.
§6.3 Bond dipoles, bond lengths and atomic radii
Bond dipoles
The trends and relative electron donating and accepting (or in other words, the relative electron withdrawing nature of an atom, group, or orbital) are of paramount importance when predicting organic chemistry. When two atoms of different electronegativities are bonded, one end of the bond will be δ+ and the other will be δ-. A bond dipole is the local moment associated with a polar covalent bond. A dipole moment, μ = q × r, is expressed in units of Debye (D, where 1D = 10-18 esu cm).
* “Esu” stands for “electrostatic unit”, and the charge of an electron or proton is negative or positive 4.80 × 10-10 esu, respectively.