26 BONDS BETWEEN ADJACENT ATOMS Bonding Molecular Orbital(Orbital):Bond o Antibonding Mo olecular Orbital (o*Orbital) 238 pi Atomic Or it cular Orbital (n Orbital ng Molecular orhital (orhitaly 241 cules 244 MOED for 2nd Row Homodiatomic Molecules 2.45 MOED for the 2nd Row Heteroatomic Molecule:Carbon Monoxide 2.46 Coefficients of Atomic Orbitalsc 2.47 Normalized Orbital 2.48 Normalization 2.49 Orthogonal Orbitals 2 Orthonormal Orbitals 2.51 Wave Functions in Valence Bond(VB)Theory Electrons are the cement that binds together atoms in molecules.Knowledge con- cerning the forces acting on these electrons,the energy of the electrons,and their location in space with spect to the nucli they hold together are fundamental to the understand of all che istry .The na ng of a another is ly des o major the molecular orbital (MO)theory.The starting point for the development of VB theory was a 1927 paper by Walter Heitler and Fritz London that appeared in Z Physik deal ing with the calculation of the energy of the hydrogen molecule.Several years later J.Slater and then Linus Pauling (1901-1994)extended the VB approach to organic molecules,and VB theory became known as HLSP theory from the first letters of the sumames of the men who contributed so much to the theory.The popularity of VB y owe uch to the brilliant work of Pauling and his explaining the the ch nical bond using res ce co ncepts According to VB theory,a molecule cannot be represented solely by one valence bond structure.Thus,CO in valence bond notation is written as:o=c=o:,which shows that eight electrons surround each oxygen atom as well as the carbon atom. This one structure adequately describes the bonding in CO2,and one does not ordi- narily consider all the other less important but relevant resonance structures,such a o-c=o+and o=c-.Because resonance theory is such a powerful tool for understanding delocalized bonding the subiect of the ext ch ther discus merits of the VB ter, e will defer fur n of it here.Des ith its nphas wbac ding in some simple mole is tempted to write the structure of this molecule as:o=0:,but this representation implies that all the electrons of oxygen are paired and hence the molecule should be
2.35 σ Bonding Molecular Orbital (σ Orbital); σ Bond 44 2.36 σ Antibonding Molecular Orbital (σ* Orbital) 45 2.37 pπ Atomic Orbital 45 2.38 π Bonding Molecular Orbital (π Orbital) 45 2.39 Localized π Bond 46 2.40 π Antibonding Molecular Orbital (π* Orbital) 46 2.41 σ Skeleton 47 2.42 Molecular Orbital Energy Diagram (MOED) 47 2.43 Electronic Configuration of Molecules 48 2.44 MOED for 2nd Row Homodiatomic Molecules 48 2.45 MOED for the 2nd Row Heteroatomic Molecule; Carbon Monoxide 50 2.46 Coefficients of Atomic Orbitals cij 50 2.47 Normalized Orbital 51 2.48 Normalization 52 2.49 Orthogonal Orbitals 52 2.50 Orthonormal Orbitals 52 2.51 Wave Functions in Valence Bond (VB) Theory 52 Electrons are the cement that binds together atoms in molecules. Knowledge concerning the forces acting on these electrons, the energy of the electrons, and their location in space with respect to the nuclei they hold together are fundamental to the understanding of all chemistry. The nature of the bonding of atoms to one another is usually described by either of two major theories: valence bond (VB) theory and molecular orbital (MO) theory. The starting point for the development of VB theory was a 1927 paper by Walter Heitler and Fritz London that appeared in Z. Physik dealing with the calculation of the energy of the hydrogen molecule. Several years later J. Slater and then Linus Pauling (1901–1994) extended the VB approach to organic molecules, and VB theory became known as HLSP theory from the first letters of the surnames of the men who contributed so much to the theory. The popularity of VB theory owes much to the brilliant work of Pauling and his success in explaining the nature of the chemical bond using resonance concepts. According to VB theory, a molecule cannot be represented solely by one valence bond structure. Thus, CO2 in valence bond notation is written as , which shows that eight electrons surround each oxygen atom as well as the carbon atom. This one structure adequately describes the bonding in CO2, and one does not ordinarily consider all the other less important but relevant resonance structures, such as and . Because resonance theory is such a powerful tool for understanding delocalized bonding, the subject of the next chapter, we will defer further discussion of it here. Despite the merits of the VB approach with its emphasis on the electron pair bond, the theory has several drawbacks even for the description of the bonding in some simple molecules such as dioxygen, O2. In VB notation one is tempted to write the structure of this molecule as , but this representation implies that all the electrons of oxygen are paired and hence the molecule should be O O O C + − C O + O − O O C O 26 BONDS BETWEEN ADJACENT ATOMS c02.qxd 5/17/2005 5:13 PM Page 26
CHEMICAL BOND 27 diamagnetic.which the other hand,according to the MO deseription.the two highest occupiec molecula orbitals ofare degenerate and antibonding and each contains one electron with identical spin,thus accounting for the observed paramagnetism,the most unusual property of dioxygen. In MO theory the behavior of each electron in a molecule is described by a wave function.But calculations of wave functions for many electron atoms become very complicated.Fortunately,considerable simplification is achieved by use of the linear thod first described by Robert s.Mulliker med that wher one nucleus,t approach it is ve func resemble he tom s in the neighb hood of the other atom,the wave funct on resembles tha of the neighboring atom.Since the complete wave function has characteristics sep arately possessed by the two atomic orbitals,it is approximated by the linear com- bination of the atomic orbitals To further illustrate the difference in the two theories,consider the bonding in methane,CH..According to VB theory,the four C-H bonds are regarded as though each bond were a separate localized two-center.two-electron bond formed by the 、ofa 3 orbital and a byd gen I orbital.Each bond is a result of the pairing I two e electrons. one fr ea of the b s,and th electron density of the shared pair is at a maximum between the bonded atoms.In the molecular orbital treatment,the four 1s hydrogen orbitals are combined into four so-called group (or symmetry-adapted)orbitals,each of which belongs to a symmetry species in the T,point group to which tetrahedral methane belongs These four hydrogen group orbitals are then combined by the LCAO method with the 2s and three 2p orbitals of the carbon atom of similar symmetry to gen ate the four bondir ng and four antibondi molecular orbitals, ssary for MO de The then ced in the fou molecu orbi .each of which i is del over the five atoms.For the trea ment of the bonding in methane,the valence bond approach is simpler and usually adequate.However,for insight into some areas of chemical importance such as,for example,molecular spectroscopy,the molecular orbital approach is more satisfactory. This chapter deals with bonds between atoms in molecules in which adiacent atoms share a nair of electrons,giving rise to what is called two-center,two ron bonding Both VB theory and MO the eory are used with more emphasis or the latte 2.1 CHEMICAL BOND A general term describing the result of the attraction between two adjacent atoms such that the atoms are held in at relatively fixed distances with respect to each other. The bond may be said to occur at the distance between the two atoms that corre eminimum in the tial en rgy of the ronpomity to one another (seMorse cuveg2 the two atoms are
diamagnetic, which it is not. On the other hand, according to the MO description, the two highest occupied molecular orbitals of O2 are degenerate and antibonding and each contains one electron with identical spin, thus accounting for the observed paramagnetism, the most unusual property of dioxygen. In MO theory the behavior of each electron in a molecule is described by a wave function. But calculations of wave functions for many electron atoms become very complicated. Fortunately, considerable simplification is achieved by use of the linear combination of atomic orbitals, (LCAO) method first described by Robert S. Mulliken (1895–1986). In this approach it is assumed that when one electron is near one nucleus, the wave function resembles the atomic orbital of that atom, and when the electron is in the neighborhood of the other atom, the wave function resembles that of the neighboring atom. Since the complete wave function has characteristics separately possessed by the two atomic orbitals, it is approximated by the linear combination of the atomic orbitals. To further illustrate the difference in the two theories, consider the bonding in methane, CH4. According to VB theory, the four C–H bonds are regarded as though each bond were a separate localized two-center, two-electron bond formed by the overlap of a carbon sp3 orbital and a hydrogen 1s orbital. Each bond is a result of the pairing of two electrons, one from each of the bonded atoms, and the electron density of the shared pair is at a maximum between the bonded atoms. In the molecular orbital treatment, the four 1s hydrogen orbitals are combined into four so-called group (or symmetry-adapted) orbitals, each of which belongs to a symmetry species in the Td point group to which tetrahedral methane belongs. These four hydrogen group orbitals are then combined by the LCAO method with the 2s and three 2p orbitals of the carbon atom of similar symmetry to generate the four bonding and four antibonding molecular orbitals, necessary for the MO description. The eight valence electrons are then placed in the four bonding molecular orbitals, each of which is delocalized over the five atoms. For the treatment of the bonding in methane, the valence bond approach is simpler and usually adequate. However, for insight into some areas of chemical importance such as, for example, molecular spectroscopy, the molecular orbital approach is more satisfactory. This chapter deals with bonds between atoms in molecules in which adjacent atoms share a pair of electrons, giving rise to what is called two-center, twoelectron bonding. Both VB theory and MO theory are used with more emphasis on the latter. 2.1 CHEMICAL BOND A general term describing the result of the attraction between two adjacent atoms such that the atoms are held in at relatively fixed distances with respect to each other. The bond may be said to occur at the distance between the two atoms that corresponds to the minimum in the potential energy of the system as the two atoms are brought into proximity to one another (see Morse curve, Fig. 2.18). CHEMICAL BOND 27 c02.qxd 5/17/2005 5:13 PM Page 27
28 BONDS BETWEEN ADJACENT ATOMS 2.2 COVALENT BOND A chemical bond resulting from the sharing of electrons between adjacent atoms.If the sharing is approximately equal,the bond is designated as nonpolar covalent (Sect.)and f substantally the bond is polr(Sect.25). Only in the case where the bond betw oincides with a c ter of syn metry of a molecule is the sharing of electrons between the two atoms exactly equal 2.3 LOCALIZED TWO-CENTER,TWO-ELECTRON (2c-2e)BOND;ELECTRON PAIR BOND The covalent bond between two adjacent atoms involving two electrons.Such bonds treated th nolecular orbital (MO) theory or valence bond 2.4 VALENCE BOND (VB)THEORY This theory postulates that bond formation occurs as two initially distant atomic orbitals,each containing one valence electron of opposite spin,are brought into mtto cch other As the overlap of the atomic or localized t ing to a minimum in the potential energy of the system(see Morse curve,Sect.2.18). 2.5 LONE PAIR ELECTRONS A pair of electrons in the valence shell of an atom that is not involved in bonding to other aton s in the molecule 2.6 LEWIS ELECTRON (DOT)STRUCTURES Gilbert N.Lewis (1875-1946)devised the use of dots to represent the valence electrons(usually an octet)surrounding an atom in molecules or ions.For con- venience,most authors now use a dash to represent a single two-electron bond shared betw een adjacent atoms and a pair of dots on a single atom to symbolize lone pair of electrons Example.Water,ammonia,hydrogen cyanide,in Figs.2.6a,b,and c.Some authors also indicate the lone pair electrons as a dash or bar,as shown in Fig. 2.6d
2.2 COVALENT BOND A chemical bond resulting from the sharing of electrons between adjacent atoms. If the sharing is approximately equal, the bond is designated as nonpolar covalent (Sect. 2.12), and if substantially unequal, the bond is polar covalent (Sect. 2.15). Only in the case where the bond between two atoms coincides with a center of symmetry of a molecule is the sharing of electrons between the two atoms exactly equal. 2.3 LOCALIZED TWO-CENTER, TWO-ELECTRON (2c-2e) BOND; ELECTRON PAIR BOND The covalent bond between two adjacent atoms involving two electrons. Such bonds may be treated theoretically by either molecular orbital (MO) theory or valence bond (VB) theory (see introductory material). 2.4 VALENCE BOND (VB) THEORY This theory postulates that bond formation occurs as two initially distant atomic orbitals, each containing one valence electron of opposite spin, are brought into proximity to each other. As the overlap of the atomic orbitals increases, each electron is attracted to the opposite nucleus eventually to form a localized two-center, two-electron bond at a distance between the atoms corresponding to a minimum in the potential energy of the system (see Morse curve, Sect. 2.18). 2.5 LONE PAIR ELECTRONS A pair of electrons in the valence shell of an atom that is not involved in bonding to other atoms in the molecule. 2.6 LEWIS ELECTRON (DOT) STRUCTURES Gilbert N. Lewis (1875–1946) devised the use of dots to represent the valence electrons (usually an octet) surrounding an atom in molecules or ions. For convenience, most authors now use a dash to represent a single two-electron bond shared between adjacent atoms and a pair of dots on a single atom to symbolize a lone pair of electrons. Example. Water, ammonia, hydrogen cyanide, in Figs. 2.6a, b, and c. Some authors also indicate the lone pair electrons as a dash or bar, as shown in Fig. 2.6d. 28 BONDS BETWEEN ADJACENT ATOMS c02.qxd 5/17/2005 5:13 PM Page 28
ELECTRONEGATIVITY 29 o H HC=N: H (a) (b) (c) (d) Figure 2.6.Lewis electron structures for(a)HO.(b)NH.(c)HCN.and (d)the use of bars to represent lone pair electrons in H,O. 2.7 OCTET RULE The tendency of the main group elements(Sect.1.44)to surround themselves with a total of eight valence electrons,the number of valence electrons characteristic of the noble gases (with the exception of He,which has a closed shell of only two elec- trons).The octet rule rationalizes the bonding arrangement in most Lewis structures but there are exceptions involving both fewer and m nore than eight valence electrons Example.The oxygen. nitrogen,and carbon atoms of the molecules shown in Fig.2.6 Compounds involving the elements boron (e.g..BF)and aluminum(e.g..AlBr).each of which has six rather than eight electrons in their valence shells,not unexpectedly react with a partner molecule having a lone pair of electrons available for bonding. The formation of the addition complex (Fig.2.7a)involving the lone pair on nitrogen (see Sect.2.11)and the dimer of AlBr:(Fig.2.7b)involving a lone pair on each of the bridging bromine atoms are examples of the operation of the octet rule(for the explanation of the charges on the at s.see Sect.2.11).Ex ceptions involvir than eigh nce ele the 3rd ro ement nd sulf for example,such as PCls and SF where vacant or in compoun lence orbitals are presumably utilized. (a) (b) Figure 2.7.Complexes of boron and aluminum that obey the octet rule 2.8 ELECTRONEGATIVITY The relative a action by an atom for the valence electrons onor near that atom.Pauling who ongir the concept of electronega d that the experiment energy of the bond A-B was greater than the average bond energies of A-A and B-B
2.7 OCTET RULE The tendency of the main group elements (Sect. 1.44) to surround themselves with a total of eight valence electrons, the number of valence electrons characteristic of the noble gases (with the exception of He, which has a closed shell of only two electrons). The octet rule rationalizes the bonding arrangement in most Lewis structures, but there are exceptions involving both fewer and more than eight valence electrons. Example. The oxygen, nitrogen, and carbon atoms of the molecules shown in Fig. 2.6. Compounds involving the elements boron (e.g., BF3) and aluminum (e.g., AlBr3), each of which has six rather than eight electrons in their valence shells, not unexpectedly react with a partner molecule having a lone pair of electrons available for bonding. The formation of the addition complex (Fig. 2.7a) involving the lone pair on nitrogen (see Sect. 2.11) and the dimer of AlBr3 (Fig. 2.7b) involving a lone pair on each of the bridging bromine atoms are examples of the operation of the octet rule (for the explanation of the charges on the atoms, see Sect. 2.11). Exceptions involving more than eight valence electrons involve the 3rd row elements phosphorus and sulfur in compounds, for example, such as PCl5 and SF6 where vacant 3d valence orbitals are presumably utilized. 2.8 ELECTRONEGATIVITY The relative attraction by an atom for the valence electrons on or near that atom. Pauling who originated the concept of electronegativity recognized that the experimental bond energy of the bond A–B was greater than the average bond energies of A–A and B–B. ELECTRONEGATIVITY 29 O H H N H H H H C N (d ) O H H (a) (b) (c ) Figure 2.6. Lewis electron structures for (a) H2O, (b) NH3, (c) HCN, and (d) the use of bars to represent lone pair electrons in H2O. N H H H B F F F Al Br Br Al Br Br Br Br (a) (b) + + + − − − Figure 2.7. Complexes of boron and aluminum that obey the octet rule. c02.qxd 5/17/2005 5:13 PM Page 29
30 BONDS BETWEEN ADJACENT ATOMS The additional bond strength is due to the ionic resonance energy arising from the con- tributions of ionic resonance structures A+B-,and if A is more electronegative than B. A-B+.The ionic resonance energy A can be calculated from the equation: A=E(A-B)-IE(A-A)XE(B-B)11 (2.8a where E is the energy of the bond between the atoms shown in parentheses Pauling set the square root of A equal to the electronegativity difference between A and B.Then if an electronegativity value of 2.20 is arbitrarily assigned to the element hydrogen,the electronegativities of most other atoms may be calculated. Several other scales for rating the electronegativity of atoms have been proposed. One of the most useful is the one suggested by Mulliken.He proposed that the elec- tronegativity of an atom is the average of its ionization energy or IE (the energy required for the removal of an electron from an atom in the gas phase)and its elec affiniry or EA(the energy released by adding an electron to th e atom in the gas phase) Electronegativity=(IE+EA)/2 (2.8b) Nearly all methods of calculating electronegativities lead to approximately the same values,which are almost always expressed as dimensionless numbers. Example.Typically.Pauling electronegativity values.for example.that of the f atom.are obtained as follows:The ex xperimentally observed bond ene reV(1eV=96. ce energy A of H-】 cal from Eq.2.8a a3.15 and there 1.77.If the electronegativity of H is 2.20,then the electronegativity of F is (2.20+1.77)=3.98.The Pauling electronegativities of the 2nd row elements in the Periodic Table are Li.0.98:Be.1.57:B.2.04:C.2.55:N.3.04:O.3.44:F.3.98. The extremes in the scale of electronegativities are Cs,0.79,and F,3.98.From these values it is clear that the electrons in,for example,a C-F bond,will reside much closer to the fatom than to the c ato m.The une qual sharing of the electrons in a bond gives rise to a partial arge on the elect ive aton charge on the le ectronegative atom.This paaen e m2p既we by placing partial negative to assign fixed values for the electronegativity of a particular atom because its electronegativity may vary,depending on the number and kind of other atoms attached to it.Thus,the electronegativity of an sp hybridized carbon(50%s char- acter)is 0.6 higher than that of an sp hybridized carbon (25%s character). 2.9 VALENCE,IONIC VALENCE,COVALENCE Terms used to describe the capacity of an element to form chemical bonds with other elements.In the case of a covalent compound,the valence,more precisely called
The additional bond strength is due to the ionic resonance energy arising from the contributions of ionic resonance structures AB, and if A is more electronegative than B, AB. The ionic resonance energy ∆ can be calculated from the equation: ∆ E(A B) [E(A A) ×E(B B)]1/2 (2.8a) where E is the energy of the bond between the atoms shown in parentheses. Pauling set the square root of ∆ equal to the electronegativity difference between A and B. Then if an electronegativity value of 2.20 is arbitrarily assigned to the element hydrogen, the electronegativities of most other atoms may be calculated. Several other scales for rating the electronegativity of atoms have been proposed. One of the most useful is the one suggested by Mulliken. He proposed that the electronegativity of an atom is the average of its ionization energy or IE (the energy required for the removal of an electron from an atom in the gas phase) and its electron affinity or EA (the energy released by adding an electron to the atom in the gas phase): Electronegativity (IE EA)/2 (2.8b) Nearly all methods of calculating electronegativities lead to approximately the same values, which are almost always expressed as dimensionless numbers. Example. Typically, Pauling electronegativity values, for example, that of the F atom, are obtained as follows: The experimentally observed bond energy of H–F is 5.82 electron volts or eV (1 eV 96.49 kJ mol1 or 23.06 kcal mol1). The ionic resonance energy ∆ of H–F calculated from Eq. 2.8a is 3.15 and therefore ∆1/2 is 1.77. If the electronegativity of H is 2.20, then the electronegativity of F is (2.20 1.77) 3.98. The Pauling electronegativities of the 2nd row elements in the Periodic Table are Li, 0.98; Be, 1.57; B, 2.04; C, 2.55; N, 3.04; O, 3.44; F, 3.98. The extremes in the scale of electronegativities are Cs, 0.79, and F, 3.98. From these values it is clear that the electrons in, for example, a C–F bond, will reside much closer to the F atom than to the C atom. The unequal sharing of the electrons in a bond gives rise to a partial negative charge on the more electronegative atom and a partial positive charge on the less electronegative atom. This fact is sometimes incorporated into the structure of the molecule by placing partial negative and partial positive signs above the atoms as in δC–Fδ. It is not always possible to assign fixed values for the electronegativity of a particular atom because its electronegativity may vary, depending on the number and kind of other atoms attached to it. Thus, the electronegativity of an sp hybridized carbon (50% s character) is 0.6 higher than that of an sp3 hybridized carbon (25% s character). 2.9 VALENCE, IONIC VALENCE, COVALENCE Terms used to describe the capacity of an element to form chemical bonds with other elements. In the case of a covalent compound, the valence, more precisely called 30 BONDS BETWEEN ADJACENT ATOMS c02.qxd 5/17/2005 5:13 PM Page 30