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Unformatted text preview: CAREY, " onetime Cuemus'rkv " I I. Tacoma: To Descense Cowman? Become Aflnwuw Bonn mm Hvemmtnnou B. More come Dee-Tm. , . V II. amuse-r Sommnm Ar em: 0F Mowers Imme‘rnwr To Bounties. um; E xammes 1.12 ELECTRON WAVES AND CHEMICAL BONDS . B€E>ebeue 2; Lewis proposed his shared electron-pair model of bonding in 1916, almost a decade h before de Broglie’s theory of wave—particle duality. De Broglie’s radically different View of an electron, and Schrodingerk success in’using wave equations to calculate the energy u . of an electron in a hydrogen atom, encouraged the belief that bonding in molecules could Seflflom N (9 m be explained on the basis of interactions between electron waves. This thinking produced H if", E? two widely used theories of chemical bonding: one is called the valence bond model, , .1 f _ v the other the molecular orbital model. by “L6 waFqu—lm‘} Before we describe these theories, let’s first think about bonding between two PQQBflBKLV-fl? hydrogen atoms in the most fundamental terms. We’ll begin with two hydrogen atoms Deng“ » that are far apart and see what happens as the distance between them decreases. The forces involved are electron—electron (— —) repulsions, nucleus—nucleus (+ +) repul- sions, and electron—nucleus (— +) attractions. All of the'Se forces increase as the dis- .THEDMEWS OF tance between the two hydrogens decreases. Because the electrons are so mobile, how- _ ’ ever, they can choreograph their motions so as to minimize their mutual repulsion ’while UN “WOT Bewb‘wb maximizing their attractive forces with the protons. Thus, as shown in Figure 1.14,.there . \) {*LENOL; Emma) is a net, albeit weak, attractive force between the two hydrogens even when the atoms - _ I _ _ are far apart. This interaction becomes stronger as the two atoms approach each other— mow HT 0‘7"?) ran“ the electron of-iféach hydrogen increasingly feels the attractive force of two protons rather I “ than one, the total energy decreases, and the system becomes more stable. A potential _ energy minimum is reached when the separation between the nuclei reaches 74 pm, , which corresponds to the H—H bond length in H2. At distances shorter than this, the a ' nucleus—nucleus and electron—electron repulsions dominate, and the system becomes less stable. , p ' . I The valence bond and molecular orbital theories differ in how they use the orbitals of two hydrogen atoms to describe the orbital that contains the electron pair in H2. Both, theories assume that electrOn Waves behave much like more familiar waves, such as sound and light waves; One property of waves that is important here is called “interfer- ' ence” in physics. Constructive inter erence occurs when two. anes combine so as to' reinforce each other “in- hase”); destructive inter erence occurs when the o ose each ‘other (“out of phase”) (Figure 1.15). In the valence bond model constructive interference between two electron waves is seen as the basis for the shared electron-pair bond. In the ‘ molecular orbital model, the wave functions of molecules are derived by combining wave functions of atoms. '7‘ COME'VED I” 1%; wage Lawmain 70 Gamma Catamaran Sweep-T5 32 CHAPTER ONE Chemical Bonding ‘Pongu'rmt/ Wanna CUWE For: H; FIGURE 1.14 Plot 0 potential energy versus dlS- tance for two hydrogen atoms. At long distances, there is a weak attractive force. As the distance de— creases, the potential energy » decreases, and the system be- comes more stable because each electron now feels the attractive force of two pro- tons rather than one. The op— timum distance of separation (74 pm) corresponds to the normal bond distance of an H2 molecule. At shorter dis— tances, nucleus—nucleus and 74 pm Internuclear distance ————>— I Potential energy V 0 4560.1) EnTHnHD‘r electron—electron repulsions 3| - . are. greater than electron— _ n. L . ._ . ‘ , ‘ ‘v' nucleus attractions, and the (_4fg4kl:él;}zlml) _ ____________ __ Ewmbi Mil)“ Ml?!“ (M057 Smgw 3 system becomes-less stable.- H ‘H_H WT— MOQMAL EWDD We?“ - END Dison'Tl‘OD 5503391 Waves reinforce ‘ Waves cancel / Distance 09 berm) art \1 E Des-mo cm v E (a) Amplitudes of wave functions added (b) Amplitudes of wave functions subtracted _LL) image (997 0P Dense FIGURE 1.15 Interference between waves. (a) Constructive interference occurs when two waves combine in phase with each other. The amplitude of the resulting wave at each point is the sum of the amplitudes of the original waves. (b) Destructive interference in the case of two phases out of phase with each other causes a mutual cancellation. m?) THEM : 1.13 BOING IN 2: THE VALENCE BOND MODEL fissomfi’s Morger The characteristic feature of valence bond theory is that it describes a covalent bond :5 QDAS‘UVHVV A between two atoms in terms of an in—phase Overlap of a half—filled orbital of one atom with a half-filled orbital of the Other, illustrated for the case of H2 in Figure 1.16. Two hydrogen atoms, each containing an electron in a Is orbital, Combine so that their orbitals ‘ overlap to give a new orbital associated with both of them. In—phase orbital overlap (con- BOMDS E3157 w GEE—ls) structive interference) increases the. probability of finding an electron in the region of gm PA“; 8% (tron/LS overlap. ' I , ‘ Figure 1.17 uses electrostatic potential maps to show the buildup of electron den- 3e DDS PERM/180 1291 sity in the region between the atoms as two hydrogen atoms approach each other closely avmkAp 9F awkmks enough for their orbitals to overlap. " -' I Were awe‘ItO slice throu h the H2 molecule perpendicular to the internuclear ‘aXis, its cross s'é’c‘fidri'Would a ear as a circle. We describe. the electron distribution in such ' a bond as Hana”: rotational s mme""" and refer to it as a Si ma (0). bond. GOWCTTUD 0 P Atoms “Wm Loefkuifié‘D seen-ms Reamer) i8“ l‘t‘fEiZiDtZ'fi‘TlOM 1.13 Bonding in H2: The Valence Bond Model in-phase overlap of two ls orbitals gives new orbital encompassing both hydrogen atoms ls orbitals of two hydrogen atoms FIGURE 1.16 Valence bond picture of bonding in H2. Overlap of half—filled 1s orbitals of two hydrogen atoms gives a new orbital encompassing both atoms. This new orbital contains the .two original electrons. The electron density (electron probability) is highest in the region between the two atoms. The black dots correspond to the nuclei, and the + signs to the signs of the wave functions. When the wave functions are of the same sign, constructive interfer- ence leads to an increase in the probability of finding an electron in the region where the two orbitals overlap. (a) The ls orbitals of two separated hydrogen ’ atoms, sufficiently far apart so that essentially no interaction takes place between them. Each electron is associated with only a single proton. (b) As the hydrogen atoms approach each other, their ls orbitals begin to overlap and each electron begins to feel the attractive force of both protons. (c) The hydrogen atoms are close enough so that appreciable overlap of the two ls orbitals occurs. The concentration of electron density in the region between the two protons is more readily apparent. (d) A molecule of H2. The center—to-center distance between the hydrogen atoms is 74 pm. The two individual 1s orbitals have been replaced by a‘ new orbital that encompasses both hydrogens and contains both electrons. The electron density is greatest in the region between the two hydrogens. 33 «aerosmoclvwg IUTBLFETZETO cg . FIGURE 1.17 .jValence bond picture of bonding in H2. The drawings illustrate how the 1s orbitals of two hy- drogen atoms overlap to give the orbital that contains both electrons of a hydrogen mole— cule. The colors of the rain- bow, red through violet, are used to depict highest to low- est electrostatic potential, _ respectively. 34 ND Tia/30M Assumes (Macon; is P: QeLLEc/‘now 0e DUULEi vecWCE Evacmmas W "Per it) memes-— W @Qi‘bimls THAT Esra» overt aw forte Me;wa mole Foreman Fiber“ {3: UNWK Cemem omen Ge Hmnmctite.) Hr- Drwewie) emet- TWw) Eliot: Prwm Efrem Pn'mm ' Stigma Evoubi Dilemma or» a H ls Orbfiirms ' FFGURE 1.18 Genera tion of 0' and 0* molecular or— bitals of H2 by combining 1s orbitals of two hydrogen atoms. CHAPTER ONE Chemical Bonding We will use the valence bond approach extensively in our discussion-of organic molecules and expand on it later in this chapter. First though, let’s introduce the molec— ular orbital method to see how it uses the ls orbitals of two hydrogen atoms to gener- ate the orbitals of an H2 molecule. ' 1.14 : THE OECULAR ORBITAL MODEL The molecular orbital approach to chemical bonding is based on the notion that, as elec— trons in atoms occupy atomic orbitals, electrons in molecules occupy molecular orbitals. Just as the first task in writing the electron configuration of an atom is to identify the atomic orbitals that are available to it, so too must we first describe the orbitals avail— able to a molecule. In the molecular orbital method this is accomplished by represent- in molecular orbitals as combinations of atomic orbitals, the linear combination 0 atoic obital-zolecular orbital (LCAO—MO) method. M A '“H“ olecular orbitals (MOS) are generated by combining the is atomic orbitals (AOs) of two hydrogen atoms. In one combinationrthe two wave functions are added; in the other the are subtracted. The two'new orbitals that are pro— duced are portrayed in Figure 1.18. The additive combination enerates a bondin orbital; the subtractive combination enerates an antibondin orbital. Both the bond— ing and antibonding orbitals have rotational symmetry around the line connecting the two atoms; they have a symmetry. The two are differentiated b callin the bondin orbital o and the antibondin orbital 0* ‘(“Si ma star”). The bonding orbital is charac— terized bya region of high electron probability between the two atoms, and the anti- bonding orbital has a nodal surface between them. A molecular orbital diagram for H2 is shown in Figure 1.19. The customary for— mat shows the starting AOs at the left and right sides and the M08 in the middle. It must always be true that the number of MOS is the same as the number of AOS that combine to produce them. Thus, when the ls AOs of two hydrogen atoms combine, two MOS result. The bonding MO (0) is lower in energy and the antibonding MO (0*) higher in energy than either of the original ls orbitals. I (a) Add the 1s wave functions of two hydrogen atoms to generate a bonding molecular orbital (0') of H2. There is a high probability of finding both electrons in the region between the two nuclei. been m a mo , c:- w Cows'TlZoCTNE (in Masai :meeeeaemc (b) Subtract the 1s wave function of one hydrogen atom from the other to generate an antibonding molecular orbital (0*) of H2. There is a nodal surface where there is a zero probability of finding the electrons in the region between the two nuclei. Sea-motor ‘ node ‘ « besrrwcrve (Ber 03“ @Hnse) TNTETLPEREZNCLJ i? magnum W?) ‘3'” 1.15 Bonding in Methane and Orbital Hybridization ‘ 35 mo Eoemeetwleevep ‘biaeeam' For: Hal Antibonding L FIGURE 1.19 Two molecu- . Iar orbitals are generated by combining two hydrogen 1s orbitals. One molecular orbital is a bonding molecu- lar orbital and is lower in Is + + 13 energy than either of the atomic orbitals that combine ‘ to produce it. The other T molecular orbital is anti- bonding and is of higher _H_ energy than either atomic ' orbital. Each arrow indicates Bonding one electron; the electron spins are opposite in sign. The bonding orbital contains both electrons of H2. Increasing energy —> Hydrogen ls Molecular orbitals Hydrogen ls atomic orbital of H2 atomic orbital When assigning electrons to MOS, the same rules apply as for writin electron con— figurations of atoms. Electrons fill the MOs in order of increasing orbital energy, and the maximum number of electrons in any orbital is 2. The 2 electrons of H2 occupy the bonding orbital, have opposite spins, and both are held more strongly than they would be in separated hydrogen atoms. There are no electrons in the antibonding orbital. For a molecule as simple as H2, it is hard to see much difference between the EDmD‘EDE g valence bond and molecular orbital methods. The most important differences appear in, . . .. . H H molecules With more than two atoms—a very common Situation 1ndeed. In those cases, \0: G” ' u the valence bond method continues to view a molecule as a collection of bonds between A H / \C 5 0 connected atoms. The molecular orbital method, however, leads to a picture in which the ' HI "T \ H same electron can be associated with many, or even all, of the atoms in a molecule. _ In the remaining sections of this chapter we will use a modification of valence Digit/“t SHva Duncan- bond theory to describe CH and CC bonds in some fundamental types of organic com- WU? M9 V '3 V5 m0 pounds. 1.15 BONDING IN METHANE AND ORBITAL HYBRlDlZATlON| VMGE BEND fl’Ht‘ZUllfi/t A vexing puzzle in the early days of valence bond theory concerned the bonding in methane (CH4). Since covalent bonding requires the overlap of half-filled orbitals of the connected atoms, carbon With an electron configuration of 1s22322plepy1 has only two half—filled orbitals (Figure 1.20a), so how can it have bonds to four hydrogens? H + —— 212+ 4— + 2519—1?— —Al—- FIGURE 1.20 (a) Electron configuration of carbon in its most stable state. (b) An . electron is “promoted” from 23 _% gs + the 25 orbital to the vacant ~ g, . 2p orbital. (c) The 25 orbital ’ and the three 2p orbitals are Ground electronic Higher energy electronic 7 sp3 hybrid ~combined to give a set of state of carbon state of carbon state of carbon four equa|_energy 5p3_ , hybridized orbitals, each of (a) (b) » (C) which contains one electron. Energy —> : I wk; :7- ' ‘ x, Cu is 215 lP-glPY . ' ' N45 95 pra’lpy 2?? 36' *Vtmmm C AWO— CWTG: WHO more ‘Two main Flakes 1 ENE Io cite'rnismw (Fort EWCLtDa‘fime THE DHTUQE 6:11“: Cara“ “DALI Bowl» ems) Tm»: QTm-rfz. EM 951%? Sreruc Domem = Li :5 6‘93 Manama/*- ‘riw {we Tammie:— DML/ greener;th QEDMET X FIGURE 1.21 tion of orbital mixing in 5p3 hybridization. Mixing of one s orbital with three p orbitals generates four Sp3 hybrid orbitals. Each sp3 hybrid orbital has 25% 5 character and 75% p charac— ter. The four sp3 hybrid orbitals have their major lobes directed toward the corners of a tetrahedron, which has the carbon atom at its center. Representa— . CHAPTER ONE Chemical Bonding «K- In the 19303 Linus Pauling offered an ingenious solution to the puzzle. He began with a simple idea: “promoting” one of the 23 electrons to the empty 2p, orbital gives four half—filled orbitals and allows for four C—H bonds (Figure 1.201)). The electron configuration that results (ls22s12px12py12pzl), however, is inconsistent with the fact that all of these bonds are equivalent and directed toward the corners of a tetrahedron. The second part of Pauling’s idea was novel: mix together (hybridize) the four valence orbitals of carbon (2s, 2px, Zpy, and 21),) to give four half-fillecl—orbitals of equal energy (Figure 1208—)TThe four new orbitals in Pauling’s scheme are called Sp3 hybrid orbitals because they come from one s orbital and three 3 orbitals. Figure 1.21 depicts some of the spatial. aspects of orbital hybridization. Each Sp3 hybrid orbital has two lobes of unequal size, making the electron density greater on one side of the nucleus than the other. In a bond to hydrogen, it is the larger lobe of a car- bon Sp3 orbital that overlaps with a hydrogen ls orbital. The orbital OVerlaps corre— sponding to the four C—H bonds of methane are portrayed in Figure 1.22. Orbital over- lap alOng the internuclear axis generates a bond with rotational symmetry—in this case a C(2Sp3)—H(1S) 0' bond. 'A etrahdl emem‘pof four .0 b0nds‘i’S"'Characteristic of Sp3_hybridized carbon. ‘ ., .. The peculiar shape of sp3 hybrid orbitals turn out to have an important consequence. Since most of the electron density in an sp3 hybrid orbital lies to one side of a carbon , atom, overlap with a half-filled ls orbital of hydrogen, for example, on that side produces a stronger bond than would result otherwise. If the electron probabilities were equal on both sides of the nucleus, as it would be in a p orbital, half of the time the electron would be remote from the region between the bonded atoms, and the bond would be weaker. Thus, not only does Pauling’s orbital hybridization proposal account for carbon forming four bonds rert t, tee 03 e also on r thanthe ould be therwise. Combine one 2s and three 2p orbitals to give four equivalent sp3 hybrid orbitals: The two lobes of each sp3 hybrid orbital are of different size. More of the electron density is concentrated on one side of the nucleus than on the other. SP Siemle [db Bent) S _ 1.16 sp3 Hybridization and‘Bonding in Ethane I 37 Oil-arm? o? Castes/His DQBtTA’LS FIGURE 1.22 The sp3 hy- brid orbitals are arranged in a tetrahedral fashion around carbon. Each orbital 3 contains one electron and H H(15)‘C(23p) can form a bond with a “bond hydrogen atom to give a m C H tetrahedral methane mole— Coming ‘ cule. (Note: Only the major toward you \ / 1095" ‘ lobe of each sp3 orbital is Inthe plane H - shown. As indicated in Fig- ofthepaper . ure 1.21, each orbital con- ’ tains a smaller back lobe, In the plane - . which has been omitted for 0fthe paper . I the sake _of clarity.) - ’ , . ‘ H il l C, .\ $0 , ' . ' l . PROBLEM 1.20 Construct an orbital diagram like that of Figure 1.20 for nitro- H”, . . . 3 . . . . . . ‘\ gen m ammonia, assuming 5p hybridization. In what kind of orbital IS the H Unshared pair? What orbital overlaps are involved in the N—H bonds? H 1.16 Sp3 HYBRIDIZATION AND BONDING IN ETHANEI VRLEDOE TESOUD “ilrEDtLfi’ The orbital hybridization model of covalent bonding is readily extended to carbon—- carbon bonds. As Figure 1.23 illustrates, ethane is described in terms of a carbon— ; egg-ethane; carbon 0 bond joining two CH3 (methyl) groups. Each methyl group consists of an I d'l53 Pmlrespectivel off-hybridized carbon attached to three hydrogens by Sp3—1S C bonds. Overlap of the he b9.'ld-,a”9'e I. remaining half~filled orbital of one carbon with that of the other generates a 0‘ bond between them. Here is a third kind of 0' bond, one that has as its basis the overlap of i€fi+fiw6 two sp3-hybridized orbitals. In general, you can expect that carbon will be sing-hybridized " u u when it is directly bonded to tour atoms. i , r ' H—evcvn PROBLEM 1.21 Describe the bonding in methylsilane (H3CSiH3), assuming that .l- A ‘ it is analogous to that of ethane. What is the principal quantum number of the orbitals of silicon that are hybridized? - Cal-lb . The orbital hybridization model of bonding is not limited to compounds in which Sggmfi gout) . all the bonds are single, but can be adapted to compounds with double and triple bonds, as described in the following two sections. Drench? at: sealer}; Ci" Eowbs I .H u CIW I . - i i i FIGURE 1.23 Orbital over- lap description of the sp3—s‘p3 0 bond between the two carbon atoms of ethane. {meme Econ i 00mm? OF ISL {15?} Gamma—.5 38 FIGURE 1.24 (a) All the atoms of ethylene lie in the same plane.’ All the bond angles are close to 120°, and. the carbon—carbon bond dis- tance is significantly shorter than that of ethane. (b) A space—filling model of ethyl- ene. 5mg Domi’étfle 5 v£7$PlrW6Rwrzflflvfl CHAPTER ONE Chemical Bonding 1.17 sYlDZTl N BONDIG l ETHYLENE VB ‘TH’C’DIZW Ethylene is a planar molecule, as the structural representations of Figure 1.24 indi- cate. Because sp3 hybridization is associated with a tetrahedral geometry at carbon, it is not appropriate for ethylene, which has a trigonal planar geometry at both of its carbons. The hybridization scheme is determined by the number of atoms to which the carbon is directly attached. In ethane, four atoms are attached to carbon by 0’ bonds, and so four equivalent sp3 hybrid orbitals are required. In ethylene, three atoms are attached to each carbon, so three equivalent hybrid orbitals are required. As shown in Figure 1.25, these three orbitals are enerated b mixin the carbon 23 orbital with two of the 2p orbitals and are called sp hybrid orbitals. One of the 2p orbitals is left unhybridized. ( 3 P23 beogce Bambi \ :c, e Hf ‘H ETHYLEHE \¢,nr Apo' "Tm (gummy ‘Puw ML Ewe-meme GB‘OMETYUT Energy —-»- 23 +£— 23 Ground electronic state of carbon spz hybrid state of carbon Higher energy electronic state of carbon ((1) (b) (C) ‘FIGURE 1.25 (a) Electron configuration of carbon in its most stable state. (b) An electron is “promoted” from the 25 orbital to the vacant 2p orbital. (C) The 25 orbital and two of the three 2p orbitals are combined to give a set of three equal—energy spz—hybridized orbitals. One of the 2p orbitals'remains unchanged. 1.17 sp2 Hybridization and Bonding in Ethylene Figure 1.26 illustrates the mixing of orbitals in Sp2 hybridization. The three sp2 orbitals are of equal energy; each has one—third 3 character and two~thirds p character. Their axes are coplanar, and each has a shape much like that of an Sp3 orbital. Each carbon of ethylene uses two of its sp2 hybrid orbitals to form 0 bonds to two hydrogen atoms, as illustrated in the first part of Figure 1.27. The remaining Sp2 orbitals, one on each carbon, overlap along the internuclear axis to give a a bond connecting the two carbons. > As Figure 1.27 shows, each carbon atom still has, at this point, an unhybridized szprbital available for bonding. These two half-filled 2p£orbitals have their axes per— pendicular to the framework of 0 bonds of the molecule and overlap in a side—by-side manner to give whatis called 21 pi (7:) bond. According to this analysis, the carbon—car— bon double bond of ethylene is viewed as a combination of a 0' bond plus a at bond. The additional increment of bonding makes a carbon—carbon double bond both stronger and shorter than a carbon—carbon single bond. Electrons in a at bond are called 1': electrons. The probability of finding a 7r elec- tron'is highest in the region above and below the plane of the molecule. The plane of the molecule corresponds to a nodal plane, where the probability of finding a 'n' electron IS zero. In general, you can expect that carbon will be spz-hybriclized when it is directly W bonded to three atoms. Leave this orbital alone Rs -RPK 1P7 w Combine one 2s and two 2p orbitals Three sp2 hybrid orbitals FIGURE 1.26 Representation of orbital mixing in 5p2 hybridization. Mixing of one s orbital with two p orbitals generates three 5p2 hybrid orbitals. Each sp2 hybrid orbital has one—third 5 character and two-thirds p character. The axes of the three 5p2 hybrid orbitals are coplanar. One 2p orbital remains unhybridized, and its axis is perpendicular to the plane defined by the axes of the 5p2 orbitals. } 5192 39 at er» Benn: Oventh 0F 3 up extei'mLs ‘ Sim?st :7 Dover)? (DOUUE'CTED 4o ' CHAPTERONE ChemicalBonding Begin with two sp2 hybridized carbon atoms and four hydrogen atoms: FIGURE 1.27 The Half.fi11ed 2p carbon—carbon double bond orbital in ethylene has a (r compo- / nent and a it component. The 0' component arises from overlap of spz-hybridized or— bitals along the internuclear axis. The 7r component re- sults from a side—by—side overlap of 2p orbitals. In plane of paper SP2 hybrid orbitals of carbon overlap to form 0 bonds to C‘(25p2)— Has) ~ hydrogens and to each other 0' bond Sigma (6”) Booms-3.0 ng-‘M LEDE i§ ovmmp 0e H is l esp?“ OefinnL-S 9;) Overrun? 5? a, LES-pi” 9.624%": Tlfll’ivs Pt Ctr» F3090 is) Erm MEDE Stoewms Ovi‘fiLLR—P or: 3. UMH’W EVA Dyng 113; O (Len-m3 p orbitals that remain on carbons overlap to form n bond C(2sp2),~ C(2sp2) 0 bond C(2p) -— C(Zp) 'n' bond 1.18 5 One more hybridization scheme is important in organic chemistry. It is called sp hybridization and applies when carbon is directly bonded to two atoms, as it is in ace??- lene. The structure of acetylene is shown in Figure 1.28 along with its bond distances and bond angles. Since each carbon in acetylene is bonded to two other atoms, the orbital hybridiza— tion model requires each carbon to have two equivalent orbitals available for’the for— mation of 0 bonds as outlined in Figures 1.29 and 1.30. According to this model the _ca_r_—_ bon 23 orbital and one of the 2p orbitals combine to generate a pair of two equivalent sp 2 n or 1ta 3. ac sp y n or 1ta as 0 so aracter an 5 op c aracter. These two Sp orbitals share a common axis, but their major lobes are oriented at an angle of 180° to each other. Two of the original 2p orbitals remain unhybridized. Their axes are I . MI. perpendicular to each other and to the common axrs of the pair of Sp hybrld orbitals. 180° 180° t 1H H C=C 106 120 106 Pm Pm Pm (a) 2a+w Energy —-—> 23 4t . Ground electronic state of carbon (61) Two 23p hybrid orbitals 1.18 sp Hybridization and Bonding in Acetylene (b) w+++ 2a+ 2sp—l— —l— __T__ Higher energy electronic - state of carbon 2s Sp hybrid state of carbon (c) (b) Leave these two orbitals alone Unhybridized p orbitals As portrayed in Figure 1.31, the two carbons of acetyleneare connected to each other by a 23p~23p 0 bond, and each 0 bond. The unhybridized 2p orbitals is attached to a hydrogen substituent by a ZSp—ls on one carbon overlap with their counterparts on the other to form two 1T bonds. The carbon~carbon triple bond in acetylene is viewed as a multiple bond of the o + 7r + n type. In general, you can expect that bonded to two atoms. “ carbon will be sp—hybridized when it is directly 41 FIGURE 1.28 Acety— lene is a linear molecule as indicated in the (a) structural formula and a (b) space—fill- ing model. FIGURE 1.29 (a) Electron configuration of carbon in its most stable state. (b) An electron is "promoted" from the 25 orbital to-the vacant 2p orbital. (c) The 25 orbital and one of the three 2p .' orbitals are combined to give a set of two equal—energy sp—hybridized orbitals. Two of the 2p orbitals remain unchanged. FIGURE 1.30 Representa- tion of orbital mixing in 5p hybridization. Mixing of the 25 orbital with one of the p orbitals generates two sp hybrid orbitals. Each 5p hybrid orbital has 50% 5 character and 50% p charac- ter. The axes of the two sp hybrid orbitals are colinear. Two 2p orbitals remain unhybridized, and their axes are perpendicular to each other'and to the long axis of the molecule. Sterne Dumow: :L =7 3? Hktfifzioflfimev Pmb Linear; Erect— Trumic, Ge’bmmrf 42 CHAPTER ONE Chemical Bonding ' FIGURE 1.31 A description of bonding in acetylene based on sp hybridization of carbon. The carbon—carbon triple bond is viewed as‘con~ sisting of one 0' bond and two w bonds. C(ZSP) 0' bond H(ls) Carbons are connected by a C(ZSp) C (25p) a bond gramme-h “ewes "iio W'T‘fivEDE '. ' i) (N mica/P OF HIS l6 s? DQBi'rmcS 15®veflcm0 he a Cs? Qmimis 'iD-i (rd Bepos "in Mew ice‘ioe: Du enka 5’? a owiwea’imm c1? Decor-mp5 (a9?) 3?}; flame) C(ZPZ) —— C(sz) 1T 'bond C(Zpy) —h C(2py) w bond x Tilime “Boob ‘« . . _ . . . . PROBLEM 1.22 Give the hybridization state of each carbon in the followmg lG‘) 217T compounds: ‘ - (a) Carbon dioxide (O=C=O) ' (d) Propene (CH3CH=CH2) \l’i/ (b) Formaldehyde (H2C=O)‘ (e) Acetone [(CH3)2C=O] H~C 3 ex (4 (c) Ketene (H2C=C=O) (f) Acrylonitrile (CH2=CHCEN) SAMPLE SOLUTION (a) Carbon in C02 is directly bonded to two other atoms. It is sp—hybridized. . 1.19 I WHICH THEORY OF CHEMICAL BONDING IS BEST?I We have introduced three approaches to chemical bonding in this chapter: 1. The Lewis model I 2. The orbital hybridization model (which is a type of valence bond model) 3. The molecular orbital model Which one should you learn? Generally speaking, the three models offer complementary information. Organic chemists use all three, emphasizing whichever one best suits a particular feature of struc- ture or reactivity. Until recently, the Lewis and orbital hybridization models were used far more than the molecular orbital model. But that is changing. 1.20 Summary . 43 The Lewis rules are relatively straightforward, easiest to master, and the most familiar. You will find that your ability to write Lewis formulas increases rapidly with experience. Get as much practice as you can early in the course. Success in organic chemistry depends on writing correct Lewis structures. Orbital hybridization deseriptions, since they too are based on the shared electron- pair bond, enhance the information content of Lewis formulas by distinguishing among various types of atoms, electrons, and bonds. As you become more familiar with a vari— ety of structural types, you will find that the term “sf-hybridized carbon” triggers a group of associations in your mind that are different from those of Some other term, such as “spZ—hybridized carbon,” for example. Molecular orbital theor can rovide insiohts into structure and reactivit that the 'Lewis and orbital-hybridization models can’t. It is the least intuitive of the three meth— ods, howeverfand requires the most training, background, and chemical knowledge to apply. We have discussed molecular orbital theory so far only in the context of the bond— ing in H2. We have used the results of molecular orbital theory, however, several times without acknowledging it until now. The electrostatic potential map of methane that opened this chapter and was repeated as Figure 1.7d was obtained by a molecular orbital calculation. Four molecular orbital calculations provided the drawings that illustrated how electron density builds up between the atoms in the valence bond (l) treatment of H2 (see Figure 1.17). Molecular orbital theory is well suited to quantitative applications and is becoming increasingly available for routine use via software that runs on personal computers. You will see the results of molecular orbital theory often in this text, but the theory itself will be developed only at an introductory level. 1.20 —SU-_lylARY- The first half of this chapter reviews the Lewis model of chemical bonding and the pro— cedures for writing structural formulas of chemical compounds, especially organic ones. The second half discusses bonding in terms of the wave nature of electrons and con- cludes with its application to compounds that contain carbon—carbon single bonds, dou— ble bonds, and triple bondsr . Section 1.1 A review of s0me fundamental knowledge about atoms and electrons Fort flwms v leads to a discussion of wave functions: orbitalsa and the electron con- ‘ figurations of atoms. Neutral atoms have as many electrons as the num- DOME? F0 1001’ (DD ber of protons in the nucleus. These electrons occupy orbitals in order of emigrmL/S increasing energy, with no more than two electrons in any one orbital. ., . . . . . bid?ch The most frequently encountered atomic orbitals 1n this text are s orbitals - . (spherically symmetrical) and p orbitals (“dumbbell”—shaped). CWWGWATIW Boundary surface of an s orbital Boundary surface of a p orbital with carbon at its center. with carbon at its center 44 CHAPTER ONE C Section 1.2 Some {babes . Section 1.3 Cw numr ‘30 0155) WW5 'DOT Smucmzes 0 Section 1.4 Em» Oar/013115 ‘, sweet; / Demetri I Tran? LE . Section 1.5 ewcmoro eemw Wt “379% (’50st . Section 1.6 FfimMWLcwmwe 6mm) Don/rem '_.- tL Oxv Lowe 9:75 « iii genome aflé . Section 1.7 Chemical Bonding An ionichond is the force of electrostatic attraction between two oppo— sitely charged ions. Atoms at the upper right of the periodic table, espe— cially fluorine and oxygen, tend to gain electrons to form anions. Ele- ments toward the left of the periodic table, especially metals such as sodium, tend to lose electrons to form cations. Ionic bonds in which car— bon is the cation or anion are rare. The most common kind of bonding involving carbon is covalent bond- ing. A covalent bond is the sharing of a pair of electrons between two atoms. Lewis structures are written on the basis of the octet rule, which limits second-row elements to no more than 8 electrons in their valence shells. In most of its compounds, carbon has four bonds. ’37. \HN—é—(llj—QfiH H H Each carbon has four bonds in ethyl alcohol; oxygen and each carbon are surrounded by eight electrons. Many organic compounds have double or triple bonds to carbon. Four electrons are involved in a double bond; six in a triple bond. 5 S 7’ H\ _ /H 3/ P U? mic-R H—C=C——H H H Ethylene has a carbon—carbon double bond; acetylene has a carbon—carbon triple bond. ' When two atoms that differ in electronegativity are covalently bonded, the electrons in the bond are drawn toward the more electronegative ele- ment. \\+—+ 5+ 5— C F / The electrons in a carbon~fluorine bond are drawn away from carbon, toward fluorine. Counting electrons and assessing charge distribution in molecules is essential to understanding how structure affects properties. A particular atom in axLewis structure may be neutral, positively charged, or nega- tively charged. The formal charge of an atom in the Lewis structure of a molecule can be calculated by comparing its electron count with that of the neutral atom itself. ' Formal Charge = (number of electrons in neutral atom) — (number of electrons in unshared pairs) -- % (number of electrons in covalent bonds) ‘ Table 1.4 in this section sets forth the procedure to be followed in writ— ing Lewis structures for organic molecules. It begins with experimentally Section 1.8. .Section 1.9 ' .Section 1.10 ' shell electrompair repulsions. A tetrahedral arrangement gives the max- ‘ imum separation of four electron pairs (left); a trigonal planar arrange- 1.20 Summary determined information: the molecular formula and the constitution (order in which the atoms are connected). I? ‘1” H—c—C—o—H H The Lewis structure of acetic acid Different compounds that have the same molecular formula are called isomers, If they are different because their atoms are connected in a dif- ferent order, they are called constitutional isomers. :6 HH / Formamide (left) and formaldoxime (right) are constitutional isomers; both have the same molecular formula (CH3NO), but the atoms are con- nected in a different order. Many molecules can be represented by two or more Lewrs structures that mfigfmw differ only in the placement of electrons. In such cases the electrons are {we ‘ (5 delocalized, and the real electron distribution is a composite of the con- i ‘ ' Um tributing Lewis structures, each of which is called a resonance form. The rules for resonance are summarized in Table 1.5. ' O\C—N <——> \C—N+/ / '\ / \ H H H H TwolLewis structures (resonance forms) of formamide; the atoms are connected in the same order, but the arrangment of the electrons is different. The shapes of molecules can often be predicted On the basis of valence View ment is best for three electron pairs (center), and a linear arrangement for} two electron pairs (right). \ 45 46 CHAPTER ONE Chemical Bonding . Section 1.11 Knowing the shape of a molecule and the polarity of its various bonds DWEHJ; Mom-5131 allows the presence or absence of a molecular dipole moment and its direction to be predicted. H/(i)\H 0:6:0 Both water and carbon dioxide havepolar bonds, but water is a polar molecule and carbon dioxide is not. . Section 1.12 Both modern theories of bonding, valence bond and molecular orbital ' — *- CWPVLWT EDD")! 10% theory, are based on the wave nature of an electron. Constructive inter- THCZO $55 ‘- ference between the electron wave of one atom and that of another gives ' VW BOND a region between the two atoms in which the probability of sharing an MQLECOW @015 \T‘Pflv electron is high—a bond. . Section 1.13 In valence bond theory a covalent bond is described in terms of in—phase overlap of a half—filled orbital of one atom with a half—filled orbital .of another. Overlap of two p orbitals along internuclear axis gives a a bond. . Section 1.14 In molecular orbital theory, molecular wave functions (MOS) are approx— imated by combining the wave functions of the molecule’s atoms (A03). The number of MOs must equal the number of A03 in the molecule’s atoms. Ll . Section 1.15 Bonding in methane is most often described by an orbital hybridization ‘l model, which is a modified form of valence bond theory. Four equiva- P‘ ’— CMH lent sp3 hybrid orbitals of carbon are generated by mixing the 2:, 2px, [‘1 217),, and 2132 orbitals. The C—H cr bonds are formed by overlap of each - ’ half-filled Sp3 hybrid orbital with a half—filled hydrogen ls orbital. [email protected]%ATWD stew/roan £7 3133 Overlap of an sp3—hybridized orbital of carbon with I the 2s orbital of hydrogen to give a C—H <7 bond. 0 Section 1.16 The carbon—carbon bond in ethane (CH3CH3) is a 0 bond generated by U U overlap of an Sp3 orbital of one carbon with an sp3 orbital of the other. i t ' n;eve~m ( l ——__+ H H Overlap of an sp3—hybridized orbital of each of two carbon atoms to give a C—C 0 bond. 1.20 Summary - 47 . Section 1.17 Carbon is sgz-hybridized in ethylene, and the doubl: bond is considered Hqgsu D\%|A(T10g0 to have a 0 component and a ’lT component. The Sp hybridization state 1, . . -_ of carbon is derived by mixing the 25 and two of the three 2p orbitals. STE/3‘91: 3 P7 Three equivalent sp2 orbitals result, and the axes of these orbitals are S?' coplanar. Overlap of an sp2 orbital of one carbon with an Sp2 orbital of another produces a 0 bond between them. Each carbon still has one unhy- bridized p orbital available for bonding, and “side—by-side” overlap of the , p orbitals of adjacent carbons gives a 1T bOnd between them. DOUBLE ’6qu 10'“ HT The 1r bond in ethylene generated by overlap of p orbitals of adjacent carbons C Section 1.18 Carbon is sp-hybridized in acetylene, and the triple bond is of the'o + g _ _ _ "IT + 17 type. The 23 orbital and one of the 2p orbitals combine to give ififzflub\ Ep/flo-w two equivalent sp orbitals that have their axes in a straight line. A 0' bond STE-RAG 1*“ 9- :7 between the two carbons is supplemented by two 7r bonds formed by SF overlap of the remaining half-filled p orbitals. l~t~Q£Q-H “H’an Bowo HT 831T The triple bond of acetylene has a a bond component and two 17 bonds; the two ’1T bonds are shown here and are perpendicular to each other. of bondiinw area’l ‘usedin or anic chmistr .ewis structres are used the most, MO descriptions the least. All will be used in this text. 8cme “H' Emmeotc Girom vow twggtm-gpflqow 1 Llwb‘fil’b SP 3 Tetme tame/ire epa’ Ll “T (area 1% rm L, - 3??” ...
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