VALENCE ORBITALS 21 IIIB IVB VB VIB VIIB-VIIIB IB IIB 3456789101112 ) Figure 1.44.(b)A block outline showing the Roman numeral American ABA designation nPC gai forof e Elements in Group IA are Saes ad those in Group IA are salled Recently,the Interational Union of Pure and Applied Chemistry (IUPAC)rec- ommended a version of the Periodic Table in which the A and B designations are eliminated,the Roman numerals of the columns are replaced with Arabic numerals, and the columns are numbered from I to 18.These column numbers make it possi- ble tos ach of the outer transition metak ooo le.the triads of respectively,members of Groups version has many advantages;for example,itin inates the ambiguity of the definition of transition metals as well as the group assignments of H and He.It does not,however,indicate a group number assignment to any of the two rows of inner transition metals consisting of 14 elements each (which would require 32 instead of 18 groups),nor does it provide the chemical information,for example,the number of valence electrons in each group.that is provided by the older labels.Thus,the valuable advantage of correlating the B group with the same num- ber A group inherent in the ABA for insta ce,the e fact that there five val Group VB).Neventheles the TUincrein aan 1.45 VALENCE ORBITALS The orbitals of an atom that may be involved in bonding to other atoms.For the main group or representative elem nts these are the e ns or ns+np orbitals,where n is the
VALENCE ORBITALS 21 shell and their group Roman number corresponds to the number of electrons in this shell, for example, Ca(IIA), Al(IIIA), C(IVA), and so on. Elements in Group IA are called alkali metals and those in Group IIA are called alkaline earth metals. Recently, the International Union of Pure and Applied Chemistry (IUPAC) recommended a version of the Periodic Table in which the A and B designations are eliminated, the Roman numerals of the columns are replaced with Arabic numerals, and the columns are numbered from 1 to 18. These column numbers make it possible to assign each of the outer transition metals to a separate group number, thus, for example, the triads of Group VIIIB transition metals: Fe, Co, Ni; Ru, Rh, Pd; and Os, Ir, Pt in Fig. 1.44a become, respectively, members of Groups 8, 9, and 10 in the IUPAC version. This version has many advantages; for example, it eliminates the ambiguity of the definition of transition metals as well as the group assignments of H and He. It does not, however, indicate a group number assignment to any of the two rows of inner transition metals consisting of 14 elements each (which would require 32 instead of 18 groups), nor does it provide the chemical information, for example, the number of valence electrons in each group, that is provided by the older labels. Thus, the valuable advantage of correlating the B group with the same number A group inherent in the ABA system is lost, for instance, the fact that there are five valence electrons in the structure of both nitrogen (Group VA) and vanadium (Group VB). Nevertheless the IUPAC version is gaining increasing acceptance. 1.45 VALENCE ORBITALS The orbitals of an atom that may be involved in bonding to other atoms. For the main group or representative elements, these are the ns or ns np orbitals, where n is the 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 IIA (b) IA IIIB IIIA IVB IVA VB VA VIB VIA VIIB VIIA VIIIB VIIIA IB IIB Figure 1.44. (b) A block outline showing the Roman numeral American ABA designation and the corresponding Arabic numeral IUPAC designation for families of elements in the Periodic Table. c01.qxd 5/17/2005 5:12 PM Page 21
22 ATOMIC ORBITAL THEORY quantum number of the highest occupied orbital;for the outer transition metals. these are the(n-1)d+ns orbitals;and for the inner transition metals,these are the (n-2)f+ns orbitals.Electrons in these orbitals are valence electrons. Example.The valence orbitals occupied by the four valence electrons of the car bon atom are the 2s+2p orbitals.For a 3rd row element such as Si (atomic num- ber 14)with the electronic configuration [1s22s22p5]3s23p2,shortened to [Ne]3s23p2,the 3s and 3p orbitals are the valence orbitals.For a 4th row (n=4) element such as sc (atomic number 21)with the electronic configuration larl 3d4s2,the valence orbitals are 3d and 4s,and these are occupied by the thre valence In the fo ion of coordinatio ade of low est-energy vacant orbitals,and because ese are invo ved in bo may be considered vacant valence orbitals.Coordination complexes are common in transition metals chemistry. 1.46 ATOMIC CORE (OR KERNEL) The electronic structure of an atom after the removal of its valence electrons. Example.The atomic core structure consists of the electrons making up the noble gas or pseudo-noble gas structure immediately preceding the atom in the Periodic Table.A seudo-noble gas configuration is one having all the electrons of the noble for the oute als the 10 electr sin completely filled itals;and for the inne transitio e gas co nguratio are not considered valence electrons.The core structure of Sc,atomic number 21,is that corresponding to the preceding rare gas,which in this case is the Ar core.For Ga,atomic number 31,with valence electrons 4s24p,the core structure consists of the pseudo-rare gas structure ([Ar]3d10). 1.47 HYBRIDIZATION OF ATOMIC ORBITALS The mathematical mixing of two or more different orbitals on a given atom to give the same number of new orbitals,each of which has some of the character of the nent orbitals.Hybridization s that the rbitals to b d are sim r in energy The re ybr rbita tional c and when use ed to bon with atomic orbi ls of other atoms,they help to determine the shape of the molecule formed. sporbitals(tetrahedral).The mixing of the 2s orbital of carbon with its 2p,to give two carbon sp orbitals is shown pictorially in Fig.1.47.These two hybrid atomic orbitals have the form=(s+p)and 2=(s-p)
quantum number of the highest occupied orbital; for the outer transition metals, these are the (n 1)d ns orbitals; and for the inner transition metals, these are the (n 2)f ns orbitals. Electrons in these orbitals are valence electrons. Example. The valence orbitals occupied by the four valence electrons of the carbon atom are the 2s 2p orbitals. For a 3rd row element such as Si (atomic number 14) with the electronic configuration [1s22s22p6]3s23p2, shortened to [Ne]3s23p2, the 3s and 3p orbitals are the valence orbitals. For a 4th row (n 4) element such as Sc (atomic number 21) with the electronic configuration [Ar] 3d14s2, the valence orbitals are 3d and 4s, and these are occupied by the three valence electrons. In the formation of coordination complexes, use is made of lowest-energy vacant orbitals, and because these are involved in bond formation, they may be considered vacant valence orbitals. Coordination complexes are common in transition metals chemistry. 1.46 ATOMIC CORE (OR KERNEL) The electronic structure of an atom after the removal of its valence electrons. Example. The atomic core structure consists of the electrons making up the noble gas or pseudo-noble gas structure immediately preceding the atom in the Periodic Table. A pseudo-noble gas configuration is one having all the electrons of the noble gas, plus, for the outer transition metals, the 10 electrons in completely filled (n 1)d orbitals; and for the inner transition metals, the noble gas configuration plus the (n 2)f 14, or the noble gas plus (n 1)d10(n 2)f 14. Electrons in these orbitals are not considered valence electrons. The core structure of Sc, atomic number 21, is that corresponding to the preceding rare gas, which in this case is the Ar core. For Ga, atomic number 31, with valence electrons 4s2 4p1 , the core structure consists of the pseudo-rare gas structure {[Ar]3d10}. 1.47 HYBRIDIZATION OF ATOMIC ORBITALS The mathematical mixing of two or more different orbitals on a given atom to give the same number of new orbitals, each of which has some of the character of the original component orbitals. Hybridization requires that the atomic orbitals to be mixed are similar in energy. The resulting hybrid orbitals have directional character, and when used to bond with atomic orbitals of other atoms, they help to determine the shape of the molecule formed. Example. In much of organic (carbon) chemistry, the 2s orbital of carbon is mixed with: (a) one p orbital to give two hybrid sp orbitals (digonal linear); (b) two p orbitals to give three sp2 orbitals (trigonal planar); or (c) three p orbitals to give four sp3 orbitals (tetrahedral). The mixing of the 2s orbital of carbon with its 2py to give two carbon sp orbitals is shown pictorially in Fig. 1.47. These two hybrid atomic orbitals have the form φ1 (s py) and φ2 (s py). 22 ATOMIC ORBITAL THEORY c01.qxd 5/17/2005 5:12 PM Page 22
NONEQUIVALENT HYBRID ATOMIC ORBITALS 23 s+Py add S-Py 2 Figure 1.47.The etwo hybrid sp atomic shaded and unshaded area represent obes of different mathematical signs. 1.48 HYBRIDIZATION INDEX This is the superscripton the p in an sp*hybrid orbital:such an orbital possesses [x/(1+x)](100)percent p character and [1/(1+x)](100)percent s character. The hybridiation index of an sporbita is(p-character)for an orbital,it is 0.894(47.2%p-character). 1.49 EQUIVALENT HYBRID ATOMIC ORBITALS A set of hybridized orbitals,each member of which possesses precisely the same value for its hybridization index. Example.If the atomic orbitals 2s and 2p,are distributed equally in two hybrid orbitals,each resulting orbital will have an equal amount of s and p character;that is,each orbital will be sp (sp00)(Fig.1.47).If the 2s and two of the 2p orbitals are distributed equally a nong three hybrid orbitals.each of the three e quivalent orbitals will bes(Fig. 1.49).Combinin ith thr gives four equivalent hybri of the oitals has an saual amout of s character.I+1025%.and an equal amount of p character,[3/(1 +3)]X 100%=75%. 1.50 NONEQUIVALENT HYBRID ATOMIC ORBITALS The hybridized orbitals that result when the constituent atomic orbitals are not
1.48 HYBRIDIZATION INDEX This is the superscript x on the p in an spx hybrid orbital; such an orbital possesses [x/(l x)] (100) percent p character and [1/(1 x)] (100) percent s character. Example. The hybridization index of an sp3 orbital is 3 (75% p-character); for an sp0.894 orbital, it is 0.894 (47.2% p-character). 1.49 EQUIVALENT HYBRID ATOMIC ORBITALS A set of hybridized orbitals, each member of which possesses precisely the same value for its hybridization index. Example. If the atomic orbitals 2s and 2pz are distributed equally in two hybrid orbitals, each resulting orbital will have an equal amount of s and p character; that is, each orbital will be sp (s1.00p1.00) (Fig. 1.47). If the 2s and two of the 2p orbitals are distributed equally among three hybrid orbitals, each of the three equivalent orbitals will be sp2 (s1.00p2.00) (Fig. 1.49). Combining a 2s orbital equally with three 2p orbitals gives four equivalent hybrid orbitals, s1.00p3.00 (sp3 ); that is, each of the four sp3 orbitals has an equal amount of s character, [1/(1 3)] 100% 25%, and an equal amount of p character, [3/(1 3)] 100% 75%. 1.50 NONEQUIVALENT HYBRID ATOMIC ORBITALS The hybridized orbitals that result when the constituent atomic orbitals are not equally distributed among a set of hybrid orbitals. NONEQUIVALENT HYBRID ATOMIC ORBITALS 23 add subtract s s + py s − py py φ1 φ2 Figure 1.47. The two hybrid sp atomic orbitals, φ1 and φ2. The shaded and unshaded areas represent lobes of different mathematical signs. c01.qxd 5/17/2005 5:12 PM Page 23
24 ATOMIC ORBITAL THEORY Example.In hybridizing a 2s with a 2p orbital to form two hybrids,it is possible to put more p character and less s character into one hybrid and less p and more s into the other.Thus,in hybridizing an s and a p.orbital,it is possible to generate one hybrid that has 52.8%p (sp)character.The second hybrid must be 47.2%p and is therefore spo9(/+r)lx 100%=472%:r=089).Such noneauivalent car oxygen h s mo re p charac a lone pair of electrons.If dissimilar atoms are bonded to a carbon atom,the sp hybrid orbitals will always be nonequivalent. Figure 1.49.The three hybrid sp2 atomic orbitals (all in the same plane). Acknowledgment.The authors thank Prof.Thomas Beck and Prof.William Jensen for helpful comments. SUGGESTED READING See,for example The Educypedia (The Educational Encyclopedia)http://users.telenet.be Mar s Oxfond Unisniy Pr Lonon.19s Coulson,C.A.Valence.Oxford University Press:London,1952. Douglas,B.MeDaniel,D.H.;and Alexander,J.J.Concepts and Models of Inorganie Chemistry.3rd ed.John Wiley Sons:New York.1994. Gamow .G.and Cleveland,J.M.Physics.Prentice-Hall:Englewood Cliffs.NJ.1960. Jensen.W.B.Computers Maths.Appl..12B.487 (1986):J.Chem.Ed.59.634 (1982) Pauling,L.Nature of the Chemical Bond,3rd ed.Comell University Press:Ithaca,NY,1960
Example. In hybridizing a 2s with a 2p orbital to form two hybrids, it is possible to put more p character and less s character into one hybrid and less p and more s into the other. Thus, in hybridizing an s and a pz orbital, it is possible to generate one hybrid that has 52.8% p (sp1.11) character. The second hybrid must be 47.2% p and is therefore sp0.89 ([x/(l x)] 100% 47.2%; x 0.89). Such nonequivalent carbon orbitals are found in CO, where the sp carbon hybrid orbital used in bonding to oxygen has more p character than the other carbon sp hybrid orbital, which contains a lone pair of electrons. If dissimilar atoms are bonded to a carbon atom, the sp hybrid orbitals will always be nonequivalent. Acknowledgment. The authors thank Prof. Thomas Beck and Prof. William Jensen for helpful comments. SUGGESTED READING See, for example, The chemistry section of Educypedia (The Educational Encyclopedia) http://users.telenet.be/ educypedia/education/chemistrymol.htm. Atkins, P. W. Molecular Quantum Mechanics, 2nd ed. Oxford University Press: London, 1983. Coulson, C. A. Valence. Oxford University Press: London, 1952. Douglas, B.; McDaniel, D. H.; and Alexander, J. J. Concepts and Models of Inorganic Chemistry, 3rd ed. John Wiley & Sons: New York, 1994. Gamow, G. and Cleveland, J. M. Physics. Prentice-Hall: Englewood Cliffs, NJ, 1960. Jensen, W. B. Computers Maths. Appl., 12B, 487 (1986); J. Chem. Ed. 59, 634 (1982). Pauling, L. Nature of the Chemical Bond, 3rd ed. Cornell University Press: Ithaca, NY, 1960. For a description of the f orbitals, see: Kikuchi, O. and Suzuki, K. J. Chem. Ed. 62, 206 (1985). 24 ATOMIC ORBITAL THEORY 120° Figure 1.49. The three hybrid sp2 atomic orbitals (all in the same plane). c01.qxd 5/17/2005 5:12 PM Page 24
2 Bonds Between Adjacent Atoms: Localized Bonding,Molecular Orbital Theory Chemical Bond Covalent Bond 3 Localized Two-Center.Two-Electron(2c-2e)Bond:Electron Pair Bond 2 Octet Rul 30 210 Oxidation Number (Oxidation State) 211 Formal Charge 2 12 Nonpolar Covalent Bond 2.13 Dipole Moment 2.14 Dipole Moments of Polyatomic Molecules;Vectorial Addition of Dipole Moments 2.15 Polar Covalent Bond:Partially lonic Bond 2.16 lonic Bond 2.17 Single,Double,and Triple Bonds 2.18 Morse Curve 20 b ciation Energy Do 223 2 Ionic Radi nd r 6677389 25 der Waals Radiu 6 Coordinate Covalent Bond (Dative Bond) 227 Hydrogen Bond 40 228 Valence Shell Electron Pair Repulsion(VSEPR) 220 Molecular Orbitals 2.30 Molecular Orbital (MO)Theory 2.31 Bonding Molecular Orbitals 2.32 Antibonding Molecular Orbitals 2.33 Linear Combination of Atomic Orbitals (LCAO) 2.34 Basis Set of Orbitals 25
2 Bonds Between Adjacent Atoms: Localized Bonding, Molecular Orbital Theory 2.1 Chemical Bond 27 2.2 Covalent Bond 28 2.3 Localized Two-Center, Two-Electron (2c-2e) Bond; Electron Pair Bond 28 2.4 Valence Bond (VB) Theory 28 2.5 Lone Pair Electrons 28 2.6 Lewis Electron (Dot) Structures 28 2.7 Octet Rule 29 2.8 Electronegativity 29 2.9 Valence, Ionic Valence, Covalence 30 2.10 Oxidation Number (Oxidation State) 31 2.11 Formal Charge 32 2.12 Nonpolar Covalent Bond 32 2.13 Dipole Moment 33 2.14 Dipole Moments of Polyatomic Molecules; Vectorial Addition of Dipole Moments 33 2.15 Polar Covalent Bond; Partially Ionic Bond 34 2.16 Ionic Bond 35 2.17 Single, Double, and Triple Bonds 35 2.18 Morse Curve 35 2.19 Bond Length d0 36 2.20 Bond Dissociation 36 2.21 Bond Dissociation Energy D0 37 2.22 Bond Angle 37 2.23 Atomic Radius r0 37 2.24 Ionic Radius r and r 38 2.25 van der Waals Radius 39 2.26 Coordinate Covalent Bond (Dative Bond) 40 2.27 Hydrogen Bond 40 2.28 Valence Shell Electron Pair Repulsion (VSEPR) 41 2.29 Molecular Orbitals 42 2.30 Molecular Orbital (MO) Theory 43 2.31 Bonding Molecular Orbitals 43 2.32 Antibonding Molecular Orbitals 43 2.33 Linear Combination of Atomic Orbitals (LCAO) 43 2.34 Basis Set of Orbitals 44 25 The Vocabulary and Concepts of Organic Chemistry, Second Edition, by Milton Orchin, Roger S. Macomber, Allan Pinhas, and R. Marshall Wilson Copyright © 2005 John Wiley & Sons, Inc. c02.qxd 5/17/2005 5:13 PM Page 25