ORBITALS and MOLECULAR REPRESENTATION

1 ORBITALSandMOLECULARREPRESENTATIONThe contents of this module were developed under grant award # P116B-001338 from the Fund for the Improve-ment of Postsecondary Education (FIPSE), United States Department of , those contents do not necessarily represent the policy of FIPSE and the Department of Education, and you should not assume endorsement by the Federal STEPHEN THOMPSONMR. JOE STALEYORBITALS AND MOLECULAR REPRESENTATIONCONTENTS2 Atomic ORBITALS (n = 1)3 Atomic ORBITALS (n = 2)4 Atomic ORBITALS (n = 3)5 Hybrid Atomic ORBITALS (sp)6 Hybrid Atomic ORBITALS (sp2)7 Hybrid Atomic ORBITALS (sp2)8 Hybrid Atomic ORBITALS (sp3)9 Overlapping ORBITALS (Bonding And Antibonding)10 Orbital Pictures For H And H211 Difl uorine12 Carbon ORBITALS (Methane And Ethane)13 Carbon ORBITALS (Ethene)14 Carbon ORBITALS (Ethene)15 Carbon ORBITALS (Ethyne)16 Carbon ORBITALS (Ethyne)17 Carbon ORBITALS (Benzene)18 Carbon ORBITALS (Benzene)

2 19 Several Representations Of Molecules20 Several Representations Of Benzene21 Representations Of Molecules22 Representations Of Molecules23 Representations Of MoleculesORBITALS AND MOLECULAR REPRESENTATIONATOMIC ORBITALSn = 22s1sWe denote the phase of the wave function by color, using light red for one phase and green for the opposite phase. Many books assign these phases plus or minus signs but the only real meaning is that they are oppo-site. Neither phase is plus or minus anything on its own but they are only opposite to each other. Sometimes when we are not concerned with phase we will draw the ORBITALS as a slightly reddish picture above shows the spherically symmetric 1s orbital in the green phase. Sometimes it is more con-venient not to show the phase, in which case we can use a greyed REPRESENTATION , as shown = 11sl = 0l = 0l1sIt is also possible to show the orbital as a simple if you are drawing his by hand, the loop does not have to be an exact are some boxes for you to practice drawing s ORBITALS in, although you do not really need we proceed developing atomic and MOLECULAR orbit-als we will show various forms of can draw the two loops for 2s in the box Lewis diagrams and energy level structures can show connectivity and energy relationships of mol-ecules, they do not show the shape of the molecules.

3 For this we need to picture atomic and MOLECULAR = 0l = 0l2 ATOMIC ORBITALS2px2py2pzl = 1xyzn = 2 This is an accurate REPRESENTATION of a 2px is a common picture of a px orbitalThis simplifi ed px orbital is often hand drawn version does not have to be this box to draw a can combine all three p ORBITALS in a three dimensional these axes to draw all three p AND MOLECULAR REPRESENTATION3 ATOMIC ORBITALSn = 33s3px3pz3py3dxy3d3dxz3d3dyz3dx2--y23d3d z2l = 2l = 2ll = 1l = 1ll = 0l = 0lDraw the 3s orbitalin the boxat PictureGrayscaleLoop Diagram3dxy3dxz3dyz3dx2--y23dz2 ORBITALS AND MOLECULAR REPRESENTATION4 HYBRID ATOMIC ORBITALS +sp+sp ORBITALS are a combination, or hybrid, of an s and a p orbital. In addition there will be two remaining unhy-bridized p ORBITALS orthogonal to each other and to the line joining the two hybrid sp x sp2 x sp + 2p2 x sp + 2 x 2pNOTE:When we write 2 x sp we mean two instances of sp and when we write 2p we mean one instance of a 2p ++sp2 x sp2 x sp + 2 x 2pWe can also draw these ORBITALS as simplifi ed is useful to draw the sp hybrid ORBITALS will recall that our color convention is to show the phases of the atomic ORBITALS with red and green.

4 We shall show the phases of hybrid ORBITALS in blue and sp hybridized atom uses one s and one p orbital to make two sp hybrid ORBITALS ; there are two remaining p we show the phase pictures of combining the sp hybrid ORBITALS with fi rst one and then both of the remaining p DiagramAxes for you to draw the loop will also see these ORBITALS in greyscale, without phases. We use reddish grey for unhybridized ORBITALS and plain gray for for hybridized x spIt is common to show hybrid ORBITALS without the small AND MOLECULAR REPRESENTATION5++HYBRID ATOMIC ORBITALSsp2trigonal view of sp2sp2 hybrid ORBITALS are formed when one 2s orbital combines or hybridizes with two 2p ORBITALS in the shapes and arrangement 120 120 2s2p2p++You will often see a simple presentation of the sp2 important points to know about are that the three bonds are in a plane and that they are 120 can also draw the sp2 hy-brid orbital as simple the loop version of the trigonal set of sp2 orbit-als in the box at greyscale:The pictures below are trigonal views of sp2.

5 Trigonal means arranged in triangular form in a AND MOLECULAR REPRESENTATION6planar view of sp2In addition to the trigonal set of hybridized ORBITALS there is a remaining 2p orbital that will point above and below the trigonal + 2p+2pHYBRID ATOMIC ORBITALSsp2 First we show the phase 120 120 120 xyyzHere we show the AND MOLECULAR REPRESENTATION7+++HYBRID ATOMIC ORBITALSsp32s2p2p2psp3sp3sp3sp3sp3 ORBITALS are formed by the hybridization of a 2s orbital and three 2p ORBITALS have a tetrahedral AND MOLECULAR REPRESENTATION8 OVERLAPPING ORBITALSC hemical bonds are formed from the overlapping of atomic ORBITALS having the same phase. Overlapping ORBITALS of opposite phase form antibond-ing ORBITALSANTIBONDING ORBITALSs + s s - s *s + p s - p *p + p p - p *p + p p - p * ORBITALS AND MOLECULAR REPRESENTATION9 ENERGY1sA1sBHAHBH21sA + 1s + 1sA + 1sAB1sA - 1sA - 1sABORBITAL PICTURES FOR H AND H2 HYDROGEN ORBITALBONDING ORBITALANTIBONDING ORBITALor1s1s1sA + 1sA + 1sAB1sA + 1sA + 1sAB1sA - 1sA - 1sAB1sA - 1sA - 1sABWe can also make orbital energy levels for AND MOLECULAR REPRESENTATION10 DIFLUORINEENERGY1sA22sA22pA51sB22sB22pB5 FBFA2pA + 2pA + 2pAB2pA - 2pA - 2pAB12In picture 1 we show the MOLECULAR orbital structure of picture 2 we show the overlapping p ORBITALS , which form the bond between the two fl uorine atoms, in red and green gradients.

6 The dashed lines show the remaining p ORBITALS which do not take part in the bonding. *xyzxyzConstruct the MOLECULAR orbital diagram for the p the s and p AND MOLECULAR REPRESENTATION11 CARBON ORBITALSM ethaneEthaneMETHANE AND ETHANECHHHHCH4 CCHHHHHHC2H612 Color conventions:Hydrogen atoms are shown in atomic ORBITALS are shown in blue and p ORBITALS are shown in red and Conventions:Hybrid ORBITALS are shown in atomic ORBITALS are shown in methane and ethane, all of the bonds are bonds, which means that they are formed by ORBITALS overlapping along a direct line between the nuclei of the two bonding AND MOLECULAR REPRESENTATION12 CARBON ORBITALSETHENEC2H4 Picture 3 shows the sigma bond formed by overlaping sp2 ORBITALS between the two carbon atoms of ethene.

7 The other sp2 ORBITALS are shown in dashed 4 shows the bond between the p ORBITALS of the carbon atoms. The pi bond is the overlap of the two red spheres and is actually coming out of the plane of the paper. 34 5 Picture 5 is similar to picture 4 but rotated 900 around the bond, so that the overlapping p ORBITALS which form the bond are shown with the red phase above the bond and with the green phase rotationORBITALS AND MOLECULAR REPRESENTATION13 Ethene in the trigonal from above the trigonal plane with the hydrogenatoms shown. The bond angles and relative bond lengths are ORBITALSC2H4 Ethene from above the trigonal plane. The carbon atoms and ORBITALS are rotationCCHHHHCCHHHH678 ETHENEC2H4 ORBITALS AND MOLECULAR REPRESENTATION14We have added the other bond which, as it needs to be orthogonal to both the fi rst bond and to the bond, must be imagined as coming out of the ORBITALSThis drawing shows the sigma bond between two carbon this drawing we have added a pi bond to the ethyne.

8 91011 ORBITALS AND MOLECULAR REPRESENTATION15 Ethyne in the trigonal plane, but with the hydrogen atoms ORBITALSU nlike ethene, ethyne has the same form and ap-pearance when rotated 900 around the C-C AND MOLECULAR REPRESENTATION16 CARBON ORBITALSBENZENEC6H6 The sigma bond ring of sigma bond ring of benzene with the additional sp2 is the ring of bonds whose ORBITALS are shown in picture 15 CCCCCC This is a former represen-tation of the resonance structure of is a contemporary REPRESENTATION of the resonance structure of AND MOLECULAR REPRESENTATION17To which we have now added the pi ORBITALS above the carbon ORBITALS viewed from the the hydrogen atoms to picture 16 we view benzene from above, from the side, complete with hydrogen rotation16171819900 rotationCARBON ORBITALS18 BENZENEC6H6 This picture illustrates the delocalization of the six 2p electrons in the benzene molecule.

9 These six electons are shared collectively among all six of the carbon AND MOLECULAR REPRESENTATIONSEVERAL REPRESENTATIONS OF 95nmETHANEC2H6 ETHENEC2H4 CHHHHCHHCHHHHCETHYNEC2H2 CHHC120 120 111 154 nm109 nm134 nm120 nm106 nmAll orbitalsTextbooktetrahedronStructuralSpa cefi llingBall andstickAll orbitalsTextbook orbitalsStructuralSpacefi llingBall andstickBall andstickSpacefi llingStructuralTextbook orbitalsAll ORBITALS but no hydrogen (for clarity)Looking along the trigonal planeAll orbitalslooking down on the trigonal planeAll orbitalsStructuralTextbook orbitalsTextbook orbitalsSpacefi llingBall andstickORBITALS AND MOLECULAR REPRESENTATION19 SEVERAL REPRESENTATIONS OF BENZENEBENZENEC6H6 CCCCCCCCCCCCHHHHHH140 nm110 nm120 Benzene showing all orbitalsBenzene textbook bondsBenzene textbook and bondsfrom the sideBenzene space fi llingBenzene ball and stickBenzene structuralcarbon ringBenzene structural carbon ringand hydrogensORBITALS AND MOLECULAR REPRESENTATION20 You can easily draw ORBITALS , bonds and by drawing a circle, like this:This is an s draw a circle (an s orbital) in the draw one circle above another one, like this:This is a p draw a p orbital.

10 (two circles tangent)You draw two overlapping circles in the box is a two s ORBITALS from different atoms overlap, this is called a (sigma) an s and a p orbital overlap, this is a can draw the s and p OF MOLECULESORBITALS AND MOLECULAR REPRESENTATION21 REPRESENTATIONS OF MOLECULESDINITROGENN2 NNAll bonding orbitalsStructuralTextbook orbitalsSpace fi llingBall and stickDIOXYGEN bond bondFor clarity, only the ORBITALS which form the bonds are fi llingBall and stick110 nm121 nmSIMPLIFIED ORBITALSWe have shown MOLECULAR pictures which are as accurate as possible, however such ORBITALS are diffi cult to draw by hand. But a simplifi ed version of them is easy to draw and shows much about mjolecular structure and py orbitala px orbitala pz orbitalan s orbital+x-x+y-y+z-zAll three p orbitalsDraw the bonding ORBITALS for:H2 ONH3 COCO2 ORBITALS AND MOLECULAR REPRESENTATION22 You draw two p ORBITALS side by side and overlapping, forming a draw an sp2 hybridized can draw hybrid ORBITALS like this:You draw an sp hybridized atom in the box are three orthogonal p ORBITALS .