why was hybridization theory developed why is this theory so important and how does it allow the chemist to envision a molecule in three dimensions in this chapter we will explore some of the reasons why hybridization theory was developed a student's ability to take a two-dimensional molecule off the blackboard during lecture and fold it into three dimensions or envision a molecule in three dimensions from a page in a book is arguably one of the most essential skills when learning chemistry the chemistry student who has the ability to visualize molecules in three dimensions is rewarded with a better understanding of chemical properties physical properties and most importantly the ability to predict chemical reactivity understanding how atoms within molecules are oriented in three dimensions requires an understanding of hybridization theory from simple molecules such as ethanol to more complex molecules such as the highly toxic tetrodotoxin the concepts of hybridization are the foundation to our understanding of molecular geometry however looking at a two dimensional lewis structure of molecule affords much information to the scientist for example the overall connection of atoms within the molecular formula after all different structural and geometric isomers can be imagined from relatively simple molecular formulas to introduce the concepts of hybridization we will first focus all of our examples on the carbon atom the basic principles discussed for the carbon atom can also be applied to other elements which are explored in later sections a carbon atom has six electrons in the following configuration 1s2 2s2 2p2 the relative energy electron configuration diagram is another way to visualize where the electrons are located each arrow in this diagram represents one of the individual electrons of carbon however only the valence or outermost electrons are responsible for bond making and bond breaky thus we can ignore the inert noble core electrons which we can represent here is the helium element this abbreviated electron configuration quickly allows one to ascertain that there are four valence electrons it would appear that there are only two unpaired valence electrons capable of forming covalent bonds one in the 2px and one and the 2py orbital however it is well-known that carbon forms a total of four covalent bonds to attain full valency thus all four valence electrons must be involved in bonding hybridization theory was developed in order to better explain the four observed bonds of carbon in addition the hybrid model best explains overall molecular geometry of carbon in other words bond angles in three dimensions can be predicted the possible hybrid combinations for a carbon atom are sp3 sp2 NSP and are explained in detail in subsequent sections let us first start by examining the shapes of the atomic orbitals for carbon the 2's atomic orbital is a sphere and the three 2p atomic orbitals are shaped like dumbbells oriented along the three axes 2px 2py and 2pz think of these four atomic orbitals as three dimensional shapes where you are most likely to find an electron 90 percent of the time [Music] notice that the electrons have access to both lobes for the 2p orbitals starting from the abbreviated electron configuration for carbon one can imagine promoting an electron from the 2's atomic orbital to the unoccupied 2 PZ atomic orbital although we now have four unpaired electrons for bonding we still can't explain the experimentally observed bond angles for a tetravalent carbon thus when we mix the 2's atomic orbital with all three 2p atomic orbitals we create four new degenerate energy hybrid orbitals the shape of the new sp3 hybrid orbital is best characterized as one part s and 3 parts P as with all orbitals think of these hybrid orbitals as in three-dimensional shapes where you can find the electron ninety percent of the time the hybridized carbon now possesses four unpaired valence electrons and is said to be an sp3 hybridized carbon when we superimpose all four sp3 hybrid orbitals on to the carbon atom it becomes quite cumbersome and confusing [Music] thus we simply show how the electrons in the hybrid orbitals are oriented in three dimensions [Music] the four new hybrid orbitals attempt to get as far apart from each other as possible 109.5 degrees think of this as the orbitals attempting to minimize repulsion between them thus they are oriented towards the corners of a tetrahedron with all angles at 109.5 degrees your instructor will often draw the sp3 hybridized carbon on the blackboard as shown the two solid lines in this drawing are in the plane of the board the wedge represents the electron coming out of the plane of the board and the dashed line represents the electron going back behind the plane of the board each of the four sp3 hybrid orbitals contains one electron capable of forming a covalent bond the sp3 hybridized carbon is now capable of forming four covalent bonds here X represents any atom with a valence electron capable of forming a covalent bond because the electron density is symmetrically located about an imaginary line that runs through the two adjacent nuclei we call these bonds Sigma bonds an example of a simple carbon compound with an sp3 hybridized carbon is methane ch4 the ideal bond angles are all 109.5 degrees due to all four equal in size hydrogen atoms attempting to get as far away from each other as possible your instructor will often draw a methane on the blackboard as shown again the two solid lines in this drawing are in the plane of the board the wedge represents one of the hydrogen's coming out of the plane of the board and the dashed line represents one of the hydrogen's going back behind the plane of the board another simple carbon compound that utilizes sp3 carbons is FA from the two dimensional Lewis diagram we see that each carbon has four single bonds thus both carbons are SP 3 hybridized starting with 2 sp3 hybridized building blocks we can start to construct the molecule in three dimensions by forming the C C Sigma bond next the six hydrogen sigma bonds are formed which affords the final 3-dimensional structure for ethane the two-dimensional Lewis diagram for ethane implies that all four bond angles are 90 degrees however employing the basic principles of hybridization theory we see that the bond angles are all nearly 109.5 degrees now that the molecular geometry for ethane in three dimensions has been determined we can begin to examine some of ethane interesting physical properties for example free rotation may occur about the carbon-carbon single bond which allows us to explore simple conformational analysis confirmations are different arrangements of atoms due to these rotations when we place the electron density around each hydrogen atom we see that the hydrogen atoms from adjacent carbons do not touch to make this diagram easier to view we will remove the electron density from two of the hydrogen atoms from the back carbon even though the hydrogen atoms from adjacent carbons do not touch there is torsional strain due to the electron clouds of the adjacent carbon hydrogen bonds which impedes the rotation about the CC bond this gives rise to the staggered and eclipsed confirmations for ethane the difference in relative energy between these two confirmations is approximately 3 kilocalories per mole it may be easier to remember that atoms want to be as far apart from each other as possible think of it as less crowding when molecules are viewed down the CC Sigma bond we call this a Newman projection often you may see your instructor represent the Newman projection on the blackboard as follows [Music] [Music] [Music] when we replace one of the hydrogen atoms with an atom that has a larger atomic radius than hydrogen steric factors will arise which will increase the barrier of rotation as the dihedral angle changes so does the relative stability of the molecule similar to the first step of sp3 hybridization one can imagine promoting an electron from the 2's atomic orbital to the unoccupied 2 PZ atomic orbital mixing the 2's atomic orbital with two of the 2p atomic orbitals creates three new degenerate energy hybrid orbitals the shape of the new sp2 hybrid orbital is best characterized as one part s and 2 parts p as with all orbitals think of these hybrid orbitals as 3-dimensional shapes where you can find the electron 90% of the time the sp2 hybridized carbon now possesses three electrons in hybrid orbitals and one electron in an unhybridized 2 PZ orbital when we superimpose all three sp2 hybrid orbitals with the unhybridized 2 PZ orbital on to the carbon atom it becomes quite cumbersome and confusing thus we simply show how the electrons and the hybrid orbitals are oriented in three dimensions in addition the electron density of the unhybridized p orbital is shrunk to a third of its size for simpler viewing the three new hybrid orbitals attempt to get as far apart from each other as possible again think of this as the hybrid orbitals attempting to minimize electron repulsion thus they are oriented 120 degrees apart your instructor will often draw the sp2 hybridized carbon on the blackboard is shown again remember that solid lines are in the plane of the board wedges are coming out of the plane of the board and dash lines are going back behind the plane of the board before we begin to show how the sp2 hybrid building block takes part in bonding it is important to remember that the electron and the unhybridized 2p orbital as XS 2 both lobes each of the three sp2 hybrid orbitals contains one electron capable of forming a sigma bond thus the sp2 hybridized carbon is now capable of forming three sigma bonds and one PI bond [Music] a simple carbon compound that utilizes sp2 carbons is ethylene from the two dimensional Lewis diagram we see that each carbon forms three sigma bonds and one PI bond thus both carbons are sp2 hybridized starting with 2 SP 2 hybridized building blocks we can begin to construct the molecule in three dimensions by forming the C C Sigma bond next the four carbon hydrogen sigma bonds are formed which affords the planar sigma bond framework for ethylene to form the second bond between the carbons called the pi bond we can imagine that the two adjacent parallel unhybridized to PZ atomic orbitals overlap when they overlap the two electrons can be shared allowing each carbon to attain full valency the two dimensional Lewis diagram for ethylene allows the chemist to view the gross connectivity of the atoms however no information is conveyed about the PI bond when the molecule is represented in three dimensions we see that half of the PI bond is above the plane and the other half of the PI bond is below the plane an understanding of this electron density within a PI bond will become very useful when predicting reactivity of alkenes [Music] [Music] to gain a better understanding of the PI bond we should recall the actual shape of the unhybridized p orbitals when we envision the actual shape of these orbitals overlap between the adjacent P orbitals as possible which allows for the sharing of these two electrons however it is very difficult to draw the molecule this way thus you will often see the PI bond represented in its abbreviated form on the right understanding the PI bond helps us realize why geometric isomers are isolobal geometric isomers have the same gross connectivity but differ only in how the groups are oriented in space due to hindered rotation about the doubly bonded carbons when we draw an imaginary line along the axis of the double bond and then compare groups on each carbon using the cahn-ingold-prelog sequence rules we can determine if the groups of priority are on the same side called the sis isomer often abbreviated Z alternatively the groups of priority can be on opposite sides of the imaginary line called the trans isomer often abbreviated e or inter conversion of the isomers to occur we need to have free rotation about the carbon-carbon double bond if this were to happen it would mean that the PI bond would have to break which requires approximately 70 kilocalories per mole this will cause each carbon to lose full valency due to the 2p orbitals no longer overlapping which will make the alkene unstable or higher in relative energy [Music] thus at room temperature geometric isomers are a syllable similar to the first step of sp3 and sp4 decision one can imagine promoting an electron from the 2's atomic orbital to the unoccupied 2p z atomic orbital mixing the 2's atomic orbital with one of the 2p atomic orbitals causes two new degenerate energy hybrid orbitals the shape of the new SP hybrid orbital is best characterized as one part s and one part P as with all orbitals think of these hybrid orbitals as three-dimensional shapes where you can find the electron ninety percent of the time the SP hybridized carbon now possesses two electrons in hybrid orbitals and two electrons in the unhybridized 2p orbitals but when we superimpose both SP hybrid orbitals with the unhybridized two PZ and two py orbitals on to the carbon atom it becomes quite cumbersome and confusing thus we simply show how the electrons and the hybrid orbitals are oriented in three dimensions in addition the electron density the unhybridized p orbitals is shrunk to a third of their size for simpler viewing the two new hybrid orbitals attempt to get as far apart from each other as possible again think of this as the orbitals attempting to minimize electron repulsions thus they are oriented 180 degrees apart before we begin to show how the SP hybrid building block takes part in bonding it is important to remember that the electrons and the unhybridized 2p orbitals have access to both lobes your instructor will often draw the SP hybridized carbon on the blackboard as shown again solid lines are in the plane of the board shaded lobes are coming out of the plane of the board and dash lines are going behind the plane of the board [Music] each of the two SP hybrid orbitals contains one electron capable of forming a sigma bond the SP hybridized carbon is now capable of forming two sigma bonds and two pi bonds a simple carbon compound that utilizes SP carbons as f-fine or acetylene from the two dimensional Lewis diagram we see that each carbon forms two sigma bonds and two PI bonds thus both carbons are SP hybridized starting with two SP hybridized building blocks we can begin to construct the molecule in three dimensions by forming the si si Sigma bond next the two carbon hydrogen sigma bonds are formed which affords the linear Sigma bond framework for ethane to form the second and third bonds between the carbons called the PI bonds we can imagine that the two pairs of adjacent parallel unhybridized 2p atomic orbitals overlap when they overlap the four electrons can be shared allowing each carbon to attain full valency the two-dimensional Lewis diagram for f-fine allows the chemist to view the gross connectivity of the atoms however no information is conveyed about the PI bonds when a molecule is represented in three dimensions we see that half of each PI bond is above and below a plane an understanding of this electron density within these two pi bonds will become very useful when predicting reactivities of alkynes to gain a better understanding of the two PI bonds we should recall the actual shape of the unhybridized 2p orbitals when we envision the actual shape in these orbitals overlap between the adjacent 2p orbitals as possible which allows for the sharing of these four electrons however it is very difficult to draw the molecule this way thus you will often see the PI bonds represented in the abbreviated form on the right [Music] an easy way to deduce hybridizations is to count groups around a central atom a group is defined as another atom or a lone pair when an atom is surrounded by four three or two groups it will adopt the sp3 sp2 or SP hybridizations respectively a helpful way to remember this is by adding the exponents together that should equal the number of groups around the hybridized atom for SP 3 the exponents add to 4 thus an SP 3 atom has four groups or SP 2 the exponents had to 3 thus an SP two hybridized atom has three groups around it these hybridizations allow the respective number of groups to be as far apart as possible again think of it as all groups attempting to minimize electron repulsion [Music] although we will use the abbreviated hybridized building block shown here for subsequent examples it is important to recall the actual shape of the unhybridized and hybridized lobes on carbon for example the unhybridized lobes were shrunk to a third of their size and we simply showed how the electrons and the hybrid orbitals were oriented in three dimensions so that the carbon building block does not become too cumbersome and confusing a simple carbon compound that utilizes both sp3 and sp4 vines' propylene from the two dimensional Lewis diagram we see that by counting groups we can deduce the hybridization for each carbon atom four groups employ the sp3 hybridised building block and three groups employ the sp2 hybridized building block starting with one SP 3 and 2 SP 2 hybridized building blocks we can start to build the molecule in three dimensions by forming the carbon-carbon Sigma framework next the six carbon hydrogen Sigma bonds are formed followed by the PI bond affording the final three-dimensional molecule notice that the methyl group can freely rotate about the carbon-carbon Sigma bond while the pi bond affords no rotation within a sediment are central atoms that we have not dealt with yet nitrogen and oxygen however we employ the same concept for deducing hybridization simply count groups on these atoms which means we also have to count the lone pairs as groups or groups around nitrogen and four groups around carbon allows us to deduce sp3 hybridization while three groups around the oxygen and carbonyl carbon allows us to employ sp2 hybridized building blocks once all the hybrid building blocks have been deduced we assemble the Sigma bond framework attach the hydrogen atoms and form the double bonds as shown [Music] again we see that the ch3 group can spin freely about the carbon-carbon Sigma bond while the PI bond affords no rotation in addition the nh-2 group can spin freely about the carbon nitrogen Sigma bond now let's look at a compound that utilizes an SP hybrid building block carbon dioxide again from the two dimensional Lewis diagram we see that by Counting groups we can deduce the hybridization for each atom two groups employ the SP hybridized building block and three groups employ the sp2 hybridized building block for both oxygen atoms starting with one SP and sp2 hybridized building blocks we can start to construct the molecule in three dimensions by forming both Co Sigma bonds for both PI bonds to form we need to rotate the oxygen on the right forward so that the adjacent unhybridized 2p orbitals are parallel thus both PI bonds form affording the final three-dimensional molecule notice that the two PI bonds are perpendicular to each other in addition the lone pairs on each oxygen atom are perpendicular to each other [Music] as you become comfortable with the concepts of hybridization you will be able to fold two-dimensional lewis structures into three dimensions in your mind with practice you will also be able to allow the molecule to undergo conformational changes in your mind while predicting the more stable conformer due to steric interactions and other effects here we see that the methyl group prefers to be in the equatorial position thus one of the chair confirmations is favored over the other as we have seen ideal bond angles are obtained from the hybrid building blocks however deviations from ideal bond angles can and do occur in virtually all molecules when groups are not equivalent for example the sp3 hybridized oxygen of water as a lone pair lone pair interaction which will cause the two hydrogen's to become closer than their ideal bond angle of 109.5 degrees about 104 degrees VSEPR valence shell electron pair repulsion theory allows the chemist to make predictions regarding deviations from ideal bond angles a general trend that allows predictions from ideal bond angles is lone pair lone pair interactions or greater than lone pair bonding pair interactions which are greater than bonding pair bonding pair interactions the sp3 hybridized nitrogen within the ammonia molecule has three lone pair bonding pair interactions which will cause the three hydrogen atoms to become closer than their ideal bond angle of 109.5 degrees about 106 degrees [Music] an interesting property of nitrogen is that it has the ability to undergo inversion of configuration demonstrating that hybridizations can transform for this umbrella-like effective happen we see that the nitrogen hybridization appears to change from sp3 to an sp2 like nitrogen and back to sp3 current Berry's predict that there are 200 billion inversions per second for a molecule of ammonia if chemistry is considered to be the central science then hybridization theory may be considered the cornerstone of chemistry after all the student who has the ability to visualize molecules in three dimensions is rewarded with a better understanding of chemical properties physical properties and most importantly the ability to predict chemical reactivity you