Orbital Hybridization Theory PDF

ORBITAL PICTURE OF BONDING: ORBITAL COMBINATIONS, HYBRIDIZATION THEORY, & MOLECULAR ORBITALS LEARNING OBJECTIVES To introduce the basic principles of molecular orbital theory and electronic geometry of molecules. ORBITAL COMBINATIONS Atomic orbitals can be combined and reshaped –much li...

ORBITAL PICTURE OF BONDING: ORBITAL COMBINATIONS, HYBRIDIZATION THEORY, & MOLECULAR ORBITALS LEARNING OBJECTIVES To introduce the basic principles of molecular orbital theory and electronic geometry of molecules. ORBITAL COMBINATIONS Atomic orbitals can be combined and reshaped –much like dough– to make other orbitals of different shapes and properties. There are two basic types of orbitals that can result from such processes. They are: 1. HYBRID ORBITALS. They result from combinations of orbitals within a given atom, either prior to or as bonding with another atom takes place. 2. MOLECULAR ORBITALS. They result from combinations of orbitals between atoms as bonding takes place to form molecules. ORBITAL HYBRIDIZATION THEORY If we look at the valence shell configuration of carbon, we find two paired electrons in the 2s orbital, and two unpaired electrons in the 2pX and 2pY orbitals, one in each: Potential energy 2pX 2py 2pz 2s In order to fulfill the octet rule, carbon must use its 4 valence electrons when bonding to other atoms. However, only unpaired electrons can bond. That means that the two paired electrons occupying the 2s orbital must become unpaired before they can bond. Since the energy gap between the 2s and 2p orbitals is very small, one of the 2s electrons can be promoted to the empty 2p orbital, leading to the following situation: Potential energy 2pX 2py 2pz 2s Now the four electrons appear to be ready for bonding, but there is a problem. The 2p orbitals are known to be at right angles to each other. If bonding occurs in this state, the 3 equivalent p electrons would form 3 equivalent bonds oriented at 90o to each other, and the s electron would form a bond of a different type and orientation from the other three. No such compound exists. The simplest hydrocarbon –methane (CH4)– is known to have tetrahedral geometry, where the four C–H bonds are all equivalent and positioned at 109.5o angles to each other. In addition, there are some carbon compounds where the bond angles are 120o or even 180o. The shapes and relative positions of the valence orbitals in atomic carbon do not explain the shapes and relative positions of the bonds in carbon compounds. HYBRIDIZATION THEORY ATTEMPTS TO EXPLAIN THE ACTUAL SHAPES OF MOLECULES BY INVOKING THE FORMATION OF HYBRID ORBITALS DURING, OR PRIOR TO, THE BONDING PROCESS. Going back to the carbon model with four unpaired electrons in the valence shell, we can take it as a point of departure for formation of hybrid orbitals. The first step is to take either 2, 3, or all four of those orbitals and equalize their energies. Let’s say that we take all four of them and form 4 equivalent new orbitals. These orbitals are now of the same energy, which is intermediate between those of the original 2s and 2p orbitals. At the same time, we cannot name the new orbitals s or p, for they’re neither. We have to find a new name that reflects the fact that they were created from one s orbital and three p orbitals. We will call them sp3 orbitals. The process that leads to their formation is called sp3 hybridization. Potential sp3 hybridization energy 2pX 2py 2pz 2s sp3 sp3 sp3 sp3 All four sp3 orbitals that result from this process are equivalent. That means that they have the same size, shape, and energy. According to VSEPR (valence shell electron pair repulsion) theory, such orbitals will orient themselves in 3-D space to be as far apart from each other as possible. The resulting shape is then a tetrahedron, where the carbon nucleus is at the center and the orbitals point to the corners of the tetrahedron. The ideal angle between orbitals is then 109.5 degrees. sp3 109.5o 3 sp3 sp sp3 When an sp3 hybridized carbon bonds to hydrogen, it forms methane, whose geometry is known to be tetrahedral. H A 3-D representation of methane. The single lines represent bonds that are positioned on the plane of the paper. The C H solid wedge represents a bond coming out of the plane of H the paper towards the front. The broken wedge represents a H bond going behind the plane of the paper towards the back. HYDROCARBONS Hydrocarbons are substances containing only carbon and hydrogen. Hydrocarbons are classified into the following major categories: alkanes, alkenes, alkynes, and aromatic hydrocarbons. In the following pages we will do an overview of the basic characteristics of the first three, but will postpone the study of aromatics until later. ALKANES AND sp3 HYBRIDIZATION OF CARBON Alkanes are hydrocarbons where all the carbon atoms are sp3-hybridized, all bonds are single bonds, and all carbons are tetrahedral. Methane is the simplest alkane, followed by ethane, propane, butane, etc. The carbon chain constitutes the basic skeleton of alkanes. Carbon chains with four or more atoms can be linear or branched. Some examples are shown below including Lewis, molecular, and condensed formulas. Refer to chapter 2 of the Wade textbook for additional examples. Linear alkanes H H H H H H H H H H H C H H C C H H C C C H H C C C C H H H H H H H H H H H methane ethane propane butane CH4 C2H6 C3H8 C4H10 CH4 CH3CH3 CH3CH2CH3 CH3CH2CH2CH3 CH4 CH3 CH3 CH3 CH2 CH3 CH3 CH2 CH2 CH3 Some examples of branched alkanes are shown below. Notice that sometimes Lewis formulas become cumbersome and difficult to write without cluttering. Condensed formulas are more convenient to use in such situations. Branched alkanes CH3 CH3 CH3 H3C C CH3 H3C C CH3 CH3 CH CH2 CH3 H CH3 isobutane isopentane neopentane C4H10 C5H12 C5H12 (CH3)3CH (CH3)2CHCH2CH3 (CH3)4C As can be seen from the above examples, all alkanes have the general formula CnH2n+2 where n is the total number of carbon atoms. This holds regardless of whether the alkane is linear or branched. SIGMA BONDING When atomic orbitals (pure or hybrid) of different atoms overlap to form covalent bonds, they may approach each other in two major ways: head to head, or sideways. Only head to head overlap is possible with s- orbitals because they are spherical. Hybrid orbitals also undergo mostly head to head overlap when forming covalent bonds. p-orbitals, on the other hand, can approach each other either sideways or head to head. For now, however, we are concerned only with head to head overlap because that’s the only type that occurs in alkanes. We’ll discuss sideways overlap later in connection with alkenes and alkynes, that is, hydrocarbons that have double and triple bonds respectively. When orbitals approach each other in a head to head fashion, the resulting covalent bonds are called sigma bonds. As illustrations, consider the bonds that have already been studied. The bond between two hydrogen atoms is an example of sigma bonding. The bonds between the sp3 orbitals of hybridized carbon and the s orbitals of hydrogen in methane are also example of sigma bonds. H sigma bond H + H H between s orbitals H sigma bonds C + 4 H C H between s and sp3 orbitals H H Two sp3 carbons can also overlap to form a C–C sigma bond where two sp3 orbitals overlap head to head, such as in the formation of the ethane molecule: H H H H head to head H H C C C C H overlap H H H H H sigma bond between two sp3 orbitals It can be easily seen that the only type of covalent bonds present in alkanes are sigma bonds, also loosely known as single bonds.  LINE-ANGLE FORMULAS In alkanes of 3 carbon atoms or more, the main carbon chain acquires a zig-zag structure due to the 109.5o angle between C–C bonds, such as in propane: H H H C C H3C CH3 H H C C H H H H H Two representations of propane, where the zig-zag structure of the carbon chain becomes apparent Writing Lewis formulas, or even condensed formulas, for alkanes of many carbon atoms can quickly become cumbersome. A short hand notation that uses zig-zag lines has been developed. The resulting representations are known as line-angle formulas. The beginning and the end of the zig-zag line, as well as any breaks in direction represent carbon atoms. Line angle representation for propane equivalent to H3C CH3 or CH3CH2CH3 CH2 The arrows point to the positions of the carbon atoms. Every carbon atom has to form 4 bonds. The bonds that are not shown are assumed to be bonds to hydrogen. Other examples are: CH3 CH3CH2CH2CH3 CH H3C CH3 butane isobutane CH3 CH3 CH CH3 H3C C CH3 H3C C H2 CH3 isopentane neopentane ALKENES AND sp2 HYBRIDIZATION OF CARBON We will now reproduce the sp3 hybridization process for carbon, but instead of taking one s and three p orbitals to make four equivalent sp3 orbitals, this time we’ll take only one s and two p orbitals to make three equivalent sp2 orbitals, leaving one p orbital untouched. The process is shown below. Potential sp2 hybridization energy 2pX 2py 2pz p 2s sp2 sp2 sp2 As shown, the three resulting sp2 orbitals are equivalent in energy, but the remaining p orbital has not been affected. It still retains its original energy and shape. Again, according to VSEPR theory, equivalent orbitals will arrange themselves in 3-D space to be as far apart from each other as possible. Therefore, the three equivalent sp2 orbitals will arrange themselves in a trigonal planar configuration. That is to say, the carbon nucleus will be at the center of an equilateral triangle, and the three sp2 orbitals will point to the corners of that triangle. The ideal angle between sp2 orbitals is therefore 120o. A top view of this arrangement is shown below. 120o C In this top view, the unhybridized p orbital cannot be seen because it also arranges itself to be as far apart from the sp2 orbitals as possible. That is to say, it is positioned at right angles to those orbitals, with one lobe coming out of the plane of the page and the other going behind the page. To see this arrangement clearly, we must switch to a side view of the orbital system. unhybridized p orbital sp2 C sp2 orbitals sp2 p When two sp2 hybridized carbon atoms approach each other to bond, two sp2 orbitals approach each other head to head, and two p orbitals approach each other sideways. The bond formed by the sp2 orbitals is a sigma bond, and the bond formed by the p orbitals is called a pi bond. The process is shown below.  sideways overlap sp2 head to head sp2 C C sp2 sp2 overlap sideways overlap p p C C pi bond sigma bond The illustration above tries to convey a basic feature of the pi bond as compared to the sigma bond. The sigma bond is short and strong. As a rule, head to head overlap is the most efficient way to bond and results in relatively strong and stable bonds. The pi bond, on the other hand, is relatively long and diffuse. Sideways overlap is less efficient than head to head overlap and results in formation of weaker bonds. This has some implications in the properties and chemical reactivity of sigma and pi bonds. The electrons in the sigma bond (or sigma electrons) are more tightly bound to the nucleus and don’t move too much. In other words, they are more LOCALIZED. The electrons in the pi bond (or pi electrons) are less tightly bound by the nucleus, and therefore they are relatively mobile. Under certain conditions, they have the capability to become DELOCALIZED, that is to say, they can move in the molecular skeleton from one atom to another, or even become spread over several atoms, according to principles we’ll study later. At the same time, in chemical reactions where electrons are to be traded, the pi electrons are more readily available because they are more exposed and less tightly bound by the nucleus. It is relatively easy to break a pi bond compared to the sigma bond. The principles of all this chemistry will be discussed later in the course. ALKENES ARE HYDROCARBONS THAT CONTAIN AT LEAST ONE PI BOND AS PART OF THEIR MOLECULAR STRUCTURE. By this definition, the simplest possible alkene must contain two carbon atoms. It is called ethene. Below is a Lewis and a line-angle representation of ethene, which is sometimes informally called ethylene. Notice that although C–H bonds are not usually shown in line-angle formulas, sometimes they are included for enhanced clarity. In this case a pure line-angle formula for ethene would look awkward because it would resemble an equal sign (=). H H H H C C CH2 CH2 H H H H Lewis formula condensed formula line-angle formula Notice that a Lewis representation does not differentiate between the sigma and the pi bonds in the so- called “double bond.” It simply shows the two together as two equal dashes. The orbital picture better represents the actual nature of the two types of bonds. Additional examples are shown below. For a full discussion of the structure of alkenes refer to chapter 7 of the Wade textbook. H CH3 CH2 CH CH3 or or H propene CH2 CH CH2 CH3 or CH3CH CH2CH3 or 1-butene 2-butene cyclopentene cyclohexene benzene Observe that the general formula for open chain monoalkenes –that is, alkenes that do not form cyclic structures and which contain only one pi bond– is CnH2n where n is the total number of carbon atoms. ALKYNES AND sp HYBRIDIZATION OF CARBON The process for understanding the sp hybridization process for carbon is basically an extension of the other two types (sp3 and sp2). You should try to work out this scheme on your own and see if your predictions agree with those presented in the textbook. sp hybridization gives rise to the formation of hydrocarbons known as alkynes. Alkynes contain at least one triple bond, and have linear geometry around the carbons comprising the triple bond. Therefore, the ideal angle between the sp hybrid orbitals is 180o. Some examples of alkynes are shown below. For additional information refer to chapter 9 of the Wade textbook. H C C H H C C CH3 H C C CH2 CH3 H3C C C CH3 Ethyne, or acetylene propyne 1-butyne 2-butyne Observe that the general formula for open chain monoalkynes is CnH2n-2 where n is the total number of carbon atoms. ORBITAL HYBRIDIZATION IN NITROGEN AND OXYGEN The hybridization schemes for nitrogen and oxygen follow the same guidelines as for carbon. For example, sp3 hybridization for nitrogen results in formation of four equivalent sp3 orbitals, except that this time only three of them contain unpaired electrons, and one of them contains paired electrons. A similar situation holds true for oxygen, which ends up with two of the sp3 orbitals occupied with unpaired electrons, and the other two with paired electrons. sp3 hybridization 2pX 2py 2pz sp3 sp3 sp3 sp3 2s Nitrogen: 5 valence electrons The four sp3 orbitals again orient themselves in 3-D space to be as far apart from each other as possible, but the ideal 109.5o angle becomes distorted because the orbital with two electrons repels the others more strongly than they repel themselves. However the geometry of this arrangement is still fundamentally tetrahedral. When this sp3 hybridized nitrogen bonds to hydrogen, the three unpaired electrons are used for bonding, and the remaining pair remains as nonbonding electrons..... N N. + 3 H N H H. H H H. 3-D representation of H the ammonia molecule A similar analysis for oxygen should lead to formation of two sp3 orbitals with unpaired electrons, and two with paired electrons. Thus, when sp3 oxygen bonds with hydrogen it forms water, which has a distorted tetrahedral angle, and two pairs of nonbonding electrons in the structure... O H O H H.. 3-D representation of H the water molecule Now, what happens when nitrogen or oxygen become sp2 hybridized? The exact same thing that happened with carbon, with some minor changes. Let’s go through the process with oxygen to illustrate how it bonds to carbon to make a class of substances known as carbonyl compounds. sp2 hybridization 2pX 2py 2pz p 2s sp2 sp2 sp2 Oxygen: 6 valence electrons Three equivalent sp2 orbitals have formed, two of them containing paired electrons, and one containing a single unpaired electron. The unhybridized p orbital remains, with an unpaired electron in it. Again, VSEPR theory dictates that the three equivalent sp2 orbitals will acquire a trigonal planar arrangement, while the unhybridized p orbital will remain at right angles to the sp2 orbitals.... sp2 O. O. sp2.. sp2.. p sp2 oxygen, top view sp2 oxygen, side view When an sp2 oxygen approaches an sp2 carbon for bonding, the process is analogous to that followed by two sp2 carbons that bond to form a “double bond.” Only those orbitals containing unpaired electrons can bond. In this case, the sp2 orbitals from oxygen and carbon that contain unpaired electrons will overlap head to head to form a sigma bond. At the same time, the p orbitals will overlap sideways to form a pi bond. Thus, we have the effective formation of a C=O “double bond.”.. O. +. C. O C..... sp2 oxygen + sp2 carbon O C C O double bond Notice that the pi bond in the C=O “double bond” appears distorted, indicating higher electron density around the oxygen than around the carbon. This is because the C=O bond is polar. The more electronegative oxygen atom attracts bonding electrons towards itself more strongly than carbon. The C O double bond O C is polar A similar analysis for nitrogen leads to the picture and geometry of a C=N double bond: N C Some examples of compounds containing sp2 carbon, nitrogen, and oxygen are shown below. Notice that Lewis and line-angle formulas frequently neglect showing the lone pairs of electrons. Unless there is a specific purpose for showing nonbonding electrons, they are usually omitted and assumed to be present. H NH O N O H H H H3C CH3 By going through an analogous process for sp hybridization of nitrogen and oxygen we can arrive at the molecular structure of species containing carbon-nitrogen and carbon-oxygen triple bonds. Notice that an oxygen containing a triple bond must also carry a positive charge in observance of the rules of covalent bonding. H3C C N H3C C O Also notice that when two sp or sp2 atoms are bonded together to form a double or triple bond, they both must be of the same hybridization. There are some exceptions, but this is true in most common situations. SUMMARY The preceding discussion covers the most common cases of atom hybridization encountered in this course. The following summarizes the concepts associated with each type of hybridization. sp3 hybridization 4 orbitals tetrahedral geometry ideal angle: 109.5o single bonds sp2 hybridization 3 orbitals trigonal planar geometry ideal angle: 120o double bonds sp hybridization 2 orbitals linear geometry ideal angle: 180o triple bonds