CHEMISTRY 115 VSEPR THEORY AND VALENCE BOND THEORY I. VSEPR THEORY: The tables which follow show how VSEPR Theory and Valence Bond Theory are both dependent upon the numbers of electron regions surrounding a central atom. In order to apply either method, it is necessary to understand how we determine the number of electron regions that exist on a particular atom. Bonding Regions: An electron region is any set of electrons that is effectively localized in a particular region of space. Any bond between atoms forms such a localized region, regardless of how many electrons are involved in the bond. It makes no difference whether the bond between two atoms is a single, double or triple bond, it will still be directed along the line between the two atoms and thus localized in that direction. For this reason, when we count the number of regions that contain electrons on an atom, each bond to another atom will count as a single region – no matter how many electrons are involved in that bond. For example, if an atom is bonded to 3 different other atoms, then there will be 3 bonding regions on that atom. Lone Pair Regions: Each lone pair on an atom counts as a single region of space that contains electrons. Lone pairs belong solely to the atom on which they reside and each lone pair will act as an independent group relative to any other lone pairs that may occur on the same atom. If an atom has a single unpaired electron on it, then that electron will occupy its own lone pair region. For example, if an atom has 3 lone pairs on it, then it will have 3 lone pair regions and if another atom has 2 lone pairs and 1 unpaired electron, (a “lone electron”, then that atom will also have 3 lone pair regions when we count. The sum of the bonding regions and lone pair regions gives us the total number of regions containing electrons on that atom. This is illustrated below with fictitious molecules of the form AB2. Under each drawing, the number of electron regions on atom A is listed below the drawing. The 1st value gives the number of bonding regions on atom A, the 2nd value gives the number of lone pair regions on atom A and the last value gives the total number of electron regions on atom A: B A B B A B B A B B A # bonding 2 2 2 2 #lone pair 0 0 1 2 Total # 2 2 3 4 B Note that each bonding region counts as 1 region, no matter how many bonds connect the two atoms – i.e., regardless of whether the bond is a single, double or triple bond. Thus atom A has 2 regions due to bonding in each of the four molecules that are shown. In –1– Raynor: 3/6/2016 addition to the bonding regions, each lone pair or lone electron counts as a single additional region. Thus the picture on the far right has 4 regions containing electrons – 2 regions which involve bonds to other atoms, 1 region containing a lone pair of electrons, (shown as a bar), and 1 containing a single lone electron. Both VSEPR Theory and Valence Bond Theory are dependent upon how many electron regions occur on the central atom in a structure. Once you know this number, everything else becomes dependent upon it. In VSEPR Theory, we use this number to determine what the electron geometry will be – i.e., the geometry formed when the electron regions are as far apart from each other as possible in 3D space. In Valence Bond Theory, this number determines the hybridization that will occur by mixing atomic orbitals on the central atom. Electron Geometries: Each electron region will repel all the other regions since they all contain negatively charged electrons. The strongest repulsions will be those between 2 lone pair sets of electrons with each other. This is because lone pair electrons are held very close to their parent atom, due to the attraction of the positively charged nucleus for the negatively charged electrons. In contrast, the electrons that are involved in bonds will be spread out along the entire length of the bond. Their repulsions on other electron regions will be less than the repulsions from lone pair electrons. However, all regions will repel others, which ultimately forces the electron regions to position themselves as far apart from each other as is possible. For example, if there are 2 regions containing electrons on the central atom in a structure, (either in bonds to other atoms or in lone pairs of electrons), then the farthest apart those electrons can get from one another is on opposite sides of the atom. This creates a linear geometry of the electrons to occur, with angles of 180 between them. [Note – an angle is defined using 3 positions in space. In this case, the angles between electron geometries are defined by the position of the first electron region, the atom it belongs to, and the position of the 2nd electron region.] If there are 3 regions, then the farthest apart those electrons can get from one another is in a trigonal planar arrangement, with angles of 120 between each set of electrons. If there are 4 regions, then the farthest apart those electrons can get from one another is to form a 3-dimensional tetrahedral electron geometry about the central atom, with angles of 109.5 between each set of electrons. When 5 regions occur, then the optimal geometry, (i.e., the one that gives the lowest repulsions between electrons), is called a trigonal bipyramid geometry. This consists of 3 regions that form a trigonal planar geometry, with angles of 120 between them, plus two more electron regions that are on opposite sides of the atom, along the line that is perpendicular to the plane formed by the trigonal planar groups. The two final regions will form 90 angles with each electron region in the trigonal planar arrangement and angles of 180 with each other. [See drawings in textbook or in the table at the end.] Finally, if 6 regions occur, then an octahedral electron geometry will be formed by the electron regions. This geometry starts with a square planar arrangement of 4 of the regions, (with 90 and 180 angles between each pair), plus one region above and one below the square planar groups. All angles are 90 and 180 between pairs of electron groups. [Again, see pictures in text and at the end.] –2– Raynor: 3/6/2016 Molecular Geometries: The molecular geometry is the geometry formed by the atoms in the molecule – i.e., it is described by the form taken by all the atoms – not by the positions of the electrons. However, the electron geometry determines the starting point. It sets for us the directions in which bonds can found. If all of the electron regions about a central atom are due to bonding regions, then the molecular geometry will be identical to the electron geometry. However, if one or more of the regions involve lone pairs of electrons, then the molecular geometry will not be the same as the electron one. However, the bond angles that occur will be identical to those expected for the angles between electron regions, except they will be somewhat modified by the differences in repulsion between lone pair electrons with bonding pairs. As discussed earlier, repulsions of lone pair electrons with other lone pair electrons will be strongest, those of lone pair electrons with bonding electrons will be next-strongest, and the repulsions between two sets of bonding electrons will be weakest. This is summarized below using “lp” to mean lone pairs of electrons and “bp” to mean bonding pairs of electrons. The weakest interactions are at the left and strongest on the right in the relations shown below: Repulsion Strengths: bp – bp < bp – lp < lp – lp The effect of this is to cause lone pairs to repel the bonding pairs, causing the bond angles to be slightly smaller than the angles occurring when all regions contain bonds. Note: in the descriptions below, we will describe the molecular geometries in terms of the numbers of one pair regions. The number of bonding regions is the difference between this value and the total number of regions occurring for that electron geometry. For example, in the description when 3 regions contain electrons, when 0 regions contain lone pair regions, then 3 regions contain bonds and when 1 region contains a lone pair, then the 2 remaining regions will involve bonds, etc. -----------------------------------------------------------------------------------------------------------------------# Regions = 2: (AB2) Electron geometry = Linear, see drawing below. Angle = 180. B A B 0 Lone Pair Regions (2 bond regions): Molecular Geometry = Electron Geometry = Linear. Bond angle = 180. [Example is BeCl2] -----------------------------------------------------------------------------------------------------------------------# Regions = 3: (AB3) Electron geometry = trigonal planar, see drawing below. Angles = 120. B A B B 0 Lone Pair Regions (3 bond regions): Molecular Geometry = Electron Geometry = Trigonal Planar. All bond angles = 120. [Example is BH3] –3– Raynor: 3/6/2016 1 Lone Pair Region (2 bond regions): Molecular Geometry = Bent. Bond Angle = < 120. [Example is SO2] -----------------------------------------------------------------------------------------------------------------------# Regions = 4: (AB4) Electron geometry = tetrahedral. Angles = 109.5. This is a 3-D structure, as shown below, where dotted lines indicate the line is going away from you, behind the page, and a triangle indicates the line is coming up closer to you, out of the page. Two different ways of drawing this structure are shown below. In the left one, the 3 B positions sit at the points of an equilateral triangle, with the one at the top sitting directly above the midpoint of the triangle. In the drawing on the right, the B positions sit at the 4 corners of a cube, with the corners on the top opposite to those at the bottom. Both forms yield identical structures. All B-A-B angles are identical and all are equal to 109.5. The atom positions in the left-hand drawing are labeled as positions B1, B2, B3 and B4. B1 A B4 B3 B2 0 Lone Pair Regions (4 bond regions): Molecular Geometry = Electron Geometry = Tetrahedral. All bond angles = 109.5. [Example is CH4] 1 Lone Pair Region (3 bond regions): Molecular Geometry = Trigonal Pyramid. Bond Angle = < 109.5. Structure is that obtained if you put the lone pair at position B1, which means bonds run from atom A to the positions at B2, another from A to B3 and the third from A to B4. The repulsion from the lone pair at B1 onto the bonding electrons causes the bond angle to become slightly smaller than 109.5 – perhaps becoming 108 or 107. [Example is NH3] 2 Lone Pair Regions (2 bond regions): Molecular Geometry = Bent. Bond Angle = < 109.5. Structure is most clearly seen if you put the lone pairs at positions B3 and B4 and the bonds from A to B1 and A to B2. What remains is one bond angle from B1 to A to B2. The repulsions from the lone pairs at B3 and B4 will cause a slight decrease in the bond angle from 109.5 to perhaps 105 or 106. [Example is H2O] -----------------------------------------------------------------------------------------------------------------------# Regions = 5: (AB5) Electron geometry = trigonal bipyramid. Angles = 90, 120 and 180. This is also a 3-D structure, as shown below, where the trigonal planar arrangement occurs among positions B1, B2 and B3. Positions B4 and B5 sit at opposite sides of the equilateral triangle formed by positions B1 – B3. All the angles are as follows: B1–A–B2 = B1–A–B3 = B2–A–B3 = 120; B4–A–B1 = B4–A–B2 = B4–A–B3 = B5–A–B1 = B5–A–B2 = B5–A–B3 = 90; B4–A–B5 = 180. –4– Raynor: 3/6/2016 What makes this structure unique is the fact that the positions on the equilateral triangle, B1, B2 and B3, are different in environment than those at B4 and B5. For example, the position at B1 is involved in 2- 120 interactions and 2 90 interactions, however the position at B4 has no 120 interactions. It has 3- 90 and 1-180 interaction, instead. B4 B3 B2 A B1 B5 0 Lone Pair Regions (5 bond regions): Molecular Geometry = Electron Geometry = Trigonal Bipyramid. Bond angles = 90, 120, 180. [Example is PCl5] 1 Lone Pair Region (4 bond regions): Molecular Geometry = “See-Saw”. Bond angles = < 90, < 120 and < 180. Because the trigonal planar positions are in a different environment than are the other two positions, the total energy of the molecule with the lone pair placed at B1, (and bonds at all other positions), will be different from the energy with the lone pair at B5 instead, (and bonds at all other sites). Since 90 angle interactions between electrons will place the electrons much closer together than will 120 angles, we want the structure that has the fewest 90 interactions between the lone pair and bonding pairs. It is easy to see that this means that the lone pair should be placed at one of the trigonal planar positions, B1, B2 or B3. It is easiest to see what the resulting molecular geometry looks like if we place the lone pair at the B1 position. The rest of the positions will therefore involve bonds between atom A and the atoms at positions B2 – B5, creating a geometry that looks like a child’s see-saw., which is then the term used for the molecular geometry. [Example is SF4] 2 Lone Pair Regions (3 bond regions): Molecular Geometry = T-Shaped. Bond Angles = < 90 and < 180. The lowest energy structure places both lone pairs at two of the trigonal planar positions. The structure is most clearly seen if you put the lone pairs at positions B2 and B3 and the bonds at all other positions. The regions that remain all are in the same plane as one another and appear to form a T, hence the name of the structure. [Example is ClF3] 3 Lone Pair Regions (2 bond regions): Molecular Geometry = Linear. Bond Angle = 180. The lowest energy structure places all three lone pairs in the trigonal planar positions, B1, B2 , B3 and the bonds at the apical positions, yielding B4–A–B5 = 180 = linear structure. [Example is XeF2] -----------------------------------------------------------------------------------------------------------------------# Regions = 6: (AB6) Electron geometry = octahedral. Angles = 90 and 180. This is also a 3-D structure, as shown below, where the square planar arrangement occurs among positions B1, B2, B3 and B4. Positions B5 and B6 sit at opposite sides of the square –5– Raynor: 3/6/2016 formed by positions B1 – B4. All the angles are 90 or 180, depending on whether the positions are next to one another, (90), or opposite to one another, (180). B5 B3 B2 A B4 B1 B6 0 Lone Pair Regions (6 bond regions): Molecular Geometry = Electron Geometry = Octahedral. Bond angles = 90, 180. [Example is SF6] 1 Lone Pair Region (4 bond regions): Molecular Geometry = Square Pyramid. Bond angles = < 90 and < 180. Since it does not matter which position is used for the lone pair, the easiest to see is when position B6 is used as the lone pair positions, with bonds occurring at the other 5 positions. If you draw lines from position B5 to positions B1 through B4 and connect the lines along the square, i.e., from B1 to B2, B2 to B3, B3 to B4 and B4 to B1, you will discover that the structure you have created is a 4-sided pyramid – i.e., a pyramid with a square bottom – hence the name square pyramid to describe the molecular geometry. [Example is BrF6] 2 Lone Pair Regions (3 bond regions): Molecular Geometry = Square Planar. Bond angles = exactly 90 and 180. The lone pairs will provide the least repulsion on each other if they are on opposite sides of the central atom. If we choose positions B5 and B6 for the lone pairs, it is easiest to see the geometry that remains for the 4 bonding regions – you can see that the atoms at positions B1 though B4 will end up on the 4 corners of a square. This geometry is called the square planar geometry for that reason. Since the lone pair electrons are on opposite sides of the central atom, the repulsions from below on any bond will be exactly matched by the repulsions from above. Thus the bond angles remain unchanged – they will be exactly 90 and 180. [Example is XeF4] -----------------------------------------------------------------------------------------------------------------------The electron geometries and molecular geometries that can arise from them are all summarized in the table on the next page. –6– Raynor: 3/6/2016 Electron and Molecular Geometries from VSEPR Theory # eregions AB2 2 AB3 Electron Geometry # lone pairs Molecular Geometry Bond Angles linear 0 linear 180 trigonal planar 0 trigonal planar B A B trigonal planar 1 bent (angular) < 120 B B A 120 3 AB2E Drawing B A B B B B A B B B A B B A B B B B B A B B B B B A B AB4 tetrahedral 0 tetrahedral 109.5 AB3E tetrahedral 1 trigonal pyramid < 109.5 AB2E2 tetrahedral 2 bent (angular) < 109.5 AB5 trigonal bipyramid 0 trigonal bipyramid 90, 120, 180 AB4E trigonal bipyramid 1 seesaw < 90, < 120, <180 AB3E2 trigonal bipyramid 2 T-shaped < 90, < 180 B A B B AB2E3 trigonal bipyramid 3 linear 180 AB6 octahedral 0 octahedral 90, 180 AB5E octahedral 1 square pyramidal < 90, < 180 octahedral 2 square planar 90, 180 B A B BB B A B BB BB B A BB BB A BB 4 5 6 AB4E2 –7– Raynor: 3/6/2016 II. VALENCE BOND THEORY: Valence Bond Theory uses the assumption that as bonds or lone pair regions are formed on an atomic center, the valence atomic orbitals will mix together to form new orbitals that are oriented along the optimal directions – those which will minimize the electronelectron repulsions occurring between them. Thus Valence Bond Theory is dependent upon the number of electron regions on the atom in the same way that VSEPR theory depends upon them. One key factor to remember is the Conservation of Orbitals. In the same way that you can’t create or destroy energy or mass, you cannot create or destroy the number of orbitals in a system. Thus if you start with a total of q orbitals, you must end with a total of q orbitals. This leads to a simple numbers game for discovering the types of hybridization that will occur among atomic orbitals. To demonstrate why this is important, consider what happens with the atomic orbitals on carbon when methane, CH4, is formed. Carbon has the [He]2s22p2 ground state configuration, as shown schematically below: Note that the 2s orbital is lower in energy than the 2p one. Thus even if we promote one of the 2s electrons up into the 2p orbital to allow for bonding with 4 H atoms, (as shown in the right-hand drawing), the bond formed using the 2s-type electron should be lower in energy than the ones involving the 2p orbitals. However, all four C-H bonds in CH4 are identical in length and energy to one another. Furthermore, they form a tetrahedral molecular geometry, with all angles equal to 109.5. If bonds were formed between hydrogen and the 2p orbitals directly, the bonds should end up at 90 angles, since the three p-orbitals are oriented at 90 to one-another. We can account for carbon forming 4 identical bonds with hydrogen when methane is formed if we assume that the atomic orbitals on carbon first mix with one another to form new orbitals, each or which is oriented along one of the 4 tetrahedral orientations around the carbon atom. Mathematically, we can show that we can create 4 identical new orbitals aligned along each of the 4 tetrahedral directions, if we mix together the 2s orbital with all three 2p orbitals. [Note – since we are mixing together 4 atomic orbitals, we must end up creating 4 new orbitals, due to the Conservation of Orbitals rule referred to earlier.] Similar outcomes occur when there are 2 regions containing electrons, or 3, or any of the numbers of regions discussed earlier. In every case, the new hybrid orbitals that are created end up being aligned along the directions prescribed for the electron geometry that is expected to form. For example, when 5 orbitals mix to create 5 new ones, they will become oriented along the 5 different directions in a trigonal bipyramid electron geometry, etc. –8– Raynor: 3/6/2016 When we mix atomic orbitals to create new hybrid ones, we describe the new hybrid orbitals in terms of the atomic orbitals used in the mixture. For example, with the carbon atom in CH4, we mixed the 2s orbital with all three of the 2p orbitals to create the hybrid orbitals. We call the new hybrid orbitals sp3 hybrids – which specifically indicates that we mixed one s-type orbital with 3 p-type orbitals to create the 4 new hybrid orbitals. Finally, when we create hybrid orbitals for bonding to other atoms, we want to generate the lowest energy orbitals we can in order to stabilize the energy of the final molecule. Thus we always mix the lowest energy orbital, (which is always an s-type orbital), with the orbitals next up in energy, (which are always p-type orbitals, since we are discussing non-metal to non-metal bonding). We will use d-type orbitals in our hybrids only if we need to create more than 4 hybrid orbitals. For example, when the electron geometry is trigonal bipyramid, we will have 5 regions around the central atom that contain electrons and we will need to mix together 5 atomic orbitals to obtain 5 hybrid orbitals. This will require that we use the lowest energy s-type orbital, all three p-type orbitals and one dtype orbital to create 5 new sp3d hybrid orbitals. For octahedral electron geometries it follows that we must mix the s-type orbital, all three p-type orbitals and 2 d-type orbitals, producing 6 new sp3d2 hybrid orbitals. [Remember: we need empty spaces available in our new orbitals that can accept electrons. Thus we will need to use the lowest energy empty d-orbitals when we create hybrid orbitals. If a d-orbital is filled with electrons, it cannot accept additional ones and thus form a bond. For example, if we have the I3– ion, which has the following Lewis Drawing, I I I 1 the central I atom will have its electrons arranged in a trigonal bipyramid electron geometry. We will need to mix its valence 5s and 5p-orbitals with one of the empty 5d orbitals to create its new sp3d hybrid orbitals. Hybrid orbitals are oriented directly along the direction of bonding, (or the direction of a lone pair of electrons). They can then overlap with an orbital from another atom to form sigma-type bonds – i.e., bonds that are directed along the bond-axis between 2 atoms – and give the framework for the single bonds and lone pairs on an atom. If a double or triple bond forms between atoms, the 2nd or 3rd bond between them arises from overlap of un-hybridized p-type atomic orbitals. Consider, for example, the double bond between carbon atoms in ethylene. Each C atom is involved in 2 single bonds to H atoms and one double bond to the other C atom. There are thus 3 regions around each C atom that contain electrons and we expect mixing of the 2s orbital with 2 or the 2p orbitals to produce the 3 sp2 hybrid orbitals at 120 angles from one another. The third p-orbital is the one perpendicular to the molecule’s plane. The lobes on the remaining p-orbital on the left-hand carbon can overlap with the lobes on the remaining p-orbital on the righthand carbon to form a pi-type bond. The sigma-type bonds and their overlap with the 1stype orbitals on H and their overlap with each other are illustrated below: –9– Raynor: 3/6/2016 H H C C H C C H On the right-hand side, the overlap of the unhybridized 2p orbitals is illustrated. These lobes actually occur with one lobe coming out of the page and the other going into the page in the left-hand drawing – i.e., they are oriented perpendicular to the plane of the molecule. The overlap of the lobes on these p-type orbitals creates one large lobe above the bond axis and one large lobe below the bond axis, and is called a pi-type orbital and thus bonds involving such orbitals are called pi-bonds. These pi-type orbitals can accept up to 2 electrons, when forming a pi-bond between two atoms. The figure below illustrates how hybrid orbitals are generated from the valence atomic orbitals: # Regions = 2: s p sp p # Regions = 3: s p sp2 p # Regions = 4: s p sp3 # Regions = 5: s p d sp3d d # Regions = 6: s p d – 10 – sp3d2 d Raynor: 3/6/2016 The table below summarizes the types of hybrid orbitals that form as a function of the number of regions around an atom that contain electrons. # Electron Regions 2 3 4 5 6 # Hybrid Orbitals Needed 2 3 4 5 6 # Atomic Orbitals Used 2 3 4 5 6 (1, 1, 0) (1, 2, 0) (1, 3, 0) (1, 3, 1) (1, 3, 2) Type of Hybrid Orbitals sp sp2 sp3 sp3d sp3d2 # and Type of Unused Orbitals 2p 1p 0 p, 5 d 4d 3d # of (s, p, d) Used Note how simple it is to remember how to generate this information. The number of electron regions tells us how many atomic orbitals will mix together and how many new hybrid orbitals will form. The type of hybrids formed can be easily determined by remembering that the valence s-type orbital is always used in the mixture, (since it will be lowest in energy). Next, we will mix in as many p-orbitals as needed to create the number of hybrids necessary. However, if more than 4 atomic orbitals are needed, (i.e., more than the number of valence s-type and p-type orbitals available), then any additional atomic orbitals will have to come from empty d-type orbitals that are close in energy to the valence s-type and p-type orbitals. If multiple bonds are formed between atoms, (i.e., double or triple bonds), then one of the bonds will involve overlap of hybrid orbitals on the two atoms and any additional bonds will form from the overlap of unhybridized atomic orbitals on the two centers. Consider, for example, the C atom in CO2 and the S atom in SO42–. Their Lewis structures are shown below: O C O O L M O S M M N O O OP P P Q 2 In CO2, the C atom has 2 regions about it that contain electrons and thus forms 2 new sphybrid orbitals, one directed towards the left-hand O atom and one toward the righthand O atom. The 2nd bond in the left-hand double bond arises from the overlap of one of the unhybridized 2p orbitals on the C atom with a 2p orbital oriented in the same direction on the left-hand O atom and the 2nd bond in the right-hand double bond involves the other unhybridized 2p orbital on the C atom with a p orbital oriented in the same direction on the right-hand O atom. [One pair of p orbitals will be oriented updown and the other will be oriented in-out, relative to the way the molecule is drawn. [In SO42–, there are 4 regions containing electrons on the S atom. Thus the molecule will have a tetrahedral molecular geometry as well as a tetrahedral electron geometry. Since all 4 3p-type atomic orbitals on sulfur will be used in creating the 4 sp3 hybrid orbitals on the S atom, the double bonds must involve overlap of unhybridized 3d-type orbitals on the – 11 – Raynor: 3/6/2016 sulfur atom with 2p-type orbitals in the appropriate directions on the O atoms. Thus, even though no d-type orbitals were needed in the formation of the hybridized orbitals, they were necessary for the formation of the two multiple bonds between sulfur and oxygen. O, S and Se are all in Group 16, but with different n quantum numbers for their valence atomic orbitals. We can thus predict that the SeO42– anion could potentially be a stable anion and its Lewis structure and geometry would be the same as that for SeO42–, since the only difference would be that Se would use its 4s, 4p and 4d orbitals to generate its hybrid orbitals and for the pi-type orbitals used in the multiple bonds. We can also predict that making the substitution of O for S in the structure to create O 52– would be highly unlikely to form a stable anion. The only allowed Lewis Diagram for O52– would be the one where all bonds are single bonds, since oxygen cannot exceed its octet. Although the O atom could use its 2s and 2p orbitals to create the sp3 hybrid orbitals that are needed, it does not have any empty d-type orbitals that are close in energy to its valence orbitals. Thus there are no unhybridized orbitals that could be used to create the double bonds. The Lewis structure with all single bonds has a +2 formal charge on the central atom. This means that if O52– were able to form at all, it would probably be very unstable. In fact, I don’t believe the O52– ion exists! – 12 – Raynor: 3/6/2016