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Chemical Bonding and VSEPR THEORY

To understand Chemical Reactions, it is first necessary to have an understanding of how chemical compounds are formed:

Chemical bonds are the attractive forces that hold atoms together in more complex units. There are two types of chemical bonds: (I) Ionic Bond – results from the transfer of one or more electrons from one group of atoms to another. An ion is an atom (or group of

atoms) that is electrically charged as a result of the loss or gain of electrons. This bond model is particularly applicable for compounds containing atoms of metallic and nonmetallic elements. When elements having low ionization energies (metals) react with elements having high electron affinity (nonmetals), ionic compounds (bases and salts) form.

(II) Covalent Bond – results from the sharing of one or more pairs of electrons between atoms. This bond model is most applicable for compounds (acids) containing only atoms of nonmetal elements. Covalent bonds are formed between similar or even identical atoms.

Lewis Electron-Dot Structure – which is the shorthand system for designating the number of valence electrons, consists of an element’s symbol with one dot for each valence electron placed around the elemental symbol.

There are three important generalizations about valence electrons: 1. Representative elements in the same group of the periodic table have the same number of valence electrons. 2. The number of valence electrons for representative elements in a group is the same as the Roman numerical periodic table group number. 3. The maximum number of valence electrons for any element is eight.

The Octet Rule – In compound formation, atoms of elements lose, gain, or share electrons in such a way as to produce a noble-gas electron configuration for each of the atoms involved. All nonmetals and most representative element metals (all Group 1A, Group IIA metals, and Ag, Zn, Cd, Al, Ga) follow the octet rule and form only one type of ion. However, there are exceptions to this rule. There are many other metals that exhibit a less predictable behaviour and are able to form more than one type of ion.

Exceptions (the atoms in some molecules cannot obey the octet rule because there are either two few or too many electrons): (i) Atoms with less than an octet: Many compounds of boron and beryllium do not follow the octet rule. Example: boron trifluoride (BF3 ) – only 6 valence electrons surround the boron atom; (BeCl2) – 4 e- around Be. Boron trifluoride, a gas at normal

temperatures and pressures, reacts very energetically with molecules such as water and ammonia that have unshared electron pairs (lone pairs). In the molecules ofBF3 , each of the fluorine atom form a single bond with the boron atom in the centre. In this structure, the boron atom has only six

electrons around it. This electron deficiency causes BF3 to react vigorously with electron-rich molecules such as3NH to form

33NBFH . It is also

characteristic of beryllium to form molecules where the beryllium atom is electron-deficient. (ii) Atoms with more than an octet: Some atoms beyond the 2nd row of the periodic table – most notably phosphorus and sulfur- sometimes form

bonds that give them more than an octet of electrons. The additional electrons fill the 3d orbitals of these atoms. Examples: the sulfur atom in SF4 - 10 valence electrons around the sulfur atom. Other examples: 6SF (12 e- around S), 5PCl (10 e- around P).

(iii) Molecules with an odd number of electrons cannot follow the octet rule. Example: nitrogen monoxide (NO) has a total of 11 electrons. The “odd” electron is usually on the nitrogen atom. So nitrogen monoxide is very unstable and very reactive. But it is a vital messenger molecule in the human body. Same situation applies to nitrogen dioxide.

(iv) The elements C, N, O, and F obey the octet rule in the vast majority of their compounds. However, there is one important exception is the oxygen molecule

2O . The octet rule of Lewis structure would be satisfied if the two oxygen atoms bond in a double bond. But experiment has shown that

oxygen is paramagnetic, meaning that it contains unpaired electrons. No simple Lewis structure can explain this Paramagnetism.

Compounds that are formed by ionic bond are called ionic compounds: 1. Ionic Compounds usually contain both a metallic and a nonmetallic element. 2. The metallic element atoms lose electrons to produce positive ions and the non-metallic elements atoms gain electrons to produce

negative ions. 3. The electrons lost by the metal atoms are the same ones that are gained by the nonmetal atoms. Electron loss must always equal

electron gain. 4. The ratio in which positive metal ions and negative nonmetal ions combine is the ratio that achieves charge neutrality for the

resulting compound. 5. Metals from Groups IA, IIA, and IIIA of the periodic table form ions with charges of +1, +2, and +3, respectively. Nonmetals of

Groups VIIA, VIA, and VA of the periodic table form ions with charges of –1, -2, and –3, respectively. When the representative elements form ions they tend to achieve noble gas configuration having 8 electrons in their outer shell.

6. All ionic compounds are solids at room temperature and tend to have high melting points. 7. Their solids are generally hard and brittle. 8. In solid state, ionic compounds do not conduct electricity because the attractive forces prevent the movement of ions through the

crystal. But the liquid conducts electricity well. Ionic solids consist of positive and negative ions arranged in such a way that each ion is surrounded by the nearest neighbours of the opposite charge. Discrete molecules do not exist in an ionic solid. Therefore, the formula for these solids cannot represent the composition of a molecule of the substance. The formulas for ionic solids only represent ratios and they are used in equations and in chemical calculations such as molecular weights in the same way as the formulas for molecular species. Thus, the molecule is not the smallest unit capable of a stable existence for all pure substance. Ionic compounds without the OH--1 are also known as salts.

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The formation of a covalent bond always involves the process of electron sharing where the octet rule and electron-dot structures apply. The number of covalent bonds that an atom forms is equal to the number of electrons it needs to achieve a noble-gas configuration with 8 electrons in its outer shell, the valence shell. The octet rule can also be used to predict formulas in covalent compounds. A single-covalent bond is a bond where a single pair of electrons is shared between two atoms. A double-covalent covalent bond is a bond where two atoms share two pairs of electrons. A triple-covalent bond is a bond where two atoms share three pairs of electrons. A double-covalent bond is stronger than a single-covalent bond, but not twice as strong, because two electron pairs repel each other and cannot become fully concentrated between the two atoms. A triple-covalent bond is not triple in bonding strength for the same reason. Not all elements can form double- or triple-covalent bonds. There must be at least two vacancies in an atom’s valence electron shell prior to bond formation. This requirement eliminates Group VIIA elements (fluorine, chlorine, bromine, iodine) and hydrogen from participating in such bonds.

Examples: (i) Triple-covalent bond - A diatomic N2molecule, the natural form in which nitrogen occurs in the atmosphere, is the simplest

triple-covalent bond: ••

••••••

••

••

••≡N N or N N

(ii) Triple-covalent bond - C H2 2 has a carbon-carbon triple-covalent bond and two carbon-hydrogen single bonds:

H C C H or H C C H••

••••••

•• − ≡ −

(iii) Triple-covalent bond – HCN has a heteroatomic carbon-nitrogen triple bond: H C N or H C N••

••••••

•• − ≡

(iv) Double-covalent bonds are found in numerous molecules – a common molecule is carbon dioxide (CO2 ), where two

carbon-oxygen double bonds are present: ••

••••••

••••

••

••

••

••

••

••=O C O or O = C O

A coordinate-covalent bond is a bond in which both electrons of a shared pair come from one of the two atoms involved in the bond. Examples: (i) N O2 - •

•••••••

••

••

••••N N O in which the nitrogen-nitrogen triple bond is a normal covalent bond; the nitrogen-oxygen bond is a coordinate-

covalent bond , where both electrons are supplied by the nitrogen atom. (ii) CO - •

•••••••

••C O in which four of the six electrons in the triple carbon-oxygen bond can be considered to have come from the

oxygen atom. (iii) Another example of a coordinate-covalent bond occurs when a molecule having an incomplete valence shell reacts with a molecule

having electrons that aren’t being used in bonding. Compounds like [ 33NHBCl ] which are formed by simply joining two smaller

molecules, are called addition compounds:

The ionic and covalent models for bonding are actually closely related to each other and represent the extremes of a broad continuum of bonding patterns. Their close relationship can be explained by the concept of electronegativity, which is a measure of the relative attraction that an atom has for the shared electrons in a bond. The higher the electronegativity value for an element is, the greater the electron-attracting ability of atoms of that element for shared electrons in bonds. Electronegativity increases from left to right across a period of the periodic table (in the same direction as the atomic size decreases), and decreases from top to bottom in a group of the periodic table (in the same way as the atomic size increases). Generally, nonmetals have higher electronegativities than metals, consistent with the fact that metals tend to lose electrons and nonmetals tend to gain electrons when an ionic bond is formed. That is why an element from Group IA or Group IIA reacts with an element from the upper right hand corner of the periodic table to form predominantly ionic compound. Electronegativity values differ from element to element because of differences in (i) atom size, (ii) nuclear charge, and (iii) number of inner-shell (non-valence) electrons. 100% ionic bonding occurs when the difference in electronegativity is very high such as 3 or higher; the bond is more than 50% ionic when the difference exceeds 1.7. In a nonpolar covalent bond, there is no difference in electronegativity, so the pair of bonding electrons is shared

equally. It is important to note that element hydrogen located to the far left in period 1 in the periodic table have an electronegativity of 2.1, which is between boron (2.0) and carbon (2.5), both elements of period 2.

3 Covalently bonded groups of atoms are called molecules. Compounds of this type are called covalent or molecular compounds. Molecules, as well as bonds, can have polarity . Molecular polarity depends on the polarity of the bonds within a molecule and the geometry of the molecule. Molecular geometry describes the way in which atoms in a molecule are arranged in space relative to each other. Within the individual molecules the atoms are held to each other very strongly, but between neighboring molecules the attractions are very weak. So molecular compounds such as water and candle wax tend to have low melting points. Molecules are uncharged particles, so they do not conduct electricity in the solid state or when melted. Most molecular substances also will not conduct electricity when dissolved in water. Resonance: When Lewis Structures Fail – The bonding in some molecules and ions cannot be adequately described by a single Lewis structure. There are some molecules and ions for which Lewis structures do not agree with experimental measurements of bond length and bond energy. For example, the structure for −

2CHO suggests that one carbon-oxygen bond should be longer than the other, but

experiment shows that they are identical. In fact, the OC − bond lengths are about halfway between that expected for a single bond and that expected for a double bond. We get around this problem by introducing the concept of resonance, that is, the actual structure of the ion is a resonance hybrid of two contributing structures as illustrated in the following diagrams:

Extending the Lewis Theory of Bonding by Nevil Sidgwick: (1) One atom could contribute both electrons that are shared; (2) An octet of electrons around an atom may be desirable, but is not necessary in all molecules and polyatomic ions.

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5 Lewis electron-dot structures conveniently illustrate the of sharing of electrons in covalent bonds. But to understand how these covalent bonds are formed involves the model of overlap of orbitals. This is called the Valence Bond Theory. All bonds with high densities along the intermolecular axis are called sigma bonds. There are 3 basic ways to form this bond: (i) Overlap of 2 s orbitals; (ii) Overlap of s orbital and p orbital; (iii) Overlap of 2 p orbitals.

Each and every covalent bond has one and only one sigma bond. In a compound that has a double or triple covalent bond, additional overlap of orbitals is needed, and bonds are formed from the sideways overlap of two p orbitals, which are called pi bonds.

The Valence Bond Theory was further extended by the Concept of Hybridization of Orbitals (by Pauling) to address the bonding situations where Lewis Electron-dot Structures cannot adequately explain. To understand why a new concept is needed, we need to examine the implications of overlap model. First, p orbitals are oriented at 900 from each other and s orbitals are spherical, having no directionality. If all covalent compounds were formed from the overlap of these orbitals we would expect all covalent molecules to have 900 bond angles, but in fact, few of the molecular geometries have angles of 900. Second, even a simple molecule such as methane,4CH ,

cannot be adequately explained using the overlap model. Methane is a tetrahedral molecule with four totally equivalent C-H bonds. Carbon in methane has only two unpaired p electrons (the s electrons are paired). Using the overlap model we would expect the formation of the 2CH molecule. These molecules would have atoms oriented at 900 angles since p orbitals are 900 apart. If the two s electrons were

allowed to un-pair so that they could also form bonds, we could obtain the 4CH molecule. However, the bond angles would still not be

correct, and we would expect two distinctly different C-H bond types in methane, one from the overlap of s orbitals and the other from the overlap of p orbitals. To better explain the formation of sigma bond, the concept of hybridization of orbitals is developed and hybrid orbitals are defined as a set of orbitals with identical properties formed from the combination of two or more different orbitals with different energies. A partial hybridization of the available orbitals would leave one or two normal p orbitals with single unpaired electrons. The half-filled p orbitals are believed to overlap sideways to form a pi bond. The pi bond is a region of electrons density appearing above and below the sigma bond directly joining the two atoms. The σ and π bonds together form a double (e. g.: ) or triple bond (e.g.: ).

Examples of molecules with hybrid orbitals are: (i) :sp (a) 2 σ, 0 π : 2BeF

(b) 2 σ , 2 π : 2CO (2 double bonds), −CN (1 triple bond), 2CS , 22 HC (1 triple bond)

(ii) :2sp (a) 3 σ , 0 π : −23SO , 3BCl

(b) 3 σ , 1 π : −3NO , −2

3CO , OCH 2 , 22CHCH (1 double bond)

(iii) :3sp (a) 2 σ , 0 π : 2SCl , SH 2

(b) 3 σ , 0 π : 3PH , 3PCl

(c) 4 σ , 0 π : 4CH , 3NH (1 lone pair), OH 2 (2 lone pairs), 4SiF , ClCH 3 , −34PO , −

4ClO

(iv) :3dsp (a) 5 σ , 0 π : 5PCl

(v) :32spd (a) 6 σ , 0 π : 6SF

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8 A nonpolar-covalent bond is one in which there is an equal sharing of electrons when two identical atoms (atoms of equal electronegativity) share one or more pairs of electrons. A polar-covalent bond is one in which there is unequal sharing of bonding electrons. The significance of a polar-covalent bond is that it creates partial positive and negative charges on atoms. Most chemical bonds are not 100% covalent (equal sharing) or 100% ionic (no sharing). Instead, most bonds are somewhere in between (unequal sharing) as shown in the diagram in previous page. Rule 1: When there is zero difference in electronegativity between bonded atoms, the bond is called a nonpolar-covalent bond. Rule 2: When the electronegativity difference between bonded atoms is greater than zero but less than 1.7, the bond is called a polar- covalent bond. Rule 3: When the difference in electronegativity between bonded atoms is 1.7 or greater, the bond is called an ionic bond. The shape of a molecule and the polarity of its bonds together determine whether the molecule is polar or nonpolar:

(a) 2CO (b) 4XeF

Not every structure

containing lone pairs

9 VSEPR theory Valence shell electron pair repulsion (VSEPR) theory is a model in chemistry used to predict the shape of individual molecules based upon the extent of electron-pair electrostatic repulsion. It is also named Gillespie-Nyholm theory after its two main developers. The acronym "VSEPR" is sometimes pronounced "vesper" for ease of pronunciation.

The premise of VSEPR is that the valence electron pairs surrounding an atom mutually repel each other, and will therefore adopt an arrangement that minimizes this repulsion, thus determining the molecular geometry. The number of electron pairs surrounding an atom, both bonding and nonbonding, is called its steric number.

VSEPR theory is usually compared and contrasted with valence bond theory, which addresses molecular shape through orbitals that are energetically accessible for bonding. Valence bond theory concerns itself with the formation of sigma and pi bonds. Molecular orbital theory is another model for understanding how atoms and electrons are assembled into molecules and polyatomic ions.

VSEPR theory has long been criticized for not being quantitative, and therefore limited to the generation of "crude", even though structurally accurate, molecular geometries of covalent molecules. However, molecular mechanics force fields based on VSEPR have also been developed.

Description VSEPR theory mainly involves predicting the layout of electron pairs surrounding one or more central atoms in a molecule, which are bonded to two or more other atoms. The geometry of these central atoms in turn determines the geometry of the larger whole.

The number of electron pairs in the valence shell of a central atom is determined by drawing the Lewis structure of the molecule, expanded to show all lone pairs of electrons, alongside protruding and projecting bonds. Where two or more resonance structures can depict a molecule, the VSEPR model is applicable to any such structure. For the purposes of VSEPR theory, the multiple electron pairs in a multiple bond are treated as though they were a single "pair".

These electron pairs are assumed to lie on the surface of a sphere centered on the central atom, and since they are negatively charged, tend to occupy positions that minimizes their mutual electrostatic repulsions by maximising the distance between them. The number of electron pairs therefore determine the overall geometry that they will adopt.

For example, when there are two electron pairs surrounding the central atom, their mutual repulsion is minimal when they lie at opposite poles of the sphere. Therefore, the central atom is predicted to adopt a linear geometry. If there are 3 electron pairs surrounding the central atom, their repulsion is minimized by placing them at the vertices of a triangle centered on the atom. Therefore, the predicted geometry is trigonal. Similarly, for 4 electron pairs, the optimal arrangement is tetrahedral.

This overall geometry is further refined by distinguishing between bonding and nonbonding electron pairs. A bonding electron pair is involved in a sigma bond with an adjacent atom, and, being shared with that other atom, lies farther away from the central atom than does a nonbonding pair (lone pair), which is held close to the central atom by its positively-charged nucleus. Therefore, the repulsion caused by the lone pair is greater than the repulsion caused by the bonding pair. As such, when the overall geometry has two sets of positions that experience different degrees of repulsion, the lone pair(s) will tend to occupy the positions that experience less repulsion. In other words, the lone pair-lone pair (lp-lp) repulsion is considered to be stronger than the lone pair-bonding pair (lp-bp) repulsion, which in turn is stronger than the bonding pair-bonding pair (bp-bp) repulsion. Hence, the weaker bp-bp repulsion is preferred over the lp-lp or lp-bp repulsion.

This distinction becomes important when the overall geometry has two or more non-equivalent positions. For example, when there are 5 electron pairs surrounding the central atom, the optimal arrangement is a trigonal bipyramid. In this geometry, two positions lie at 180° angles to each other and 90° angles to the other 3 adjacent positions, whereas the other 3 positions lie at 120° to each other and at 90° to the first two positions. The first two positions therefore experience more repulsion than the last three positions. Hence, when there are one or more lone pairs, the lone pairs will tend to occupy the last three positions first.

The classical example, of course, is the water molecule which has four electron pairs in its valence shell, two lone pairs and two bond pairs. The four electron pairs are spread so as to point roughly towards the apices of a tetrahedron. However, the bond angle between the two O-H bonds is only 104.5°, rather than the 109.5° of a regular tetrahedron, because the two lone pairs (whose density or probability envelopes lie closer to the oxygen nucleus) exert a greater mutual repulsion than the two bonds pairs.

10 Types of molecular structure - There are six basic shape types for molecules:

• Linear: In a linear model, atoms are connected in a straight line. The bond angles are set at 180°. A bond angle is very simply the geometric angle between two adjacent bonds. For example, carbon dioxide has a linear molecular shape.

• Trigonal planar: Just from its name, it can easily be said that molecules with the trigonal planar shape are somewhat triangular and in one plane (meaning a flat surface). Consequently, the bond angles are set at 120°, Example: boron trifluoride.

• Tetrahedral: Tetra- signifies four, and -hedral relates to a surface, so tetrahedral almost literally means "four surfaces." This is when there are four bonds all on one central atom, with no extra unshared electron pairs. In accordance with the VSEPR (valence-shell electron pair repulsion theory), the bond angles between the electron bonds are 109.5°. An example of a tetrahedral molecule is methane (CH4).

• Octahedral: Octa- signifies eight, and -hedral relates to a surface, so octahedral almost literally means "eight surfaces." The bond angle is 90 degrees. An example of an octahedral molecule is sulfur hexafluoride (SF6).

• Pyramidal: Pyramidal-shaped molecules have pyramid-like shapes. Unlike the linear and trigonal planar shapes but similar to the tetrahedral orientation, pyramidal shapes requires three dimensions in order to fully separate the electrons. Here, there are only three pairs of bonded electrons, leaving one unshared lone pair. Lone pair - bond pair repulsions change the angle from the tetrahedral angle to a slightly lower value. An example is NH3 (ammonia).

• Bent: The final basic shape of a molecule is the non-linear shape, also known as bent or angular. One of the most unquestionably important molecules any chemist studies is water, or H2O. A water molecule has a non-linear shape because it has two pairs of bonded electrons and two unshared lone pairs. Like in the other arrangements, electrons must be spaced as far as possible. Lone pair - bond pair repulsions push the angle from the tetrahedral angle down to around 106°.

VSEPR Table - The bond angles in the table below are ideal angles from the simple VSEPR theory, followed by the actual angle for the example given in the following column where this differs. For many cases, such as trigonal pyramidal and bent, the actual angle for the example differs from the ideal angle, but all examples differ by different amounts. For example, the angle in H2S (92°) differs from the tetrahedral angle by much more than the angle for H2O (104.5°) does. [Steric # refers to the # of valence electrons.]

Steric # Bonding electron

pairs

Lone pairs

Shape Ideal bond angle (example's bond angle)

Example Image

2 2 0 linear 180° CO2

3 3 0 trigonal planar 120° BF3

3 2 1 bent (non-linear) 120° (119°) SO2

4 4 0 tetrahedral 109.5° CH4

4 3 1 trigonal pyramidal 107.5° NH3

4 2 2 bent (V-shape) 104.5° H2O

5 5 0 trigonal bipyramidal 90°, 120° PCl5

5 4 1 seesaw 180°, 120°, 90° (173.1°, 101.6°) SF4

5 3 2 T-shaped 90°, 180° (87.5°, < 180°) ClF3

5 2 3 linear 180° XeF2

6 6 0 octahedral 90°, 180° SF6

6 5 1 square pyramidal 90° (84.8°), 180° BrF5

6 4 2 square planar 90° 180° XeF4

7 7 0 pentagonal bipyramidal 90°, 72° IF7

7 6 1 pentagonal pyramidal 90°, 72° XeOF5−

11 AXE Method - The "AXE method" of electron counting is commonly used when applying the VSEPR theory. The A represents the central atom and

always has an implied subscript one. The X represents the number of sigma bonds between the central atoms and outside atoms. Multiple covalent

bonds (double, triple, etc) count as one X. The E represents the number of lone electron pairs surrounding the central atom. The sum of X and E,

known as the steric number, is also associated with the total number of hybridized orbitals used by valence bond theory.

Based on the steric number and distribution of X's and E's, VSEPR theory makes the following predictions:

Steric No.

AXE Model Basic Geometry

0 lone pair 1 lone pair 2 lone pairs 3 lone pairs

2 AX 2E0 linear

3 AX 3E0 trigonal planar

bent (non-linear)

4 AX 4E0

tetrahedral

trigonal pyramid

bent (V-shape)

5 AX 5E0

trigonal bipyramid

seesaw

T-shaped

linear

6 AX 6E0

octahedral

square pyramid

square planar

7 AX 7E0

pentagonal bipyramid

pentagonal pyramid

Element # of Valence

Electrons # of Bonds

# of lone pairs of electrons

Steric # Molecular Structure

Be, Mg: 2 2 0 2 Linear

B, Al: 3 3 0 3 Trigonal planar

C, Si: 4 4 0 4 Tetrahedral

P, As: 5 3 1 4 Trigonal pyramidal

P, As: 5 5 0 5 Trigonal bipyramidal

S, Se: 6 2 (2 doubles) 1 3 Bent (non-linear)

S, Se: 6 3 0 3 Triangular planar

S, Se: 6 2 2 4 Bent (V-shape)

S, Se: 6 4 1 5 Seesaw,

S, Se: 6 6 0 6 Octahedral

Xe: 8 8 (4 doubles) 0 4 Tetrahedral

Xe: 8 2 3 5 Linear

Xe: 8 4 2 6 Square planar

Xe: 8 5 (1 double) 1 6 Square pyramidal

Xe: 8 6 (1 double) 1 7 Pentagonal pyramidal

12 A hypervalent molecule is a molecule that contains one or more main group elements formally bearing more than eight electrons in their valence shells. Several specific classes of hypervalent molecules exist:

• Hypervalent iodine compounds are useful reagents in organic chemistry (e.g. triiodide C13H13IO8 (Dess-Martin periodinane))

• Tetra-, penta- and hexacoordinated phosphorus, silicon, and sulfur compounds (ex. PCl5, PF5, SF6, sulfuranes and persulfuranes)

• Noble gas compounds (ex. xenon tetrafluoride, XeF4)

• Halogen polyfluorides (ex. ClF3, ClF5)

• Non-classical carbocations (ex. Norbornyl cation: an organic compound and a saturated hydrocarbon with chemical formula C7H12)

• Many common acids (ex. chloric acid, phosphoric acid, and sulfuric acid)

When the substituent (X) atoms are not all the same, the geometry is still approximately valid, but the bond angles may be slightly different from the ones where all the outside atoms are the same. For example, the double-bond carbons in alkenes like C2H4 are AX3E0, but the bond angles are not all exactly 120°. Similarly, SOCl2 is AX3E1, but because the X substituents are not identical, the XAX angles are not all equal.

Examples The methane molecule (CH4) is tetrahedral because there are four pairs of electrons. The four hydrogen atoms are positioned at the vertices of a tetrahedron, and the bond angle is cos-1(-1/3) ≈ 109°28'. This is referred to as an AX4 type of molecule. As mentioned above, A represents the central atom and X represents all of the outer atoms.

The ammonia molecule (NH3) has three pairs of electrons involved in bonding, but there is a lone pair of electrons on the nitrogen atom. It is not bonded with another atom; however, it influences the overall shape through repulsions. As in methane above, there are four regions of electron density. Therefore, the overall orientation of the regions of electron density is tetrahedral. On the other hand, there are only three outer atoms. This is referred to as an AX3E type molecule because the lone pair is represented by an E. The observed shape of the molecule is a trigonal pyramid, because the lone pair is not "visible" in experimental methods used to determine molecular geometry. The shape of a molecule is found from the relationship of the atoms even though it can be influenced by lone pairs of electrons.

A steric number of seven is possible, but it occurs in uncommon compounds such as iodine heptafluoride. The base geometry for this is pentagonal bipyramidal.

The most common geometry for a steric number of eight is a square antiprismatic geometry. Examples of this include the octafluoroxenate ion (XeF2−8) in nitrosonium octafluoroxenate, octacyanomolybdate (Mo(CN)4−8), and octafluorozirconate (ZrF4−8).

Exceptions: There are groups of compounds where VSEPR fails to predict the correct geometry. Transition metal compounds Many transition metal compounds do not have geometries explained by VSEPR which can be ascribed to there being no lone pairs in the valence shell and the interaction of core d electrons with the ligands (In coordination chemistry, a ligand is an atom, ion, or molecule (see also: functional group) that binds to a central metal-atom to form a coordination complex. The bonding between metal and ligand generally involves formal donation of one or more of the ligand's electron pairs. The metal-ligand bonding can range from covalent to more ionic. Furthermore, the metal-ligand bond order can range from one to three. Ligands are viewed as Lewis bases, although rare cases are known involving Lewis acidic "ligands."). The structure of some of these compounds, including metal hydrides and alkyl complexes such as hexamethyltungsten, can be predicted correctly using the VALBOND theory, which is based on sd hybrid orbitals and the 3-center-4-electron bonding model. Crystal field theory is another theory that can often predict the geometry of coordination complexes.

Group 2 halides The gas phase structures of the triatomic halides of the heavier members of group 2, (i.e. calcium, strontium and barium halides, MX2), are not linear as predicted but are bent, (approximate X-M-X angles: CaF2, 145°; SrF2, 120°; BaF2, 108°; SrCl2, 130°; BaCl2, 115°; BaBr2, 115°; BaI2, 105°). It has been proposed by Gillespie that this is caused by interaction of the ligands with the electron core of the metal atom, polarising it so that the inner shell is not spherically symmetric, thus influencing the molecular geometry.

Some AX2E2 molecules One example is molecular lithium oxide, Li2O, which is linear rather than being bent, and this has been ascribed to the bonding being essentially ionic leading to strong repulsion between the lithium atoms. Another example is O(SiH3)2 with an Si-O-Si angle of 144.1° which compares to the angles in Cl2O (110.9°), (CH3)2O (111.7°)and N(CH3)3 (110.9°). Gillespies rationalisation is that the localisation of the lone pairs, and therefore their ability to repel other electron pairs, is greatest when the ligand has an electronegativity similar to, or greater than, the central atom. When the central atom is more electronegative, as in O(SiH3)2, the lone pairs are less well localised, have a weaker repulsive effect and this combined with the stronger ligand-ligand repulsion (-SiH3 is a relatively large ligand compared to the examples above) gives the larger than expected Si-O-Si bond angle. Some AX6E1molecules Some AX6E1 molecules, e.g. the Te(IV) and Bi(III) anions, TeCl6

2−, TeBr62−, BiCl6

3−, BiBr63− and BiI6

3−, are regular octahedra and the lone pair does not affect the geometry. One rationalisation is that steric crowding of the ligands allows no room for the non-bonding lone pair; another rationalisation is the inert pair effect.

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Molecule Type

Steric # # of Bond

Pair # of Lone

Pair Shape

Electron arrangement

Geometry Examples

AX 1En 1 1 0 Diatomic (polar/non-

polar) HF, O2 ,

AX 2E0 2 2 0 Linear (non-polar) , , BeCl2, MgCl2, CO2

AX 3E0 3 3 0 Trigonal planar (non-

polar)

, BF3 ,

(electronic deficient), CO3

2−, NO3

−, SO3

AX 2E1 3 2 1 Bent

(non-linear :polar))

, SO2 , NO2 , O3

AX 4E0 4 4 0 Tetrahedral (non-polar)

CH4 , , PO43−

, SO42−

, ClO4−

, ,

, AX3E1 4 3 1 Trigonal pyramidal

(polar)

NH3, PCl3 , , −3ClO

AX 2E2 4 2 2 Bent (V-shape: polar))

H2O, , OF2 , 2ClO

AX 5E0 5 5 0 Trigonal Bipyramidal

(non-polar)

PCl5 , ,

(electrophilic)

AX 4E1 5 4 1 Seesaw (polar)

SF4 , , , ,

AX 3E2 5 3 2 T-shaped (polar)

ClF3 , BrF3

AX 2E3 5 2 3 Linear (non-polar)

XeF2 , I3

−

AX 6E0 6 6 0 Octahedral (non-polar)

SF6 ,

(electrophilic)

AX 5E1 6 5 1 Square Pyramidal (polar)

ClF5, BrF5,

(xenon oxytetrafluoride)

AX 4E2 6 4 2 Square Planar (non-

polar)

XeF4

AX 7E0 7 7 0 Pentagonal bipyramidal

(non-polar)

IF7

AX 6E1 7 6 1 Pentagonal pyramidal

(polar)

XeOF5−, IOF5

2−

† Electron arrangement including lone pairs, shown in pale yellow ‡ Observed geometry (excluding lone pairs)

14

Steric # 0 lone pair 1 lone pair 2 lone pairs 3 lone pairs

H – 1 HBr : linear

Be – 2 (Cl-Be-Cl) : linear

B – 3

: trigonal planar

: tetrahedral

C – 4

: tetrahedral

: trigonal planar

: trigonal planar

: trigonal planar

: linear (no lone lair)

: linear (diatomic)

N – 5

: trigonal planar

: tetrahedral

: linear

: bent

: trigonal pyramidal

P – 5

: trigonal bi[yramidal

: tetrahedral

: trigonal pyramidal

As – 5

: trigonal pyramidal

O – 6

: bent

: bent (V-shape)

: bent (V-shape)

15

S – 6

: octahedral

: trigonal planar

: seesaw

: bent

: bent

Br – 7

: pentagonal bipyramidal

: pentagonal pyramidal

: square pyramidal

: square pyramidal

: seesaw

: trigonal pyramidal

: T-shape

: T-shape

: T-shape

: bent (special)

: linear

Xe –8

: tetrahedral

: pentagonal pyramidal

: trigonal pyramidal

: seesaw

: square pyramidal

: pentagonal

pyramidal

: square planar

: linear

One- and three-electron bonds - Bonds with one or three electrons can be found in radical species, which have an odd number of electrons. The simplest example of a 1-electron bond is found in the hydrogen molecular cation, H2

+. One-electron bonds often have about half the bond energy of a 2-electron bond, and are therefore called "half bonds". However, there are exceptions: in the case of dilithium, the bond is actually stronger for the 1-electron Li2

+ than for the 2-electron Li2. This exception can be explained in terms of hybridization and inner-shell effects. The simplest example of three-electron bonding can be found in the helium dimer cation, He2

+, and can also be considered a "half bond" because, in molecular orbital terms, the third electron is in an anti-bonding orbital which cancels out half of the bond formed by the other two electrons. Another example of a molecule containing a 3-electron bond, in addition to two 2-electron bonds, is nitric oxide, NO. The oxygen molecule, O2 can also be regarded as having two 3-electron bonds and one 2-electron bond, which accounts for its paramagnetism and its formal bond order of 2. Molecules with odd-electron bonds are usually highly reactive. These types of bond are only stable between atoms with similar electronegativities Bent bonds, also known as banana bonds, are bonds in strained or otherwise sterically hindered molecules whose binding orbitals are forced into a banana-like form. Bent bonds are often more susceptible to reactions than ordinary bonds.

16 Some Special Structures and Bondings

B – 3

: hexagonal

sphalerite

wurtzite

N – 5

trigonal planar planar

: linear

:

: planar

: planar

P – 5

:

:

:

O – 6

: bent

: nonplanar

S – 6

(trisulfur): bent

: bent

: crown

:

Br – 7

: three-electron bond

17

(1) Structure of Boron nitride (BN) - Boron nitride has been produced in an amorphous (α -BN) and crystalline forms. The most stable crystalline form is the hexagonal one, also called h-BN, α-BN, or g-BN (graphitic BN). It has a layered structure similar to graphite. Within each layer, boron and nitrogen atoms are bound by strong covalent bonds, whereas the layers are held together by weak van der Waals forces. The interlayer "registry" of these sheets differs, however, from the pattern seen for graphite, because the atoms are eclipsed, with boron atoms lying over and above nitrogen atoms. This registry reflects the polarity of the B-N bonds. Still, h-BN and graphite are very close neighbors and even the BC6N hybrids have been synthesized where carbon substitutes for some B and N atoms. As diamond is less stable than graphite, cubic BN is less stable than h-BN, but the conversion rate between those forms is negligible at room temperature. The cubic form has the sphalerite crystal structure, same as diamond structure, and is also called β-BN or c-BN. The wurtzite BN form (w-BN) has similar structure as lonsdaleite, rare hexagonal polymorph of carbon. In both c-BN and w-BN boron and nitrogen atoms are grouped into tetrahedra, but the angles between neighboring tetrahedra are different.

α-BN, hexagonal β-BN, sphalerite structure BN, wurtzite structure

(2) Structure and properties of hydrogen peroxide ( )

H2O2 adopts a nonplanar structure of C2 symmetry. Although chiral, the molecule undergoes rapid racemization. The flat shape of the anti conformer would minimize steric repulsions, the 90° torsion angle of the syn conformer would optimize mixing between the filled p-type orbital of the oxygen (one of the lone pairs) and the LUMO of the vicinal O-H bond. The observed anticlinal "skewed" shape is a compromise between the two conformers. Despite the fact that the O-O bond is a single bond, the molecule has a high barrier to complete rotation of 29.45 kJ/mol (compared with 12.5 kJ/mol for the rotational barrier of ethane). The increased barrier is attributed to repulsion between one lone pair and other lone pairs. The bond angles are affected by hydrogen bonding, which is relevant to the structural difference between gaseous and crystalline forms; indeed a wide range of values is seen in crystals containing molecular H2O2. (3) Structure and properties - Dinitrogen tetroxide (N2O4) forms an equilibrium mixture with nitrogen dioxide. The molecule is planar with an N-N bond distance of 1.78 Å and N-O distances of 1.19 Å. Unlike NO2, N2O4 is diamagnetic. It is also colorless but can appear as a brownish yellow liquid due to the presence of NO2 according to the following equilibrium: N2O4 ⇌ 2 NO2

(4) Structure and bonding of Chlorine Dioxide (ClO2)

Pauling's proposal: The molecule ClO2 has an odd number of valence electrons and it is therefore a paramagnetic radical. Its electronic structure has baffled chemists for a long time because none of the possible Lewis structures are very satisfactory. In 1933 L.O. Brockway proposed a structure that involved a three-electron bond. Acclaimed chemist Linus Pauling further developed this idea and arrived at two resonance structures involving a double bond on one side and a single bond plus three-electron bond on the other. In Pauling's view the latter combination should represent a bond that is slightly weaker than the double bond. In molecular orbital theory this idea is commonplace if the third electron is placed in an anti-bonding orbital. Later work has confirmed that the HOMO is indeed an incompletely-filled orbital.

18 Initial Orbitals

Changes in Orbital Config

Hybrid Orbital of Central Atom

Number of Electron Pairs (0 Lone Pair) 1 Lone Pair 2 Lone Pairs 3 Lone Pairs

Single Bond

(Be,Mg)

2: linear

(B,Al)

3: trigonal planar ( )

2:Bent (nonlinear)

104.50

(C,Si)

4: tetrahedral ( ): 4,4,44 XeOSiHCHAX

3:trigonal pyramidal

2:bent -V-shape ( , )

(P,As)

5: trigonal bipyramidal

4:Unsymmetrical (seesaw): 4SF

3:T-shape : 3ClF

2:linear 2XeF ,−3I

(S,Se)

6: octahedral: 6SF

5:square pyramidal:

5BrF , 4XeOF

4:square planar:

4XeF

Double Bond: end-to-end

overlap : σ side-by-side

overlap: π

σ -bond

bond−π

Shape of Molecule Double Bond

Linear

3 of the 4 orbitals mixed to

form 2sp

hybrid orbitals, an unhybridized p orbital for a C atom

42: HCethene

πσ & : double

Other Examples of double bonds:

OCH2 (i)

(ii) 2CO

Double Bond: 2 orbitals mixed to form sp

hybrid, 2 unhybridized p orbitals

22: HCethyne

ρσ 2& : triple

Other Examples of triple bonds: (i)

NNN ≡:2

(iii) HCNCN or −

In Pauling’s Valence Bond Theory, the end-to-end overlap of (a) s orbitals, (b) p orbital, and (c) hybrid orbitals produces a sigma (σ ) bond, and side-by-side overlap of unhybridized orbitals (made possible by partial hybridization of all available orbitals) produces a pi (π ) bond . The additional shared pair of electrons in the pi-bond provides greater attraction to the two carbon nuclei.

Central

B atom

has 6 e:

nonoct

19

Boron tribromideBoron tribromideBoron tribromideBoron tribromide Phosphorus trichloridePhosphorus trichloridePhosphorus trichloridePhosphorus trichloride Ethane (Ethane (Ethane (Ethane (C2H6)

Trigonal Planar

Trigonal pyramidal

Tetrahedral Bipyramidal [tetrahedral at C]

*3 Examples of Unusual Structure and Bonding: (1) Hydrazine can arise via coupling a pair of ammonia molecules by removal of one hydrogen per molecule. Each H2N-N subunit is pyramidal in shape, so it has a “triangular pyramidal at N” shape. The N-N distance is 1.45 Å (145 pm), and the molecule adopts a gauche conformation. The rotational barrier is twice that of ethane. These structural properties resemble those of gaseous hydrogen peroxide, which adopts a "skewed" anticlinal conformation, and also experiences a strong rotational barrier. (2) Diborane is also named boroethane, boron hydride, and diboron hexahydride. Diborane adopts a D2h structure containing four terminal and two bridging hydrogen atoms [Tetrahedral (for boron)). The model determined by molecular orbital theory indicates that the bonds between boron and the terminal hydrogen atoms are conventional 2-center, 2-electron covalent bonds. The bonding between the boron atoms and the bridging hydrogen atoms is, however, different from that in molecules such as hydrocarbons. Having used two electrons in bonding to the terminal hydrogen atoms, each boron has one valence electron remaining for additional bonding. The bridging hydrogen atoms provide one electron each. Thus the B2H2 ring is held together with four electrons, an example of 3-center-2-electron bonding. This type of bond is sometimes called a 'banana bond'. The lengths of the B-Hbridge bonds and the B-Hterminal bonds are 1.33 and 1.19 Å respectively, and this difference in the lengths of these bonds reflects the difference in their strengths, the B-Hbridge bonds being relatively weaker. The structure is isoelectronic with C2H6

2+, which would arise from the diprotonation of the planar molecule ethene. [Ethene: This hydrocarbon has four hydrogen atoms bound to a pair of carbon atoms that are connected by a double bond. All six atoms that comprise ethylene are coplanar. The H-C-H angle is 119°, close to the 120° for ideal sp² hybridized carbon. The molecule is also relatively rigid: rotation about the C-C bond is a high energy process that requires breaking the π-bond.] Diborane is one of many compounds with such unusual bonding.

(1) Hydrazine:(1) Hydrazine:(1) Hydrazine:(1) Hydrazine:

triangular pyramidal at N (2) Diborane:(2) Diborane:(2) Diborane:(2) Diborane: Tetrahedral (for boron) ((((((((33333333)))))))) EEEEEEEEtttttttthhhhhhhhyyyyyyyylllllllleeeeeeeennnnnnnneeeeeeee ((((((((eeeeeeeetttttttthhhhhhhheeeeeeeennnnnnnneeeeeeee))))))))

All six atoms that comprise ethylene are coplanar. The H-C-H angle is 119°, close to the 120° for ideal sp² hybridized carbon.

Of the other elements in Group 13, gallium is known to form a similar compound, digallane, Ga2H6. Aluminium forms a polymeric

hydride, (AlH 3)n, although unstable Al2H6 has been isolated in solid hydrogen and is isostructural with diborane and digallane. No hydrides of indium and thallium have yet been found. [Structure: Alane or aluminum hydride is a polymer. Its formula is sometimes represented with the formula (AlH3)n. Aluminium hydride forms numerous polymorphs, which are named α-alane, α’-alane, β-alane, δ-alane, ε-alane, θ-alane, and γ-alane. α-Alane has a cubic or rhombohedral morphology, whereas α’-alane forms needle like crystals and γ-alane forms a bundle of fused needles. Monomeric AlH3 has been isolated at low temperature in a solid noble gas matrix and shown to be planar. The dimer Al2H6 has been isolated in solid hydrogen and is isostructural with diborane,B2H6, and digallane, Ga2H6.]

20

Single Bond:

sp hybrid

AX2

BeH2

Single Bond:

sp2 hybrid

AX3

Single Bond:

sp3

hybrid

AX4

Double Bond:

sp2

hybrid

AX5

For this carbon atom, the sp2

hybrids are planar at 1200 to each other and the p orbital is at right angles to the plane of the hybrid orbitals

(a) The sigma bonds for a C2H4 molecule use the sp

2 hybrid orbitals.

(b) The two half-filled p orbitals of the adjacent carbon atoms overlap sideways.

(c) The complete bonding orbitals for a C2H4 molecule

Triple Bond:

sp

Hybrid

AX5

Instead of mixing all four orbitals, valence bond theory suggests that only two are mixed to form sp hybrid orbitals and two unhybridized p orbitals for a carbon atom.

(a) The sigma bonds for a C molecule use the sp hybrid orbitals.

(b) The two pairs of half-filled p

orbitals of the adjacent carbon atoms overlap sideways.

(c) The complete bonding orbitals for a C2H2 molecule.

(d) 2s22p3

21

Single Bond

sp3d

Hybrid

AX5

PCl5 AsF5

AX5, Trigonal Bipyramidal AX4E, See-Saw AX3E2, T-Shaped AX2E3Linear

Single Bond

sp3 d

2

Hybrid

AX6

AX6, Octahedral AX5E, Square Pyramidal AX4E2, Square Planar

Single Bond

sp3d

3

Hybrid

AX7

Pentagonal

bipyramidal (90°, 72°)

sp3d3 hybridisation

E.g., IF7, V(CN)74−

Single Bond

sp3d

4

Hybrid

AX8

Square antiprismatic

sp3d4 hybridisation

E.g., IF8−, Re(CN)8

3−

Single Bond

sp3d

5

Hybrid

AX9

Tricapped trigonal prismatic

sp3d5 hybridisation

E.g., ReH92−

22

23

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++

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++

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24