Chem Ch.10
sp hybridization and triple bonds
- Hybridization of 1 s and 1 p orbital results in 2 sp hybrid orbitals and 2 leftover unhybridized p orbitals. - 1 s orbital and 1 p orbital combine to form 2 sp hybrid orbitals. 2 p orbitals remain unhybridized. The 2 sp hybrid orbitals are arranged in a linear geometry with a 180° angle between them. The unhybridized p orbitals are oriented in the plane that is perpendicular to the hybridized sp orbitals. In this configuration, carbon has 4 half-filled orbitals and can form 4 bonds. The triple bond formed between 2 carbons contains 2 π bonds (overlapping p orbitals) and 1 σ bond (overlapping sp orbitals). The sp orbitals are linear with 180° between them, so the resulting geometry is linear.
Predicting the shapes of larger molecules
- Larger molecules may have 2 or more interior atoms. When predicting the shapes of these molecules, we apply the principles we just covered to each interior atom. - Determine the geometry of each interior atom based on the number of electron groups and lone pairs it has, then use this to detainee the entire 3-D shape of the molecule.
Properties of polar and nonpolar molecules
- Polar molecuels interact strongly with other polar molecules because the positive end of one molecule is attracted to the negative end of another. In a mixture of polar and nonpolar molecules, the polar molecules clump together and exclude the nonpolar molecules, and the nonpolar molecules clump together and exclude the polar molecules. The 2 separate into distinct regions, e.g. oil (nonpolar) and water (polar).
Representing molecular geometries on paper
- Straight line: bond in plane of paper. - Hatched wedge: bond going into page. - Solid wedge: bond coming out of page. - Tetrahedral, trigonal pyramidal, trigonal bipyramidal, seesaw, and octahedral all use hatched wedges and solid wedges.
Summarizing valence bond theory
- The valence electrons of the atoms in a molecule reside in quantum-mechanical atomic orbitals. The orbitals can be the standard s, p, d, and f orbitals or they can be hybrid combinations of these. - A chemical bond results from the overlap of 2 half-filled orbitals with spin-pairing of the 2 valence electrons (or less commonly the overlap of a completely filled orbit with an empty orbital). - The geometry of the overlapping orbitals determines the shape of the molecule. - E.g. in H₂S, the half-filled 1s orbitals of the H atoms overlap and form a bond with 2 of the half-filled 3p orbitals of S. Because the overlapping orbitals on the central atom (sulfur) are p orbitals, and because p orbitals are oriented at 90° to one another, the predicted bond angle is 90°, which is more accurate (92° is the actual angle) than the VSEPR predicted bond angle of less than 109.5°.
Introduction
- VSEPR theory: combining the Lewis model (which helps explain and predict combinations of atoms that form stable molecules) with the idea that valence electron groups repel one another; allows us to predict the general shape of a molecule from its Lewis structure. - Taste and caloric values are independent properties of foods. A particular tasting fits precisely into the active site of a receptor protein, allowing us to taste. The receptor protein often splits apart, causing ion channels in the cell membrane to open, resulting in nerve signal transduction. - Immune response, the sense of smell, and many types of drug action all depend on shape-specific interactions between molecules and proteins. - VSEPR = Valence Shell Electron Pair Repulsion theory.
VSEPR theory: the effect of lone pairs
- When molecules contain central atoms with lone pairs around them, the lone pairs repel other electron groups.
Five electron groups: trigonal bipyramidal geometry
- 5 electron groups around a central atom assume a trigonal bipyramidal geometry. 3 of the groups lie in a single plane, while the other 2 are positioned above and below this plane. - The angles in the trigonal bipyramidal structure aren't all the same. The angles between the equatorial positions (the 3 bonds in the trigonal plane) are 120°, while the angle between the axial positions (the 2 bonds on either side of the trigonal plane) and the trigonal plane is 90°. - PCl₅ is an example.
sp^3d and sp^3d^2 hybridization
- According to the Lewis model, elements in the third row of the periodic table (or below) can exhibit expanded octets. The equivalent concept in valence bond theory is hybridization involving the d orbitals. For third-period elements, the 3d orbitals are involved in hybridization because their energies are close to the energies of the 3s and 3p orbitals. The hybridization of 1 s orbital, 3 p orbitals, and 1 d orbital resutls in sp³d hybrid orbitals have a trigonal bipyramidal arrangement. There is 1 s orbital, 3 p orbitals, and 1 d orbital that combine to form 5 sp³d orbitals, There is left 4 unhybridized d orbitals. - The hybridization of 1 s orbital, 3 p orbitals, and 2 d orbitals results in sp³d² hybrid orbitals. The 6 sp³d² hybrid orbitals have an octahedral geometry. 1 s orbital, 3 p orbitals, and 2 d orbitals combine to form 6 sp³d² orbitals. In this arrangement, 3 d orbitals are left unhybridized.
General statements about hybridization
- The number of standard atomic orbitals added together always equals the number of hybrid orbitals formed. The total number of orbitals is always conserved. - The particular combinations of standard atomic orbitals added together determines the shapes and energies of the hybrid orbitals formed. - The particular type of hybridization that occurs is the one that yields the lowest overall energy for the molecule. Since actual energy calculations are beyond the scope of the book, we use electron geometries determined by VSEPR theory to predict the type of hybridization.
Polyatomic molecules
- The delocalization of electrons over an entire molecule is an important contribution of molecular orbital theory to our basic understanding of chemical bonding. - A chemical bond according to the molecular orbital theory is atoms joining together (or bonding) when the electrons in the atoms can lower their energy by occupying the molecular orbitals of the resultant molecule. Unlike the Lewis model or valence bond theory, the chemical "bonds" in MO theory aren't localized between atoms, but spread throughout the entire molecule.
What is a covalent bond?
- Lewis model: the sharing of electrons; represented by dots. - Valence bond theory: the overlap of half-filled atomic orbitals. - The answers are different because the Lewis model and valence bond theory are different models for chemical bonding. They both make useful and often similar predictions but the assumptions of each model are different, and so are their respective descriptions of a chemical bond.
Common cases of adding dipole moments to determine whether a molecule is polar
- Linear/nonpolar: the dipole moments of 2 identical polar bonds pointing in opposite directions will cancel. - Bent/polar: the dipole moments of 2 polar bonds with an angle of less than 180° between them will not cancel. - Trigonal planar/nonpolar: the dipole moments of 2 identical polar bonds at 120° from each other will cancel. - Tetrahedral/nonpolar: the dipole moments of 4 identical polar bonds in a tetrahedral arrangement (109.5° from each other) will cancel. - Trigonal pyramidal/polar: the dipole moments of 3 polar bonds in a trigonal pyramidal arrangement (109.5° from each other) will not cancel. - Note that in case in which the dopes of 2 or more polar bonds cancel, the bonds are assumed to be identical. If 1 or more of the bonds are different from the other(s), the dipole won't cancel and the molecule will be polar. - *See page 441*
Steps to determine polarity
(1) Draw the Lewis structure for the molecule and determine its molecular geometry. (2) Determine if the molecule contains polar bonds. A bond is polar if the 2 bonding atoms have different electronegativities. If the molecule contains polar bonds, superimpose a vector, pointing toward the more electronegative atom, one at bond. Make the length of the vector proportional to the electronegativity difference between the bonding atoms. (3) Determine if the polar bonds add together to form a net dipole moment. If the vectors sum to 0, the molecule is nonpolar. If the vectors sum to anything else besides 0, the molecule is polar.
Predicting molecular geometries
(1) Draw the Lewis structure for the molecule. (2) Determine the total number of electron groups around the central atom. (Lone pairs, single bonds, double bonds, triple bonds, and single electrons each count as one group.) (3) Determine the number of bonding groups and the number of lone pairs around the central atom. These should sum up to your result from step 2. (Bonding groups include single bonds, double bonds, and triple bonds.) (4) Use the table on page 434 to determine the electron and molecular geometries. If no lone pairs are present around the central atoms, the bond angles will be that of the ideal geometry. If lone pairs are present, then the bond angles may be smaller than the ideal geometry.
Procedure for hybridization and bonding scheme
(1) Write the Lewis structure for the molecule. (2) Use VSEPR theory to predict the electron geometry about the central atom (or interior atoms). (3) Select the correct hybridization for the central atom (or interior atoms) based on the electron geometry. (4) Sketch the molecule, beginning with the central atom and its orbitals, Show overlap with the appropriate orbitals on the terminal atoms. (5) Label all bonds using the σ or π notation followed by the type of overlapping orbitals.
Summarizing VSEPR theory
- *See chart on pg. 434* - The geometry of a molecule is determined by the number of electron groups on the central atom (or on all interior atoms, if there's more than one). - The number of electron groups is determined from the Lewis structure of the molecule. If the Lewis structure contains resonance structures, use any one of the resonance structures to determine the number of electron groups. - Each of the following count as a single electron group: a lone pair, a single bond, a double bond, a triple bond, or a single electron (as in a free radical). - The geometry of the electron groups is determined by their repulsions. In general, electron groups repulsions vary as follows: lone pair-lone pair > lone pair-bonding pair > bonding pair-bonding pair. - Bond angles can vary from the idealized angels because double and triple bonds occupy more space than single bonds (they're bulkier even though they're shorter), and lone pairs occupy more space than bonding groups. The presence of lone paris usually makes bond angles smaller than the ideal angle for the particular geometry. - According to VSEPR theory, the shape of a molecule is determined by repulsions among all electron groups on the central atom (or interior atoms, if there's more than one).
2 electron groups: linear geometry
- 2 single bonds maximize their separation by assuming a 180° bond angle or a linear geometry. - Molecules that form only 2 single bonds, with no lone pairs, are rare because they don't follow the octet rule. However, the same geometry is observed in all molecules that have 2 electron groups (and no lone pairs). - CO₂ has 2 electron groups (the double bonds connecting each O to C) around the central carbon atom. According to VSEPR theory, the 2 double bonds repel each other (just as the 2 single bonds in BeCl₂ repel each other), resulting in a linear geometry. - A double bond counts as one electron group.
Six electron groups: octahedral geometry
- 6 electron groups around a central atom assume an octahedral geometry. In this structure, 4 of the groups lie in a single plane, with a fifth group above the plane and another below it. The angles in this geometry are all 90°. - The structure of this model is highly symmetrical; all 6 bonds are equivalent. - SF₆ is an example.
6 electron groups with lone pairs
- Central atoms with 6 electron groups (1 lone pair and 5 bonding pairs), such as BrF₅, have an octahedral electron geometry because of their 6 electron groups. However, their molecular geometry is square pyramidal because the lone pair can be situated in all 6 positions since they're all equivalent. - When 2 of the 6 electron groups around the central atom are lone pairs, as in XeF₄, the lone pairs occupy positions across from one another (to minimize lone pair-lone pair repulsions), and the resulting molecular geometry is square planar.
Molecular shape and polarity
- Entire molecules, like bonds, can be polar. This depends on their shape and the nature of their bonds. E.g. if a diatomic molecule has a polar bond, the molecule as a whole will be polar; if a bond in a diatomic molecule is nonpolar, the molecule as a whole will be nonpolar. - Electrostatic potential maps indicate regions of electron density. Red areas indicate electron rich regions; blue areas indicate electron poor regions; yellow indicates moderate electron density. The region around the more electronegative atom is more electron rich than the region around the less electronegative atom. - In polyatomic molecules, the presence of polar bonds may or may not result in a polar molecule, depending on the molecular geometry. If the molecular geometry is such that the dipole moments of individual polar bonds sum together to a net dipole moment, then the molecule won't be polar. But if the molecular geometry is such that the dipole moments of the individual polar bonds cancel each other (i.e. sum to 0), then the molecule will be nonpolar. E.g. CO₂ is a nonpolar molecule with polar bonds. H₂O is a polar molecule with polar bonds because it has a bent shape, so it's dipole moments don't sum to 0 like the do in the linear CO₂ molecule. - Vector quantities: things with a magnitude and direction. Dipole moments cancel each other out because they are vector quantities. Each polar bond is like a vector pointing in the direction of the more electronegative atom. The length of the vector is proportional to the electronegativity difference between the bonding atoms.
Second period heteronuclear diatomic molecules
- Heteronuclear diatomic molecules have 2 different atoms. More electronegative = lower energy in atomic orbitals. When 2 atomic orbitals are identical and of equal energy, the weighting of each orbital in forming a molecular orbital is identical. However, when 2 atomic orbitals are different, the weighting of each orbital in forming a molecular orbital may be different. Specifically, when a molecular orbital is approximated as a linear combination of atomic orbitals of different energies, the lower energy orbital makes a greater contribution to the bonding molecular orbital and the higher energy orbital makes a greater contribution to the antibonding molecular orbital. The more electronegative atom will also exhibit more electron density because its atomic orbitals are lower in energy that those of the less electronegative atom. - A given orbital will have lower energy in a more electronegative atom. For this reason, electronegative atoms have the ability to attract electrons to themselves. - E.g. fluorine is so electronegative that in an HF molecule, fluorine's atomic orbitals are all lower in energy than hydrogen's atomic orbitals. Fluorine's 2s orbital is so low in energy compared to hydrogen's 1s orbital that it doesn't contribute noticeably to the molecular orbitals. While fluorine's 2px orbital and hydrogen's 1s orbital combine, the other 2p orbitals of fluorine remain localized on fluoride and are nonbonding orbitals.
Period two homonuclear diatomic molecules
- Homonuclear diatomic molecules (molecules made of 2 atoms of the same kind) formed from second-period elements have between 2 and 16 valence electrons. To explain bonding in these molecules, we must consider the next set of higher energy molecular orbitals, which can be approximated by linear combinations of the valence atomic orbitals of the period 2 elements. - We approximate the molecular orbitals in, Li₂ for example, as linear combinations of the 2s atomic orbitals. The resulting molecular orbitals and MO diagram is similar to that of H₂. Li₂'s 2 valence electrons occupy a bonding MO, so it has a stable bond order of 1. - Be₂ is not stable. It's 4 valence electrons occupy 1 bonding MO and 1 antibonding MO, giving it a bond order of 0. - B₂ has 6 total valence electrons, so we approximate the next higher energy molecular orbitals for B₂ and the rest of the period 2 diatomic molecules as linear combinations of the 2p orbitals taken pairwise. Since the 3 2p orbitals orient along 3 orthogonal axes, we must assign similar axes to the molecules. the LCAO-MOs that result from combining the 2px orbitals (the one that line along the internuclear axis) form each atom looks like a candy in a wrapper, with increased electron density in the internuclear region due to constructive interference between the 2 2p atomic orbitals. It has the characteristic σ shape (cylindrically symmetrical about the bond axis) and is called the σ₂p bonding orbital. The antibonding orbital, called the σ₂p*, has a node between the 2 nuclei (due to destructive interference between the 2 2p orbitals) and is higher in energy than either of the 2px orbitals. Combining the 2pz orbitals from each atom form the π₂p bonding orbital and the π₂p* antibonding orbital. They have a side-by-side orientation (unlike the 2px orbitals, which are oriented end-to-end), and thus have a different shape than the 2px orbitals. The electron density in the bonding MO is above and below the internuclear axis with a nodal plane that includes the internuclear axis. The orbital resembles the electron density distribution of a π bond. The antibonding orbital has an additional node between the nuclei (perpendicular to the internuclear axis). Combining the spy orbitals from each atoms creates more π₂p and π₂p* orbitals, but they have a different shape than the 2pz orbitals. The 2py orbitals have a 90° rotation about the internuclear axis. The energies and names of the bonding and antibonding MOs obtained from the combination of the spy AOs are identical to those obtained from the combination of the 2pz AOs. - The energy ordering for B₂, C₂, and N₂ (σ₂s, σ₂s*, π₂p, σ₂p, π₂p*, σ₂p*) is slightly different than that for O₂, F₂, and Ne₂ (σ₂s, σ₂s*, σ₂p, π₂p, π₂p*, σ₂p*). The degree of mixing between 2 orbitals decreases with increasing energy differences between them. Since B, C, and N have atomic orbitals with energy levels more closely spaced than in O, F, and Ne, there is a change in energy ordering of their molecular orbitals. As bond order increases, the bond gets stronger (greater bond energy) and shorter (smaller bond length). - Paramagnetic = unpaired electrons in MO = attracted to magnetic field. The orbital angular momentum of unpaired electrons have spin and movement around the nucleus that generate tiny magnetic fields. - Diamagnetic = paired electrons in MO = not attracted to magnetic fields (slightly repelled) because electron spin and orbital angular momentum cancel each other out. - Finding out the bond order for these types of molecules means including the 2s and 2p orbitals into the total number of bonding orbitals, and the same for the nonbonding orbitals.
sp^2 hybridization and double bonds
- Hybridization of 1 s and 2 p orbitals results in 3 sp² hybrids and 1 leftover unhybridized p orbital. The notation "sp²" indicates that the hybrids are mixtures of 1 s orbital and 2 p orbitals. The 2 hybrid orbitals have a trigonal planar geometry with 120° angles between them. The unhybridized p orbital is oriented perpendicular to the 2 hybridized orbitals. Each of the sp² orbitals is half-filled. The remaining electron occupies the leftover p orbital even though it's slightly higher in energy. Since the atom (carbon) has 4 half-filled orbitals and can therefore form 4 bonds. - When p orbitals overlap side by side, the resulting bond is a π bond, and the electron density is above and below the internuclear axis. When orbitals overlap end-to-end, the resulting bond is a σ bond. The 2 electrons in a π bond are spread out over both the upper and lower lobes. - When orbitals overlap side-by-side, the result is a pi (π) bond. When orbitals overlap end-to-end, they form a sigma (σ) bond. 2 atoms can form only 1 sigma bond. A single bond is a sigma bond, a double bond consists of a sigma bond and a pi bond, and a triple bond consists of a sigma bond and 2 pi bonds. One, and only one, σ bond forms between any 2 atoms. Additional bonds must be π bonds. - The double bond between 2 atoms according to the valence bond theory consists of 2 different kinds of bonds (1 σ and 1 π), while in the Lewis model the 2 bonds within the double bond appear identical. A double bond in the Lewis model always corresponds to 1 σ and 1 π bond in valence bond theory. - In general π bonds are weaker than σ bonds because the side-to-side orbital overlaps tends to be less efficient than the end-to-end orbital overlap. Consequently, the π bond in a double bond is easier to break than the σ bond. - Because of the side-by-side overlap of the p orbitals, the π bond must essentially break for rotation to occur. Although rotation about a double bond is highly restricted, rotation about a single bond is relatively unrestricted. - Restricted rotation means the molecule exists in 2 forms at room temperature (as isomers; cis and trans; have different properties). Energy causes the π bond to break, the atoms to rotate around the σ bond, then the π bond to reform and the molecule to be a new isomer. - The side-to-side bond of the π bond between 2 p orbitals is different than the end-to-end σ bond. Since the bonds are different types, the bond energy of the double bond isn't just twice the energy of the single bond.
Writing hybridization and bonding schemes
- In computational valence bond theory, the energy of the molecule is calculated using a computer; the degree of hybridization as well as the type of hybridization are varied to find the combination that gives the molecule the lowest overall energy. For our purposes, hybridization schemes are assigned from the electron geometry (using VSEPR theory) of the central atom (or interior atoms) of the molecule. The 5 VSEPR electron geometries and the correpsongin hybridization are as follows: - 2 electron groups = linear = sp - 3 electron groups = trigonal planar = sp² - 4 electron groups = tetrahedral = sp³ - 5 electron groups = trigonal bipyramidal = sp³d - 6 electron groups = octahedral = sp³d² - This method of hybridization scheme isn't 100% accurate, but it's the best we can do without computers.
Valence bond theory: orbital overlap as a chemical bond
- Most advanced bonding theories treat electrons in a quantum-mechanical manner. Modern quantitive approaches to chemical bonding using these theories accurately predict many of the properties of molecules (such as bond lengths, bond strengths, molecular geometries, and dipole moments). - Valence bond theory is the simpler of the 2 more advanced bonding theories. According to this theory, electrons reside in quantum-mechanical orbitals localized on individual atoms. In many cases, these orbitals are simply the standard s, p, d, and f atomic orbitals. In other cases, these orbitals are hybridized atomic orbitals, which are a blend or combination of 2 or more standard atomic orbitals. - When 2 atoms approach each other, the electrons and nucleus of one atom interact with the electrons and nucleus of the other atom. In valence bond theory, we calculate the effect of these interactions on the energies of the electrons in the atomic orbitals. If the energy of the system is lowered because of the interactions, then a chemical bond forms. If the energy of the system is raised by the interactions, then a bond is not formed. - The interaction energy is usually calculated as a function of the internuclear distance between the 2 bonding atoms. When atoms are far apart, interaction energy is nearly 0 because the 2 atoms don't interact to any significant extent. As the atoms get closer, the interaction energy becomes negative. This is a net stabilization that attracts atoms to each other. If the atoms get too close, however, the interaction energy begins to rise, mostly because of the mutual repulsion of the 2 positively charged nuclei. The most stable point occurs at the minimum of the interaction energy, i.e. the equilibrium bond length. At this distance, the 1s orbitals of the 2 atoms have a significant amount of overlap and the electrons spend time in the internuclear region where they can interact with both nuclei. The value of the interaction energy at the equilibrium bond distance is the bond energy. - The interaction energy is usually negative (or stabilizing) when the interacting atomic orbitals contain a total of 2 electrons that can spin-pair (orient with opposing spins). Most commonly, the 2 electrons come from 2 half-filled orbitals, but in some cases the 2 electrons can come from one filled orbital overlapping with a completely empty orbital (called a coordinate covalent bond). In other words, when 2 atoms with half-filled orbitals approach each other, the half-filled orbitals overlap (parts of the orbitals occupy the same space) and the electron occupying them align with opposite spins. This results in a net energy stabilization that constitutes a covalent chemical bond. The resulting geometry of the molecule emerges from geometry of the overlapping orbitals. - When completely filled orbitals overlap, the interaction energy is positive (destabilizing), and no bond forms.
5 electron groups with lone pairs
- SF₄ has 5 electron groups (1 lone pair and 4 bonding pairs). The electron geometry (due to the 5 electron groups) is trigonal bipyramidal. - The lone pair could occupy either an equatorial position or an axial position within the trigonal bipyramidal electron geometry. Since lone pair-bonding pair repulsions are greater than bonding pair-bonding pair repulsions, the lone pair occupies the position that minimizes its interaction wit the bonding pairs. If the lone pair were in an axial position, it would have 3 90° interactions bonding pairs. In an equatorial position, it has only 2 90° interactions. Thus the lone pair occupies the equatorial position. The resulting molecular geometry is called seesaw because it resembles a seesaw. - When 2 of the 5 electron groups around the central atom are lone pairs, as in BrF₃, the lone pairs occupy 2 of the 3 equatorial positions (minimizing the 90° interactions with bonding pairs and also avoiding a lone pair-lone pair 90° repulsion. The resulting molecular geometry is T-shaped. - When 3 of the 5 electron groups around the central atom are lone pairs, as in XeF₂, the lone pairs occupy all 3 of the equatorial positions, and the resulting molecular geometry is linear.
sp^3 hybridization
- The 2s (2 electrons) 2p (2 electrons) form 4 sp³ hybrid orbitals. The notation "sp³" indicates that the hybrid orbitals are mixtures of one s orbital and 2 p orbitals. The hybrid orbitals all have the same energy, so they are degenerate. The 4 hybrid orbitals are arranged in a tetrahedral geometry with 109.5°. The 4 valence electrons occupy the orbitals singly with parallel spins (Hund's rule), so the atoms (in this case carbon) can form 4 bonds with 4 hydrogen atoms. The geometry of the overlapping orbitals (the hybrids) is tetrahedral, with angles of 109.5° between the orbitals, so the resulting geometry of the molecule is tetrahedral, with angles of 109.5° between the orbitals. - Hybridized orbitals readily form chemical bonds because they tend to maximize overlap with other orbitals. However, if the central atom of a molecule contains lone pairs, hybrid orbitals can also accommodate them. The presence of lone pairs in an orbital lower the tendency of the atom to hybridize (the tendency to hybridize increase with the number of bonds formed).
4 electron groups with lone pairs
- The 4 electron groups around the central atom repel one another. If we don't distinguish between bonding electron groups and lone pairs, we find that the electron geometry (the geometrical arrangement of the electron groups) is tetrahedral. However, the molecular geometry (the geometrical arrangement of the atoms) is trigonal pyramidal. The image shows the atom's molecular geometry. - Although the electron geometry and molecular geometry are different, the electron geometry is relevant to the molecular geometry. The lone pair exerts its influence on the bonding pairs. - Different kinds of electron groups result in different amounts of repulsion. Lone pair electrons generally exert slightly greater repulsions than bonding electrons. - If all 4 electron groups in ammonia exerted equal repulsions on one another, the bond angles in the molecule would all be the ideal tetrahedral angle, 109.5°. However, the actual angle between N-H bonds in ammonia is slightly smaller: 107°. - A lone electron pair is more spread out in space than a bonding electron pair because a lone pair is attracted to only 1 nucleus while a bonding pair is attracted to 2. The lone pair occupies more of the angular space around a nucleus, thus exerting a greater repulsive force on neighboring electrons and compressing the N-H bond angles. - A water molecule has 2 bonding pairs and 2 lone pairs. Its electron geometry is tetrahedral, but its molecular geometry is bent. The bond angles in H₂O are smaller (104.5°) than the ideal tetrahedral angles (109.5°) because of the greater repulsion exerted by the lone pair electrons. The bond angle in H₂O is even smaller than in NH₃ because H₂O has 2 lone pairs of electrons on the central atom, which compress the H₂O bond angles to a greater extent than in NH₃. - Electron group repulsions from most repulsive to least repulsive: lone pair-lone pair > lone pair-bonding pair > bonding pair-bonding pair. - Furthermore, the bond angles are as follows: no lone pairs > 1 lone pair > 2 lone pairs. Bond angles get progressively smaller as the number of lone pairs on the central atom increases from 0 to 2.
4 electron groups: tetrahedral geometry
- The VSEPR geometries of molecules with 2 or 3 electron groups around the central atom are 2-D, so they're easily represented on paper. For molecules with 4+ electron groups around the central atom, the geometries are 3-D and more difficult to imagine and draw. The electron groups want to spread out as much as possible. - With 4 electron groups, the molecule assumes a three-dimensional tetrahedral geometry with 109.5° angles between the exterior atoms. This tetrahedral shape allows maximum separation between the 4 electron groups. - Methane is an example.
Linear combination of atomic orbitals (LCAO)
- The simplest trial functions are linear combinations of atomic orbitals, or LCAOs. An LCAO molecular orbital is a weighted linear sum (analogous to a weighted average) of the valence atomic orbitals of the atoms in the molecule. - In the valence bond theory, hybrid orbital are weighted linear sums of the valence atomic orbitals of a particular atom, and the hybrid orbitals remain localized on that atom. In molecular orbital theory, the molecular orbitals are weighted linear sums of the valence atomic orbitals of all the atoms in a molecule, and many of the molecular orbitals are delocalized over the entire molecule. - When molecular orbitals are calculated mathematically, it's actually the wave functions corresponding to the orbitals that are combined. - The name of this molecular orbital is σ₁s. The σ comes from the shape of the orbital, which looks like a σ bond in the valence bond theory, and the 1s comes from its formation by a linear sum of 1s orbitals. The σ₁s orbital is lower in energy than either of the 2 1s atomic orbitals form which it was formed. For this reason, this orbital is called a bonding orbital. When electrons occupy bonding molecular orbitals, the energy of the electrons is lower than it'd be if they were occupying atomic orbitals. - Electrons will seek the lowest energy molecular orbital available, but just as an atom has more than 1 atomic orbital, a molecule has more than one molecular orbital. These orbitals can have different (positive and negative) phases. The different phases of orbitals results in destructive interference between them. The resulting molecular orbital thus has a node between the 2 atoms. The name of this molecular orbit is σ₁s*. The star indicates that this orbital is an antibonding orbital; electrons in antibonding orbitals have higher energies than they did in their respective atomic orbitals and thus tend to raise the energy of the system. - In general, when 2 atomic orbitals are added together to form molecular orbitals, 1 of the resultant molecular orbitals will be lower in energy (the bonding orbital) than the atomic orbitals and the other will be higher in energy (the antibonding orbital). The bonding molecular orbital arises out of constructive interference between overlapping atomic orbitals because both orbitals have the same phase. The antibonding orbital arises out of destructive interference between the overlapping atomic orbitals because subtracting one from the other means the 2 interacting orbitals have opposite phases. For this reason, the bonding orbital has an increased electron density in the internuclear region while the antibonding orbital has a node in the internuclear region. The greater electron density in the internuclear region of bonding orbitals lowers their energy compared to the orbitals in nonbonded atoms. Antibonding orbitals have less electron density in their internuclear region, and their energies are generally higher than in the orbitals of nonbonded atoms. - The picture is of a molecular orbital energy diagram. The molecular orbital (MO) diagram shows how atoms can lower their overall energy by forming bonds because electrons can move from higher energy atomic orbitals into the lower energy σ₁s bonding molecular orbital. - In molecular orbital theory, we define the bond order of a diatomic molecule as: bond order = (number of electrons in bonding MOs - number of electrons in antibonding MOs)/ 2 - A positive bond order means that there are more electrons in bonding MOs than in antibonding MOs. The electrons will therefore have a lower energy than they did in the orbitals of the isolated atoms, and a chemical bond will form. In general, the higher the bond order, the stronger the bond. - A negative or 0 bond order indicates that a bond will NOT form between the 2 atoms because their is no stabilization from the atoms bonding.
Vector addition
- To add 2 vectors that lie on the same line, assign one direction as positive; vectors pointing in that direction have positive magnitudes. Consider vectors pointing in the opposite direction to have negative magnitudes. Then sum the vectors. The positive and negative vectors cancel each other out. - To add 2 vectors in 2 or more direction together, draw a parallelogram in which the 2 vectors form 2 adjacent sides. draw the other 2 sides of the parallelogram parallel to and the same length as the 2 original vectors. Draw the resultant vector beginning at the origin and extending to the far corner of the parallelogram. - To add 3 or more vectors together, add 2 of them together first, then add the 3rd vector to the result.
VSEPR Theory: 5 basic shapes
- VSEPR theory is based on the simple idea that electron groups (lone pairs, single bond, multiple bonds, and even single electrons) repel one another through coulombic forces. - According to VSEPR theory, the repulsions between electron groups on INTERIOR atoms of a molecule determine the geometry of the molecule. - We don't consider electron groups on terminal atoms when determining electron geometry (only the electron groups on the interior atom) because a molecule's geometry is determined by how the terminal atoms are arranged around the central atom, which is determined by how the electron groups are arranged around the central atom. The electron groups on the terminal atoms don't affect this arrangement. - The preferred geometry of a molecule is the one in which the electron groups have the maximum separation (and therefore the minimum energy) possible. - For molecules with just one interior atom (the central atom), the molecular geometry depends on (1) the number of electron groups around the central atom and (2) how many of those electron groups are bonding groups and how many are lone pairs. - When we look at the molecular geometries associated with 2-6 electron groups around the central atom when all of those groups are bonding groups (single or multiple bonds) we get the 5 basic shapes of molecules.
Valence bond theory: hybridization of orbitals
- Valence bond theory accounts for the bonding of polyatomic molecules by incorporating an additional concept called orbital hybridization. - Valence bond theory treats the electrons in a molecule as if they occupied s, p, or d atomic orbitals, but this is a major oversimplification. The concept of hybridization in valence bond theory is a step toward recognizing that the orbitals in a molecule aren't necessarily the same as the orbitals in an atom. - Hybridization: a mathematical procedure in which the standard atomic orbitals are combined to form new atomic orbitals called hybrid orbitals that correspond more closely to the actual distribution of electrons in chemically bonded atoms. Hybrid orbitals are still localized on individual atoms, but they have different shapes and energies form those of standard atomic orbitals. - In valence bond theory, a chemical bond is the overlap of 2 orbitals that together contain 2 electrons. The greater the overlap, the stronger the bond and lower the energy. In hybrid orbitals, the electron probability density is more concentrated in a single directional lobe, allowing greater overlap with the orbitals of other atoms. Hybrid orbitals minimize the energy of the molecule by maximizing the orbital overlap in a bond. - Hybridization often costs energy in most cases, so it only occurs to the degree that the energy payback of the bond formation is large. In general, the more bonds that an atom forms, the greater the tendency of orbitals to hybridize. Central (interior) atoms, which form the most bonds, have the greatest tendency to hybridize; terminal atoms, which form the fewest bonds have the least tendency to hybridize. This book focuses on the hybridization of interior atoms and assumes that all terminal atoms (those bonding to only one other atom) are unhybridized. Hybridization is especially important in carbon, which tends to form 4 bonds in its compounds and therefore always hybridizes.
Molecular orbital theory: electron delocalization
- Valence bond theory can explain the rigidity of a double bond, but it also oversimplifies. We know that the mathematical derivation of energies and orbitals for electrons in atoms comes from solving the Schrodinger equation for the atom of interest. For a molecule, we can theoretically do the same thing. The resulting orbitals would be the actual molecular orbitals of the molecule as a whole (in contrast to valence bond theory, in which the orbitals are those of individual atoms). However, we must still make some approximation. - In molecular orbital theory (MO), we don't solve the Schrodinger equation for a molecule directly; instead we use a trial function, an "educated guess", as to what the solution might be. So instead of a mathematical solution, which would give us a mathematical function describing an orbital, we start with a trial mathematical function for the orbital then test the trial function to see how well it "works." - In order to determine how well a trial function for an orbital "works" in molecular orbital theory, we calculate its energy. No matter how good our trial function, we can never do better than nature at minimizing the energy of the orbital. In other words, we can devise any trial function for an orbital in a molecule and calculate its energy. The energy we calculate for the devised orbital will always be greater than or (at best) equal to the energy of the actual orbital. The best possible orbital will therefore be the one with the minimum energy.
Summarizing LCAO-MO theory
- We can approximate molecular orbitals (MOs) as a linear combination of atomic orbitals (AOs). The total number of MOs formed from a particular set of AOs always equals the number of AOs in the set. - When 2 AOs combine to form 2 MOs, 1 MO is lower in energy (the bonding MO) and the other is higher in energy (the antibonding MO). - When assigning the electrons of a molecule to MOs, fill the lowest energy MOs first with a maximum of 2 spin-paired electrons per orbital. - When assigning electrons to 2 MOs of the same energy, follow Hund's rule: fill the orbitals singly first, with parallel spins, before pairing. - The bond order in a diatomic molecule is the number of electrons in bonding MOs minus then number in antibonding MOs all divided by 2. Stable bonds require a positive bond order (more electrons in bonding MOs than in antibonding MOs). - With the molecular orbital approach, every electron that enters a bonding molecular orbital stabilizes the molecule or polyatomic ion, and every electron that enters an antibonding MO destabilizes it.
3 electron groups: trigonal planar geometry
- When 3 electron groups are around the central atoms, they maximize their separtion by assuming 120° bond angles in a plane, resulting in trigonal planar geometry. BF₃ is an example. - When 1 double bond and 2 single bonds are around the central atom, such as in formaldehyde (CH₂O), there are still 3 electron groups since the double bond counts as a single electron group. However, the bond angles between the atoms (H and O) surrounding the central atom (C) are 116.2° between the 2 H's and 121.9° between the O and each H. These bond angles are close to 120°, but the double bond contains more electron density than the single bond and therefore exerts a slightly greater repulsion on the single bonds. Thus, the angle between the O (which has a double bond) and H molecules is greater than the angle between the 2 H molecules. - In general, different types of electron groups exert slightly different repulsions; the resulting bond angles reflect these differences. - When a molecule has 3 hybrid structures (which makes the 3 bonds equivalent), each exerts the same repulsion on the other 2 and the molecule has 3 equal bond angles of 120°. NO₃⁻ is an example
