Atomic and Molecular Orbitals

1. Atomic and Molecular Orbitals Recall the following principles from General Chemistry • The horizontal rows of the periodic table are called Periods. • Each period represents a different quantum energy level. • All of the atoms in a given row have a set of electrons at various energy levels (i.e. the principle quantum level; 1, 2, 3 etc.) • The highest energy level is called the valence shell. • Within each period there may be 1, 2, 3 or 4 sublevels, designated as s, p, d, and f. These are atomic orbitals.

2. 5. Atomic and Molecular Orbitals One way to show the relative energies of the quantum levels and the atomic orbitals is the diagram below: We are most interested in level 2, where carbon is. Note that when atomic orbitals are of the same energy, they are called degenerate. For simplicity, we refer to atomic orbitals and their quantum levels as 1s, 2s, 2p, 3s etc.

3. 5. Atomic and Molecular Orbitals The three dimensional picture of an atomic orbital is actually a combination of all the individual equations which describe, in terms of energy, repulsive forces, etc., just where an electron is most likely to be found in relation to the nucleus at any given point in time. The calculations provide what is known as a probability distribution. This model is used for isolated atoms. So, pictures that you see that describe the “shape” of an orbital, are really probability distributions. For example, when we say that an s orbital is spherical, what we are really mean is that there is a 90% probability that you can find an electron in that spherical space at any given time.

4. 5. Atomic and Molecular Orbitals 1. The location of an electron can be considered as a wave property. Different amplitudes are shown as different colors or by using + (positive) and - (negative) signs. Note that these do not signify charge. Nodes are areas where the probability of finding an electron is zero. 2. An atomic orbital is an area of high probable electron density. p orbitals; there are 3 of these

5. 5. Atomic and Molecular Orbitals When two atomic orbitals overlap, and one electron from each is shared between the two nuclei, the new probability distribution is called a molecular orbital (MO). When two atomic orbitals overlap, we get two molecular orbitals, not one. This is called the linear combination of atomic orbitals (LCAO).

6. 5. Atomic and Molecular Orbitals The p MO’s that we will consider result from side by side overlap of two p AO’s. Lobes of the same wave amplitude can line up (constructive overlap), which give bonding MO’s. The lining up of lobes with opposite amplitudes (destructive overlap) gives anti-bonding MO’s. The bond formed by the constructive parallel overlap of two p AO’s is a  bond.

7. 5. Atomic and Molecular Orbitals Using the AO and MO theory that we have just reviewed, we can draw an MO diagram for a typical C-H bond. To do so, we must consider the electronic configuration of carbon. Since we are interested in the valence electrons, we look at quantum number 2 electrons only, the 2s22p2. Based upon this, we would expect C to form only two bonds, since only two electrons, those in the p AO, are unpaired.

8. 5. Atomic and Molecular Orbitals The MO diagram for one C-H bond using the classic AO model would look something like the diagram to the right. One of the p electrons from C is bonding to the s electron from H to form a C-H bond. This looks good on paper, but we know from experimental evidence that C doesn’t just form two bonds, it forms four bonds! Thus, our model needs to be changed. Experimental evidence indicates that C forms 4 identical bonds to H.

9. 5. Atomic and Molecular Orbitals We know that: 1. Carbon always forms 4 bonds. 2. But carbon can be bonded to 2,3 or 4 ‘things’. 3. If all the ‘things’ are the same, like 4 H’s, all the bonds are identical in length and strength. 4. When bonded to three ‘things’, one bond is shorter and stronger than the other two degenerate bonds. 5. When bonded to two ‘things’, one bond is even shorter and stronger.

10. 5. Atomic and Molecular Orbitals To accommodate the experimental observations we need: Four degenerate AO’s which will ‘mix’ or combine to form four degenerate MO’s. This mixing is also known as “hybridizing”. For carbon, we have an s and three p orbitals in the second energy level. This means that we have a total of four orbitals; one of them is s, and the other three are p’s. When these four orbitals mix or hybridize, we get four degenerate sp3 orbitals.

11. 5. Atomic and Molecular Orbitals When C has only three ‘things’ bonded to it, we need three AO’s to form those three bonds. This means that we have to combine one s and two p atomic orbitals, to give a total of three degenerate sp2 orbitals. Remember that there is a p AO that has not been pulled into this overlap. This unhybridized p AO has an unshared electron and it forms a bond, a second bond, to ‘something else’. The situation when C is only bonded to two things is analogous.

12. 5. Atomic and Molecular Orbitals Sp3 Hybridized Orbitals: Tetrahedral Geometry

13. 5. Atomic and Molecular Orbitals Sp2 Hybridized Orbitals: Trigonal Planar Geometry

14. 5. Atomic and Molecular Orbitals Sp Hybridized Orbitals: Linear Geometry

15. 5. Atomic and Molecular Orbitals Single Bond:  bond

16. 5. Atomic and Molecular Orbitals Double Bond: 1  and 1 

17. 5. Atomic and Molecular Orbitals Triple Bond: 1  bond and 2  bonds

18. 5. Atomic and Molecular Orbitals Tetrahedral geometry: bond angle = 109.5 0 Trigonal planar geometry: bond angle = 120 0 Linear geometry: bond angle = 180 0

19. Isomers Isomers are different compounds with the same molecular formula. For example, if you are given the molecular formula C3H8, there are two possible structures that you could draw: n-butane and isobutane

20. Isomers Also, whereas you can have rotation about single bonds, you cannot have rotation about double bonds. In other words, double bonds are rigid. One of the consequences of this is that there may be more than one way to draw a formula that contains double bonds. For example, there are two ways to draw the molecule CH3-CH=CH=CH3: These two structures actually represent two completely different molecules. When the two identical groups are on the same side, it is called cis. When they are on opposite sides, it is called trans.

21. Isomers Cis and Trans isomers are called Stereoisomers. Stereoisomers are isomers that differ from one another only in terms of the spatial orientation of the atoms, not in the bonding order of the atoms. Cis and trans isomers are also known as geometric isomers. n-Butane and isobutane are constitutional isomers. Constitutional (structural) isomers differ in their bonding sequence. In other words, their atoms are connected differently.

22. Molecular Dipole Moments The polarity of an individual bond is measured as its dipole moment. The symbol for dipole moment is , and it is measured in units of debye (D). You already know how to identify a polar bond, and how to determine the direction of the bond polarity. But it is possible to consider the dipole moment of the molecule as a whole. The molecular dipole moment is the vector sum of all the individual bond dipole moments. This vector sum reflects both the magnitude and direction of each individual bond dipole moment. Example: both formaldehyde and CO2 have the have polar C=O bonds, but only formaldehyde has a molecular dipole moment.

23. Dipole-Dipole Forces Dipole-dipole forces are attractive intermolecular forces resulting from the attraction of the positive and negative ends of the molecular dipole moments in polar molecules. Two types of dipole-dipole forces are London Dispersion Forces and Hydrogen Bonding.

24. Hydrogen Bonding Hydrogen bonding refers to a particularly strong inter- molecular attraction between a nonbonding pair of electrons and an electrophilic O-H or N-H hydrogen. Note, however, that it is much weaker than a single bond. To see examples of hydrogen bonding, refer to page 65 in your text book. Molecules capable of hydrogen bonding have higher boiling points than molecules of comparable size and molecular weights.

25. London Dispersion Forces London dispersion forces are intermolecular forces resulting from the attraction of coordinated temporary dipole moments induced adjacent molecules. It is the principle attractive force in nonpolar molecules. See page 64 of your text book for examples of this phenomenon. The effects of London forces can be observed when examining the boiling points of simple hydrocarbons. The more highly branched isomeric alkanes are, the lower the boiling point because of decreased surface area.