Bonding and Structure: Part 1 Organic Molecular Structure PDF

Bonding and Structure: Part 1 Organic Molecular Structure 1 Energies of Electrons in Atoms and Molecules Bonding, structure, shape, and reactions of organic molecules are determined primarily by the energies of the electrons in atomic orbitals (AOs) and mo...

Bonding and Structure: Part 1 Organic Molecular Structure 1 Energies of Electrons in Atoms and Molecules Bonding, structure, shape, and reactions of organic molecules are determined primarily by the energies of the electrons in atomic orbitals (AOs) and molecular orbitals (MOs). In organic chemistry, we use models, generally the simplest one that explains what we are trying to understand. Here, we use a simple model for AOs that describes the factors that determine electron energies in atoms. Later, we will use more sophisticated models for orbitals to understand electron energies in molecules. 1.1 Energies of Electrons in AOs electron in larger 2s A.O., electron stabilized by further from nucleus and nucleus, held "tightly" 3+ shielded by two 1s electrons, close to nucleus, relatively not held tightly, relatively low energy electron H 1s1 high energy electron Li 1s22s1 electron in even larger 2p even higher positive charge A.O., but, higher positive on the nucleus (8+), but now 6+ charge on the nucleus (6+), 8+ atomic orbital has another thus outer electrons held negatively charged electron, reasonably tightly by outer electrons held nucleus, moderate energy reasonably tightly by C 1s22s22p2 O 1s22s22p4 nucleus, moderate energy 1.2 Quantitative Energies of Electrons in Atoms Quantitative information about the relative energies of electrons is obtained from measurements of Ionization Energies (IE), or Ionization Potentials (IP). The first IE/IP is the energy required to completely remove the highest energy electron from an atom or molecule. We are interested mainly in the energies of these highest energy electrons since these are the ones that are involved in chemical bonding and reactions. Higher energy electrons in an atom require less energy to remove, they have smaller IEs. First IEs for some atoms are given below in electron Volts (eV) (don’t memorize these!). Energy energy of an electron infinitely far from any nucleus 13.6 5.4eV 11.3 14.5 13.6 higher eV 2s eV eV eV energy lower 1s energy H 2p 2p 2p 1s1 2p 1s 2s 2p 2p 2p 2p 2p Li 2 1 1s 2s 1s 2s 2s C 1s22s22p2 1s N 1s – "valence" electrons, are involved in reactions/bonding O 1s 2s 2p3 2 2 – "core" electrons, not involved in reactions/bonding 1s 2s22p4 2 Bonding 1 : page 1  Valence electrons are in the outer shell; they are highest in energy and are involved in bonding. Core electrons are in the inner shells; they are not involved in bonding. Understanding the Connection Between IP/IE and Electron Energy The IE is a measure of the energy of the highest energy electron. An electron that has been completely removed from an atom/molecule has a very high energy because it is not stabilized by any nuclei. Electrons associated with an atom in an orbital are lowered in energy because they are negatively charged and are stabilized by the positively charged nucleus. If the energy of an electron in an atom is low (the electron is held “tightly” by the atom), more energy is required to remove it from the atom, the energy required to ionize is large, the IE or IP is large. If the energy of an electron in an atom is high, less energy is required to remove it from the atom, the energy required to ionize is small, and the IE or IP is small. Energy energy of an electron infinitely far from any nucleus very high energy electron smaller less energy larger 5.4eV required to remove more energy 13.6 required to remove 2s higher energy electron eV larger I.P. lower 1s energy electron H 1s1 1s Li 1s22s1 Many factors influence atomic IEs, (orbital size, nuclear charge, orbital occupancy, etc.). However, a detailed understanding of these factors is not necessary at this point. What you should know for now is that electron energy decreases and IE increases, and roughly with increasing electronegativity (i.e., left to right and from bottom to top in the periodic table): hydrogen helium 1 2 H increasing electronegativity He increasing 1.0079 4.0026 DECREASING electron energy lithium beryllium boron carbon nitrogen oxygen fluorine neon 3 4 5 6 7 8 9 10 Li Be 6.941 9.012 INCREASING IP B 10.811 C 12.0107 N 14.007 O 15.999 F 18.998 Ne 20.180 electronegativity DECREASING sodium magnesium aluminium silicon phosphorus sulfur chlorine argon 11 12 13 14 15 16 17 18 Na Mg Al Si P S Cl Ar 22.990 24.306 26.912 28.086 30.974 32.067 35.453 39.948 electron energy INCREASING IP potassium calcium scandium titanium vanadium chromium manganese iron cobalt nickel copper zinc gallium germanium arsenic selenium bromine krypton 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 K Ca 39.098 40.078 Sc Ti 44.956 47.867 V 50.942 Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br 51.996 54.938 55.845 39.098 58.693 63.546 65.39 69.723 72.61 74.922 78.96 79.904 Kr 83.80 rubidium strontium yttrium zirconium niobium molybdenum technetium ruthenium rhodium palladium silver cadmium indium tin antimony tellurium iodine xenon 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 Rb Sr 85.468 87.62 Y Zr Nb Mo Tc Ru Rh Pd Ag Cd 91.224 92.906 95.94 [98.91] 101.07 85.468 106.42 107.87 112.41 In Sn Sb Te 114.818 118.71 121.760 127.60 I 126.904 Xe 131.29 88.906 1.3 Energies of Electrons in Molecules, for example, Hydrogen We can also measure energies of electrons in molecules as IEs. The energies of electrons in molecules are lower than the energies of electrons in atoms. Energy energy of an electron that is infinitely far from any nucleus IP ~ 13.6 IP ~ 15.4 H atom lower energy 1s atomic orbital IN A BOND H2 molecule σ molecular orbital The IE of the electron in the hydrogen molecule is larger than that in the hydrogen atom. Bonding 1 : page 2  The energy of the electrons in the molecule must be lower than in the atom. Why? Because in the electrons in the molecule are in a bond—this is really important! electron stabilized each electron H atom by one nucleus stabilized by H2 molecule, covalent bond 1s atomic orbital two nuclei σ molecular orbital In the atom, the negatively charged electron is stabilized by one positively charged nucleus; in the molecule, the negatively charged electrons are stabilized by two positively charged nuclei. We have just learned why hydrogen exists as the molecule H2 not as hydrogen atoms, making the molecule lowers the energy of the electrons by getting them into a bond: H + H H H atoms molecule This is our first very simple chemical reaction. Two hydrogen atoms react to form a hydrogen molecule, the electrons in the hydrogen atoms are chemically reactive, they want to do a chemical recation to form H2. We have already learned two critical concepts for understanding organic chemistry: 1. Forming bonds stabilizes (lowers the energies of) electrons. 2. Higher energy electrons are more chemically reactive (because they want to form bonds). 2 Bonding in Molecules: The Lewis Structure Model Lewis structures represent a model for bonding in organic molecules, they are not always 100% accurate, but they are useful because they are simple, and we tend to use the simplest model wherever possible. 2.1 Atomic Valence and Lewis Structures Making a Molecule of Hydrogen (H2) as a Simple Example Each hydrogen atom makes one bond, because in doing so it lowers the energy of its one valence electron. Hydrogen can only make one bond because it only has one valence electron. Making one bond fills the first shell of the hydrogen atom with two electrons. 1 valence electron shared electrons: covalent bond 1s H H H H H H H H electron configuration Lewis or Kekule Lewis "dot" structure structure Note the use of curved arrow notation, “move or use an electron from each atom to make a new bond.” Making a Molecule of CH4 as an Example 2 core H shares 8 electrons 4 valence electrons shares 2 H filled second shell H C H H C H H C H 1s2 2s22p2 C H H H C electron configuration H Lewis "dot" structure Lewis or Kekule structure After making four bonds, a carbon atom’s second outer shell is “full” with eight shared electrons, it obeys the “filled shell,” sometimes called the “octet rule,” for second row elements. Bonding 1 : page 3  The hydrogens also have a “full"” first shell with two electrons. The filled shell “rule” and the pictures of the Lewis dot structures are models of organic structures. Making a Molecule of NH3 as a Simple Example 2 2 core core H no more bonds electrons electrons 55 valence electrons valence electrons shares 2 X shares 8 shares 2 octet rule 1s2 2s22p3 N H N H H HN N H H H N H shares 8 HH H N electron configuration Lewis "dot" structure Lewis or Kekule H structure Nitrogen has five valence electrons, but it can only lower the energy of three electrons in bonds before the outer electron shell is filled with eight electrons. Attempting to make another bond “overfills” the shell, violating the filled shell “rule.” Nitrogen in this structure therefore has two nonbonding electrons in the outer shell. Lewis “dot” structures are tedious to draw, we will use them rarely. Unfortunately, there is more than one use of the word Valence. 1. The outer shell is the valence shell, the electrons in the outer shell are the valence electrons. 2. The number of bonds an atom normally makes without violating the “filled shell rule” is the normal valence. The normal number of bonds, the “Normal Rules of Valence” for different atoms are obtained from the atomic configuration and the filled shell rule. Do not memorize this table! Learn the normal valences by working with and building organic structures. electron # valence maximum possible normal valence atom configuration electrons electrons in outer shell (normal # of bonds) 1st shell H 1s 1 2 11 B 1s2 2s22p1 3 8 33 only 3 valence electrons C 1s2 2s22p2 4 8 44 2nd shell N 1s2 2s22p3 5 8 33 octet "rule" O 1s2 2s22p4 6 8 22 octet "rule" F 1s2 2s22p5 7 8 11 octet "rule" P 1s2 2s22p63s23p3 5 8 33 or or 5! 5! violates 3rd shell S 1s2 2s22p63s23p4 6 8 2,4 2, 4,oror6!6! octet rule! The number of valence electrons is the number of electrons in the highest energy shell. The Normal Valence is the number of electrons that can be used to make a bond before the highest energy shell is filled, it is equal to the number of bonds an atom “normally” makes. Boron has only three valence electrons and so it can make only three bonds, it does not have enough electrons to fill the shell, even if all electrons are involved in bonding. Nitrogen has five valence electrons, but after making three bonds the valence shell is full and the remaining two electrons cannot make bonds, therefore, the normal valence of nitrogen is also three. Oxygen has six valence electrons, after making two bonds the valence shell is full, the normal valence is two. The filled shell or octet rule doesn’t really work for third row elements, for example, phosphorus and sulfur. Example Problem: Draw two different Lewis structures for C2H6O. The Normal Rules of Valence require: Four bonds to each tetravalent carbon (each carbon wants to make four bonds). Two bonds to each divalent oxygen (each oxygen wants to make two bonds). One bond to each monovalent hydrogen (each hydrogen wants to make one bond). Bonding 1 : page 4  To generate Lewis structures, we will learn to assemble molecules using common organic structural motifs, for example, a carbon at the end of a chain usually has three hydrogen atoms bonded to it, -CH3. different structures (isomers) H H same structure O H H H H O H C C O C C drawn H C C H H H H H H H H differently H H Lewis/Kekule structures indicate connectivity of atoms, the orientation or the direction the bonds point doesn’t matter (at least for now). Different Lewis (Kekule) structures for a specific molecular formula are isomers, more on isomers later. 2.2 Condensed Structures In condensed structures, the order of atom connectivity/bonding is implied by the “written” order of the atoms, but the bonds are not explicitly shown, they are implied. This means that the normal valences for the atoms in the structure must be assumed. Example Problem 1: Convert the provided condensed formula into a Lewis/Kekule structure. H H H carbon with 3 H's connected to CH3CH2CH2OH carbon with 2 H's connected to H C C C O carbon with 2 H's connected to oxygen with 1 H H H H H condensed Lewis Obeying the normal rules of valence can generate only one possible Lewis structure. Nonbonding electrons are shown in Lewis structures. Example Problem 2: Convert the provided condensed formula into a Lewis/Kekule structure. Obeying the normal rules of valence for C (four bonds), H (one bond), and O (two bonds) can only generate one possible Lewis structure. parenthesis means repeated unit CH3C(CH3)2CH(OH)CO2CH3 parenthesis means "off" the main chain functional group H H C H H "double bond" H O O 2 bonds to C H C C C C H C H O C H -CO2CH3 = only possible H H C H H O O C H connectivity order H H H Note the carbon to oxygen double bond, which is required to satisfy the normal rules of valence for all atoms. Note the two different uses of parentheses. 1. Parentheses are used to indicate repeating units along the main chain, for example, (CH2)3 in the earlier structure. 2. Parentheses can be used to indicate a part of the structure that comes “off” the main chain, for example, (OH) in the earlier structure. Bonding 1 : page 5  “Rules” for condensed structures are not strictly observed, for example, the parentheses around the “OH” in the earlier structure may be omitted if it is considered obvious that it is “off” the main chain. Example Problem 3: Convert the provided condensed formula into a Lewis/Kekule structure. parenthesis means 2 -CH2- groups in a row CH3(CH2)2CCCOCH2CO2H acid functional group H H H O H O must be a triple bond here H C C C C C C C C H H H O H H Note the use of parentheses in this case to indicate repeating units. The two uses of parentheses are easily distinguishable using the normal rules of valence, only one will “work” in a particular context. 2.3 Line-Angle Structures Line-angle or skeletal structures are most commonly used in organic chemistry. The lines show bonds between carbon atoms; hydrogen atoms are not included unless they are part of a functional group (see later for definition). Example 1 the "kink" H indicates the H H O H C O position of a (CH3)3CCOCH2OCH3 H C C C H carbon atom condensed H C H H Line angle H C H H O C H O (skeletal) Lewis structure H There is an atom (carbon, unless otherwise specified) at the “end” of each line, each line is a covalent bond. Example 2 Draw one example of Lewis (Kekule), condensed and line-angle structures for C4H6O. Lewis structure Condensed structure Line Angle structure H O O H C C 4 1 2 3 4 this H is part of C 2 C H CH2CHCH2CHO the aldehyde 2 4 H H 1 H 3 H 1 3 functional group Where reasonable, draw the angles roughly correct for the molecular shape, see later. Which kind of structure to draw (condensed, Lewis, line angle, etc.) depends upon the context, we will use mainly line angle or even a mixture of line angle and Lewis in one structure. Bonding 1 : page 6  3 Functional Groups 3.1 Anatomy of an Organic Structure Organic molecules consist of a carbon/hydrogen (hydrocarbon) “skeleton” that mainly determines the size and shape of the molecule. Added to this skeleton are the functional groups, which generally include atoms that are more electronegative than carbon, such as O, N, S, and so on. Chemistry takes place at the functional groups. When we start to discuss reactions, we will divide the reactions into those that are characteristic of the different functional groups. Line-angle or skeletal structures are most commonly used, especially for larger molecules. The main structural features of a typical organic molecule are the following: Nonbonding electrons are not included in most of the structures in this section for clarity HO O functional groups OH functional groups O cortisone anti-inflammatory carbon/hydrogen "skeleton" O functional groups The alkane or alkyl part of a molecule is the “skeleton” or “backbone” of the molecule. Alkanes or alkyl groups consist of chains (or rings) of carbon atoms connected together by single C–C and an appropriate number of C–H bonds. C–C and C–H bonds tend to be strong and relatively unreactive. H H H H an example 3 carbon H C C an example alkane (heptane) C C H alkyl chain in a molecule only C and H, no double bonds O H H R stands for any alkyl chain, e.g., R–OH could be: an alkyl chain H3C–OH or CH3CH2OH or NH N R-OH = bupivacaine, an OH epidural anesthetic etc. O Carbon or nitrogen atoms are characterized by the number of alkyl chain (-R) or aryl (aromatic) groups (-Ar, see below) attached to them. Atoms with one substituent are primary (1°). Atoms with two substituents are secondary (2°). Atoms with three substituents are tertiary (3°). Atoms with four substituents are quaternary (4°). H is not counted as a substituent in this context. H is H H R R H not a H C R C C R C R substituent R R R H R H R Primary or 1° Secondary or 2° Tertiary or 3° Quaternary or 4° carbon carbon carbon carbon Bonding 1 : page 7  3.2 Important Functional Groups Alkene Functional Group Carbon–carbon double bond: OH alkene diene C C alkene NOT aromatic (see next section) linalool, used in the perfume industry does not have alternating double/single bonds Aromatic Functional Group Alternating C–C and C=C bonds in a ring—be careful to distinguish from alkene: Ar stands for any aromatic ring system, e.g. Ar–OH could be: O OH aromatic OH Cl OH O aspirin or etc. O this is aromatic because it has alternating single/ double bonds in a (large) ring, an aromatic ring can have more than 6 carbon atoms! Alkyne Functional Group Carbon–carbon triple bond: HO alkyne C mestranol, the estrogen used in many oral C contraceptives O Amine Functional Group Contain a nitrogen with at least one alkyl or aryl group, here R1, R2, and so on, stands for any alkyl chain that may or may not be the same: R1 3° amine 1° amine R or Ar 2° amine HO O N S R2 R3 N N O NH2 H coniine, the tertiary (3°) amine triethylamine taurine, supposedly active ingredient in fishy smell! poison in hemlock energy drinks e.g. Red Bull Ether and Epoxide Functional Group An ether is an oxygen between two alkyl or aryl groups. For the specific case where the oxygen is part of a 3-membered ring the functional group is an epoxide. O ether 4,5-benzo[a]pyrene oxide, O O highly carcinognic (R, Ar) (R, Ar) tetrahydrofuran epoxide THF, a common O organic solvent Bonding 1 : page 8 Alcohol Functional Group Oxygen with one R or Ar group and one hydrogen. Hydrogen atoms are not included in line-angle structures unless they are part of a functional group, the alcohol functional group provides an example of this: 3° carbon bisabolol is used to aid in the O OH transfer of drugs through the skin (R, Ar) H 3° alcohol H is PART of the functional group! Halide Functional Group Aryl or alkyl group with fluoride, chloride, bromide, and iodide: bromide Cl Cl O H R or Ar chloride chloride N Br R Br bromide R F R Cl chloride chloride N Br R I Cl Cl H O a polychlorinated biphenyl (PCB), many industrial 6,6'-dibromoindigo, a component uses but toxic, bioaccumulates in animals of a natural purple dye Ketone Functional Group C=O double bond with two alkyl or aryl groups: O ketone O acetone, the simplest ketone, common organic C C (R, Ar) (R, Ar) H 3C CH3 solvent, nail-polish remover Aldehyde Functional Group C=O double bond with one R or Ar group and one H. Hydrogen atoms are not included in line-angle structures unless they are part of a functional group, the aldehyde functional group provides another example of this: O aldehyde O H vanillin, main extract fron vanilla bean C (R, Ar) H HO H is PART of the OMe functional group! Carboxylic Acid Functional Group C=O with one R or Ar group and one -OH. Hydrogen atoms are not included in line-angle structures unless they are part of a functional group, the carboxylic acid functional group provides another example of this. carboxylic acid O O sorbic acid, food C preservative (R, Ar) OH OH H is PART of the functional group! NOT ketone, NOT alcohol! Bonding 1 : page 9 Ester Functional Group C=O double bond with -OR or -OAr group: ester O O methyl paraben, food C HO preservative, cosmetics (R, Ar) O (R, Ar) O additive, anibacterial/fungal NOT ketone, NOT ether! Amide Functional Group C=O with -NR2 (R or Ar): 3° amide N O OH O H 2° amiDe C R N N N R O 3° amiNe 3° amide Cl loperamide, anti-diarrhea drug Acid Chloride Functional Group C=O double bond with -Cl group: O acid chloride O acetyl chloride, many useful C (R, Ar) Cl Cl reactions Nitrile Functional Group Aryl or alkyl group with carbon–nitrogen triple bond: O nitrile N C N (Ar, R) C N citalopram, antidepressant drug (Ar,R) means aryl or alkyl take after first midterm How Functional Groups Are Represented? Here are some functional groups incorporated into line-angle and condensed structures that you will see and need to understand: nitrile aldehyde carboxylic acid alcohol amide and amine O O O O H H N C N H H OH N H or or or or or OH O CHO CO2H NC NH2 NH Bonding 1 : page 10 Example problems: Indicate all functional groups, do not include alkanes. ester (not ketone or ether) O aromatic (not alkene) H alcohol N amine OH O ether aromatic (not alkene) ether O N amine O Heroin ketone O O aromatic O alkene testosterone ester fluoride CF3 alkene Fluoxetine (Prozac) (not ketone or ether) We like to minimize the amount of memorization in this course, but functional groups have names that can’t be worked out, you just have to know them. You can think of learning the functional groups a couple of ways, by memorization, or by using them. There is nothing wrong with some memorization in any course, things that are memorized are recalled more quickly and accurately, but memorizing names is boring and not the most efficicent use of your time! We suggest you learn the functional groups by working the homework problems, solve as many problems as you can with this list of functional groups, don’t use flashcards! This way you will learn many of the names of the functional groups by doing, and the small number left over that you have not learned yet, those you can memorize! 4 Structural Isomers Isomers are different compounds with the same molecular formula (we have already seen some of these). We meet two kinds of isomers in this course: structural isomers and stereoisomers, to be discussed later. Structural isomers differ in the order in which the atoms are connected (connectivity of the atoms), the order in which the atoms are bonded together are different. The physical and chemical properties of structural isomers are different; they are different molecules. Example 1: Structural isomers for C4H10 CH3 C4H10 H3C CH2 CH2 CH3 H3C CH TWO isomers are CH3 possible butane b.p. = -0.5° isobutane b.p. = -11.7° Example 2: Structural isomers for C5H12 3 4 CH2 CH3 4 CH3 CH3 (5) 2 C5H12 H3C CH2 CH2 CH2 CH3 H3C CH 3 CH2 CH3 H3C C CH3 1 THREE isomers 1 CH3 2 CH CH3 are possible (5) CH3 same structure NOT isomers Note that for now, the direction in which the bonds “point” is irrelevant, structural isomers are generated by connecting atoms together in a different order only. There are thus three different structural isomers with the molecular formula C5H12. Bonding 1 : page 11 Example 3: Generate all of the structural isomers for C6H14. A useful strategy is often to start with the longest possible chain, and progressively “branch”: CH3 CH2 CH2 CH2 CH2 CH3 CH3 same structure CH3 CH2 CH2 CH CH3 generates a new isomer CH3 CH3 CH3 H3C CH CH2 CH2 CH3 CH3 CH2 CH CH2 CH3 CH3 CH2 C CH3 generates a new isomer CH3 CH3 CH3 CH CH CH3 CH3 We find that there are five possible structural isomers. The direction in which the bonds “point” doesn’t matter (for now), the structures are defined only by the order in which the atoms are bonded together. Example 4: How many different structural isomers are shown below? 5 CH A CH3 3 1 2 3 4 5 1 2 3 4 CH3 CH2 CH CH2 CH3 CH3 CH2 CH CH2 CH3 CH3 CH2 CH CH2 1 2 3 4 5 1 2 bond CH3 CH3 H 3C CH2 CH3 rotation B CH2 CH CH2 3 2 3 4 HC CH3 2 bond rotations converts A into B H 3C 1 5 CH 5 4 3 H3C CH2 These are all the same structure, none of them are isomers. Rotation around single C–C bonds does not generate a new chemical structure, just the same structure drawn a different way (later we will see that these different ways of drawing the structures are called conformers). 5 Formal Charges The Lewis structure model attempts to obey the filled shell/octet rule for all atoms by getting as many electrons as possible into bonds (remember, forming bonds lowers electron energy). Sometimes, this can result in structures that disobey the normal rules of valence, resulting in an atom “owning” either more or less electrons than its normal number of valence electrons. This results in a mismatch of protons and electrons, which results in the atom having a formal charge. Example 1 O sees 8, owns 6 electrons, neutral # of valence electrons H O O=6 CH3NO2 H C N N sees 8 electrons, owns 4, positive charge N=5 H O O sees 8, owns 7 electrons, negative charge This is the only reasonable way to draw a Lewis structure for CH3NO2 that gets as many valence electrons into bonds as possible. Bonding 1 : page 12  The “filled shell/octet rule” is obeyed for all atoms, but the normal rules of valence are not (there are four bonds to the nitrogen instead of three, and one bond to the lower oxygen instead of two). The central nitrogen “sees” eight electrons, that is, the ones that are shared in the four bonds, and “owns” four electrons (half of the shared electrons), but is required to “own” five valence electrons to be neutral. It “owns” one fewer electron than required to balance the positive charge on the nucleus, its charge is thus +1. The lower oxygen “sees” eight electrons (six nonbonding and the shared pair in the bond), it “owns” seven electrons (the nonbonding ones and half the shared pair), but it requires six valence electrons to be neutral. This oxygen thus “owns” one extra electron than would be required to balance the positive charge on the nucleus, its charge is thus −1. The Calculation of Formal Charge Using a Formula Formal charge = # valence electrons − (# nonbonding electrons) − 1/2 (# electrons in bonds) Example 2: valence nonbonding bonding H O N = (5) - (0) - 1/2 (8) = +1 H C N C = (4) - (0) - 1/2 (8) = 0 H O O = (6) - (6) - 1/2 (2) = –1 (zero formal charge) valence nonbonding bonding Later, we will learn better ways to determine formal charges that do not use this formula, but it may be useful to use the formula at least for now as a way of making progress in understanding structures. Example 3 Na 5 valance electrons : 5 electrons to be NEUTRAL Na formally "owns" 1 electron for each bond = 4 Na has zero non-bonding electrons "owns" one eless lectron than needed for neutrality : POSITIVE CHARGE H CH2N2 C Na Nb H Nb = (5) - (4) - 1/2 (4) = –1 (one negative charge) valence bonding nonbonding The “filled shell/octet” rule is obeyed in all cases, but the normal rules of valence are not. Formal charges are associated with structures in which the normal rules of valence are not obeyed. # nonbonding zero formal charge Charge = 4 - 2 - 1/2 (4) = 0 C H H # bonding # valence This is methylene (you do not have to know this), it is very reactive (its lifetime is less than 0.0000000001 second in solution), but we can still draw a valid Lewis structure for it. The carbon atom has only two bonds but no charge, not all atoms that disobey the normal rules of valence have a charge! 6 Quantum Mechanical Description of Atomic Orbitals The Lewis structure model works well but doesn’t give a proper description of exactly where the electrons are in the orbitals, we need a much better understanding of what atomic and molecular orbitals really look like so that we will know where the electrons are in atoms and molecules. We also need to learn that electron properties are more complex than indicated by simple Lewis structures. Quantum Mechanics provides a more realistic description of electrons in orbitals. Bonding 1 : page 13 An Apparent Problem: Quantum Mechanics shows that it is impossible to say exactly where an electron is in an orbital, only the probability of finding the electron at a particular point in space can be obtained. However, this is not really a problem, since it is a natural consequence of the wave nature of electrons. Without understanding this wave nature of electrons we cannot properly understand orbitals and bonding. Quantum Mechanics describes atomic and MOs in terms of a wave function equation. The wave function is given the Greek letter capital ψ (pronounced Psi), and for AOs has the form: quantum numbers is a function of wavefunction Ψ = f ( n, l, m, s, r,...) these parameters (and more) symbol distance from nucleus Here, n, l, m, and s are the quantum numbers you encountered in general chemistry: n = principal quantum number l = angular momentum quantum number m = magnetic quantum number s = spin quantum number Another parameter that is important for us is the distance of the electron from the nucleus, r. Wave functions exhibit wave behavior, that is, just like any wave they can be positive, negative, or zero. Solving the wave equation for the different quantum numbers gives the different AOs. The probability of finding an electron at a particular distance from the nucleus, P(r), is given by the value of the wave function squared, this is our answer to where are the electrons in an orbital! P(r) = Ψ (r) 2 Quantum Mechanics is highly mathematical, however, we do it in pictures, as a plot, or a pictorial representation of the wave function versus distance from the nucleus, which is much easier! At this point, you should be confused since all of this is difficult to understand without examples. 6.1 2p Atomic Orbital From general chemistry, we know the values of the atomic quantum numbers n, l, m, and so on... Ψ = f (n, l, m, s, r,...) in this case n = 2, l = 1, m = 0, +1, -1 n = 2 means the second shell. l = 1 in this case means a p AO and not an s AO. m = 0, +1, −1 means that there are three p AOs, px, py, and pz. Let’s start with the familiar “hourglass” shape for the 2p AO: probability zero here distance from nucleus WRONG!! nucleus r r probability largest here orbital shape should NOT be interpreted to orbital shape SHOULD be interpreted to illustrate illustrate a "figure of 8" movement of electrons the probability of finding the electron The “electron cloud” picture from general chemistry relates the idea of electron density to the probability of finding the electron, the higher the probability of finding the electron, the “denser” the apparent electron cloud. density zero here "cloud" picture of the electron density density largest here We can derive the shape of the wave function for the 2p AO by making a plot of probability of finding the electron, P(r) = wave function squared, as a function of distance from the nucleus, r. Bonding 1 : page 14  Then, take the square root to get a plot of the wave function. picture of P(r) = Ψ2 probability zero here max away from nucleus P(r) = Ψ2 NOT a node never reaches zero 10% here r r 0 Ψ goes through zero, 1 PLANE node! never goes to zero plot of Ψ looks like a wave! r r 0 picture of Ψ shows phase information AND Ψ need to consider BOTH wavefunctions r r 0 picture of Ψ 1 node shows the OTHER phasing situation that must also be considered The orbital shape given by the wave function defines an arbitrary “boundary” beyond which the probability of finding the electron is small. The wave function squared gives the probability of finding the electron as a function of distance from the nucleus (P(r)). This probability plot contains no phase information since a probability (and indeed any number that is squared) can only be positive or zero, never negative. The plot of the wave function looks like a wave, it gives phase information associated with the wave, that is, the positive and negative regions due to the wave behavior. For the 2p AO, the wave function has one node at the nucleus, that is, the electron is never at the nucleus. There are different kinds of nodes, the p AO has a plane node. PLANE NODE The wave function is the square root of the probability plot, thus we don’t know which phase is positive and which is negative, which is why we need to consider possibilities, shown in both plots and both pictures. Positive and negative are arbitrary in wave functions, thus we distinguish the different phases by shading (or coloring) in the picture rather than assigning an absolute positive or negative sign. Understanding this wave nature is essential for building MOs! Bonding 1 : page 15  6.2 2s Atomic Orbital Ψ = f (n, l, m, s, r,...) in this case n = 2, l = 0, m = 0 The quantum numbers tell us about the wave nature of the orbitals, the number of nodes is the value of the principal quantum number n − 1, therefore, a 2s AO (n = 2) must have one node. zero electron density WRONG!! (sperical node) The familiar spherical orbital should not be interpreted to illustrate a circular movement of electrons. The “cloud” picture of electron density reveals a spherical region within the orbital where the electron density is zero, that is, where the wave function must have a node. picture of P(r) = Ψ2 no phase information here P(r) = Ψ2 highest closest to the nucleus (r = 0) never goes to zero here 10% r r electron probability zero here Ψ goes through zero, ONE (spherical) node plot of Ψ looks like a wave! 0 never goes to zero picture of Ψ shows phase information ONE spherical node change in "phase" at the node Ψ AND Again r r we need to consider both ONE spherical node wavefunctions picture of Ψ shows the other phasing situation that must also be considered need BOTH pictures The wave function squared gives the probability of finding the electron as a function of distance from the nucleus (P(r)). The probability plot contains no phase information since a probability (in fact any number squared) can only be positive or zero, never negative. The wave function for the 2s AO has a spherical node that surrounds the nucleus, the probability of finding the electron this distance from the nucleus is zero at all distances from the nucleus defined by the sphere. Bonding 1 : page 16  z z spherical node x x y y The wave function is the square root of the probability plot, thus we don’t know which phase is positive and which negative, which is why we need to consider possibilities, shown in both plots and both pictures. Positive and negative are arbitrary in wave functions, thus we distinguish the different phases by shading (or coloring) rather than positive or negative signs. The colors are arbitrary, just like shading and nonshading. 6.3 1s Atomic Orbital Ψ = f (n, l, m, s, r,...) in this case n = 1, l = 0, m = 0 The quantum numbers tell us about the wave nature of the orbitals, the number of nodes is the value of the principal quantum number n − 1; therefore, a 1s AO (n = 1) must have zero nodes. The familiar spherical orbital should not be interpreted to illustrate a circular movement of electrons. The “cloud” picture of electron density, zero nodes in this case. electron WRONG!! “cloud” picture picture of P(r) = Ψ2 no phase information here P(r) = Ψ2 highest closest to the nucleus (r = 0) never goes to zero plot of Ψ 10% looks sort of like a wave! r r 0 Ψ never goes to zero picture of Ψ shows phase positive information 10% r r 0 AND never goes to zero Ψ r r need to consider BOTH 0 wavefunctions negative picture of Ψ shows the OTHER phasing situation that must also be considered Bonding 1 : page 17  6.4 So, Why Are There Orbitals? The wave nature of electrons is an odd concept, it doesn't seem to make sense in our macroscopic world; however, the wave nature of electrons is the most important factor that determines their properties! If we accept that electrons have wave nature, there must be orbitals, there is no other explanation for orbitals. Consider the sound waves related to vibration of a string: a plucked string fundamental harmonic only CERTAIN waves allowed boundary boundary standing waves Only the fundamental wave and its harmonics are observed, because the boundary conditions imposed by the length of the string requires these to be standing waves, only certain standing waves are allowed. Now consider the electron waves defined by the attraction of the negatively charged electron and a positively charged nucleus: standing wave (orbital )"allowed" only CERTAIN STANDING waves allowed wave (orbital) NOT "allowed" the "ends" don't meet! Because of the boundary conditions of the charge on the nucleus and the requirement for proper overlap of the wave structure where it “meets,” only certain standing waves are allowed. The allowed standing waves represent the allowed ways that electrons can be distributed around a nucleus and their associated allowed energies. These standing waves are the orbitals. If the electron does not have wave nature, then there are no standing waves, there are no orbitals, and there is no other way to explain the existence of orbitals without taking the wave nature of the electrons into account. only CERTAIN waves are allowed these are the orbitals 1s 2s 2pz 2px 2py 7 The MO Theory Model of Bonding 7.1 Introduction to Localized MO Theory: The Simple Example of H2 Electrons in atoms are in AOs, electrons in molecules are in MOs. MOs can be constructed by combining the familiar AOs into MOs. A completely accurate MO theory would take all of the AOs associated with all of the atoms in the molecule, which is impossible to do without complicated math, instead, we will use an approximate method to generate localized MOs. Bonding 1 : page 18  The approximate method is called a Linear Combination of Atomic Orbitals (LCAO). The LCAO model generates approximate MOs that are localized on individual bonds. Localized MO theory “pretends” that MOs are localized between the two atoms that “make” the bond. This is the “next level” up from Lewis structures in models of bonding and structure. LCAO is very quantitative, but we will do it qualitatively, using pictures. The LCAO “Rules” to make a pictorial localized MO that describes a bond between two atoms are the following: 1. Choose the appropriate two AOs to make the bond (one from each atom). 2. Draw pictures of the two wave functions that correspond to these AOs. 3. Make two new MOs by combining (overlapping) the two AOs both in-phase and out-of-phase. This is why we need the phase information contained in the wave functions to make MOs. Note that when the AOs are combined in a molecule, we must get both in-phase and out-of-phase overlap of the wave functions, which generates two new orbitals in the molecule (orbitals can’t disappear, two AOs must make two MOs). Let’s look at molecular hydrogen as an (easy) example: H + H H H atomic orbitals molecular orbital Overlap the wave function of one 1s AO from each hydrogen atom to make the new MOs. Bonding Anti-Bonding H 1s A.O. Ψ x x H 1s A.O. Ψ H 1s A.O. Ψ H 1s A.O. Ψ x x combine (overlap) IN PHASE combine (overlap) OUT OF PHASE When the AOs are close enough that overlapping (combining) in-phase occurs, then overlapping (combining) out-of-phase also happens simultaneously, it is an unavoidable consequence of the wave nature of the orbitals. The two situations are called bonding (in-phase) and antibonding (out-of-phase). This is how the two AOs are combined to make the two MOs in molecular hydrogen. Each hydrogen atom provides one electron each to make the bond. One of these two new MOs will contain the two valence electrons in the new covalent bond. Energy diagram for formation of localized MOs overlap wavefunctions OUT of phase Energy x = x DESTRUCTIVE INTERFERENCE ANTI-BONDING σ* M.O. x = negative phase (arbitrary) bring or x 1s A.O. together 1s A.O. = positive phase x (arbitrary) bring σ M.O. together x = nucleus = electron BONDING x x = x x CONSTRUCTIVE INTERFERENCE overlap wavefunctions IN phase Bonding 1 : page 19  Bringing the atoms together to make a bond results in the overlap of the AOs. Because of the wave nature of the AOs, when they overlap, they do so “in-phase” and also “out-of-phase,” at the same time, whether we like it or not! Overlap of the AO wave functions in-phase results in constructive interference of the wave structures to generate a new wave structure, which is largest where constructive overlap is greatest, that is, between the nuclei. The result is a localized σ bonding MO (σ pronounced as sigma). This is where the two electrons “go.” An electron in the bonding σ–MO is lower in energy than an electron in either of the two AOs that were used to construct it, both electrons are thus lowered in energy, this is the definition of bonding. Corresponding overlap of the wave functions out of phase results in the destructive interference of the wave structures to generate another new wave structure. This new structure has a node where the destructive overlap occurs, that is, between the nuclei, the result is a localized σ*–antibonding MO. The electrons do not “go” there, since they would be higher in energy. Antibonding Orbitals: Antibonding orbitals must form if bonding orbitals are formed, the combination of two AOs must generate two MOs, orbitals can’t disappear. There is nothing wrong with having antibonding MOs with no electrons in them! Think about a hydrogen atom. It has a 2p AO, for example, it just doesn’t have any electrons in it, it is an empty orbital the atom has. Antibonding orbitals are empty orbitals that molecules have. Antibonding orbitals become important later when we come to chemical reactions. BOTH are symmetrical σ x x with respect to the x σ∗ internuclear axis Ψ for σ-bonding M.O. Ψ for σ∗-ANTIbonding M.O. Both of the orbitals are symmetrical with respect to the internuclear axis (they are both the same above and below the internuclear axis), which is why they are called σ orbitals. This picture also gives us the real explanation for why electrons form bonds. The conventional explanation is that in the MOs the charges are “balanced,” each electron “sees” two nuclei, in essence this an electrostatic argument, but it doesn’t really make sense because in the MO the nuclei are very close to each other too! H + H H–H lower volume larger volume higher kinetic energy + lower kinetic energy Ψ for 1s A.O. Ψ for σ-bonding M.O. The best explanation is that the new MO is larger (has a larger volume) and is less curved than the AOs. An electron moves more slowly in a larger volume orbital, the electrons thus have lower kinetic energy in the bonding MO. Now, square the wave function to give the probability of finding the electrons in the MO. H H square σ M.O. Highest electron density between nuclei, x x fits our understanding of "balanced" charges x x Ψ Ψ2 Bonding 1 : page 20  square ZERO electron density between nuclei, no σ* M.O. x x x x shielding of nuclei, high in energy Higher Energy Antibonding M.O. Ψ Ψ2 7.2 Valence Shell Electron Pair Repulsion Determines (Almost) Everything Before we get to the more complex MOs, we need to learn how electrons are arranged in organic molecules. Everything Starts with Valence Shell Electron Pair Repulsion The orbitals you learned in general chemistry for atoms are appropriate for isolated atoms. But most atoms aren’t isolated like that, they are associated with other atoms, for example, in molecules, where they are surrounded by other atoms, electrons and protons, that is, other charges and are in bonds. The AOs respond and change as a result of making bonds to the surrounding atoms. When an atom is in a molecule, the electrons around the atom arrange themselves to make bonds and keep out of each other’s way, that is, they minimize electron repulsion. The AOs the atom had when it was an isolated atom are don’t work when in a molecule. valence H "dashed bond" these atomic 1s, 2s and 2p orbitals can’t points away from viewer C atomic orbitals work here C H "wedged bond" work here H isolated carbon atom points towards viewer H 1s2 2s2 2p2 carbon atom in a molecule CH4, methane This means that we can’t use the normal AOs in LCAO to make the MOs. We need to use rearranged (hybridized) AOs and it is the electron repulsion that allows us to work out how to do this. Valence Shell Electron Pair Repulsion (VSEPR) takes all of this into account! New Notation: The wedged and dashed bonds above are a method of describing a three-dimensional structure on a two-dimensional piece of paper that is very useful for the tetrahedral geometry (see below). VSEPR Accounts for the locations of the surrounding atoms, and the bonding and nonbonding electron pairs. Determines what each atom needs to “do,” and where in space the electrons around each atom need to go. VSEPR thus determines hybridization, how the AOs change, which determines how the MOs are built. VSEPR with Four Valence Electron Domains The following structures have four sets or domains of Valence Shell Electron Pairs around C, N, and O atoms. The four sets or domains of electron pairs avoid each other as much as possible to minimize electron repulsion. the 2s and 2p valence shell atomic orbitals won’t work for these C, N and O atoms they are surrounded by other atoms (charges) - 4 electron domains the atomic orbitals in the C, N and O must respond by “hybridizing” non-bonding electrons R R ~109° N ~109° C R R O A R B R C ~109° R R R 4 electron domains 4 electron domains 4 electron domains in the 4 single bonds 3 bonding domains, 1 non-bonding domain 2 in bonds, 2 non-bonding tetrahedral electron geometry tetrahedral electron geometry tetrahedral electron all four angles are the same three angles are the same geometry tetrahedral molecular geometry trigonal pyramidal molecular geometry one bond angle bent molecular geometry Bonding 1 : page 21  The locations of atoms (nuclei) can be well defined, but the locations of electrons cannot. Each structure has four electron domains, all four have tetrahedral electron geometry due to VSEPR. The molecular geometry of structure A (above) can be defined by the positions of the atoms as tetrahedral. For structure B, the molecular geometry can only describe the positions of the four atoms: trigonal pyramidal. For structure C, the molecular geometry can only describe the positions of the H–O–H atoms, thus bent. VSEPR with Three Valence Electron Domains The following structures have three sets or domains of valence electrons around the indicated C and N atom The three electron domains separate from each other as much as possible due to electron repulsion. the 2s and 2p valence shell atomic orbitals won’t work for these C and N atoms the atomic orbitals must respond to the 3 new electron domains by “hybridizing” HH H 120° H H CH 120° 3 electron C C H A C C B H ~120° domains 3 electron H H H C C H domains H N 2 domains in C-H single bonds 1 domain in N-C single bond 1 domain in a C=C double bond 1 domain in a N=C double bond all 3 angles roughly the same 1 non-bonding domain trigonal planar molecular geometry bent molecular geometry The electron geometry at each of the earlier circled atoms is trigonal planar. The molecular geometry at carbon in A (above) is defined by the positions of four atoms as trigonal planar. For structure B, the molecular geometry at nitrogen can only describe the positions of the C–N=C atoms: bent. Knowing there are three electrons domains around an atom helps in building the MOs. VSEPR with Two Valence Electron Domains The following structures have two sets or domains of valence electrons around the indicated C and N atoms. The two electron domains separate from each other as much as possible due to electron repulsion. the 2s and 2p valence shell atomic orbitals won’t work for these C and N atoms the atomic orbitals must respond to the 2 new electron domains by “hybridizing” 180° 2 electron H C C H domains 2 electron H C N domains 1 domain in C-H single bond 1 domain in N non-bonding pair 1 domain in a C–C triple bond 1 domain in a C–C triple bond angle = 180° the geometry at N can't be defined linear molecular geometry The electron geometry at each of the earlier circled atoms is linear. The molecular geometry at carbon of structure A (above) is defined by the positions of the two atoms as linear. The molecular geometry at the nitrogen cannot be defined. Practice Using VSEPR: VSEPR analysis of geometries and angles considers one atom at a time in a molecule. For the circled atoms, give the electron geometry, the molecular geometry and the relevant bond angles. H H H ~120° H C ~120° H C O 3 electron domains C H C ~120° trigonal planar electron geometry 3 electron domains H H ~120°C H trigonal planar molecular geometry trigonal planar electron geometry H H trigonal planar molecular geometry Bonding 1 : page 22  H H C C 4 electron domains all tetrahedral electron geometry N H angles H ~120° CH3 tetrahedral molecular geometry H ~109° 3 electron domains H trigonal planar electron geometry bent molecular geometry 7.3 Methane as a Simple Organic Molecular Structure Everything Starts with VSEPR There are four C–H bonds around the central carbon atom, there are thus four electron domains that need to be as far apart from each other as possible to lower the total electron energy. The lowest energy molecular geometry is tetrahedral at the central carbon atom. H H H ~109° ~1.1Å CH4 H C H 4 electron domains C C H tetrahedral H H H H H methane H The central carbon thus needs four identical AOs to construct four identical C–H bonds. These four AOs must be separated by ~109° in order to generate the correct structure and geometry. The Valence Shell electrons in atomic carbon are associated with the 2s and the three 2p AOs. Methane cannot use these orbitals to make the four identical C–H bonds since these four orbitals are obviously not identical and they are not separated by angles of ~109°. these orbitals are at 90° they can’t make these bonds carbon 2py 2px 2pz X H 2s ~109° 1s2 2s2 2p2 C H valence electrons H 2 electrons 1 electron 1 electron 0 electrons H Hybridize (mix together) the four different valence AOs that carbon has in an isolated atom to make four new identical hybridized (mixed) AOs that can make the required four identical bonds. Each new hybrid orbital consists of an equal mixture of a 2s, a 2px, a 2py and a 2pz orbital. Mixing the four 2s, 2p, 2p, and 2p AOs must make four new hybridized sp3 orbitals (orbitals can’t disappear!). 4 valence orbitals the isolated atom has four identical sp3 hybrid (mixed) orbitals Energy valence orbitals the carbon NEEDS in methane (molecule) Ψ 2px 2py 2pz Ψ sp3 sp3 sp3 sp3 mix and ALL 4 Ψ EACH sp3 = (25% 2s + 25% 2px + 25% 2py + 25% 2pz) Ψ sp3 = (25% 2s + 75% p) 2s All of the valance orbitals are mix