CHEM 340 CHEMICAL BONDING - in General Lect-07 IONIC COVALENT METAL COVALENT NETWORK

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1 CHEM 340 CHEMICAL BONDING in General Lect07 BONDING between atoms classified as belonging to one of the following types: IONIC COVALENT METAL COVALENT NETWORK or each bond type, the valence shell electrons of bonded atoms actively participate in bond formation by gain/loss/sharing of v.s.e. Consequently, vse are emphasized and identified setely in configurations b/c of their critical role in bonding. Core electrons (inner electrons) are not involved in chemical bonding. IONIC bonding only occurs in the crystalline solid state and involves oppositely charged ions located in very specific relative positions within the crystal. COVALENT bonding most commonly involves the sharing of electron pairs between bonded atoms in independent molecules or molecular ions. Sharing of electron pairs may, or may not be equal, according to EN of bonded atoms. METALLIC bonding is viewed as (relatively) stationary nuclei embedded in a "sea of mobile vse". COVALENT NETWORK bonding involves extended covalent bonding throughout the entire expanse of a substance or material, resulting in a macroscopic molecule. Accordingly, a diamond (of any size) can be considered as a single molecule because the covalent bonding between carbon atoms extends throughout the entire crystal. ing Interactions, Nuts & Bolts, Attractions & Repulsions Consider two atoms, A and B. They need to come in contact in order to bond. As they do so, vse of atom A repel vse of atom B, and the nuclear charge of atom A also repels the nuclear charge of atom B. But the vse of atom A are attracted to the nuclear charge of atom B, and visa versa. ing occurs when the net attractive forces are greater than net repulsive forces. LennardJones 612 potential.. is a rather simple equation that expresses the interaction of these attractive / repulsive forces as a function of distance ( r ) between two atoms. It has the form: 12 6 LJP 1 1 r r. The first term is endothermic/repulsive, and becomes very large at short distances. The second term is exothermic/attractive. A graph the LJP function is shown to the right. The equilibrium bonding distance is at the energy minimum. Covalent ing Theories A. MOLECULAR ORBITAL MODEL employs linear combinations of symmetryrelated atomic orbitals from bonded atoms, and constructs molecular orbitals (m.o.'s) to contain vse electrons. M.O.'s may be bonding, antibonding or nonbonding. MO theory allows electron configurations to be written for molecules. This model lends itself to graphic displays called molecular orbital diagrams. B. VALENCE BOND suggests that in order for bonding to occur, atomic orbitals need to overlap. Each overlapped set of orbitals accommodates TWO electrons. When overlapping orbitals lie on a straight line between bonded nuclei, they form a SIGMA bond. When overlapping orbitals are offset from a straight line between bonded nuclei, they form a PI bond. Hybridization is a construct of VB theory. VALENCE BOND THEORY, a little bit about... In order for atoms A and B to be bonded, they must be close enough so their vs orbitals overlap and share a common space. VSE's of the two atoms are placed in such overlapping orbitals and this arrangement constitutes covalent bonding. To apply this concept fully requires knowledge about the SHAPES of atomic orbitals, i.e., their angular distribution functions. Graphical representation of s, p, d atomic orbitals are shown in the text, ig. 27 on page 29. Apply the VB approach to analyze bonding in hydrogen molecule, H 2 :

2 H atom a H atom b H 2 molecule H atom 1s atomic orbitals are spherical in shape. They make contact on a direct line between the two nuclei. This type of overlap defines a SIGMA bond. Two "spin paired" electrons share this space and make a single bond (bond order is one). Each nuclei "sees" both electrons part of the time. This arrangement is more stable than two individual and seted atoms, so VB suggests that H 2 molecule should exist under ordinary conditions. Apply the VB approach to analyze bonding in nitrogen molecule, N 2 : 2 3 N atom has a vse configuration of. The orbital diagram is shown in the box: The s atomic orbital is spherical. The three p atomic orbitals are "dumbbell" in shape. Taken together they lie on xyz Cartesian axes and are labeled p p p x y z,,, as shown: x N atom a N atom b N 2 molecule x z z y y The atomic orbitals are not shown because they are filled (closed) subshells. By convention, p z atomic orbitals overlap on a direct line between the two nuclei and can accommodate a spinpaired set of electrons to form a SIGMA bond. Overlap between the two p x and two p y orbitals can only occur along the dashed lines in the diagram, i.e., they CANNOT overlap on a direct line between the two nuclei. This defines a PI bond. The net bonding in nitrogen molecule consists of ONE SIGMA bond and TWO PI bonds for a triple bond (bond order of three). Apply the VB approach to analyze bonding in oxygen molecule, O 2. The bonding consists of ONE SIGMA bond and ONE PI bond for a double bond overall (bond order of two). Take note of vse spins in oxygen molecule. What magnetic character (i.e., magnetism or diamagnetism) is expected for oxygen molecule according to the Valence approach? CHEMISTRY IS AN Theories are expected to provide information and insights consistent with experimental observations. With this in mind, apply the Valence approach to analyze bonding in Be 2 (a linear structure with two equal Be bonds), BCl 3 (a plane triangular structure with three equal B Cl bonds), and CH 4 (a tetrahedral structure with four equal C H bonds). The indicated structures are the result of experimental determinations. (In each case construct a LDD, apply VSEPR, and then apply Valence.) Beryllium difluoride Central atom beryllium has the following vse orbital diagram: A spinpaired set of electrons completely fills an atomic orbital. As they stand they seem to be unavailable for bonding.

3 In anticipation of bonding, VB suggests a redistribution of vse resulting in a new orbital diagram as show in the box. This process is called "promotion", and the vse are now available for bonding. However, s orbitals and p orbitals have different properties and shapes. Would one expect bonds from Be vse in s, and p orbitals to be equivalent? equal? Probably not. But experiment indicates both bonds are completely equivalent. Que pasa? VB responds by suggesting a "mixing" of atomic orbitals, i.e., combining "s" character with "p" character in a 1:1 manner to form two equivalent "hybrid" orbitals. Indeed the mathematical result of such a hybridization produces TWO equivalent orbitals, AND furthermore, they are oriented about the central atom in a LINEAR manner. Hybridized orbitals are labeled according to the mix of atomic orbitals used in their formation. sp sp p p So this LINEAR set is labeled as an" sp" hybrid. There are as many hybrid orbitals in a set as there are atomic orbital used in their formation. So there are two " sp " hybrid orbitals in this set and they form TWO SIGMA bonds. The angle between bonds, with central atom as vertex, is 180 degrees. Hybridization allows theory to emulate observations and determinations. Boron trichloride Central atom boron has the following vse orbital diagram: Promotion leads to the configuration: "Mixing" of ONE s and TWO p orbitals leads to a THREEorbital hybrid set labeled as " sp 2 " with THREE SIGMA bonds at 120 deg. Remaining "p" type orbital is available for pibonding or unshared electron pairs sp 2 sp 2 sp 2 p Methane Central atom carbon has the following vse orbital diagram: Promotion leads to the configuration: Mixing of ONE s and THREE p orbitals leads to a OUR orbital hybrid set labeled as " sp 3 " OUR SIGMA bonds at deg. Similar mixing of "s", "p", and "d" character leads to hybrid sets for trigonal bipyramid and octahedral geometries. A collection of hybrid sets is shown in the following table, all entries refer to bonding of the Central Atom. CentralAtom " s" orbitals Central Atom " p" orbitals Central Atom " d" orbitals CentralAtom Hybrid set CentralAtom SIGMAbonds Central Atom Geometry CentralAtom bond angles 1 1 sp 2 linear d( z ) d( z ), d ( x y ) sp 2 3 (plane) 120 triangle 3 4 tetrahedron sp d sp sp 3 sp 3 sp 3 sp 3 dsp 3 5 trigonal 90, 120, bipyramid octahedron 90, 180

4 Relating Valence to VSEPR: The VSEPR method does not use pi bonding information in arriving at a molecular geometry. Similarlyr, Valence does not use pi bonding in the construction of hybrid sets. So the relation between VSEPR and VB is very direct: the sum of subscripts (n m) in the VSEPR formula is the same as the number of orbitals used in constructing the Valence hybrid set. VSEPR subscripts n m Orbitals used in Hybrid set VB Hybrid Set sp sp 2 sp 3 dsp 3 d sp Valence and Piing: or RO8 elements as Central Atom, any" p " vse orbital NOT used in the construction of Hybrid sets IS available for pi bonding. So RO8 Hybrid Set sp sp 2 sp 3 " " 2 1 none p orbitals available for pibonding MOLECULAR ORBITAL THEORY, a little bit about... Molecular Orbital methods use linear combinations of symmetryrelated orbitals of bonded atoms, to form molecular orbitals that contain vse of the molecule. Molecular orbitals are energy levels for electrons in the molecule and a corresponding energy level diagram can be constructed. Electrons are introduced into the diagram and a net bond order is determined. The magnitude of the bond order depends on the number of electrons in the molecule and the type of molecular orbitals they occupy. Consider the MO analysis of bonding in hydrogen molecule as formed from two seted hydrogen atoms: Each seted hydrogen atom has one electron in its vs and it is in a 1s atomic orbital. Both electrons have the same energy, and this feature is represented by placing them at the same vertical level in the diagram. Next consider the shapes and trigonometric signs of s atomic orbitals. They are spherical in shape and have a positive trigonometric sign. Orbitals can overlap if they have the same symmetry and trigonometric sign. ONE obvious linear combination is the SUM of their wavefunctions [ψ1s( H atom a) ψ1s( H atom b) ] which can be diagrammed as shown to the right. The result INCREASES electron density directly between the two nuclei, and forms a SIGNA BOND ( σ ) The OTHER is the DIERENCE of their wavefunctions ψ 1s ψ 1s ( H atom a) ( H atom b) This decreases electron density directly between the two nuclei and is called a SIGMA ANTIBOND ( σ * ) plus SUM Combination of two 1s atomic orbitals The signs are trignometric, NOT CHARGES. MINUS DIERENCE Combination of two 1s atomic orbitals The signs are trignometric, NOT CHARGES.

5 Of the two bonds, the sigma bonding MO ( σ ) is MORE stable than the seted atoms and is represented on a LOWER level in the energy diagram, relative to the two seted hydrogen atoms. The sigma antibonding MO ( σ * ) is LESS stable than the seted atoms and is represented on a HIGHER level in the energy diagram, relative to the two seted hydrogen atoms. The resulting molecular orbital energy diagram has three sections. The CENTER section displays energy levels for the molecule. Left and right sections display energies of seted atoms 1s H a σ * 1s H b σ It remains to introduce two electrons into the center part of the diagram. They are entered in lower levels first, then into higher levels. As before, pairing of electrons is avoided until necessary. In this case both electrons are placed in the lower SIGMA BONDING MO, and paired. This happens because the energy difference between σ bonding and σ * is greater (in this case) than the repulsion between two paired electrons occupying the same molecular orbital. In molecular orbital energy level diagrams the BOND ORDER is calculated using the following expression: Order = ( bonding electrons antibonding electrons) In H 2, there are TWO electrons in the SIGMA BONDING MO, and NONE in the SIGMA STAR ANTIBONDING MO, so Order = single bond. 2 0 = 1 2 1s H a 2 This analysis informs that the two atoms in hydrogen molecule are joined by a urthermore, all electrons are paired so the molecule will be diamagnetic. Using this same MOLECULAR ORBITAL approach, analyze the bonding, and resulting properties, for each of the following: 1 1 ex. H 2 H 2 Include hydrogen molecule in this series and decide which of the four substances has the longest bond length? is diamagnetic? is least likely to be stable? has smallest bond dissociation energy? The atomic orbitals also combine to form σ and σ * molecular orbitals. So this approach can be expanded to include larger atoms. Accordingly, analyze the bonding in each of the following cases: ex. Li 2 Be 2 LiBe Be 2 1 In this series which specie has the shortest bond length? is diamagnetic? is least likely to be stable? has the largest bond dissociation energy? σ * He 2 σ 1s H b

6 Consider next how atomic orbitals combine to form molecular orbitals. Recall the shape of p atomic orbitals and also make note of their trigonometric signs as shown below: pz px py Orbitals can combine when (1) they are of the same symmetry, i.e., pz of atom A can overlap with pz of atom B, but not with the py or px of atom B, and (2) when their lobes are of same trigonometric sign. Linear combinations of two pz atomic orbitals. Note the orientation and resulting molecular orbitals formed: ψ ψ ψ ψ 2 pz( atom a) 2 pz( atom b) z atom a PLUS z atom b 2 pz( atom a) 2 pz( atom b) p "sigma" antibonding MO MINUS p "sigma" bonding MO Relative Energy z atom a z atom b Conservation of energy is at play here. Two atomic orbitals form two molecular orbitals no more, no less. In this case TWO pz atomic orbitals combine to form TWO molecular orbitals, labeled as σ ( p z ) and a σ *( ) Linear combinations of two px atomic orbitals. Note the orientation shown and resulting molecular orbitals formed. Linear combinations of two py atomic orbitals result in a similar set of bonding and antibonding molecular orbitals, except for the fact that they are normal to the MO sets from the px and pz. So six p type atomic orbitals combine to form six MO's; one σ and two Π bonding, and one σ * and two Π * antibonding. ψ ψ ψ ψ 2 px( atom a) 2 px( atom b) 2 px( atom a) 2 px( atom b) p z. x atom a x atom b PLUS A* antibonding MO MINUS A bonding MO RELATIVE ENERGY x atom a x atom b

7 As noted before, SIGMA bonds overlap on a direct line between the two nuclei of the bonded atoms, and PI bonds do not. The molecular orbital energy level diagram including p type atomic orbitals becomes a little more involved in that some levels change relative energies as heavier RO8 homonuclear diatomic molecules are encountered. or our purposes, two diagrams will be used: (1) one is for RO8 diatomics up to, and including dinitrogen ( N 2 ), and (2) the other for heavier RO8 atoms. As noted before, each molecular orbital energy level can accommodate TWO electrons, and recall that electrons don't pair until necessary. Consider the first diagram (igure A) and use it to analyze bonding in the following homonuclear diatomic molecules: ex. B C N Compare bond lengths, magnetic character, and bond dissociation energies for this series. igure A. * A* A * 1s * 1s The second diagram (igure B) is used for RO8 diatomic igure B. molecules/ions heavier than N 2. It differs in that relative energies of the PI BONDING MO's, and the SIGMA BONDING MO resulting from combining z atomic orbitals, are SWITCHED. This diagram is shown to the right. * A* A Use it to analyze bonding in the following homonuclear diatomic molecules: ex. O 2 2 Compare bond lengths, magnetic character, and bond dissociation energies for this series. * 1s * 1s Use both diagrams (as required) to analyze bonding and properties of the following substances: ex. BC NO CO O B CN O O O A table showing bond orders and some properties of diatomic substances is on the next page.

8 Main Group RO8 Diatomic Molecules and Ions Orders and Magnetic Character via Molecular Orbital Theory (above the bold horizontal line) Experimental Dissociation Energies (kj / mole) and Lengths (Angstroms) (below the bold horizontal line) BOND ORDER Total VSE Magnetic Char. 2 1 diamag 1 diamag diamag igure A A A A A B B B B Specie B 2 C 2 N 2 O 2 2 BDE Length Specie BN BO B O 2 1 O 2 1 O 2 2 BDE Length Specie BeO Be BDE Length Specie CN 1 CN CN 1 Cl 2 1 Cl 2 BDE Length Specie CO 1 CO C Br 2 BDE Length Specie N 2 1 NO 1 NO I 2 BDE Length BOND ORDER Total VSE