Molecular Modeling Problems

Chapter 21

1. Electron Counting. Two systems for “electron counting” around a metal are in common use. One method assumes that each ligand donates one or more pairs of electrons to the metal, whereas the other method assumes that each ligand is neutral and donates either one or two electrons. For many common ligands such as the two-electron donors carbon monoxide, ethylene and trimethylphosphine and the six-electron donor, benzene, the two systems are the same. However, different descriptions occur for other ligands. For example, chlorine bonded to a metal can either be classified as chloride anion and donate two electrons, or as chlorine atom and donate a single electron. The cyclopentadienyl ligand can be classified as cyclopentadienyl anion, six-electron donor or as cyclopentadienyl radical, a five-electron donor. The fact that there multiple schemes for counting electrons can be problematic for students, in that this seems to imply knowledge about the distribution of charge in the molecule. However, any classification scheme is simply nomenclature.

Obtain the geometry of ferrocene using the B3LYP/6-31G* model. Sum up the charges on both carbons and hydrogens on one of the cyclopentadienyl rings. Is the ring neutral, does it bear a unit negative charge or is the charge in between the two? Repeat your calculations for ruthenocene (the ruthenium analogue of ferrocene). Display electrostatic potential maps for ferrocene and rutheocene side by side (and on the same scale). Is the cyclopentadienyl ring in rutheocene more or less negatively charged than that in ferrocene? What does your result tell you about the relative electronegativies of iron and ruthenium?

2. Strengths of σ-Donor, π-Acceptor Ligands. Carbon monoxide is classified as a σ donor and a π acceptor ligand. This implies that the molecule possesses a high-energy occupied σ orbital pointing from carbon and one or more low-energy unoccupied π orbitals. Presumably, the higher the energy of the σ orbital and the lower the energy of the π orbital the stronger will be the metal-ligand bond.

Obtain the geometry of carbon monoxide using the B3LYP/6-31G* model and display the HOMO and LUMO. Are they consistent with the above classification? Elaborate. Next, obtain geometries for other potential σ-donor, π-acceptor ligands, for example methyl isocyanide (MeN+≡C-) and carbon monosulfide (-C≡S+). For each, identify the molecular orbitals that are analogous to the HOMO and LUMO of carbon monoxide, and compare HOMO and LUMO energies to those of carbon monoxide. Relative to carbon monoxide, would you expect each of the ligands you have examined to bind less strongly or more strongly to a metal center. Test your expectations by obtaining iron pentacarbonyl as well as compounds (CO)4Fe-L and evaluating energies of the ligand- exchange reactions. Assume the L occupies an equatorial site on iron.

(CO)4Fe-L + CO → Fe(CO)5 + L

3. Clelated Ligands. Is a ligand that offers two or more coordination sites to a metal necessarily more strongly bound than two separate ligands that each offer an “equivalent”

To accompany Inorganic Chemistry, Fifth Edition by Shriver & Atkins

Molecular Modeling Problems

coordination site? For example, is dmpe ligand (Me2PCH2CH2PMe2) more strongly bound than two trimethylphosphine ligands?

4. Geometries of Coordinated Alkenes. Alkenes coordinate to transition metals. Is the bonding best viewed in terms of two one-electron metal carbon σ bonds or as the π bond acting as a two-electron donor? Does this depend in a “predictable” way on the specific metal and on the specific substituents attached to the double bond? One way to answer these questions is to examine the length of the carbon-carbon bond as a function of the metal and substituents. A “short” bond (analogous to that in a normal alkene) would favor interpretation in terms of weak π bonding, while a “long” bond (analogous to that in a normal cycloalkane) would favor interpretation in terms of σ bonding. Experimental structural data can be (and has been) employed for this purpose, but calculations allow a broader survey.

Use the B3LYP/6-31G* model to obtain the geometry of ethylene iron tetracarbonyl with the ethylene in an equatorial site. Also obtain geometries for cyclopropane and ethylene as examples of a molecule with a strained single bond and normal double bond. Is the CC bond length in the metal carbonyl characteristic of a single or bond or is it in between? What other structural features suggest for ethylene iron tetracarbonyl suggest the mode of binding?

5. Metal-Ligand Binding Energies of Alkenes and Alkynes. Both alkenes and alkynes are typically viewed as two-electron donors. However, alkynes have a second π bond available and could conceivable also act as four-electron donors. An interesting consequence might be that it would be that loss of a ligand (for example, carbon monoxide) should be easier (less unfavorable) for an (18-electron) alkyne complex than it should be for the analogous alkene complex.

Obtain geometries for ethylene and acetylene complexes of both iron tetracarbonyl with 18 electrons and iron tricarbonyl with 16 electrons (four complexes in total). Place the ethylene (acetylene) ligand in an equatorial site in the iron tetracarbonyl complexes (which have trigonal bipyramidal structures). Also obtain geometries for iron pentacarbonyl, iron tetracarbonyl, ethylene, acetylene and carbon monoxide. Use the B3LYP/6-31G* model. Calculate energies for the four ligand exchange reactions.

(CO)4Fe-L + CO → Fe(CO)5 + L

(CO)3Fe-L + CO → Fe(CO)4 + L L = H2C=CH2, HC≡CH

6. Is Chromium Tricarbonyl a π Donor or π Acceptor? Chromium tricarbonyl complexes to one of the faces of benzene leaving the other face exposed for further reaction.

To accompany Inorganic Chemistry, Fifth Edition by Shriver & Atkins

Molecular Modeling Problems

Cr CO OC CO Is there a significant change in the geometry of benzene as a result of complexing to chromium tricarbonyl? In particular, is there evidence of bond localization? To decide, use the B3LYP/6-31G* model to calculate equilibrium geometries for both benzene and benzene chromium tricarbonyl. Does the Cr(CO)3 group act to donate electrons leading to enhanced affinity toward electrophiles or to accept electrons leading to diminished reactivity? Compare electrostatic potential maps for “free” and complexed benzene. To establish a point of reference, include electrostatic potential maps (based on equilibrium geometries from the B3LYP/6-31G* model for (“free”) aniline (an electron-rich arene) and nitrobenzene (an electron-poor arene). You need to make certain that all four maps are on the same scale. Do you see the expected trend in electrostatic potential in the maps for benzene, aniline and nitrobenzene? Elaborate. Where does benzene chromium tricarbonyl fit in? Classify the Cr(CO)3 group as an electron donor or acceptor. Rank the chromium tricarbonyl group relative to either the amino group or the nitro group as appropriate.

7. 18-Electron Rule. To what extent does the 18-electon rule apply to all organometallic compounds? The suggestion based on what compounds are not observed is that it functions well for metals in the center but not those on the left or right-hand sides. One way that calculations can be used to probe such a supposition, is to use them to evaluate energies of reactions resulting in loss of an electron pair.

LnMCO Æ LnM + CO

Obtain equilibrium geometries for the 18-electron metal carbonyl compounds, Ti(CO)7, Cr(CO)6, Fe(CO)5 and Ni(CO)4, along with those of the corresponding 16-electron compounds (resulting from the loss of a molecule of carbon monoxide) and carbon monoxide itself using the B3LYP/6-31G* model. Titanium heptacarbonyl is bipyramdal with one pyramid square based and the other trigonal, titanium hexacarbonyl and chromium hexacarbonyl are octahedral, chromium pentacarbonyl is square-based pyramidal, iron pentacarbonyl is trigonal bipyramidal, iron tetracarbonyl is a distorted tetrahedral, nickel tetracarbonyl is tetrahedral and nickel tricarbonyl is pyramidal. Is the energy associated with loss of carbon monoxide similar for all four 18-electron carbonyls or is it easier for some of the compounds? If so, for which is it easier. How do your results fit into with what is known about the 18-electron rule?

Repeat you calculations and analysis to second-row carbonyls (Zr(CO)7, Mo(CO)6, Ru(CO)5 and Pd(CO)4) and to third-row carbonyls (Hf(CO)7, W(CO)6, Os(CO)5 and Pt(CO)4).

To accompany Inorganic Chemistry, Fifth Edition by Shriver & Atkins

Molecular Modeling Problems

To accompany Inorganic Chemistry, Fifth Edition by Shriver & Atkins