As noted in Molecular Modeling I, there are many definitions for a model. Two of them from Webster's Dictionary are most appropriate to applications in organic chemistry. The first is: "a description or analogy used to help visualize something that cannot be observed", which applies to exercises in Molecular Modeling I. The second is: "a system of postulates, data and inferences presented as a mathematical description of an entity". Molecular Modeling II incorporates both definitions in its exercises.

The background reading in the following links gives an idea of the mathematics and basis for the generation of computationally generated, energetically minimized images. There are many public domain and commercial software programs that can be used to do this. In Molecular Modeling II, a number of these systems are described, and visualization exercises illustrate some of their applications. The computational methods which generate the structure files will not actually be used in the exercises since the free, public domain programs are not particularly user-friendly and the user-friendly commercial products are presently unavailable on this campus. Structures have been generated and energetically minimized for your use with MacSpartan and stored as .pdb files which you will examine with RasMol and/or WebLabViewerLite.

The Schrodinger equation is the basis for quantum mechanics and provides a mathematical model for atomic orbitals. It demands enormous computational power to solve for all but the simplest of atoms and focuses on nuclei, electrons and orbitals. It is virtually impossible to apply it to organic molecules. Several alternatives have evolved which provide approximations through simplification of the classical Schrodinger equation. These alternatives are computational techniques or methods referred to as "Molecular Mechanics" and describe atoms as classical particles whose interactions are represented by potential energy functions based on mechanical force field(s). The simplest model is the sum of all of the energy terms for the structure. An improvement considers various possible conformations for the molecule, and total energy is calculated by considering all of the molecule's possible conformations, summing the energies from individual bond characteristics such as bending, stretching and bond angle, torsional strain and weak repulsive forces. These calculations produce minimized energy structures which are energetically favored conformations for the molecule. A further refinement is Molecular Dynamics which involves additional calculations that include the particle's acceleration and velocity and provide a better correlation to observed data for molecules' physical properties. These approaches offer great possibilities in developing strong visual models for many different large and small molecules. They are widely applied in molecular biology and in bioorganic chemistry particularly for imaging proteins, RNA, DNA as well as small organic molecules.

Molecular orbital theory has produced a wide range of computational methods that perform molecular calculations:

There are also many, many variations within each. See the QCPE, Quantum Chemistry Program Exchange Catalogue for a list of the hundreds of computational programs that are available.

Also, see Dr. Mike Colvin's pages on Computational Chemistry for a description of research being done at Lawrence Livermore National Laboratory.

There are two basic bond features that relate to conformation: 1) There is free rotation about single bonds (sigma bonds), but due to repulsion, spatial distances between atoms are minimized. Therefore, different forms of rotational possibilities will have higher or lower frequency of occurence depending on the proximity and interaction of atoms. 2) Carbon-carbon double bonds have fixed geometry. Key terms: rotamer, conformer, syn, gauche, eclipsed, anti, staggered, chair, boat, twist boat, axial, equatorial, cis (Z), trans (E), dihedral angle, inter-atomic distance, torsional strain

See:

1) Dublin City University's: Introduction to Conformational Analysis

2) Western Washington University Virtual Molecular Model Kit

3) http://ep.llnl.gov/msds/orgchem/Chem226/Alk-anes-enes-ynes.html

Part I:

1) Acyclic conformers: (Butane)

Refer to the following gauche, anti, eclipsed and staggered images of butane and complete the instructions which follow.

The approximate dihedral angle for conformer number one was determined with a RasMol feature. The angle is relative to the C₁-C₄ carbons and is indicated in yellow. The four conformational files of butane are in .pdb format and viewable with Chime. They are numbered clockwise: one, two,three, four. To view them with RasMol save each of them to the desk top or an accessible directory and open RasMol.

• Draw Newman Projection Formulas for the four butane conformers. Use a viewing perspective through the C₂-C₃ bond. Identify each by name.
• Using RasMol / report the dihedral angle relative to the C₁-C₄ carbons for conformer number three.
• Draw a relative, torsional energy diagram starting with a 0^o dihedral angle and rotate about the C₂-C₃ bond through 360^o labeling the conformations of all of the peaks and valleys. Circle the least favored conformer.


2) Conformers in cyclic systems: (Cyclohexane / Ambrox)

Cyclohexane can exist in a boat or chair conformation. The boat is illustrated below with the interatomic distance in yellow for the "Bowsprit Flagpole" hydrogens. Click on the image and view the stick structure in Chime with the dot surface option and select Van der Waal's radii. The dot surface gives an indication of the significant interaction between these two atoms. Their surfaces overlap. Generally, if the hydrogen atoms are closer than 2.40 Angstroms they will interact "sterically" which is an energetically unfavorable interaction. Steric effects are very important in explaining the conformation and chemical behavior of organic molecules.

a) Answer the following questions for the chair form of cyclohexane.

1. What is the distance between the axial-axial C₁-C₃ hydrogens?
2. What is the dihedal angle for C₁-C₂ axial-equatorial hydrogens?


b) Answer the following question for the boat form of cyclohexane.

What is the smallest dihedal angle for C₁-C₂ hydrogens (hydrogens on adjacent carbon atoms), do not include any hydrogens on the Bowsprit carbons?c)

c) For the most stable conformation of cylcohexane:
 

1. What is the C-C-C bond angle?
2. What is the heat of combustion for the molecule in kJ per mole of CH₂? (To find this data search the NIST database for cyclohexane. The NIST WebBook can be accessed through WEB-sters' Organic Chemistry under Databases.)


d) View cyclopropane in RasMol.
 

1. What is the C-C-C bond angle?
2. What is the heat of combustion for the molecule in kJ per mole of CH₂? (Search the NIST database for cyclopropane.)


e) Which compound is more stable; cylcopropane or cyclohexane? Briefly explain what could account for the difference in stability.

f) Identify the following di-substituted cyclohexane chair forms as being cis- or trans-, and if it is the most stable of the two possible chair forms and why.

1. one,
2. two,
3. three,
4. four

Herman Melville describes ambergris in the epoch novel, Moby Dick: ".......ambergris is soft, waxy, and so highly fragrant and spicy, that it is largely used in perfumery, in pastiles, precious candles, hair-powders, and pomatum. The Turks use it in cooking, and also carry it to Mecca, for the same purpose that frankincense is carried to St. Peter's in Rome. Some wine merchants drop a few grains into claret, to flavor it. Who would think, then, that such fine ladies and gentlemen should regale themselves with an essence found in the inglorious bowels of a sick whale! Yet so it is."

Moby Dick or The Whale was written by Melville in 1851. If you are interested in reading the novel, it is available on the Web: http://www.americanliterature.com/MD/MDINDEX.HTML

For further background information on ambergris, ambrox and ambreine see Dr. Randy Ralph's comprehensive site: "Ambergris: A Pathfinder and Annotated Bibliography" http://www.netstrider.com/documents/ambergris

Since the decline of whaling and the restriction of global whaling operations, ambergris has not been commercially used for some time. With the loss of this material, the perfume industry turned to organic synthesis to prepare a substitute, and many, many compounds were synthesized and tested. One that was selected for use is Ambrox. In analyzing the correlation between structure and the smell of the synthesized analogs it was found that certain positions and interatomic distances were critical for the bio-activity. This discovery was framed as the "ambergris triangle" which is illustrated by the examples in the following three images, and later became know as the "Triaxial Rule". In order to smell like ambergris the analogs must have two axial hydrogens within 2.38 Angstroms +/-0.35 A of each other, and one hydrogen must be within 2.90 Angstroms +/-0.40 A of an oxygen atom in an adjacent ring, with the other hydrogen 2.45 Angstroms +/-0.35 A from the oxygen atom. Ambrox meets these criteria as illustrated in the examples with RasMol.
 

Define the distances in the spatial triangle for analog A and analog B, and determine if one, or the other, or both will smell like ambergris. Be sure to clearly state your conclusion. Note: the ring system is different than Ambrox, but the Rule still applies.