Analysis, conformational

The pioneering applications of molecular mechanics to coordination compounds were conformational analyses127,281. Recent applications involving the computation of conformer equilibria discussed in this chapter are studies of solution structure refinements126,29 1, racemate separations131 3il and the evaluation of reaction pathways11 1,34,3S1. The importance of conformer equilibria in the areas of electron transfer rates and redox potentials is discussed in Chapter 10, and many examples discussed in the other chapters of Part II indicate how important the prediction of conformational equilibria is in various areas of coordination chemistry. 

The main problem that occurs when strain energies are used for the evaluation of relative stabilities have been discussed in Chapter 2, and they will be only briefly mentioned here  

Approaches related to overcoming these limitations will be discussed, based on the examples presented ahead. Furthermore, the modeling of electronic effects is not usually addressed specifically. This can lead to additional uncertainties in terms of the computed structures and conformer distributions. 

One of the most extensively studied systems is that of [Co(dien)2]3+ (Table 7.1). The mer- isomer is chiral (C2) because of the two possible orientations of the proton at the secondary nitrogen atomst38,39], the unsym-fac-vsoiasi is also chiral (C2) while the sym-fac-isomer is achiral (Q). For the five-membered chelate rings all possible combinations of S and X conformations (see Fig. 6.5 for the SIX nomenclature) have to be considered, leading to a total of 40 isomers and conformers (some conformers are calculated to be unstable and may therefore be neglected144,451). The calculated distribution is based on partition functions (Eqs. 7.1, 7.2)  

One of the most extensively studied systems is that of [Co(dien)2]3+ (Table 8.1). 

The physical, chemical and biological properties of a molecule often depend critically upon the three-dimensional structures, or conformations, that it can adopt. Conformational analysis is the study of the conformations of a molecule and their influence on its properties. The development of modem conformational analysis is often attributed to D H R Benton, who showed in 1950 that the reactivity of substituted cyclohexanes was influenced by the equatorial or axial nature of the substituents [Barton 1950]. An equally important reason for the development of conformational analysis at that time was the introduction of analytical techniques such as infrared spectroscopy, NMR and X-ray crystallography, which actually enabled the conformation to be determined. 

The conformations of a molecule are traditionally defmed as those arrangements of its atoms in space that can be interconverted purely by rotation about single bonds. This definition is usually relaxed in recognition of the fact that small distortions in bond angles and bond lengths often accompany conformational changes, and that rotations can occur about bonds in conjugated systems that have an order between one and two. 

We next introduce the basic algorithms and then describe some of the many variants upon them. We then discuss two methods called evolutionary algorithms and simulated annealing, which are generic methods for locating the globally optimal solution. Finally, we discuss some of the ways in which one might analyse the data from a conformational analysis in order to identify a representative set of conformations. 

Bond rotation allows chains of atoms to adopt a number of conformations 

on a slightly larger scale, shape is not usually so well defined. Rotation is possible about single bonds and this rotation means that, while the localized arrangement of atoms stays the same (every saturated carbon atom is still always tetrahedral), the molecule as a whole can adopt a number of different shapes. Shown on the next page are several snapshot views of one molecule—it happens to be a pheromone used by pea moths to attract a mate. Although the structures look dissimilar, they differ from one another only hy rotation about one or more single bonds. Whilst the overall shapes differ, the localized structure is stiU the 

At room temperature in solution, all the single bonds in the molecule are constantly rotating—the chances that two molecules will have exactly the same shape at any one time are quite small. 

even though no two molecules have exactly the same shape at any one time, they are still all the same chemical compound—they have all the same atoms attached in the same way. We call the different shapes of molecules of the same compound different conformations. 

To get from one conformation to another, we can rotate about as many single bonds as we like. The one thing we can t do though is to break any bonds. This is why we can t rotate about a double bond—to do so we would need to break the n bond. Below are some pairs of structures that can be interconverted by rotating about single bonds they are all different conformations of the same molecule. 

Most molecules tend to favor one conformer over the others based on the stereochemistry of the particular monosaccharide and the steric bulk of the groups that are appended to it. For example, most aldohexoses prefer the chair conformation that places the bulky C5 hydroxymethyl group in the equatorial position. Having said that, the energy barrier between the two possible chair conformations is 

Furanose rings also exhibit a degree of conformational mobility, albeit to a lesser extent. The two predominant conformations adopted by these five-membered rings are envelope (E) and twist (T). There are 10 individual envelope 

A chemical molecule, by contrast consists of many particles. In the most general case N independent constituent electrons and nuclei generate a molecular Hamiltonian as the sum over N kinetic energy operators. The common wave function encodes all information pertaining to the system. In order to constitute a molecule in any but a formal sense it is necessary for the set of particles to stay confined to a common region of space-time. The effect is the same as on the single confined particle. Their behaviour becomes more structured and interactions between individual particles occur. Each interaction generates a Coulombic term in the molecular Hamiltonian. The effect of these terms are the same as of potential barriers and wells that modify the boundary conditions. The wave function stays the same, only some specific solutions become disallowed by the boundary conditions imposed by the environment. 

The ultimate implication should be clear. A given set of sub-atomic particles may be conditioned in an infinite variety of ways by different environments and histories. All of these constraints should be stipulated in the molecular Hamiltonian in order to avoid confusion with irrelevant permutations. The degree of structure becomes a function of the complete Hamiltonian. 

All familiar molecular structures have been identified in the crystalline state. To describe such molecules quantum-mechanically requires specification of a crystal Hamiltonian. This procedure is never attempted in practice. Instead, history is taken for granted by assuming a specific connectivity among nuclei and the crystal environment is assumed to generate well-defined conformational features characteristic of all molecules. Although these decisions may not always be taken consciously, the conventional approach knows no other route from wave equation to molecular conformation. 

Despite the vague definition of molecular shape, this concept remains central in chemical thinking [198]. It features at all explanatory levels, shaping important concepts such as chemical reactivity, reaction mechanism, phase transition and reaction pathway. It enters these arguments in the guise of 

The eclipsed conformation of ethane is 3 kcal/mol less stable than the staggered conformation ( 1 kcal/mol for each eclipsed H/H pair). Any conformation between staggered and eclipsed is referred to as a skew conformation. 

The instability of the eclipsed form of ethane was originally postulated to result from repulsion of filled hydrogen orbitals. However, state-of-the-art quantum chemical calculations now indicate that two main factors contribute to the preference for the staggered conformation of ethane. First, the eclipsed form is selectively destabilized by unfavorable four-electron interactions between the filled C-H bonding orbitals of 

The energy required to rotate the ethane molecule about the C-C bond is called its torsional energy. Torsional strain is the repulsion between neighboring bonds (electron clouds) that are in an eclipsed relationship. 

The CH3-H eclipsed interaction imposes 1.4 kcal/mol of strain on top of the 2.0 kcal/mol H-H torsional strains in the eclipsed conformation of propane. The 0.4 kcal/mol of additional strain is referred to as steric strain, the repulsion between nonbonded atoms or groups. 

A potential energy plot for rotation about the C2-C3 bond in butane shows unique maxima and minima. There are two kinds of staggered conformations, gauche (steric strain) and anti, and two distinct eclipsed conformations (torsional and steric strain). 

Depending on the available experimental structural data, different approaches can or have to be used to extract the information. Whereas careful inspection of the conformation of single structures can give the spark to explain unusual chemical behavior, analyses of the variation in molecular geometry from a large number of chemical fragments need to be done by statistical and graphical methods. 

In the following sections a number of examples are summarized with an emphasis on the chemical information that can be obtained from them. Some have already been mentioned in previous chapters to illustrate specific methodological aspects of structure-structure and of structure-energy correlation. Others will merely be mentioned to provide a reference to the primary literature for the interested reader. 

A study of annealed polycarbonate showed that the heating process was primarily a modification of trans-trans and trans-cis population of the carbonate group, leading to a more stable structure with a lower internal energy. Ageing proceeded mainly by extremely local rearrangements compatible with a densified structure (177). 

The conformational structures of polycarbonate were studied in the solid state and in solution. Based on the temperature dependences of the IR spectra, bands sensitive to transitions between the trans-trans and trans-cis conformations of the carbonate group were identified (361). 

The conformers of the ethylene glycoxy moeity of PET, have been studied in the amorphous and crystalline regions. The profiles of the 382 cm band and the 1020 cm band for a series of specimens annealed at different temperatures. Consistent results were obtained from both bands for the compositions of the three conformers, i.e., the trans conformer in the crystalline state and both the trans conformer and the gauche conformer in the amorphous state (365). 

Poly(ethylene 2,6-naphthalate) (PEN) film containing alpha, beta and amorphous phases were prepared, and the amorphous contribution digitally subtracted to yield the characteristic spectra of the amorphous, alpha, and beta phases. In other words, the amorphous spectrum is determined by melting the polymer, so after subtraction, one knows the spectrum of all of them. The alpha crystal form adopts an all-rran conformation, while the beta crystal form adopts a conformation with appreciable gauche character. Conformational changes in PEN occur due to the rotation of the naphthalene ring as well as rotation of the ethylene glycol units. The normalised absorbances of the bands at 824 and 814 cm were correlated to polymer density, and can be used to represent the amorphous and alpha crystalline phases, respectively (56). 

The IR characteristic bands at 1230/1250 cm of stereoregular polyacrylonitrile (PAN) are dependent on not only the configuration, but also on the conformation through the arrangements of the configurations on the polymer chain. The effect of configuration and conformation on the IR results was determined to be a function of the film preparation conditions (180). 

Either of these two kinds of hydrogen can be replaced by an X to give a propyl compound (Fig. 2.29). The linear compound CH3 — CH2—CH2—X, in which X replaces a methyl hydrogen, is called propyl X (in the old days, w-propyl X). The branched compound CH3 — CHX—CH3, in which X replaces a hydrogen on the methylene carbon, is called isopropyl X (and sometimes 1-propyl X). Propyl compounds and isopropyl compounds are structural isomers of each other they are compounds with the same formula but different structures. 

PROBLEM 2.20 Make a three-dimensional drawing of propyl alcohol (CH3—CH2—CH2—OH) and one of the related isopropyl alcohol (CH3—CHOH—CH3). 

8 Butanes CC4Hio]r Butyl Compounds CC4H9X), and Conformational Analysis 

FIGURE 2.32 (a) Newman projections for butane. The staggered conformations are shown, (b) A graph of dihedral angle (0) versus energy for hutane as the molecule changes through rotation about the C(2)—C(3) bond. AH three eclipsed conformations are shown. 

PROBLEM 2.22 Draw Newman projections constructed by looking down the indicated carbon-carbon bond in the following molecules. For the molecule on the right, make a graph of energy versus dihedral angle. 

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Neuhaus D and Williamson M 1989 The Nuclear Overhauser Effect in Structural and Conformational Analysis (New York VCH)... 

Piela L, Kostrowicki J and Scheraga H A 1989 The multiple-minima problem in the conformational analysis of molecules. Deformation of the potential energy hypersurface by the diffusion equation method J. Phys. Chem. 93 3339... 

Shephard M J and Paddon-Row M N 1996 Conformational analysis of Cgg ball and chain molecules a molecular orbital study Aust. J. Chem. 49 395-403... 

M. Robb, M. Garavelli, M. Olivucci, and F, Bernardi, in Reviews in Computational Chemistry, K. Lipkowitz and D. Boyd, eds., Vol. 15, John Wiley Sons, New York, 2000, pp. 87-146. M. Olivucci, M, Robb, and F. Bernardi, in Conformational analysis of molecules in excited states, Wiley-VCH, New York, 2000, pp. 297-366. 

M. Oobatake and G.M. Crippen, Residue-residue potential function for conformational analysis of proteins, J.Phys. Chem. 85 (1981), 1187-1197. 

Obtaining an Ensemble of Conformations What is Conformational Analysis ... 

Other methods which are applied to conformational analysis and to generating multiple conformations and which can be regarded as random or stochastic techniques, since they explore the conformational space in a non-deterministic fashion, arc genetic algorithms (GA) [137, 1381 simulation methods, such as molecular dynamics (MD) and Monte Carlo (MC) simulations 1139], as well as simulated annealing [140], All of those approaches and their application to generate ensembles of conformations arc discussed in Chapter II, Section 7.2 in the Handbook. 

A molecular dynamics simulation samples the phase space of a molecule (defined by the position of the atoms and their velocities) by integrating Newton s equations of motion. Because MD accounts for thermal motion, the molecules simulated may possess enough thermal energy to overcome potential barriers, which makes the technique suitable in principle for conformational analysis of especially large molecules. In the case of small molecules, other techniques such as systematic, random. Genetic Algorithm-based, or Monte Carlo searches may be better suited for effectively sampling conformational space. 

There is a lot of confusion over the meaning of the terms theoretical chemistry, computational chemistry and molecular modelling. Indeed, many practitioners use all three labels to describe aspects of their research, as the occasion demands "Theoretical chemistry is often considered synonymous with quantum mechanics, whereas computational chemistry encompasses not only quantum mechanics but also molecular mechaiucs, minimisation, simulations, conformational analysis and other computer-based methods for understanding and predicting the behaviour of molecular systems. Molecular modellers use all of these methods and so we shall not concern ourselves with semantics but rather shall consider any theoretical or computational tecluiique that provides insight into the behaviour of molecular systems to be an example of molecular modelling. If a distinction has to be... 

Volumen and Hydratationswarme der lonen. Zeitschrift filr Physik 1 45-48. aan C M and K B Wiberg 1990. Determining Atom-Centred Monopoles from Molecular Electro-itic Potentials. The Need for High Sampling Density in Formamide Conformational Analysis. imal of Computational Chemistry 11 361-373. 

As we have discussed, a common strategy in conformational analysis is to perform two-stage process involving first, the generation of a large number of minimum enerj... 

A R, D P Dolata and K Prout 1990. Automated Conformational Analysis and Structure Generation Algorithms for Molecular Perception. Journal of Chemical Information and Computer Science 30 316-324. 

Gilson M K and B Honig 1988. Calculation of the Total Electrostatic Energy of a Macromoleculai System Solvation Energies, Binding Energies and Conformational Analysis. Proteins Structure Function and Genetics 4 7-18. 

R and M M Hann 2000. The In Silico World of Virtual Libraries. Drug Discovery Today 5 326-336. R and I D Kuntz 1990. Conformational Analysis of Flexible Ligands in Macromolecular eptor Sites. Journal of Computational Chemistry 13 730-748. 

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