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Molecular Geometry

Molecular Geometry


Molecules, from simple diatomic ones to macromolecules consisting of hundreds of atoms or more, come in many shapes and sizes. The term "molecular geometry" is used to describe the shape of a molecule or polyatomic ion as it would appear to the eye (if we could actually see one). For this discussion, the terms "molecule" and "molecular geometry" pertain to polyatomic ions as well as molecules.

Molecular Orbitals

When two or more atoms approach each other closely enough, pairs of valence shell electrons frequently fall under the influence of two, and sometimes more, nuclei. Electrons move to occupy new regions of space (new orbitalsmolecular orbitals) that allow them to "see" the nuclear charge of multiple nuclei. When this activity results in a lower overall energy for all involved atoms, the atoms remain attached and a molecule has been formed. In such cases, we refer to the interatomic attractions holding the atoms together as covalent bonds. These molecular orbitals may be classified according to strict mathematical (probabilistic) determinations of atomic behaviors. For this discussion, the two most important classifications of this kind are sigma (σ ) and pi (π ). Though we may be oversimplifying a highly complex mathematics, it may help one to visualize sigma molecular orbitals as those that build up electron density along the (internuclear) axis connecting bonded nuclei, and pi molecular orbitals as those that build up electron density above and below the internuclear axis.

Bonding Theories

This discussion will examine two approaches chemists have used to explain bonding and the formation of molecules, the molecular orbital (MO) theory and the valence bond (VB) theory. At their simplest levels, both approaches ignore nonvalence shell electrons, treating them as occupants of molecular orbitals so similar to the original (premolecular formation) atomic orbitals that they are localized around the original nuclei and do not participate in bonding. The two approaches diverge mainly with respect to how they treat the electrons that are extensively influenced by two or more nuclei. Though the approaches differ, they must ultimately converge because they describe the same physical reality: the same nuclei, the same electrons.

Molecular orbital theory. In MO theory, there are three types of molecular orbitals that electrons may occupy.

1. Nonbonding molecular orbitals. Nonbonding molecular orbitals closely resemble atomic orbitals localized around a single nucleus. They are called nonbonding because their occupation by electrons confers no net advantage toward keeping the atoms together.

2. Bonding molecular orbitals. Bonding molecular orbitals correspond to regions where electron density builds up between two, sometimes more, nuclei. When these orbitals are occupied by electrons, the electrons "see" more positive nuclear charge than they would if the atoms had not come together. In addition, with increased electron density in the spaces between the nuclei, nucleus-nucleus repulsions are minimized. Bonding orbitals allow for increased electron-nucleus attraction and decreased nucleus-nucleus repulsion, therefore electrons in such orbitals tend to draw atoms together and bond them to each other.

3. Antibonding molecular orbitals. One antibonding molecular orbital is formed for each bonding molecular orbital that is formed. Antibonding orbitals tend to localize electrons outside the regions between nuclei, resulting in significant nucleus-nucleus repulsionwith little, if any, improvement in electron-nucleus attraction. Electrons in antibonding orbitals work against the formation of bonds, which is why they are called antibonding.

According to MO theory, atoms remain close to one another (forming molecules) when there are more electrons occupying lower energy sigma and/or pi bonding orbitals than occupying higher energy antibonding orbitals; such atoms have a lower overall energy than if they had not come together. However, when the number of bonding electrons is matched by the number of antibonding electrons, there is actually a dis advantage to having the atoms stay together, therefore no molecule forms.

Valence bond theory. Valence bond (VB) theory assumes that atoms form covalent bonds as they share pairs of electrons via overlapping valence shell orbitals. A single covalent bond forms when two atoms share a pair of electrons via the sigma overlap of two atomic orbitalsa valence orbital from each atom. A double bond forms when two atoms share two pairs of electrons, one pair via a sigma overlap of two atomic orbitals and one via a pi overlap. A triple bond forms by three sets of orbital overlap, one of the sigma type and two of the pi type, accompanied by the sharing of three pairs of electrons via those overlaps. (When a pair of valence shell electrons is localized at only one atom, that is, when the pair is not shared between atoms, it is called a lone or nonbonding pair.)

Let us apply this greatly simplified picture of VB theory to three diatomic molecules: H2, F2, and HF. VB theory says that an H2 molecule forms when a 1s orbital containing an electron that belongs to one atom overlaps a 1s orbital with an electron of opposite spin belonging to the other, creating a sigma molecular orbital containing two electrons. The two nuclei share the pair of electrons and draw together, giving both electrons access to the positive charge of both nuclei. Diatomic fluorine, F2, forms similarly, via the sigma overlap of singly occupied 2p orbitals. The HF molecule results from the sharing of a pair of electrons whereby an electron in a hydrogen 1s orbital experiences sigma overlap with an electron in a fluorine 2p orbital.

Molecular Geometries

This VB approach allows us to return to the focus of our discussion. The geometry of a molecule or polyatomic ion is determined by the positions of individual atoms and their positions relative to one another. It can get very complicated. However, let us start with some simple examples and your imagination will help you to extend this discussion to more complicated ones. What happens when two atoms are bonded together in a diatomic molecule? The only possible geometry is a straight line. Hence, such a molecular geometry (or shape) is called "linear." When we have three bonded atoms (in a triatomic molecule), the three atoms may form either a straight line, creating a linear molecule, or a bent line (similar to the letter V), creating a "bent," "angular," "nonlinear," or "V-shaped" molecule. When four atoms bond together, they may form a straight or a zigzag line, a square or other two-dimensional shape in which all four atoms occupy the same flat plane, or they may take on one of several three-dimensional geometries (such as a pyramid, with one atom sitting atop a base formed by the other three atoms). With so many possibilities, it may come as a surprise that we can "predict" the shape of a molecule (or polyatomic ion) using some basic assumptions about electron-electron repulsions.

We start by recognizing that, ultimately, the shape of a molecule is the equilibrium geometry that gives us the lowest possible energy for the system. Such a geometry comes about as the electrons and nuclei settle into positions that minimize nucleus-nucleus and electron-electron repulsions, and maximize electron-nucleus attractions.

Modern computer programs allow us to perform complex mathematical calculations for multiatomic systems with high predictive accuracy. However, without doing all the mathematics, we may "predict" molecular geometries quite well using VB theory.

Valence shell electron pair repulsion approach. In the valence shell electron pair repulsion (VSEPR) approach to molecular geometry, we begin by seeing the valence shell of a bonded atom as a spherical surface. Repulsions among pairs of valence electrons force the pairs to locate on this surface as far from each other as possible. Based on such considerations, somewhat simplified herein, we determine where all the electron pairs on the spherical surface of the atom "settle down," and identify which of those pairs correspond to bonds. Once we know which pairs of electrons bond (or glue) atoms together, we can more easily picture the shape of the corresponding (simple) molecule.

However, in using VSEPR, we must realize that in a double or triple bond, the sigma and pi orbital overlaps, and the electrons contained therein, are located in the same basic region between the two atoms. Thus, the four electrons of a double bond or the six electrons of a triple bond are not independent of one another, but form coordinated "sets" of four or six electrons that try to get as far away from other sets of electrons as possible. In an atom's valence shell, a lone pair of electrons or, collectively, the two, four, or six electrons of a single, double, or triple bond each form a set of electrons. It is repulsions among sets of valence shell electrons that determine the geometry around an atom.

Consider the two molecules carbon dioxide (CO2) and formaldehyde (H2CO). Their Lewis structures are and

and

In CO2, the double bonds group the carbon atom's eight valence electrons into two sets. The two sets get as far as possible from each other by residing on opposite sides of the carbon atom, creating a straight line extending from one set of electrons through the carbon nucleus to the other. With oxygen atoms bonded to these sets of electrons, the oxygencarbonoxygen axis is a straight line, making the molecular geometry a straight line. Carbon dioxide is a linear molecule.

In H2CO, the carbon atom's eight valence electrons are grouped into three sets, corresponding to the two single bonds and the one double bond. These sets minimize the repulsions among themselves by becoming as distant from one another as possibleeach set pointing at a vertex of a triangle surrounding the carbon atom in the center. Attaching the oxygen and hydrogen atoms to their bonding electrons has them forming the triangle with the carbon remaining in the center; all four atoms are in the same plane. Formaldehyde has the geometry of a trigonal (or triangular) planar molecule, "planar" emphasizing that the carbon occupies the same plane as the three peripheral atoms.

COMMONLY ENCOUNTERED ELECTRON GEOMETRIES
Most Common "Set"
Number of Sets Geometry Appearance
2 Linear
3 Trigonal (Triangular) Planar
4 Tetrahedral
5 Trigonal Pyramidal
6 Octahedral

We may extend this approach to central atoms with four, five, six, or even more sets of valence shell electrons. The most common geometries found in small molecules appear in Table 1.

Until now, this article has focused on all the electrons in a central atom's valence shell, including sets not engaged in bonding. Though all such sets must be included in the conceptualization of the electron-electron repulsions, a molecule's geometry is determined solely by where its atoms are: A molecule's geometry is identified by what people would see if they could see atoms. In the carbon dioxide and formaldehyde examples, the molecules have the same overall geometries as the electron sets, because in both cases all sets are attached to peripheral atoms: Carbon dioxide is a linear molecule and formaldehyde is a trigonal (or triangular) planar one.

On the other hand, a water molecule (H2O)

has four sets of electrons around the O atom (two lone pairs and those making up two sigma bonds) that assume a tetrahedral arrangement, but the molecular geometry as determined by the positions of the three atoms is a bent, or V-shaped, molecule, with a HOH angle approaching the tetrahedral angle of 109.5°.

Similarly, a hydronium ion (H3O+)

has four sets of electrons around the central O atom (one lone pair and those making up three sigma bonds) in a tetrahedral arrangement, but the molecular geometry as determined by the four atoms is a trigonal (three-pointed base) pyramidal ion with the O atom "sitting" atop the three H atoms. The hydronium ion also has a HOH angle approaching the tetrahedral angle of 109.5°.

Table 2 outlines the most common molecular geometries for different combinations of lone pairs and up to four total sets of electrons that have assumed positions around a central atom, and the hybridizations (see below) required on the central atom.

Hybridization. Finally, what does valence bond theory say about the atomic orbitals demanded by VSEPR? For example, though the regions occupied by sets of electrons having a tetrahedral arrangement around a central atom make angles of 109.5° to one another, valence p -orbitals are at 90° angles.

To reduce the complex task of finding orbitals that "fit" VSEPR, we base their descriptions on mathematical combinations of "standard" atomic orbitals, a process called hybridization; the orbitals thus "formed" are hybrid orbitals. The number of hybrid orbitals is equal to the number of "standard" valence atomic orbitals used in the mathematics. For example, combining two p -orbitals with one s -orbital creates three unique and equivalent sp 2 (s -p -two) hybrid orbitals pointing toward the vertices of a triangle surrounding the atom.

ELECTRON SETS, HYBRIDIZATION AND MOLECULAR GEOMETRIES
Number of
Electrons Electron "Set" Number of Molecular
Sets Geometry Lone Pairs Geometry Hybridization Appearance
2 Linear Linear sp
0 Trigonal Planar
3 Trigonal (Triangular) Planner 1 Bent or V-shaped sp2
2 Linear
0 Tetrahedral
1 Trigonal Pyramid
4 Tetrahedral sp3
2 Bent or V-shaped
3 Linear

Valence electron sets (lone pairs and electrons in sigma bonds) are "housed," at least in part, in hybrid orbitals. This means that an atom surrounded by three electron sets uses three hybrid orbitals, as in formaldehyde. There, the central carbon atom uses hybrid orbitals in forming the CH single bonds and the sigma portion of the C=O double bond. The carbon's remaining unhybridized p -orbital overlaps a p -orbital on the oxygen, creating the pi bond that completes the carbon-oxygen double bond. The HCO and HCH angles are 120°, as is found among sp 2 hybridized orbitals in general. The hybridizations required for two, three, and four electron sets are given in Table 2, along with their corresponding electron geometries.

see also Isomerism; Lewis Structures; Molecules; Nuclear Magnetic Resonance.

Mark Freilich

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Molecular Structure

Molecular Structure


The Rise and Reemergence of Atomism

Throughout history, humans have created models to help them explain the observed character of substances and phenomena in the material world. The ancient philosophers Democritus and Lucretius were among the first to speculate that matter was discontinuous, and that small, indivisible particles not only made up substances but also gave them their observed properties. The Greeks called these particles "atoms" (the English equivalent), a word that meant indivisible. Lucretius imagined that the particles that made up vapor had smooth surfaces and could not interconnect, giving vapors (gases) their extreme mobility. Liquids, on the other hand, were thought to be made up of particles, each particle having a few hooks. These few hooks would get entwined but would not immobilize the particles, thereby causing the particles to cling, yet still be fluid. The particles that made up solids, by contrast, were thought to have many hooks, resulting in the extremely sturdy nature of solid materials. The hypothesis of finite particles implied empty space between them. Yet, the majority of Greek philosophers did not believe that nothingness (the vacuums between particles) could exist, so the idea of atoms did not last long in the ancient times. Ironically, the objection was not to the existence of particles, but to the vacancies that must exist between them.

Most cultures have linked properties of matter with religious and/or superstitious ideas. The term "gold" derives from an Old English word meaning "something shiny and yellow like the Sun"; it served not only as the name of the metal but also identified its properties. Polished gold nearly captures the sunlight it reflects, and the astronomical, astrological, medical, and religious attributes of the Sun were thought to be present in gold metal. For thousands of years, substances were said to contain essences or essential parts that gave them their characters. In a sense modern ideas about molecular structure do something similar. Chemists construct explanations for observed, macroscopic phenomena (e.g., reactivity) by describing the assemblages, shapes, and motions of submicroscopic particles.

The theory of atoms did not reemerge until the seventeenth century. The discovery of elements rapidly led to the idea that nonelementary substances were made up of molecules that were, in turn, collections of elemental atoms. During the first years of chemical analyses, different substances were observed to have different compositions; the deduction was made that substances were different because their compositions were different. One type of mineral might be 34 percent iron and 66 percent oxygen. Each sample of that mineral would give the same results (34% iron and 66% oxygen). A different mineral, that is, one with different properties, might be 56 percent iron and 44 percent oxygen. Although there was still no concept of bonding between atoms or of molecular geometry at the beginning of the nineteenth century, chemists had developed the idea that different molecules were different collections of atoms.

Isomerism and the Development of Molecular Structural Models

Scientific theories are sometimes discarded. When information that contradicts a theory is reliable, the theory must be changed to fit the new data. As the elemental analysis of compounds expanded greatly during the early 1800s, observations that different substances were of the same elemental composition were inevitable. In his History of Chemistry (1830), Thomas Thomson drew illustrations of varying hypothetical particle arrangements, using symbols that were used at that time (those of John Dalton), as a way to explain why two acids of the same elemental composition could have different physical and chemical properties (see Figure 1). These are believed to be the earliest recorded representations of molecular structure that showed varying arrangements of the same atoms; the phenomenon would soon be called isomerism (from the Greek iso, meaning same, and meros, meaning part). In 1828 Friedrich Wöhler (18001882) synthesized urea, (NH2)2C = O or CH4N2O, that was indistinguishable from that that had been isolated from urine. He prepared this organic substance from the clearly inorganic (mineralogical) starting material ammonium cyanate, NH4(+) NCO(), also CH4N2O, the result of the combination of ammonium chloride and silver cyanate. Urea and ammonium cyanate are constitutional isomers , and together illustrate the fact that fixed arrangements of atoms, molecular structures, must be invoked to explain observed phenomena.

The constitution of a molecule (number of, kind of, and connectivities of atoms) may be represented by a two-dimensional "map" in which the interatomic linkages (bonds) are drawn as lines. There are two constitutional isomers that are represented by the molecular formula C2H6O: ethanol and dimethyl ether. The differences in connectivities, which are not evident in the common constitutional inventory C2H6O, can be conveyed by typographical line formulas (CH3CH2OH for ethanol and CH3OCH3 for dimethyl ether), or by structural representations (see Figure 2). As the number and kinds of atoms in substances increase, the number of constitutional isomers increases.

By the mid-1850s, a new theory of molecular structure had emerged. Given a unique collection of atoms, it was not the identities of the atoms that distinguished one molecule from another, but rather the connectivity,

or bonding, of those atoms. The nature of the chemical bond was unknown, and the phenomenon of chemical bonding was described as "chemical affinity." Because it was observed that the passing of electricity through some substances, such as water, could "break" the molecules apart into their elements (electrolysis), the electrostatic attractions of charged particles (ions) were used to contribute to an explanation of chemical affinity. Just as the hypothesis of the varying connectivities of atoms emerged as a response to observations that could not be explained, variation in the three-dimensional arrangements of atoms in space was proposed to reconcile other observed phenomena. Jacobus van't Hoff (18521911) and Joseph-Achille Le Bel (18471930) proposed (independently of one another, in 1874) that molecules of the same connectivity yet different physical properties (e.g., optical activity) might be explained if, in the case of four different particles, the arrangement (configuration) of the particles was tetrahedral. Macroscopically or microscopically, a tetrahedral array of four different things gives rise to two and only two different arrangements that are nonsuperimposable mirror images (enantiomers; see Figure 3). Distinct molecular structural units that have the same connectivities but varying three-dimensional arrangements are also isomers. The term "stereoisomer" was introduced by Viktor Meyer in 1888 to describe molecules that differ only in their three-dimensional arrangements.

Connectivity and stereoisomerism give chemists a way to uniquely differentiate one molecular structure from another. The molecular formula C4H9Br, for instance, represents five different substances (see Figure 4). Predictably, although there is only one compound for each of the connectivities designated 1-bromobutane, 2-bromo-2-methylpropane, and 1-bromo-2-methylpropane, there are two compounds represented by the connectivity designated 2-bromobutane (carbon 2 has four different groups attached, and thus two three-dimensional arrangements of the molecule, whose geometries are labeled R and S, exist). There are no other isomers of C4H9Br that are predicted, and none that are observed.

Although the arrangement of molecular atoms around a given point is fixed, molecules are not static objects. The sequence of links in a chain, for instance, is constant, but the chain can be twisted and knotted into countless shapes. In the case of a molecule, twists do not affect the identity of a substance, but the overall molecular shape is part of molecular structure and can have an impact on the observed properties. According to Ernest Eliel and Samuel Wilen (1994, p. 102), configurational stereoisomers result from "arrangements of atoms in space of a molecule with a defined constitution, without regard to arrangements that differ only by rotation about one or more single bonds, providing that such a rotation is so fast as not to allow isolation of the species so differing." Conformational stereoisomers are

molecular shapes resulting from bond rotations that do not affect molecular identity . The drawings shown in Figure 5 represent some of the different conformational shapes that the single molecule (S )-2-bromobutane can assume.

The overall geometry of a molecule was recognized as contributing to its chemical reactivity in the 1950s, and methods used to determine molecular structure have grown dramatically since that time. Throughout the early 1900s, direct experimental evidence of the three-dimensional arrangements of atoms was becoming available as a result of x-ray diffraction crystallography. Nuclear magnetic resonance spectroscopy (first used in the 1960s) and atomic force microscopy (in the 1980s) are two techniques of many that are now used to gather experiment-based information about molecular structure. What might have taken years to determine in 1950, and what was impossible to know about extremely large biopolymers (e.g., DNA , enzymes, and polysaccharides at a cell surface) as late as 1990 can now sometimes be determined in a matter of seconds.

Molecular environment influences molecular structure. The shape that a molecule assumes within a crystal lattice is necessarily different from its shape in water and will vary according to solvent and other environmental factors (e.g., temperature and pH). Beginning in the late 1980s the significance of the noncovalent aggregation of large numbers of molecular entities began to be understood. A protein, for instance, folds into its three-dimensional shape because water is present; without water, the shape is quite different. Thus, molecular structure is determined by a combination of extrinsic as well as intrinsic factors. The field of molecular structure and reactivity that deals with large aggregations of molecules and how they influence each other is called supramolecular chemistry.

Molecular Structural Theory

The electron was discovered in 1900, and it took about twenty years for the electronic nature of the chemical bond to come into wide acceptance. Particle-based models for atomic and molecular structure soon gave way to the quantum mechanical view, in which electrons are not treated as localized, discrete particles (electrons orbiting around a nucleus), but as delocalized areas of wavelike charge, each possessing a given probability of being found in a given location near an atomic nucleus (an orbital). The chemical bonding in molecules, which began the twentieth century as shared electron pairs between atoms, evolved to become a matter of molecular orbitals. Molecular orbitals describe three-dimensional arrangements of the atomic nuclei in a molecule and the probability that any given electron of a given energy will occupy a given location with respect to those nuclei. Single bonds are explained by the overlap of atomic orbitals along the internuclear axis of two atoms. Multiple bonds are the combination of sigma plus pi bonding, the latter corresponding to the overlap of atomic orbitals that is not along the internuclear axis. A rough guide to the bonding molecular orbitals in methane is depicted in Figure 6. The eight valence shell electrons (four from carbon, four from the four hydrogens) are

distributed among four molecular orbitals. One of the four orbitals is composed of favorable bonding interactions between the 2s -orbital of carbon and the four 1s -orbitals of the hydrogen atoms, whereas the other three are the equally likely combinations of one of the three 2p -orbitals of carbon and the 1s orbitals of hydrogen atoms. Computer-based models for chemical bonding are as important to modern molecular structural theory as experimental measurements.

see also Isomerism; Le Bel, Joseph-Achille; Molecules; Nuclear Magnetic Resonance; van't Hoff, Jacobus; WÖhler, Friedrich.

Brian P. Coppola

Bibliography

Eliel, Ernest L., and Wilen, Samuel H. (1994). Stereochemistry of Organic Compounds. New York: Wiley.

Thomson, Thomas (1830). The History of Chemistry. London: Colburn and Bentley.

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molecular structure

molecular structure. Building of tubes and balls arranged to resemble a diagram of a molecule, as in the Atomium erected for the Brussels Exposition (1958).

Bibliography

Lewis & and Darley (1986)

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