Molecular Geometry

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Molecular Geomefty Charles D. Mickey Department of Marine Sciences Texas A&M University at Galveston Galveston,Texas 77553

either to instrumentation that magnifies matter and allows him to see in detail that which is normally beyond definition, or to his imagination in deoictine the structure of matter in ~~" terms of forms, models, or concepts that characterize the behavior of visible and ponderahle units. Subsequently, geometrical configurations are developed that enable us to envision the manner in which fundamental particles of matter are joined together to form molecules. Logic teaches us that external molecular form is a manifestation of the way in which the fundamental particles of matter are bonded~together. These structural arrangements or molecular geometries hecome reasonable concepts when subjected to study using various analytical and physical methods, especially the methods of diffraction of X-rays, electrons, and neutrons. Molecular structure concepts are frequently more useful than ahstract mathematical and . ohvsical oictures. It thus " hecomes simpler to consider properties of matter in terms of particles having- form and dimensions. Yet, recognizing that . matter is electrical in nature, we de employ concepts of charge and size to account for the attraction andlor repulsion between molecules in developing our knowledge of the nature of the chemical hond and molecular architecture. The structure of a molecule. or the shaoe of a narticular reeion within the molecule, has a significant influence on its physical, chemical, and hioloeical Inasmuch as mdecular structure " oronerties. . determines most o> the characteristics of matter, a detailed insight into the phenomenon of molecular geometry is required to explain molecular behavior. For example, polarity and hence boiling points and melting points, absorption of electromagnetic radiation, and soluhilities in various solvents, in principle are predictable (albeit qualitatively) from a detailed knowledge of molecular geometry. Moreover, molecular shape is especially important in biochemistry. There is considerable evidence indicatine that odor.. enzvmatic activitv. " .. toxin-antitoxin and histamine-antihistamine interactions, vision and color oercention are all subiect to stereochemical control. Charlcs Mickev received his B.S. from ~ r i n i t yUniversity in 1957, M.A. from St. Mary's University in 19fi6, and his Ph.D. from Texas A&M University in 1973. Charles taught chemistry at Alamo Heights Senior High 3 School. San Antonio, Texas, I'or 13 years. He also has over seven yearn university experience, havine.. taueht at San Antonio ., Junior Collegeand Texas A&M Univeriili. lir is pre*ently an Associate Professor of Chemislry in thp 1)cpaitrntmt d ; \ r l a r i n e Science st the Galveston hranch of T e x a s ARM. DF.Mickey's excellence and dedication to teaching has heen cited in his achievement of the ACS .lames Bryant Conant Award in 1970 and the 197fi-77 "Most Effective Teacher Award: Texas A&M University at Galveston." Charles has axauthored three problem solving textbooks, the most recent entitled "Solving Pmhlems in Chemistry." His research interests are in the areas of inorganic and hiochemistry of Group Vand VI elements, and selected prohlems in the chemistry envircmmental pollution.

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210 1 Journal of Chemical Education

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Experimental Determination of Molecular Geometry Historically, some chemical methods such as synthesis or degradation reactions were utilized for structural determination, hut their applicability was acutely limited by their accuracy. Currently, the quantitative elucidation of molecular geometry is effected by the precise measurement of bond aneles and hond leneths. The main exoerimental methods used to obtain these structural parameters may he conveniently cateeorized as diffraction, spectroscopic, and resonance-methids. Diffraction Methods In this category are included X-Yay, electron, and neutron diffraction. This method, a very powerful tool for structure elucidation, is based on the interaction of X-radiation or subatomic particles with molecules. When a beam of X-rays or subatomic particles such as electrons or neutrons are focused on a substance, their interaction with the substance may produce a diffraction pattern, i.e., molecular photograph. X-ray diffraction is most successful when applied to systems in the crystalline state that contain relatively heavy atomic nuclei. Electron diffraction. a techniaue similar to X-rav ~ R T Pt i.e w diflr;lrtic.n, i. used iur suhitnnces in rhe pils~o~ls trrmi. unlikt, N-ra\.s and 1.1errron~. Inlvmct onli. a i r h ;~romic nuclei and are, thkrefnre, useful in locating light atoms like hydrogen. The careful interpretation of diffraction patterns by the-trained observer permits the accurate determination of molecular shape. Spectroscopic Methods Spectroscopic methods of structural determination include infrared, ultraviolet-visible, and microwave spectroscopy. These methods rely upon the absorption of a relatively narrow wavelength range of electromagnetic radiation by atoms and

The spectra of m'oieculei are consequently much more complex than atomic spectra. The molecular spectra are characteristic of vibrational frequencies, moments of inertia, dissociation energies, changes in size accompanying absorption, and symmetry properties of the molecule. Thus, molecular spectra provide a very important source of quantitative data about hond aneles and hond leneth. Bond angles and hond lengths are the two parameters most essential for defining molecular geometry. Resonance Methods Nuclear magnetic resonance and electron spin resonace spectroscopy are very powerful tools and serve as invaluable supplements to the infrared and ultraviolet methods of structural analysis. Nuclear mawetic resonance capitalizes upon the magnetic properties of atomic nuclei to identify the types and structure of functional groups in complex molecules. The most universally investigated atomic nucleus is hydrogen, however, carhon-13 and phosphorus-31 have also heen the subject of many investigations. Electron spin resonance finds direct application in the study of free radical structure.

ranged around the central atom in a way that will maximize their senaration and concomitantlv minimize their i n t e r ~ a r ticle repulsions.

O-o-0 linear

The Application of VSEPR to Some Real Molecules

The central atom, Be, in BeF2 has two bonding electron pairs in its valence shell. The hond pairs will arrange themselves on opposite sides of the central Be atom so as to maximize their angle of separation. The hond angle in BeF2 is thus 180°, and the three atoms lie along a colinear axis.

distorted tetrahedron

Boron has three valence electrons and ultimately three electron pairs in the covalent molecule, BFs. The three electron pairs around boron in the BFa molecule maximize their angle of separation a t 120' therefore, the molecule has a trigonal planar geometry.

Each carbon atom has four valence electrons and in CH4 pairs them with valence electrons from four hydrogen atoms. The four electron pairs arrange themselves tetrahedrally about the central carbon atom. The angles separating the hydrogen atoms are 109.5O.

Common Geometric Shape$ in Covalent Molecules

Molecular Geometry

In the years following the development of the powder diffraction method of A. W. Hull (19161, which made it possible to study the structure of matter by X-ray diffraction, it was generallv determined that covalent molecules exist as discrete particles that have all sorts of geometrical shapes. Some of the very common geometric patterns observed in simple molecules and polyatomic ions are shown in the accompanying figure.

Elemental nitrogen has five valence electrons, three of which are paired in compounds such as NHs. Consequently, the central nitrogen atom has three bonding electron pairs and one nonhonding pair or lone pair. The three hond pairs and the lone pair tend to arrange themselves tetrahedrally around the central nitrogen atom. A lone pair occupies one corner of the tetrahedron. Considering the four atoms alone, the molecular shape is trigonal pyramidal.

The Valence Shell Electron Pair Repulsion Theory (VSEPR)

Several approaches have been offered to account for the experimentally determined molecular geometry of compounds. One method, the VSEPR theory, was offered by N. V. Sidgwick and H. M. Powell (1940) as a first approximation for nredictine molecular eeometrv. Subseouentlv. this theorv wa;refined,extended, and popuiarized b; R. ~ i l l e s ~ i e . The VSEPR model is founded on the Pauli Exclusion Principle, which states that no two electrons in an atom can have the same set of four auantum numbers. The i m ~ o r t a n t physical consequence of ihe Pauli Exclusion ~ r i n ~ i p lin e, terms of molecular geometry, is that electrons having parallel spins tend to maximize their angle of separation. Hence, for the central atom in a molecule the valence shell electrons are viewed as localized pairs that tend to maximize their distance apart. The approximation of molecular shape using the VSEPR method takes into account that there may he bond pairs and lone pairs of electrons in the valence shell of the central atom. To apply the VSEPR method to real molecules you need to determine the numher of lone pair and bond pair electrons around the central atom in the covalent molecule or polyatomic ion. Draw a Lewis formula for the molecule, characterizing each atom or lone pair of electrons associated with the central atom as a group. The groups are subsequently ar-

Recognize, of course, that electrons in lone pairs behave differently than electrons in hond pairs. A bonding electron pair is, fur example, constrained or localized within a central internuclear region. The lone pair volume will hence he larger than a bond pair volume. The lone pair region tends to repel the neiehhorine hond nair reeions. .. , forcine them closer together and reducing their angle of separation. The hond angle in the NH- is actuallv 107.3". rather than the Dure tetrahedral angle of 109.5'. * Oxvaen has six valence electrons, hut in the formation of covalent molecules like water, only two of these electrons pair with electrons from other atoms. In c o m ~ o u n d of s this sort, the central oxygen atom has two bond pairs and two lone pairs. These four pairs tend to occupy the tetrahedral positions around the central atom. Here the distortion of the tetrahedral angle resulting from the two lone pairs is even greater. The actual bond angle in H 2 0 is 104.5'. The water molecule, therefore, has a bent or angular shape. Volume 57, Number 3. March 1980 / 211

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When chlorine forms CIFs, five of the original seven electrons are paired, leaving one lone pair and five bond pairs. Since the lone pair occupies an axial site the molecular shape is descrihed as square pyramidal.

\ 'H H Sulfur has six valence electrons. Four of these are shared with fluorine atoms in a molecule of SF4 to provide the sulfur atom with a total of ten valence shell electrons (four hond pairs and one lone pair). These five electron pairs have a trigonal bipyramidal arrangement with the lone pair being in an equatorial position. F I

S F E C The shape of this molecule is generally descrihed as a distorted 0 tetrahedron.

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Finally, in SF6 the central sulfur atom has all six of its valence electrons paired to give six bond pairs. Consequently, the electron pair arrangement and the molecular shape are octahedral.

Chlorine combines with fluorine to form ClF3, in which the central chlorine atom has a total of ten valence electrons; three hond pairs and two lone pairs. The idealized geometry indicates a trigonal bipyramidal arrangement for the five electron pairs. Since the two lone pairs occupy equatorial positions a T-shaped molecule is generated.

Summary of VSEPR Method in Molecular Geometry

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The molecular shape of PCls must he trigonal bipyramidal, because there are no lone pairs around the central phosphorus atom. However, the axial hond lengths are greater than the equatorial hond lengths. This occurs because each axial bond experiences three 90° repulsions compared to only two 90° repulsions for the equatorial positions.

The VSEPR method is fairly easy to apply and gives the correct molecular geometry for an extraordinarily large number of molecules. This means that the predicted shapes for these molecules are in accord with experimentally determined molecular shapes. According to the VSEPR method the first approximation of molecular geometry is made on the basis of three principles.

1) T h e electron pairs (hond pairs and lone pairs) around

In a number of molecules the central atom has a total of six electron pairs in its valence shell. For example, in XeF4, the xenon atom originally has eight valence electrons; four are found in hond pairs while four remain as two lone pairs. The lone pairs are separated by angles of 180° in the axial positions. The four bond airs are located a t eauatorial sites eivine the XeF4 a square planar molecular shape. I

a central atom will adopt a spatial arrangement that maximizes their angle of separation. 2) Agreement between predicted and measured molecular shapes is enhanced hy the assumption that electrostatic reoulsions between electron nairs in a eiven valence shell decrease in the order: lone pair:loneLpair > lone pair: hond pair > hond pairbond pair. 3) Where there are several possible molecular structures involving 9O0 interactions, the mnst favored spatial arrangement is the one that minimizes the number of 90° lone-pair interactions.

Relerences Batp8.R.B. andschnefor, d . P.."Research Techniques in o l w i c C h e m i r t , y "Prentice-Hall. Enplewood Cliffs, N.J., 1971. R E.,Clsy, H. R..an,l Hairhl,C. P., ' T h e m i d P.ineiples,"BPnjamin/Cummings Di~k~rs"", Publishin8 Cu.,Menlo Park. Caliiomia. 1979. Cillespie. R..I..J.CHF.M. EDUC., 47. In i1970). Cillerpie, R. J.,J CHF'M. EDIIC..51,:176 1isi4). Ifft. J. B..snd Hearst.J B., 1;meralChemirtry Rendinesfrum Scientific American? W. H. Fmeman and Company,San Fnnciscl. l97d. Wonnnr. R d , "Fundamentalr ~i C h ~ m i ~ r y .2nd " ed.. Harper and Raw. New Yurk. 1977.

212 1 Journal of Chemical Edocafion