Frontier Orbitals_CHEM 236_Spring 2010_REVISED_01_26_10

Frontier Orbitals_CHEM 236_Spring 2010_REVISED_01_26_10 -...

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Unformatted text preview: CHEMISTRY 236 Frontier Orbitals Peter Beak Department of Chemistry UIUC The discussion of the geometries of molecules showed how VSEPR and MO theory could be used to rationalize bond angles. As noted the two approaches proved the same result. However, MO theory has an additional dimension which can be described by Frontier Orbital Theory. Hybrid Molecular Orbital Theog (Review) Atomic orbitals in chemistry define regions in space around atoms where the probability of electron location is high. These orbitals can be combined to make new regions of favored electron location which are termed hybrid orbitals. Overlap of these orbitals between atoms can lead bonding which is localized in the hybrid molecular orbital. For carbon, the one 2s atomic orbital and the three 2p atomic orbitals can be hybridized to make four sp3 orbitals, which are disposed around carbon at angles of 109.5°. Each of these orbitals may overlap with the 1s orbital of hydrogens to make for carbon-hydrogen bonds. The result is the tetrahedral arrangement of CH4 with bond angles of 109.5°. The bonds are represented as in the Lewis structure. These bonds localized between the bonding atoms are sigma bonds. Other hybridizations are possible. If the 2s orbital of carbon is combines with two p orbitals the result is a planar arrangement with each orbital at the 120° trigonal angles for three sp2 orbitals. Overlap of these hybrid orbitals with orbitals of other atoms creates a sigma bond. The remaining p atomic orbital on carbon is available for overlap and bonding with another p atomic orbital. The resulting bond, called a pi bond has electron density above and below the sigma bond. In a hybrid molecular orbital representation this bonding is represented by shading in an electron cloud. In the case of a combination of the 25 orbital with one p orbital the result is a sp orbital with the sigma bonds at 180°. The two p atomic orbitals can then overlap to provide two pi bonds. The Lewis structures and the MO representations may look different but they represent the same molecule and have different advantages in discussions of structure and reactions. The bonding molecular orbitals for methane, ethylene and acetylene can be represented as shown: VJ Frontier Orbitals The representation of methane by hybrid molecular theory shows carbon bonded to four hydrogens. If we focus on a single bond between carbon and hydrogen it can be represented as a combination of the 3p3 orbital on carbon with the s orbital on hydrogen to make both a bonding and an antibonding molecular orbital. Each atom donates one electron which when spin paired combine into the lowest energy bonding molecular orbital. The electrons represented by arrows with dots provide the resulting bond. The bond is a sigma (0‘) bond and the orbital which is occupied by two electrons is the highest occupied molecular orbital (HOMO) in the system described. The antibonding orbital which is created in the same way as the bonding orbital is not occupied in the ?? state. It is shown Figtire l as the sigma—star (0*) orbital and it is the lowest unoccupied molecular orbital (LUMO) in this system. These representations are shown in Figure 1. 5* antibonding 'F-fl \ " “ a’ ‘5 Energy 0 0,0 “2'— ® /”a ' f 6- ‘ ‘~ ' ’ bonding Figure i - Bonding and Antibonding Combinations sp3 Carbon and s Hydrogen Orbitals . The orbi’ials in Figure 2 describe contours which indicate the probability of findmg the bdnding electrons in the region indicated. For the bonding orbital (HOMO) the probability is highest between the two nuclei involved in the bonding. Although the antibonding orbital (LUMO) is usually unoccupied, a contour in which the electrons would have a higher probability of being found if the orbital were occupied can be constructed. The electrons in this case would be away from the two nuclei. 5 a - ® 6* an antibonding orbital jg Lowest Unoccupied Molecular Orbital (LUMO) 1 Energy - S:@ 0' a bonding orbital 94 Y Highest Occupied Molecular Orbital (HOMO) Figure‘l'i- Contours of Electron Density for Sigma Bonds If we consider carbon engaged in multiple bonding the same principles apply to-the sigma bonds but the bonding also involves overlap of p atomic orbitals to give it orbitals. Thus, a carbon which engages in a double bond is an sp2 hybrid in which one p-atomic orbital remains on carbon. The sp2 sigma orbitals are at bond angles of 120° and in a common plane. A picture of two such carbons with two of the sigma bonds combined with hydrogen and one remaining sp2 bond bearing one electron which combines with another carbon and a p-atomic orbital bearing one electron is shown in Figure 3. Two types of carbon-carbon bonds are indicated: a sigma bond located directly between the two nuclei and a 1:: bond which has maximum probability for finding electrons above and below a plane containing the carbon and hydrogen atoms. In this case we will focus on the bonding by the p electrons, which can Combine to form pi bonding (1:) and pi antibonding (713*) bonds. antibonding bonding Figure 3- Bonding and Antibonding Combinations of p-atomic Orbitals of an spg Hybridized Carbon to Form 1: Bonds n . The picture of this it and 7t* bonding in terms of electron contours is shown 1n F igure 4. The d1fferent shadin s re resent overla of the orbitals to ive ._...._ .______ an antibonding 6 “— orbital (LUMO) \C. = a bonding orbital / o (How Energy Figure — Contours of Electron Density for at Bonds For both sigma and 1: bonds there are bonding and antibonding orbital associated with each pond. Generally the occupied 1r orbitals will be of higher energy than the occupied sigma orbitals and the unoccupied 1t* orbitals will be of lower energy than the unoccupied 6* orbitals. The highest occupied and lowest unoccupied orbitals in a molecule are called the frontier orbitals. Like the valence electrons in atoms, these orbitals are considered to be very important in reactions of molecules. \ IC Kahlil“ 'T\ Cum ‘06 S’Moim%eo /O 0\ The picture for ethylene can be extended to other double-bonded carbon 1systems. Thus, the carbon oxygen double-bond of formaldehyde is represented in 1gure 5. C——-O H/€\ Energy H \Cm H/O 0 Figures The 1: and 11* Orbitals of Formaldehyde The molecular geometry of acetylene is described by two sp hybridized carbons which have bond angles of 180° and two orthogonal overlapping 1: molecular orbitals. In all cases the geometries of simple molecules are in general agreement with the predictions of molecular orbital theory. As a result the theory is widely accepted. Recently the use of fiontier orbitals has become an accepted method for understanding the changes which take place in molecular geometry as reactions occur. Problem 1 — Draw the frontier orbitals for: a) The carbon bromine 0 bond in CH3Br b) The 1: bond of H2C=CC12 c) The 11: bond of H2C=NH Predict the molecular geometry of each of the molecules you have drawn. «Fifi b) —O'at- ft“ '—1Ex- fin: —T|3at- LUMO a) Bond angles of 109° 28' HOMO LUMO HOMO b) an}! 0) Bond angles of 120' I LUMO fl» TC HOMO ...
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Frontier Orbitals_CHEM 236_Spring 2010_REVISED_01_26_10 -...

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