Chemistry
Hybrid Orbitals
Hybrid orbitals are a concept in chemistry that result from the mixing of atomic orbitals to form new hybrid orbitals. These hybrid orbitals have different shapes and energies than the original atomic orbitals and are used to explain the molecular geometry and bonding in molecules. They are formed to accommodate the bonding requirements of the atoms in a molecule.
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8 Key excerpts on "Hybrid Orbitals"
eBook - PDF- T. W. Graham Solomons, Craig B. Fryhle, Scott A. Snyder(Authors)
- 2017(Publication Date)
- Wiley(Publisher)
7. Hybrid atomic orbitals are obtained by mixing (hybridizing) the wave functions for orbitals of different types (i.e., s and p orbitals) but from the same atom. 8. Hybridizing three p orbitals with one s orbital yields four sp 3 orbitals. Atoms that are sp 3 hybridized direct the axes of their four sp 3 orbitals toward the corners of a tet- rahedron. The carbon of methane is sp 3 hybridized and tetrahedral. 9. Hybridizing two p orbitals with one s orbital yields three sp 2 orbitals. Atoms that are sp 2 hybridized point the axes of their three sp 2 orbitals toward the corners of an equilateral triangle. The carbon atoms of ethene are sp 2 hybridized and trigonal planar. A summary of sp 3 , sp 2 , and sp hybrid orbital geometries. HINT 44 CHAPTER 1 THE BASICS: Bonding and Molecular Structure 10. Hybridizing one p orbital with one s orbital yields two sp orbitals. Atoms that are sp hybridized orient the axes of their two sp orbitals in opposite directions (at an angle of 180°). The carbon atoms of ethyne are sp hybridized and ethyne is a linear molecule. 11. A sigma (σ) bond (a type of single bond) is one in which the electron density has circular symmetry when viewed along the bond axis. In general, the skeletons of organic molecules are constructed of atoms linked by sigma bonds. 12. A pi (π) bond, part of double and triple carbon–carbon bonds, is one in which the electron densities of two adjacent parallel p orbitals overlap sideways to form a bonding pi molecular orbital. 1.16 HOW TO PREDICT MOLECULAR GEOMETRY: THE VALENCE SHELL ELECTRON PAIR REPULSION MODEL We can predict the arrangement of atoms in molecules and ions on the basis of a relatively simple idea called the valence shell electron pair repulsion (VSEPR) model. We apply the VSEPR model in the following way: 1. We consider molecules (or ions) in which the central atom is covalently bonded to two or more atoms or groups.
eBook - PDFCondensed Matter Optical Spectroscopy
An Illustrated Introduction
- Iulian Ionita(Author)
- 2014(Publication Date)
- CRC Press(Publisher)
3.4 Hybrid Orbitals AS LINEAR COMBINATIONS OF ATOMIC ORBITALS We know to find the atomic orbitals that could combine to make Hybrid Orbitals. The symmetry can only suggest the possible combinations, but not if and how they are done. The energy of orbitals is the main crite-rion. The Schrödinger equation circumflexnosp H E Ψ Ψ = should be solved in order to find the energy. Ĥ is the Hamiltonian operator of the molecule and Ψ is the eigenfunction of the molecular orbital. In an atom, all orbitals are centered on the nucleus, while in a molecule they are located on two or more nuclei. Thus, the electron is delocalized or, more precisely, local-ized on many atoms. This property of delocalizing electrons provides the stability of the molecule because the repulsion between two nuclei is compensated for by the attraction between electrons and both nuclei. We note that the last sentence is just the expression of a classic way to imagine a purely quantum phenomenon, so it is not exact. If molecular orbitals are localized on an entire molecule, then the molecular sym-metry properties will show which integrals are zero. This will reduce the calculation to be done. 3.4.1 LCAO IN A TWO-CENTER BOND The eigenfunction of the hybrid orbital can be written as a linear com-bination of eigenfunctions of atomic orbitals centered on atoms and involved in the construction of a molecular orbital.
eBook - PDFChemistry
The Molecular Nature of Matter
- Neil D. Jespersen, Alison Hyslop(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
Each B—Cl bond is formed by the overlap of a half-filled 3p orbital of a Cl atom with one of the sp 2 Hybrid Orbitals of boron. (For simplicity, only the half-filled 3p orbital of each Cl atom is shown.) unhybridized p orbitals 446 CHAPTER 9 Theories of Bonding and Structure Hybrid Orbitals Formed from s, p, and d Orbitals Earlier we saw that certain molecules have atoms that must violate the octet rule because they form more than four bonds. In these cases, the atom must reach beyond its s and p valence shell orbitals to form sufficient half-filled orbitals for bonding. This is because the s and p orbitals can be mixed to form a maximum of only four Hybrid Orbitals. When five or more Hybrid Orbitals are needed, d orbitals are brought into the mix. The two most common kinds of Hybrid Orbitals involving d orbitals are sp 3 d and sp 3 d 2 Hybrid Orbitals. Their direc- tional properties are illustrated in Figure 9.26. Notice that the sp 3 d hybrids point toward the corners of a trigonal bipyramid and the sp 3 d 2 hybrids point toward the corners of an octahedron. TOOLS Hybrid Orbitals us- ing s, p, and d atomic orbitals FIGURE 9.26 Orientations of Hybrid Orbitals that involve d orbitals. a. sp 3 d Hybrid Orbitals formed from an s orbital, three p orbitals, and a d orbital. The orbitals point toward the vertices of a trigonal bipyramid. b. sp 3 d 2 Hybrid Orbitals formed from an s orbital, three p orbitals, and two d orbitals. The orbitals point toward the vertices of an octahedron. Five sp 3 d hybrids Six sp 3 d 2 hybrids Trigonal bipyramidal Octahedral 90° 90° 120° All angles = 90 EXAMPLE 9.7 Explaining Bonding with Hybrid Orbitals Predict the shape of the sulfur hexafluoride molecule and describe the bonding in the molecule in terms of valence bond theory. Analysis: Based on the formula, we will write a Lewis structure for the molecule.
eBook - ePub- M. S. Prasada Rao(Author)
- 2022(Publication Date)
- CRC Press(Publisher)
3 .Further, in case of BeH2 , BF3 and CH4 molecules the number of unpaired electrons present on the central atom is less than the number of covalent bonds formed. In order to explain this, it was presumed that the electrons are excited to the higher orbitals during the formation of covalent bonds. For example, beryllium has the excited state configuration 1s2 , 2s1 , 2px 1 . This should result in two nonequivalent bonds due to the overlap of the hydrogen atoms with 2s and 2px orbitals. However, in BeH2 both the bonds are equivalent and are at an angle of 180°. In order to explain such cases the concept of hybridization was introduced.According to the concept of hybridization, in cases where pure orbitals cannot affect good overlap in the formation of covalent bonds, combination of pure orbitals having same or similar energy takes place, resulting in the formation of equivalent Hybrid Orbitals. The number of Hybrid Orbitals formed is equal to the number of combining pure orbitals. If suppose ϕ1 and ϕ2 are the two combining atomic orbitals the resulting hybridized orbitals ψh 1 and ψh 2 areThe values of the coefficients should be such that each of the hybridized orbital is normalized and the two Hybrid Orbitals should be orthogonal to each other.ψ=h 1c 1ϕ 1+c 2ϕ 2ψ=h 2c 3ϕ 1+c 4ϕ 2.
eBook - PDF- David R. Klein(Author)
- 2016(Publication Date)
- Wiley(Publisher)
1.8 Molecular Orbital Theory 17 1.8 Molecular Orbital Theory In most situations, valence bond theory will be sufficient for our purposes. However, there will be cases in the upcoming chapters where valence bond theory will be inadequate to describe the observa- tions. In such cases, we will utilize molecular orbital theory, a more sophisticated approach to viewing the nature of bonds. Molecular orbital (MO) theory uses mathematics as a tool to explore the consequences of atomic orbital overlap. The mathematical method is called the linear combination of atomic orbitals (LCAO). According to this theory, atomic orbitals are mathematically combined to produce new orbitals, called molecular orbitals. It is important to understand the distinction between atomic orbitals and molecular orbitals. Both types of orbitals are used to accommodate electrons, but an atomic orbital is a region of space associated with an individual atom, while a molecular orbital is associated with an entire molecule. That is, the molecule is considered to be a single entity held together by many electron clouds, some of which can actually span the entire length of the molecule. These molecular orbitals are filled with electrons in a particular order in much the same way that atomic orbitals are filled. Specifically, electrons first occupy the lowest energy orbitals, with a maximum of two electrons per orbital. In order to visualize what it means for an orbital to be associated with an entire molecule, we will explore two molecules: molecular hydrogen (H 2 ) and bromomethane (CH 3 Br). Consider the bond formed between the two hydrogen atoms in molecular hydrogen. This bond is the result of the overlap of two atomic orbitals (s orbitals), each of which is occupied by one electron. According to MO theory, when two atomic orbitals overlap, they cease to exist. Instead, they are replaced by two molecular orbitals, each of which is associated with the entire molecule (Figure 1.15).
eBook - PDFChemistry
An Atoms First Approach
- Steven Zumdahl, Susan Zumdahl, Donald J. DeCoste, , Steven Zumdahl, Steven Zumdahl, Susan Zumdahl, Donald J. DeCoste(Authors)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
The arrangement of valence electrons is represented by the Lewis structure (or structures, where resonance occurs), and the molecular geometry can be predicted from the VSEPR model. In this section we will describe the atomic orbitals used to share elec- trons and hence to form the bonds. sp 3 Hybridization Let us reconsider the bonding in methane, which has the Lewis structure and molecu- lar geometry shown in Fig. 4.13. In general, we assume that bonding involves only the valence orbitals. This means that the hydrogen atoms in methane use 1s orbitals. The presence of polar bonds does not always yield a polar molecule. The valence orbitals are the orbitals associated with the highest principal quantum level that contains electrons on a given atom. 159 4.3 Hybridization and the Localized Electron Model Copyright 2021 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. The valence orbitals of a carbon atom are the 2s and 2p orbitals shown in Fig. 4.14. In thinking about how carbon can use these orbitals to bond to the hydrogen atoms, we can see two related problems: 1. Using the 2p and 2s atomic orbitals will lead to two different types of COH bonds: (a) those from the overlap of a 2p orbital of carbon and a 1s orbital of hydrogen (there will be three of these) and (b) those from the overlap of a 2s orbital of carbon and a 1s orbital of hydrogen (there will be one of these). This is a problem because methane is known to have four identical COH bonds.
eBook - PDF- David R. Klein(Author)
- 2021(Publication Date)
- Wiley(Publisher)
It is important to understand the distinction between atomic orbitals and molecular orbitals. Both types of orbitals are used to accommodate electrons, but an atomic orbital is a region of space associated with an individual atom, while a molecular orbital is associated with an entire molecule. That is, the molecule is considered to be a single entity held together by many electron clouds, some of which can actually span the entire length of the molecule. These molecular orbitals are filled with electrons in a particular order in much the same way that atomic orbitals are filled. Specifically, elec- trons first occupy the lowest energy orbitals, with a maximum of two electrons per orbital. In order to visualize what it means for an orbital to be associated with an entire molecule, we will explore two molecules: molecular hydrogen (H 2 ) and bromomethane (CH 3 Br). 1.9 Molecular Orbital Theory 19 Consider the bond formed between the two hydrogen atoms in molecular hydrogen. This bond is the result of the overlap of two atomic orbitals (s orbitals), each of which is occupied by one electron. According to MO theory, when two atomic orbitals overlap, they cease to exist. Instead, they are replaced by two molecular orbitals, each of which is associated with the entire molecule (Figure 1.15). Node Antibonding MO Bonding MO Energy 1s 1s FIGURE 1.15 An energy diagram showing the relative energy levels of bonding and antibonding molecular orbitals. In the energy diagram shown in Figure 1.15, the individual atomic orbitals are represented on the right and left, with each atomic orbital having one electron. These atomic orbitals are combined mathematically (using the LCAO method) to produce two molecular orbitals. The lower energy molecular orbital, or bonding MO, is the result of constructive interference of the original two atomic orbitals. The higher energy molecular orbital, or antibonding MO, is the result of destruc- tive interference.
- Milton Orchin, Allan R. Pinhas, R. Marshall Wilson, Roger S. Macomber(Authors)
- 2005(Publication Date)
- Wiley-Interscience(Publisher)
Example. As two hydrogen atoms [H A (1) and H B (2)] approach each other, the 1s orbital overlap increases and the electron in each orbital feels the influence of the opposite nucleus and is increasingly associated with it. The molecule is stabilized at the appropriate H–H bond distance by the exchange between two equivalent struc- tures: H A (1) H B (2) and H A (2) H B (1), where A and B refer to the hydrogen atoms and (1) and (2) refer to electrons of opposite spin. The wave function for the occupied 52 BONDS BETWEEN ADJACENT ATOMS orbital of the hydrogen molecule may then be written as ψ [(φ A (1)φ B (2) φ A (2)φ B (1)], where φ A and φ B are the atomic 1s orbitals on hydrogens A and B. This wave function indicates that the two electrons are never associated together at one atom. SUGGESTED READING Bowser, J. R. Inorganic Chemistry. Brooks/Cole: Pacific Grove, CA, 1993. Coulson, C. A. Valence. Oxford University Press: London, 1952. Gray, H. B. Electrons and Chemical Bonding. W.A. Benjamin: New York, 1964. Harris, D. C., and Bertolucci, M. D. Symmetry and Spectroscopy. Oxford University Press: New York, 1978. Jaffé, H. H. and Orchin, M. “Hybridization in Carbon Monoxide.” Tetrahedron 10, 212 (1960). Jean, Y., Volatron, F., and Burdett, J. An Introduction to Molecular Orbitals. Oxford University Press: New York, 1993. Orchin, M., and Jaffé, H. H. Symmetry, Orbitals and Spectra. Wiley-Interscience: New York, 1971. Streitwieser, A. Molecular Orbital Theory for Organic Chemists. John Wiley & Sons: New York, 1961. WAVE FUNCTIONS IN VALENCE BOND (VB) THEORY 53
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