Chemistry
Sigma and Pi Bonds
Sigma and pi bonds are types of covalent bonds formed between atoms. A sigma bond is a single covalent bond formed by the head-on overlap of atomic orbitals, while a pi bond is a type of double or triple bond formed by the side-to-side overlap of p orbitals. These bonds play a crucial role in determining the structure and properties of molecules.
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11 Key excerpts on "Sigma and Pi Bonds"
eBook - PDF- Young, William Vining, Roberta Day, Beatrice Botch(Authors)
- 2017(Publication Date)
- Cengage Learning EMEA(Publisher)
As a result, a single, two-electron bond between two atoms is always a sigma-type bond. When two or more covalent bonds form between two atoms, one is always a sigma bond and the additional bonds are pi bonds. Interactive Figure 7.3.1 Explore the formation of pi bonds from the overlap of p orbitals. Pi bond formation from two p orbitals Example Problem 7.3.1 Identify Sigma and Pi Bonds. How many Sigma and Pi Bonds are in the following molecule? H H C l C C C N Solution: You are asked to identify the number of Sigma and Pi Bonds in a molecule. You are given the Lewis structure of the compound. Each line represents a two-electron bond. A single bond (one line) represents a sigma bond; a double bond (two lines) represents one sigma bond and one pi bond; a triple bond (three lines) represents one sigma bond and two pi bonds. H H C l C C C N s , p s s s s s , p , p There are six sigma bonds and three pi bonds in the molecule. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 Unit 7 Molecular Shape and Bonding Theories 179 7.3b Pi Bonding in Ethene, C 2 H 4 ; Acetylene, C 2 H 2 ; and Allene, CH 2 CCH 2 Each C atom in ethene is sp 2 hybridized, and each sp 2 hybrid orbital is used to form a sigma bond to another atom (Figure 7.3.2). The sp 2 -hybridized carbon atoms in ethene each have an unhybridized p orbital that is not involved in sigma bonding and that contains a single electron (Figure 7.3.3). H H H H C — H s bond One C—C s bond and one C — C p bond C C C C H H H H Figure 7.3.2 Sigma bonding in ethene Energy, E 2 p 2 s Isolated C atom Orbital hybridization One unhybridized p orbital Three sp 2 hybrid orbital s on each C in C 2 H 4 Figure 7.3.3 Formation of hybrid orbitals for the carbon atoms in ethene The unhybridized 2 p orbitals are used to form a pi bond between the two carbon atoms (Figure 7.3.4).
eBook - PDFChemistry
The Molecular Nature of Matter
- Neil D. Jespersen, Alison Hyslop(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
Sigma bonds allow free rotation around the bond axis. The side-by-side overlap of p orbitals pro- duces a pi bond (π bond). Pi bonds do not permit free rotation around the bond axis because such a rotation involves bond breaking. In com- plex molecules, the basic molecular framework is built with σ bonds. Describe the nature of multiple bonds using orbital diagrams and hybridization. A double bond consists of one σ bond and one π bond. A triple bond consists of one σ bond and two π bonds. Use molecular orbitals to explain the bonding of simple diatomic molecules. MO theory begins with the supposition that molecules are similar to atoms, except that they have more than one positive center. They are treated as collections of nuclei and electrons, with the electrons of the molecule distributed among molecular orbitals of different energies. Molecular orbitals can spread over two or more nuclei, and can be considered to be formed by the constructive and destructive interference of the overlapping electron waves corresponding to the atomic orbitals of the atoms in the molecule. Bonding MOs concen- trate electron density between nuclei; antibonding MOs remove electron density from between nuclei. Nonbonding MOs do not affect the energy of the molecule. The rules for the filling of MOs are the same as those for atomic orbitals. Compare and contrast resonance structures to delocalized molecular orbitals. The ability of MO theory to describe delocalized orbitals avoids the need for resonance theory. Delocalization of bonds leads to a low- ering of the energy by an amount called the delocalization energy and produces more stable molecular structures. Use band theory to explain bonding in solids and physical properties. In solids, atomic orbitals of the atoms combine to yield energy bands that consist of many energy levels. The valence band is formed by orbitals of the valence shells of the atoms. A conduction band is a partially filled or empty band.
eBook - PDF- William R. Robinson, Edward J. Neth, Paul Flowers, Klaus Theopold, Richard Langley(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
In a π bond, the regions of orbital overlap lie on opposite sides of the internuclear axis. Along the axis itself, there is a node, that is, a plane with no probability of finding an electron. Figure 5.5 Pi (π) bonds form from the side-by-side overlap of two p orbitals. The dots indicate the location of the nuclei. While all single bonds are σ bonds, multiple bonds consist of both σ and π bonds. As the Lewis structures in suggest, O 2 contains a double bond, and N 2 contains a triple bond. The double bond consists of one σ bond and one π bond, and the triple bond consists of one σ bond and two π bonds. Between any two atoms, the first bond formed will always be a σ bond, but there can only be one σ bond in any one location. In any multiple bond, there will be one σ bond, and the remaining one or two bonds will be π bonds. These bonds are described in more detail later in this chapter. Example 5.1 Counting σ and π Bonds Butadiene, C 6 H 6 , is used to make synthetic rubber. Identify the number of σ and π bonds contained in this molecule. Solution There are six σ C–H bonds and one σ C–C bond, for a total of seven from the single bonds. There are two double bonds that each have a π bond in addition to the σ bond. This gives a total nine σ and two π bonds overall. 264 Chapter 5 | Advanced Theories of Bonding This OpenStax book is available for free at http://cnx.org/content/col12012/1.7 Check Your Learning Identify each illustration as depicting a σ or π bond: (a) side-by-side overlap of a 4p and a 2p orbital (b) end-to-end overlap of a 4p and 4p orbital (c) end-to-end overlap of a 4p and a 2p orbital Answer: (a) is a π bond with a node along the axis connecting the nuclei while (b) and (c) are σ bonds that overlap along the axis. Dipole Moments and Ionic Character Now that we have seen the importance of understanding the connection between the location of electrons in atoms and the properties of elements, we can expand our understanding of the connection between atoms.
eBook - PDF- William H. Brown, Thomas Poon(Authors)
- 2017(Publication Date)
- Wiley(Publisher)
Figure 1.19(a) shows a Lewis structure for ethylene, C 2 H 4 . A sigma bond between the carbons in ethylene forms by the overlap of sp 2 hybrid orbitals along a common axis [Figure 1.19(b)]. Each carbon also forms sigma bonds to two hydrogens. The remaining 2p orbitals on adjacent carbon atoms lie parallel to each other and overlap to form a pi bond [Figure 1.19(c)]. A pi (π) bond is a covalent bond formed by the overlap of parallel p orbitals. Because of the lesser degree of overlap of orbitals forming pi bonds compared with those forming sigma bonds, pi bonds are generally weaker than sigma bonds. Pi (π) bond A covalent bond formed by the overlap of parallel p orbitals. The orbital overlap model describes all double bonds in the same way that we have described a carbon–carbon double bond. In formaldehyde, CH 2 O, the simplest organic mol- ecule containing a carbon–oxygen double bond, carbon forms sigma bonds to two hydrogens by the overlap of an sp 2 hybrid orbital of carbon and the 1s atomic orbital of each hydrogen. Carbon and oxygen are joined by a sigma bond formed by the overlap of sp 2 hybrid orbitals and a pi bond formed by the overlap of unhybridized 2p atomic orbitals (Figure 1.20). 24 C H A P T E R 1 Covalent Bonding and Shapes of Molecules sp sp sp z y y x x sp p y p y p z p z 180° (a) (b) (c) (d) sp sp p p FIGURE 1.21 sp Hybrid orbitals. (a) A single sp hybrid orbital consisting of two lobes of unequal size. (b) Two sp hybrid orbitals in a linear arrange- ment. (c) Unhybridized 2p atomic orbitals are perpendicular to the line created by the axes of the two sp hybrid orbitals. (d) An sp hybridized atom, as you would draw it, with its full complement of orbitals. FIGURE 1.22 Covalent bonding in acetylene. (a) The sigma bond framework shown along with nonover- lapping 2p atomic orbitals. (b) Formation of two pi bonds by overlap of two sets of parallel 2p atomic orbitals.
eBook - PDF- David R. Klein(Author)
- 2020(Publication Date)
- Wiley(Publisher)
According to valence bond theory, a bond is simply the sharing of electron density between two atoms as a result of the constructive interference of their atomic orbitals. Consider, for example, the bond that is formed between the two hydrogen atoms in molecular hydrogen (H 2 ). This bond is formed from the overlap of the 1s orbitals of each hydrogen atom (Figure 1.13). The electron density of this bond is primarily located on the bond axis (the line that can be drawn between the two hydrogen atoms). This type of bond is called a sigma (σ) bond and is char- acterized by circular symmetry with respect to the bond axis. To visualize what this means, imagine a plane that is drawn perpendicular to the bond axis. This plane will carve out a circle (Figure 1.14). This is the defining feature of σ bonds and will be true of all purely single bonds. Therefore, all single bonds are σ bonds. FIGURE 1.13 The overlap of the 1s atomic orbitals of two hydrogen atoms, forming molecular hydrogen (H 2 ). Circular cross section + FIGURE 1.14 An illustration of a sigma bond, showing the circular symmetry with respect to the bond axis. 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.
eBook - PDF- B. R. Coles, A. D. Caplin(Authors)
- 2013(Publication Date)
- Arnold(Publisher)
Because π bonds are effective only if the interatomic distance is small they are not found in heavier elements of group VI which have large ion cores. In the solid state both Se and Te form two σ bonds (Fig. 2.8) at approximately 90° to one another with consequent long chain molecules, although S can achieve a compromise closed molecule by closing its chain into an 8-membered ring, the S 8 molecule. The charge cloud distributions of o b and ii b bonds are shown schematically in Fig. 2.9. z plane Figure 2.9 Details of σ and π bonds. A very important type of covalent bond involves the construction of molecular orbitals which, for at least one of the bonded atoms, use a linear combination of orbitals of different /, this process being described as hybridiza-tion. Hybridization plays a vital part in the chemistry of C where the molecular orbitals bonding C to, say, H must often be written as (see p. 26) Ψηι.ο. = ΡΨη + 4
eBook - PDF- William H. Brown, Thomas Poon(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
All C C triple bonds are a combination of one sigma bond formed by the overlap of sp hybrid orbitals and two pi bonds formed by the overlap of two pairs of parallel 2p atomic orbitals. Hybrid orbitals can be arranged in tetrahedral, trigonal planar, and linear geometries. 1.7 What Are Functional Groups? Functional groups are characteristic structural units by which we divide organic compounds into classes and that serve as a basis for nomenclature.They are also sites of chemical reac- tivity; a particular functional group, in whatever compound we find it, undergoes the same types of reactions. Important functional groups for us at this stage in the course are the hydroxyl group of 1°, 2°, and 3° alcohols the amino group of 1°, 2°, and 3° amines the carbonyl group of aldehydes and ketones the carboxyl group of carboxylic acids QUICK QUIZ Answer true or false to the following questions to assess your general knowledge of the concepts in this chapter. If you have difficulty with any of them, you should review the appropriate section in the chapter (shown in parentheses) before attempting the more challenging end‐of‐chapter problems. 1. These bonds are arranged in order of increasing polarity C H < N H < O H. (1.2) 2. All atoms in a contributing structure must have complete valence shells. (1.5) 3. An electron in a 1s orbital is held closer to the nucleus than an electron in a 2s orbital. (1.1) 4. A sigma bond and a pi bond have in common that each can result from the overlap of atomic orbitals. (1.6) Quick Quiz 3 3 5. The molecular formula of the smallest aldehyde is C 3 H 6 O, and that of the smallest ketone is also C 3 H 6 O. (1.7) 6. To predict whether a covalent molecule is polar or non‐ polar, you must know both the polarity of each covalent bond and the geometry (shape) of the molecule. (1.4) 7. An orbital is a region of space that can hold two elec- trons.
eBook - PDF- David R. Klein(Author)
- 2016(Publication Date)
- Wiley(Publisher)
Molecular orbital theory provides a fairly similar image of a π bond. Compare Figure 1.29 with the bonding MO in Figure 1.30. To summarize, we have seen that the carbon atoms of ethylene are connected via a σ bond and a π bond. The σ bond results from the overlap of sp 2 -hybridized atomic orbitals, while the π bond results from the overlap of p orbitals. These two separate bonding interactions (σ and π) comprise the double bond of ethylene. FIGURE 1.30 An energy diagram showing images of bonding and antibonding MOs in ethylene. π Antibonding MO π Bonding MO Node Energy 2p 2p 22 CHAPTER 1 A Review of General Chemistry CONCEPTUAL CHECKPOINT 1.22 Consider the structure of formaldehyde: O Formaldehyde C H H (a) Identify the type of bonds that form the C =O double bond. (b) Identify the atomic orbitals that form each C −H bond. (c) What type of atomic orbitals do the lone pairs occupy? 1.23 Sigma bonds experience free rotation at room temperature: C H H H H H H C In contrast, π bonds do not experience free rotation. Explain. (Hint: Compare Figures 1.24 and 1.29, focusing on the orbitals used in forming a σ bond and the orbitals used in forming a π bond. In each case, what happens to the orbital overlap during bond rotation?) Triple Bonds and sp Hybridization Now let’s consider the bonding structure of a compound bearing a triple bond, such as acetylene: C C H H Acetylene A triple bond is formed by sp-hybridized carbon atoms. To achieve sp hybridization, one s orbital is mathematically averaged with only one p orbital (Figure 1.31). This leaves two p orbitals FIGURE 1.31 An energy diagram showing two degenerate sp‑hybridized atomic orbitals. 1s 2s 2p 2p 1s Energy Hybridize Two degenerate sp orbitals These orbitals are not affected unaffected by the mathematical operation. As a result, an sp-hybridized carbon atom has two sp orbitals and two p orbitals (Figure 1.32).
eBook - PDFChemistry of the Non-Metals
With an Introduction to Atomic Structure and Chemical Bonding
- Ralf Steudel, Frederick C. Nachod, Jerry J. Zuckerman, Frederick C. Nachod, Jerry J. Zuckerman(Authors)
- 2011(Publication Date)
- De Gruyter(Publisher)
94 Atomic Structure and Chemical Bonding 104.5 Fig. 42. Mutual orientation of bonding and free electron pairs in the NH 3 and H 2 O mole-cules. Hybridization in molecules with multiple bonds: The three bonds in the N 2 molecule can be described in two ways in the framework of VB theory. According to the σ-π-model, one σ- and two π-bonds are present (cf. p. 80) with the π-bonds arising from overlap of p x and p y orbitals, but it cannot be decided whether two pure p z , or sp-hybrids formed from the filled 2s and singly-occupied 2p z overlap in the σ-bond: 2s Pz Px Py N: Τ τ τ π The resulting distribution would be similar to the one in acetylene, HC=CH, in which the σ-bonds originate from sp-hybridized orbitals of the carbon atoms. If N 2 is sp-hybridized, the two free electron pairs would be located on the distal sides of the molecule. The density difference diagram in Figure 35 shows that this is clearly the case, and the free electron pair is involved in the hybridization of the σ-bond framework in almost all compounds of three-valent nitrogen. The magnitude of this effect cannot be determined in the diatomic N 2 molecule which lacks valence angles. A lesser-known model with individual arc bonds will be discussed for ethylene, C 2 H 4 . According to the σ-π-model, the carbon atoms of C 2 H 4 have trigonal-planar, sp 2 hybridization with valence angles of 120°. A π-bond lying above and below the carbon-carbon σ-bond has no influence upon the symmetry, but hinders free rotation around the bond axis. The energy barrier is a function of the strength of the π-bond. The arc model starts with the carbon atoms as sp 3 hybrids, two orbitals of which bind the hydrogen atoms, and two of which engage in double bond formation (cf. Figure 43). Maximum overlap is assumed to take place along arc lines which connect the carbon atoms. The bond length is thus larger than the internuclear
eBook - PDF- Brian W. Pfennig(Author)
- 2021(Publication Date)
- Wiley(Publisher)
In general, sigma MOs are cylindrical and are characterized by the absence of a node along the internuclear axis, while pi MOs share their electron density above and below the bond path and have a nodal plane that lies along the internuclear axis. Likewise, bonding MOs are char- acterized by the absence of a nodal plane perpendicular to the internuclear axis and an increase in electron density between the nuclei, whereas antibonding MOs have a nodal plane perpendicular to the plane that connects the two nuclei. Because the magnitude of the overlap integral is larger when the orbitals combine “head-on” than when they combine “sideways”, the σ b MO is more sta- bilized with respect to the isolated 2p AOs than is the degenerate pair of π b MOs. The one-electron MO diagram for O 2 , which is shown in Figure 7.23, highlights this feature. The bond order for O 2 , calculated using Equation (7.31), is two, consistent with the O=O double bond predicted using VBT. Furthermore, the Lewis structure for O 2 has a total of four lone pairs of electrons in its valence shell. These four pairs of nonbonding electrons can be identified in the MO diagram for O 2 as the four “cancelling” pairs of σ b and σ ∗ or π b and π ∗ electrons. Furthermore, two of the uncancelled bonding electrons lie in sigma MOs and two lie in pi MOs, so that the O 2 molecule can be said to have one sigma and one pi bond. Dioxygen was chosen for this example because it demonstrates one of the advantages of MOT over VBT: it can also predict the magnetism of the molecule. It has long been known that if you pour liquid oxygen between the poles of a strong electromagnet, the liquid is attracted to one of the poles of the magnet. Because the π b MOs are degenerate (have the same energy), Hund’s rule of maximum multiplic- ity states that they should fill with their electrons unpaired, such that its electron configuration is written as follows: KK (σ 2s ) 2 (σ ∗ 2s ) 2 (σ 2p ) 2 (π 2p ) 4 (π ∗ 2px ) 1 (π ∗ 2py ) 1 .
eBook - PDF- Allan Blackman, Steven E. Bottle, Siegbert Schmid, Mauro Mocerino, Uta Wille(Authors)
- 2022(Publication Date)
- Wiley(Publisher)
A bond has its maximum electron density above and below the plane of the nuclei, and has zero electron density along the internuclear axis between the nuclei. A double bond always consists of one bond and one bond. The bond forms from the end-on overlap of the two hybrid orbitals, and the bond forms from the side- by-side overlap of the two atomic p orbitals. As the side-by-side overlap is not as efficient as the end-on overlap, double bonds are not twice as strong as single bonds between the same atoms. Figure 5.45 shows the complete orbital picture of the bonding in ethene. Ethene is the simplest of a class of molecules, the alkenes, which contain CC double bonds (see the chapter on the chemistry of carbon). FIGURE 5.44 Orbital overlaps used to form the σ framework of ethene. Note that all orbitals shown are of the same phase and colours are used for clarity only. Diminished lobes of opposite phrase in the sp 2 hybrid orbitals have been omitted. FIGURE 5.45 Orbital pictures of the bonding in ethene from three perspectives: (a) view of the p z atomic orbitals which overlap to form the π bond, (b) view of the π bond formed from the overlap of the p z atomic orbitals and (c) the π bond superimposed on the σ framework. Note that the pink and blue lobes together represent a single π bond, which is occupied by two electrons. Diminished lobes of opposite phase have been omitted. (a) (b) (c) π π σ σ σ σ σ The availability of an unhybridised valence p orbital to form bonds is characteristic of sp 2 hybridisation and is not restricted to carbon atoms. Many organic molecules contain CN and CO double bonds and we can describe the bonding in such compounds in a similar fashion to the above description of a CC double bond. To summarise, we can construct the valence bond description of any double bond using the following four-step procedure. 1. Determine the Lewis structure. 2. Use the Lewis structure to determine the type of hybridisation.
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