Article Cite This: J. Chem. Educ. 2019, 96, 1412−1417
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Systematic Procedure for Drawing Lewis Structures Based on Electron Pairing Priority and the Explicit Use of Donor Bonds: An Alternative to the Normal Procedure Which Can Be Pen and Paper Based or Automated on a PC in User Interactive 3D Patrick McArdle*
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School of Chemistry, National University of Ireland, Galway H91 TK33, Ireland ABSTRACT: This article contrasts the normal method for drawing Lewis structures with a two-step systematic approach. The latter approach uses a known molecular connectivity and a knowledge of the number of valence electrons that each atom possesses to visualize bonds that are formed by pairing electrons, one from each atom. This process is repeated until at least one of the non-hydrogen atoms in each bond has an octet. Donor bonds are added when atoms with six and eight electrons are adjacent. In forming donor bonds charges are added to the atoms involved to maintain electron accounting and there is no need to use a formula to calculate formal charges. The general importance of adhering to the octet rule for p-block compounds is stressed and the difference between covalent and donor bonds and the use of the recent IUPAC definition of oxidation state which is based on Lewis structures is included in the discussion. When students are able to draw Lewis structures they can be given access to PC software, available on an academic free basis, which will draw rotatable Lewis structures in 3D for p-block compounds. The software allows the user to move electron pairs in a bow and arrow fashion within the structures and atoms are highlighted when the octet is exceeded. KEYWORDS: Lewis Structures, First-Year Undergraduate/General
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INTRODUCTION Despite the age of the ideas on which Lewis structures are based, this method is still important such that chemistry students are able to draw these simple pictures of the bonding in molecules.1 Some of the drawings in Lewis’s 1916 paper would not look out of place in current publications, Figure 1.
atoms in electron pair bonds to try to achieve an octet or some other number of electrons in the valence shell of each atom and finally apply a formula to each atom to see if there are any formal charges which should be added. Some authors advocate the use of up to seven steps in the process of producing a structure.12
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ATOM CHARGES IN LEWIS STRUCTURES The discussion of structures with atom charges by Lewis in his 1916 paper is limited to the formation of NH4+ and the electron dot structure for the acetylide anion. Atom charges in Lewis diagrams were first introduced in a general way as “residual charge” by Langmuir.21 The first use of the term “formal charge” that I can find is in a paper by Huggins.22
Figure 1. Water, ethene, and ethyne in Lewis’s 1916 paper. Reproduced with permission from ref 1. Copyright 1916 American Chemical Society.
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The basic idea is that each atom’s valence electrons are used to form electron pair bonds, and an attempt is made to achieve an octet on non-hydrogen atoms. These ideas still influence the way chemists today think of molecules. There is an excellent overview of Lewis’s contribution to chemical bonding in a paper by Jensen, and a description of the backstabbing to which Lewis was subjected is given in Coffey’s book.2,3
CHEMICAL BONDS IN LEWIS STRUCTURES There are three ways in which adjacent atoms A and B can involve their electrons in bond formation. A covalent bond can be formed between the atoms by each atom contributing one electron to the bond, and this can be represented by two dots or a line between the atoms, Figure 2a,b.
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LACK OF A SYSTEMATIC APPROACH TO DRAWING LEWIS STRUCTURES There are many articles in this Journal and elsewhere which propose methods for teaching the drawing of Lewis structures starting from an assumed or known molecular connectivity.4−20 A common approach is to start with the known molecular connectivity and to add bonds of different orders between the atoms using the valence electrons from all of the © 2019 American Chemical Society and Division of Chemical Education, Inc.
Figure 2. A−B bond representations. Received: October 23, 2018 Revised: March 20, 2019 Published: May 24, 2019 1412
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chemistry courses, and a simpler octet obeying scheme is discussed below.
Second atom A could donate a pair of electrons to the bond to B forming a donor, dative, or coordinate bond which can be represented by Figure 2c−e. These formal charges are used to indicate that there has been net electron transfer from A to B in bond formation. A donor bond can be considered to be a combination of a covalent bond and an ionic bond. The term ionocovalent can be used to describe these bonds between atoms which have formal atom charges.23 Third, an ionic bond can be formed by transferring one electron from A to B as in Figure 2f. Thus, Lewis structures are a form of electron accounting applied to the process of bond formation between atoms.
Rare Exceptions to the Strict Application of the Octet Rule
Electron localization function, ELF, calculations suggest that when the electronegativity difference between elements is very small the octet may be exceeded.28 Rare examples of this type are provided by AsMe5 and TeMe6. However, ELF calculations also show that in all other cases where there is an electronegativity difference the octet is not exceeded. The computer program described below will warn the user if these exceptions are detected. Tutorials provided with the program also show how to do ELF calculations on a Windows PC using academic free software.
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OCTET RULE SHOULD BE OBSERVED FOR p-BLOCK COMPOUNDS BUT IT IS WIDELY IGNORED The terms hypovalence and hypervalence have been used to describe atoms which have less and more than an octet in their valence shell, and the use of these terms has been reviewed recently.24,25 The hypovalence exhibited by boron in BF3 where boron has six electrons in its valence shell does not pose any problems for the present discussion. However, there is a problem with the still widespread use of the notion that larger p-block atoms (those with atomic numbers greater than 10) may expand their valence shell beyond the octet. Wellknown examples are the use of SO double bonds in sulfate and the use of five two-center−two-electron bonds, 2c−2e, in PCl 5 . The use of d-orbitals by p-block elements to accommodate valence electron expansion beyond the octet is still found in many standard textbooks and university undergraduate courses despite strong evidence that p-block elements do not use d-orbitals in bonding. In a landmark paper in 1954, the role of d-orbitals in bonding by p-block elements was examined, and it was concluded that they did not have an important role. The PCl5 molecule was one of the molecules that was examined in some detail.26 In 2013 a viewpoint article was published which examined the almost 60 years that had elapsed since the 1954 paper appeared, and it was concluded that nothing had changed over those years that would suggest that d-orbitals were involved in the bonding of PCl5.26,27 The bonding in PCl5 involves an sp2 hybridized P which forms three normal 2c−2e bonds to the three equatorial Cl atoms, Figure 3a. The axial Cl atoms form a multicenter 3c−4e bond
Natural Bond Orbital Analysis and Lewis Structures
Natural bond orbital, NBO, analysis can be applied to molecular orbital calculation results with the aim of finding the best Lewis representation of bonding. In the NBO analysis of SF6, the best representation of the structure is an S3+(F0.5−)6 donor−acceptor model.29 These authors also state that “We therefore concur with the suggestions of Maclagani and Kutzelnigg that models of sp3d and sp3d2 hypervalent bonding in non-metals should no longer be taught in chemistry courses.”30,31 In an article entitled “Common Textbook and Teaching Misrepresentations of Lewis Structures”, it is shown using natural resonance theory that the octet obeying structure in Figure 4b is a better representation of sulfate than the
Figure 4. Structures representing the sulfate ion.
doubly bonded structure in Figure 4a.32 The S−O bond lengths in sulfate are shorter than single bonds due to the presence of ionic bonding in addition to the covalent bond (an ionocovalent bond). Ionocovalent bonds are stronger that simple covalent bonds when the atom charges are aligned with electronegativity. The best current experimentally based description of the bonding in sulfate comes from a very low temperature, high resolution X-ray diffraction study which shows that the experimental electron density is consistent with the structure in Figure 4b which is not hypervalent.33
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DRAWING LEWIS STRUCTURES The way in which students are taught to draw Lewis structures will vary from one chemistry course to another. However, the aim here is to contrast the typical current approach with a systematic stepwise approach.
Figure 3. (a) Three equatorial P−Cl 2c−2e bonds and (b, c) 3c−4e bonding of the axial Cl atoms.
A Typical Current Approach to Drawing Lewis Structures
The first step is to count the total number of valence electrons for all atoms in the molecule. The total electron count needs to include the effect of any overall charge on the system. This number is most often even, and divided by two, it gives the total number of available electron pairs. Using an assumed or known atom connectivity, electron pairs are placed between and on atoms starting with atoms with one connection in an effort to give each hydrogen an electron count of two and all
with one electron pair in a bonding orbital, ψ1, and the other in a nonbonding orbital located on the axial Cl atoms, ψ2, which has a node at P, Figure 3b,c. The other orbital, ψ3, is antibonding.25 This bonding scheme has four bonding electron pairs on P and no hypervalency. This molecular orbital picture of the bonding in PCl5 is not suitable for introductory 1413
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Figure 5b. In the stepwise procedure starting in Figure 5c, the number of nonbonded electrons is shown below the atoms in blue, and the total electron count is shown above the atom in red. Electron pairing to give single and double bonds is shown in Figure 5d,e. This latter structure is a candidate for formation of a donor bond as described in Step 2a. When the donor bond is formed, charges are added across the bond to acknowledge that both electrons have come from the oxygen atom. These charges arise from simple electron accounting. In practice only the structure in Figure 5f would be drawn. There is of course a donor bond in structure in Figure 5b; however, its presence is less explicit in the normal procedure. The triple bond in Figure 5b,f gives a reasonable explanation for the strength of the bond which at 1076 kJ mol−1 is the strongest known chemical bond.35 CO was the first molecule to have the direction of its dipole moment measured experimentally. The dipole moment is small, 0.122 D, but its negative end points to C in the direction opposite to that which would be expected from electronegativity.36−38 Thus, the donor bond and the movement of electron density from O to C which it suggests provide a simple rationalization for the observed dipole moment.39 A theoretical discussion of the formation of CO gives a detailed account of the transfer of electron density from O to C.40
non-hydrogen atoms an octet. A formula is then applied to each atom to decide if it should carry a formal charge. This formula in its most simple form is that the charge is equal to the atom’s valence electron count minus the number of bonds minus the number of nonbonded electrons. A Systematic Procedure for Drawing Lewis Structures
In this approach the process is stepwise, and the electron accounting is more explicit. Of all the schemes suggested for drawing Lewis diagrams, that I have found, the one suggested by Miburo is closest to the stepwise procedure suggested here.34 Step 1. With the atoms arranged to show molecular connectivity, and with each atom having its valence electrons, single bonds are formed starting with atoms with one connection, by sharing electrons, one from each atom. This step will give all H atoms a share of 2 electrons. The bonds formed here by electron sharing will not place charges on any atom. Step 2. Continue pairing electrons on adjacent atoms until octets are achieved on as many non-hydrogen atoms as possible. The following points need to be considered: (a) If two adjacent atoms have 6 and 8 electrons, then use a nonbonded pair (if available) from the 8 electron atom to form a donor bond to the 6 electron one. When adding the donor bond add atom charges +1 on the 8 electron atom and −1 on the 6 electron atom to account for the electron transfer. Both atoms now have total electron counts of 8. (b) If pairing electrons on adjacent atoms would exceed the octet on either atom, then form an ionic bond transferring an electron from the atom that would exceed the octet. (c) When drawing the structures of ions it is necessary to place any ion charges on specific atoms before bond formation is attempted. A positive charge can be placed on the atom with the largest number of connections relative to its normal valence. For example, in ammonium salts the positive charge is placed on a nitrogen atom with four connections. Negative charges can be placed on the atoms with the highest electronegativity and the lowest number of connections.
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Azide Anion, N3−
The connectivity of azide is NNN; in the normal procedure the total number of electrons is 16, and the eight electron pairs could be placed as in Figure 6a. The atom charges are as shown
Figure 6. Stepwise bond formation in azide anion.
in Figure 6b. In the stepwise procedure as suggested in Step 2c above, the negative charge can be placed on a terminal N. Thus, before bonds are formed the neutral N atoms have five electrons, and the negatively charged N atom has six electrons, Figure 6c. After single bonds are formed, the electron counts are as given in Figure 6d. Pairing electrons between the atoms with 7 electrons gives the structure in Figure 6e. Two atoms now have octets, and one has six electrons. The adjacent pairs which have 6 and 8 electrons in Figure 6e can use the lone pair on the central atom to form a donor bond as described in Step 2a above to give Figure 6f which is equivalent to Figure 6b. The sequence from Figure 6c to Figure 6f would in practice be combined in the single structure, Figure 6f.
EXAMPLES
Lewis Structure of Carbon Monoxide, CO
Application of the normal and stepwise procedures to CO is illustrated in Figure 5. Since carbon has four valence electrons and oxygen has six, the normal procedure will start by adding five electron pairs between and on the atoms in an effort to give each atom an octet. It is convenient to use short lines to represent electron pairs, Figure 5a. Application of the charge formula to each of the atoms in Figure 5a gives the charges in
Amine Oxides or Amine-N-oxides, R3NO
The amine oxides can be considered to be an R3N group bonded to an oxygen atom. Since tertiary amines like R3N are stable compounds with normal covalent single bonds between their atoms, we can concentrate here on the bond between N and O. In the normal procedure, the electrons available for N− O bond formation can be placed as shown in Figure 7a, and the formal charges are shown in Figure 7b. In the stepwise procedure starting with Figure 7c, the adjacent N and O atoms
Figure 5. With a Lewis structure drawn for CO, the number of nonbonded electrons is shown below the atom in blue and the total electron count is shown above the atom in red. 1414
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exceeding the octet at phosphorus as shown in Figure 9a. The formal charges are shown in Figure 9e. In the stepwise
Figure 7. N to O bonding in R3NO.
having 8 and 6 electrons, respectively, can form a donor bond from N to O giving both atoms a share of 8 electrons and the charges shown in Figure 7d. The structure in Figure 7d is equivalent to the structure in Figure 7b. It is mentioned above that a donor bond is an ionocovalent bond, and in this case, the length of the donor bond in the gas phase is 1.379(3) Å which is intermediate between the expected single and double bond distances; also, the bond energy is 295 kJ mol−1.41 The donor bond is a strong one in this case as the atom charges are aligned with electronegativity.
Figure 9. Lewis structure of PCl5.
procedure starting with Figure 9b, after the formation of three bonds the electron count is shown in Figure 9c. Since there is now an octet at phosphorus, Step 2b above suggests that an ionic bond could be formed by transferring an electron from phosphorus to, in this case, the top seven-electron chlorine as in Figure 9d. The remaining unpaired electron on phosphorus can then be used to form a bond to the seven-electron chlorine to give the structure in Figure 9e. This strict adherence to the octet rule in PCl5 does not invalidate the use of the well-known valence shell electron pair repulsion theory, VSEPR.42 The Lewis structure in Figure 9e, when combined with its other four resonance forms, gives the averaged structure shown in Figure 9f which can be used in VSEPR discussions. It is only the number of independent and sterically active entities in an atom’s valence shell that is important for VSEPR. In contrast to the molecular orbital description of PCl5 bonding described above, the ionic structure in Figure 9d and other resonance forms do provide a description of PCl5 bonding that is suitable for introductory chemistry courses. In a review of the chemical bond published on the 100th anniversary of the 1916 Lewis paper, it is stated with respect to structures like that in Figure 9e that “charge separated species not only obey the eight-electron rule but also place the formal charges frequently with the right polarity at the right atoms. They avoid additional assumptions difficult to teach to beginners.”24
Nitrate Anion, NO3−
The nitrate anion is an example which illustrates most of the possibilities in the stepwise procedure. The normal procedure which involves the distribution of 12 electron pairs and the determination of atom charges is shown in Figure 8a,b. In the
Figure 8. Lewis structure of the nitrate anion.
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stepwise procedure the negative charge should be added to an atom which has high electronegativity and a low number of connections. Any of the oxygens can be chosen to have the negative charge, and the O on the left of Figure 8c is chosen here. When three single bonds are formed by sharing one electron from each atom, the electron counts are as shown in Figure 8d. The negatively charged oxygen and the nitrogen atoms have octets, and the two equivalent oxygens have seven electrons. If one of the two nonbonded electrons on the nitrogen is used to form a bond with either of the sevenelectron oxygens, the electron count on the oxygen will be eight, but that on the nitrogen will be nine which exceeds the octet. Step 2b suggests that an ionic bond should be added. This is done by transferring an electron from the nitrogen atom to the top right oxygen atom, and the charges shown in Figure 8e are added. The formation of a bond between the two 7 electron atoms will give all atoms octets, and the structures in Figure 8e,b are equivalent.
IMPORTANT DIFFERENCE BETWEEN COVALENT AND DONOR BONDS There is an important difference between the chemistry of covalent and donor bonds. Donor bonds often have a lower thermal stability than covalent bonds. Haaland examined a range of main group donor bonds and concluded that they were all weaker than related covalent bonds.43 The heterolytic or homolytic rupture of covalent bonds will in general be unfavorable due to the formation of high energy radical or ionic products, Figure 10a.
Phosphorus Pentachloride
Phosphorus has five valence electrons, and chlorine has seven. In the normal procedure there will be a total of 40 electrons in 20 electron pairs to be distributed. This can be done without
Figure 10. Thermal rupture of covalent and donor bonds. 1415
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In contrast, the thermal heterolytic cleavage of donor bonds can lead to stable uncharged products, Figure 10b. High purity materials required for doping in the electronics industry can be prepared by this type of adduct formation followed by subsequent thermal decomposition of the adduct. For example, pure Me2Zn can be obtained by purification of and subsequent thermal decomposition of Me2ZnNEt3, Figure 10c.44 DFT calculations suggest that the donor bond in this adduct is weak with a bond energy of 46 kJ mol−1 and a bond length of 2.27 Å which is larger than the sum of the covalent radii of 1.93 Å. All of the weak donor bonds examined by Haaland had, like Me2ZnNEt3, their atom charges associated with the donor bond aligned against electronegativity. Another interesting example of the thermal rupture of a donor bond is the quantitative thermal decomposition of NaNO3 above 374 °C to NaNO2 and O2. It is easy to spot the donor bond in the nitrate Lewis structure when parts b and f in Figure 8 are compared; notice that in this case the donor bond has charges that are aligned with electronegativity. Thus, it is strong and requires a relatively high temperature to break the bond.
In the Lewis drawing, bond electrons and atom charges are in black and nonbonded electrons, bonded electrons in donor bonds, and oxidation state, OS, values are in blue. In the default picture the OS values are not shown, and the number of donor bonds in the structure is given on the status line. Lines are drawn between the atoms to indicate connectivity, not electron pairs. If the lines are not drawn, it is difficult to follow larger structures as they are rotated on screen. While the algorithm used to draw the Lewis diagram produces the most important resonance form for CO, this may not always be the case. There is also the problem that more than one structure may need to be considered. In N2O for example the program produces the structure in Figure 12a.
DETERMINATION OF OXIDATION STATE The IUPAC definition of oxidation state, OS, supplies two algorithms for OS determination based on Lewis structures. The algorithm closest to the procedure suggested here for drawing Lewis structures is the algorithm of summing bond orders: “Heteronuclear-bond orders are summed at the atom; as positive if that atom is the electropositive partner in a particular bond, and negative if it is not: the atom’s formal charge (if any) is added to that sum, yielding the OS”. Homonuclear bonds are ignored, and bond polarity is decided on the basis of Allen’s scale of electronegativity.45,46 Application of this definition to the CO structure in Figure 5b yields OS as follows: the three CO bonds will, from the electronegativity difference, give +3 at C and −3 at O which when combined with the formal charges give OS values of +2 and −2 at C and O, respectively. The OS values for the atoms in N3− are identical to the formal charges alone as the bonds, being homonuclear, make no contribution to OS. The OS values from left to right in Figure 6b are −1, +1, and −1, respectively.
Figure 12. (a, b) N2O resonance structures. (c−e) Moilı ́n screen shots (with arrows added to indicate electron pair movements) showing the transformation from resonance form structures a to b.
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However, the structure in Figure 12b may be more important as the N−N bond is closer to a triple bond distance than a double bond distance. It is possible to move the electron pairs using mouse clicks, as indicated in Figure 12c−e to produce the structure in Figure 12b. During electron pair movements, if an atom exceeds an octet it is highlighted. Software Availability
Moilı ́n can be operated independently or as part of the Oscail software package and can be installed under most versions of MS Windows.47 32- and 64-bit versions are available. Installation files may be downloaded from https://nuigalway. ie/crystallography/ on an academic free basis. Instructions for downloading and installing Moilı ́n and Oscail are provided in the help files and on the download web page.
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STUDENT FEEDBACK I would like thank students from the second year undergraduate class for providing feedback on drawing Lewis structures, and I am particularly grateful to Golden Chigozie and Joseph Flemming, two undergraduates who were on placement in the inorganic laboratory for more detailed feedback on this article. Students found that when compared to the normal procedure for drawing Lewis structures, the stepwise procedure was helpful in two ways. First, it gave them more confidence when dealing with molecules they had not met before, and second, its explicit use of donor bonds helped their understanding of chemical bond formation.
AUTOMATION AND 3D VISUALIZATION OF LEWIS STRUCTURES The stepwise procedure described above can be automated and has been added to the molecular modeling program Moilı ́n. In Figure 11, CO is shown within Moilı ́n and in its Lewis drawing function.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Patrick McArdle: 0000-0002-3565-0527 Notes
Figure 11. Screen shots of CO in Moilı ́n and in the Lewis drawing function.
The author declares no competing financial interest. 1416
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ACKNOWLEDGMENTS The author is grateful to Professor Josef Takats for helpful discussion and Science Foundation Ireland for support under Grant 12/RC/2275 as part of the Synthesis and Solid State Pharmaceutical Centre (SSPC).
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DOI: 10.1021/acs.jchemed.8b00868 J. Chem. Educ. 2019, 96, 1412−1417
