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This book cannot be a comprehensive compilation of all the periodic properties. And it is certainly not intended to be a turgid, endless, boring, collection of tabulated data and graphical plots. In this chapter, there will be a focus just upon four major parameters: electronegativity, ionization energy, electron affinity, and relativistic factors. But first …

What is a chemical element? This question may seem self-evident, but it is not. In Chapter 1, a chemical element was defined, by inference, as an atom with a specific number of protons. Now, entering the world of chemistry, things become murkier. Many electrons have been put to work to produce erudite articles on the subject [1–3].

An atom clearly is a chemical element. It is a minuscule fragment of matter with no color, and no sense of whether it is supposed to be a metal or nonmetal; or have any other bulk properties. It does have an electron configuration, an ionization energy, and an electron affinity. However, to define its electronegativity (discussed in the next section), comparison must be undertaken using a pair of dissimilar atoms.

But most chemists deal with real, visible materials, that is, “elements and compounds,” rather than “atoms and molecules.” Thus, the question arises, if the word “element” is used to describe the identity of an atom, can it also be used to do double duty for a bulk collection of atoms [4]? And, indeed, at what size does a cluster of atoms begin to exhibit bulk properties [5]?

The proposal has been made to use the term “elementary substance” for a bulk substance that does not undergo chemical decomposition into other substances [6]. There are two challenges with adoption of this new terminology: first, the cumbersomeness of a two-word term; and second, the acceptance among, not just chemists, but also the wider community at large. As much as this author, in general, espouses precise and correct terminology wherever feasible, here, the word “element” will continue to do “double duty.”

Electronegativity

It may seem odd that the first parameter in this chapter is not a simple measurable property of an atom. However, the concept of electronegativity underlies much of our interpretation of chemical properties and behavior. Jensen has traced the origins of the electronegativity concept back to the early 1800s, with Berzelius naming the concept “electronegativity” in 1811 [7]. In fact, it was in the late 19th and first half of the 20th centuries when the concept became refined into its modern form [8].

Electronegativity as a Fundamental Property

Leach has produced a comprehensive study of the various parameters that have been used to obtain numerical values for electronegativity. He argued that even though electronegativity is not a single parameter of an atom’s properties, it is a fundamental property itself. Among his conclusions were the following (edited) statements [9]:

•Electronegativity is an extremely successful but ill-defined heuristic concept for the description of central properties of entities in the dappled chemical world.

•Electronegativity is a theoretical construction than a natural property. That is, it is cannot be measured directly.

•Electronegativity’s main applications (descriptions of polarities and bonding modes in substances, depiction of oxidation numbers, explanation of reaction mechanisms and acidity, etc.) are qualitative. In Leach’s view, the mathematization of electronegativity is excessive and tends to lead to apparent scientificity.

•Electronegativity is a dimensionless number that — like other measures in the applied sciences — has a complex referential background. It is conceptually rooted in the realm of chemical reactivity on the one hand, but it is supplied by the physics of isolated particles on the other.

Electronegativity Scales

Though electronegativity is commonly associated with Pauling and his scale [10], there are many other scales, including the widely used Allred–Rochow [11]. All numerical ranges share a common definition:

Electronegativity is a chemical property that describes the tendency of an atom to attract a shared pair of electrons (or electron density) toward itself.

If electronegativity is such a vague concept with disparate definitions, why is it so important, and why has it not been replaced by a clearly quantifiable atomic parameter? It was Rodebush in 1924 who provided an elegant answer [12]:

I had hoped that we might be able to substitute electron affinity or ionizing potential for the wretched term electronegativity, but these quantities are measured for the gaseous state and our ordinary chemical properties are concerned with the condensed phases.

Even in the 21st century, the nature of electronegativity is a continuing topic of discourse and debate [13, 14].

The Sanderson Electronegativity Scale

In addition to the well-known scales, in an oft-overlooked series of articles, Sanderson developed and applied his own electronegativity scale [15]. Though his value system did not gain acceptance, the plot that he generated provided a useful qualitative overview of comparative electronegativities (Figure 2.1).

Sanderson indicated in his plot that the “secondary” linkages progressed from the 3rd Period to the 4th Period. Of particular note in the context of Chapter 9, he high-lighted in the article the closer resemblance in electronegativity (and electron configuration) of aluminum with the Group 3 elements, and of silicon with the Group 4 elements. The plot also showed the “saw-tooth” pattern in electronegativities that are observed when descending groups in the later main group elements.

Figure 2.1 Patterns in the Sanderson electronegativities of the elements (adapted from Ref. [15]).

The van Arkel–Ketelaar Bond Triangle

One of the many applications of the electronegativity concept is that of the bond triangle [16]. Devised by van Arkel, then improved upon by Ketelaar, the triangle categorizes elements, alloys, and compounds according to their degrees of ionic, covalent, and metallic character [17]. The triangle was originally more conceptual than detailed. However, using electronegativity values, Jensen semiquantified the diagram as shown in Figure 2.2 [18].

Sproul and his coresearchers have refined and updated the bond triangle, both from a practical and theoretical perspective [19]. The triangle has become popular as a means of assigning bonding in newly synthesized solid-state compounds, such as Y₃AlC [20] and the AgXY₂ family where X is a Group 13 element, and Y is a Group 16 element [21]. In addition, Sproul has attempted to revive the triangle in the context of teaching bond type at university level [22].

Figure 2.2 A semiquantitative bond triangle (adapted from Ref. [15]).

In Britain, an advanced high school qualification, called the Pre-U has been devised by the University of Cambridge International Examinations. A key part of the chemistry Pre-U is devoted to the van Arkel–Ketelaar Triangle as a basis for the bonding discussion [23].

Oxidation State

Another rather nebulous — but very useful — property is oxidation state [24]. To use the deductive approach as will be shown shortly, the value is determined upon the basis of comparative electronegativities.

According to Jensen, the first use of the term was by Talbot and Blanchard in 1907 [25]. Actually, there are two terms: “oxidation state” and “oxidation number.” In 1990, the International Union of Pure and Applied Chemistry (IUPAC) provided a set of recommended lengthy rules by which the “oxidation state” of any element could be calculated (given in Arabic numerals). IUPAC reserved the term “oxidation number” for the central atom in a coordination compound (given in Roman numerals) [26]. This latter usage corresponded to the use of Roman numerals in the Stock system of inorganic nomenclature.

The 1990 IUPAC definition of oxidation state was critiqued by Loock, who pointed out the significant shortcoming that the IUPAC method would only give an average oxidation state if there were two atoms in a compound in dissimilar environments. Instead, he proposed a succinct definition based on Pauling’s use of the term [27]:

The oxidation state of an atom in a compound is given by the hypothetical charge of the corresponding atom ion that is obtained by heterolytically cleaving its bonds such that the atom with the higher electronegativity in a bond is allocated all electrons in this bond. Bonds between like atoms (having the same formal charge) are cleaved homolytically.

Jensen strongly supported the Pauling/Loock definition, adding a summary of the difference in the approaches [28]:

…the memorized IUPAC rules …are ultimately traceable to an attempt to assign oxidation values based solely on the use of a species’ compositional formula, whereas the Pauling[/Loock] approach requires instead a knowledge of the species’ electronic bonding topology as represented by a Lewis diagram.

A variation of the Pauling/Loock approach — the “exploded structure method” — was devised by Kauffman [29], though its shortcomings were described by Woolf [30]. IUPAC subsequently reversed their view, changing from a mechanical rule-based approach (still widely used in textbooks) to the electronegativity–Lewis structure approach of Pauling/Loock. However, compared with Loock’s definition, the IUPAC definition seems technical and obtuse [31]:

The oxidation state of an atom is the change of this atom after ionic approximation of its heteronuclear bonds. Bonds between atoms of the same element are not replaced by ionic ones: they are always divided equally.

In many cases, both the algebraic and the electronegativity–Lewis structure approach give the same result. For example, in the sulfate ion, both methods assign an oxidation state of +6 for sulfur. However, very different results are obtained where there are two (or more) atoms of the same element in different environments.

An example is provided by the thiosulfate ion, S₂O₃²⁻, with a peripheral and a central sulfur atom. When this ion decomposes in acid, the fates of the two sulfur atoms are quite different, indicating that they have come from very different environments and oxidation states in the thiosulfate ion itself. However, the algebraic calculation provides an average oxidation state of +2 for each sulfur atom. The Lewis structure of the ion (Figure 2.3) confirms the experimental finding of two very different electron environments for the sulfur atoms. Utilizing the Pauling/Loock electronegativity–Lewis structure approach, the central sulfur atom is assigned an oxidation state of +5 while the peripheral one has a resulting oxidation state of −1. These values make much more chemical sense.

Figure 2.3 Electron assignment for the thiosulfate ion to use for electronegativity determination by the Pauling/Loock deductive method.

Abegg’s Rule

The range of oxidation states for a specific element is sometimes alluded to in introductory chemistry. As examples, values for sulfur range from −2 to +6, while for chlorine the range is from −1 to +7. It was Abegg who, in 1904, noticed that the sum of the extreme oxidation states of an element often equaled eight. The popularization of this observation did not happen until 1916, in a long-overlooked contribution to chemical bonding by Lewis [32]. The rule can be states as follows:

Abegg’s Law states that, for a main group element, the total difference between the maximum negative and positive oxidation states of an element is frequently eight and is in no case more than eight.

As an example, sulfur has the oxidation state limits of −2 and +6. Thus, applying Abegg’s law: [{+6} − {−2}] = +8.

Electron Gain and Loss

Having devoted the first part of this chapter to the variously defined concept of electronegativity, the second part will be on the very specifically defined topics of ionization energy and electron affinity. Values of which are mostly known to considerable precision.

First a comment upon a statement that appears in many introductory chemistry texts: “Ionic compounds form because metals want to give up valence electrons and non-metals want to gain valence electrons.” The statement is a convenient fiction for students starting out in chemistry, but nothing could be farther from the truth! This false explanation can be demolished by simply considering the ionization energy (IE₁) and electron affinity (EA₁) of the sodium atom:

As can be seen from the values, sodium actually “wants” to gain an electron not lose one! It is only the fact that the nonmetal counter-atom has a higher electron affinity that “forces” sodium to lose its valence electron. That is, ionic bonding is not benign, but atomic “nature red in tooth and claw,” in other words, a competition for the valence electrons [33]. The two related phenomena are discussed in the following.

Ionization Energy

One pattern explicable in terms of electron configuration is that of ionization energy. Usually we are interested in the 1st ionization energy. As the orbital occupancy may change between the neutral atom and the ionized ion, a correct definition is as follows [34]:

The experimental 1st ionization energy is equal to the difference between the total electronic energy of the atom X and the total electronic energy of the ion X⁺, both in their ground states. That is, X(g) → X⁺(g) + e⁻

Periodic Trends in Ionization Energy

Unlike the molecule-dependent values of covalent radii, ionization energies can be measured with great precision. Figure 2.4 shows the IE₁ for the 1st, 2nd, and 3rd Period elements. As can be seen, the pattern is repetitious, the Group 1 elements at the low point and the Group 18 elements at the peaks. Most of the variations can be explained in terms of screening/shielding from the nucleus of the outermost electron by the inner electrons [35].

Figure 2.4 1st ionization energy for the first 19 elements (adapted from Ref. [35]).

Instead of discussing IE₁ of each element shown, one cycle will be chosen for examination: that of the 2nd Period elements. The patterns can be explained as follows:

•Lithium has a small IE₁ as the 2s electron is largely shielded from the nuclear attraction by the 1s²:

[He]2s¹ → [He]

•Beryllium has a larger IE₁ primarily as a result of the greater effective nuclear charge:

[He]2s² → [He]2s¹

•Boron has a lower IE₁ as, even though there is an increase in nuclear charge, the 2p electron is partially shielded by the 2s² electrons:

[He]2s²2p¹ → [He]2s²

•Carbon has a higher IE₁ primarily as a result of the greater effective nuclear charge:

[He]2s²2p² → [He]2s²2p¹

•Nitrogen has a higher IE₁ primarily as a result of the greater effective nuclear charge:

[He]2s²2p³ → [He]2s²2p²

•Oxygen has a lower IE₁ which will be discussed separately in the following:

[He]2s²2p⁴ → [He]2s²2p³

•Fluorine has a higher IE₁ primarily as a result of the greater effective nuclear charge:

[He]2s²2p⁵ → [He]2s²2p⁴

•Neon has a much higher IE₁ primarily as a result of the greater effective nuclear charge:

[He]2s²2p⁶ → [He]2s²2p⁵

The Half-Filled Shell Myth

Ingrained in the vocabulary of chemistry is the term “the stability of the half-filled shell.” However, it is not the “stability” of the p³ configuration, but the reduced “stability” of the subsequent electrons, which accounts for the break in near-linearity of the plot. Cann has compared some of the explanations for the discontinuity and concluded the following one to be the best [35]:

Because of the Pauli Exclusion Principle, electrons with parallel (unpaired) spins tend to avoid each other, thus decreasing the electrostatic repulsion between them. This will be the situation when filling the first half of the shell. When electrons are forced to doubly occupy orbitals in the second half, their spins are constrained to be paired (antiparallel). Because they are no longer obliged to avoid each other, the [inter-electron] electrostatic repulsion increases.

In Figure 2.5, the IE₁ are shown for the 2p and 3p block elements. Continuing the line of the p¹ to p³ configurations, a line parallel to the actual p⁴ to p⁶ values is obtained. The difference between the two represents the coulombic repulsion between pairs of electrons within the same orbital. For the 2p series, this amounts to about 430 kJ⋅mol⁻¹, while for the 3p series it is 250 kJ⋅mol⁻¹. Cann attributed the difference between the two series to the more diffuse 3p orbitals compared with the 2p orbitals. Thus, any paired 3p electrons are sharing a larger volume of space and therefore have less mutual repulsive forces.

Figure 2.5 First ionization energy for the p-block elements of the 2nd and 3rd Periods (adapted from Ref. [35]).

To review, there is nothing exceptional about the “half-filled shell.” It is instead the interelectron repulsive forces between the electron pairs beyond the p³ configuration, which result in a lower ionization energy. To reinforce the point, as Rich and Suter added [36]:

Likewise, when one compares the energy to remove an electron from the half-filled p subshell with that needed for a p² structure, nothing special is found.

Rich and Suter then referred to the claimed stability of the “filled shell.” They continued [36]:

Similarly, the large energy difference between electrons in 3s¹ and 2p⁶ configurations is readily explained by the difference in principal quantum number; this again indicates no more “extra” stability of a filled p shell than it does for a p⁵ or any other structure in which the electron being removed is at the lower principal number.

3d-Series Metal Ionization Energies

The 1st and 2nd ionization energies of the 3d-series metals, corresponding to the removal of each of the 3s² electrons, show a steady increase without any major deviations [37]. More interesting are the 3rd ionization energies, IE₃, of the 3d-series metals. With these subsequent ionization energies, it is the d electrons that are being “plucked off” one by one. As can be seen from Figure 2.6, it is an almost identically shaped plot to that for the 2p and 3p electrons in Figure 2.5, except that the greater coulombic repulsion between any electron pairs commences with the d⁶ configuration (instead of p⁴), as expected.

Figure 2.6 3rd ionization energy (IE₃) for the 3d-block elements (adapted from Ref. [35]).

Group Trends in Ionization Energy

Proceeding down a group, the 1st ionization energy generally decreases. This is especially systematic for the noble gases.

Though the number of protons in the nucleus has increased, so has the number of shielding electron shells. In addition, as the sequential orbitals are filled, the electrons in the outermost shell occupy a larger volume of space and thus have lower interelectrons repulsion factors.

Successive Ionization Energies

There are also patterns in successive ionizations of an element [38]. One of the simplest examples is lithium:

Lithium has the electron configuration 1s²2s¹. Thus, the first electron to be removed is strongly shielded by the two 1s electrons. Then, to remove each of the 1s electrons requires very much greater energy. The lesser value for removing the second electron compared to the third can be accounted for by two factors: First, there are always electron–electron repulsions when two electrons occupy the same orbital; second, even within the same orbital, one electron does partially shield the other electron.

Electron Affinity

Much space is usually given to ionization energy and little to electron affinity (rarely, but more correctly, called electron attachment energy). Yet as mentioned earlier, atoms usually “want” to gain electrons and certainly not lose them! The following definition is parallel to that given for ionization energy.

The experimental 1st electron affinity is equal to the difference between the total electronic energy of the atom X and the total electronic energy of the ion X^–, both in their ground states. That is, X(g) + e⁻ → X⁻(g)

Sign Convention for Electron Affinity

For clarity, it is important to commence with a mention of the confusion over the sign convention for electron affinity. A proponent of the traditional sign convention (no longer in common use) was Wheeler, who contended that [39]:

With this convention, the electron affinity is positive for elements such as fluorine, for which energy is released when an electron is added to make an ion, while the widely quoted values for the alkaline earth metals and noble gases are negative.

This convention, however, is the opposite of that used for ionization energy. To remove the ambiguity, Brooks et al. proposed that the term “electron affinity” should be eliminated and, instead, the reverse process should be regarded as the 0th ionization energy [40]:

This format, which never gained wide acceptance, would correspond with the sign convention used here for electron affinity:

Period Patterns in Electron Affinity

If anything, the patterns for electron affinity are more interesting than those of ionization energy [41, 42]. The graph in Figure 2.7 shows the first electron attachment energies for the 1st, 2nd, and 3rd Periods.

As with ionization energy, there are the two factors involved: interelectron repulsion and exchange energy. There is still an effective nuclear charge on the periphery of each atom, which increases as the number of protons increases. In the 2nd Period, for example, the greatest EA₁ is that of fluorine. There are three exceptions to the negative EA₁: beryllium, nitrogen, and neon.

Figure 2.7 Electron affinity (EA₁) hydrogen to calcium.

•Beryllium has a positive EA₁ as an added electron would have to enter a 2p orbital where it would be shielded by the 2s² electrons. In fact, the electron repulsion must exceed the nuclear attraction:

[He]2s² → [He]2s²2p¹

•Nitrogen has a positive EA₁ as a result of the interelectronic repulsion being greater than the effective nuclear attraction:

[He]2s²2p³ → [He]2s²2p⁴

•Neon has a positive EA₁ as an added electron would have to enter a 3s orbital where it would be shielded from the nuclear attraction particularly by the 2s² and 2p⁶ electrons. In fact, the electron repulsion must exceed the nuclear attraction from the nucleus:

[He]2s²2p⁶ → [He]2s²2p⁶3s¹

Group Trends in Electron Affinities

Down a group, as the atoms become larger and the nuclear attraction becomes less, so the electron affinities decrease. The trend is illustrated in Figure 2.8.

The 2nd Period elements from boron to fluorine are clearly exceptions to the trends in their respective groups. Their electron attachment energies are significant deviations from the smooth progressions of the other members of their groups. That is, their electron attraction energy is significantly less than expected. For example, that of nitrogen is +7 kJ⋅mol⁻¹ while that for phosphorus is −72 kJ⋅mol⁻¹; similarly, that of oxygen is −141 kJ⋅mol⁻¹ while that for sulfur is −200 kJ⋅mol⁻¹. An accepted explanation is that the atoms are so small that the interelectron repulsion factor is exceptionally large and, as a result, the attraction for an additional electron is significantly reduced. The anomalous electron affinity of gold will be discussed later in the chapter.

Figure 2.8 A plot of 1st electron affinities by period (adapted from Ref. [41]).

Multiple Electron Affinities

Just as there are multiple ionization energies, so there are the corresponding multiple electron affinities. However, whereas the atomic ionization energies are always positive, as discussed earlier, the 1st electron affinity is often negative. Nevertheless, the subsequent electron affinities are all positive as a result of the increasing electron–electron repulsions. This can be illustrated by the electron affinities of the nitrogen atom:

Alkalide Ions

As the formation of the Na⁻ ion is energetically favored, then compounds containing that ion should be feasible.

It was in 1974 that Dye et al. synthesized the first known compound containing the sodide ion [43]. The team realized that, in the solid phase, there was little energy needed for the formation of the sodium cation–anion pair:

The key, then, was to find a way of keeping the two ions separated. To do this, Dye et al. caged the sodium ion in a bicyclic diaminoether, commonly known as 2,2,2-crypt. The synthesis was successful and gold-colored crystals of [Na(C₁₈H₃₆N₂O₆)]⁺⋅Na⁻ were produced. From the crystal structure, the radius of the sodide ion was calculated to be 217 pm, close to that of the iodide ion, and the sodide compound has a structure similar to that of the analogous iodide: [Na(C₁₈H₃₆N₂O₆)]⁺⋅I⁻. The preparation of anions of the other alkali metals followed [44]. Then in 1987, Concepcion and Dye synthesized a simpler compound of the sodide ion: [Li(diaminoethane)₂]⁺⋅Na⁻ [45].

Since then, simple stable compounds of both the sodide ion and the potasside ion have been synthesized [46]. Of note, the tradition of using the Latin-derived name for the anion was not followed as these anions should have been named “natride” and “kalide,” respectively. No explanation was stated, though perhaps it was to avoid confusion of “natride” with “nitride.”

A particularly intriguing compound is the so-called “inverse sodium hydride.” Sodium hydride itself, Na⁺H⁻, is a well-known reducing agent as a result of the “naked” hydride ion [47]. By “caging” the hydrogen ion, it has been possible to synthesize [H⁺]_cageNa⁻ [48].

The Auride Ion

Looking at the plot of electron affinities (Figure 2.8), gold stands out as an obvious candidate for anion formation.

In fact, the first evidence for the formation of an auride came in 1937 by the equimolar mixing of cesium and gold [49]. This transparent yellow compound was shown in 1959 not to be an alloy, but to be Cs⁺Au⁻, with a sodium chloride crystal structure. Since then, several other auride compounds have been synthesized [50], including tetramethylammonium auride, [N(CH₃)₄]⁺⋅Au⁻. The compound is isostructural to the corresponding bromide, which further illustrates the similarities between the auride and halide ions [51].

The Platinide Ion

At −205 kJ⋅mol⁻¹, EA₁ for platinum is close to that of gold. Thus, it should come as no surprise that there is an increasing chemistry of the platinide ion, Pt²⁻, including cesium platinide, Cs₂Pt [52].

Relativistic Effects on Atomic Properties

As an explanation for the significantly negative electron affinity, and other anomalous behavior, relativistic effects must be invoked [53]. These effects are rarely discussed in general chemistry [54], yet they are vital to the comprehension of many facets of atomic behavior [55]. Two of the contexts in which relativistic effects are discussed are the color of gold [56, 57] and the liquid phase of mercury at room temperature [58]. In this section, the focus will be on the relativistic explanation for the formation of auride and platinide ions and then in later chapters on some other relevant relativistic phenomena.

Though the electrons in all atoms experience some degree of relativistic effects, they only become important for the heavier elements. There are two significant factors that can be ascribed to relativistic effects [59] (Figure 2.9 shows both factors for the 5d, 6s, and 6p energy levels):

Figure 2.9 Nonrelativistic and relativistic energy levels for the 5d, 6s, and 6p orbitals (adapted from Ref. [59]).

•Changing in relative energy levels of atomic orbitals

s orbitals decrease substantially in energy and p orbitals decrease to a lesser extent when relativistic effects are taken into consideration. This results in increased shielding of the nucleus, causing d orbitals and f orbitals to increase in energy.

•Splitting of energy levels having l > 0 into two sublevels as a result of spin–orbit coupling

p levels split into p_1/2 and p_3/2 while the d levels split into d_3/2 and d_5/2 levels.

Platinum and Gold Electron Affinities

It is relativistic effects that can explain the high EA₁ for platinum and gold. The additional electron enters the 6s orbital:

Figure 2.10 Plot of ratio of relativistic to nonrelativistic atom radii for the 6s orbital (adapted from Ref. [60]).

As can be seen from Figure 2.10, the relativistic decrease in relative radius for an added 6s electron reaches a minimum at gold, with the value for platinum being not substantially different [60]. That is, there will be a greater effective nuclear charge on any additional 6s electron for platinum and gold than would be expected without taking relativistic effects into account.

Commentary

In this chapter, a mere selection of atomic periodic properties have been chosen for discussion. In this way, the Reader is not overwhelmed by endless tables and graphs of data. Those who wish to indulge should look elsewhere. This book is designed to make the many concepts of elemental relationships become alive and stimulating, not boring and soporific. The chapter has ended with an introduction to relativistic effects. This oft-overlooked aspect will not be simply a passing reference, but a topic that will be revisited in different contexts in later chapters.

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