Foundations of Chemistry

, Volume 11, Issue 2, pp 123–129

Isoelectronic series: a fundamental periodic property

Authors

    • Sir Wilfred Grenfell College
Article

DOI: 10.1007/s10698-008-9055-4

Cite this article as:
Rayner-Canham, G. Found Chem (2009) 11: 123. doi:10.1007/s10698-008-9055-4

Abstract

The usefulness of isoelectronic series (same number of total electrons and atoms and of valence electrons) across Periods is often overlooked. Here we show the ubiquitousness of isoelectronic sets by means of matrices, arrays, and sequential series. Some of these series have not previously been identified. In addition, we recommend the use of the term valence-isoelectronic for species which differ in the number of core electrons and pseudo-isoelectronic for matching (n) and (n + 10) species.

Keywords

IsoelectronicPeriodic tableValence-isoelectronicPseudo-isoelectronic

Patterns and trends in the periodic table continue to fascinate (Rouvray and King 2004). As part of a series of studies on periodic patterns, we recently confirmed the validity of the ‘knight’s move’ relationship (Rayner-Canham and Oldford 2007). Another periodic trend is that of isoelectronic series across periods, yet these seem to have been little studied. This paper is intended to provide such a review using arrays of isoelectronic species to illustrate a range of periodic patterns.

A brief background

Irving Langmuir, in his pioneering 66-page discourse on the arrangement of electrons in atoms and molecules, commented on patterns among compounds (Langmuir 1919). Though some of the terms he used were archaic, the discussions clearly laid the foundation of the isoelectronic concept. He employed the symbol, N, to denote the total number of electrons, while E was used to represent the outer, valence, electrons. Of particular note, Langmuir saw the predictive ability of the isoelectronic concept:

For example, since phosphorus and nitrogen atoms contain the same number of electrons in their shells, the simple octet theory … indicates that nitrogen compounds corresponding to all known phosphorus compounds could exist and vice versa. Thus we might expect the following compounds: H3NO4, Na4N2O7, P2O.

However, Langmuir, like most chemists, seemed to be interested in isoelectronic species within groups (same E, different N) rather than patterns across periods.

The definition of isoelectronic

Humpty Dumpty, in Alice Through the Looking Glass, remarked (Carroll et al. 1990): “When I use a word, it means just what I choose it to mean-neither more nor less.” In the chemical context, isoelectronic seems to mean whatever a chemist wishes it to mean. Two particular definitions are used widely, as was bought to this author’s attention by Penny LeCouteur, of Capilano College, North Vancouver, Canada: species having the same number of valence electrons are isoelectronic while the second definition adds the narrowing criteria that the species also have to have the same total number of electrons.

This author would suggest some clarification which, hopefully, the chemistry community might consider for general adoption. Throughout science, the prefix iso- means ‘the same.’ Thus, strictly speaking, the term ‘iso-electronic’ should simply mean the same number of electrons, period. In reality, we have to narrow down the meaning if it has to have a useful role in identifying chemical patterns and trends. For true (or exact) isoelectronic status, the most logical definition would be the following:

Species (atoms, molecules, ions) are isoelectronic with each other if they have the same total number of atoms and electrons and of valence electrons.

True isoelectronic species will usually have matching valence-level molecular orbitals which will undergo systematic energy changes across the series as Sima has shown (1995).

For series which have the same number of valence electrons but not the same total number of electrons, this author proposes the use of the term valence-isoelectronic as used by Elliott and Boldyrev (2004). Valence-isoelectronic would seem the most appropriate term as the reader is immediately aware of the meaning without need to resort to a chemical dictionary.

Species (atoms, molecules, ions) are valence-isoelectronic with each other if they have the same number of valence electrons.

For example, OCO and NCO would be identified as isoelectronic, while OCO, OCS, and SCS would be considered valence-isoelectronic. Here we will address the significance of true isoelectronic series by demonstrating patterns among compounds of elements of the same period and neighbouring groups.

The isoelectronic principle

Isoelectronic molecules and ions are often isostructural. This observation was first made by Penney and Sutherland (1936) for the linear 16-valence electron triatomic species (such as carbon dioxide) and the vee-shaped 18-valence electron species (such as sulfur dioxide and ozone). The isoelectronic principle can be defined as:

Two or more polyatomic species (ions and/or molecules) that are isoelectronic have a high probability of being isostructural.

Use of the term ‘isoelectronic principle’ seems to have become prevalent in the 1950s and 1960s. Moody (1969) used the principle to explain the identical structures of the highest oxidation state of the heavier Group 14/15/16 fluoro-anions shown below, to which this author has added the corresponding Group 13 hexahalide ions and the Group 17 hexahalonium ions (most of the formulas in this paper have been obtained from Greenwood and Earnshaw (1997) together with more recent literature sources). These species are all isostructural (octahedral) in addition to being isoelectronic across each Period. This array is one of several that can be constructed in which, intriguingly, the species span the ‘weak’ metals (Rayner-Canham 2006), the semi-metals, and the nonmetals.
 

Group 13

Group 14

Group 15

Group 16

Group 17

Period 3

AlF63−

SiF62−

PF6

SF6

ClF6+

Period 4

GaF63−

GeF62−

AsF6

SeF6

BrF6+

Period 5

InF63−

SnF62−

SbF6

TeF6

IF6+

Isoelectronic matrices

This author defines an isoelectronic matrix as one in which all species are isoelectronic and the variation along each axis is provided by a progression in Group number. As an example, there is an isoelectronic matrix of 14/10-electron diatomic species, where 14 is the total number of electrons and 10 the number of valence electrons. The O22+ ion is included for completion though it is placed in parentheses as its existence is fleeting and no stable compounds have been synthesized to date (Larsson et al. 1990). In subsequent tables, we have not included transient species produced in gas-phase reactions.
 

Group 14

Group 15

Group 16

Group 14

C22−

CN

CO

Group 15

 

N2

NO+

Group 16

  

[O22+]

Among the triatomic combinations of Period 2 elements there is a matrix of the linear two-element 22/16-electron series, XY2, where element X varies by column and element Y by row. The boron oxoanion is placed in parenthesis as it is a polymeric species. Though N2O and N2F+ fit the formula sequence, unlike the others, they are asymmetric. This can be simplistically explained in terms of the central atom usually being that of lower electronegativity. In N2F+, the N–F bond is exceptionally short (Bickelhaupt et al. 2002), indicating a similarity with the strong N–O bond in N2O.
 

Group 13

Group 14

Group 15

Group 16

Group 17

Group 14

BC25−

C34−

C2N3−

  

Group 15

BN23−

CN22−

N3

N2O

N2F+

Group 16

[BO2]

CO2

NO2+

  

Three-atom isoelectronic arrays

In addition to isoelectronic matrices, arrays of other forms can be constructed. In the two tables below, the peripheral atom is stepwise replaced by another with the charge altering to maintain the isoelectronic relationship. The first array contains the 42/32-electron penta-atomic species involving second period atoms.

# of F/O

Group 12

Group 13

Group 14

Group 15

4/0

BeF42−

BF4

CF4

NF4+

3/1

 

OBF32−

OCF3

ONF3

The second array displays the 50/32-electron combinations of the third Period non-metals with oxygen and fluorine atoms. As in earlier matrices and arrays, all of these isoelectronic species are also essentially isostructural.

# of F/O

Group 14

Group 15

Group 16

Group 17

4/0

SiO44−

PO43−

SO42−

ClO4

3/1

SiO3F3−

PO3F2−

SO3F

ClO3F

2/2

SiO2F22−

PO2F2

SO2F2

ClO2F2+

1/3

 

POF3

  

0/4

SiF4

PF4+

  

Sequential isoelectronic series

It is also possible to construct informative series in which only the horizontal rows are isoelectronic, but successive rows are linked in some simple stepwise manner. For example, in an isoelectronic oxidation-state array, each row contains species having one more electron than the preceding row, thus the oxidation state of each atom-combination decreases down the array.

In the array shown below of di- and tri-oxo species, as the oxidation number decreases, so the bond angles decrease from 180° to progressively smaller values as one, two, and finally three non-bonding electrons are added to the central atom. NO2 is one of the few stable radical species and it is noteworthy that isoelectronic CO2 is stable enough to be found in biological systems (LaCagnin et al. 1988).

Electrons

Group 14

Group 15

Group 16

Bond angle

22/16

CO2

NO2+

 

180°

23/17

CO2

NO2

O3+

~135°

24/18

 

NO2

O3

~116°

25/19

  

O3

114°

In the matrices and arrays shown above, the numbers of atoms remain the same. Some interesting arrays can be created in which the number of peripheral atoms is decreased stepwise. The following table shows the second Period 10/8 hydride isoelectronic species. The horizontal axis tracks the group number while the vertical axis represents decreasing numbers of hydrogen atoms.

# of H

Group 13

Group 14

Group 15

Group 16

Group 17

4

BH4

CH4

NH4+

  

3

BH32−

CH3

NH3

H3O+

 

2

  

NH2

H2O

H2F+

1

   

OH

HF

Sima (1995) has used comparisons of atomic orbital energies to examine why such series cannot be further extended, such as H4O2+ for the top series above, and HNe+ for the bottom series.

The following array shows the successive isoelectronic rows of third Period main-Group chloro-species compounds as chlorine atoms are subtracted. In each column, the element is in its highest oxidation state. One interesting feature of this particular array is its progression horizontally from the ‘weak’ metal (aluminum), through the semi-metal (silicon), to the non-metals (phosphorus and sulfur). Vertically, the geometry changes from octahedral, through trigonal bipyramidal, to tetrahedral geometries.

# of Cl

Group 13

Group 14

Group 15

Group 16

Geometry

6

 

SiCl62−

PCl6

 

Octahedral

5

 

SiCl5

PCl5

SCl5+

Trigonal bipyramidal

4

AlCl4

SiCl4

PCl4+

 

Tetrahedral

Among the transition metals, it is the ‘heavy’ transition metals that show some of the most interesting isoelectronic patterns. The array below has each Period 5 early transition metal in its highest oxidation state, while the number of fluorine atoms decreases until it matches the oxidation number.

# of F

Group 4

Group 5

Group 6

Group 7

8

HfF84−

TaF83−

WF82−

ReF8

7

HfF73−

TaF72−

WF7

ReF7

6

HfF62−

TaF6

WF6

 

5

HfF5

TaF5

  

4

HfF4

   
In the preceding arrays, each of the central elements were in their highest oxidation state. We can construct arrays of isoelectronic species in which the variable is not only the number of atoms, but also the oxidation state. This type of array can be illustrated using three successive isoelectronic series of fifth period fluorides which extend from the metals across to the noble gases.

# of F

Group 13

Group 14

Group 15

Group 16

Group 17

Group 18

6

InF63− (+3)

SnF62− (+4)

SbF6 (+5)

TeF6 (+6)

IF6+ (+7)

 

5

  

SbF52− (+3)

TeF5 (+4)

IF5 (+5)

XeF5+ (+6)

4

    

IF4 (+3)

XeF4 (+4)

With the common 18-electron rule governing much of organometallic chemistry, it is not surprising that there are many isoelectronic organometallic complexes. In the table below, each row contains an isoelectronic series and each subsequent row has one carbonyl unit less (modified from Huheey et al. 1993).

# of CO

Group 4

Group 5

Group 6

Group 7

Group 8

Group 9

Group 10

6

[Ti(CO)6]2−

[V(CO)6]

Cr(CO)6

[Mn(CO)6]+

   

5

 

[V(CO)5)3−

[Cr(CO)5]2−

[Mn(CO)5]

Fe(CO)5

[Co(CO)4]+

 

4

  

[Cr(CO)4]4−

[Mn(CO)4]3−

[Fe(CO)4]2−

[Co(CO)4]

Ni(CO)4

Pseudo-isoelectronic series

Elsewhere (Rayner-Canham 2006), we have discussed the similarities between elements in their highest oxidation state in Group (n) with those in Group (n + 10). The (n) species atom has a noble-gas core configuration, while that of the (n + 10) species atom has, in addition, a d10 electron set. These pairs are not strictly isoelectronic or even valence-isoelectronic, thus perhaps a more appropriate term would be pseudo-isoelectronic. A definition would therefore be:

Species (atoms, molecules, ions) are pseudo-isoelectronic if they differ by only a d10 set of electrons.

One of the many examples is that of the following set of oxoanions in which each row is isoelectronic, while each vertical pair is pseudo-isoelectronic.

Group (n)

Group 5

Group 6

Group 7

(n)

VO43−

CrO42−

MnO4

(+ 10)

AsO43−

SeO42−

BrO4

Commentary

We have endeavoured to show that the concept of isoelectronic arrays enables chemists to perceive periodic patterns across segments of the periodic table. Such isoelectronic patterns ‘lurk’ not only across the nonmetallic elements of each period but even stretch through the semi-metal members into the weak metals. There is not just one ‘type’ of table: there are matrices with group variation along both axes, then there are arrays in which there are step-wise changes in numbers of substituent atoms and/or changes in oxidation states.

These matrices and arrays are a powerful addition to the ways of demonstrating periodic behaviour. The existence of gaps in such arrays might prompt synthetic inorganic chemists to attempt to synthesize missing members of arrays.

This author would appreciate hearing from readers of additional isoelectronic series together with information on the existence of ‘missing’ members of series shown in the matrices above. The author also thanks the two anonymous referees for very constructive comments which have led to a significant improvement in the manuscript.

Copyright information

© Springer Science+Business Media B.V. 2008