Dispensa Sul Covalent Bond Classification Method

8/12/2019 Dispensa Sul Covalent Bond Classification Method

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Scaricato dal sito web di Ged Parkin, http://www.columbia.edu/cu/chemistry/groups/parkin/cbc.htm

The Covalent Bond Classification Method:

A New Approach to the Formal Classification of Covalent Compounds of the Elements

Introduction

Covalent molecules are often described in terms of the oxidation state formalism in which a charge is assigned to the atom ofinterest. While the oxidation state concept has proven to be of use in the traditional coordination chemistry with simple ligands,

e.g.Cl

and NH3, it has become evident that this concept is of limited utility in organometallic and modern coordination

chemistry because of the more complex nature of the ligands involved. For example, the cycloheptatrienyl (C 7H7) ligand has

been assigned charges of +1, 1, and 3; as such, it is evident that the oxidation state of the metal has little meaning in

complexes with such ligands. In this regard, a recent IUPAC article concludes that it is inappropriate to assign oxidation

numbers with respect to the nomenclature of organometallic compounds, viz: As oxidation numbers cannot be assigned

unambigously to many organometallic compounds, no formal oxidation numbers will be attributed to the central atoms in the

following section on organometallic nomenclature.1999,71, 1557-1585).

Also criticizing the use of oxidation states, Seddon and Seddon have written: the oxidation state concept can be thought of

as the Dewey Decimal Classification of inorganic chemistry if the rules are applied, a number is obtained. But Seddon and

Seddon continue: Does oxidation state have a chemical significance? A number is always obtained does it mean anything?(The Chemistry of Ruthenium, Seddon, E. A.; Seddon, K. R. Elsevier, New York, 1984; Chapter 2.)

In addition to problems associated with assignment of oxidation number, the assignment of coordination number is often

ambiguous because the term is interpreted with more than one meaning in the literature. For example, what is the coordination

number of chromium in (6-C6H6)2Cr? Common answers include 2, 6 and 12, depending on ones notion of coordination

number.

The problems associated with classifying molecules by oxidation number and coordination number stem from the application

of a classification system to a set of molecules for which it is not appropriate. In order to surmount problems of the types

described above, Malcolm Green introduced an innovative method for the formal classification of covalent compounds (Green,

M. L. H.J. Organomet. Chem. 1995,500, 127-148). The principal advantage of the so-called Covalent Bond Classification

(CBC) Method is that it was specifically designed for covalent molecules.

In essence, the CBC method seeks to classify a molecule according to the nature of the ligands around the central element of

interest. The method is based on the notion that there are three basic types of interaction by which a ligand may bond to a metal

center and the ligand is classified according to the nature and number of these interactions.The three basic types of interaction are represented by the symbols L, X, and Z, which correspond respectively to 2-electron, 1-

electron and 0-electronneutralligands and are clearly differentiated according to a molecular orbital representation of the

bonding.

An L -function li gandis one which interacts with a metal centervia a dative covalent bond (i.e.a coordinate bond), in which

both electrons are donated by the L ligand. As such, an L-function ligand donates two electrons to a metal center. Since the

metal uses no electrons in forming the ML bond, an L-function ligand does not influence the valence of a metal center.

Simple examples of L-type ligands include R3P, R2O, and CO,i.e.donor molecules that have lone pairs (Lewis bases).

An X-f unction l igandis one which interacts with a metal centervia a normal 2-electron covalent bond, composed of 1 electron

from the metal and 1 electron from the X ligand. As such, an X-function ligand donates one electron to a metal center. Since

the metal uses one electron in forming the MX bond, each X-function ligand raises the valence of the metal center by one

unit. Simple examples of X-type ligands include H and CH3,i.e.radicals.

A Z-function ligandalso interacts with a metal centervia a dative covalent bond, but differs from the L-function in that bothelectrons are donated by the metal rather than the ligand. As such, a Z-function ligand donates zero electrons to a metal center.

Since the metal uses two electrons in forming the MZ bond, a Z-function ligand raises the valence of the metal center by two

units. Simple examples of Z-type ligands include BF3, BR3and AlR3,i.e.molecules that have a vacant orbital (Lewis acids).

More important than merely referring to the nu mberof electrons involved in the bonding is the fact that the types of

interaction are differentiated according to thenatureof the molecular orbital interaction (see above). It is, therefore, apparent

that the CBC method is of much more relevance to classifying and providing insight into the nature ofcovalentorganometallic

molecules than are methods based on (i) oxidation number (which merely hypothetically decomposes a molecule into its

constituent ions) and (ii) electron count (that focuses only on the number of electrons, regardless of their origin).


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A given ligand may have one or more of the above functions. As such, the ligand may be classified as [XxZz], wherel,x, and

are the respective number of L, X, and Z functionalities. For example, the 6-benzene ligand is classified as [L3], with the three

L functionalities corresponding to the three olefinic moieties (see below). Likewise, the 5-cyclopentadienyl ligand is

classified as [L2X], with the two L functionalities corresponding to the two olefinic fragments while the X functionality

corresponds to the CH radical portion of the resonance structure.

At a more fundamental level than merely relating to the number of electrons a ligand donates, however, the [L lXxZz]

classification refers to thenatur of the frontier orbitalsof the neutral ligand, as illustrated for the C symmetric C H ligands

(see below).


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For example, the three highest energy occupied orbitals of the C5symmetric C5H5radical comprise a pair of doubly

degenerate orbitals (HOMO) and a nondegenerate orbital (HOMO1). The HOMO1 orbital is fully occupied and correspondsto an L function, while the HOMO is occupied by three electrons and corresponds to an L and an X function. As such, C5H5is

classified as an [L2X] ligand. The three highest energy occupied orbitals of C 6H6also comprise a pair of doubly degenerate

orbitals (HOMO) and a nondegenerate orbital (HOMO1), but since these are all occupied, C 6H6is classified as an L3ligand.

An interesting situation arises, however, with C7symmetric C7H7because the HOMO is a singly occupied doublydegenerate

orbital. As such, the HOMO is an XZ combination. Coupled with the L2nature of the fully occupied doubly degenerate

HOMO1 orbital, and the L nature of the HOMO2 orbital, the C7H7ligand is classified as L3XZ; however, this classificationreduces to L2X3because an LZ combination is equivalent to that of an X2combination. In essence, one may view the valence

state of the C7H7ligand to have three unpaired electrons, in much the same way that carbon has a sp3

valence state with four

unpaired electrons when it combines to form a tetrahedral compound.

The Equivalent Neutral Class

Once all the ligands about a metal center have been classified as described above, the molecule itself is classified as

[MLlXxZz]Q

by summing all the L-, X-, and Z- functionalities, as illustrated below for some tungsten complexes.

For example, Cp2WH2is classifed as [ML4X4] since Cp [L2X] and H [X]. Correspondingly, [Cp2WH3]+

would be

classified as [ML4X5]+

. However, in order to allow for comparisons between molecules that have different charges, it is useful


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to reduce the [MLlXxZz]Q

assignment to its equivalent neutral class, which is essentially the classification that would be

obtained if the Q charge were to be localized on the ligand and not on the metal center.

For cations, the transformations are: (i) L+

X,i.e.a cationic 2-electron donor is equivalent to a neutral 1-electron donor,

and (ii) X+

Z,i.e.a cationic 1-electron ligand is equivalent to a neutral 0electron ligand. For anions, the most commonly

encountered transformations are: (i) X

L,i.e.an anionic 1-electron donor is equivalent to a neutral 2-electron donor and

(ii) L

LX,i.e.an anionic 2-electron donor is equivalent to a 3-electron donor. It is important to emphasize that the latter

two transformations should be applied sequentially, i.e.a negative charge is only placed on an Lfunction if there is no Xfunction. Finally, if the derived classification after performing the above transformations contains both an L and a Z function,

the classification is reduced further by using the transformation LZ = X 2.A consideration of some simple compounds serves to indicate the rationale for describing a molecule in terms of its equivalent

neutral class. For example, the cationic, neutral, and anionic octahedral Co(III) species [Co(NH 3)6]3+

, [Co(NH3)3Cl3], and

[CoCl6]3_

, which are related by the formal substitution of Cl

by NH3, each belong to the same fundamental molecular class,i.e.[ML3X3] (see below). Thus, even though the compounds have different charges, the CBC method indicates that the three

molecules belong to the same class of compound.

The [MLlXxZz] classification, electron number, valence and ligand bond number

Once the [MLlXxZz] classification of a molecule is known, it is a simple matter to extract other useful information pertaining to

the nature of a molecule, including the electron count, valence, and ligand bond number (Table 1).

Table 1.Definitions pertaining to the CBC method.

Symbol Definition

L 2electron donor function

l number of L functions

X 1electron donor function

x number of X functions

Z 0electron donor function

number of Z functions

m number of electrons on neutral metal

VN valence number

VN = x + 2z

LBN ligand bond number

l + x + z

EN electron count

m+ 2l+ x

d number of electrons in nonbonding metal orbitals

n = m x 2 = m VN

For example, the electron number (EN) of the metal in [ML lXxZz],i.e.the electron count, is given by EN = m + 2l+ x, wheremis the number of valence electrons on the neutral metal atom.

The valence number (VN) of the metal center, i.e.the number of electrons that the metal uses in bonding, is VN = x + 2 . In

most organotransition metal complexes, the number of Z ligands in the equivalent neutral class is zero. As such, the valence

number is typically equal to x,i.e.the number of one-electron donor X-ligands. The value of the d configuration is given by n=m x 2 =m VN.

Finally, the ligand bond number (LBN) represents the effective total number of ligand functionssurrounding M, and is definedas LBN =l+ x + . While not defined as the coordination number, it is pertinent to note how the ligand bond number as


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defined byl+ x + gives the value that organometallic chemists want the coordination number to be in many compounds.

For example, both (5C5H5)2Cr and (

6C6H6)2Cr (i.e.ML4X2 and ML6, respectively) have a ligand bond number of six, even

though the classical definition of coordination number gives values of 10 and 12, respectively. Furthermore, it is noteworthy

that the ligand bond number reduces to the classical definition of coordination number when the ligands are simple, i.e.

monofunctional ligands that coordinate to the metal using a single orbital, e.g.H and CH3.

MLX Plots

Since the [MLlXxZz] classification contains information that relates to the electron count, the valence and ligand bond number,

it provides a greater dimension for classifying compounds than methods based on either electron count or oxidation number.

The [MLlXxZz] classification may be represented as a function of the electron count and valence number of the metal indiagrams are often simply referred to as MLX plots. An illustration of an MLX plot is provided by the example for

organometallic compounds of iron is shown below (data compiled by Cary Zachmanoglou from compounds listed in the

Dictionary of Organometallic Compounds); MLX plots for other elements are presented at the end of this article.

For example, while consideration of the electron count for iron compounds results in the conclusion that the organometallic

chemistry of iron is dominated by 18electron molecules, i.e.a single class of molecules, consideration of the MLX plot shows

that this class of molecule can be further conveniently divided into additional classes. Specifically, 18electron iron complexes

belong to [ML5], [ML4X2], and [ML3X4] classes, representatives of which are Fe(CO)5, Cp 2Fe, and [CpFe(CO)(CO)]2.

MLX plots are a characteristic of each element and are provided at the end of this article for organometallic compounds of

Groups 3 10 transition metals (Parkin, G. inComprehensive Organometallic Chemistry III, Volume 1, Chapter 1; Crabtree,R. H. and Mingos, D. M. P. (Eds), Elsevier, Oxford, 2006). In general, each element favors one or several [ML lXxZz] classes

and the three most common for each element are summarized below.

Group 3 Group 4 Group 5 Group 6 Group 7 Group 8 Group 9 Group 10

ScL4X3(36%)

TiL4X4(49%)

VL6X (22%)

VL4X4(16%)

CrL6(48%)

CrL5X2

MnL5X

(79%)

FeL4X2(69%)

CoL3X3(54%)

NiL2X2(33%)


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ScL5X3(33%)

ScL3X3(10%)

TiL5X3(9%)

TiL2X4(7%)

VL4X3(14%) (24%)

CrL4X4(7%)

MnL4X3(12%)

MnL3X5(1%)

FeL5(20%)

FeL3X4(7%)

CoL4X

(34%)

CoL2X5(4%)

NiL3X2(26%)

NiL4(16%)

YL5X3(37%)

YL6X3

(22%)YL4X3(19%)

ZrL4X4(55%)

ZrL5X4

(25%)ZrL6X2(6%)

NbL5X3(32%)

NbL6X

(17%)NbL4X5(15%)

MoL5X2(40%)

MoL4X4

(25%)MoL6(19%)

TcL5X (75%)

TcL4X3(14%)

TcL3X5(2%)

RuL4X2(79%)

RuL3X4(9%)

RuL5(8%)

RhL3X

(41%)

RhL3X3

(27%)RhL4X

(22%)

PdL2X2(81%)

PdL3X2(9%)

PdL3(4%)

LaL4X3(31%)

LaL6X3(22%)

LaL3X3(17%)

HfL4X4(58%)

HfL6X2(11%)

HfL5X4(8%)

TaL2X5(23%)

TaL4X5(15%)

TaL5X3(14%)

WL5X2(34%)

WL4X4(27%)

WL6(15%)

ReL5X (49%)

ReL4X3(29%)

ReL3X5(4%)

OsL4X2(83%)

OsL5(8%)

OsL3X4 (7%)

IrL3X3(47%)

IrL3X (26%)

IrL4X (20%)

PtL2X2(69%)

PtL2X4(11%)

PtL3(9%)

Trends elucidated from MLX plots

By summarizing a vast quantity of factual information, the MLX plot reveals important characteristics of the chemistry of the

element under consideration and the information embodied in an MLX plot enables a variety of periodic trends to be

established by comparing the distributions for the elements.

(i) Electron count

Since the electron count for a molecule of class [ML lXxZz] is given by EN = m + 2l+ x, it is a simple matter to use the

[MLlXxZz] classification to evaluate the distribution of molecules according to a specific electron count. For example, the data

indicate that 18-electron rule is most closely obeyed for the middle portion of the transition series (Groups 6 8), as

illustrated by the blue bars. Both the earlier and later transition metals exhibit many deviations from this rule.

(ii) Valence

With respect to the distribution of valence as a function of group, it is evident that the occurrence of the group valence iscommon up to Group 5, after which the two lowest valence states with an even d configuration become prevalent (see below).


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(iii) Ligand bond numberThe ligand bond number (cf.coordination number) decreases smoothly upon passing from Group 3 to Group 10 (see above).

Specifically, the most common ligand bond number decreases from 8 for Group 3 to a value of 4 for Group 10.

Summary


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In summary, the CBC method is based on an elementary molecular orbital analysis of metalligand bonding interactions and a

molecule is described in terms of the representation ML lXxZzwhere Ll, Xxand Zzrefer to the number of 2electron, 1electron,

and 0electron donor functions. By embodying the electron count (m+ 2l+ x), the valence of the metal (x+ 2 ), the ligand

bond number (l+ x + z), and the d configuration (n =m x 2 ), the MLlXxZzclassification affords much more information

than that provided by the oxidation number. Furthermore, by identifying the different types of metalligand bonding

interactions, the MLlXxZzclassification describes the nature of the metal in the molecul of interest, while the oxidation

number merely describes the charge on the metal after all li gands have been r emoved(!). Finally, since there are several

different methods used to assign oxidation numbers, there is often ambiguity in the derived values. These problems are

exacerbated for organometallic compounds and, as such, the MLlXxZzclassification provides a much more useful method of

classification for these molecules.

MLX plots for organometallic compounds of the transition metals of Groups 3 10 and distributions of electron count, valence

and ligand bond number are availablehere. For further discussion of the CBC method, see: Parkin, G. in Comprehensive

Organometallic Chemistry III, Volume 1, Chapter 1; Crabtree, R. H. and Mingos, D. M. P. (Eds), Elsevier, Oxford, 2006.
http://www.columbia.edu/cu/chemistry/groups/parkin/rightmlxz.htmhttp://www.columbia.edu/cu/chemistry/groups/parkin/rightmlxz.htm

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Dispensa Sul Covalent Bond Classification Method