D electron count

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The d electron count or number of d electrons is a chemistry formalism used to describe the electron configuration of the valence electrons of a transition metal center in a coordination complex. [1] [2] The d electron count is an effective way to understand the geometry and reactivity of transition metal complexes. The formalism has been incorporated into the two major models used to describe coordination complexes; crystal field theory and ligand field theory, which is a more advanced version based on molecular orbital theory. [3] However the d electron count of an atom in a complex is often different from the d electron count of a free atom or a free ion of the same element.

Contents

Electron configurations of transition metal atoms

For free atoms, electron configurations have been determined by atomic spectroscopy. Lists of atomic energy levels and their electron configurations have been published by the National Institute of Standards and Technology (NIST) for both neutral and ionized atoms. [4]

For neutral atoms of all elements, the ground-state electron configurations are listed in general chemistry [5] and inorganic chemistry [3] : 38  textbooks. The ground-state configurations are often explained using two principles: the Aufbau principle that subshells are filled in order of increasing energy, and the Madelung rule that this order corresponds to the order of increasing values of (n + l) where n is the principal quantum number and l is the azimuthal quantum number. This rule predicts for example that the 4s orbital (n = 4, l = 0, n + l = 4) is filled before the 3d orbital (n = 3, l = 2, n + l = 5), as in titanium with configuration [Ar]4s23d2.

There are a few exceptions with only one electron (or zero for palladium) in the ns orbital in favor of completing a half or a whole d shell. The usual explanation in chemistry textbooks is that half-filled or completely filled subshells are particularly stable arrangements of electrons. [6] An example is chromium whose electron configuration is [Ar]4s13d5 with a d electron count of 5 for a half-filled d subshell, although Madelung's rule predicts [Ar]4s23d4. Similarly copper is [Ar]4s13d10 with a full d subshell, and not [Ar]4s23d9. The configuration of palladium is [Kr]4d10 with zero 5s electrons. [3] : 38  However, this explanation is not supported by the facts, as tungsten (W) has a Madelung-following d4 s2 configuration and not d5 s1, and niobium (Nb) has an anomalous d4 s1 configuration that does not give it a half-filled or completely filled subshell. [7]

When a transition metal atom loses one or more electrons to form a positive ion, overall electron repulsion is reduced and the n d orbital energy is lowered more than the (n+1) s orbital energy. The ion is formed by removal of the outer s electrons and tends to have a dn configuration, [3] : 40  even though the s subshell is added to neutral atoms before the d subshell. For example, the Ti2+ ion has the ground-state configuration [Ar]3d2 [8] with a d electron count of 2, even though the total number of electrons is the same as the neutral calcium atom which is [Ar]4s2.

In coordination complexes between an electropositive transition metal atom and an electronegative ligand, the transition metal is approximately in an ionic state as assumed in crystal field theory, so that the electron configuration and d electron count are those of the transition metal ion rather than the neutral atom.

Ligand field perspective

Ligand field scheme summarizing s-bonding in the octahedral complex [Ti(H2O)6] . LFTi(III).png
Ligand field scheme summarizing σ-bonding in the octahedral complex [Ti(H2O)6] .

According to Ligand Field Theory, the ns orbital is involved in bonding to the ligands and forms a strongly bonding orbital which has predominantly ligand character and the correspondingly strong anti-bonding orbital which is unfilled and usually well above the lowest unoccupied molecular orbital (LUMO). Since the orbitals resulting from the ns orbital are either buried in bonding or elevated well above the valence, the ns orbitals are not relevant to describing the valence. Depending on the geometry of the final complex, either all three of the np orbitals or portions of them are involved in bonding, similar to the ns orbitals. The np orbitals if any that remain non-bonding still exceed the valence of the complex. That leaves the (n − 1)d orbitals to be involved in some portion of the bonding and in the process also describes the metal complex's valence electrons. The final description of the valence is highly dependent on the complex's geometry, in turn highly dependent on the d electron count and character of the associated ligands.

For example, in the MO diagram provided for the [Ti(H2O)6]3+ the ns orbital – which is placed above (n − 1)d in the representation of atomic orbitals (AOs) – is used in a linear combination with the ligand orbitals, forming a very stable bonding orbital with significant ligand character as well as an unoccupied high energy antibonding orbital which is not shown. In this situation the complex geometry is octahedral, which means two of the d orbitals have the proper geometry to be involved in bonding. The other three d orbitals in the basic model do not have significant interactions with the ligands and remain as three degenerate non-bonding orbitals. The two orbitals that are involved in bonding form a linear combination with two ligand orbitals with the proper symmetry. This results in two filled bonding orbitals and two orbitals which are usually the lowest unoccupied molecular orbitals (LUMO) or the highest partially filled molecular orbitals – a variation on the highest occupied molecular orbitals (HOMO).

Crystal field theory is an alternative description of electronic configurations that is simplified relative to LFT. It rationalizes a number of phenomena, but does not describe bonding nor offer an explanation for why ns electrons are ionized before (n − 1)d electrons.

Tanabe–Sugano diagram

Each of the ten possible d electron counts has an associated Tanabe–Sugano diagram describing gradations of possible ligand field environments a metal center could experience in an octahedral geometry. The Tanabe–Sugano diagram with a small amount of information accurately predicts absorptions in the UV and visible electromagnetic spectrum resulting from d to d orbital electron transitions. It is these d–d transitions, ligand to metal charge transfers (LMCT), or metal to ligand charge transfers (MLCT) that generally give metals complexes their vibrant colors.

Limitation

Counting d electrons is a formalism. Often it is difficult or impossible to assign electrons and charge to the metal center or a ligand. For a high-oxidation-state metal center with a +4 charge or greater it is understood that the true charge separation is much smaller. But referring to the formal oxidation state and d electron count can still be useful when trying to understand the chemistry.

Possible d electron counts

There are many examples of every possible d electron configuration. What follows is a short description of common geometries and characteristics of each possible d electron count and representative examples.

d0
Commonly tetrahedral; however it is possible for d0 complexes to accommodate many electron pairs (bonds/coordination number) since their d orbitals are empty and well away from the 18-electron ceiling. Often colorless due to the lack of d to d transitions.
Examples: titanium tetrachloride, titanocene dichloride, Schwartz's reagent.
d1
Examples: molybdenum(V) chloride, vanadyl acetylacetonate, vanadocene dichloride, vanadium tetrachloride.
d2
Examples: titanocene dicarbonyl.
d3
Examples: Reinecke's salt.
d4
Octahedral high-spin: 4 unpaired electrons, paramagnetic, substitutionally labile.
Octahedral low-spin: 2 unpaired electrons, paramagnetic, substitutionally inert.
d5
High-spin [Fe(NO2)6] crystal field diagram CFT-High Spin Splitting Diagram-Vector.svg
High-spin [Fe(NO2)6] crystal field diagram
Low-spin [Fe(NO2)6] crystal field diagram CFT-Low Spin Splitting Diagram-Vector.svg
Low-spin [Fe(NO2)6] crystal field diagram
Octahedral high-spin: 5 unpaired electrons, paramagnetic, substitutionally labile.
Octahedral low-spin: 1 unpaired electron, paramagnetic, substitutionally inert.
Examples: potassium ferrioxalate, vanadium carbonyl.
d6
Commonly octahedral complexes in both high spin and low spin.
Octahedral high-spin: 4 unpaired electrons, paramagnetic, substitutionally labile.
Octahedral low-spin: no unpaired electrons, diamagnetic, substitutionally inert.
Examples: hexamminecobalt(III) chloride, sodium cobaltinitrite, molybdenum hexacarbonyl, ferrocene, ferroin, chromium carbonyl.
d7
Octahedral high spin: 3 unpaired electrons, paramagnetic, substitutionally labile.
Octahedral low spin: 1 unpaired electron, paramagnetic, substitutionally labile.
Examples: cobaltocene.
d8
Complexes which are d8 high-spin are usually octahedral (or tetrahedral) while low-spin d8 complexes are generally 16-electron square planar complexes. For first row transition metal complexes such as Ni2+ and Cu+ also form five-coordinate 18-electron species which vary from square pyramidal to trigonal bipyramidal.
Octahedral high spin: 2 unpaired electrons, paramagnetic, substitutionally labile.
Square planar low spin: no unpaired electrons, diamagnetic, substitutionally inert.
Examples: cisplatin, nickelocene, dichlorobis(ethylenediamine)nickel(II), iron pentacarbonyl, Zeise's salt, Vaska's complex, Wilkinson's catalyst.
d9
Stable complexes with this electron count are more common for first row (period four) transition metals center than they are for complexes based around second or third row transition metals centers. These include both four-coordinate 17-electron species and five-coordinate 19-electron species.
Examples: Schweizer's reagent.
d10
Often tetrahedral complexes limited to form 4 additional bonds (8 additional electrons) by the 18-electron ceiling. Often colorless due to the lack of d to d transitions.
Examples: tetrakis(triphenylphosphine)palladium(0), nickel carbonyl.

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<span class="mw-page-title-main">Coordination complex</span> Molecule or ion containing ligands datively bonded to a central metallic atom

A coordination complex is a chemical compound consisting of a central atom or ion, which is usually metallic and is called the coordination centre, and a surrounding array of bound molecules or ions, that are in turn known as ligands or complexing agents. Many metal-containing compounds, especially those that include transition metals, are coordination complexes.

<span class="mw-page-title-main">Inorganic chemistry</span> Field of chemistry

Inorganic chemistry deals with synthesis and behavior of inorganic and organometallic compounds. This field covers chemical compounds that are not carbon-based, which are the subjects of organic chemistry. The distinction between the two disciplines is far from absolute, as there is much overlap in the subdiscipline of organometallic chemistry. It has applications in every aspect of the chemical industry, including catalysis, materials science, pigments, surfactants, coatings, medications, fuels, and agriculture.

<span class="mw-page-title-main">Ligand</span> Ion or molecule that binds to a central metal atom to form a coordination complex

In coordination chemistry, a ligand is an ion or molecule with a functional group that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's electron pairs, often through Lewis bases. The nature of metal–ligand bonding can range from covalent to ionic. Furthermore, the metal–ligand bond order can range from one to three. Ligands are viewed as Lewis bases, although rare cases are known to involve Lewis acidic "ligands".

In chemistry, a transition metal is a chemical element in the d-block of the periodic table, though the elements of group 12 are sometimes excluded. The lanthanide and actinide elements are called inner transition metals and are sometimes considered to be transition metals as well.

<span class="mw-page-title-main">Electron configuration</span> Mode of arrangement of electrons in different shells of an atom

In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals. For example, the electron configuration of the neon atom is 1s2 2s2 2p6, meaning that the 1s, 2s and 2p subshells are occupied by 2, 2 and 6 electrons respectively.

<span class="mw-page-title-main">Octet rule</span> Chemical rule of thumb

The octet rule is a chemical rule of thumb that reflects the theory that main-group elements tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. The rule is especially applicable to carbon, nitrogen, oxygen, and the halogens; although more generally the rule is applicable for the s-block and p-block of the periodic table. Other rules exist for other elements, such as the duplet rule for hydrogen and helium, or the 18-electron rule for transition metals.

Hund's rule of maximum multiplicity is a rule based on observation of atomic spectra, which is used to predict the ground state of an atom or molecule with one or more open electronic shells. The rule states that for a given electron configuration, the lowest energy term is the one with the greatest value of spin multiplicity. This implies that if two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pairs. The rule, discovered by Friedrich Hund in 1925, is of important use in atomic chemistry, spectroscopy, and quantum chemistry, and is often abbreviated to Hund's rule, ignoring Hund's other two rules.

<span class="mw-page-title-main">Valence electron</span> An outer shell electron which is associated with an atom

In chemistry and physics, a valence electron is an electron in the outer shell associated with an atom, and that can participate in the formation of a chemical bond if the outer shell is not closed. In a single covalent bond, a shared pair forms with both atoms in the bond each contributing one valence electron.

<span class="mw-page-title-main">VSEPR theory</span> Model for predicting molecular geometry

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In molecular physics, crystal field theory (CFT) describes the breaking of degeneracies of electron orbital states, usually d or f orbitals, due to a static electric field produced by a surrounding charge distribution. This theory has been used to describe various spectroscopies of transition metal coordination complexes, in particular optical spectra (colors). CFT successfully accounts for some magnetic properties, colors, hydration enthalpies, and spinel structures of transition metal complexes, but it does not attempt to describe bonding. CFT was developed by physicists Hans Bethe and John Hasbrouck van Vleck in the 1930s. CFT was subsequently combined with molecular orbital theory to form the more realistic and complex ligand field theory (LFT), which delivers insight into the process of chemical bonding in transition metal complexes. CFT can be complicated further by breaking assumptions made of relative metal and ligand orbital energies, requiring the use of inverted ligand field theory (ILFT) to better describe bonding.

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<span class="mw-page-title-main">Square planar molecular geometry</span>

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The 18-electron rule is a chemical rule of thumb used primarily for predicting and rationalizing formulas for stable transition metal complexes, especially organometallic compounds. The rule is based on the fact that the valence orbitals in the electron configuration of transition metals consist of five (n−1)d orbitals, one ns orbital, and three np orbitals, where n is the principal quantum number. These orbitals can collectively accommodate 18 electrons as either bonding or non-bonding electron pairs. This means that the combination of these nine atomic orbitals with ligand orbitals creates nine molecular orbitals that are either metal-ligand bonding or non-bonding. When a metal complex has 18 valence electrons, it is said to have achieved the same electron configuration as the noble gas in the period, lending stability to the complex. Transition metal complexes that deviate from the rule are often interesting or useful because they tend to be more reactive. The rule is not helpful for complexes of metals that are not transition metals. The rule was first proposed by American chemist Irving Langmuir in 1921.

In coordination chemistry, Tanabe–Sugano diagrams are used to predict absorptions in the ultraviolet (UV), visible and infrared (IR) electromagnetic spectrum of coordination compounds. The results from a Tanabe–Sugano diagram analysis of a metal complex can also be compared to experimental spectroscopic data. They are qualitatively useful and can be used to approximate the value of 10Dq, the ligand field splitting energy. Tanabe–Sugano diagrams can be used for both high spin and low spin complexes, unlike Orgel diagrams, which apply only to high spin complexes. Tanabe–Sugano diagrams can also be used to predict the size of the ligand field necessary to cause high-spin to low-spin transitions.

In chemistry, crystallography, and materials science, the coordination number, also called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it. The ion/molecule/atom surrounding the central ion/molecule/atom is called a ligand. This number is determined somewhat differently for molecules than for crystals.

An electronic effect influences the structure, reactivity, or properties of molecule but is neither a traditional bond nor a steric effect. In organic chemistry, the term stereoelectronic effect is also used to emphasize the relation between the electronic structure and the geometry (stereochemistry) of a molecule.

Spin states when describing transition metal coordination complexes refers to the potential spin configurations of the central metal's d electrons. For several oxidation states, metals can adopt high-spin and low-spin configurations. The ambiguity only applies to first row metals, because second- and third-row metals are invariably low-spin. These configurations can be understood through the two major models used to describe coordination complexes; crystal field theory and ligand field theory.

Magnetochemistry is concerned with the magnetic properties of chemical compounds. Magnetic properties arise from the spin and orbital angular momentum of the electrons contained in a compound. Compounds are diamagnetic when they contain no unpaired electrons. Molecular compounds that contain one or more unpaired electrons are paramagnetic. The magnitude of the paramagnetism is expressed as an effective magnetic moment, μeff. For first-row transition metals the magnitude of μeff is, to a first approximation, a simple function of the number of unpaired electrons, the spin-only formula. In general, spin–orbit coupling causes μeff to deviate from the spin-only formula. For the heavier transition metals, lanthanides and actinides, spin–orbit coupling cannot be ignored. Exchange interaction can occur in clusters and infinite lattices, resulting in ferromagnetism, antiferromagnetism or ferrimagnetism depending on the relative orientations of the individual spins.

References

  1. ↑ Green, Malcolm L. H. (1995-09-20). "A new approach to the formal classification of covalent compounds of the elements". Journal of Organometallic Chemistry. 500 (1–2): 127–148. doi:10.1016/0022-328X(95)00508-N. ISSN   0022-328X.
  2. ↑ MLX Plots (Ged Parkin group website, Columbia University)
  3. 1 2 3 4 Miessler, Gary L.; Tarr, Donald A. (1998). Inorganic Chemistry (2nd ed.). Upper Saddle River, NJ: Pearson Education. ISBN   0-13-841891-8.
  4. ↑ NIST Atomic Spectrum Database
  5. ↑ Whitten, Kenneth W.; Galley, Kenneth D.; Davis, Raymond E. (1992). "Appendix B". General Chemistry (4th ed.). Saunders College Publishing. pp. 10–11. ISBN   0-03-072373-6. Electron Configurations of the Atoms of the Elements
  6. ↑ Petrucci, Ralph H.; Harwood, William S.; Herring, F. Geoffrey (2002). General Chemistry (8th ed.). Prentice Hall. p. 340. ISBN   0-13014329-4.
  7. ↑ Scerri, Eric (2019). "Five ideas in chemical education that must die". Foundations of Chemistry. 21: 61–69. doi:10.1007/s10698-018-09327-y. S2CID   104311030.
  8. ↑ Corliss, Charles; Sugar, Jack (15 October 2009). "Energy levels of titanium, Ti I through Ti XXII" (PDF). Journal of Physical and Chemical Reference Data. p. 20. Retrieved 5 March 2023. In this table Ti I = neutral Ti atom and Ti III = Ti2+
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