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Formal charge
Formal charge
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Formal charges in ozone and the nitrate anion

In chemistry, a formal charge (F.C. or q*), in the covalent view of chemical bonding, is the hypothetical charge assigned to an atom in a molecule, assuming that electrons in all chemical bonds are shared equally between atoms, regardless of relative electronegativity.[1][2] In simple terms, formal charge is the difference between the number of valence electrons of an atom in a neutral free state and the number assigned to that atom in a Lewis structure. When determining the best Lewis structure (or predominant resonance structure) for a molecule, the structure is chosen such that the formal charge on each of the atoms is as close to zero as possible.[2]

The formal charge of any atom in a molecule can be calculated by the following equation:

where V is the number of valence electrons of the neutral atom in isolation (in its ground state); L is the number of non-bonding valence electrons assigned to this atom in the Lewis structure of the molecule; and B is the total number of electrons shared in bonds with other atoms in the molecule.[2] It can also be found visually as shown below.

Formal charge and oxidation state both assign a number to each individual atom within a compound; they are compared and contrasted in a section below.

Examples

[edit]
  • Example: CO2 is a neutral molecule with 16 total valence electrons. There are different ways to draw the Lewis structure
    • Carbon single bonded to both oxygen atoms (carbon = +2, oxygens = −1 each, total formal charge = 0)
    • Carbon single bonded to one oxygen and double bonded to another (carbon = +1, oxygendouble = 0, oxygensingle = −1, total formal charge = 0)
    • Carbon double bonded to both oxygen atoms (carbon = 0, oxygens = 0, total formal charge = 0)

Even though all three structures gave us a total charge of zero, the final structure is the superior one because there are no charges in the molecule at all.

Pictorial method

[edit]

The following is equivalent:

  • Draw a circle around the atom for which the formal charge is requested (as with carbon dioxide, below)
  • Count up the number of electrons in the atom's "circle." Since the circle cuts the covalent bond "in half," each covalent bond counts as one electron instead of two.
  • Subtract the number of electrons in the circle from the number of valence electrons of the neutral atom in isolation (in its ground state) to determine the formal charge.
  • The formal charges computed for the remaining atoms in this Lewis structure of carbon dioxide are shown below.

It is important to keep in mind that formal charges are just that – formal, in the sense that this system is a formalism. The formal charge system is just a method to keep track of all of the valence electrons that each atom brings with it when the molecule is formed.

Usage conventions

[edit]

In organic chemistry convention, formal charges are an essential feature of a correctly rendered Lewis–Kekulé structure, and a structure omitting nonzero formal charges is considered incorrect, or at least, incomplete. Formal charges are drawn in close proximity to the atom bearing the charge. They may or may not be enclosed in a circle for clarity.

In contrast, this convention is not followed in inorganic chemistry. Many workers in organometallic and a majority of workers in coordination chemistry will omit formal charges, unless they are needed for emphasis, or they are needed to make a particular point.[3] Instead a top-right corner ⌝ will be drawn following the covalently-bound, charged entity, in turn followed immediately by the overall charge.

Three different depictions of the charges on trichloro(triphenylphosphine)palladium(1-). The first two follow the "organic" convention, by showing formal charges. In the first structure on the left, it is implied that palladium has two valence electrons (V = 2), zero lone pairs (L = 0), and eight bonding electrons (B = 8), giving a formal charge of -2 for palladium (q* = 2 - 0 - 8/2 = -2). In the second structure, the L-type ligand is depicted with a coordinate or "dative" bond to avoid additional formal charges. The dative bond in the second structure reduces the number of bonding electrons (B) by 2 for both the phosphorus and the palladium. The third structure, on the other hand, follows the "inorganic" convention, and only the total charge is given. (Note that this is arguably not an organic compound or even an organometallic compound, because the palladium is not directly bound to any carbons.)

The top-right corner ⌝ is sometimes replaced by square brackets enclosing the entire charged species, again with the total charge written in the upper right corner, just outside the brackets.

This difference in practice stems from the relatively straightforward assignment of bond order, valence electron count, and hence, formal charge for compounds only containing main-group elements (though oligomeric compounds like organolithium reagents and enolates tend to be depicted in an oversimplified and idealized manner), but transition metals have an unclear number of valence electrons so there is no unambiguous way to assign formal charges.

Formal charge compared to oxidation state

[edit]

The formal charge is a tool for estimating the distribution of electric charge within a molecule.[1][2] The concept of oxidation states constitutes a competing method to assess the distribution of electrons in molecules. If the formal charges and oxidation states of the atoms in carbon dioxide are compared, the following values are arrived at:

The reason for the difference between these values is that formal charges and oxidation states represent fundamentally different ways of looking at the distribution of electrons amongst the atoms in the molecule. With the formal charge, the electrons in each covalent bond are assumed to be split exactly evenly between the two atoms in the bond (hence the dividing by two in the method described above). The formal charge view of the CO2 molecule is essentially shown below:

The covalent (sharing) aspect of the bonding is overemphasized in the use of formal charges since in reality there is a higher electron density around the oxygen atoms due to their higher electronegativity compared to the carbon atom. This can be most effectively visualized in an electrostatic potential map.

With the oxidation state formalism, the electrons in the bonds are "awarded" to the atom with the greater electronegativity. The oxidation state view of the CO2 molecule is shown below:

Oxidation states overemphasize the ionic nature of the bonding; the difference in electronegativity between carbon and oxygen is insufficient to regard the bonds as being ionic in nature.

In reality, the distribution of electrons in the molecule lies somewhere between these two extremes. The inadequacy of the simple Lewis structure view of molecules led to the development of the more generally applicable and accurate valence bond theory of Slater, Pauling, et al., and henceforth the molecular orbital theory developed by Mulliken and Hund.


See also

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References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Formal charge

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from Grokipedia
In chemistry, formal charge is a hypothetical charge assigned to an individual atom within a molecule or ion, calculated under the assumption that all bonding electrons are shared equally between the bonded atoms, regardless of electronegativity differences. This concept allows chemists to assess electron distribution in Lewis structures without considering actual partial charges from unequal sharing. The formal charge (FC) on an atom is determined by the formula FC = V - N - (1/2)B, where V represents the number of valence electrons in a neutral atom of that element, N is the number of nonbonding (lone pair) electrons assigned to the atom, and B is the total number of bonding electrons surrounding the atom. For instance, in the carbonate ion (CO₃²⁻), the central carbon atom has V = 4, N = 0, and B = 8 (four bonds), yielding FC = 4 - 0 - 4 = 0, while each oxygen atom adjusts accordingly to reflect the overall -2 charge. The sum of all formal charges in a species must equal its net charge: zero for neutral molecules and the ionic charge for polyatomic ions. Formal charges serve as a key tool for selecting the most stable Lewis structure among possible resonance forms, prioritizing those with minimal formal charges—ideally zero—and where any negative charges reside on the most electronegative atoms. This approach, developed by Gilbert N. Lewis in 1916 and refined through subsequent early 20th-century developments in chemical bonding, aids in predicting molecular reactivity, stability, and electron delocalization in compounds like ozone (O₃) or nitrate (NO₃⁻). By minimizing formal charges, chemists can better approximate the actual electron distribution, though formal charge differs from true atomic charge, which accounts for electronegativity-induced polarization.

Fundamentals

Definition

Formal charge is a hypothetical charge assigned to an atom within a molecule or ion, calculated under the assumption that all bonding electrons are shared equally between the bonded atoms, irrespective of differences in electronegativity. This concept treats covalent bonds as if each atom contributes equally to the shared electron pairs, allowing chemists to assess the electron distribution in a structure as a simple bookkeeping device. The idea originates from Lewis electron dot structures, where atoms are represented by their valence electrons as dots, and bonds are depicted as pairs of dots shared between atoms. In these structures, formal charge ignores actual electron density shifts due to electronegativity, instead assuming a neutral covalent bond where each atom "owns" one electron from each bond pair. This approach simplifies the analysis of molecular electron arrangements without considering ionic character or polarization effects. Key components in determining formal charge include the atom's valence electrons (those available for bonding in its neutral state), non-bonding electrons (lone pairs fully assigned to the atom), and bonding electrons (shared pairs, with half assigned to the atom in this model). These elements enable a straightforward evaluation of charge assignment in Lewis diagrams. The concept of formal charge developed from the Lewis electron dot structures introduced by Gilbert N. Lewis in his 1916 paper on the octet rule and shared-pair bonding theory. Lewis's framework emphasized stable electron configurations resembling noble gases, laying the foundation for using formal charges to evaluate structure plausibility.

Purpose

The formal charge concept serves as a key tool in chemistry for evaluating the stability of Lewis structures by providing a method to assess electron distribution under the assumption of equal sharing in bonds. Structures that minimize the sum of absolute formal charges, particularly those where most atoms have a formal charge of zero, are generally considered the most stable and preferred representations of molecules. This approach allows chemists to select among possible resonance forms or alternative arrangements, favoring those that align with observed molecular behaviors without requiring advanced computational methods. Beyond stability assessment, formal charge helps distinguish between ionic and covalent bonding characteristics by modeling bonds as fully covalent, in contrast to oxidation states that assume complete electron transfer typical of ionic compounds. This distinction highlights the modeling of bonds as fully covalent in formal charge calculations, in contrast to oxidation states that assume complete electron transfer as in ionic compounds. Furthermore, it informs reactivity patterns by identifying potential nucleophilic or electrophilic sites; atoms with negative formal charges are more likely to act as nucleophiles, donating electrons, while those with positive charges serve as electrophiles, accepting them in reactions. In educational contexts, formal charge facilitates teaching electron distribution and bonding principles at an introductory level, bypassing the complexities of quantum mechanics to emphasize classical valence shell models. This bookkeeping method reinforces conceptual understanding of how electrons contribute to molecular geometry and properties, making it accessible for students learning Lewis structures.

Calculation Method

Formula

The formal charge on an atom within a Lewis structure of a molecule or ion is given by the equation FC=V−N−B2,\text{FC} = V - N - \frac{B}{2}, where VV is the number of valence electrons assigned to the neutral atom (typically equal to its group number in the periodic table for main-group elements), NN is the number of nonbonding electrons (i.e., electrons in lone pairs) assigned to that atom, and BB is the total number of bonding electrons (i.e., twice the number of bonds, since each bond consists of a shared pair of electrons) surrounding the atom. This formula derives from the principles of electron distribution in Lewis structures, where valence electrons represent the atom's inherent capacity for bonding based on its periodic table group, nonbonding electrons are those held exclusively by the atom in lone pairs (counted as 2 electrons per pair), and bonding electrons are the shared pairs in covalent bonds, with each atom formally assigned half of these shared electrons to reflect an equal division of the bond. The concept of formal charge, including this equal splitting of bonding electrons, was developed as part of G. N. Lewis's foundational work on Lewis structures in 1916, which introduced shared electron pairs and the octet rule to describe bonding and assess charge separation without implying actual electron transfer. All quantities in the formula are integers representing the count of electrons, yielding integer values for formal charge (positive, negative, or zero), and electrons are conventionally tallied in pairs within Lewis diagrams for consistency.

Step-by-Step Procedure

To calculate formal charges in a molecule or ion, begin by constructing an accurate Lewis structure that accounts for the total valence electrons contributed by all atoms, adjusted for any overall molecular charge. This ensures the electron distribution is properly represented before assigning charges to individual atoms. The procedure involves the following steps for each atom in the structure:
  1. Determine the number of valence electrons for the atom in its neutral state, which corresponds to its group number in the periodic table for main-group elements.
  2. Identify and count the nonbonding electrons (lone pairs) directly assigned to that atom in the Lewis structure.
  3. Count the total number of bonding electrons surrounding the atom (twice the number of bonds, since each bond consists of two electrons), then divide by two to find the atom's assigned share of those bonding electrons.
  4. Subtract the number of nonbonding electrons and the atom's share of bonding electrons from the number of valence electrons to obtain the formal charge for that atom.
  5. Repeat the calculation for every atom in the structure, then sum the formal charges; the total should equal zero for a neutral molecule or match the overall charge of an ion to verify the structure's validity.
This verification step confirms the consistency of the electron bookkeeping and helps identify any errors in the Lewis structure.

Applications

In Lewis Structures

Formal charge plays a crucial role in the construction and evaluation of Lewis structures by providing a method to assess the relative stability of different possible diagrams for a given molecule or ion. When multiple Lewis structures can be drawn that satisfy the octet rule, the preferred structure is the one that minimizes the absolute values of the formal charges on the atoms, ideally resulting in all formal charges being zero. Additionally, any negative formal charges should be placed on the most electronegative atoms to better reflect the electron distribution in the molecule. This approach ensures the selected structure aligns more closely with the actual bonding and electron density. A fundamental rule in applying formal charge to Lewis structures is that the sum of the formal charges on all atoms must equal the overall charge of the molecular species; for neutral molecules, this sum is zero, while for ions, it matches the ion's charge. This conservation principle serves as a quick check for the validity of a proposed Lewis structure. If the sum does not match, the structure is incorrect and must be revised. To illustrate the workflow, consider carbon dioxide (CO₂), a neutral molecule with several possible Lewis representations. One structure features carbon double-bonded to both oxygen atoms (O=C=O), where the formal charge on carbon is calculated as 4 valence electrons minus 0 nonbonding electrons minus half of 8 bonding electrons, yielding zero; each oxygen similarly has a formal charge of zero (6 - 4 - 4). Alternative structures, such as O≡C–O with a triple bond to one oxygen and a single bond to the other, result in formal charges of +1 on carbon, 0 on the triple-bonded oxygen, and -1 on the single-bonded oxygen. The double-bonded structure is preferred because it has the lowest absolute formal charges (all zero) and avoids positive charge on the less electronegative carbon. Formal charge integrates seamlessly with the octet rule during Lewis structure development: initial diagrams are sketched to distribute valence electrons such that most atoms achieve eight electrons in their valence shells through bonds and lone pairs, after which formal charges are computed to identify adjustments. Lone pairs may be converted to bonding pairs (or vice versa) to reduce high formal charges while preserving octets where possible, leading to the most stable configuration. This iterative process, which relies on the step-by-step formal charge calculation procedure, refines the structure without violating valence electron totals. In hypervalent molecules, where the central atom exceeds the octet rule, formal charge analysis confirms the viability of expanded octet structures. For instance, in sulfur hexafluoride (SF₆), the central sulfur atom bonds to six fluorines with no lone pairs on sulfur, resulting in a formal charge of zero on sulfur (6 valence electrons minus 0 nonbonding minus half of 12 bonding electrons) and zero on each fluorine, validating this arrangement despite the 12 electrons around sulfur. However, hypervalent molecules like the sulfate ion (SO₄²⁻) may show positive formal charges on the central atom in certain resonance forms, such as +2 on sulfur, highlighting how formal charge guides the depiction of such expanded systems.

In Resonance and Bonding Analysis

Formal charge plays a crucial role in analyzing resonance structures by helping to identify the most stable contributors to the resonance hybrid, which in turn informs the prediction of partial charges and bond properties. In molecules exhibiting resonance, such as ozone (O₃), the formal charges calculated for each contributing Lewis structure are averaged to approximate the partial charges on the atoms in the hybrid form. For ozone, the two primary resonance structures each assign a formal charge of +1 to the central oxygen and -1 to one terminal oxygen, with the other terminal oxygen at 0; averaging these yields partial charges of +1 on the central oxygen and -0.5 on each terminal oxygen, reflecting the delocalized electron distribution. This averaging also aids in determining bond orders, as structures with minimal formal charge differences—such as small magnitudes or separations between positive and negative charges—contribute more significantly to the hybrid, influencing the effective bond strength. Resonance forms that minimize formal charges or avoid placing like charges on adjacent atoms are deemed more stable and thus weighted more heavily, leading to fractional bond orders that indicate intermediate bond lengths and strengths between single and double bonds. For instance, in the nitrate ion (NO₃⁻), the three equivalent resonance structures each show a formal charge of +1 on nitrogen and -1 on one oxygen (with the others at 0), resulting in an averaged partial charge of +1 on nitrogen and -⅔ on each oxygen; this equivalence underscores the delocalized nature of the bonds, yielding a bond order of 1.333 for each N-O linkage and explaining their uniformity. In the context of aromaticity, formal charge analysis highlights the stability of systems like benzene, where the two Kekulé resonance structures exhibit identical formal charges of zero on all atoms, allowing equal contribution and producing a uniform bond order of 1.5 across the ring; this symmetry and lack of charge separation contribute to the enhanced stability characteristic of aromatic compounds. However, while formal charge provides a useful bookkeeping tool for these analyses, it offers a simplified approximation and overlooks the true electron density distribution in the molecule, which may require advanced computational approaches for precise evaluation (as discussed in later sections).

Comparisons and Limitations

With Oxidation State

Formal charge and oxidation state represent two distinct methods for assigning charges to atoms in chemical compounds, differing fundamentally in how bonding electrons are allocated. In calculating formal charge, bonding electrons are assumed to be shared equally between the bonded atoms, regardless of electronegativity differences. In contrast, oxidation state assigns all bonding electrons to the more electronegative atom, treating bonds as fully ionic. This ionic model in oxidation states emphasizes the hypothetical charge an atom would have if all bonds were completely polarized. A clear example of this distinction appears in the water molecule (H₂O). The formal charges are zero for both the oxygen and hydrogen atoms, as the bonding electrons are equally divided and the octet on oxygen is satisfied without excess or deficit. However, the oxidation state of oxygen is -2, as it is assigned both electrons from each O-H bond due to its higher electronegativity, while each hydrogen has an oxidation state of +1. This highlights how formal charge reflects a covalent sharing model, whereas oxidation state imposes an ionic perspective. The primary purposes of these concepts also diverge. Oxidation states are essential for tracking electron transfer in redox reactions and balancing chemical equations, providing insight into an atom's degree of oxidation or reduction. Formal charges, on the other hand, aid in evaluating the stability and plausibility of Lewis structures, helping chemists select the most representative resonance form by minimizing charge separation. Formal charge and oxidation state align in cases of purely ionic compounds, where there are no shared electrons to divide. For instance, in sodium chloride (NaCl), the formal charge on Na⁺ is +1 and on Cl⁻ is -1, matching their oxidation states exactly, as the bond is fully ionic with complete electron transfer. Historically, the concept of oxidation states predates formal charge, originating in the late 18th and early 19th centuries from Antoine Lavoisier's oxygen-based dualistic theory of chemistry, which was later expanded electrochemically by Jöns Jacob Berzelius. Formal charge emerged later in the early 20th century as part of the development of Lewis electron-pair bonding models.

With Partial Charge

Partial charges, also known as atomic charges, are fractional values that estimate the uneven distribution of electron density around atoms in a molecule, derived from quantum mechanical methods like Mulliken population analysis or empirical approaches based on electronegativity differences. These charges reflect the actual electron density, capturing the partial ionic character of bonds due to differences in atomic electronegativities, in contrast to formal charges, which treat bonding electrons as equally shared and yield integer values independent of such differences. A key distinction is that formal charges serve as a simplified approximation for Lewis structure analysis, while partial charges provide a more nuanced view of electron distribution; for instance, in the hydrogen fluoride (HF) molecule, the Lewis structure assigns zero formal charge to both hydrogen and fluorine, but Mulliken population analysis typically yields partial charges of approximately +0.4 e on hydrogen and -0.4 e on fluorine, highlighting the bond's polarity. This difference stems from formal charge's neglect of electronegativity, which causes it to overlook the electron shift toward the more electronegative atom in polar bonds like H–F. Partial charges find primary use in computational chemistry for modeling properties sensitive to electron density, such as dipole moments in spectroscopy and molecular polarizability in intermolecular interactions, whereas formal charges are favored for rapid qualitative assessments of bonding and valence in organic structures.

Limitations

Formal charge, while useful for analyzing Lewis structures, has notable limitations, particularly in hypervalent molecules where it often suggests expanded octets that do not align with modern bonding descriptions. For instance, in phosphorus pentachloride (PCl₅), the central phosphorus atom is assigned a formal charge of 0 in the standard Lewis representation, depicting 10 electrons around phosphorus and implying hypervalency through d-orbital involvement. However, quantum chemical analyses, such as those using the quantum theory of atoms in molecules (QTAIM), reveal that the actual electron density on phosphorus remains close to an octet due to significant ionic character in the P–Cl bonds, rendering the formal charge misleading. The debate over d-orbital participation further underscores this issue; early models invoked dsp³ hybridization, but contemporary studies demonstrate that d-orbitals serve primarily as polarization functions rather than active bonding orbitals, challenging the hypervalent interpretation derived from formal charges. Another shortcoming arises in systems involving transition metals, where formal charge neglects the influence of electronegativity differences and electron delocalization, leading to oversimplified views of bonding. In transition metal complexes, electrons are often delocalized across metal-ligand interactions via π-backbonding or other mechanisms, but formal charge treats bonds as equal shares, ignoring how higher electronegativity of ligands shifts electron density. This results in formal charges that do not reflect the true partial ionic character or the nuanced electron distribution observed in molecular orbital descriptions. For example, in carbonyl complexes like Ni(CO)₄, formal charge assigns a +6 charge to Ni, which does not reflect the actual partial negative charge on the metal due to backbonding delocalization. The conventional preference for Lewis structures with minimal or zero formal charges can also promote incorrect representations, especially in radicals or resonance hybrids. An overemphasis on achieving zero formal charges may favor localized structures that ignore resonance stabilization, as seen in species like the allyl cation, where delocalized forms with non-zero formal charges on terminal carbons better capture the actual electron distribution and reactivity. In computational chemistry, formal charge proves inadequate for quantitative simulations, as it provides discrete integer values that fail to capture the continuous nature of electron distribution needed for accurate force fields or electrostatic potentials. Partial charges, derived from methods like Mulliken population analysis or CHELPG, are preferred because they account for bond polarity and delocalization, enabling better modeling of intermolecular interactions and molecular properties in techniques such as molecular dynamics or density functional theory. Finally, the formal charge concept originated in the pre-quantum mechanical era of Lewis structures (circa 1916), making it inherently limited for frameworks like molecular orbital theory, which emphasize delocalized electrons over localized pairs. Developed before the advent of wavefunction-based quantum mechanics in the 1920s, it relies on a valence-shell approximation that does not incorporate orbital overlap or hybridization as rigorously as modern theories, rendering it outdated for detailed electronic structure analysis.

References

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