Electron configuration Shells, subshells, ground state and excited states
In atomic physics and quantum chemistry, the electron configuration is
the distribution of electrons of an atom or molecule (or other physical
structure) in atomic or molecular
orbitals. For example, the electron
configuration of the neon atom is 1s2 2s2 2p6.
Electronic configurations describe electrons as each moving independently
in an orbital, in an average field created by all other orbitals.
Mathematically, configurations are described by Slater determinants or configuration
state functions.
According to the laws of quantum mechanics, for systems with only one
electron, an energy is associated with each electron configuration and, upon
certain conditions, electrons are able to move from one configuration to
another by the emission or absorption of a quantum of energy, in the form of a
photon.
Knowledge of the electron configuration of different atoms is useful in
understanding the structure of the periodic table of elements. This is also
useful for describing the chemical bonds that hold atoms together. In bulk
materials, this same idea helps explain the peculiar properties of lasers and
semiconductors.
Shells and subshells
s (â„“=0) | p (â„“=1) | |||
---|---|---|---|---|
m=0 | m=0 | m=±1 | ||
s | pz | px | py | |
n=1 | ||||
n=2 |
Electron configuration was first conceived of under the Bohr model of the
atom, and it is still common to speak of shells and subshells despite the
advances in understanding of the quantum-mechanical nature of electrons.
An electron shell is the set of allowed states that share the same
principal quantum number, n (the number before the letter in the orbital
label), that electrons may occupy. An atom's nth electron shell can accommodate
2n2 electrons, e.g. the first shell can accommodate 2 electrons, the second
shell 8 electrons, and the third shell 18 electrons. The factor of two arises
because the allowed states are doubled due to electron spin—each atomic orbital
admits up to two otherwise identical electrons with opposite spin, one with a
spin +1/2 (usually denoted by an up-arrow) and one with a spin −1/2 (with a
down-arrow).
A subshell is the set of states defined by a common azimuthal quantum
number, â„“, within a shell. The values â„“ = 0, 1, 2, 3 correspond to the s, p, d,
and f labels, respectively. For example the 3d subshell has n = 3 and â„“ = 2.
The maximum number of electrons that can be placed in a subshell is given by
2(2â„“+1). This gives two electrons in an s subshell, six electrons in a p
subshell, ten electrons in a d subshell and fourteen electrons in an f
subshell.
The numbers of electrons that can occupy each shell and each subshell
arise from the equations of quantum mechanics,[2] in particular the Pauli
exclusion principle, which states that no two electrons in the same atom can
have the same values of the four quantum numbers.
Notation
Physicists and chemists use a standard notation to indicate the electron
configurations of atoms and molecules. For atoms, the notation consists of a
sequence of atomic subshell labels (e.g. for phosphorus the sequence 1s, 2s,
2p, 3s, 3p) with the number of electrons assigned to each subshell placed as a
superscript. For example, hydrogen has one electron in the s-orbital of the
first shell, so its configuration is written 1s1. Lithium has two electrons in
the 1s-subshell and one in the (higher-energy) 2s-subshell, so its
configuration is written 1s2 2s1 (pronounced "one-s-two, two-s-one").
Phosphorus (atomic number 15) is as follows: 1s2 2s2 2p6 3s2 3p3.
For atoms with many electrons, this notation can become lengthy and so an
abbreviated notation is used. The electron configuration can be visualized as
the core electrons, equivalent to the noble gas of the preceding period, and
the valence electrons: each element in a period differs only by the last few
subshells. Phosphorus, for instance, is in the third period. It differs from
the second-period neon, whose configuration is 1s2 2s2 2p6, only by the
presence of a third shell. The portion of its configuration that is equivalent
to neon is abbreviated as [Ne], allowing the configuration of phosphorus to be
written as [Ne] 3s2 3p3 rather than writing out the details of the
configuration of neon explicitly. This convention is useful as it is the
electrons in the outermost shell that most determine the chemistry of the
element.
For a given configuration, the order of writing the orbitals is not
completely fixed since only the orbital occupancies have physical significance.
For example, the electron configuration of the titanium ground state can be
written as either [Ar] 4s2 3d2 or [Ar] 3d2 4s2. The first notation follows the
order based on the Madelung rule for the configurations of neutral atoms; 4s is
filled before 3d in the sequence Ar, K, Ca, Sc, Ti. The second notation groups
all orbitals with the same value of n together, corresponding to the
"spectroscopic" order of orbital energies that is the reverse of the
order in which electrons are removed from a given atom to form positive ions;
3d is filled before 4s in the sequence Ti4+, Ti3+, Ti2+, Ti+, Ti.
The superscript 1 for a singly occupied subshell is not compulsory; for
example aluminium may be written as either [Ne] 3s2 3p1 or [Ne] 3s2 3p. It is
quite common to see the letters of the orbital labels (s, p, d, f) written in
an italic or slanting typeface, although the International Union of Pure and
Applied Chemistry (IUPAC) recommends a normal typeface (as used here). The
choice of letters originates from a now-obsolete system of categorizing
spectral lines as "sharp", "principal", "diffuse"
and "fundamental" (or "fine"), based on their observed fine
structure: their modern usage indicates orbitals with an azimuthal quantum
number, l, of 0, 1, 2 or 3 respectively. After "f", the sequence
continues alphabetically "g", "h", "i"... (l = 4,
5, 6...), skipping "j", although orbitals of these types are rarely
required.[4][5]
The electron configurations of molecules are written in a similar way,
except that molecular orbital labels are used instead of atomic orbital labels
(see below).
Energy — ground state and excited states
The energy associated to an electron is that of its orbital. The energy
of a configuration is often approximated as the sum of the energy of each
electron, neglecting the electron-electron interactions. The configuration that
corresponds to the lowest electronic energy is called the ground state. Any
other configuration is an excited state.
As an example, the ground state configuration of the sodium atom is
1s22s22p63s, as deduced from the Aufbau principle (see below). The first
excited state is obtained by promoting a 3s electron to the 3p orbital, to
obtain the 1s22s22p63p configuration, abbreviated as the 3p level. Atoms can
move from one configuration to another by absorbing or emitting energy. In a
sodium-vapor lamp for example, sodium atoms are excited to the 3p level by an
electrical discharge, and return to the ground state by emitting yellow light
of wavelength 589 nm.
Usually, the excitation of valence electrons (such as 3s for sodium)
involves energies corresponding to photons of visible or ultraviolet light. The
excitation of core electrons is possible, but requires much higher energies,
generally corresponding to x-ray photons. This would be the case for example to
excite a 2p electron to the 3s level and form the excited 1s22s22p53s2
configuration.
The remainder of this article deals only with the ground-state
configuration, often referred to as "the" configuration of an atom or
molecule.
History
Niels Bohr (1923) was the first to propose that the periodicity in the
properties of the elements might be explained by the electronic structure of
the atom.
His proposals were based on the then current Bohr model of the
atom, in which the electron shells were orbits at a fixed distance from the
nucleus. Bohr's original configurations would seem strange to a present-day
chemist: sulfur was given as 2.4.4.6 instead of 1s2 2s2 2p6 3s2 3p4 (2.8.6).
The following year, E. C. Stoner incorporated Sommerfeld's third quantum
number into the description of electron shells, and correctly predicted the
shell structure of sulfur to be 2.8.6.
However neither Bohr's system nor
Stoner's could correctly describe the changes in atomic spectra in a magnetic
field (the Zeeman effect).
Bohr was well aware of this shortcoming (and others), and had written to
his friend Wolfgang Pauli to ask for his help in saving quantum theory (the
system now known as "old quantum theory"). Pauli realized that the
Zeeman effect must be due only to the outermost electrons of the atom, and was
able to reproduce Stoner's shell structure, but with the correct structure of
subshells, by his inclusion of a fourth quantum number and his exclusion
principle (1925)
It should be forbidden for more than one electron with the same value of
the main quantum number n to have the same value for the other three quantum
numbers k , j [ml] and m [ms].
The Schrödinger equation, published in 1926, gave three of the four
quantum numbers as a direct consequence of its solution for the hydrogen
atom:[2] this solution yields the atomic orbitals that are shown today in
textbooks of chemistry (and above). The examination of atomic spectra allowed
the electron configurations of atoms to be determined experimentally, and led
to an empirical rule (known as Madelung's rule (1936),see below) for the
order in which atomic orbitals are filled with electrons.
Atoms: Aufbau principle and Madelung rule
The Aufbau principle (from the German Aufbau, "building up,
construction") was an important part of Bohr's original concept of
electron configuration. It may be stated as:
a maximum of two electrons are put into orbitals in the order of
increasing orbital energy: the lowest-energy orbitals are filled before
electrons are placed in higher-energy orbitals.
The principle works very well (for the ground states of the atoms) for
the first 18 elements, then decreasingly well for the following 100 elements.
The modern form of the Aufbau principle describes an order of orbital energies
given by Madelung's rule (or Klechkowski's rule). This rule was first stated by
Charles Janet in 1929, rediscovered by Erwin Madelung in 1936,[9] and later
given a theoretical justification by V.M. Klechkowski.
Orbitals are filled in the order of increasing n+l;
Where two orbitals have the same value of n+l, they are filled in order
of increasing n.
This gives the following order for filling the orbitals:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d,
7p, (8s, 5g, 6f, 7d, 8p, and 9s)
In this list the orbitals in parentheses are not occupied in the ground
state of the heaviest atom now known (Og, Z = 118).
The Aufbau principle can be applied, in a modified form, to the protons
and neutrons in the atomic nucleus, as in the shell model of nuclear physics
and nuclear chemistry.
Periodic table
The form of the periodic table is closely related to the electron
configuration of the atoms of the elements. For example, all the elements of
group 2 have an electron configuration of [E] ns2(where [E] is an inert gas
configuration), and have notable similarities in their chemical properties. In
general, the periodicity of the periodic table in terms of periodic table
blocks is clearly due to the number of electrons (2, 6, 10, 14...) needed to
fill s, p, d, and f subshells.
The outermost electron shell is often referred to as the "valence
shell" and (to a first approximation) determines the chemical properties.
It should be remembered that the similarities in the chemical properties were
remarked on more than a century before the idea of electron configuration.[12]
It is not clear how far Madelung's rule explains (rather than simply describes)
the periodic table,[13] although some properties (such as the common +2
oxidation state in the first row of the transition metals) would obviously be
different with a different order of orbital filling.
Shortcomings of the Aufbau principle
The Aufbau principle rests on a fundamental postulate that the order of
orbital energies is fixed, both for a given element and between different
elements; in both cases this is only approximately true. It considers atomic
orbitals as "boxes" of fixed energy into which can be placed two
electrons and no more. However, the energy of an electron "in" an
atomic orbital depends on the energies of all the other electrons of the atom
(or ion, or molecule, etc.). There are no "one-electron solutions"
for systems of more than one electron, only a set of many-electron solutions
that cannot be calculated exactly[14] (although there are mathematical
approximations available, such as the Hartree–Fock method).
The fact that the Aufbau principle is based on an approximation can be
seen from the fact that there is an almost-fixed filling order at all, that,
within a given shell, the s-orbital is always filled before the p-orbitals. In
a hydrogen-like atom, which only has one electron, the s-orbital and the
p-orbitals of the same shell have exactly the same energy, to a very good approximation
in the absence of external electromagnetic fields. (However, in a real hydrogen
atom, the energy levels are slightly split by the magnetic field of the
nucleus, and by the quantum electrodynamic effects of the Lamb shift.)
Ionization of the transition metals[edit]
The naïve application of the Aufbau principle leads to a well-known
paradox (or apparent paradox) in the basic chemistry of the transition metals.
Potassium and calcium appear in the periodic table before the transition
metals, and have electron configurations [Ar] 4s1 and [Ar] 4s2 respectively,
i.e. the 4s-orbital is filled before the 3d-orbital. This is in line with
Madelung's rule, as the 4s-orbital has n+l
= 4 (n = 4, l = 0) while the 3d-orbital has n+l = 5 (n = 3, l = 2). After calcium, most
neutral atoms in the first series of transition metals (Sc-Zn) have
configurations with two 4s electrons, but there are two exceptions. Chromium
and copper have electron configurations [Ar] 3d5 4s1 and [Ar] 3d10 4s1
respectively, i.e. one electron has passed from the 4s-orbital to a 3d-orbital
to generate a half-filled or filled subshell. In this case, the usual
explanation is that "half-filled or completely filled subshells are
particularly stable arrangements of electrons".
The apparent paradox arises when electrons are removed from the
transition metal atoms to form ions. The first electrons to be ionized come not
from the 3d-orbital, as one would expect if it were "higher in
energy", but from the 4s-orbital. This interchange of electrons between 4s
and 3d is found for all atoms of the first series of transition metals.[15] The
configurations of the neutral atoms (K, Ca, Sc, Ti, V, Cr, ...) usually follow
the order 1s, 2s, 2p, 3s, 3p, 4s, 3d, ...; however the successive stages of
ionization of a given atom (such as Fe4+, Fe3+, Fe2+, Fe+, Fe) usually follow
the order 1s, 2s, 2p, 3s, 3p, 3d, 4s, ...
This phenomenon is only paradoxical if it is assumed that the energy
order of atomic orbitals is fixed and unaffected by the nuclear charge or by the
presence of electrons in other orbitals. If that were the case, the 3d-orbital
would have the same energy as the 3p-orbital, as it does in hydrogen, yet it
clearly doesn't. There is no special reason why the Fe2+ ion should have the
same electron configuration as the chromium atom, given that iron has two more
protons in its nucleus than chromium, and that the chemistry of the two species
is very different. Melrose and Eric Scerri have analyzed the changes of orbital
energy with orbital occupations in terms of the two-electron repulsion
integrals of the Hartree-Fock method of atomic structure calculation.[16]
Similar ion-like 3dx4s0 configurations occur in transition metal
complexes as described by the simple crystal field theory, even if the metal
has oxidation state 0. For example, chromium hexacarbonyl can be described as a
chromium atom (not ion) surrounded by six carbon monoxide ligands. The electron
configuration of the central chromium atom is described as 3d6 with the six
electrons filling the three lower-energy d orbitals between the ligands. The
other two d orbitals are at higher energy due to the crystal field of the
ligands. This picture is consistent with the experimental fact that the complex
is diamagnetic, meaning that it has no unpaired electrons. However, in a more
accurate description using molecular orbital theory, the d-like orbitals
occupied by the six electrons are no longer identical with the d orbitals of
the free atom.
Other exceptions to Madelung's rule[edit]
There are several more exceptions to Madelung's rule among the heavier
elements, and as atomic number increases it becomes more and more difficult to
find simple explanations such as the stability of half-filled subshells. It is
possible to predict most of the exceptions by Hartree–Fock calculations,[17]
which are an approximate method for taking account of the effect of the other
electrons on orbital energies. For the heavier elements, it is also necessary
to take account of the effects of Special Relativity on the energies of the
atomic orbitals, as the inner-shell electrons are moving at speeds approaching
the speed of light. In general, these relativistic effects[18] tend to decrease
the energy of the s-orbitals in relation to the other atomic orbitals.[19] The
table below shows the ground state configuration in terms of orbital occupancy,
but it does not show the ground state in terms of the sequence of orbital
energies as determined spectroscopically. For example, in the transition
metals, the 4s orbital is of a higher energy than the 3d orbitals; and in the
lanthanides, the 6s is higher than the 4f and 5d. The ground states can be seen
in the Electron configurations of the elements below
view tableElectron configuration in molecules
In molecules, the situation becomes more complex, as each molecule has a
different orbital structure. The molecular orbitals are labelled according to
their symmetry,[23] rather than the atomic orbital labels used for atoms and
monatomic ions: hence, the electron configuration of the dioxygen molecule, O2,
is written 1σg2 1σu2 2σg2 2σu2 3σg2 1πu4 1πg2,[24][25] or equivalently 1σg2
1σu2 2σg2 2σu2 1πu4 3σg2 1πg2.
The term 1Ï€g2 represents the two electrons in
the two degenerate π*-orbitals (antibonding). From Hund's rules, these
electrons have parallel spins in the ground state, and so dioxygen has a net
magnetic moment (it is paramagnetic). The explanation of the paramagnetism of
dioxygen was a major success for molecular orbital theory.
The electronic configuration of polyatomic molecules can change without
absorption or emission of a photon through vibronic couplings.
Electron configuration in solids[edit
In a solid, the electron states become very numerous. They cease to be
discrete, and effectively blend into continuous ranges of possible states (an
electron band). The notion of electron configuration ceases to be relevant, and
yields to band theory.
Applications[edit]
The most widespread application of electron configurations is in the
rationalization of chemical properties, in both inorganic and organic
chemistry. In effect, electron configurations, along with some simplified form
of molecular orbital theory, have become the modern equivalent of the valence
concept, describing the number and type of chemical bonds that an atom can be
expected to form.
This approach is taken further in computational chemistry, which
typically attempts to make quantitative estimates of chemical properties. For
many years, most such calculations relied upon the "linear combination of
atomic orbitals" (LCAO) approximation, using an ever-larger and more
complex basis set of atomic orbitals as the starting point. The last step in
such a calculation is the assignment of electrons among the molecular orbitals
according to the Aufbau principle. Not all methods in calculational chemistry
rely on electron configuration: density functional theory (DFT) is an important
example of a method that discards the model.
For atoms or molecules with more than one electron, the motion of
electrons are correlated and such a picture is no longer exact. A very large
number of electronic configurations are needed to exactly describe any
multi-electron system, and no energy can be associated with one single
configuration. However, the electronic wave function is usually dominated by a
very small number of configurations and therefore the notion of electronic
configuration remains essential for multi-electron systems.
A fundamental application of electron configurations is in the
interpretation of atomic spectra. In this case, it is necessary to supplement
the electron configuration with one or more term symbols, which describe the
different energy levels available to an atom. Term symbols can be calculated
for any electron configuration, not just the ground-state configuration listed
in tables, although not all the energy levels are observed in practice. It is
through the analysis of atomic spectra that the ground-state electron
configurations of the elements were experimentally determined.
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