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
(or other physical structure) in
atomic
or
molecular orbitals
.
[1]
For example, the electron configuration of the
neon
atom is
1s
2
2s
2
2p
6
, meaning that the 1s, 2s, and 2p
subshells
are occupied by two, two, and six electrons, respectively.
Electronic configurations describe each electron as moving independently in an
orbital
, in an average
field
created by the
nuclei
and all the other electrons. Mathematically, configurations are described by
Slater determinants
or
configuration state functions
.
According to the laws of
quantum mechanics
, a
level of energy
is associated with each electron configuration. In 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
, for describing the
chemical bonds
that hold atoms together, and in understanding the
chemical formulas
of compounds and the
geometries of molecules
. In bulk materials, this same idea helps explain the peculiar properties of
lasers
and
semiconductors
.
Shells and subshells
[
edit
]
|
s (
l
= 0)
|
p (
l
= 1)
|
|
m
= 0
|
m
= 0
|
m
= ±1
|
|
s
|
p
z
|
p
x
|
p
y
|
n
= 1
|
|
|
|
|
n
= 2
|
|
|
|
|
Electron configuration was first conceived 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
, that electrons may occupy. In each
term
of an electron configuration,
n
is the
positive integer
that precedes each
orbital letter
(
helium
's electron configuration is 1s
2
, therefore
n
= 1, and the orbital contains two electrons). An atom's
n
th electron shell can accommodate 2
n
2
electrons. For example, the first shell can accommodate two electrons, the second shell eight electrons, the third shell eighteen, and so on. The factor of two arises because the number of allowed states doubles with each successive shell 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 of ?
1
⁄
2
(with a down-arrow).
A
subshell
is the set of states defined by a common
azimuthal quantum number
,
l
, within a shell. The value of
l
is in the range from 0 to
n
? 1. The values
l
= 0, 1, 2, 3 correspond to the s, p, d, and f labels, respectively. For example, the 3d subshell has
n
= 3 and
l
= 2. The maximum number of electrons that can be placed in a subshell is given by 2(2
l
+ 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,
[a]
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
.
[2]
Notation
[
edit
]
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 1s
1
.
Lithium
has two electrons in the 1s-subshell and one in the (higher-energy) 2s-subshell, so its configuration is written 1s
2
2s
1
(pronounced "one-s-two, two-s-one").
Phosphorus
(
atomic number
15) is as follows: 1s
2
2s
2
2p
6
3s
2
3p
3
.
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 1s
2
2s
2
2p
6
, 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] 3s
2
3p
3
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] 4s
2
3d
2
or [Ar] 3d
2
4s
2
. 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 Ti
4+
, Ti
3+
, Ti
2+
, Ti
+
, Ti.
The superscript 1 for a singly occupied subshell is not compulsory; for example
aluminium
may be written as either [Ne] 3s
2
3p
1
or [Ne] 3s
2
3p. In atoms where a subshell is unoccupied despite higher subshells being occupied (as is the case in some ions, as well as certain neutral atoms shown to deviate from the
Madelung rule
), the empty subshell is either denoted with a superscript 0 or left out altogether. For example, neutral
palladium
may be written as either
[Kr] 4d
10
5s
0
or simply
[Kr] 4d
10
, and the
lanthanum(III)
ion may be written as either
[Xe] 4f
0
or simply [Xe].
[3]
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 "
s
harp
", "
p
rincipal
", "
d
iffuse
" and "
f
undamental
" (or "
f
ine"), 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 of ground state and excited states
[
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]
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 1s
2
2s
2
2p
6
3s
1
, as deduced from the Aufbau principle (see below). The first excited state is obtained by promoting a 3s electron to the 3p subshell, to obtain the
1s
2
2s
2
2p
6
3p
1
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 of sodium to the 3s level and form the excited 1s
2
2s
2
2p
5
3s
2
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
[
edit
]
Irving Langmuir
was the first to propose in his 1919 article "The Arrangement of Electrons in Atoms and Molecules" in which, building on
Gilbert N. Lewis
's
cubical atom
theory and
Walther Kossel
's chemical bonding theory, he outlined his "concentric theory of atomic structure".
[6]
Langmuir had developed his work on electron atomic structure from other chemists as is shown in the development of the
History of the periodic table
and the
Octet rule
.
Niels Bohr
(1923) incorporated Langmuir's model that the
periodicity
in the properties of the elements might be explained by the electronic structure of the atom.
[7]
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 1s
2
2s
2
2p
6
3s
2
3p
4
(2.8.6). Bohr used 4 and 6 following
Alfred Werner
's 1893 paper. In fact, the chemists accepted the concept of atoms long before the physicists. Langmuir began his paper referenced above by saying,
≪…The problem of the structure of atoms has been attacked mainly by physicists who have given little consideration to the chemical properties which must ultimately be explained by a theory of atomic structure. The vast store of knowledge of chemical properties and relationships, such as is summarized by the Periodic Table, should serve as a better foundation for a theory of atomic structure than the relatively meager experimental data along purely physical lines... These electrons arrange themselves in a series of concentric shells, the first shell containing two electrons, while all other shells tend to
hold eight
.…≫
The valence electrons in the atom were described by
Richard Abegg
in 1904.
[8]
In 1924,
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.
[9]
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
in 1923 to ask for his help in saving quantum theory (the system now known as "
old quantum theory
"). Pauli hypothesized successfully that the Zeeman effect can be explained as depending only on the response of the outermost (i.e., valence) electrons of the atom. Pauli 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):
[10]
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
[
l
],
j
[
m
l
] and
m
[
m
s
].
The
Schrodinger equation
, published in 1926, gave three of the four quantum numbers as a direct consequence of its solution for the hydrogen atom:
[a]
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),
[11]
see below) for the order in which atomic orbitals are filled with electrons.
Atoms: Aufbau principle and Madelung rule
[
edit
]
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:
[12]
- a maximum of two electrons are put into orbitals in the order of increasing orbital energy: the lowest-energy subshells are filled before electrons are placed in higher-energy orbitals.
The principle works very well (for the ground states of the atoms) for the known 118 elements, although it is sometimes slightly wrong. 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,
[11]
and later given a theoretical justification by
V. M. Klechkowski
:
[13]
- Subshells
are filled in the order of increasing
n
+
l
.
- Where two subshells 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 subshells 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
[
edit
]
The form of the
periodic table
is closely related to the atomic electron configuration for each element. For example, all the elements of
group 2
(the table's second column) have an electron configuration of [E]
n
s
2
(where [E] is a
noble gas
configuration), and have notable similarities in their chemical properties. The periodicity of the periodic table in terms of
periodic table blocks
is due to the number of electrons (2, 6, 10, and 14) needed to fill s, p, d, and f subshells. These blocks appear as the rectangular sections of the periodic table. The single exception is
helium
, which despite being an s-block atom is conventionally placed with the other
noble gasses
in the p-block due to its chemical inertness, a consequence of its full outer shell (though there is discussion in the contemporary literature on whether this exception should be retained).
The electrons in the
valence (outermost) shell
largely determine each element's
chemical properties
. The similarities in the chemical properties were remarked on more than a century before the idea of electron configuration.
[b]
Shortcomings of the aufbau principle
[
edit
]
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
[c]
(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 naive 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] 4s
1
and [Ar] 4s
2
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 (
scandium
through
zinc
) have configurations with two 4s electrons, but there are two exceptions.
Chromium
and
copper
have electron configurations [Ar] 3d
5
4s
1
and [Ar] 3d
10
4s
1
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". However, this is not supported by the facts, as
tungsten
(W) has a Madelung-following d
4
s
2
configuration and not d
5
s
1
, and
niobium
(Nb) has an anomalous d
4
s
1
configuration that does not give it a half-filled or completely filled subshell.
[14]
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.
[d]
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 Fe
4+
, Fe
3+
, Fe
2+
, 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 does not. There is no special reason why the Fe
2+
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.
[15]
More recently Scerri has argued that contrary to what is stated in the vast majority of sources including the title of his previous article on the subject, 3d orbitals rather than 4s are in fact preferentially occupied.
[16]
In chemical environments, configurations can change even more: Th
3+
as a bare ion has a configuration of [Rn] 5f
1
, yet in most Th
III
compounds the thorium atom has a 6d
1
configuration instead.
[17]
[18]
Mostly, what is present is rather a superposition of various configurations.
[14]
For instance, copper metal is poorly described by either an [Ar] 3d
10
4s
1
or an [Ar] 3d
9
4s
2
configuration, but is rather well described as a 90% contribution of the first and a 10% contribution of the second. Indeed, visible light is already enough to excite electrons in most transition metals, and they often continuously "flow" through different configurations when that happens (copper and its group are an exception).
[19]
Similar ion-like 3d
x
4s
0
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 3d
6
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,
[20]
which are an approximate method for taking account of the effect of the other electrons on orbital energies. Qualitatively, for example, the 4d elements have the greatest concentration of Madelung anomalies, because the 4d?5s gap is larger than the 3d?4s and 5d?6s gaps.
[21]
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
[22]
tend to decrease the energy of the s-orbitals in relation to the other atomic orbitals.
[23]
This is the reason why the 6d elements are predicted to have no Madelung anomalies apart from lawrencium (for which relativistic effects stabilise the p
1/2
orbital as well and cause its occupancy in the ground state), as relativity intervenes to make the 7s orbitals lower in energy than the 6d ones.
The table below shows the configurations of the f-block (green) and d-block (blue) atoms. It 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 (data page)
. However this also depends on the charge: a
calcium
atom has 4s lower in energy than 3d, but a Ca
2+
cation has 3d lower in energy than 4s. In practice the configurations predicted by the Madelung rule are at least close to the ground state even in these anomalous cases.
[24]
The empty f orbitals in lanthanum, actinium, and thorium contribute to chemical bonding,
[25]
[26]
as do the empty p orbitals in transition metals.
[27]
Vacant s, d, and f orbitals have been shown explicitly, as is occasionally done,
[28]
to emphasise the filling order and to clarify that even orbitals unoccupied in the ground state (e.g.
lanthanum
4f or
palladium
5s) may be occupied and bonding in chemical compounds. (The same is also true for the p-orbitals, which are not explicitly shown because they are only actually occupied for lawrencium in gas-phase ground states.)
The various anomalies describe the free atoms and do not necessarily predict chemical behavior. Thus for example neodymium typically forms the +3 oxidation state, despite its configuration
[Xe] 4f
4
5d
0
6s
2
that if interpreted naively would suggest a more stable +2 oxidation state corresponding to losing only the 6s electrons. Contrariwise, uranium as
[Rn] 5f
3
6d
1
7s
2
is not very stable in the +3 oxidation state either, preferring +4 and +6.
[32]
The electron-shell configuration of elements beyond
hassium
has not yet been empirically verified, but they are expected to follow Madelung's rule without exceptions until
element 120
.
Element 121
should have the anomalous configuration
[
Og
] 8s
2
5g
0
6f
0
7d
0
8p
1
, having a p rather than a g electron. Electron configurations beyond this are tentative and predictions differ between models,
[33]
but Madelung's rule is expected to break down due to the closeness in energy of the 5g, 6f, 7d, and 8p
1/2
orbitals.
[30]
That said, the filling sequence 8s, 5g, 6f, 7d, 8p is predicted to hold approximately, with perturbations due to the huge spin-orbit splitting of the 8p and 9p shells, and the huge relativistic stabilisation of the 9s shell.
[34]
Open and closed shells
[
edit
]
This section is about the concept in physics. For the software, see
Open Shell
.
In the context of
atomic orbitals
, an
open shell
is a
valence shell
which is not completely filled with
electrons
or that has not given all of its valence electrons through
chemical bonds
with other
atoms
or
molecules
during a
chemical reaction
. Conversely a
closed shell
is obtained with a completely filled valence shell. This configuration is very
stable
.
[35]
For molecules, "open shell" signifies that there are
unpaired electrons
. In
molecular orbital
theory, this leads to molecular orbitals that are singly occupied. In
computational chemistry
implementations of molecular orbital theory, open-shell molecules have to be handled by either the
restricted open-shell Hartree?Fock
method or the
unrestricted Hartree?Fock
method. Conversely a closed-shell configuration corresponds to a state where all
molecular orbitals
are either doubly occupied or empty (a
singlet state
).
[36]
Open shell molecules are more difficult to study computationally.
[37]
Noble gas configuration
[
edit
]
Noble gas configuration
is the electron configuration of
noble gases
. The basis of all
chemical reactions
is the tendency of
chemical elements
to acquire
stability
.
Main-group atoms
generally obey the
octet rule
, while
transition metals
generally obey the
18-electron rule
. The
noble gases
(
He
,
Ne
,
Ar
,
Kr
,
Xe
,
Rn
) are less
reactive
than other
elements
because they already have a noble gas configuration.
Oganesson is predicted
to be more reactive due to
relativistic effects
for heavy atoms.
Period
|
Element
|
Configuration
|
1
|
He
|
1s
2
|
|
|
|
|
|
|
2
|
Ne
|
1s
2
|
2s
2
2p
6
|
|
|
|
|
|
3
|
Ar
|
1s
2
|
2s
2
2p
6
|
3s
2
3p
6
|
|
|
|
|
4
|
Kr
|
1s
2
|
2s
2
2p
6
|
3s
2
3p
6
|
4s
2
3d
10
4p
6
|
|
|
|
5
|
Xe
|
1s
2
|
2s
2
2p
6
|
3s
2
3p
6
|
4s
2
3d
10
4p
6
|
5s
2
4d
10
5p
6
|
|
|
6
|
Rn
|
1s
2
|
2s
2
2p
6
|
3s
2
3p
6
|
4s
2
3d
10
4p
6
|
5s
2
4d
10
5p
6
|
6s
2
4f
14
5d
10
6p
6
|
|
7
|
Og
|
1s
2
|
2s
2
2p
6
|
3s
2
3p
6
|
4s
2
3d
10
4p
6
|
5s
2
4d
10
5p
6
|
6s
2
4f
14
5d
10
6p
6
|
7s
2
5f
14
6d
10
7p
6
|
Every system has the tendency to acquire the state of stability or a state of minimum energy, and so chemical elements take part in chemical reactions to acquire a stable electronic configuration similar to that of its nearest
noble gas
. An example of this tendency is two
hydrogen
(H) atoms reacting with one
oxygen
(O) atom to form
water
(H
2
O). Neutral atomic hydrogen has one electron in its
valence shell
, and on formation of water it acquires a share of a second electron coming from oxygen, so that its configuration is similar to that of its nearest noble gas
helium
(He) with two electrons in its valence shell. Similarly, neutral atomic oxygen has six electrons in its valence shell, and acquires a share of two electrons from the two hydrogen atoms, so that its configuration is similar to that of its nearest noble gas
neon
with eight electrons in its valence shell.
Electron configuration in molecules
[
edit
]
Electron configuration in molecules
is more complex than the electron configuration of atoms, as each
molecule
has a different
orbital structure
. The
molecular orbitals
are labelled according to their
symmetry
,
[e]
rather than the
atomic orbital
labels used for
atoms
and
monatomic ions
; hence, the electron configuration of the
dioxygen
molecule, O
2
, is written 1σ
g
2
1σ
u
2
2σ
g
2
2σ
u
2
3σ
g
2
1π
u
4
1π
g
2
,
[38]
[39]
or equivalently 1σ
g
2
1σ
u
2
2σ
g
2
2σ
u
2
1π
u
4
3σ
g
2
1π
g
2
.
[1]
The term 1π
g
2
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 forms 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 computational 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.
See also
[
edit
]
Notes
[
edit
]
- ^
a
b
In formal terms, the
quantum numbers
n
,
l
and
m
l
arise from the fact that the solutions to the time-independent
Schrodinger equation
for
hydrogen-like atoms
are based on
spherical harmonics
.
- ^
The similarities in chemical properties and the numerical relationship between the
atomic weights
of
calcium
,
strontium
and
barium
was first noted by
Johann Wolfgang Dobereiner
in 1817.
- ^
Electrons are
identical particles
, a fact that is sometimes referred to as "indistinguishability of electrons". A one-electron solution to a many-electron system would imply that the electrons could be distinguished from one another, and there is strong experimental evidence that they can't be. The exact solution of a many-electron system is a
n
-body problem
with
n
≥ 3 (the nucleus counts as one of the "bodies"): such problems have evaded
analytical solution
since at least the time of
Euler
.
- ^
There are some cases in the second and third series where the electron remains in an s-orbital.
- ^
The labels are written in lowercase to indicate that they correspond to one-electron functions. They are numbered consecutively for each symmetry type (
irreducible representation
in the
character table
of the
point group
for the molecule), starting from the orbital of lowest energy for that type.
References
[
edit
]
- ^
a
b
IUPAC
,
Compendium of Chemical Terminology
, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "
configuration (electronic)
".
doi
:
10.1351/goldbook.C01248
- ^
IUPAC
,
Compendium of Chemical Terminology
, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "
Pauli exclusion principle
".
doi
:
10.1351/goldbook.PT07089
- ^
Rayner-Canham, Geoff; Overton, Tina (2014).
Descriptive Inorganic Chemistry
(6 ed.). Macmillan Education. pp. 13?15.
ISBN
978-1-319-15411-0
.
- ^
Weisstein, Eric W. (2007).
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.
wolfram
.
- ^
Ebbing, Darrell D.; Gammon, Steven D. (12 January 2007).
General Chemistry
. p. 284.
ISBN
978-0-618-73879-3
.
- ^
Langmuir, Irving
(June 1919).
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.
Journal of the American Chemical Society
.
41
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doi
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10.1021/ja02227a002
.
- ^
Bohr, Niels
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.
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Bibcode
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.
S2CID
123582460
.
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Abegg, R. (1904).
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Stoner, E.C.
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Pauli, Wolfgang
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.
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a
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Madelung, Erwin
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Mathematische Hilfsmittel des Physikers
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".
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10.1351/goldbook.AT06996
- ^
Wong, D. Pan (1979). "Theoretical justification of Madelung's rule".
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.
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a
b
Scerri, Eric (2019). "Five ideas in chemical education that must die".
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.
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10.1007/s10698-018-09327-y
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104311030
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- ^
Melrose, Melvyn P.; Scerri, Eric R. (1996). "Why the 4s Orbital is Occupied before the 3d".
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:
1996JChEd..73..498M
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doi
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Scerri, Eric
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.
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. Vol. 50, no. 6.
Royal Society of Chemistry
. pp. 24?26.
Archived
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. Retrieved
12 June
2018
.
- ^
Langeslay, Ryan R.; Fieser, Megan E.; Ziller, Joseph W.; Furche, Philip; Evans, William J. (2015).
"Synthesis, structure, and reactivity of crystalline molecular complexes of the {[C
5
H
3
(SiMe
3
)
2
]
3
Th}
1?
anion containing thorium in the formal +2 oxidation state"
.
Chem. Sci
.
6
(1): 517?521.
doi
:
10.1039/C4SC03033H
.
PMC
5811171
.
PMID
29560172
.
- ^
Wickleder, Mathias S.; Fourest, Blandine; Dorhout, Peter K. (2006). "Thorium". In Morss, Lester R.; Edelstein, Norman M.; Fuger, Jean (eds.).
The Chemistry of the Actinide and Transactinide Elements
(PDF)
. Vol. 3 (3rd ed.). Dordrecht, the Netherlands: Springer. pp. 52?160.
doi
:
10.1007/1-4020-3598-5_3
. Archived from
the original
(PDF)
on 7 March 2016.
- ^
Ferrao, Luiz; Machado, Francisco Bolivar Correto; Cunha, Leonardo dos Anjos; Fernandes, Gabriel Freire Sanzovo.
"The Chemical Bond Across the Periodic Table: Part 1 ? First Row and Simple Metals"
.
ChemRxiv
.
doi
:
10.26434/chemrxiv.11860941
.
S2CID
226121612
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the original
on 1 December 2020
. Retrieved
23 August
2020
.
- ^
Meek, Terry L.; Allen, Leland C. (2002). "Configuration irregularities: deviations from the Madelung rule and inversion of orbital energy levels".
Chemical Physics Letters
.
362
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:
2002CPL...362..362M
.
doi
:
10.1016/S0009-2614(02)00919-3
.
- ^
Kulsha, Andrey (2004).
"Периодическая система химических элементов Д. И. Менделеева"
[D. I. Mendeleev's periodic system of the chemical elements]
(PDF)
.
primefan.ru
(in Russian)
. Retrieved
17 May
2020
.
- ^
IUPAC
,
Compendium of Chemical Terminology
, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "
relativistic effects
".
doi
:
10.1351/goldbook.RT07093
- ^
Pyykko, Pekka (1988). "Relativistic effects in structural chemistry".
Chemical Reviews
.
88
(3): 563?94.
doi
:
10.1021/cr00085a006
.
- ^
See the
NIST tables
- ^
Glotzel, D. (1978). "Ground-state properties of f band metals: lanthanum, cerium and thorium".
Journal of Physics F: Metal Physics
.
8
(7): L163?L168.
Bibcode
:
1978JPhF....8L.163G
.
doi
:
10.1088/0305-4608/8/7/004
.
- ^
Xu, Wei; Ji, Wen-Xin; Qiu, Yi-Xiang; Schwarz, W. H. Eugen; Wang, Shu-Guang (2013). "On structure and bonding of lanthanoid trifluorides LnF
3
(Ln = La to Lu)".
Physical Chemistry Chemical Physics
.
2013
(15): 7839?47.
Bibcode
:
2013PCCP...15.7839X
.
doi
:
10.1039/C3CP50717C
.
PMID
23598823
.
- ^
Example for platinum
- ^
See for example
this Russian periodic table poster
by A. V. Kulsha and T. A. Kolevich
- ^
Miessler, G. L.; Tarr, D. A. (1999).
Inorganic Chemistry
(2nd ed.). Prentice-Hall. p. 38.
- ^
a
b
Hoffman, Darleane C.; Lee, Diana M.; Pershina, Valeria (2006). "Transactinides and the future elements". In Morss; Edelstein, Norman M.; Fuger, Jean (eds.).
The Chemistry of the Actinide and Transactinide Elements
(3rd ed.). Dordrecht, The Netherlands:
Springer Science+Business Media
.
ISBN
978-1-4020-3555-5
.
- ^
Scerri, Eric R. (2007).
The periodic table: its story and its significance
. Oxford University Press. pp.
239
?240.
ISBN
978-0-19-530573-9
.
- ^
Jørgensen, Christian K. (1988). "Influence of rare earths on chemical understanding and classification".
Handbook on the Physics and Chemistry of Rare Earths
. Vol. 11. pp. 197?292.
doi
:
10.1016/S0168-1273(88)11007-6
.
ISBN
978-0-444-87080-3
.
- ^
Umemoto, Koichiro; Saito, Susumu (1996).
"Electronic Configurations of Superheavy Elements"
.
Journal of the Physical Society of Japan
.
65
(10): 3175?9.
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:
1996JPSJ...65.3175U
.
doi
:
10.1143/JPSJ.65.3175
. Retrieved
31 January
2021
.
- ^
Pyykko, Pekka (2016).
Is the Periodic Table all right ("PT OK")?
(PDF)
. Nobel Symposium NS160 ? Chemistry and Physics of Heavy and Superheavy Elements.
- ^
"Periodic table"
. Archived from
the original
on 3 November 2007
. Retrieved
1 November
2007
.
- ^
"Chapter 11. Configuration Interaction"
.
www.semichem.com
.
- ^
"Laboratory for Theoretical Studies of Electronic Structure and Spectroscopy of Open-Shell and Electronically Excited Species ? iOpenShell"
.
iopenshell.usc.edu
.
- ^
Levine I.N.
Quantum Chemistry
(4th ed., Prentice Hall 1991) p.376
ISBN
0-205-12770-3
- ^
Miessler G.L. and Tarr D.A.
Inorganic Chemistry
(2nd ed., Prentice Hall 1999) p.118
ISBN
0-13-841891-8
External links
[
edit
]