Electron configuration

Electron atomic and molecular orbitals

In atomic physics and quantum chemistry, electron configuration is the arrangement of electrons of an atom, a molecule, or other physical structure.^[1] It concerns the way electrons can be distributed in the orbitals of the given system (atomic or molecular for instance).
Like other elementary particles, the electron is subject to the laws of quantum mechanics, and exhibits both particle-like and wave-like nature. Formally, the quantum state of a particular electron is defined by its wave function, a complex-valued function of space and time. According to the Copenhagen interpretation of quantum mechanics, the position of a particular electron is not well defined until an act of measurement causes it to be detected. The probability that the act of measurement will detect the electron at a particular point in space is proportional to the square of the absolute value of the wavefunction at that point.
An energy is associated to each electron configuration and, upon certain conditions, electrons are able to move from one orbital to another by 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. The concept 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

Electron configuration table

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 electrons may occupy which share the same principal quantum number, n (the number before the letter in the orbital label). An electron shell can accommodate 2n² electrons, i.e. the first shell can accommodate 2 electrons, the second shell 8 electrons, the third shell 18 electrons, etc. 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 noted 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, l, within a shell. The values l = 0, 1, 2, 3 correspond to the s, p, d, and f labels, respectively. The number of electrons which can be placed in a subshell is given by 2(2l + 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.^[3]

Notation

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 was the first to propose (1923) that the periodicity in the properties of the elements might be explained by the electronic structure of the atom.^[5] 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.^[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):^[7]

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 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 which 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),^[8] see below) for the order in which atomic orbitals are filled with electrons.

Aufbau principle

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:^[9]

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 approximate order of filling of atomic orbitals, following the arrows.

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, first stated by Erwin Madelung in 1936.^[8]^[10]

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, and 7p

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.

The 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. 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 more than a century before the idea of electron configuration,^[11] It is not clear how far Madelung's rule explains (rather than simply describes) the periodic table,^[12] 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: neither of these is true (although they are approximately true enough for the principle to be useful). 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 which cannot be calculated exactly^[13] (although there are mathematical approximations available, such 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

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] 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). However, 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. The same is true when chemical compounds are formed. Chromium hexacarbonyl can be described as a chromium atom (not ion, it is in the oxidation state 0) surrounded by six carbon monoxide ligands: it is diamagnetic, and the electron configuration of the central chromium atom is described as 3d⁶, i.e. the electron which was in the 4s-orbital in the free atom has passed into a 3d-orbital on forming the compound. This interchange of electrons between 4s and 3d is universal among the first series of the transition metals.^[14] The phenomenon is only paradoxical if it is assumed that the energies of atomic orbitals are fixed and unaffected 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. When care is taken to compare "like with like", the paradox disappears.^[15]

Other exceptions to Madelung's rule

There are several more exceptions to Madelung's rule among the heavier elements, and it is more and more difficult to resort to simple explanations such as the stability of half-filled subshells. It is possible to predict most of the exceptions by Hartree–Fock calculations,^[16] 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^[17] tend to decrease the energy of the s-orbitals in relation to the other atomic orbitals.^[18]

Electron shells filled in violation of Madelung's rule (red)
Period 5			Period 6			Period 7
Element	Z	Electron Configuration	Element	Z	Electron Configuration	Element	Z	Electron Configuration
			Lanthanum	57	[Xe] 6s² 5d¹	Actinium	89	[Rn] 7s² 6d¹
			Cerium	58	[Xe] 6s² 4f¹ 5d¹	Thorium	90	[Rn] 7s² 6d²
			Praseodymium	59	[Xe] 6s² 4f³	Protactinium	91	[Rn] 7s² 5f² 6d¹
			Neodymium	60	[Xe] 6s² 4f⁴	Uranium	92	[Rn] 7s² 5f³ 6d¹
			Promethium	61	[Xe] 6s² 4f⁵	Neptunium	93	[Rn] 7s² 5f⁴ 6d¹
			Samarium	62	[Xe] 6s² 4f⁶	Plutonium	94	[Rn] 7s² 5f⁶
			Europium	63	[Xe] 6s² 4f⁷	Americium	95	[Rn] 7s² 5f⁷
			Gadolinium	64	[Xe] 6s² 4f⁷ 5d¹	Curium	96	[Rn] 7s² 5f⁷ 6d¹
			Terbium	65	[Xe] 6s² 4f⁹	Berkelium	97	[Rn] 7s² 5f⁹

Yttrium	39	[Kr] 5s² 4d¹	Lutetium	71	[Xe] 6s² 4f¹⁴ 5d¹	Lawrencium	103	[Rn] 7s² 5f¹⁴ 7p¹
Zirconium	40	[Kr] 5s² 4d²	Hafnium	72	[Xe] 6s² 4f¹⁴ 5d²	Rutherfordium	104	(unknown)
Niobium	41	[Kr] 5s¹ 4d⁴	Tantalium	73	[Xe] 6s² 4f¹⁴ 5d³
Molybdenum	42	[Kr] 5s¹ 4d⁵	Tungsten	74	[Xe] 6s² 4f¹⁴ 5d⁴
Technetium	43	[Kr] 5s² 4d⁵	Rhenium	75	[Xe] 6s² 4f¹⁴ 5d⁵
Ruthenium	44	[Kr] 5s¹ 4d⁷	Osmium	76	[Xe] 6s² 4f¹⁴ 5d⁶
Rhodium	45	[Kr] 5s¹ 4d⁸	Iridium	77	[Xe] 6s² 4f¹⁴ 5d⁷
Palladium	46	[Kr] 4d¹⁰	Platinum	78	[Xe] 6s¹ 4f¹⁴ 5d⁹
Silver	47	[Kr] 5s¹ 4d¹⁰	Gold	79	[Xe] 6s¹ 4f¹⁴ 5d¹⁰
Cadmium	48	[Kr] 5s² 4d¹⁰	Mercury	80	[Xe] 6s² 4f¹⁴ 5d¹⁰
Indium	49	[Kr] 5s² 4d¹⁰ 5p¹	Thallium	81	[Xe] 6s² 4f¹⁴ 5d¹⁰ 6p¹

By the Madelung rule, 103 Lawrencium would be an expected *[Rn] 7s² 5f¹⁴ 6d¹. The electron-shell configuration of heavier elements is not yet known.

Electron 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,^[19] rather than the atomic orbital labels used for atoms and monoatomic ions: hence, the electron configuration of the dioxygen molecule, O₂, is 1σ_g² 1σ_u² 2σ_g² 2σ_u² 1π_u⁴ 3σ_g² 1π_g².^[1] The term 1π_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.

Electron configuration in solids

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

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 which discards the model. A fundamental application of electron configurations is in the interpretation of atomic spectra. In this case, it is necessary to convert the electron configuration into 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.

Hernandez Caballero Indiana M. CI: 15.242.745 Asignacion: EES Fuente:http://en.wikipedia.org/wiki/Electron_configuration

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sábado, 13 de febrero de 2010