Editing Hassium (section)

=== Relativistic effects ===

{{Main|Relativistic quantum chemistry}}
[[File:Energy levels of outermost orbitals of Hs and Os.jpg|left|thumb|upright=1.50|alt=Energy levels of outermost orbitals of Hs and Os|Energy levels of outermost orbitals of hassium and osmium atoms in [[electronvolt]]s, with and without taking relativistic effects into account. Note the lack of [[spin–orbit splitting]] (and thus the lack of distinction between d{{sub|3/2}} and d{{sub|5/2}} orbitals) in nonrelativistic calculations.]]

[[Relativistic quantum chemistry|Relativistic effects]] in hassium should arise due to the high charge of its nuclei, which causes the electrons around the nucleus to move faster—so fast their speed is comparable to the speed of light.{{sfn|Hoffman|Lee|Pershina|2006|p=1666}} There are three main effects: the direct relativistic effect, the indirect relativistic effect, and [[spin–orbit splitting]]. (The existing calculations do not account for [[Breit equation|Breit interactions]], but those are negligible, and their omission can only result in an uncertainty of the current calculations of no more than 2%.){{sfn|Hoffman|Lee|Pershina|2006|p=1669}}

As atomic number increases, so does the electrostatic attraction between an electron and the nucleus. This causes the velocity of the electron to increase, which leads to an increase in its [[Mass in special relativity|mass]]. This in turn leads to contraction of the [[atomic orbital]]s, most specifically the s and p{{sub|1/2}} orbitals. Their electrons become more closely attached to the atom and harder to pull from the nucleus. This is the direct relativistic effect. It was originally thought to be strong only for the innermost electrons, but was later established to significantly influence valence electrons as well.{{sfn|Hoffman|Lee|Pershina|2006|pp=1666–1667}}

Since the s and p{{sub|1/2}} orbitals are closer to the nucleus, they take a bigger portion of the electric charge of the nucleus on themselves ("shield" it). This leaves less charge for attraction of the remaining electrons, whose orbitals therefore expand, making them easier to pull from the nucleus. This is the indirect relativistic effect.{{sfn|Hoffman|Lee|Pershina|2006|p=1667–1668}} As a result of the combination of the direct and indirect relativistic effects, the Hs{{sup|+}} ion, compared to the neutral atom, lacks a 6d electron, rather than a 7s electron. In comparison, Os{{sup|+}} lacks a 6s electron compared to the neutral atom.{{sfn|Hoffman|Lee|Pershina|2006|p=1672}} The ionic radius (in oxidation state +8) of hassium is greater than that of osmium because of the relativistic expansion of the 6p{{sub|3/2}} orbitals, which are the outermost orbitals for an Hs{{sup|8+}} ion (although in practice such highly charged ions would be too polarized in chemical environments to have much reality).{{sfn|Hoffman|Lee|Pershina|2006|p=1676}}

There are several kinds of electron orbitals, denoted s, p, d, and f (g orbitals are expected to start being chemically active among elements after [[unbinilium|element 120]]). Each of these corresponds to an [[azimuthal quantum number]] ''l'': s to 0, p to 1, d to 2, and f to 3. Every electron also corresponds to a [[spin quantum number]] ''s'', which may equal either +1/2 or −1/2.<ref name="SO splitting">{{Cite web|url=http://www.xpsfitting.com/2012/08/spin-orbit-splitting.html|title=Spin Orbit Splitting|date=2012|website=X-ray Photoelectron Spectroscopy (XPS) Reference Pages|publisher=[[University of Western Ontario]]|access-date=2020-01-26|archive-date=25 January 2020|archive-url=https://web.archive.org/web/20200125152012/http://www.xpsfitting.com/2012/08/spin-orbit-splitting.html|url-status=live}}</ref> Thus, the [[total angular momentum quantum number]] ''j = l'' + ''s'' is equal to ''j'' = ''l'' ± 1/2 (except for ''l'' = 0, for which for both electrons in each orbital ''j ='' 0 + 1/2 = 1/2).<ref name="SO splitting" /> [[Spin (physics)|Spin]] of an electron relativistically [[spin–orbit interaction|interacts]] with its orbit, and this interaction leads to a split of a subshell into two with different energies (the one with ''j'' = ''l'' − 1/2 is lower in energy and thus these electrons more difficult to extract):<ref>{{cite book|last=Thayer|first=J. S.|chapter=Relativistic effects and the chemistry of the heavier main group elements|date=2010|title=Relativistic Methods for Chemists|volume=10|page=65|editor-last=Barysz|editor-first=M.|publisher=Springer Netherlands|doi=10.1007/978-1-4020-9975-5_2|isbn=978-1-4020-9974-8|editor2-last=Ishikawa|editor2-first=Ya.|series=Challenges and Advances in Computational Chemistry and Physics}}</ref> for instance, of the six 6p electrons, two become 6p{{sub|1/2}} and four become 6p{{sub|3/2}}. This is the spin–orbit splitting (also called subshell splitting or [[Jj coupling|''jj'' coupling]]).{{sfn|Hoffman|Lee|Pershina|2006|pp=1668–1669}}{{Efn|The spin–orbit interaction is the interaction between the [[magnetic field]] caused by the spin of an electron and the effective magnetic field caused by the [[electric field]] of a nucleus and movement of an electron orbiting it. (According to the [[special theory of relativity]], electric and magnetic fields are both occurrences of common [[electromagnetic field]]s that can be seen as more or less electric and more or less magnetic depending on the [[reference frame]]. The effective magnetic field from the reference frame of the electron is obtained from the nucleus's electric field after a relativistic transformation from the reference frame of the nucleus.) The splitting occurs because depending on the spin of an electron, it may be either attracted to or repealed by the nucleus; this attraction or repulsion is significantly weaker the electrostatic attraction between them and it can thus only somewhat affect the electron overall.<ref>{{Cite journal|last1=Spavieri|first1=G.|last2=Mansuripur|first2=M.|date=2015|title=Origin of the spin–orbit interaction|journal=[[Physica Scripta]]|volume=90|issue=8|pages=085501-1–085501-2|doi=10.1088/0031-8949/90/8/085501|issn=0031-8949|arxiv=1506.07239|bibcode=2015PhyS...90h5501S|s2cid=119196998}}</ref>}} It is most visible with p electrons,{{sfn|Hoffman|Lee|Pershina|2006|p=1669}} which do not play an important role in the chemistry of hassium,{{sfn|Hoffman|Lee|Pershina|2006|p=1673}} but those for d and f electrons are within the same order of magnitude{{sfn|Hoffman|Lee|Pershina|2006|p=1669}} (quantitatively, spin–orbit splitting in expressed in energy units, such as [[electronvolt]]s).<ref name="SO splitting" />

These relativistic effects are responsible for the expected increase of the [[ionization energy]], decrease of the [[electron affinity]], and increase of stability of the +8 oxidation state compared to osmium; without them, the trends would be reversed.{{sfn|Hoffman|Lee|Pershina|2006|p=1679}} Relativistic effects decrease the atomization energies of hassium compounds because the spin–orbit splitting of the d orbital lowers binding energy between electrons and the nucleus and because relativistic effects decrease [[ionic bond|ionic character]] in bonding.{{sfn|Hoffman|Lee|Pershina|2006|p=1679}}