Scope–severity grid from Bostrom's paper "Existential Risk Prevention as Global Priority"
Risks of astronomical suffering, also called suffering risks or s-risks, are risks involving much more suffering than all that has occurred on Earth so far. They are sometimes categorized as a subclass of existential risks.
According to some scholars, s-risks warrant serious consideration
as they are not extremely unlikely and can arise from unforeseen
scenarios. Although they may appear speculative, factors such as
technological advancement, power dynamics, and historical precedents
indicate that advanced technology could inadvertently result in
substantial suffering. Thus, s-risks are considered to be a morally
urgent matter, despite the possibility of technological benefits.
Sources of possible s-risks include embodied artificial intelligence and superintelligence, as well as space colonization, which could potentially lead to "constant and catastrophic wars" and an immense increase in wild animal suffering
by introducing wild animals, who "generally lead short, miserable lives
full of sometimes the most brutal suffering", to other planets, either
intentionally or inadvertently.
Types of S-risk
Artificial intelligence
Artificial intelligence
is central to s-risk discussions because it may eventually enable
powerful actors to control vast technological systems. In a worst-case
scenario, AI could be used to create systems of perpetual suffering,
such as a totalitarian regime expanding across space. Additionally, s-risks might arise incidentally, such as through
AI-driven simulations of conscious beings experiencing suffering, or
from economic activities that disregard the well-being of nonhuman or
digital minds. Steven Umbrello, an AI ethics researcher, has warned that biological computing may make system design more prone to s-risks.
Space colonization
Space colonization
could increase suffering by introducing wild animals to new
environments, leading to ecological imbalances. In unfamiliar habitats,
animals may struggle to survive, facing hunger, disease, and predation.
These challenges, combined with unstable ecosystems, could cause
population crashes or explosions, resulting in widespread suffering.
Additionally, the lack of natural predators or proper biodiversity on
colonized planets could worsen the situation, mirroring Earth’s
ecological problems on a larger scale. This raises ethical concerns
about the unintended consequences of space colonization, as it could
propagate immense animal suffering in new, unstable ecosystems. Phil
Torres argues that space colonization poses significant "suffering
risks", where expansion into space will lead to the creation of diverse
species and civilizations with conflicting interests. These differences,
combined with advanced weaponry and the vast distances between
civilizations, would result in catastrophic and unresolvable conflicts.
Strategies like a "cosmic Leviathan" to impose order or deterrence
policies are unlikely to succeed due to physical limitations in space
and the destructive power of future technologies. Thus, Torres concludes
that space colonization could create immense suffering and should be
delayed or avoided altogether.
Magnus Vinding's "astronomical atrocity problem" questions
whether vast amounts of happiness can justify extreme suffering from
space colonization. He highlights moral concerns such as diminishing
returns on positive goods, the potentially incomparable weight of severe
suffering, and the priority of preventing misery. He argues that if
colonization is inevitable, it should be led by agents deeply committed
to minimizing harm.
Genetic engineering
David Pearce has argued that genetic engineering is a potential s-risk. Pearce argues that while technological mastery over the pleasure-pain axis and solving the hard problem of consciousness could lead to the potential eradication of suffering,
it could also potentially increase the level of contrast in the hedonic
range that sentient beings could experience. He argues that these
technologies might make it feasible to create "hyperpain" or "dolorium"
that experience levels of suffering beyond the human range.
Excessive criminal punishment
S-risk
scenarios may arise from excessive criminal punishment, with precedents
in both historical and in modern penal systems. These risks escalate in
situations such as warfare or terrorism, especially when advanced
technology is involved, as conflicts can amplify destructive tendencies
like sadism, tribalism, and retributivism.
War often intensifies these dynamics, with the possibility of
catastrophic threats being used to force concessions. Agential s-risks
are further aggravated by malevolent traits in powerful individuals,
such as narcissism or psychopathy. This is exemplified by totalitarian
dictators like Hitler and Stalin, whose actions in the 20th century inflicted widespread suffering.
Exotic risks
According to David Pearce, there are other potential s-risks that are more exotic, such as those posed by the many-worlds interpretation of quantum mechanics.
Mitigation strategies
To
mitigate s-risks, efforts focus on researching and understanding the
factors that exacerbate them, particularly in emerging technologies and
social structures. Targeted strategies include promoting safe AI design,
ensuring cooperation among AI developers, and modeling future
civilizations to anticipate risks. Broad strategies may advocate for
moral norms against large-scale suffering and stable political
institutions. According to Anthony DiGiovanni, prioritizing s-risk
reduction is essential, as it may be more manageable than other
long-term challenges, while avoiding catastrophic outcomes could be
easier than achieving an entirely utopian future.
Induced amnesia
Induced amnesia has been proposed as a way to mitigate s-risks in locked-in conscious AI and certain AI-adjacent biological systems like brain organoids.
Cosmic rescue missions
David
Pearce's concept of "cosmic rescue missions" proposes the idea of
sending probes to alleviate potential suffering in extraterrestrial
environments. These missions aim to identify and mitigate suffering
among hypothetical extraterrestrial life forms, ensuring that if life
exists elsewhere, it is treated ethically. However, challenges include the lack of confirmed extraterrestrial
life, uncertainty about their consciousness, and public support
concerns, with environmentalists advocating for non-interference and
others focusing on resource extraction.
In 2023, the use of molten salts as electrolytes for high-energy rechargeable lithium metal batteries was demonstrated.
History
Thermal batteries originated during World War II
when German scientist Georg Otto Erb developed the first practical
cells using a salt mixture as an electrolyte. Erb developed batteries
for military applications, including the V-1 flying bomb and the V-2
rocket, and artillery fuzing systems. None of these batteries entered
field use during the war. Afterwards, Erb was interrogated by British
intelligence. His work was reported in "The Theory and Practice of
Thermal Cells". This information was subsequently passed on to the
United States Ordnance Development Division of the National Bureau of Standards. When the technology reached the United States
in 1946, it was immediately applied to replacing the troublesome
liquid-based systems that had previously been used to power artillery proximity fuzes. They were used for ordnance applications (e.g., proximity fuzes) since WWII and later in nuclear weapons. The same technology was studied by Argonne National Laboratories and other researchers in the 1980s for use in electric vehicles.
Rechargeable configurations
Since the mid-1960s much development work has been undertaken on rechargeable batteries using sodium (Na) for the negative electrodes. Sodium is attractive because of its high reduction potential
of −2.71 volts, low weight, relative abundance, and low cost. In order
to construct practical batteries, the sodium must be in liquid form. The
melting point
of sodium is 98 °C (208 °F). This means that sodium-based batteries
operate at temperatures between 245 and 350 °C (470 and 660 °F). Research has investigated metal combinations with operating temperatures at 200 °C (390 °F) and room temperature.
The sodium–sulfur battery (NaS battery), along with the related lithium–sulfur battery employs cheap and abundant electrode materials. It was the first alkali-metal commercial battery. It used liquid sulfur for the positive electrode and a ceramic tube of beta-alumina solid electrolyte (BASE). Insulator corrosion was a problem because they gradually became conductive, and the self-discharge rate increased.
Because of their high specific power, NaS batteries have been proposed for space applications. An NaS battery for space use was successfully tested on the Space Shuttle mission STS-87 in 1997, but the batteries have not been used operationally in space. NaS
batteries have been proposed for use in the high-temperature environment
of Venus.
A consortium formed by Tokyo Electric Power Co.
(TEPCO) and NGK Insulators Ltd. declared their interest in researching
the NaS battery in 1983, and became the primary drivers behind the
development of this type ever since. TEPCO chose the NaS battery because
its component elements (sodium, sulfur and ceramics) are abundant in
Japan. The first large-scale field testing took place at TEPCO's
Tsunashima substation between 1993 and 1996, using 3 × 2
MW, 6.6 kV battery banks. Based on the findings from this trial,
improved battery modules were developed and were made commercially
available in 2000. The commercial NaS battery bank offers:
Capacity : 25–250 kWh per bank
Efficiency of 87%
Lifetime of 2,500 cycles at 100% depth of discharge (DOD), or 4,500 cycles at 80% DOD
The Citroën Berlingo First Electric "Powered by Venturi" used a ZEBRA storage battery; a specially-prepared version was driven from Shanghai to Paris in 2010.
A lower-temperature variant of molten-salt batteries was the development of the ZEBRA
(originally, "Zeolite Battery Research Africa"; later, the "Zero
Emissions Batteries Research Activity") battery in 1985, originally
developed for electric vehicle applications. The battery uses NaNiCl 2 with Na+-beta-alumina ceramic electrolyte.
The NaNiCl 2 battery operates at 245 °C (473 °F) and uses molten sodium tetrachloroaluminate (NaAlCl 4),
which has a melting point of 157 °C (315 °F), as the electrolyte. The
negative electrode is molten sodium. The positive electrode is nickel in the discharged state and nickel chloride in the charged state. Because nickel and nickel chloride are nearly insoluble in neutral and basic melts, contact is allowed, providing little resistance to charge transfer. Since both NaAlCl 4 and Na are liquid at the operating temperature, a sodium-conducting β-alumina ceramic is used to separate the liquid sodium from the molten NaAlCl 4.
The primary elements used in the manufacture of these batteries have
much higher worldwide reserves and annual production than lithium.
It was invented in 1985 by the Zeolite Battery Research Africa Project (ZEBRA) group at the Council for Scientific and Industrial Research (CSIR) in Pretoria, South Africa.
It can be assembled in the discharged state, using NaCl, Al, nickel and
iron powder. The positive electrode is composed mostly of materials in
the solid state, which reduces the likelihood of corrosion, improving
safety. Its specific energy
is 100 Wh/kg; specific power is 150 W/kg. The β-alumina solid ceramic
is unreactive to sodium metal and sodium aluminum chloride. Lifetimes of
over 2,000 cycles and twenty years have been demonstrated with
full-sized batteries, and over 4,500 cycles and fifteen years with 10-
and 20-cell modules. For comparison, LiFePO4lithium iron phosphate batteries store 90–110 Wh/kg, and the more common LiCoO2 lithium-ion batteries store 150–200 Wh/kg. A nano lithium-titanate battery stores 72 Wh/kg and can provide power of 760 W/kg.
The ZEBRA's liquid electrolyte freezes at 157 °C (315 °F), and
the normal operating temperature range is 270–350 °C (520–660 °F).
Adding iron to the cell increases its power response. ZEBRA batteries are currently manufactured by FZSoNick and used as a power backup in the telecommunication industries,
Oil&Gas and Railways. It is also used in special electric vehicles
used in mining. In the past it was adopted in the Modec Electric Van, the Iveco Daily 3.5-ton delivery vehicle, the prototype Smart ED, and the Th!nk City. In 2011 the US Postal Service began testing all-electric delivery vans, one powered by a ZEBRA battery.
In 2010 General Electric announced a Na-NiCl 2
battery that it called a sodium–metal halide battery, with a 20-year
lifetime. Its cathode structure consists of a conductive nickel network,
molten salt electrolyte, metal current collector, carbon felt
electrolyte reservoir and the active sodium–metal halide salts. In 2015, as a result of a global restructuring, the company abandoned the project. In 2017 Chinese battery maker Chilwee Group (also known as Chaowei)
created a new company with General Electric (GE) to bring to market a
Na-NiCl battery for industrial and energy storage applications.
When not in use, Na-NiCl 2
batteries are typically kept molten and ready for use because if
allowed to solidify they typically take twelve hours to reheat and
charge. This reheating time varies depending on the battery-pack temperature,
and power available for reheating. After shutdown a fully charged
battery pack loses enough energy to cool and solidify in five-to-seven
days depending on the amount of insulation.
Sodium metal chloride batteries are very safe; a thermal runaway
can be activated only by piercing the battery and also, in this
unlikely event, no fire or explosion will be generated. For this reason
and also for the possibility to be installed outdoor without cooling
systems, make the sodium metal chloride batteries very suitable for the
industrial and commercial energy storage installations.
Sumitomo
studied a battery using a salt that is molten at 61 °C (142 °F), far
lower than sodium based batteries, and operational at 90 °C (194 °F). It
offers energy densities as high as 290 Wh/L and 224 Wh/kg and
charge/discharge rates of 1C with a lifetime of 100–1000 charge cycles.
The battery employs only nonflammable materials and neither ignites on
contact with air nor risks thermal runaway. This eliminates waste-heat
storage or fire- and explosion-proof equipment, and allows closer cell
packing. The company claimed that the battery required half the volume
of lithium-ion batteries and one quarter that of sodium–sulfur
batteries. The cell used a nickel cathode and a glassy carbon anode.
In 2014 researchers identified a liquid sodium–cesium alloy that
operates at 50 °C (122 °F) and produced 420 milliampere-hours per gram.
The new material was able to fully coat, or "wet," the electrolyte.
After 100 charge/discharge cycles, a test battery maintained about 97%
of its initial storage capacity. The lower operating temperature allowed
the use of a less-expensive polymer external casing instead of steel,
offsetting some of the increased cost of cesium.
Innovenergy in Meiringen, Switzerland
has further optimised this technology with the use of domestically
sourced raw materials, except for the nickel powder component. Despite
the reduced capacity compared with lithium-ion batteries, the ZEBRA technology is applicable for stationary energy storage from solar power.
In 2022, the company operated a 540 kWh storage facility for solar
cells on the roof of a shopping center, and currently produces over a
million battery units per year from sustainable, non-toxic materials (table salt).
Professor Donald Sadoway
at the Massachusetts Institute of Technology has pioneered the research
of liquid-metal rechargeable batteries, using both magnesium–antimony
and more recently lead–antimony. The electrode and electrolyte layers are heated until they are liquid and self-segregate due to density and immiscibility.
Such batteries may have longer lifetimes than conventional batteries,
as the electrodes go through a cycle of creation and destruction during
the charge–discharge cycle, which makes them immune to the degradation
that afflicts conventional battery electrodes.
The technology was proposed in 2009 based on magnesium and antimony separated by a molten salt. Magnesium was chosen as the negative electrode for its low cost and low
solubility in the molten-salt electrolyte. Antimony was selected as the
positive electrode due to its low cost and higher anticipated discharge
voltage.
In 2011, the researchers demonstrated a cell with a lithium anode
and a lead–antimony cathode, which had higher ionic conductivity and
lower melting points (350–430 °C). The drawback of the Li chemistry is higher cost. A Li/LiF + LiCl +
LiI/Pb-Sb cell with about 0.9 V open-circuit potential operating at
450 °C had electroactive material costs of US$100/kWh and US$100/kW and a
projected 25-year lifetime. Its discharge power at 1.1 A/cm2 is only 44% (and 88% at 0.14 A/cm2).
Experimental data shows 69% storage efficiency, with good storage capacity (over 1000 mAh/cm2), low leakage (< 1 mA/cm2) and high maximal discharge capacity (over 200 mA/cm2). By October 2014 the MIT team achieved an operational efficiency of approximately 70% at high charge/discharge rates (275 mA/cm2), similar to that of pumped-storage hydroelectricity
and higher efficiencies at lower currents. Tests showed that after 10
years of regular use, the system would retain about 85% of its initial
capacity. In September 2014, a study described an arrangement using a molten
alloy of lead and antimony for the positive electrode, liquid lithium
for the negative electrode; and a molten mixture of lithium salts as the
electrolyte.
A recent innovation is the PbBi alloy which enables lower melting
point lithium-based battery. It uses a molten salt electrolyte based on
LiCl-LiI and operates at 410 °C.
Ionic liquids
have been shown to have prowess for use in rechargeable batteries. The
electrolyte is pure molten salt with no added solvent, which is
accomplished by using a salt having a room temperature liquid phase.
This causes a highly viscous solution, and is typically made with
structurally large salts with malleable lattice structures.
Thermal
batteries use an electrolyte that is solid and inactive at ambient
temperatures. They can be stored indefinitely (over 50 years) yet
provide full power in an instant when required. Once activated, they
provide a burst of high power for a short period (a few tens of seconds
to 60 minutes or more), with output ranging from watts to kilowatts. The high power is due to the high ionic conductivity
of the molten salt (resulting in a low internal resistance), which is
three orders of magnitude (or more) greater than that of the sulfuric acid in a lead–acid car battery.
One design uses a fuze strip (containing barium chromate and powdered zirconium
metal in a ceramic paper) along the edge of the heat pellets to
initiate the electrochemical reaction. The fuze strip is typically fired
by an electrical igniter or squib which is activated with an electric current.
Another design uses a central hole in the middle of the battery
stack, into which the high-energy electrical igniter fires a mixture of
hot gases and incandescent
particles. This allows much shorter activation times (tens of
milliseconds) vs. hundreds of milliseconds for the edge-strip design.
Battery activation can be accomplished by a percussion primer, similar to a shotgun shell. The heat source should be gasless. The standard heat source typically consists of mixtures of iron powder and potassium perchlorate in weight ratios of 88/12, 86/14, or 84/16. The higher the potassium perchlorate level, the higher the heat output (nominally 200, 259, and 297 cal/g
respectively). This property of unactivated storage has the double
benefit of avoiding deterioration of the active materials during storage
and eliminating capacity loss due to self-discharge until the battery is activated.
More recently, other lower-melting, eutectic electrolytes based on lithium bromide, potassium bromide, and lithium chloride or lithium fluoride
have also been used to provide longer operational lifetimes; they are
also better conductors. The so-called "all-lithium" electrolyte based on
lithium chloride, lithium bromide, and lithium fluoride (no potassium salts) is also used for high-power applications, because of its high ionic conductivity. A radioisotope thermal generator, such as in the form of pellets of 90SrTiO4, can be used for long-term delivery of heat for the battery after activation, keeping it in a molten state.
Uses
Thermal batteries are used almost exclusively for military applications, notably for nuclear weapons and guided missiles. They are the primary power source for many missiles such as the AIM-9 Sidewinder, AIM-54 Phoenix, MIM-104 Patriot, BGM-71 TOW, BGM-109 Tomahawk and others. In these batteries the electrolyte is immobilized when molten by a special grade of magnesium oxide that holds it in place by capillary action. This powdered mixture is pressed into pellets to form a separator between the anode and cathode
of each cell in the battery stack. As long as the electrolyte (salt) is
solid, the battery is inert and remains inactive. Each cell also
contains a pyrotechnic heat source, which is used to heat the cell to the typical operating temperature of 400–550 °C.
In chemistry, electron counting is a formalism for assigning a number of valence electrons
to individual atoms in a molecule. It is used for classifying
compounds and for explaining or predicting their electronic structure
and bonding. Many rules in chemistry rely on electron-counting:
Atoms are called "electron-deficient" when they have too few electrons as compared to their respective rules, or "hypervalent"
when they have too many electrons. Since these compounds tend to be
more reactive than compounds that obey their rule, electron counting is
an important tool for identifying the reactivity of molecules. While
the counting formalism considers each atom separately, these individual
atoms (with their hypothetical assigned charge) do not generally exist
as free species.
Counting rules
Two
methods of electron counting are "neutral counting" and "ionic
counting". Both approaches give the same result (and can therefore be
used to verify one's calculation).
The neutral counting approach assumes the molecule or fragment being studied consists of purely covalent bonds. It was popularized by Malcolm Green along with the L and X ligand notation. It is usually considered easier especially for low-valent transition metals.
The "ionic counting" approach assumes purely ionic bonds between atoms.
It is important, though, to be aware that most chemical species exist between the purely covalent and ionic extremes.
Neutral counting
Neutral counting assumes each bond is equally split between two atoms.
This method begins with locating the central atom on the periodic
table and determining the number of its valence electrons. One counts
valence electrons for main group elements differently from transition
metals, which use d electron count.
E.g. in period 2: B, C, N, O, and F have 3, 4, 5, 6, and 7 valence electrons, respectively.
E.g. in period 4: K, Ca, Sc, Ti, V, Cr, Fe, Ni have 1, 2, 3, 4, 5, 6, 8, 10 valence electrons respectively.
One is added for every halide or other anionic ligand which binds to the central atom through a sigma bond.
Two is added for every lone pair bonding to the metal (e.g. each
Lewis base binds with a lone pair). Unsaturated hydrocarbons such as
alkenes and alkynes are considered Lewis bases. Similarly Lewis and Bronsted acids (protons) contribute nothing.
One is added for each homoelement bond.
One is added for each negative charge, and one is subtracted for each positive charge.
Ionic counting
Ionic
counting assumes unequal sharing of electrons in the bond. The more
electronegative atom in the bond gains electron lost from the less
electronegative atom.
This method begins by calculating the number of electrons of the element, assuming an oxidation state.
E.g. for a Fe2+ has 6 electrons
S2− has 8 electrons
Two is added for every halide or other anionic ligand which binds to the metal through a sigma bond.
Two is added for every lone pair bonding to the metal (e.g. each
phosphine ligand can bind with a lone pair). Similarly Lewis and
Bronsted acids (protons) contribute nothing.
For unsaturated ligands such as alkenes, one electron is added for each carbon atom binding to the metal.
The
numbers of electrons "donated" by some ligands depends on the geometry
of the metal-ligand ensemble. An example of this complication is the M–NO
entity. When this grouping is linear, the NO ligand is considered to be
a three-electron ligand. When the M–NO subunit is strongly bent at N,
the NO is treated as a pseudohalide and is thus a one electron (in the
neutral counting approach). The situation is not very different from
the η3 versus the η1 allyl. Another unusual ligand from the electron counting perspective is sulfur dioxide.
For a water molecule (H2O), using both neutral counting and ionic counting result in a total of 8 electrons.
This
figure of the water molecule shows how the electrons are distributed
with the covalent counting method. The red ones are the oxygen
electrons, and the blue ones are electrons from the hydrogen atoms.
Neutral counting
Atom
Electrons contributed
Electron count
H.
1 electron x 2
2 electrons
O
6 electrons
6 electrons
Total = 8 electrons
The neutral counting method assumes each OH bond is split equally
(each atom gets one electron from the bond). Thus both hydrogen atoms
have an electron count of one. The oxygen atom has 6 valence electrons.
The total electron count is 8, which agrees with the octet rule.
This
figure of the water molecule shows how the electrons are distributed
with the ionic counting method. The red ones are the oxygen electrons,
and the blue ones are electrons from hydrogen. All electrons in the OH
bonds belong to the more electronegative oxygen.
Ionic counting
Atom
Electrons contributed
Electron count
H+
none
0 electron
O2-
8 electrons
8 electrons
Total = 8 electrons
With the ionic counting method, the more electronegative oxygen will
gain electrons donated by the two hydrogen atoms in the two OH bonds to
become O2-. It now has 8 total valence electrons, which obeys the octet rule.
neutral counting: H contributes 1 electron, the C contributes 1
electron (the other 3 electrons of C are for the other 3 hydrogens in
the molecule): 1 + 1 × 1 = 2 valence electrons.
conclusion: Methane follows the octet-rule for carbon, and the duet
rule for hydrogen, and hence is expected to be a stable molecule (as we
see from daily life)
conclusion: ionic counting indicates a molecule lacking lone pairs
of electrons, therefore its structure will be octahedral, as predicted
by VSEPR. One might conclude that this molecule would be highly reactive - but the opposite is true: SF6 is inert, and it is widely used in industry because of this property.
The geometry of cis-Dichlorobis(bipyridine)ruthenium(II).
RuCl2(bpy)2 is an octahedral metal complex with two bidentate2,2′-Bipyridine (bpy) ligands and two chloride ligands.
Neutral counting
Metal/ligand
Electrons contributed
Electron count
Ru(0)
d8 (8 d electrons)
8 electrons
bpy
4 electrons x 2
8 electrons
Cl .
1 electron x 2
2 electrons
Total = 18 electrons
In the neutral counting method, the Ruthenium of the complex is
treated as Ru(0). It has 8 d electrons to contribute to the electron
count. The two bpy ligands are L-type ligand
neutral ligands, thus contributing two electrons each. The two chloride
ligands halides and thus 1 electron donors, donating 1 electron each to
the electron count. The total electron count of RuCl2(bpy)2 is 18.
Ionic counting
metal/ligand
electrons contributed
number of electrons
Ru(II)
d6 (6 d electrons)
6 electrons
bpy
4 electrons x 2
8 electrons
Cl−
2 electrons x 2
4 electrons
Total = 18 electrons
In the ionic counting method, the Ruthenium of the complex is treated
as Ru(II). It has 6 d electrons to contribute to the electron count.
The two bpy ligands are L-type ligand
neutral ligands, thus contributing two electrons each. The two chloride
ligands are anionic ligands, thus donating 2 electrons each to the
electron count. The total electron count of RuCl2(bpy)2 is 18, agreeing with the result of neural counting.
conclusion: Having only 8e (vs. 18 possible), we can anticipate that TiCl4 will be a good Lewis acid. Indeed, it reacts (in some cases violently) with water, alcohols, ethers, amines.
neutral counting: Fe contributes 8 electrons, each CO contributes 2 each: 8 + 2 × 5 = 18 valence electrons
ionic counting: Fe(0) contributes 8 electrons, each CO contributes 2 each: 8 + 2 × 5 = 18 valence electrons
conclusions: this is a special case, where ionic counting is the
same as neutral counting, all fragments being neutral. Since this is an
18-electron complex, it is expected to be isolable compound.
Hypervalent
molecules were first formally defined by Jeremy I. Musher in 1969 as
molecules having central atoms of group 15–18 in any valence other than the lowest (i.e. 3, 2, 1, 0 for Groups 15, 16, 17, 18 respectively, based on the octet rule).
Several specific classes of hypervalent molecules exist:
N-X-L nomenclature, introduced collaboratively by the research groups of Martin, Arduengo, and Kochi in 1980, is often used to classify hypervalent compounds of main group elements, where:
The debate over the nature and classification of hypervalent molecules goes back to Gilbert N. Lewis and Irving Langmuir and the debate over the nature of the chemical bond in the 1920s. Lewis maintained the importance of the two-center two-electron (2c–2e)
bond in describing hypervalence, thus using expanded octets to account
for such molecules. Using the language of orbital hybridization, the
bonds of molecules like PF5 and SF6 were said to be constructed from sp3dn
orbitals on the central atom. Langmuir, on the other hand, upheld the
dominance of the octet rule and preferred the use of ionic bonds to
account for hypervalence without violating the rule (e.g. "SF2+ 4 2F−" for SF6).
In the late 1920s and 1930s, Sugden argued for the existence of a
two-center one-electron (2c–1e) bond and thus rationalized bonding in
hypervalent molecules without the need for expanded octets or ionic bond
character; this was poorly accepted at the time. In the 1940s and 1950s, Rundle and Pimentel popularized the idea of the three-center four-electron bond,
which is essentially the same concept which Sugden attempted to advance
decades earlier; the three-center four-electron bond can be
alternatively viewed as consisting of two collinear two-center
one-electron bonds, with the remaining two nonbonding electrons
localized to the ligands.
The attempt to actually prepare hypervalent organic molecules began with Hermann Staudinger and Georg Wittig
in the first half of the twentieth century, who sought to challenge the
extant valence theory and successfully prepare nitrogen and
phosphorus-centered hypervalent molecules. The theoretical basis for hypervalency was not delineated until J.I. Musher's work in 1969.
In 1990, Magnusson published a seminal work definitively
excluding the significance of d-orbital hybridization in the bonding of
hypervalent compounds of second-row elements. This had long been a
point of contention and confusion in describing these molecules using molecular orbital theory.
Part of the confusion here originates from the fact that one must
include d-functions in the basis sets used to describe these compounds
(or else unreasonably high energies and distorted geometries result),
and the contribution of the d-function to the molecular wavefunction is
large. These facts were historically interpreted to mean that
d-orbitals must be involved in bonding. However, Magnusson concludes in
his work that d-orbital involvement is not implicated in hypervalency.
Nevertheless, a 2013 study showed that although the Pimentel
ionic model best accounts for the bonding of hypervalent species, the
energetic contribution of an expanded octet structure is also not null.
In this modern valence bond theory study of the bonding of xenon difluoride,
it was found that ionic structures account for about 81% of the overall
wavefunction, of which 70% arises from ionic structures employing only
the p orbital on xenon while 11% arises from ionic structures employing
an hybrid on xenon. The contribution of a formally hypervalent structure employing an orbital of sp3d
hybridization on xenon accounts for 11% of the wavefunction, with a
diradical contribution making up the remaining 8%. The 11% sp3d contribution results in a net stabilization of the molecule by 7.2 kcal (30 kJ) mol−1, a minor but significant fraction of the total energy of the total bond energy (64 kcal (270 kJ) mol−1). Other studies have similarly found minor but non-negligible energetic contributions from expanded octet structures in SF6 (17%) and XeF6 (14%).
Despite the lack of chemical realism, the IUPAC recommends the drawing of expanded octet structures for functional groups like sulfones and phosphoranes, in order to avoid the drawing of a large number of formal charges or partial single bonds.
Hypervalent hydrides
A
special type of hypervalent molecules is hypervalent hydrides. Most
known hypervalent molecules contain substituents more electronegative
than their central atoms. Hypervalent hydrides are of special interest because hydrogen is
usually less electronegative than the central atom. A number of
computational studies have been performed on chalcogen hydrides and pnictogen hydrides. Recently, a new computational study has shown that most hypervalent halogen hydrides XHn can exist. It is suggested that IH3 and IH5 are stable enough to be observable or, possibly, even isolable.
Criticism
Both the term and concept of hypervalency still fall under criticism. In 1984, in response to this general controversy, Paul von Ragué Schleyer proposed the replacement of 'hypervalency' with use of the term hypercoordination because this term does not imply any mode of chemical bonding and the question could thus be avoided altogether.
The concept itself has been criticized by Ronald Gillespie
who, based on an analysis of electron localization functions, wrote in
2002 that "as there is no fundamental difference between the bonds in
hypervalent and non-hypervalent (Lewis octet) molecules there is no
reason to continue to use the term hypervalent."
For hypercoordinated molecules with electronegative ligands such as PF5,
it has been demonstrated that the ligands can pull away enough electron
density from the central atom so that its net content is again 8
electrons or fewer. Consistent with this alternative view is the finding
that hypercoordinated molecules based on fluorine ligands, for example
PF5 do not have hydride counterparts, e.g. phosphorane (PH5) which is unknown.
The ionic model holds up well in thermochemical calculations. It predicts favorable exothermic formation of PF+ 4F− from phosphorus trifluoride PF3 and fluorine F2 whereas a similar reaction forming PH+ 4H− is not favorable.
Alternative definition
Durrant has proposed an alternative definition of hypervalency, based on the analysis of atomic charge maps obtained from atoms in molecules theory. This approach defines a parameter called the valence electron
equivalent, γ, as “the formal shared electron count at a given atom,
obtained by any combination of valid ionic and covalent resonance forms
that reproduces the observed charge distribution”. For any particular
atom X, if the value of γ(X) is greater than 8, that atom is
hypervalent. Using this alternative definition, many species such as PCl5, SO2− 4, and XeF4,
that are hypervalent by Musher's definition, are reclassified as
hypercoordinate but not hypervalent, due to strongly ionic bonding that
draws electrons away from the central atom. On the other hand, some
compounds that are normally written with ionic bonds in order to conform
to the octet rule, such as ozone O3, nitrous oxide NNO, and trimethylamine N-oxide(CH 3) 3NO, are found to be genuinely hypervalent. Examples of γ calculations for phosphatePO3− 4 (γ(P) = 2.6, non-hypervalent) and orthonitrateNO3− 4 (γ(N) = 8.5, hypervalent) are shown below.
Calculation of the valence electron equivalent for phosphate and orthonitrate
Bonding in hypervalent molecules
Early
considerations of the geometry of hypervalent molecules returned
familiar arrangements that were well explained by the VSEPR model for
atomic bonding. Accordingly, AB₅ and AB₆ type molecules would possess a
trigonal bipyramidal and octahedral geometry, respectively. However, in
order to account for the observed bond angles, bond lengths, and
apparent violation of the Lewis octet rule, several alternative models
have been proposed.
In the 1950s, an expanded valence shell treatment of hypervalent
bonding was proposed, in which the central atom of penta- and
hexacoordinated molecules was thought to utilize vacant d atomic
orbitals in addition to its valence s and p orbitals to form hybrid
orbitals. For example, phosphorus in PCl₅ was described as undergoing
sp³d hybridization to accommodate five bonding pairs in a trigonal
bipyramidal geometry, while sulfur in SF₆ was treated as sp³d²
hybridized, consistent with an octahedral structure. This model provided
a straightforward explanation within the valence bond framework for how
atoms in the third period and beyond could exceed the octet rule by
expanding their valence shells into the 3d subshell.
However, advances in ab initio quantum chemical calculations have
suggested that the energetic contribution of d-orbitals to bonding in
main group hypervalent molecules might be minimal. The high energy and
poor radial overlap of the 3d orbitals with ligand orbitals result in
negligible participation in bond formation. It was shown that in the
case of hexacoordinated SF₆, d-orbitals might not be significantly
involved in S–F bond formation; rather, charge transfer between the
central atom and ligands, along with appropriate resonance structures,
can adequately explain the bonding characteristics and apparent
hypervalency (see below). As a result, the d-orbital hybridization model
is now regarded primarily as a historical or pedagogical tool.
Additional modifications to the octet rule have been attempted to
involve ionic characteristics in hypervalent bonding. As one of these
modifications, in 1951, the concept of the three-center four-electron
(3c–4e) bond, which described hypervalent bonding using a qualitative
molecular orbital framework, was proposed. The 3c–4e bond is described
as three molecular orbitals formed by the combination of a p atomic
orbital on the central atom with atomic orbitals from two ligands
positioned linearly. Only one of the two pairs of electrons occupies a
bonding orbital involving the central atom, while the second pair is
nonbonding and delocalized between the two ligands. This model, which
preserves the octet rule by distributing electrons across a delocalized
system, was also later advocated by Musher.
A
complete description of hypervalent molecules arises from consideration
of molecular orbital theory through quantum mechanical methods. An LCAO
in, for example, sulfur hexafluoride, taking a basis set of the one
sulfur 3s-orbital, the three sulfur 3p-orbitals, and six octahedral
geometry symmetry-adapted linear combinations (SALCs) of fluorine
orbitals, a total of ten molecular orbitals are obtained (four fully
occupied bonding MOs of the lowest energy, two fully occupied
intermediate energy non-bonding MOs and four vacant antibonding MOs with
the highest energy) providing room for all 12 valence electrons. This
is a stable configuration only for SX6 molecules containing electronegative ligand atoms like fluorine, which explains why SH6 is not a stable molecule. In the bonding model, the two non-bonding MOs (1eg) are localized equally on all six fluorine atoms.
d-Orbital Hybridization Model for Hypervalent Molecules
In
classical valence bond theory, hypervalent molecules are explained
using d-orbital hybridization. This model is commonly applied to
elements in the third period and beyond of the periodic table (e.g.,
phosphorus, sulfur, chlorine), where low-lying vacant d orbitals are
available.
According to this model, the central atom expands its valence
shell by hybridizing its valence s and p orbitals with one or more d
orbitals to form hybrid orbitals capable of accommodating more than four
electron pairs. For example:
In phosphorus pentachloride (PCl₅), the phosphorus atom is said
to use sp³d hybridization to form five equivalent bonding orbitals
arranged in a trigonal bipyramidal geometry.
In sulfur hexafluoride (SF₆), the sulfur atom is described as
undergoing sp³d² hybridization, resulting in six equivalent orbitals
arranged octahedrally.
This use of d orbitals allows the molecule to accommodate five or six
electron domains, respectively, thereby explaining the observed
molecular geometries and bonding patterns within the valence bond
framework.
Although the d-orbital hybridization model is still widely taught
and used, it has been challenged by more advanced quantum chemical
analyses. Computational studies and molecular orbital theory suggest
that:
The contribution of d orbitals to bonding in main group
hypervalent molecules might be less then thought before due to their
relatively high energy and poor radial overlap with bonding partners.
Instead, bonding in such molecules can be explained using
three-center four-electron (3c–4e) bonds or delocalized molecular
orbitals that do not require invoking d-orbital participation.
Nevertheless, the d-orbital hybridization model remains a popular and widely used model to this day despite the controversy.
Three-Center Four-Electron Bond Model
An
important alternative to expanded shell models is the three-center
four-electron (3c–4e) bond, introduced in 1951 by Rundle and Pimentel.
This model describes hypervalent bonding in terms of molecular orbital
theory rather than invoking participation of d-orbitals or violation of
the octet rule. In this framework, hypervalent bonding arises when a
central atom shares a bonding interaction simultaneously with two
ligands through a delocalized orbital system. Specifically, a 3c–4e bond
involves three atoms—typically two ligands and a central atom—sharing
four electrons across three molecular orbitals: one bonding, one
nonbonding, and one antibonding. Only the bonding and nonbonding
orbitals are occupied, leading to an overall stable configuration.
This model is particularly effective in describing linear
arrangements such as those found in I₃⁻ and XeF₂, where the central atom
retains a formal octet while bonding with more than four atoms. The
central atom contributes a p orbital which overlaps with ligand orbitals
from opposite sides, forming a delocalized interaction across all three
atoms. The presence of one bonding and one nonbonding pair of electrons
in the system provides an energetically favorable arrangement without
requiring d-orbital participation. The 3c–4e model thus preserves the
octet rule and aligns with modern quantum mechanical calculations,
offering a more accurate depiction of bonding in many hypervalent
compounds than earlier d-orbital hybridization approaches.
Structure, reactivity, and kinetics
Structure
Hexacoordinated phosphorus
Hexacoordinate phosphorus molecules involving nitrogen, oxygen, or sulfur ligands provide examples of Lewis acid-Lewis base hexacoordination. For the two similar complexes shown below, the length of the C–P bond
increases with decreasing length of the N–P bond; the strength of the
C–P bond decreases with increasing strength of the N–P Lewis acid–Lewis
base interaction.
Relative bond strengths in hexacoordinated phosphorus compounds. In A,
the N–P bond is 1.980 Å long and the C–P is 1.833 Å long, and in B, the
N–P bond increases to 2.013 Å as the C–P bond decreases to 1.814 Å.
Pentacoordinated silicon
This
trend is also generally true of pentacoordinated main-group elements
with one or more lone-pair-containing ligand, including the
oxygen-pentacoordinated silicon examples shown below.
Relative bond strengths in pentacoordinated silicon compounds. In A,
the Si-O bond length is 1.749Å and the Si-I bond length is 3.734Å; in B,
the Si-O bond lengthens to 1.800Å and the Si-Br bond shortens to
3.122Å, and in C, the Si-O bond is the longest at 1.954Å and the Si-Cl
bond the shortest at 2.307A.
The Si-halogen bonds range from close to the expected van der Waals
value in A (a weak bond) almost to the expected covalent single bond
value in C (a strong bond).
Reactivity
Silicon
Observed third-order reaction rate constants for hydrolysis (displacement of chloride from silicon)
Corriu and coworkers performed early work characterizing reactions thought to proceed through a hypervalent transition state. Measurements of the reaction rates of hydrolysis of tetravalent chlorosilanes incubated with catalytic amounts of water returned a rate that is first order
in chlorosilane and second order in water. This indicated that two
water molecules interacted with the silane during hydrolysis and from
this a binucleophilic reaction mechanism was proposed. Corriu and
coworkers then measured the rates of hydrolysis in the presence of
nucleophilic catalyst HMPT, DMSO or DMF. It was shown that the rate of
hydrolysis was again first order in chlorosilane, first order in
catalyst and now first order in water. Appropriately, the rates of
hydrolysis also exhibited a dependence on the magnitude of charge on the
oxygen of the nucleophile.
Taken together this led the group to propose a reaction mechanism
in which there is a pre-rate determining nucleophilic attack of the
tetracoordinated silane by the nucleophile (or water) in which a
hypervalent pentacoordinated silane is formed. This is followed by a
nucleophilic attack of the intermediate by water in a rate determining
step leading to hexacoordinated species that quickly decomposes giving
the hydroxysilane.
Silane hydrolysis was further investigated by Holmes and coworkers in which tetracoordinated Mes 2SiF 2 (Mes = mesityl) and pentacoordinated Mes 2SiF− 3
were reacted with two equivalents of water. Following twenty-four
hours, almost no hydrolysis of the tetracoordinated silane was observed,
while the pentacoordinated silane was completely hydrolyzed after
fifteen minutes. Additionally, X-ray diffraction data collected for the
tetraethylammonium salts of the fluorosilanes showed the formation of
hydrogen bisilonate lattice supporting a hexacoordinated intermediate
from which HF− 2
is quickly displaced leading to the hydroxylated product. This reaction
and crystallographic data support the mechanism proposed by Corriu et al..
Mechanism of silane hydrolysis and structure of the hydrogen bisilonate lattice
The apparent increased reactivity of hypervalent molecules,
contrasted with tetravalent analogues, has also been observed for
Grignard reactions. The Corriu group measured Grignard reaction half-times by NMR for related 18-crown-6 potassium
salts of a variety of tetra- and pentacoordinated fluorosilanes in the
presence of catalytic amounts of nucleophile.
Though the half reaction method is imprecise, the magnitudinal
differences in reactions rates allowed for a proposed reaction scheme
wherein, a pre-rate determining attack of the tetravalent silane by the
nucleophile results in an equilibrium between the neutral
tetracoordinated species and the anionic pentavalent compound. This is
followed by nucleophilic coordination by two Grignard reagents as
normally seen, forming a hexacoordinated transition state and yielding the expected product.
Grignard reaction mechanism for tetracoordinate silanes and the analogous hypervalent pentacoordinated silanes
The mechanistic implications of this are extended to a
hexacoordinated silicon species that is thought to be active as a
transition state in some reactions. The reaction of allyl- or crotyl-trifluorosilanes
with aldehydes and ketones only precedes with fluoride activation to
give a pentacoordinated silicon. This intermediate then acts as a Lewis acid
to coordinate with the carbonyl oxygen atom. The further weakening of
the silicon–carbon bond as the silicon becomes hexacoordinate helps
drive this reaction.
Phosphorus
Similar
reactivity has also been observed for other hypervalent structures such
as the miscellany of phosphorus compounds, for which hexacoordinated
transition states have been proposed.
Hydrolysis of phosphoranes and oxyphosphoranes have been studied and shown to be second order in water. Bel'skii et al..
have proposed a prerate determining nucleophilic attack by water
resulting in an equilibrium between the penta- and hexacoordinated
phosphorus species, which is followed by a proton transfer involving the
second water molecule in a rate determining ring-opening step, leading
to the hydroxylated product.
Mechanism of the hydrolysis of pentacoordinated phosphorus
Alcoholysis of pentacoordinated phosphorus compounds, such as
trimethoxyphospholene with benzyl alcohol, have also been postulated to
occur through a similar octahedral transition state, as in hydrolysis,
however without ring opening.
Mechanism of the base catalyzed alcoholysis of pentacoordinated phosphorus
It can be understood from these experiments that the increased
reactivity observed for hypervalent molecules, contrasted with analogous
nonhypervalent compounds, can be attributed to the congruence of these
species to the hypercoordinated activated states normally formed during
the course of the reaction.
Ab initio calculations
The
enhanced reactivity at pentacoordinated silicon is not fully
understood. Corriu and coworkers suggested that greater electropositive
character at the pentavalent silicon atom may be responsible for its
increased reactivity. Preliminary ab initio calculations supported this hypothesis to some degree, but used a small basis set.
A software program for ab initio calculations, Gaussian 86, was used by Dieters and coworkers to compare tetracoordinated silicon and phosphorus to their pentacoordinate analogues. This ab initio
approach is used as a supplement to determine why reactivity improves
in nucleophilic reactions with pentacoordinated compounds. For silicon,
the 6-31+G* basis set was used because of its pentacoordinated anionic character and for phosphorus, the 6-31G* basis set was used.
Pentacoordinated compounds should theoretically be less
electrophilic than tetracoordinated analogues due to steric hindrance
and greater electron density from the ligands, yet experimentally show
greater reactivity with nucleophiles than their tetracoordinated
analogues. Advanced ab initio calculations were performed on series of
tetracoordinated and pentacoordinated species to further understand this
reactivity phenomenon. Each series varied by degree of fluorination.
Bond lengths and charge densities are shown as functions of how many
hydride ligands are on the central atoms. For every new hydride, there
is one less fluoride.
For silicon and phosphorus bond lengths, charge densities, and Mulliken
bond overlap, populations were calculated for tetra and pentacoordinated
species by this ab initio approach. Addition of a fluoride ion to tetracoordinated silicon shows an overall
average increase of 0.1 electron charge, which is considered
insignificant. In general, bond lengths in trigonal bipyramidal
pentacoordinate species are longer than those in tetracoordinate
analogues. Si-F bonds and Si-H bonds both increase in length upon
pentacoordination and related effects are seen in phosphorus species,
but to a lesser degree. The reason for the greater magnitude in bond
length change for silicon species over phosphorus species is the
increased effective nuclear charge at phosphorus. Therefore, silicon is
concluded to be more loosely bound to its ligands.
Effects of fluorine substitution on positive charge density
Comparison of Charge Densities with Degree of Fluorination for Tetra and Pentacoordinated Silicon
In addition Dieters and coworkers show an inverse correlation between bond length and bond overlap for
all series. Pentacoordinated species are concluded to be more reactive
because of their looser bonds as trigonal-bipyramidal structures.
Calculated bond length and bond overlap with degree of fluorination
Comparison of Bond Lengths with Degree of Fluorination for Tetra and Pentacoordinated Silicon
Comparison of Bond Lengths with Degree of Fluorination for Tetra and Pentacoordinated Phosphorus
By calculating the energies for the addition and removal of a
fluoride ion in various silicon and phosphorus species, several trends
were found. In particular, the tetracoordinated species have much higher
energy requirements for ligand removal than do pentacoordinated
species. Further, silicon species have lower energy requirements for
ligand removal than do phosphorus species, which is an indication of
weaker bonds in silicon.
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