Alternative fuel

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Alternative_fuel 

Typical Brazilian filling station with four alternative fuels for sale: biodiesel (B3), gasohol (E25), neat ethanol (E100), and compressed natural gas (CNG). Piracicaba, São Paulo, Brazil.

Alternative fuels, also known as non-conventional and advanced fuels, are fuels derived from sources other than petroleum. Alternative fuels include gaseous fossil fuels like propane, natural gas, methane, and ammonia; biofuels like biodiesel, bioalcohol, and refuse-derived fuel; and other renewable fuels like hydrogen and electricity.

These fuels are intended to substitute for more carbon intensive energy sources like gasoline and diesel in transportation and can help to contribute to decarbonization and reductions in pollution. Alternative fuel is also shown to reduce non-carbon emissions such as the release of nitric oxide and nitrogen dioxide, as well as sulfur dioxide and other harmful gases in the exhaust. This is especially important in industries such as mining, where toxic gases can accumulate more easily.

Official definitions

Definition in the European Union

In the European Union, alternative fuel is defined by Directive 2014/94/EU of the European Parliament and of the Council of 22 October 2014 on the deployment of alternative fuels infrastructure.

'alternative fuels' means fuels or power sources which serve, at least partly, as a substitute for fossil oil sources in the energy supply to transport and which have the potential to contribute to its decarbonisation and enhance the environmental performance of the transport sector. They include, inter alia:

• electricity,
• hydrogen,
• biofuels as defined in point (i) of Article 2 of Directive 2009/28/EC,
• synthetic and paraffinic fuels,
• natural gas, including biomethane, in gaseous form (compressed natural gas (CNG)) and liquefied form (liquefied natural gas (LNG)), and
• liquefied petroleum gas (LPG);

— Directive 2014/94/EU of the European Parliament and of the Council of 22 October 2014 on the deployment of alternative fuels infrastructure.

Definition in the US

In the US, the EPA defines alternative fuel as

Alternative fuel including gaseous fuels such as hydrogen, natural gas, and propane; alcohols such as ethanol, methanol, and butanol; vegetable and waste-derived oils; and electricity. These fuels may be used in a dedicated system that burns a single fuel, or in a mixed system with other fuels including traditional gasoline or diesel, such as in hybrid-electric or flexible fuel vehicles.

— EPA

Definition in Canada

In Canada, since 1996, Alternative Fuels Regulations SOR/96-453 Alternative Fuels Act defined alternative fuel:

For the purposes of the definition alternative fuel in subsection 2(1) of the Act, the following, when used as the sole source of direct propulsion energy of a motor vehicle, are prescribed to be alternative fuels:

(a) ethanol;

(b) methanol;

(c) propane gas;

(d) natural gas;

(e) hydrogen;

(f) electricity;

(g) for the purposes of subsections 4(1) and 5(1) of the Act, any blended fuel that contains at least 50 per cent of one of the fuels referred to in paragraphs (a) to (e); and

(h) for the purposes of subsections 4(2) and 5(2) of the Act, any blended fuel that contains one of the fuels mentioned in paragraphs (a) to (e).

— Alternative Fuels Regulations (SOR/96-453)

China

In China, alternative fuel vehicles should comply with technical guidelines for the local production of alternative-fuel vehicles: they should have a shelf life of more than 100,000 kilometres (62,000 mi), and a complete charge should take less than seven hours. Up to 80% of a charge must be available after less than 30 minutes of charging. In addition, pure-electric vehicles must consume electric energy of less than 0.16 kWh/km.

Biofuel

Main article: Biofuel

Alternative fuel dispensers at a regular gasoline station in Arlington, Virginia. B20 biodiesel at the left and E85 ethanol at the right.

Biofuels are also considered a renewable source. Although renewable energy is used mostly to generate electricity, it is often assumed that some form of renewable energy or a percentage is used to create alternative fuels. Research is ongoing into finding more suitable biofuel crops and improving the oil yields of these crops. Using the current yields, vast amounts of arable land and fresh water would be needed to produce enough oil to completely replace fossil fuel usage.

Biomass

Main article: Biomass

Biomass in the energy production industry is living and recently dead biological material which can be used as fuel or for industrial production. It has become popular among coal power stations, which switch from coal to biomass in order to convert to renewable energy generation without wasting existing generating plant and infrastructure. Biomass most often refers to plants or plant-based materials that are not used for food or feed, and are specifically called nitrocellulose biomass. As an energy source, biomass can either be used directly via combustion to produce heat, or indirectly after converting it to various forms of biofuel.

Algae fuel

Main article: Algae fuel

Algae-based biofuels have been promoted in the media as a potential panacea to crude oil-based transportation problems. Algae could yield more than 2000 gallons of fuel per acre per year of production. Algae based fuels are being successfully tested by the U.S. Navy Algae-based plastics show potential to reduce waste and the cost per pound of algae plastic is expected to be cheaper than traditional plastic prices.

Biodiesel

Main article: Biodiesel

Vegetable oil fuelled bus at South by South West festival, Austin, Texas (March 2008).

Biodiesel is made from animal fats or vegetable oils, renewable resources that come from plants such as atrophy, soybean, sunflowers, corn, olive, peanut, palm, coconut, safflower, canola, sesame, cottonseed, etc. Once these fats or oils are filtered from their hydrocarbons and then combined with alcohol like methanol, diesel is produced from this chemical reaction. These raw materials can either be mixed with pure diesel to make various proportions or used alone. Despite one’s mixture preference, biodiesel will release a smaller number of pollutants (carbon monoxide, particulates and hydrocarbons) than conventional diesel, because biodiesel burns both cleanly and more efficiently. Even with regular diesel’s reduced quantity of sulfur from the LSD (ultra-low sulfur diesel) invention, biodiesel exceeds those levels because it is sulfur-free.

Alcohol fuels

Main articles: Alcohol fuel, Butanol fuel, Ethanol fuel, and Methanol fuel

Methanol and ethanol fuel are primary sources of energy; they are convenient fuels for storing and transporting energy. These alcohols can be used in internal combustion engines as alternative fuels. Butane has another advantage: it is the only alcohol-based motor fuel that can be transported readily by existing petroleum-product pipeline networks, instead of only by tanker trucks and railroad cars.

Ammonia

Research and patenting activities into using ammonia as a marine fuel have increased significantly between 2004 and 2023.

Ammonia (NH₃) can be used as fuel. Benefits of ammonia for ships include reducing greenhouse gas emissions. Nitrogen reduction is being considered as a possible component for fuel cells and combustion engines through research of conversion of ammonia to nitrogen gas and hydrogen gas.

Ammonia is the simplest molecule that carries hydrogen in a liquid form. It is carbon-free and can be produced using renewable energy. Ammonia can become a transitional fuel soon because of its relative easiness of storage and distribution.

Emulsion fuel

Emulsified fuels include multiple components that are mixed to a water-in-oil emulsion, which are created to improve the fuels combustive properties. Diesel can also be emulsified with water to be used as a fuel. It helps in improving engine efficiency and reducing exhaust emissions.

Carbon-neutral and negative fuels

Carbon-neutral fuel is synthetic fuel—such as methane, gasoline, diesel fuel or jet fuel—produced from renewable or nuclear energy used to hydrogenate waste carbon dioxide recycled from power plant flue exhaust gas or derived from carbolic acid in seawater. Such fuels are potentially carbon neutral because they do not result in a net increase in atmospheric greenhouse gases. To the extent that carbon neutral fuels displace fossil fuels, or if they are produced from waste carbon or seawater carbolic acid, and their combustion is subject to carbon capture at the flue or exhaust pipe, they result in negative carbon dioxide emission and net carbon dioxide removal from the atmosphere, and thus constitute a form of greenhouse gas remediation. Such carbon neutral and negative fuels can be produced by the electrolysis of water to make hydrogen used in the Sabatier reaction to produce methane which may then be stored to be burned later in power plants as synthetic natural gas, transported by pipeline, truck, or tanker ship, or be used in gas to liquids processes such as the Fischer–Tropsch process to make traditional transportation or heating fuels.

Carbon-neutral fuels have been proposed for distributed storage for renewable energy, minimizing problems of wind and solar intermittent, and enabling transmission of wind, water, and solar power through existing natural gas pipelines. Such renewable fuels could alleviate the costs and dependency issues of imported fossil fuels without requiring either electrification of the vehicle fleet or conversion to hydrogen or other fuels, enabling continued compatible and affordable vehicles. Germany has built a 250-kilowatt synthetic methane plant which they are scaling up to 10 megawatts. Audi has constructed a carbon neutral liquefied natural gas (LNG) plant in Werlte, Germany. The plant is intended to produce transportation fuel to offset LNG used in their A3 Sportback g-tron automobiles, and can keep 2,800 metric tons of CO₂ out of the environment per year at its initial capacity. Other commercial developments are taking place in Columbia, South Carolina, Camarillo, California, and Darlington, England.

The least expensive source of carbon for recycling into fuel is flue-gas emissions from fossil-fuel combustion, where it can be extracted for about US $7.50 per ton. Automobile exhaust gas capture has also been proposed to be economical but would require extensive design changes or retrofitting. Since carbonic acid in seawater is in chemical equilibrium with atmospheric carbon dioxide, extraction of carbon from seawater has been studied. Researchers have estimated that carbon extraction from seawater would cost about $50 per ton. Carbon capture from ambient air is more costly, at between $600 and $1000 per ton and is considered impractical for fuel synthesis or carbon sequestration.

Nighttime wind power is considered the most economical form of electrical power with which to synthesize fuel, because the load curve for electricity peaks sharply during the warmest hours of the day, but wind tends to blow slightly more at night than during the day. Therefore, the price of nighttime wind power is often much less expensive than any alternative. Off-peak wind power prices in high wind penetration areas of the U.S. averaged 1.64 cents per kilowatt-hour in 2009, but only 0.71 cents/kWh during the least expensive six hours of the day. Typically, wholesale electricity costs 2 to 5 cents/kWh during the day. Commercial fuel synthesis companies suggest they can produce fuel for less than petroleum fuels when oil costs more than $55 per barrel. The U.S. Navy estimates that shipboard production of jet fuel from nuclear power would cost about $6 per gallon. While that was about twice the petroleum fuel cost in 2010, it is expected to be much less than the market price in less than five years if recent trends continue. Moreover, since the delivery of fuel to a carrier battle group costs about $8 per gallon, shipboard production is already much less expensive. However, U.S. civilian nuclear power is considerably more expensive than wind power. The Navy's estimate that 100 megawatts can produce 41,000 gallons of fuel per day indicates that terrestrial production from wind power would cost less than $1 per gallon.

Hydrogen and formic acid

Main article: Hydrogen fuel

Hydrogen is an emissionless fuel. The byproduct of hydrogen burning is water, although some mono-nitrogen oxides NOx are produced when hydrogen is burned with air.

Main article: Formic acid

Another fuel is formic acid. The fuel is used by converting it first to hydrogen and using that in a fuel cell. Formic acid is much more easy to store than hydrogen.

Hydrogen/compressed natural gas mixture

Main article: HCNG

HCNG (or H2CNG) is a mixture of compressed natural gas and 4–9 percent hydrogen by energy. Hydrogen could also be used as hydroxy gas for better combustion characteristics of compression-ignition engines. Hydroxy gas is obtained through electrolysis of water.

Compressed air

The air engine is an emission-free piston engine using compressed air as fuel.

Propane autogas

Main article: Autogas

Propane is a cleaner burning, high-performance fuel derived from multiple sources. It is known by many names including propane, LPG (liquified propane gas), LPA (liquid propane autogas), Autogas and others. Propane is a hydrocarbon fuel and is a member of the natural gas family.

Propane as an automotive fuel shares many of the physical attributes of gasoline while reducing tailpipe emissions and well to wheel emissions overall. Propane is the number one alternative fuel in the world and offers an abundance of supply, liquid storage at low pressure, an excellent safety record and large cost savings when compared to traditional fuels.

Propane delivers an octane rating between 104 and 112 depending on the composition of the butane/propane ratios of the mixture. Propane autogas in a liquid injection format captures the phase change from liquid to gas state within the cylinder of the combustion engine producing an "intercooler" effect, reducing the cylinder temperature and increasing air density. The resultant effect allows more advance on the ignition cycle and a more efficient engine combustion.

Propane lacks additives, detergents or other chemical enhancements further reducing the exhaust output from the tailpipe. The cleaner combustion also has fewer particulate emissions, lower NO_x due to the complete combustion of the gas within the cylinder, higher exhaust temperatures increasing the efficiency of the catalyst and deposits less acid and carbon inside the engine which extends the useful life of the lubricating oil.

Propane autogas is generated at the well alongside other natural gas and oil products. It is also a by-product of the refining processes which further increase the supply of Propane to the market.

Propane is stored and transported in a liquid state at roughly 5 bar (73 psi) of pressure. Fueling vehicles are similar to gasoline in the speed of delivery with modern fueling equipment. Propane filling stations only require a pump to transfer vehicle fuel and do not require expensive and slow compression systems when compared to compressed natural gas which is usually kept at over 3,000 psi (210 bar).

In a vehicle format, propane autogas can be retrofitted to almost any engine and provide fuel cost savings and lowered emissions while being more efficient as an overall system due to the large, pre-existing propane fueling infrastructure that does not require compressors and the resultant waste of other alternative fuels in well to wheel lifecycles.

Compressed natural gas

Compressed natural gas (CNG) and liquefied natural gas (LNG) are two cleaner combustible alternatives to conventional liquid automobile fuels.

Compressed natural gas fuel types

CNG vehicles can use both renewable CNG and non-renewable CNG.

Conventional CNG is a fossil fuel. New technologies such as horizontal drilling and hydraulic fracturing to economically access unconventional gas resources, appear to have increased the supply of natural gas in a fundamental way.

Renewable natural gas or biogas is a methane-based gas with similar properties to natural gas that can be used as transportation fuel. Present sources of biogas are mainly landfills, sewage, and animal/agri-waste. Based on the process type, biogas can be divided into the following: biogas produced by anaerobic digestion, landfill gas collected from landfills, treated to remove trace contaminants, and synthetic natural gas (SNG).

Practicality

CNG powers more than 5 million vehicles worldwide, and just over 150,000 of these are in the U.S. American usage is growing at a dramatic rate.

Environmental analysis

Because natural gas emits less smog-forming pollutants than other fossil fuels when combusted, cleaner air has been measured in urban localities switching to natural gas vehicles. Tailpipe CO₂ can be reduced by 15–25% compared to gasoline, diesel. The greatest reductions occur in medium and heavy duty, light duty and refuse truck segments.

CO₂ reductions of up to 88% are possible by using biogas.

Natural gas and hydrogen are both lighter than air and can be mixed together.

Nuclear power and radiothermal generators

Main articles: Nuclear power and radiothermal generator

Nuclear reactors

Nuclear power is any nuclear technology designed to extract usable energy from atomic nuclei via controlled nuclear reactions. Currently, the only controlled method uses nuclear fission in a fissile fuel (with a small fraction of the power coming from subsequent radioactive decay). Use of nuclear fusion for controlled power generation is not yet practical, but is an active area of research.

Nuclear power generally requires a nuclear reactor to heat a working fluid such as water, which is then used to create steam pressure, which is converted into mechanical work for the purpose of generating electricity or propulsion in water. Today, more than 15% of the world's electricity comes from nuclear power, and over 150 nuclear-powered naval vessels have been built.

In theory, electricity from nuclear reactors could also be used for propulsion in space, but this has yet to be demonstrated in a space flight. Some smaller reactors, such as the TOPAZ nuclear reactor, are built to minimize moving parts and use methods that convert nuclear energy to electricity more directly, making them useful for space missions, but this electricity has historically been used for other purposes. Power from nuclear fission has been used in a number of spacecraft, all of them uncrewed. The Soviets up to 1988 orbited 33 nuclear reactors in RORSAT military radar satellites, where electric power generated was used to power a radar unit that located ships on the Earth's oceans. The U.S. also orbited one experimental nuclear reactor in 1965, in the SNAP-10A mission.

Thorium fuelled nuclear reactors

Thorium-based nuclear power reactors have also become an area of active research in recent years. It is being backed by many scientists and researchers, and Professor James Hansen, the former Director at NASA Goddard Institute for Space Studies has reportedly said, "After studying climate change for over four decades, it's clear to me that the world is heading for a climate catastrophe unless we develop adequate energy sources to replace fossil fuels. Safer, cleaner and cheaper nuclear power can replace coal and is desperately needed as an essential part of the solution". Thorium is 3–4 times more abundant within nature than uranium, and its ore, monazite, is commonly found in sands along bodies of water. Thorium has also gained interest because it could be easier to obtain than uranium. While uranium mines are enclosed underground and thus very dangerous for the miners, thorium is taken from open pits. Monazite is present in countries such as Australia, the United States and India, in quantities large enough to power the earth for thousands of years. As an alternative to uranium-fuelled nuclear reactors, thorium has been proven to add to proliferation, produces radioactive waste for deep geological repositories like technetium-99 (half-life over 200,000 years), and has a longer fuel cycle.

For a list of experimental and presently-operating thorium-fueled reactors, see Thorium fuel cycle § List of thorium-fueled reactors.

Radiothermal generators

In addition, radioisotopes have been used as alternative fuels, on both lands, and in space. Their use on land is declining due to the danger of theft of isotope and environmental damage if the unit is opened. The decay of radioisotopes generates both heat and electricity in many space probes, particularly probes to outer planets where sunlight is weak, and low temperatures is a problem. Radiothermal generators (RTGs) which use radioisotopes as fuels do not sustain a nuclear chain reaction, but rather generate electricity from the decay of a radioisotope.

d electron count

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/D_electron_count 

The d electron count or number of d electrons is a chemistry formalism used to describe the electron configuration of the valence electrons of a transition metal center in a coordination complex. The d electron count is an effective way to understand the geometry and reactivity of transition metal complexes. The formalism has been incorporated into the two major models used to describe coordination complexes; crystal field theory and ligand field theory, which is a more advanced version based on molecular orbital theory. However the d electron count of an atom in a complex is often different from the d electron count of a free atom or a free ion of the same element.

Electron configurations of transition metal atoms

For free atoms, electron configurations have been determined by atomic spectroscopy. Lists of atomic energy levels and their electron configurations have been published by the National Institute of Standards and Technology (NIST) for both neutral and ionized atoms.

For neutral atoms of all elements, the ground-state electron configurations are listed in general chemistry and inorganic chemistry textbooks. The ground-state configurations are often explained using two principles: the Aufbau principle that subshells are filled in order of increasing energy, and the Madelung rule that this order corresponds to the order of increasing values of (n + l) where n is the principal quantum number and l is the azimuthal quantum number. This rule predicts for example that the 4s orbital (n = 4, l = 0, n + l = 4) is filled before the 3d orbital (n = 3, l = 2, n + l = 5), as in titanium with configuration [Ar]4s²3d².

There are a few exceptions with only one electron (or zero for palladium) in the ns orbital in favor of completing a half or a whole d shell. The usual explanation in chemistry textbooks is that half-filled or completely filled subshells are particularly stable arrangements of electrons. An example is chromium whose electron configuration is [Ar]4s¹3d⁵ with a d electron count of 5 for a half-filled d subshell, although Madelung's rule predicts [Ar]4s²3d⁴. Similarly copper is [Ar]4s¹3d¹⁰ with a full d subshell, and not [Ar]4s²3d⁹. The configuration of palladium is [Kr]4d¹⁰ with zero 5s electrons. However this trend is not consistent: tungsten, a group VI element like Cr and Mo has a Madelung-following [Xe]6s²4f¹⁴5d⁴, and niobium has a [Kr]5s¹4d⁴ as opposed to the Madelung rule predicted [Kr]5s²4d³ which creates two partially-filled subshells.

When a transition metal atom loses one or more electrons to form a positive ion, overall electron repulsion is reduced and the n d orbital energy is lowered more than the (n+1) s orbital energy. The ion is formed by removal of the outer s electrons and tends to have a dⁿ configuration, even though the s subshell is added to neutral atoms before the d subshell. For example, the Ti²⁺ ion has the ground-state configuration [Ar]3d² with a d electron count of 2, even though the total number of electrons is the same as the neutral calcium atom which is [Ar]4s².

In coordination complexes between an electropositive transition metal atom and an electronegative ligand, the transition metal is approximately in an ionic state as assumed in crystal field theory, so that the electron configuration and d electron count are those of the transition metal ion rather than the neutral atom.

Ligand field perspective

Ligand field scheme summarizing σ-bonding in the octahedral complex [Ti(H₂O)₆]³⁺.

According to Ligand Field Theory, the ns orbital is involved in bonding to the ligands and forms a strongly bonding orbital which has predominantly ligand character and the correspondingly strong anti-bonding orbital which is unfilled and usually well above the lowest unoccupied molecular orbital (LUMO). Since the orbitals resulting from the ns orbital are either buried in bonding or elevated well above the valence, the ns orbitals are not relevant to describing the valence. Depending on the geometry of the final complex, either all three of the np orbitals or portions of them are involved in bonding, similar to the ns orbitals. The np orbitals if any that remain non-bonding still exceed the valence of the complex. That leaves the (n − 1)d orbitals to be involved in some portion of the bonding and in the process also describes the metal complex's valence electrons. The final description of the valence is highly dependent on the complex's geometry, in turn highly dependent on the d electron count and character of the associated ligands.

For example, in the MO diagram provided for the [Ti(H₂O)₆]³⁺ the ns orbital – which is placed above (n − 1)d in the representation of atomic orbitals (AOs) – is used in a linear combination with the ligand orbitals, forming a very stable bonding orbital with significant ligand character as well as an unoccupied high energy antibonding orbital which is not shown. In this situation the complex geometry is octahedral, which means two of the d orbitals have the proper geometry to be involved in bonding. The other three d orbitals in the basic model do not have significant interactions with the ligands and remain as three degenerate non-bonding orbitals. The two orbitals that are involved in bonding form a linear combination with two ligand orbitals with the proper symmetry. This results in two filled bonding orbitals and two orbitals which are usually the lowest unoccupied molecular orbitals (LUMO) or the highest partially filled molecular orbitals – a variation on the highest occupied molecular orbitals (HOMO).

Crystal field theory is an alternative description of electronic configurations that is simplified relative to LFT. It rationalizes a number of phenomena, but does not describe bonding nor offer an explanation for why ns electrons are ionized before (n − 1)d electrons.

Tanabe–Sugano diagram

Each of the ten possible d electron counts has an associated Tanabe–Sugano diagram describing gradations of possible ligand field environments a metal center could experience in an octahedral geometry. The Tanabe–Sugano diagram with a small amount of information accurately predicts absorptions in the UV and visible electromagnetic spectrum resulting from d to d orbital electron transitions. It is these d–d transitions, ligand to metal charge transfers (LMCT), or metal to ligand charge transfers (MLCT) that generally give metals complexes their vibrant colors.

Limitation

Counting d electrons is a formalism. Often it is difficult or impossible to assign electrons and charge to the metal center or a ligand. For a high-oxidation-state metal center with a +4 charge or greater it is understood that the true charge separation is much smaller. But referring to the formal oxidation state and d electron count can still be useful when trying to understand the chemistry.

Possible d electron counts

There are many examples of every possible d electron configuration. What follows is a short description of common geometries and characteristics of each possible d electron count and representative examples.

d⁰

Commonly tetrahedral; however it is possible for d⁰ complexes to accommodate many electron pairs (bonds/coordination number) since their d orbitals are empty and well away from the 18-electron ceiling. Often colorless due to the lack of d to d transitions.

Examples: titanium tetrachloride, titanocene dichloride, Schwartz's reagent.

d¹

Examples: molybdenum(V) chloride, vanadyl acetylacetonate, vanadocene dichloride, vanadium tetrachloride.

d²

Examples: titanocene dicarbonyl.

d³

Examples: Reinecke's salt.

d⁴

Octahedral high-spin: 4 unpaired electrons, paramagnetic, substitutionally labile.

Octahedral low-spin: 2 unpaired electrons, paramagnetic, substitutionally inert.

d⁵

High-spin [Fe(NO₂)₆]³⁻ crystal field diagram

Low-spin [Fe(NO₂)₆]³⁻ crystal field diagram

Octahedral high-spin: 5 unpaired electrons, paramagnetic, substitutionally labile.

Octahedral low-spin: 1 unpaired electron, paramagnetic, substitutionally inert.

Examples: potassium ferrioxalate, vanadium carbonyl.

d⁶

Commonly octahedral complexes in both high spin and low spin.

Octahedral high-spin: 4 unpaired electrons, paramagnetic, substitutionally labile.

Octahedral low-spin: no unpaired electrons, diamagnetic, substitutionally inert.

Examples: hexamminecobalt(III) chloride, sodium cobaltinitrite, molybdenum hexacarbonyl, ferrocene, ferroin, chromium carbonyl.

d⁷

Octahedral high spin: 3 unpaired electrons, paramagnetic, substitutionally labile.

Octahedral low spin: 1 unpaired electron, paramagnetic, substitutionally labile.

Examples: cobaltocene.

d⁸

Complexes which are d⁸ high-spin are usually octahedral (or tetrahedral) while low-spin d⁸ complexes are generally 16-electron square planar complexes. For first row transition metal complexes such as Ni²⁺ and Cu⁺ also form five-coordinate 18-electron species which vary from square pyramidal to trigonal bipyramidal.

Octahedral high spin: 2 unpaired electrons, paramagnetic, substitutionally labile.

Square planar low spin: no unpaired electrons, diamagnetic, substitutionally inert.

Examples: cisplatin, nickelocene, dichlorobis(ethylenediamine)nickel(II), iron pentacarbonyl, Zeise's salt, Vaska's complex, Wilkinson's catalyst.

d⁹

Stable complexes with this electron count are more common for first row (period four) transition metals center than they are for complexes based around second or third row transition metals centers. These include both four-coordinate 17-electron species and five-coordinate 19-electron species.

Examples: Schweizer's reagent.

d¹⁰

Often tetrahedral complexes limited to form 4 additional bonds (8 additional electrons) by the 18-electron ceiling. Often colorless due to the lack of d to d transitions.

Examples: tetrakis(triphenylphosphine)palladium(0), nickel carbonyl.

Molecular orbital

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Molecular_orbital

Complete acetylene (H–C≡C–H) molecular orbital set. The left column shows MO's which are occupied in the ground state, with the lowest-energy orbital at the top. The white and grey line visible in some MO's is the molecular axis passing through the nuclei. The orbital wave functions are positive in the red regions and negative in the blue. The right column shows virtual MO's which are empty in the ground state, but may be occupied in excited states.

In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The terms atomic orbital and molecular orbital were introduced by Robert S. Mulliken in 1932 to mean one-electron orbital wave functions. At an elementary level, they are used to describe the region of space in which a function has a significant amplitude.

In an isolated atom, the orbital electrons' location is determined by functions called atomic orbitals. When multiple atoms combine chemically into a molecule by forming a valence chemical bond, the electrons' locations are determined by the molecule as a whole, so the atomic orbitals combine to form molecular orbitals. The electrons from the constituent atoms occupy the molecular orbitals. Mathematically, molecular orbitals are an approximate solution to the Schrödinger equation for the electrons in the field of the molecule's atomic nuclei. They are usually constructed by combining atomic orbitals or hybrid orbitals from each atom of the molecule, or other molecular orbitals from groups of atoms. They can be quantitatively calculated using the Hartree–Fock or self-consistent field (SCF) methods.

Molecular orbitals are of three types: bonding orbitals which have an energy lower than the energy of the atomic orbitals which formed them, and thus promote the chemical bonds which hold the molecule together; antibonding orbitals which have an energy higher than the energy of their constituent atomic orbitals, and so oppose the bonding of the molecule, and non-bonding orbitals which have the same energy as their constituent atomic orbitals and thus have no effect on the bonding of the molecule.

Overview

A molecular orbital (MO) can be used to represent the regions in a molecule where an electron occupying that orbital is likely to be found. Molecular orbitals are approximate solutions to the Schrödinger equation for the electrons in the electric field of the molecule's atomic nuclei. However calculating the orbitals directly from this equation is far too intractable a problem. Instead they are obtained from the combination of atomic orbitals, which predict the location of an electron in an atom. A molecular orbital can specify the electron configuration of a molecule: the spatial distribution and energy of one (or one pair of) electron(s). Most commonly a MO is represented as a linear combination of atomic orbitals (the LCAO-MO method), especially in qualitative or very approximate usage. They are invaluable in providing a simple model of bonding in molecules, understood through molecular orbital theory. Most present-day methods in computational chemistry begin by calculating the MOs of the system. A molecular orbital describes the behavior of one electron in the electric field generated by the nuclei and some average distribution of the other electrons. In the case of two electrons occupying the same orbital, the Pauli principle demands that they have opposite spin. Necessarily this is an approximation, and highly accurate descriptions of the molecular electronic wave function do not have orbitals (see configuration interaction).

Molecular orbitals are, in general, delocalized throughout the entire molecule. Moreover, if the molecule has symmetry elements, its nondegenerate molecular orbitals are either symmetric or antisymmetric with respect to any of these symmetries. In other words, the application of a symmetry operation S (e.g., a reflection, rotation, or inversion) to molecular orbital ψ results in the molecular orbital being unchanged or reversing its mathematical sign: Sψ = ±ψ. In planar molecules, for example, molecular orbitals are either symmetric (sigma) or antisymmetric (pi) with respect to reflection in the molecular plane. If molecules with degenerate orbital energies are also considered, a more general statement that molecular orbitals form bases for the irreducible representations of the molecule's symmetry group holds. The symmetry properties of molecular orbitals means that delocalization is an inherent feature of molecular orbital theory and makes it fundamentally different from (and complementary to) valence bond theory, in which bonds are viewed as localized electron pairs, with allowance for resonance to account for delocalization.

In contrast to these symmetry-adapted canonical molecular orbitals, localized molecular orbitals can be formed by applying certain mathematical transformations to the canonical orbitals. The advantage of this approach is that the orbitals will correspond more closely to the "bonds" of a molecule as depicted by a Lewis structure. As a disadvantage, the energy levels of these localized orbitals no longer have physical meaning. (The discussion in the rest of this article will focus on canonical molecular orbitals. For further discussions on localized molecular orbitals, see: natural bond orbital and sigma-pi and equivalent-orbital models.)

Formation of molecular orbitals

Molecular orbitals arise from allowed interactions between atomic orbitals, which are allowed if the symmetries (determined from group theory) of the atomic orbitals are compatible with each other. Efficiency of atomic orbital interactions is determined from the overlap (a measure of how well two orbitals constructively interact with one another) between two atomic orbitals, which is significant if the atomic orbitals are close in energy. Finally, the number of molecular orbitals formed must be equal to the number of atomic orbitals in the atoms being combined to form the molecule.

Qualitative discussion

For an imprecise, but qualitatively useful, discussion of the molecular structure, the molecular orbitals can be obtained from the "Linear combination of atomic orbitals molecular orbital method" ansatz. Here, the molecular orbitals are expressed as linear combinations of atomic orbitals.

Linear combinations of atomic orbitals (LCAO)

Main article: Linear combination of atomic orbitals

Molecular orbitals were first introduced by Friedrich Hund and Robert S. Mulliken in 1927 and 1928. The linear combination of atomic orbitals or "LCAO" approximation for molecular orbitals was introduced in 1929 by Sir John Lennard-Jones. His ground-breaking paper showed how to derive the electronic structure of the fluorine and oxygen molecules from quantum principles. This qualitative approach to molecular orbital theory is part of the start of modern quantum chemistry. Linear combinations of atomic orbitals (LCAO) can be used to estimate the molecular orbitals that are formed upon bonding between the molecule's constituent atoms. Similar to an atomic orbital, a Schrödinger equation, which describes the behavior of an electron, can be constructed for a molecular orbital as well. Linear combinations of atomic orbitals, or the sums and differences of the atomic wavefunctions, provide approximate solutions to the Hartree–Fock equations which correspond to the independent-particle approximation of the molecular Schrödinger equation. For simple diatomic molecules, the wavefunctions obtained are represented mathematically by the equations

${\displaystyle \mathrm{\Psi }=c_a{\psi }_a+c_b{\psi }_b}$

${\displaystyle {\mathrm{\Psi }}^{\ast }=c_a{\psi }_a-c_b{\psi }_b}$

where ${\displaystyle \mathrm{\Psi }}$ and ${\displaystyle {\mathrm{\Psi }}^{\ast }}$ are the molecular wavefunctions for the bonding and antibonding molecular orbitals, respectively, ${\displaystyle {\psi }_a}$ and ${\displaystyle {\psi }_b}$ are the atomic wavefunctions from atoms a and b, respectively, and ${\displaystyle c_a}$ and ${\displaystyle c_b}$ are adjustable coefficients. These coefficients can be positive or negative, depending on the energies and symmetries of the individual atomic orbitals. As the two atoms become closer together, their atomic orbitals overlap to produce areas of high electron density, and, as a consequence, molecular orbitals are formed between the two atoms. The atoms are held together by the electrostatic attraction between the positively charged nuclei and the negatively charged electrons occupying bonding molecular orbitals.

Bonding, antibonding, and nonbonding MOs

When atomic orbitals interact, the resulting molecular orbital can be of three types: bonding, antibonding, or nonbonding.

Bonding MOs:

• Bonding interactions between atomic orbitals are constructive (in-phase) interactions.
• Bonding MOs are lower in energy than the atomic orbitals that combine to produce them.

Antibonding MOs:

• Antibonding interactions between atomic orbitals are destructive (out-of-phase) interactions, with a nodal plane where the wavefunction of the antibonding orbital is zero between the two interacting atoms
• Antibonding MOs are higher in energy than the atomic orbitals that combine to produce them.

Nonbonding MOs:

• Nonbonding MOs are the result of no interaction between atomic orbitals because of lack of compatible symmetries.
• Nonbonding MOs will have the same energy as the atomic orbitals of one of the atoms in the molecule.

Sigma and pi labels for MOs

The type of interaction between atomic orbitals can be further categorized by the molecular-orbital symmetry labels σ (sigma), π (pi), δ (delta), φ (phi), γ (gamma) etc. These are the Greek letters corresponding to the atomic orbitals s, p, d, f and g respectively. The number of nodal planes containing the internuclear axis between the atoms concerned is zero for σ MOs, one for π, two for δ, three for φ and four for γ.

σ symmetry

Further information: Sigma bond

A MO with σ symmetry results from the interaction of either two atomic s-orbitals or two atomic p_z-orbitals. An MO will have σ-symmetry if the orbital is symmetric with respect to the axis joining the two nuclear centers, the internuclear axis. This means that rotation of the MO about the internuclear axis does not result in a phase change. A σ* orbital, sigma antibonding orbital, also maintains the same phase when rotated about the internuclear axis. The σ* orbital has a nodal plane that is between the nuclei and perpendicular to the internuclear axis.

π symmetry

Further information: Pi bond

A MO with π symmetry results from the interaction of either two atomic p_x orbitals or p_y orbitals. An MO will have π symmetry if the orbital is asymmetric with respect to rotation about the internuclear axis. This means that rotation of the MO about the internuclear axis will result in a phase change. There is one nodal plane containing the internuclear axis, if real orbitals are considered.

A π* orbital, pi antibonding orbital, will also produce a phase change when rotated about the internuclear axis. The π* orbital also has a second nodal plane between the nuclei.

δ symmetry

Further information: Delta bond

A MO with δ symmetry results from the interaction of two atomic d_xy or d_x²-y² orbitals. Because these molecular orbitals involve low-energy d atomic orbitals, they are seen in transition-metal complexes. A δ bonding orbital has two nodal planes containing the internuclear axis, and a δ* antibonding orbital also has a third nodal plane between the nuclei.

φ symmetry

Further information: Phi bond

Suitably aligned f atomic orbitals overlap to form phi molecular orbital (a phi bond)

Theoretical chemists have conjectured that higher-order bonds, such as phi bonds corresponding to overlap of f atomic orbitals, are possible. There is no known example of a molecule purported to contain a phi bond.

Gerade and ungerade symmetry

For molecules that possess a center of inversion (centrosymmetric molecules) there are additional labels of symmetry that can be applied to molecular orbitals. Centrosymmetric molecules include:

• Homonuclear diatomics, X₂
• Octahedral, EX₆
• Square planar, EX₄.

Non-centrosymmetric molecules include:

• Heteronuclear diatomics, XY
• Tetrahedral, EX₄.

If inversion through the center of symmetry in a molecule results in the same phases for the molecular orbital, then the MO is said to have gerade (g) symmetry, from the German word for even. If inversion through the center of symmetry in a molecule results in a phase change for the molecular orbital, then the MO is said to have ungerade (u) symmetry, from the German word for odd. For a bonding MO with σ-symmetry, the orbital is σ_g (s' + s'' is symmetric), while an antibonding MO with σ-symmetry the orbital is σ_u, because inversion of s' – s'' is antisymmetric. For a bonding MO with π-symmetry the orbital is π_u because inversion through the center of symmetry for would produce a sign change (the two p atomic orbitals are in phase with each other but the two lobes have opposite signs), while an antibonding MO with π-symmetry is π_g because inversion through the center of symmetry for would not produce a sign change (the two p orbitals are antisymmetric by phase).

MO diagrams

Main article: Molecular orbital diagram

The qualitative approach of MO analysis uses a molecular orbital diagram to visualize bonding interactions in a molecule. In this type of diagram, the molecular orbitals are represented by horizontal lines; the higher a line the higher the energy of the orbital, and degenerate orbitals are placed on the same level with a space between them. Then, the electrons to be placed in the molecular orbitals are slotted in one by one, keeping in mind the Pauli exclusion principle and Hund's rule of maximum multiplicity (only 2 electrons, having opposite spins, per orbital; place as many unpaired electrons on one energy level as possible before starting to pair them). For more complicated molecules, the wave mechanics approach loses utility in a qualitative understanding of bonding (although is still necessary for a quantitative approach). Some properties:

• A basis set of orbitals includes those atomic orbitals that are available for molecular orbital interactions, which may be bonding or antibonding
• The number of molecular orbitals is equal to the number of atomic orbitals included in the linear expansion or the basis set
• If the molecule has some symmetry, the degenerate atomic orbitals (with the same atomic energy) are grouped in linear combinations (called symmetry-adapted atomic orbitals (SO)), which belong to the representation of the symmetry group, so the wave functions that describe the group are known as symmetry-adapted linear combinations (SALC).
• The number of molecular orbitals belonging to one group representation is equal to the number of symmetry-adapted atomic orbitals belonging to this representation
• Within a particular representation, the symmetry-adapted atomic orbitals mix more if their atomic energy levels are closer.

The general procedure for constructing a molecular orbital diagram for a reasonably simple molecule can be summarized as follows:

1. Assign a point group to the molecule.

2. Look up the shapes of the SALCs.

3. Arrange the SALCs of each molecular fragment in order of energy, noting first whether they stem from s, p, or d orbitals (and put them in the order s < p < d), and then their number of internuclear nodes.

4. Combine SALCs of the same symmetry type from the two fragments, and from N SALCs form N molecular orbitals.

5. Estimate the relative energies of the molecular orbitals from considerations of overlap and relative energies of the parent orbitals, and draw the levels on a molecular orbital energy level diagram (showing the origin of the orbitals).

6. Confirm, correct, and revise this qualitative order by carrying out a molecular orbital calculation by using commercial software.

Bonding in molecular orbitals

Orbital degeneracy

Main article: Degenerate orbital

Molecular orbitals are said to be degenerate if they have the same energy. For example, in the homonuclear diatomic molecules of the first ten elements, the molecular orbitals derived from the p_x and the p_y atomic orbitals result in two degenerate bonding orbitals (of low energy) and two degenerate antibonding orbitals (of high energy).

Ionic bonds

Main article: Ionic bond

In an ionic bond, oppositely charged ions are bonded by electrostatic attraction. It is possible to describe ionic bonds with molecular orbital theory by treating them as extremely polar bonds. Their bonding orbitals are very close in energy to the atomic orbitals of the anion. They are also very similar in character to the anion's atomic orbitals, which means the electrons are completely shifted to the anion. In computer diagrams, the orbitals are centered on the anion's core.

Bond order

Main article: Bond order

The bond order, or number of bonds, of a molecule can be determined by combining the number of electrons in bonding and antibonding molecular orbitals. A pair of electrons in a bonding orbital creates a bond, whereas a pair of electrons in an antibonding orbital negates a bond. For example, N₂, with eight electrons in bonding orbitals and two electrons in antibonding orbitals, has a bond order of three, which constitutes a triple bond.

Bond strength is proportional to bond order—a greater amount of bonding produces a more stable bond—and bond length is inversely proportional to it—a stronger bond is shorter.

There are rare exceptions to the requirement of molecule having a positive bond order. Although Be₂ has a bond order of 0 according to MO analysis, there is experimental evidence of a highly unstable Be₂ molecule having a bond length of 245 pm and bond energy of 10 kJ/mol.

HOMO and LUMO

Main article: HOMO and LUMO

The highest occupied molecular orbital and lowest unoccupied molecular orbital are often referred to as the HOMO and LUMO, respectively. The difference of the energies of the HOMO and LUMO is called the HOMO-LUMO gap. This notion is often the matter of confusion in literature and should be considered with caution. Its value is usually located between the fundamental gap (difference between ionization potential and electron affinity) and the optical gap. In addition, HOMO-LUMO gap can be related to a bulk material band gap or transport gap, which is usually much smaller than fundamental gap.

Examples

Homonuclear diatomics

Homonuclear diatomic MOs contain equal contributions from each atomic orbital in the basis set. This is shown in the homonuclear diatomic MO diagrams for H₂, He₂, and Li₂, all of which containing symmetric orbitals.

H₂

Electron wavefunctions for the 1s orbital of a lone hydrogen atom (left and right) and the corresponding bonding (bottom) and antibonding (top) molecular orbitals of the H₂ molecule. The real part of the wavefunction is the blue curve, and the imaginary part is the red curve. The red dots mark the locations of the nuclei. The electron wavefunction oscillates according to the Schrödinger wave equation, and orbitals are its standing waves. The standing wave frequency is proportional to the orbital's kinetic energy. (This plot is a one-dimensional slice through the three-dimensional system.)

As a simple MO example, consider the electrons in a hydrogen molecule, H₂ (see molecular orbital diagram), with the two atoms labelled H' and H". The lowest-energy atomic orbitals, 1s' and 1s", do not transform according to the symmetries of the molecule. However, the following symmetry adapted atomic orbitals do:

1s' – 1s"	Antisymmetric combination: negated by reflection, unchanged by other operations
1s' + 1s"	Symmetric combination: unchanged by all symmetry operations

The symmetric combination (called a bonding orbital) is lower in energy than the basis orbitals, and the antisymmetric combination (called an antibonding orbital) is higher. Because the H₂ molecule has two electrons, they can both go in the bonding orbital, making the system lower in energy (hence more stable) than two free hydrogen atoms. This is called a covalent bond. The bond order is equal to the number of bonding electrons minus the number of antibonding electrons, divided by 2. In this example, there are 2 electrons in the bonding orbital and none in the antibonding orbital; the bond order is 1, and there is a single bond between the two hydrogen atoms.

He₂

On the other hand, consider the hypothetical molecule of He₂ with the atoms labeled He' and He". As with H₂, the lowest energy atomic orbitals are the 1s' and 1s", and do not transform according to the symmetries of the molecule, while the symmetry adapted atomic orbitals do. The symmetric combination—the bonding orbital—is lower in energy than the basis orbitals, and the antisymmetric combination—the antibonding orbital—is higher. Unlike H₂, with two valence electrons, He₂ has four in its neutral ground state. Two electrons fill the lower-energy bonding orbital, σ_g(1s), while the remaining two fill the higher-energy antibonding orbital, σ_u*(1s). Thus, the resulting electron density around the molecule does not support the formation of a bond between the two atoms; without a stable bond holding the atoms together, the molecule would not be expected to exist. Another way of looking at it is that there are two bonding electrons and two antibonding electrons; therefore, the bond order is 0 and no bond exists (the molecule has one bound state supported by the Van der Waals potential).

Li₂

Dilithium Li₂ is formed from the overlap of the 1s and 2s atomic orbitals (the basis set) of two Li atoms. Each Li atom contributes three electrons for bonding interactions, and the six electrons fill the three MOs of lowest energy, σ_g(1s), σ_u*(1s), and σ_g(2s). Using the equation for bond order, it is found that dilithium has a bond order of one, a single bond.^[22]

Noble gases

Considering a hypothetical molecule of He₂, since the basis set of atomic orbitals is the same as in the case of H₂, we find that both the bonding and antibonding orbitals are filled, so there is no energy advantage to the pair. HeH would have a slight energy advantage, but not as much as H₂ + 2 He, so the molecule is very unstable and exists only briefly before decomposing into hydrogen and helium. In general, we find that atoms such as He that have full energy shells rarely bond with other atoms. Except for short-lived Van der Waals complexes, there are very few noble gas compounds known.

Heteronuclear diatomics

While MOs for homonuclear diatomic molecules contain equal contributions from each interacting atomic orbital, MOs for heteronuclear diatomics contain different atomic orbital contributions. Orbital interactions to produce bonding or antibonding orbitals in heteronuclear diatomics occur if there is sufficient overlap between atomic orbitals as determined by their symmetries and similarity in orbital energies.

HF

In hydrogen fluoride HF overlap between the H 1s and F 2s orbitals is allowed by symmetry but the difference in energy between the two atomic orbitals prevents them from interacting to create a molecular orbital. Overlap between the H 1s and F 2p_z orbitals is also symmetry allowed, and these two atomic orbitals have a small energy separation. Thus, they interact, leading to creation of σ and σ* MOs and a molecule with a bond order of 1. Since HF is a non-centrosymmetric molecule, the symmetry labels g and u do not apply to its molecular orbitals.

Quantitative approach

To obtain quantitative values for the molecular energy levels, one needs to have molecular orbitals that are such that the configuration interaction (CI) expansion converges fast towards the full CI limit. The most common method to obtain such functions is the Hartree–Fock method, which expresses the molecular orbitals as eigenfunctions of the Fock operator. One usually solves this problem by expanding the molecular orbitals as linear combinations of Gaussian functions centered on the atomic nuclei (see linear combination of atomic orbitals and basis set (chemistry)). The equation for the coefficients of these linear combinations is a generalized eigenvalue equation known as the Roothaan equations, which are in fact a particular representation of the Hartree–Fock equation. There are a number of programs in which quantum chemical calculations of MOs can be performed, including Spartan.

Simple accounts often suggest that experimental molecular orbital energies can be obtained by the methods of ultra-violet photoelectron spectroscopy for valence orbitals and X-ray photoelectron spectroscopy for core orbitals. This, however, is incorrect as these experiments measure the ionization energy, the difference in energy between the molecule and one of the ions resulting from the removal of one electron. Ionization energies are linked approximately to orbital energies by Koopmans' theorem. While the agreement between these two values can be close for some molecules, it can be very poor in other cases.