Organomagnesium chemistry, a subfield of organometallic compounds, refers to the study of magnesium compounds that contains Mg-C bonds. Magnesium is the second element in group 2 (alkaline earth metals), and the ionic radius of Mg2+ is 86 pm, which is larger than Be2+ (59 pm) and smaller than the heavier alkaline earth metal dications (Ca2+ 114 pm, Sr2+ 132 pm, Ba2+ 149 pm), [1] in accordance with periodic trends. Magnesium is less covalent compared to beryllium, and the radius is not large enough for accommodating large number of ligands compared to calcium, strontium and barium. Thus, organomagnesium compounds exhibit unique structure and reactivity in group 2. [2]
The most important type of organomagnesium compound is the Grignard reagents, [3] which are widely used in different fields of synthetic chemistry, especially in organic synthesis, for Grignard reagents serves as a robust source of carbanion. Although most other directions in organomagnesium chemistry are mainly limited to research interest, some areas, such as their application in catalysis and materials, are fast developing. Although most characterized Mg(I) and Mg(0) compounds do not contain Mg-C bonds, [4] [5] [6] which means they cannot be rigorously categorized as organomagnesium compounds, they will be briefly discussed at the end of this page because of their great importance.
Discovered by Victor Grignard at the University of in 1900, [7] compounds with empirical formula RMgX (R = carbanion, X = Cl, Br, I) are known as Grignard reagents, which are widely used in organic synthesis and ligand preparation. [8] [9] [10] Grignard reagents are a common source of carbanion, which can be used to perform nucleophilic addition, substitution, transmetalation, and metal-halogen exchange reactions. The first crystal structure of Grignard reagents was reported by Guggenberger and Rundle in 1964, [11] [12] from a crystalline EtMgBr(THF)2 (Et = ethyl, THF = tetrahydrofuran). The Mg-C bond length was found to be 2.15(2) Å, which is about the sum of covalent radii of magnesium (141(7) pm) and carbon (76(1) pm at sp3 hybridization). [13]
Although Grignard reagents were discovered and commonly used in 1900s, the corresponding fluoride RMgF was not synthesized until 1970, plausibly because of the difficulty in breaking the strong C-F bond. [14] In 1920 Swarts reported the reduction of amyl fluoride to the corresponding hydrocarbon with activated magnesium, [15] while no intermediates were separated. Alkylmagnesium fluoride was first prepared by Ashly and co-workers in 1970, using metal magnesium and catalytic iodine in refluxing tetrahydrofuran or 1,2-dimethoxyethane from the corresponding alkyl fluoride. [16] [17]
Grignard reagents forms dimers in solutions, and the R and X groups are exchanged between magnesium centers, enabling the Schlenk equilibrium between RMgX and MgR2 and MgX2. Recent ab initio molecular dynamics computations [18] [19] have shown that the formation of such dimers is crucial for explaining the reactivity of Grignard reagents.
Dialkylmagnesium is another convenient precursor of magnesium complexes, which is useful when halides are unwanted. Dialkylmagnesium is usually prepared from Grignard reagents, via precipitation of magnesium halide. [20] Solid state dialkylmagnesium forms one-dimensional chains via Mg-C-Mg 3c-2e bonds, and the Mg-C bond length is 2.24(3) Å in dimethylmagnesium (Me2Mg)n, [21] which is about 10 pm longer than the terminal alkyl-Mg bonds (e.g. 2.15(2) Å in EtMgBr(THF)2). Molecular oligomer of dialkylmagnesium with terminal ligands were also synthesized with similar Mg-C bonding scheme. [22] With large steric hinderance, diaryl magnesium [(2,6-Et2C6H3)2Mg] was found to be a molecular dimer with bridging aryl groups, and the bridging Mg-C distances range between 2.243(7) to 2.296(7) Å. [23] Similar bridging alkynyl groups were found in [(Me3Si)2NMg(C≡CR)(THF)]2 (R = Ph, SiMe3) with the bridging Mg-C distance ranging from 2.189(4) to 2.283(4) Å. [24]
By applying synergistic effect of magnesium and another alkaline metal, [25] [26] deprotonation of hydrocarbon derivatives has become another facile method to achieve the corresponding magnesium complexes. For example, in 2001 Mulvey achieved tetradeprotonation of ferrocene trapped in an amide cationic ring with four magnesium and four sodium, [(iPr2N)8Na4Mg4{Fe(C5H3)2}], from free ferrocene and [Na(iPr2N)2Mg(nBu)]. [27] [28]
Unlike beryllium [30] [31] , calcium, strontium, and barium, [32] no homoleptic carbonyl complex of magnesium has been found, probably because it lacks available (n-1)d orbitals, and it has low covalency. However, [Mg(O3)2(CO)2] which contains ozonide anion (O3-) was identified when condensing atomic magnesium, oxygen and carbon monoxide in solid argon matrix. [29] The compound shows increased C-O stretching frequency at 2188.9 cm-1, compared to free carbon monoxide (2143 cm-1), indicating little back-bonding from magnesium to the carbonyl.
The first characterized N-heterocyclic carbene (NHC) complex of magnesium, [(IMes)MgEt2]2 were synthesized in 1993 by Arduengo and co-workers, by simply mixing the stable carbene with diethylmagnesium. [33] In [(IMes)MgEt2]2 the Mg-C(IMes) bond length was found to be 2.279(3) Å, which is significantly longer than the terminal Mg-C(Et) bond of 2.133(4) Å.
In 1995 Arduengo and co-workers characterized NHC adduct of MgCp*2 (Cp* = pentamethylcyclopentadienyl), which features one η5- and one η3-Cp* ligands. [34] NHCs with side arms were also explored. The amido NHC complex of magnesium was synthesized by Arnold and colleagues in 2004, [35] and the magnesium complex using NHC with phenol arms were synthesized and characterized by Zhang and Kawaguchi in 2006. [36]
Since NHCs are better σ donors than ethers like THF, [37] it provides a scaffold for cationic molecular magnesium complexes, for it is categorized as neutral L-type ligand. In 2019, Dagorne and co-workers reported the first cationic alkyl magnesium supported by NHC ligand, [LMgMe(THF)2]+ BPh4- (L = IMes, IPr). [38] The synthesis proceeds through an interesting dimeric intermediate with two uncommon μ2-Me bridges. In [(IPr)MgMe(THF)2]+, the Mg-C(IPr) distance was found to be 2.2224(13) Å, which is slightly shorter than the distance in neutral NHC complexes.
Notably, Gilliard and co-workers reported the equilibrium between L2MgMeBr and [L3MgMe]+Br- (L = 1,3,4,5-tetramethylimidazol-2-ylidene) in d5-bromobenzene, [39] showing the substitution is facile despite its being endothermic.
Allyl Grignard reagents exhibit high reactivity and special selectivity compared to alkyl ones. [40] [41] X-ray determination of single crystal structure [42] [43] [44] and NMR spectroscopy [45] [46] [47] both suggest that the allyl groups favor an η1- instead of η3-coordination pattern. Density functional theory (DFT) computations [48] have shown that the homoleptic complex (C3H5)2Mg adopts a C2-symmetric geometry with two η3-allyl groups, while coordination of THF molecules changed the allyl groups to η1.
Allyl groups can also serve as bridging ligands. In 2001, Balley and co-workers reported a magnesium complex {(Dipp-tBu NacNac)Mg(C3H5)}6 (Dipp-tBuNacnac = [HC{C(tBu)NDipp}2]-) featuring six μ-η1:η1 allyl ligands. [49] Bridging μ-η1:η2 allyl ligands were also identified in a dimeric silyl allyl magnesium complex. [48]
Dicyclopentadienyl (Cp) magnesium or magnesocene (Cp2Mg) was first characterized in 1954 by Wilkinson and Cotton, [50] and later crystal structure analysis [51] [52] shows that it features a 5-fold symmetry with two η5-cyclopentadienyl ligands. MgCp2 has an average Mg-C distance of 2.304(8) Å an average C-C distance of 1.39(2) Å, which is in agreement with a later gas-phase diffraction study. [53] For comparison, in ferrocene the Fe-C distance is 2.04(1) Å and the C-C distance is 1.40(2) Å. Magnesocene derivatives generally adopt the ideal structures with staggered parallel Cp rings, though introducing large steric hinderance may distort the geometry, such as [{1,2,4-(Me3Si)3C5H2}2Mg] which has slightly bent sandwich structure. [54]
25Mg-NMR spectroscopy suggested the Mg-Cp interaction has significant covalent character. [55] However, because of lacking (n-1)d orbitals and back bonding, [56] the Mg-Cp interaction is weak, enabling cyclopentadienyl magnesium complexes to serve as Cp- precursor. For example, in the following reaction Cp2Mg transfers two Cp- ligands to synthesize the [MnCp3]- anion: [57]
Adding ligands to magnesocene derivatives gives bent Cp2MgL species, and the bonding modes of the cyclopentadiene are sensitive to the changes in the coordination environment. [34] In [(C5Me4H)2MgL] (L = 1,3-di-iso-propyl-4,5-dimethylimidazol-2-ylidene), [58] one of the C5Me4H ligand is slipped by 0.807 Å from the center, which makes difference of 0.69 Å between the shortest and the longest Mg-C distance on the ligand. Thus the complex can be described as [(η5-C5Me4H)(η3-C5Me4H)MgL].
Another important complex is the magnesium anthracene, which was first prepared by Ramsden in 1965, using a THF suspension of magnesium and anthracene. [59] From the solution crystalline [(C14H10)Mg(THF)3] can be obtained, showing two relatively shorter Mg-C distances of 2.225(1) Å, on C9 and C10 of the anthracene. [60] [61] [(C14H10)Mg(THF)3] reacts like [C14H10]2- with the two negative charges mainly localized on C9 and C10, and can thus act as nucleophile to give functionalized anthracene or 9,10-dihydroanthracene derivatives. [62] One of its recent application is to synthesize dibenzo-7λ3-phosphanorbornadiene (RPC14H10), which can be used as phosphinidene transfer reagent. [63]
One of the first magnesium-neutral C=C π interactions was identified in [(DBAP)2Mg]2 (DBAP = dibenzo[b,f]azepinate) by Harder and co-workers in 2017. [64] The structure features one magnesium atom coordinated by four amino groups, and the other magnesium atom is weakly bound to three nitrogen atoms and three C=C π bonds. The Mg-olefin geometry is slightly asymmetric, with the shorter Mg-C distance range from 2.653(3) to 2.832(3) Å with an average of 2.740 Å, and the longer ones vary from 2.792(3) to 2.920(3) Å with an average of 2.848 Å. Previous research has also shown Mg-C distances of 2.559(6) to 2.638(3) Å in a tetrakis(2-aryloxy)ethylene system, [65] but the shorter distance may be attributed to steric restriction. [64]
In 2018, Harder and co-workers identified the first intramolecular Mg-π interaction in a cationic NacNac supported system, i.e., [(Dipp-NacNac)Mg(EtC≡CEt)][B(C6F5)4] and [(Dipp-NacNac)Mg(η3-C6H6)][B(C6F5)4] (Dipp-Nacnac = [HC{C(Me)NDipp}2]-). [66] In the alkyne complex the two Mg-C distances are 2.480(2) and 2.399(2) Å, and in the arene complex the shortest Mg-C bond length is 2.520(2) Å. Later study showed that the binding mode of arenes is sensitive to substitution on the arene, e.g., [(Dipp-NacNac)Mg(η6-mesitylene)][B(C6F5)4] features a η6-like mesitylene with Mg-C distance ranging from 2.5325(17) to 2.6988(16) Å. [67] [68] The first intramolecular Mg-alkene binding was later identified in 2020. [69] In [(Dipp-NacNac)Mg(H2C=CEt2)][B(C6F5)4], Mg is closer to the terminal methylene with Mg-C distance of 2.338(2) Å, and the longer Mg-C distance is 2.944(5) Å. DFT calculations and AIM analysis [64] [69] [70] suggested that the Mg-alkene interaction is less covalent and should be mainly described as ion-induced dipole interactions, and the large asymmetry in the 2-ethylbutene complex should be attributed to charge distribution on the two sp2 carbon atoms.
Although [(C6H6)2Mg]2+ remains unknown, the isoelectronic boratabenzene complex has been synthesized by Herberich and co-workers in 2000. [71] In the work [(C5H5BMe)2Mg] and [(3,5-Me2C5H3BNMe2)2Mg] were characterized, with [(C5H5BMe)2Mg] having average Mg-C distance of 2.403 Å (2.359(2) to 2.453(2) Å) and [(3,5-Me2C5H3BNMe2)2Mg] having average Mg-C distance of 2.391 Å (2.350(1) to 2.429(2) Å). The slightly longer Mg-C distance compared to Cp2Mg indicates a weaker donor ability of the boratabenzene, likely due to a more dispersed electron density among six instead of five atoms. Similar to Cp2Mg derivatives, adding ligands like bipyridine (bipy) makes one of the boratabenzene slipped to form [(η5-3,5-Me2C5H3BNMe2) (η1-3,5-Me2C5H3BNMe2)Mg(bipy)], while coordination of THF changes the ligand to N-donor in [(N-3,5-Me2C5H3BNMe2)2Mg(THF)2].
For the wide applications of Grignard reagents, please refer to the corresponding page.
The luminescence properties of magnesium compounds have been studied since the pioneering work by Chandrasekhar and co-workers in 2005, where a phosphorus-based tris-hydrazone complex of Mg(II) was synthesized and determined to have an intense fluorescence emission peak at 442 nm in dichloromethane solution. [72]
In 2018, Roesky and co-workers developed a diamidophosphine ligand, with the ligated dimagnesium(II) compound having a fluorescence quantum yield of 34% in the solution. [73] Munz and co-workers developed a pincer-like carbazole-mesoionic carbene ligand in 2021, delivering its magnesium complex a quantum yield of 14%. [74] In 2022, Sen and colleagues reported two 2,2′-pyridylpyrrolide supported magnesium complexes, one mononuclear and one dinuclear, with quantum yield of 14% and 22%, respectively. [75]
Catalytic systems for hydroboration reactions based on magnesium complexes have been investigated, [76] with the pioneering work by Hill in 2012, where a Nacnac supported magnesium(II) hydride dimer was used to catalyze the hydroboration of ketones. [77] Magnesium complexes have also been found to catalyze nucleophilic cyclization reactions. [78]
The first molecular Mg(I) compound, which contains a Mg-Mg bond, was synthesized by Jones, Stasch, and co-workers in 2007, from potassium metal reduction of Nacnac or priso ligand supported magnesium halide. [80] In the [(Dipp-Nacnac)Mg]2 the Mg-Mg distance is 2.8457(8) Å, and in the [(Dipp-NMe2Priso)Mg]2 (Dipp-NMe2Priso = [Me2NC(NDipp)2]-) the Mg-Mg distance is 2.8508(12) Å, both approximately equal to twice of the covalent radius of magnesium. In 2016, Jones and co-workers reported Mg(I) compounds with super bulky amido ligands, delivering a two-coordinate Mg(I). [81] In [{2,6-(Ph2CH)2-4-iPr-C6H2}Mg]2, the Mg-Mg distance of 2.8223(11) Å is significantly shorter than the N,N’-chelated Mg(I) dimers.
The first Mg(0) compound was reported in 2021 by Harder and co-workers, by reducing a similar Nacnac chelated in a harsher condition using newly prepared Na/NaCl. [82]
In 2010, Platts and co-workers characterized a non-nuclear attractor in the Mg-Mg bond of [(Dipp-Nacnac)Mg]2 from experimental electron density, which suggest the specialty of the Mg-Mg bond. [83]
Mg(I) compounds have been proven to be useful reductants in synthetic chemistry. They have been found to be doing reversible addition to C=C double bonds, [84] C-F bond activation, [85] CO reduction, [86] [87] defluorination of PTFE, [88] and reduction of OCP-. [89]
In organometallic chemistry, organolithium reagents are chemical compounds that contain carbon–lithium (C–Li) bonds. These reagents are important in organic synthesis, and are frequently used to transfer the organic group or the lithium atom to the substrates in synthetic steps, through nucleophilic addition or simple deprotonation. Organolithium reagents are used in industry as an initiator for anionic polymerization, which leads to the production of various elastomers. They have also been applied in asymmetric synthesis in the pharmaceutical industry. Due to the large difference in electronegativity between the carbon atom and the lithium atom, the C−Li bond is highly ionic. Owing to the polar nature of the C−Li bond, organolithium reagents are good nucleophiles and strong bases. For laboratory organic synthesis, many organolithium reagents are commercially available in solution form. These reagents are highly reactive, and are sometimes pyrophoric.
A transition metal carbene complex is an organometallic compound featuring a divalent carbon ligand, itself also called a carbene. Carbene complexes have been synthesized from most transition metals and f-block metals, using many different synthetic routes such as nucleophilic addition and alpha-hydrogen abstraction. The term carbene ligand is a formalism since many are not directly derived from carbenes and most are much less reactive than lone carbenes. Described often as =CR2, carbene ligands are intermediate between alkyls (−CR3) and carbynes (≡CR). Many different carbene-based reagents such as Tebbe's reagent are used in synthesis. They also feature in catalytic reactions, especially alkene metathesis, and are of value in both industrial heterogeneous and in homogeneous catalysis for laboratory- and industrial-scale preparation of fine chemicals.
Molybdenum hexacarbonyl (also called molybdenum carbonyl) is the chemical compound with the formula Mo(CO)6. This colorless solid, like its chromium, tungsten, and seaborgium analogues, is noteworthy as a volatile, air-stable derivative of a metal in its zero oxidation state.
Chromium hexacarbonyl is a chromium(0) organometallic compound with the formula Cr(CO)6. It is a homoleptic complex, which means that all the ligands are identical. It is a colorless crystalline air-stable solid, with a high vapor pressure.
Grignard reagents or Grignard compounds are chemical compounds with the general formula R−Mg−X, where X is a halogen and R is an organic group, normally an alkyl or aryl. Two typical examples are methylmagnesium chloride Cl−Mg−CH3 and phenylmagnesium bromide (C6H5)−Mg−Br. They are a subclass of the organomagnesium compounds.
The triazol-5-ylidenes are a group of persistent carbenes which includes the 1,2,4-triazol-5-ylidene system and the 1,2,3-triazol-5-ylidene system. As opposed to the now ubiquitous NHC systems based on imidazole rings, these carbenes are structured from triazole rings. 1,2,4-triazol-5-ylidene can be thought of as an analog member of the NHC family, with an extra nitrogen in the ring, while 1,2,3-triazol-5-ylidene is better thought of as a mesoionic carbene (MIC). Both isomers of this group of carbenes benefit from enhanced stability, with certain examples exhibiting greater thermal stability, and others extended shelf life.
Group 2 organometallic chemistry refers to the organic derivativess of any group 2 element. It is a subtheme to main group organometallic chemistry. By far the most common group 2 organometallic compounds are the magnesium-containing Grignard reagents which are widely used in organic chemistry. Other organometallic group 2 compounds are typically limited to academic interests.
Organonickel chemistry is a branch of organometallic chemistry that deals with organic compounds featuring nickel-carbon bonds. They are used as a catalyst, as a building block in organic chemistry and in chemical vapor deposition. Organonickel compounds are also short-lived intermediates in organic reactions. The first organonickel compound was nickel tetracarbonyl Ni(CO)4, reported in 1890 and quickly applied in the Mond process for nickel purification. Organonickel complexes are prominent in numerous industrial processes including carbonylations, hydrocyanation, and the Shell higher olefin process.
Methylmagnesium chloride is an organometallic compound with the general formula CH3MgCl. This highly flammable, colorless, and moisture sensitive material is the simplest Grignard reagent and is commercially available, usually as a solution in tetrahydrofuran.
Organoscandium chemistry is an area with organometallic compounds focused on compounds with at least one carbon to scandium chemical bond. The interest in organoscandium compounds is mostly academic but motivated by potential practical applications in catalysis, especially in polymerization. A common precursor is scandium chloride, especially its THF complex.
Dimethylmagnesium is an organomagnesium compound. It is a white pyrophoric solid. Dimethylmagnesium is used in the synthesis of organometallic compounds.
Transition metal carbyne complexes are organometallic compounds with a triple bond between carbon and the transition metal. This triple bond consists of a σ-bond and two π-bonds. The HOMO of the carbyne ligand interacts with the LUMO of the metal to create the σ-bond. The two π-bonds are formed when the two HOMO orbitals of the metal back-donate to the LUMO of the carbyne. They are also called metal alkylidynes—the carbon is a carbyne ligand. Such compounds are useful in organic synthesis of alkynes and nitriles. They have been the focus on much fundamental research.
Transition metal alkyl complexes are coordination complexes that contain a bond between a transition metal and an alkyl ligand. Such complexes are not only pervasive but are of practical and theoretical interest.
Turbo-Hauser bases are amido magnesium halides that contain stoichiometric amounts of LiCl. These mixed Mg/Li amides of the type R2NMgCl⋅LiCl are used in organic chemistry as non-nucleophilic bases for metalation reactions of aromatic and heteroaromatic substrates. Compared to their LiCl free ancestors Turbo-Hauser bases show an enhanced kinetic basicity, excellent regioselectivity, high functional group tolerance and a better solubility.
Magnesocene, also known as bis(cyclopentadienyl)magnesium(II) and sometimes abbreviated as MgCp2, is an organometallic compound with the formula Mg(η5-C5H5)2. It is an example of an s-block main group sandwich compound, structurally related to the d-block element metallocenes, and consists of a central magnesium atom sandwiched between two cyclopentadienyl rings.
Rosenthal's reagent is a metallocene bis(trimethylsilyl)acetylene complex with zirconium (Cp2Zr) or titanium (Cp2Ti) used as central atom of the metallocene fragment Cp2M. Additional ligands such as pyridine or THF are commonly used as well. With zirconium as central atom and pyridine as ligand (Zirconocene bis(trimethylsilyl)acetylene pyridine), a dark purple to black solid with a melting point of 125–126 °C is obtained. Synthesizing Rosenthal's reagent of a titanocene source yields golden-yellow crystals of the titanocene bis(trimethylsilyl)acetylene complex with a melting point of 81–82 °C. This reagent enables the generation of the themselves unstable titanocene and zirconocene under mild conditions.
Magnesium anthracene is an organomagnesium compound that is almost invariably isolated as its adduct with three tetrahydrofuran (thf) ligands. With the formula Mg(C14H10)(thf)3, this air- and water-sensitive orange solid is obtained by heating a suspension of magnesium in a thf solution of anthracene.
An N-heterocyclic carbene boryl anion is an isoelectronic structure of an N-heterocyclic carbene (NHC), where the carbene carbon is replaced with a boron atom that has a -1 charge. NHC boryl anions have a planar geometry, and the boron atom is considered to be sp2-hybridized. They serve as extremely strong bases, as they are very nucleophilic. They also have a very strong trans influence, due to the σ-donation coming from the boron atom. NHC boryl anions have stronger electron-releasing character when compared to normal NHCs. These characteristics make NHC boryl anions key ligands in many applications, such as polycyclic aromatic hydrocarbons, and more commonly low oxidation state main group element bonding.
A magnesium(I) dimer is a molecular compound containing a magnesium to magnesium bond (Mg-Mg), giving the metal an apparent +1 oxidation state. Alkaline earth metals are commonly found in the +2-oxidation state, such as magnesium. The M2+ are considered as redox-inert, meaning that the +2 state is significant. However, recent advancements in main group chemistry have yielded low-valent magnesium(I) dimers, also given as Mg(I), with the first compound being reported in 2007. They can be generally represented as LMg-MgL, with L being a monoanionic ligand. For example, β-diketiminate, commonly referred to as Nacnac, is a useful chelate regarding these complexes. By tuning the ligand, the thermodynamics of the complex change. For instance, the ability to add substituents onto Nacnac can contribute to the steric bulk, which can affect reactivity and stability. As their discovery has grown, so has their usefulness. They are employed in organic and inorganic reduction reactions. It is soluble in a hydrocarbon solvent, like toluene, stoichiometric, selective, and safe.
Organocalcium chemistry is the chemistry of compounds containing a calcium to carbon bond, or in broader definitions, organic compounds that contain calcium. Although discovered around the same time as the now commonly utilized organomagnesium compounds, organocalcium compounds were subject to greatly reduced interest due to drastic differences in stability. However, recent advances in stabilization of these highly reactive compounds has spurred increased interest in organocalcium compounds and allowed for multiple research directions to form. Because calcium metal is less reactive to organic reagents than magnesium and the organocalcium compounds are more reactive than organomagnesium compounds, synthesis of novel compounds still poses a significant challenge. Calcium also has access to empty d orbitals that the lighter alkaline earth metals cannot access, and the degree to which this affects bonding and reactivity has sparked a fundamental debate. Lastly, despite the inherent instability of most organocalcium complexes, the unique basicity and size of the calcium ion together with the highly polarized bonds formed has opened up applications for organocalcium compounds in organic transformations and catalytic cycles.