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| [[image:ConeAng.png|270px|right|thumb]]
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| The '''ligand cone angle''' (a common example being the '''Tolman cone angle''' or '''θ''') is a measure of the size of a [[ligand]]. It is defined as the [[solid angle]] formed with the metal at the vertex and the hydrogen atoms at the perimeter of the cone (see figure). Tertiary phosphine ligands are commonly classified using this parameter, but the method can be applied to any ligand. The term cone angle was introduced by [[Chadwick A. Tolman]], a research chemist at Dupont. Originally applied to phosphines, the cone angles were originally determined by taking measurements from accurate physical models of them.<ref name="tolman1970">{{Cite journal | |
| | doi = 10.1021/ja00713a007
| |
| | volume = 92
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| | issue = 10
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| | pages = 2956–2965
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| | last = Tolman
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| | first = Chadwick A.
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| | title = Phosphorus ligand exchange equilibriums on zerovalent nickel. Dominant role for steric effects
| |
| | journal = [[J. Am. Chem. Soc.]]
| |
| | accessdate = 2009-12-04
| |
| | date = 1970-05-01
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| }}</ref><ref>{{Cite journal
| |
| | doi = 10.1021/ja00808a009
| |
| | volume = 96
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| | issue = 1
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| | pages = 53–60
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| | last = Tolman
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| | first = C. A.
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| | coauthors = W. C. Seidel, L. W. Gosser
| |
| | title = Formation of three-coordinate nickel(0) complexes by phosphorus ligand dissociation from NiL4
| |
| | journal = [[J. Am. Chem. Soc.]]
| |
| | accessdate = 2009-12-04
| |
| | date = 1974-01-01
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| }}</ref><ref>{{cite journal | author = Tolman, C. A. | title = Steric Effects of Phosphorus Ligands in Organometallic Chemistry and Homogeneous Catalysis | journal = [[Chem. Rev.]] | year = 1977 | volume = 77 | pages = 313–48 | doi = 10.1021/cr60307a002 | issue = 3}}</ref>
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| ==Asymmetric cases==
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| The concept of cone angle is most easily visualized with symmetrical ligands, e.g. PR<sub>3</sub>. But the approach has been refined to include less symmetrical ligands of the type PRR'R" as well as diphosphines. In such asymmetric cases the substituent angles half angles, ''θ<sub>i</sub>''/2, are averaged and then doubled to find the total cone angle, θ. In the case of diphosphines the ''θ<sub>i</sub>''/2 of the backbone is approximated as half the chelate [[bite angle]] assuming a bite angle of 74, 85, 90 deg. for diphosphines with methylene, ethylene, and propylene back bones respectively. The Manz cone angle is often easier to compute than the Tolman cone angle.<ref name = "JACS2007">{{cite journal | author1 = Manz, T. A. | author2 = Phomphrai, K. | author3 = Medvedev, G. | author4 = Krishnamurthy, B. B. | author5 = Sharma, S. | author6 = Haq, J. | author7 = Novstrup, K. A. | author8 = Thomson, K. T. | author9 = Delgass, W. N. | author10 = Caruthers, J. M. | author11 = Abu-Omar, M. M. | title = Structure−Activity Correlation in Titanium Single-Site Olefin Polymerization Catalysts Containing Mixed Cyclopentadienyl/Aryloxide Ligation | journal = J. Am. Chem. Soc. | year = 2007 | volume = 129 | pages = 3776–3777 | doi = 10.1021/ja0640849 | issue = 13 | pmid=17348648}}</ref>
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| :<math>\theta = \frac{2}{3} \Sigma \frac{\theta_i}{2}</math>
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| ==Variations==
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| The Tolman cone angles assume empirical bond data and defines the perimeter as the maximum possible circumscription of an idealized free spinning substituent. In contrast the solid-angle concept derives both bond length and the perimeter form empirical solid state crystal structures.<ref>{{Cite journal
| |
| | doi = 10.1016/S0020-1693(00)95635-4
| |
| | volume = 25
| |
| | pages = L41–L42
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| | last = Immirzi
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| | first = A.
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| | coauthors = A. Musco
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| | title = A method to measure the size of phosphorus ligands in coordination complexes
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| | journal = Inorganica Chimica Acta
| |
| | accessdate = 2009-12-04
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| | year = 1977
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| | url = http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TG5-43B8S8H-KF&_user=10&_coverDate=12%2F31%2F1977&_rdoc=60&_fmt=high&_orig=browse&_srch=doc-info(%23toc%235245%231977%23999749999%23253901%23FLP%23display%23Volume)&_cdi=5245&_sort=d&_docanchor=&_ct=107&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=59cd327789cffac36f7a8627f88eaec5
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| }}</ref><ref>{{Cite journal
| |
| | volume = 9999
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| | issue = 9999
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| | pages = NA
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| | last = Niksch
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| | first = Tobias
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| | coauthors = Helmar Görls, Wolfgang Weigand
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| | title = The Extension of the Solid-Angle Concept to Bidentate Ligands
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| | journal = European Journal of Inorganic Chemistry
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| | accessdate = 2009-12-04
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| | year = 2009
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| | doi = 10.1002/ejic.200900825
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| }}</ref> There are advantages to each system.
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| ==Application==
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| The concept of cone angle is of practical importance in [[homogeneous catalysis]] because the size of the ligand affects the reactivity of the attached metal center. In a famous{{cn|date=January 2013}} example, the selectivity of [[hydroformylation]] catalysts is strongly influenced by the size of the coligands. Despite being [[monovalent]], some phosphines are large enough to occupy more than half of the [[coordination sphere]] of a metal center.
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| ==Cone angle values==
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| {| class="wikitable"
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| |+Cone angles of common phosphine ligands
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| |-
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| ! Ligand !! Angle (°)
| |
| |-
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| | [[Phosphine|PH<sub>3</sub>]] || 87<ref name="tolman1970" />
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| |-
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| | [[Phosphorus trifluoride|PF<sub>3</sub>]] || 104<ref name="tolman1970" />
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| |-
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| | [[Trimethyl phosphite|P(OCH<sub>3</sub>)<sub>3</sub>]] || 107<ref name="tolman1970" />
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| |-
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| | [[1,2-Bis(dimethylphosphino)ethane|dmpe]] || 107
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| |-
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| | depe || 115
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| |-
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| | [[Trimethylphosphine|P(CH<sub>3</sub>)<sub>3</sub>]] || 118<ref name="tolman1970" />
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| |-
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| | [[1,1-Bis(diphenylphosphino)methane|dppm]] || 121
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| |-
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| | [[1,2-Bis(diphenylphosphino)ethane|dppe]] || 125
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| |-
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| | [[1,3-Bis(diphenylphosphino)propane|dppp]] || 127
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| |-
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| | P(CH<sub>2</sub>CH<sub>3</sub>)<sub>3</sub> || 132<ref name="tolman1970" />
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| |-
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| | dcpe || 142
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| |-
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| | [[Triphenylphosphine|P(C<sub>6</sub>H<sub>5</sub>)<sub>3</sub>]] || 145<ref name="tolman1970" />
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| |-
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| | [[Tricyclohexylphosphine|P(cyclo-C<sub>6</sub>H<sub>11</sub>)<sub>3</sub>]] || 179<ref name="tolman1970" />
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| |-
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| | P(t-Bu)<sub>3</sub> || 182<ref name="tolman1970" />
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| |-
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| | P(C<sub>6</sub>F<sub>5</sub>)<sub>3</sub> || 184<ref name="tolman1970" />
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| |-
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| | P(2,4,6-[[mesityl|Me<sub>3</sub>C<sub>6</sub>H<sub>2</sub>]])<sub>3</sub> || 212
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| |}
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| == See also ==
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| *[[Bite angle]]
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| *[[Steric effects]] (vs. electronic effects)
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| * [[Tolman electronic parameter]]
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| ==References==
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| {{Reflist|2}}
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| | |
| | |
| [[Category:Tertiary phosphines]]
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| [[Category:Stereochemistry]]
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| [[Category:Organometallic chemistry]]
| |
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