സഹസംയോജകബന്ധനത്തിലെ ആരം

സഹസംയോജകബന്ധനത്തിലുള്ള ഒരു ആറ്റത്തിന്റെ വലിപ്പത്തെ സൂചിപ്പിക്കുന്ന ഒരു അളവാണ് കൊവാലന്റ് റേഡിയസ് അഥവാ സഹസംയോജകബന്ധനത്തിലെ ആരം (The covalent radius, rcov). ഇത് പൈക്കോമീറ്ററിലോ (pm) ആങ്ങ്‌സ്ട്രമിലോ (angstroms (Å), with 1 Å = 100 pm) ആണ് അളക്കുന്നത്.

In principle, the sum of the two covalent radii should equal the covalent bond length between two atoms, R(AB) = r(A) + r(B). Moreover, different radii can be introduced for single, double and triple bonds (r1, r2 and r3 below), in a purely operational sense. These relationships are certainly not exact because the size of an atom is not constant but depends on its chemical environment. For heteroatomic A–B bonds, ionic terms may enter. Often the polar covalent bonds are shorter than would be expected on the basis of the sum of covalent radii. Tabulated values of covalent radii are either average or idealized values, which nevertheless show a certain transferability between different situations, which makes them useful.

The bond lengths R(AB) are measured by X-ray diffraction (more rarely, neutron diffraction on molecular crystals). Rotational spectroscopy can also give extremely accurate values of bond lengths. For homonuclear A–A bonds, Linus Pauling took the covalent radius to be half the single-bond length in the element, e.g. R(H–H, in H2) = 74.14 pm so rcov(H) = 37.07 pm: in practice, it is usual to obtain an average value from a variety of covalent compounds, although the difference is usually small. Sanderson has published a recent set of non-polar covalent radii for the main-group elements, but the availability of large collections of bond lengths, which are more transferable, from the Cambridge Crystallographic Database has rendered covalent radii obsolete in many situations.

 ആവറേജ് ആരങ്ങൾ 
താഴെ പട്ടികയിൽ കാണുന്നത് 228000 പരീക്ഷണങ്ങളിൽക്കൂടി ഉരുത്തിരിഞ്ഞ വിവരങ്ങളാണ്. മുന്നിൽച്ചേർത്ത അക്കം C, N അല്ലെങ്കിൽ O യുടെ ഹൈബ്രഡൈസേഷൻ ഓർബിറ്റലിനെ സൂചിപ്പിക്കുന്നു.
+ Covalent radii in pm from analysis of the Cambridge Structural Database, which contains about 426,000 crystal structuresHHe1231(5)28LiBeBCNOFNe34Radius (standard deviation) / pm5678910128(7)96(3)84(3)sp3 76(1)sp2 73(2)sp  69(1)71(1)66(2)57(3)58NaMgAlSiPSClAr1112131415161718166(9)141(7)121(4)111(2)107(3)105(3)102(4)106(10)KCaScTiVCrMnFeCoNiCuZnGaGeAsSeBrKr192021222324252627282930313233343536203(12)176(10)170(7)160(8)153(8)139(5)l.s. 139(5)h.s. 161(8)l.s. 132(3)h.s. 152(6)l.s. 126(3)h.s. 150(7)124(4)132(4)122(4)122(3)120(4)119(4)120(4)120(3)116(4)RbSrYZrNbMoTcRuRhPdAgCdInSnSbTeIXe373839404142434445464748495051525354220(9)195(10)190(7)175(7)164(6)154(5)147(7)146(7)142(7)139(6)145(5)144(9)142(5)139(4)139(5)138(4)139(3)140(9)CsBaLaLuHfTaWReOsIrPtAuHgTlPbBiPoAtRn555671727374757677787980818283848586244(11)215(11)187(8)175(10)170(8)162(7)151(7)144(4)141(6)136(5)136(6)132(5)145(7)146(5)148(4)140(4)150150FrRaAc8788260221(2)LaCePrNdPmSmEuGdTbDyHoErTmYb5758596061626364656667686970207(8)204(9)203(7)201(6)199198(8)198(6)196(6)194(5)192(7)192(7)189(6)190(10)187(8)AcThPaUNpPuAmCm8990919293949596215206(6)200196(7)190(1)187(1)180(6)169(3)

 ബഹുബന്ധനത്തിലെ ആരങ്ങൾ 
A different approach is to make a self-consistent fit for all elements in a smaller set of molecules. This was done separately for single,
double,. Figure 3 of this paper contains all radii of refs. [5-7]. The mean-square deviation of each set is 3 pm.
and triple bonds
up to superheavy elements. Both experimental and computational data were used. 
The single-bond results are often similar to those of Cordero et al. When they are different, the coordination numbers used can be different. This is notably the case for most (d and f) transition metals. Normally one expects that r1 > r2  > r3. Deviations may occur for weak multiple bonds, if the differences of the ligand are larger than the differences of R in the data used.

Note that elements up to atomic number 118 (oganesson) have now been experimentally produced and that there are chemical studies on an increasing number of them. The same, self-consistent approach was used to fit tetrahedral covalent radii for 30 elements in 48 crystals with subpicometer accuracy.
+ Single-, double-, and triple-bond covalent radii,  determined using typically 400 experimental or calculated primary distances, R, per set.HHe1232--46--LiBeBCNOFNe34Radius / pm:5678910133124-1029085single-bond
double-bond

triple-bond 8578737567607160546357536459536796-NaMgAlSiPSClAr1112131415161718155160-1391321271261131111161071021111029410394959995939610796KCaScTiVCrMnFeCoNiCuZnGaGeAsSeBrKr192021222324252627282930313233343536196193-17114713314811611413611710813411210612211110311910510311610910211110396110101101112115120118120-124117121121111114121114106116107107114109110117121108RbSrYZrNbMoTcRuRhPdAgCdInSnSbTeIXe373839404142434445464748495051525354210202-185157139163130124154127121147125116138121113128120110125114103125110106120117112128139137136144-142136146140130132140133127136128121133129125131135122CsBaLa-YbLuHfTaWReOsIrPtAuHgTlPbBiPoAtRn555671727374757677787980818283848586232209-196161149162131131152128122146126119137120115131119110129116109122115107123112110124121123133142-144142150144135137151141135145135129147138138142145133FrRaAc-NoLrRfDbSgBhHsMtDsRgCnNhFlMcLvTsOg8788103104105106107108109110111112113114115116117118223218-201173159161141-157140131149136126143128121141128119134125118129125113128116112121116118122137130136--143--162--175--165--157--LaCePrNdPmSmEuGdTbDyHoErTmYb5758596061626364656667686970180139139163137131176138128174137173135172134168134169135132168135167133166133165133164131170129AcThPaUNpPuAmCmBkCfEsFmMdNo8990919293949596979899100101102186153140175143136169138129170134118171136116172135166135166136168139168140165140167173139176

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