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,[1] but the availability of large collections of bond lengths, which are more transferable, from the Cambridge Crystallographic Database[2][3] has rendered covalent radii obsolete in many situations.

ആവറേജ് ആരങ്ങൾ

താഴെ പട്ടികയിൽ കാണുന്നത് 228000 പരീക്ഷണങ്ങളിൽക്കൂടി ഉരുത്തിരിഞ്ഞ വിവരങ്ങളാണ്.[4] മുന്നിൽച്ചേർത്ത അക്കം C, N അല്ലെങ്കിൽ O യുടെ ഹൈബ്രഡൈസേഷൻ ഓർബിറ്റലിനെ സൂചിപ്പിക്കുന്നു.

 H He 1 2 31(5) 28 Li Be B C N O F Ne 3 4 Radius (standard deviation) / pm 5 6 7 8 9 10 128(7) 96(3) 84(3) sp3 76(1)sp2 73(2)sp  69(1) 71(1) 66(2) 57(3) 58 Na Mg Al Si P S Cl Ar 11 12 13 14 15 16 17 18 166(9) 141(7) 121(4) 111(2) 107(3) 105(3) 102(4) 106(10) K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 203(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) Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 220(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) Cs Ba La Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn 55 56 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 244(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) 150 150 Fr Ra Ac 87 88 260 221(2) La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb 57 58 59 60 61 62 63 64 65 66 67 68 69 70 207(8) 204(9) 203(7) 201(6) 199 198(8) 198(6) 196(6) 194(5) 192(7) 192(7) 189(6) 190(10) 187(8) Ac Th Pa U Np Pu Am Cm 89 90 91 92 93 94 95 96 215 206(6) 200 196(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,[5] double,[6] and triple bonds[7] 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.[8]

 H He 1 2 32-- 46-- Li Be B C N O F Ne 3 4 Radius / pm: 5 6 7 8 9 10 133124- 1029085 single-bond double-bond triple-bond 857873 756760 716054 635753 645953 6796- Na Mg Al Si P S Cl Ar 11 12 13 14 15 16 17 18 155160- 139132127 126113111 116107102 11110294 1039495 999593 9610796 K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 196193- 171147133 148116114 136117108 134112106 122111103 119105103 116109102 11110396 110101101 112115120 118120- 124117121 121111114 121114106 116107107 114109110 117121108 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 210202- 185157139 163130124 154127121 147125116 138121113 128120110 125114103 125110106 120117112 128139137 136144- 142136146 140130132 140133127 136128121 133129125 131135122 Cs Ba La-Yb Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn 55 56 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 232209- 196161149 162131131 152128122 146126119 137120115 131119110 129116109 122115107 123112110 124121123 133142- 144142150 144135137 151141135 145135129 147138138 142145133 Fr Ra Ac-No Lr Rf Db Sg Bh Hs Mt Ds Rg Cn Nh Fl Mc Lv Ts Og 87 88 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 223218- 201173159 161141- 157140131 149136126 143128121 141128119 134125118 129125113 128116112 121116118 122137130 136-- 143-- 162-- 175-- 165-- 157-- La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb 57 58 59 60 61 62 63 64 65 66 67 68 69 70 180139139 163137131 176138128 174137 173135 172134 168134 169135132 168135 167133 166133 165133 164131 170129 Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No 89 90 91 92 93 94 95 96 97 98 99 100 101 102 186153140 175143136 169138129 170134118 171136116 172135 166135 166136 168139 168140 165140 167 173139 176

അവലംബം

1. Sanderson, R. T. (1983). "Electronegativity and Bond Energy". Journal of the American Chemical Society. 105 (8): 2259–2261. doi:10.1021/ja00346a026.
2. Allen, F. H.; Kennard, O.; Watson, D. G.; Brammer, L.; Orpen, A. G.; Taylor, R. (1987). "Table of Bond Lengths Determined by X-Ray and Neutron Diffraction". J. Chem. Soc., Perkin Trans. 2 (12): S1–S19. doi:10.1039/P298700000S1.
3. Orpen, A. Guy; Brammer, Lee; Allen, Frank H.; Kennard, Olga; Watson, David G.; Taylor, Robin (1989). "Supplement. Tables of bond lengths determined by X-ray and neutron diffraction. Part 2. Organometallic compounds and co-ordination complexes of the d- and f-block metals". Journal of the Chemical Society, Dalton Transactions (12): S1. doi:10.1039/DT98900000S1.
4. Beatriz Cordero; Verónica Gómez; Ana E. Platero-Prats; Marc Revés; Jorge Echeverría; Eduard Cremades; Flavia Barragán; Santiago Alvarez (2008). "Covalent radii revisited". Dalton Trans. (21): 2832–2838. doi:10.1039/b801115j.
5. P. Pyykkö; M. Atsumi (2009). "Molecular Single-Bond Covalent Radii for Elements 1-118". Chemistry: A European Journal. 15: 186–197. doi:10.1002/chem.200800987.
6. P. Pyykkö; M. Atsumi (2009). "Molecular Double-Bond Covalent Radii for Elements Li–E112". Chemistry: A European Journal. 15 (46): 12770–12779. doi:10.1002/chem.200901472.. Figure 3 of this paper contains all radii of refs. [5-7]. The mean-square deviation of each set is 3 pm.
7. P. Pyykkö; S. Riedel; M. Patzschke (2005). "Triple-Bond Covalent Radii". Chemistry: A European Journal. 11 (12): 3511–3520. doi:10.1002/chem.200401299. PMID 15832398.
8. P. Pyykkö (2012). "Refitted tetrahedral covalent radii for solids". Physical Review B. 85 (2): 024115, 7 p. Bibcode:2012PhRvB..85b4115P. doi:10.1103/PhysRevB.85.024115.