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On the calculations of the anisotropic hyperfine coupling constants of CH3 and NH2 free radicals
I.5 August 197 1
Volume 10, number-4.
ON ‘iBE CALCULATIONS
8F THE ANISOTKOPIC KYPERFlI$E OF CFIj AND NH2 FREE RA?ICALs
COUPLINGCONSTANTS
GM. ZHIDOMIROV, N.D. CHDVYLRIN and 0.1. BROTIKOVSKY~ Institute of Orgwic Chemistry, USSR Academy of &%wes.
MO~ZOIV~ &WR
Received 4 May 1991
Inconsistency in the results of calcuk&~s of the isotwpic and a&sotmpic hype&& coupling constants of xelectronic free radic& is investigated using CHQ Snd NH2 ss models. A posible ream of thio incondstency h disCUSS&.
For the C-H fragment we have the.following exThere is a peculiar inccnsistency in the rest& of pressions for the anisotrc$c components of the elecca@lations of the hyperfme coupling constants (hfc). tron-spin-proton-spin hyperfiie interaction in terms of 7r+lectronic free radicals. It is a failure to obtain the of two-cent&r &polar integrals (in G) [3] and spin simultaneous fit of the experimental hfc values and all populations of !!XO of the carbon and hydrogen atoms. anisotropic and isotropic theoretical magnitudes. Some @&e radical x, y, z-axis system is illtistrsted in fig. 1, aspects of this problem were earlier considered for the. ~=1.62S,~=I,r~=I.O8~.) radicalCH3in[l]. .As has been noted [ 11, a quantitative fit to the.&-. TH = 16.2~~~ + 24.8pss f 42.2~;~ + 16.2~~~ ‘_ xX perimental hfc data may be obtained when the n-atomiC orbital of CH, differs essent&lly from the A0 of the + 39.6~~~ f 24.0~~~ f 32.8~~~ , (;I free qhbbn atom (Slate: type orbital (STO) or HartreeFock atomic orbital). In *thatcakwhen n-A0 was apTH-_ ‘,- -lhpl(n - ‘2.4~9; -.21 JpXx - 2.1~~~ YY prohated by ST0 it was necessary to accept two different values for the effe’ctive core charge of the carbon .- 19.8~~ - 12_Op,, - 16.4p,, , (2) atom in order to reproduce the carbon and hydrogen principal cdmjjonents (7$& T&) of the anisotropic TH = - 2;ipzn i 12:4p,, 7 21 _‘pxx - 14.1pyy . z* hyperfine iiitera&ori; viz. n& = 3.0 and nk,= 2.6 l corresponding to the cases of fl and Tfq respective-. iy:Recently BarReId .[2]- came- 8” out~similar calcula. . tions’for the radical CH3-_andobtained the same results. -. h the present work we return to.the considered inconsiSten& or& more in order td discuss‘iu detail,the &isotropic hfc for two’radic&NHZ and CHs.+thin the-framework of the INI?0 method [4] ; on the basis :. of the experimentaldatafor the sub&ted methyl radic&&rd CH3_it_se!f[ 5; 6 ] atid also~,forthe am&oigi*, I?,@j . It ~ILIIE ~~~.th;it:an~~p~o~ation:-., ..~ of-r_+O ofthese rad+ls,by a..sum of two STO’s. may. ‘. a Ossiiilit~ : e p. -. ,.:periment..‘-
of obt+nb$ &-zigee&nt ,- ‘.: .-‘, .,
~kitlrzxr : ,_,_ ; ,, (’ ._.
:.Vdu&l~,
number 4 _.
CHEhfICAL PHYSICS I&TTERS
*i5 August
1971
I
-.
-.>s&population of n-ST0 ofthe carbonatom (EC = 1.625) changes within the limits: pnn = OS-O.95 for kok the Z&H fragment the formulae for &anise different .substi&& Ri and R-J. Such limits for pn,, ~r~pitj,&mpc&&s of :thczdipolar interaction are g&en arelunreasonable. So the range of variety of the pro -. belbw_in%cactly the‘same form is that irthecase‘of’ <. :, ton isotropic‘hfc &H = 19S23 G. If.one accepts .. .. : C-lj figment 1,.r2,-y -23..G,[lO] (ai = Q+,,J one will find pnr = .0.8-l. It was mentioned above how.the change of the ‘.T.! i. 25:oj;t . +37.8&s + 63.6&+ 2§.Op,,, ,.. effective core charge-of the carbon atom influences th6 calculated vahres of the anisotropic dipolar comI- +61..1,, +_19.6/$, +33.6pXh , (5). ‘. aponentst : As in the case of CH, exactly &&me inconsistT&= -~19.7p,, -;8:9& - 31.8&. : 5.$,,, -. ency exists for the amino-radical NH2. The absolute : value Tfiz which is calculated for this radical with ST0 _. - 30.,Spsx -:9_8p,, - 16.8&h , (6) _of the nitrogen atom (EN = l-95), is 7 times greater .than the experimental one Tg = -1 G [7]. A good ii.=.5jp,, :18.9pss’31.8~~~ - 19.7p,, agreement with the experimental data on the protorl anisotropic hfc for NH2 may be obtained with &$ = - 30.8~~~ - 9.8psh - 16.8p,, , (3 1.5. Subtracting the isotropic contribution cr;v = 10 G ‘.._ [?I. from the total value A$ .= 37 G [7] for the radi-- T,Hy:‘~4k6d,y f 42.3~~; .y 6b.3& . (8) cal NH2 one can find &experimental magnitude TFz :_ = 27 G which is almost 1.5 times as little.as the theo. : If oni substitutes the spin populations of A0 of: -mtical one for the free nitrogen atom 14N. In this case .the.CHj and NH2 mdicals calculated by.the INDO the agreement .&th experiment may be attained with r&hod in eqs. (l)T(8),.one will obtain the values of -the anisotropic dipolar components presented in table i& = 1.85 which is substantially.greater than& = 1.5 estimated from the proton anisotropic component 1. .’ In the same. table there are similar results which T&. were foundby a more simple CNDOjSP method [9] To understand a possible cause of this inconsistency it does-seem necessary to consider the influence of the based on the restricted HartreelFock (RHF) approach following factors: ..with.the’following account of spin polarization (SP). ‘. The experimental magnitudes for a number of sub(1) change of the radical geometrical parameters within the reasonable limits, Rl s&ted methyl~radicals ->C-H are within the fol.- (2) consideration of the inner-shell Is-A0 of the ceipral atom (carbon or nitrogen); R2 (3) consideration of the omitted terms k eqs. (1) lowing lirkits [5;6) T$lz e -T$ i= 9-13 G, -T$ _-(8) which &-e connected with the spin populations e O-4-2 G: These rkgnirude~ are much less tharr : &,h of the hydrogen‘ Is-AO, ., those presented in table 1 for .the radical CH3. They (4). greater accuticy of cakulatious at the expense r&y be reprodiced~s&isfactori!y withmthe scope of .of consideration of the additional low-lying excited &e INDO‘and dNDO/SP.methodsprovided that the ~. corifiguratitins,. ;. ,’ z. (5) greater. accuracy of calculations due to the use :.- Table 1 of HF A0 instead.of ST0 of tile c&al atom; _~@x~ Method ,‘.. _tg-:, T” TE.. i$ .. (6) inaccuracy of the spin’,density representation :-..YY. :: .. within ‘the’frtir%ork of JXAO~&lO, ... : i .: ~: .: iii--_... .IN&IO _L ‘I i9.3 :_ 4;.; %; .. ~0.D I (7) inaktrac~~of the e_xpres$on for. the .elect,r&~I CNIiO/SP 19;s 0.0 :. spin&nucleai+r @polar interact&i hami@iari,:~ ‘. .. .. effeityfoi L _.. ::N+._,-INDO ., .-.2&p:’ 121.3 .-L-7.1. +-0.6.. ’ :;. -(8).bonsid&ation of th@&i&tig~ .: qy;-
_;
:. :
3!.fp,j
+32.4&y-,+ 3q&
I--CFC?/SP.
-_28_.0. .: :
.
-_2!.?
,... ..
(41. :-
,‘f.t+
I
0.0_._
.:
:,
_:, -& ,, t;y~ro~~41s--b,6~~~~~y; .._--:;(9).co&id$ti&+~~f &e
‘.
‘, :_ :, \ :- __.-. .. ;; .. ,:. .‘y;:.
oye+p.of
n-A0
ofthe-';!- .-!‘.
Volume .lO, number 4.
hydrogen and central atoms, (101 inadeauacv of the reoiesentakn of n-A0 of the‘c&tral at&n 6 a radkalby one ST0 only. The $actors l-7 w&e considered in detail for the radidal CH; in refs. [ 1.21 in tihich it wasdemonstrated t,hat they are negligible. The situation is just the same & the case of the NHz- radical. The last three factors are analysed below. A polarised A0 of the hydrogen atom may be presented in terms of ST0 in the form !z = (1 +x2)-1’2
[SH +xpN ] .
81
With the use of eq. (9) it is quite simple to obtain e.g. the correction (in G) to the anisotropic component Tg for the radical CH3
x2$
AT,H, = -25.4 -. (l+xz)PH
15 August 1971
CiiEtilCAL pHySICS LETTERS
*
combinatjon of two STO’s (.& i 1, .$ = i) .7r = Ihost
.-
fe~‘+iJZe-*‘I
WI
and the values of the TF .and F$tnisotropic compobents were obtained with this tiavefunc’tion. In the next c‘alculation we.attempted to imitate these values with the use of one STO, tie &-parame’ter of which ~8s varied. As a rksult two different values were found for this parameter, viz. EN = l&S and EN = 1.45 for fN and Z@ iespectively. So within the scope of the model caI&&idn we have come to exactly the same inconsistency at the expense of the substitution of one ST0 instead of two STOls. If two STO’s are enough it is convenient to rewrite the normalized expression (12) for c-A0 in the following way 77=fVhrcosO ,i$)“’ e -E1r f x(&*” e -E2r ] , (13)
Adopting ,@ = 1 and &j = -0.05 one can find that it gives ~44% only from the required value of correction - ATE with X,,
= 00 and less than 3% with h&t G 0.1. The role of the overlap of the hydrogen 2P,, (EF = 0.5) and carbon 2P, (.$C = 1.625) A0 may be analysed on the basis of the following expression (in G)
(11) aT,H, = 6.4~; The value of p’;I was estimated by the restricted Hiickei theory(RHT) [11,12]: l~~y-~~pvil=o,H,,,=-~.
which led to pH = 0.046. So the contribution of the z-A0 overlap is nearly equal to 1% i.e. it is ne&$bk also.
(14) It must be emphasized that the unknown parameters (h~k~7 x) may be determkied on the basis Of the ex-
-perimental data on the anisotropic hyperfine coupling constants. Such a method of conkuctitin of the wavefunctions in free .radicaIs implies the use of the mag netic nuclei as “probes*’ which allow the form of these functions to be analysed in th& different regions of space. This approach may prove to be a useful alternative to the variation piocedure. The cakuIations in this direction are now in progress. References
Therefore we believe on the basis of all these results of n-A0 of the radical centre at ~. least by one ST0 is tinsatisfactory. It is worth mentioning at this point that there are some attempts to X$ resent n-A0 of ato* by twq STO’s iri ~alcdathns of n-electronic molecular systems [ 1’31 . In the case of 7f~elec&ic free radica1s.a simila; approach may_be extremely helpful as it makes po&i$le to remove the : : above inconsistency in-results of cal
[ 11 G.M. Zhidoni$ov and P.V. Schastnev, zh. Strukt Kbim. 7 (1966) 66.
[21 M. Barfield, I. bhem. Phys 53 (I9701 3836.
(31 G.M. Zhidomimv and P.V.
S~hastnev,
Zh. Sptkt
E&in
5 (1964) 83;6 (1965) 655.
[g) J.A. Popte, D.L. Beveridge @ P.A. Dobosh, J. Chem. Phys. 47 (1967) 2026. [s] XT.-RogeTsTand 5.D. Kispert, J:Chem. Phys. 46 (1967) ?21., [6] J.R. M?st& Chem, Rev_ 64 (19.64) 453s [7] 0.l Bmticavsky..G.lK Zhidomiyti, V-9. Kmansky, A-I. ..Maschenko‘z@ B.N; SheIimov, Kinetikri i Kataliz. to be published: [8i S, F&er,B. CaChra& V. Bqwess yd C. J& Phys. RF. Letters 1 (l958)9’1, 1 ’ ._...” -_ ,I .I
343.
‘is AU&dtj7i
..:
_
:-
Volume 10, number-4.
ON ‘iBE CALCULATIONS
8F THE ANISOTKOPIC KYPERFlI$E OF CFIj AND NH2 FREE RA?ICALs
COUPLINGCONSTANTS
GM. ZHIDOMIROV, N.D. CHDVYLRIN and 0.1. BROTIKOVSKY~ Institute of Orgwic Chemistry, USSR Academy of &%wes.
MO~ZOIV~ &WR
Received 4 May 1991
Inconsistency in the results of calcuk&~s of the isotwpic and a&sotmpic hype&& coupling constants of xelectronic free radic& is investigated using CHQ Snd NH2 ss models. A posible ream of thio incondstency h disCUSS&.
For the C-H fragment we have the.following exThere is a peculiar inccnsistency in the rest& of pressions for the anisotrc$c components of the elecca@lations of the hyperfme coupling constants (hfc). tron-spin-proton-spin hyperfiie interaction in terms of 7r+lectronic free radicals. It is a failure to obtain the of two-cent&r &polar integrals (in G) [3] and spin simultaneous fit of the experimental hfc values and all populations of !!XO of the carbon and hydrogen atoms. anisotropic and isotropic theoretical magnitudes. Some @&e radical x, y, z-axis system is illtistrsted in fig. 1, aspects of this problem were earlier considered for the. ~=1.62S,~=I,r~=I.O8~.) radicalCH3in[l]. .As has been noted [ 11, a quantitative fit to the.&-. TH = 16.2~~~ + 24.8pss f 42.2~;~ + 16.2~~~ ‘_ xX perimental hfc data may be obtained when the n-atomiC orbital of CH, differs essent&lly from the A0 of the + 39.6~~~ f 24.0~~~ f 32.8~~~ , (;I free qhbbn atom (Slate: type orbital (STO) or HartreeFock atomic orbital). In *thatcakwhen n-A0 was apTH-_ ‘,- -lhpl(n - ‘2.4~9; -.21 JpXx - 2.1~~~ YY prohated by ST0 it was necessary to accept two different values for the effe’ctive core charge of the carbon .- 19.8~~ - 12_Op,, - 16.4p,, , (2) atom in order to reproduce the carbon and hydrogen principal cdmjjonents (7$& T&) of the anisotropic TH = - 2;ipzn i 12:4p,, 7 21 _‘pxx - 14.1pyy . z* hyperfine iiitera&ori; viz. n& = 3.0 and nk,= 2.6 l corresponding to the cases of fl and Tfq respective-. iy:Recently BarReId .[2]- came- 8” out~similar calcula. . tions’for the radical CH3-_andobtained the same results. -. h the present work we return to.the considered inconsiSten& or& more in order td discuss‘iu detail,the &isotropic hfc for two’radic&NHZ and CHs.+thin the-framework of the INI?0 method [4] ; on the basis :. of the experimentaldatafor the sub&ted methyl radic&&rd CH3_it_se!f[ 5; 6 ] atid also~,forthe am&oigi*, I?,@j . It ~ILIIE ~~~.th;it:an~~p~o~ation:-., ..~ of-r_+O ofthese rad+ls,by a..sum of two STO’s. may. ‘. a Ossiiilit~ : e p. -. ,.:periment..‘-
of obt+nb$ &-zigee&nt ,- ‘.: .-‘, .,
~kitlrzxr : ,_,_ ; ,, (’ ._.
:.Vdu&l~,
number 4 _.
CHEhfICAL PHYSICS I&TTERS
*i5 August
1971
I
-.
-.>s&population of n-ST0 ofthe carbonatom (EC = 1.625) changes within the limits: pnn = OS-O.95 for kok the Z&H fragment the formulae for &anise different .substi&& Ri and R-J. Such limits for pn,, ~r~pitj,&mpc&&s of :thczdipolar interaction are g&en arelunreasonable. So the range of variety of the pro -. belbw_in%cactly the‘same form is that irthecase‘of’ <. :, ton isotropic‘hfc &H = 19S23 G. If.one accepts .. .. : C-lj figment 1,.r2,-y -23..G,[lO] (ai = Q+,,J one will find pnr = .0.8-l. It was mentioned above how.the change of the ‘.T.! i. 25:oj;t . +37.8&s + 63.6&+ 2§.Op,,, ,.. effective core charge-of the carbon atom influences th6 calculated vahres of the anisotropic dipolar comI- +61..1,, +_19.6/$, +33.6pXh , (5). ‘. aponentst : As in the case of CH, exactly &&me inconsistT&= -~19.7p,, -;8:9& - 31.8&. : 5.$,,, -. ency exists for the amino-radical NH2. The absolute : value Tfiz which is calculated for this radical with ST0 _. - 30.,Spsx -:9_8p,, - 16.8&h , (6) _of the nitrogen atom (EN = l-95), is 7 times greater .than the experimental one Tg = -1 G [7]. A good ii.=.5jp,, :18.9pss’31.8~~~ - 19.7p,, agreement with the experimental data on the protorl anisotropic hfc for NH2 may be obtained with &$ = - 30.8~~~ - 9.8psh - 16.8p,, , (3 1.5. Subtracting the isotropic contribution cr;v = 10 G ‘.._ [?I. from the total value A$ .= 37 G [7] for the radi-- T,Hy:‘~4k6d,y f 42.3~~; .y 6b.3& . (8) cal NH2 one can find &experimental magnitude TFz :_ = 27 G which is almost 1.5 times as little.as the theo. : If oni substitutes the spin populations of A0 of: -mtical one for the free nitrogen atom 14N. In this case .the.CHj and NH2 mdicals calculated by.the INDO the agreement .&th experiment may be attained with r&hod in eqs. (l)T(8),.one will obtain the values of -the anisotropic dipolar components presented in table i& = 1.85 which is substantially.greater than& = 1.5 estimated from the proton anisotropic component 1. .’ In the same. table there are similar results which T&. were foundby a more simple CNDOjSP method [9] To understand a possible cause of this inconsistency it does-seem necessary to consider the influence of the based on the restricted HartreelFock (RHF) approach following factors: ..with.the’following account of spin polarization (SP). ‘. The experimental magnitudes for a number of sub(1) change of the radical geometrical parameters within the reasonable limits, Rl s&ted methyl~radicals ->C-H are within the fol.- (2) consideration of the inner-shell Is-A0 of the ceipral atom (carbon or nitrogen); R2 (3) consideration of the omitted terms k eqs. (1) lowing lirkits [5;6) T$lz e -T$ i= 9-13 G, -T$ _-(8) which &-e connected with the spin populations e O-4-2 G: These rkgnirude~ are much less tharr : &,h of the hydrogen‘ Is-AO, ., those presented in table 1 for .the radical CH3. They (4). greater accuticy of cakulatious at the expense r&y be reprodiced~s&isfactori!y withmthe scope of .of consideration of the additional low-lying excited &e INDO‘and dNDO/SP.methodsprovided that the ~. corifiguratitins,. ;. ,’ z. (5) greater. accuracy of calculations due to the use :.- Table 1 of HF A0 instead.of ST0 of tile c&al atom; _~@x~ Method ,‘.. _tg-:, T” TE.. i$ .. (6) inaccuracy of the spin’,density representation :-..YY. :: .. within ‘the’frtir%ork of JXAO~&lO, ... : i .: ~: .: iii--_... .IN&IO _L ‘I i9.3 :_ 4;.; %; .. ~0.D I (7) inaktrac~~of the e_xpres$on for. the .elect,r&~I CNIiO/SP 19;s 0.0 :. spin&nucleai+r @polar interact&i hami@iari,:~ ‘. .. .. effeityfoi L _.. ::N+._,-INDO ., .-.2&p:’ 121.3 .-L-7.1. +-0.6.. ’ :;. -(8).bonsid&ation of th@&i&tig~ .: qy;-
_;
:. :
3!.fp,j
+32.4&y-,+ 3q&
I--CFC?/SP.
-_28_.0. .: :
.
-_2!.?
,... ..
(41. :-
,‘f.t+
I
0.0_._
.:
:,
_:, -& ,, t;y~ro~~41s--b,6~~~~~y; .._--:;(9).co&id$ti&+~~f &e
‘.
‘, :_ :, \ :- __.-. .. ;; .. ,:. .‘y;:.
oye+p.of
n-A0
ofthe-';!- .-!‘.
Volume .lO, number 4.
hydrogen and central atoms, (101 inadeauacv of the reoiesentakn of n-A0 of the‘c&tral at&n 6 a radkalby one ST0 only. The $actors l-7 w&e considered in detail for the radidal CH; in refs. [ 1.21 in tihich it wasdemonstrated t,hat they are negligible. The situation is just the same & the case of the NHz- radical. The last three factors are analysed below. A polarised A0 of the hydrogen atom may be presented in terms of ST0 in the form !z = (1 +x2)-1’2
[SH +xpN ] .
81
With the use of eq. (9) it is quite simple to obtain e.g. the correction (in G) to the anisotropic component Tg for the radical CH3
x2$
AT,H, = -25.4 -. (l+xz)PH
15 August 1971
CiiEtilCAL pHySICS LETTERS
*
combinatjon of two STO’s (.& i 1, .$ = i) .7r = Ihost
.-
fe~‘+iJZe-*‘I
WI
and the values of the TF .and F$tnisotropic compobents were obtained with this tiavefunc’tion. In the next c‘alculation we.attempted to imitate these values with the use of one STO, tie &-parame’ter of which ~8s varied. As a rksult two different values were found for this parameter, viz. EN = l&S and EN = 1.45 for fN and Z@ iespectively. So within the scope of the model caI&&idn we have come to exactly the same inconsistency at the expense of the substitution of one ST0 instead of two STOls. If two STO’s are enough it is convenient to rewrite the normalized expression (12) for c-A0 in the following way 77=fVhrcosO ,i$)“’ e -E1r f x(&*” e -E2r ] , (13)
Adopting ,@ = 1 and &j = -0.05 one can find that it gives ~44% only from the required value of correction - ATE with X,,
= 00 and less than 3% with h&t G 0.1. The role of the overlap of the hydrogen 2P,, (EF = 0.5) and carbon 2P, (.$C = 1.625) A0 may be analysed on the basis of the following expression (in G)
(11) aT,H, = 6.4~; The value of p’;I was estimated by the restricted Hiickei theory(RHT) [11,12]: l~~y-~~pvil=o,H,,,=-~.
which led to pH = 0.046. So the contribution of the z-A0 overlap is nearly equal to 1% i.e. it is ne&$bk also.
(14) It must be emphasized that the unknown parameters (h~k~7 x) may be determkied on the basis Of the ex-
-perimental data on the anisotropic hyperfine coupling constants. Such a method of conkuctitin of the wavefunctions in free .radicaIs implies the use of the mag netic nuclei as “probes*’ which allow the form of these functions to be analysed in th& different regions of space. This approach may prove to be a useful alternative to the variation piocedure. The cakuIations in this direction are now in progress. References
Therefore we believe on the basis of all these results of n-A0 of the radical centre at ~. least by one ST0 is tinsatisfactory. It is worth mentioning at this point that there are some attempts to X$ resent n-A0 of ato* by twq STO’s iri ~alcdathns of n-electronic molecular systems [ 1’31 . In the case of 7f~elec&ic free radica1s.a simila; approach may_be extremely helpful as it makes po&i$le to remove the : : above inconsistency in-results of cal
[ 11 G.M. Zhidoni$ov and P.V. Schastnev, zh. Strukt Kbim. 7 (1966) 66.
[21 M. Barfield, I. bhem. Phys 53 (I9701 3836.
(31 G.M. Zhidomimv and P.V.
S~hastnev,
Zh. Sptkt
E&in
5 (1964) 83;6 (1965) 655.
[g) J.A. Popte, D.L. Beveridge @ P.A. Dobosh, J. Chem. Phys. 47 (1967) 2026. [s] XT.-RogeTsTand 5.D. Kispert, J:Chem. Phys. 46 (1967) ?21., [6] J.R. M?st& Chem, Rev_ 64 (19.64) 453s [7] 0.l Bmticavsky..G.lK Zhidomiyti, V-9. Kmansky, A-I. ..Maschenko‘z@ B.N; SheIimov, Kinetikri i Kataliz. to be published: [8i S, F&er,B. CaChra& V. Bqwess yd C. J& Phys. RF. Letters 1 (l958)9’1, 1 ’ ._...” -_ ,I .I
343.
‘is AU&dtj7i
..:
_
:-