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Ab initio MO LCAO UHF calculations of magnetic hyperfine interactions in σ radicals. Isotropic and anisotropic couplings of NO2 and CO2−
; CHEKCAL :
Volume i8, number 2
. ..’
PHYSICS LETTERS
I.5 ‘beptembcr 1974
.. .. AEI INITIO MO LCAO UHF CALCULATIONS 06 MAGNETIC HYPEkFlNF,.INTERACTIONS IN (TRADICALS.. ISOTROPIC~-ANti ANISOTROPIC COUPLINGS 6F NO2 AND ,CO,.
Jzn ALMLijF Institute of l%eoretical Physics, University of Stockholm, Sltieden and
Anders LUND and Karl&e Swedish Re:earch.Councils’Loboratory
THUOMAS
And AB Atomenergi. Studsvik. iyk6pin.g. Sw
Received 19 June 1974
The magnetic hype&e coupling constants in NO2 and CO, have been computed by ab initio methods. Spin annihfition is found to be essential in order to obtain useful results for the dipolar couplings, but has much Less influence on the isotropic couplings. The electric quadrupole coupling constants have also been evaluated. and ax in good agreement with avdbble experimental data. _
Recent calculations [l] have demonstrated that unrestricted Hartree-Fock calculations followed by spin annihilation of the quartet contamination give quite reliable estimates of the dipolar hyperfine coupling constants for n-eIectron iadicals. Agreement with experimenta! measurements of the isotropic couplings was more difficult to obtain using this methsd. It would be of interest ‘also to test the method for utype radicals. Accurate and detailed experimental data are available [2-I] on the isotropic and dipolar hyperfine interactions for the nuclides 13C, 14N and I70 in the isoelectronic species CO, and N02. For NO, the electric nuclear quadrupole coupling te,nsor has recently been measured using ENDOR spectrascopy [4]. The procedure to compute’ the magnetic properties has been described karlier [l]. In a first step an ab initio calculation’was performed usirig the program system MQLECULE [S] . This program solves the spin unrestricted Hartree--Fock equations in.a symmetry; adapted basis set made up of contracted gaussian-type -l$is functions. The spin densities at the,nuclei were then_computed in-a second step. A computer program based on.tha theory of +nbi and Snyder [S] was ‘. _-
_,
used to remove the S = 3/2 component of the wavefunction.‘FinaLly, in a third step, the dipoIar hyperfine interactions were evaluated. The same integrals were evaluated as in the calculation of the electric field gradient, substituting the spin density for the total electron density. The basis sets used employ zven s- and three groups.of p-type gaussians for C, N and 0, contracted to four s- and two groups of p-type function? [6]. For NO, the experimentdy determined geometry was used [7]. The total enerw was E = -203.67749 au. The geometry of CO, was optimized since no reliable values are given in the literature. A C-O bond Ien@ of 1.43 d and an O-C-O angle of 134.1a was found ‘to give the I&west total energy (_F= -187.19587 au).. The results of the calculations have been collected in table 1. The isotrqpic coupling constants remain constant or diminish slightly upon spin annihilation. -The values thus obtained for the 13C and lGN couplings agree rather well with experlmentai results.-The co& puted ralues.of the 170 couplings show rr&?h wctse $eem&t with the experimental data; It is w@h noting, however, that there is some ambiguity in the experimentally obtained date,‘owing tb the d@?culti .179
.‘_,Volume28;numbs;‘l _,,’ :..: 1.._._ :,.: ,‘_ .._,,: “.
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.,:
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.,, .
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,‘, ,_
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136
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.,
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,:’
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‘,
,..I
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,... :
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.
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-11+ t-14.8)
:
234.60 ‘. 1856
15.6
,‘,
15.9
16.03 .:
:
.’
“. ,‘.
(6.7)
:
(0.7969)
:
-31.5 I-13.8):
(7.t).
:
,.
,,‘
&p. ., .-
(UHF)
-
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.. ‘. : .
:.
.‘:.
:;.
the S =, 3/2’ wmpq.’ :
.:
,_ ‘.’
.’
.,.’
,. :
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~+:~,-::.‘. .;., . . .‘._1. y’ ‘.(,
..-
-9.2 ;’
:
‘.
UH,FAA(UHFj,: -.:‘kxp;
,.
..,;
>.
.iJJkFj iui;lhfterannih~8tion.(U’~EiAA),pf
-.;
,,
0 ., ,.’
-.‘..
;. .,‘.
T&.1
: .,. ._ -’ ;
:
,,z’::,
..I.
‘.
-,
. .
Rid!@
.:: _’
::_; C~~~CALPHYSICS’LE~ERS
co&.rtg~befor~ spin a&hi&ion
th~.~~-~~i~~,~i~~~~~ ,.
_, .-
:‘: .‘, ::
+Aar!lgijor&e
” ~Is&r&&:an~_ .‘:’ nbnf
...
:_
27.1 _(103).
., B2: -14.2 C-76.1) .‘& : -12.9 (-4.2)
;. .,’
’ 28.3 :,
-16.7 -11.7 -18-7
-32.2
..’
10.1. 8.7 .-
” :. ‘.
.,
:
._
,’
[2,3]. We kke the principal v&es of the I76 hyper.. fine interaction tensor tp.be negative. Tj~e mag~tudes.of the dipolar hyperfine couplings increase substantially upon spin animation. The con-
:
(inh1H.z)~
,‘ : Radic& Nucleus. ‘ ., __... -. .-
Efkctric quachpok
-
UXFAA -’ $?I: -1.4’ .. :.
c&.iplings
:
exp. -1.0
:
.-1. ,(
plings thus obtained are in k-n& &tt& agreement’ with’expeiimerit than the values obtained, before spin
.
anniJ$ation. O’ur direction cosines agree very’ iveIl .: -I).5 :‘ Pz: 4.2 . . . . . _. with experimental values. _For instanc,e, if: we cornpar. : ,. -~ ‘, i 3 ..P3: ‘1.0. ),o ..,‘ ..‘ .I direction co&es for Is’, ‘of thc’i?O coupling, we find , &-, ‘ 5.0. ... ., : ,’ .’ : ‘ ,’ “.’ :- -_, ,,,’ for-E\‘ 0 2 0.9Tl., O.l33’.arid O.O.Thqexpe$mentat ,:. ,‘ ,I$:,-53 .-: ,. ;. ,. :‘. Pi;. .:0.3: ._ ,.,-. .,_’.‘. ,: ). . :. values are 0.991,0,13.l @pd,O.O,iespectively. Fbr CSJ: ,’ ,IcOg~.‘.:r,-; ‘.‘_(j :. ,: ” we ~1~~~,0.970,.0.24~ P,; :.3.7, ” ._ .,’ atid 0.0. The~experimtnfaJ values ‘. ..pz:._@ ‘: .: ‘ , . - .- .-, .. ,.
_ .‘
:
..P3-,;q
..
V&me
28, number 2
The qusdr&le
CHEFCAL
cotipling
tensors wqe
P~SICS
calculated
using the electric,quadrtipoie,, moments.for atomic nuclei’given in yeF. [7] _The principal values shbwn in table 2 are in good agreement with’ the experim&tz: results [4] for 14N in NO,. The agre?ment is &fen betier if the experimental Values are reinterpieted with a new method [9] for, hatidLing ENDOR data: This treatment would give PI, = -114, P, = rO.2 and P, = 1.6 MHz, in complete agreement with experiment.At present there exist no‘experimental data for I70 with which comparison.can bc made. The literature &ntains several dalculations on-the spin properties of CO, and N02. A semi-empirical UHF treetment IlO] taking into account only the valence electrons gave spin densities of the‘carbon and nitrogen 2s orbital! which we;e too high when compared with experimentally obtained hyperfiuie splitting. In this calculation the conthbution to the spin density from 1s orbitals was neglected, however. No attempt was made to estimate the I70 hyperfine couplings*or the dipolar interactions. S,chaefe; and. Rothenberg [I I] made a non-empirical calculaticn on ‘NO, in the restricted
Hartree-Fock
appro>;imation
using a (9,5) gaussian basis set. The spin density at the nitrogen nucleus agreed well with experiment, particularly when d functions were included in the basis set. The computed values of the dipolar hyperfine coupling integrals fdr the &trogen nucleus were a!so in good agreement with experiment, whereas 2lI parameters computed for I70 were too small. McCain and Palke [12] obtained spin densities for CO, and NO2 close to those experimentally obtained for nitrogen
and carbon,
using a minimal
restricted Hartree-r‘ock c&d?jion. dipolar hyperfine coupling constants however. It is concluded that for the &type and NO2 the isotropic coupling with the central
atom is wellpredicted
Slater
basis in a
Their calcclated were too small, radicals
CO,
the nucleus of
by ab initio calcul&
tions and is rather insensitive to differences in basis
”
15 September 1974
LEFERS
sets and also to whether
restricted
or unrestricted
H+rec-Fock methods are used. Tile latter observation is in contrast tc the situation for r-electron radicals where only the UHF method-is applicable. Another noteworthy observation is that in tire present UHF calculations the spin annihilr?tion does not change the magnitudes df the isotropic coupling to the same extent, 2s for n-eiectron radicaIs. This can he explained by a theoj in which the UHF spin density is sepa:ate.d into two components due to spin polarization and spin delocalization [ 131. For dipolar hyperfine coupling constar&, however, spin annihilation is essential to obtain agreement. with experiment for the CO, and NO2 molecu!es. The reason for this is not ?Jear at present. The problem thus merits further calculations on u-electron radicals. ..
References [l] J. Almliif, A. Lund and K.;S. Thuomas, to be published. [2] Z. Luz and A. Reuveni, I. Chem. Phys. 51 (1964) 4017. (31 S. Schtick, B.L. Silver and 2. Luz, j.Chcm. Phys. 54 <1971) 867: [i] S.N. Rustgi and H.C. Box;J. Chem. Pbys. 59 (1973) 4763. [S ] J. AlmlGf, USIP-Report 7249, Univ. oEStockholm
(1972). [6] B. Roes and P. Siegbahn,Tkeoret. Chim. Acta 17 (1970) 1.09. [7] Handbook of chemistry and physics, 54th Ed. (Chemical P.ubbir Co., Cleveland, 1.9731, -[P] T. Amos and L.C. Snyder, J. Chem. Phys. 41 (1954) 1773. [9] A.-Lun? and K.-A. Thuoma, to be published. [ 101 T. Y~nczawa, H. Nakatsuji, T. Kawamura xd H. Kate. Bull. Chem. Sot. Japvl42 (1969) 2437. [ll] H.F:Schaefer III and S. Roihenberg, J.Chem. Phys. 54 (1971) 1423. [12] D.C. McCain and W.E. Pa&e, I. Chem. Phys. 56 (19fZ) 4957. [13] T. Yonezawa, H. Na!ztsuni; Ti K~wamur~a&i H. Kato, Chem’. Phys. Letters 2 (1968) 454.
Volume i8, number 2
. ..’
PHYSICS LETTERS
I.5 ‘beptembcr 1974
.. .. AEI INITIO MO LCAO UHF CALCULATIONS 06 MAGNETIC HYPEkFlNF,.INTERACTIONS IN (TRADICALS.. ISOTROPIC~-ANti ANISOTROPIC COUPLINGS 6F NO2 AND ,CO,.
Jzn ALMLijF Institute of l%eoretical Physics, University of Stockholm, Sltieden and
Anders LUND and Karl&e Swedish Re:earch.Councils’Loboratory
THUOMAS
And AB Atomenergi. Studsvik. iyk6pin.g. Sw
Received 19 June 1974
The magnetic hype&e coupling constants in NO2 and CO, have been computed by ab initio methods. Spin annihfition is found to be essential in order to obtain useful results for the dipolar couplings, but has much Less influence on the isotropic couplings. The electric quadrupole coupling constants have also been evaluated. and ax in good agreement with avdbble experimental data. _
Recent calculations [l] have demonstrated that unrestricted Hartree-Fock calculations followed by spin annihilation of the quartet contamination give quite reliable estimates of the dipolar hyperfine coupling constants for n-eIectron iadicals. Agreement with experimenta! measurements of the isotropic couplings was more difficult to obtain using this methsd. It would be of interest ‘also to test the method for utype radicals. Accurate and detailed experimental data are available [2-I] on the isotropic and dipolar hyperfine interactions for the nuclides 13C, 14N and I70 in the isoelectronic species CO, and N02. For NO, the electric nuclear quadrupole coupling te,nsor has recently been measured using ENDOR spectrascopy [4]. The procedure to compute’ the magnetic properties has been described karlier [l]. In a first step an ab initio calculation’was performed usirig the program system MQLECULE [S] . This program solves the spin unrestricted Hartree--Fock equations in.a symmetry; adapted basis set made up of contracted gaussian-type -l$is functions. The spin densities at the,nuclei were then_computed in-a second step. A computer program based on.tha theory of +nbi and Snyder [S] was ‘. _-
_,
used to remove the S = 3/2 component of the wavefunction.‘FinaLly, in a third step, the dipoIar hyperfine interactions were evaluated. The same integrals were evaluated as in the calculation of the electric field gradient, substituting the spin density for the total electron density. The basis sets used employ zven s- and three groups.of p-type gaussians for C, N and 0, contracted to four s- and two groups of p-type function? [6]. For NO, the experimentdy determined geometry was used [7]. The total enerw was E = -203.67749 au. The geometry of CO, was optimized since no reliable values are given in the literature. A C-O bond Ien@ of 1.43 d and an O-C-O angle of 134.1a was found ‘to give the I&west total energy (_F= -187.19587 au).. The results of the calculations have been collected in table 1. The isotrqpic coupling constants remain constant or diminish slightly upon spin annihilation. -The values thus obtained for the 13C and lGN couplings agree rather well with experlmentai results.-The co& puted ralues.of the 170 couplings show rr&?h wctse $eem&t with the experimental data; It is w@h noting, however, that there is some ambiguity in the experimentally obtained date,‘owing tb the d@?culti .179
.‘_,Volume28;numbs;‘l _,,’ :..: 1.._._ :,.: ,‘_ .._,,: “.
,;.
nf
‘.
;:,
‘.:^,.
:
-.;
.I
‘< ;
4
‘_~ .. :’
I ,. .,:
“...
G)’
.:
N..‘-..y.
.
‘.‘,‘.
‘.
_
NucIcus : .’ :.
.,:
t4h,
.JQ ‘
:.
:‘
-.,
..
..‘
.,’
:. ...
,.
_‘,‘,’.
: .:.:
,‘
:‘ _.
1‘ ,.c.
.,, ‘
,’
- ; .. .;
: ,,
(‘_
I:: .’
,‘...
(s2,
.,, .
.. Dipolar coqplings .. .
:
: UHFAA (U&F) : :.‘~ : T&F&
._.
,I
ii.9.
,.
,. . .
,f41.*) :,.;_: ,: ., . .. ,_ .. .. .‘.,I :-20.3
,
,‘, ,_
.’
,-
c*; ‘
136
: ,::
.,
(-12.3):
(-2.7) 5,i
.,
.‘
..
.‘176.2
, ..
,:’
‘:,
‘,
,..I
_.
,... :
166.7 _,
.
‘02:
:
Es:
0.7517
‘E,: -.
.
(210.2)
-11+ t-14.8)
:
234.60 ‘. 1856
15.6
,‘,
15.9
16.03 .:
:
.’
“. ,‘.
(6.7)
:
(0.7969)
:
-31.5 I-13.8):
(7.t).
:
,.
,,‘
&p. ., .-
(UHF)
-
‘-
.. ‘. : .
:.
.‘:.
:;.
the S =, 3/2’ wmpq.’ :
.:
,_ ‘.’
.’
.,.’
,. :
” ‘‘. 15 gmxdJi~.l9?4 :
~+:~,-::.‘. .;., . . .‘._1. y’ ‘.(,
..-
-9.2 ;’
:
‘.
UH,FAA(UHFj,: -.:‘kxp;
,.
..,;
>.
.iJJkFj iui;lhfterannih~8tion.(U’~EiAA),pf
-.;
,,
0 ., ,.’
-.‘..
;. .,‘.
T&.1
: .,. ._ -’ ;
:
,,z’::,
..I.
‘.
-,
. .
Rid!@
.:: _’
::_; C~~~CALPHYSICS’LE~ERS
co&.rtg~befor~ spin a&hi&ion
th~.~~-~~i~~,~i~~~~~ ,.
_, .-
:‘: .‘, ::
+Aar!lgijor&e
” ~Is&r&&:an~_ .‘:’ nbnf
...
:_
27.1 _(103).
., B2: -14.2 C-76.1) .‘& : -12.9 (-4.2)
;. .,’
’ 28.3 :,
-16.7 -11.7 -18-7
-32.2
..’
10.1. 8.7 .-
” :. ‘.
.,
:
._
,’
[2,3]. We kke the principal v&es of the I76 hyper.. fine interaction tensor tp.be negative. Tj~e mag~tudes.of the dipolar hyperfine couplings increase substantially upon spin animation. The con-
:
(inh1H.z)~
,‘ : Radic& Nucleus. ‘ ., __... -. .-
Efkctric quachpok
-
UXFAA -’ $?I: -1.4’ .. :.
c&.iplings
:
exp. -1.0
:
.-1. ,(
plings thus obtained are in k-n& &tt& agreement’ with’expeiimerit than the values obtained, before spin
.
anniJ$ation. O’ur direction cosines agree very’ iveIl .: -I).5 :‘ Pz: 4.2 . . . . . _. with experimental values. _For instanc,e, if: we cornpar. : ,. -~ ‘, i 3 ..P3: ‘1.0. ),o ..,‘ ..‘ .I direction co&es for Is’, ‘of thc’i?O coupling, we find , &-, ‘ 5.0. ... ., : ,’ .’ : ‘ ,’ “.’ :- -_, ,,,’ for-E\‘ 0 2 0.9Tl., O.l33’.arid O.O.Thqexpe$mentat ,:. ,‘ ,I$:,-53 .-: ,. ;. ,. :‘. Pi;. .:0.3: ._ ,.,-. .,_’.‘. ,: ). . :. values are 0.991,0,13.l @pd,O.O,iespectively. Fbr CSJ: ,’ ,IcOg~.‘.:r,-; ‘.‘_(j :. ,: ” we ~1~~~,0.970,.0.24~ P,; :.3.7, ” ._ .,’ atid 0.0. The~experimtnfaJ values ‘. ..pz:._@ ‘: .: ‘ , . - .- .-, .. ,.
_ .‘
:
..P3-,;q
..
V&me
28, number 2
The qusdr&le
CHEFCAL
cotipling
tensors wqe
P~SICS
calculated
using the electric,quadrtipoie,, moments.for atomic nuclei’given in yeF. [7] _The principal values shbwn in table 2 are in good agreement with’ the experim&tz: results [4] for 14N in NO,. The agre?ment is &fen betier if the experimental Values are reinterpieted with a new method [9] for, hatidLing ENDOR data: This treatment would give PI, = -114, P, = rO.2 and P, = 1.6 MHz, in complete agreement with experiment.At present there exist no‘experimental data for I70 with which comparison.can bc made. The literature &ntains several dalculations on-the spin properties of CO, and N02. A semi-empirical UHF treetment IlO] taking into account only the valence electrons gave spin densities of the‘carbon and nitrogen 2s orbital! which we;e too high when compared with experimentally obtained hyperfiuie splitting. In this calculation the conthbution to the spin density from 1s orbitals was neglected, however. No attempt was made to estimate the I70 hyperfine couplings*or the dipolar interactions. S,chaefe; and. Rothenberg [I I] made a non-empirical calculaticn on ‘NO, in the restricted
Hartree-Fock
appro>;imation
using a (9,5) gaussian basis set. The spin density at the nitrogen nucleus agreed well with experiment, particularly when d functions were included in the basis set. The computed values of the dipolar hyperfine coupling integrals fdr the &trogen nucleus were a!so in good agreement with experiment, whereas 2lI parameters computed for I70 were too small. McCain and Palke [12] obtained spin densities for CO, and NO2 close to those experimentally obtained for nitrogen
and carbon,
using a minimal
restricted Hartree-r‘ock c&d?jion. dipolar hyperfine coupling constants however. It is concluded that for the &type and NO2 the isotropic coupling with the central
atom is wellpredicted
Slater
basis in a
Their calcclated were too small, radicals
CO,
the nucleus of
by ab initio calcul&
tions and is rather insensitive to differences in basis
”
15 September 1974
LEFERS
sets and also to whether
restricted
or unrestricted
H+rec-Fock methods are used. Tile latter observation is in contrast tc the situation for r-electron radicals where only the UHF method-is applicable. Another noteworthy observation is that in tire present UHF calculations the spin annihilr?tion does not change the magnitudes df the isotropic coupling to the same extent, 2s for n-eiectron radicaIs. This can he explained by a theoj in which the UHF spin density is sepa:ate.d into two components due to spin polarization and spin delocalization [ 131. For dipolar hyperfine coupling constar&, however, spin annihilation is essential to obtain agreement. with experiment for the CO, and NO2 molecu!es. The reason for this is not ?Jear at present. The problem thus merits further calculations on u-electron radicals. ..
References [l] J. Almliif, A. Lund and K.;S. Thuomas, to be published. [2] Z. Luz and A. Reuveni, I. Chem. Phys. 51 (1964) 4017. (31 S. Schtick, B.L. Silver and 2. Luz, j.Chcm. Phys. 54 <1971) 867: [i] S.N. Rustgi and H.C. Box;J. Chem. Pbys. 59 (1973) 4763. [S ] J. AlmlGf, USIP-Report 7249, Univ. oEStockholm
(1972). [6] B. Roes and P. Siegbahn,Tkeoret. Chim. Acta 17 (1970) 1.09. [7] Handbook of chemistry and physics, 54th Ed. (Chemical P.ubbir Co., Cleveland, 1.9731, -[P] T. Amos and L.C. Snyder, J. Chem. Phys. 41 (1954) 1773. [9] A.-Lun? and K.-A. Thuoma, to be published. [ 101 T. Y~nczawa, H. Nakatsuji, T. Kawamura xd H. Kate. Bull. Chem. Sot. Japvl42 (1969) 2437. [ll] H.F:Schaefer III and S. Roihenberg, J.Chem. Phys. 54 (1971) 1423. [12] D.C. McCain and W.E. Pa&e, I. Chem. Phys. 56 (19fZ) 4957. [13] T. Yonezawa, H. Na!ztsuni; Ti K~wamur~a&i H. Kato, Chem’. Phys. Letters 2 (1968) 454.