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Ab initio UHF calculations of hyperfine coupling constants
Volume 1. number 6
AB
ZNZTZO
CHERIICALPHYSICSLETTERS
UHF
CALCULATIONS
OF
HYPERFINE
L &3xluary
COUPLING
1970
CONSTANTS
T. A. CLAXTON, D. McWILLIAMS and N. A. SMITH Depnrtment of Clren~isfry, The Ukversity, L.&ceder, UK
Received 29 October 1969 calculations using a minimal basis set of orbitals for the radicals H.-,S, H9S’, NHzi,
Ab iw?ioUIIF =+, cn3SCP ato6ic Recently is generally
and
NH7
orbital:
predict
the
h)Terfine
coupling
constants
to
all
nuclei
with
a consiCknt
rr&urac-
lf
are used.
[l] it has been suggested poor agreement between
that there the calcu-
lated hyperfine coupling constants to heavy nuclei and experiment. This was associated with the very strong dependence of the spin density at the nucleus with the orbital exponent of the 1s Slater type orbital. Firstly it is our view that the very good atomic self-consistent field orbitals. expressed as linear combinations of gaussian functions which are readily available for many atoms, should be used in the calculation of hyperfine coupling constants in preference to Slater type orbita!s. Secondly the very attractive proposition [1,2] to use a “mixed basis” is easily extended in principle to SCF orbitals if different size gaussian expansions of the SCF orbitals are used to achieve the same reduction in computer time that the “mixed basis” method achieves. We have done preliminary calculations on the following radicals; H2S-, H2S+, NH3+, CH3, BH3- and NH3, and have obtained significant differences from the results of Cook, Hinchliffe and Palmieri [l]. We have used the ab ittitio UHFAA method using the gaussian function expansions of the minimal basis set orbitals as given by Huzinaga [3] (nine s-type and five p-type) and Veillard [4] (twelve s-type and nine p-type) for the first and second row atoms respectively. The hydrogen 1s orbital was represented analogously us:ng a six term gaussian expansion suitably modified for different orbital exponents [3]. The hydrogen hyperfine coupling constants may be underestimated by as much as 10% due to inadequate representation of the hydrogen orbital by gaussian functions as described previously [5]. The results are collected in table 1, and it is stressed that the calculations are being further optimised by varying the orbital exponents of the hydrogen atom and bond lengths
until the energy is minimized. The hydrogen atom orbital qonent used in the calculation was 1.2. except for NH2 which has been partially optimised to have an orbital exponent close to 1.4 at an optimum angle of lO5O [S]. The bond lengths for NH3+, CH3, BH3- and NH2 were assumed to be 2 au. It is expected that optimisation will put the bond lengths in order r(NHsf) .; r(CH3) 5.r(BH3-) and the hydrogen orbital exponents, LY,in order [15] a(NH2-) > (u(CK3)> a(BH3-). Since the hydrogen coupling constant increases with increasing bond length and increasing orbital exponent in these radicaIs the discrepancies with the hydrogen coupling constants are readily rationalised. The variation of the heavy atom nuclei coupling con.stants with bond distance is less clearly defined, but ali the results, except for H2S- [‘i’] are in agreement with experiment. It may be significant that the heavy atom hyperfine coupling constants are all smaller than experiment which can be rationalised in terms of either an inadequate representation of the electron density at the nucleus of the gaussian expansion approximation to the SCF orbital (as already observed forthe hydrogen 1s orbital [5]) or a modification (contraction) of the SCF orbitals due to molecular formation (e. g. the hydrogen orbitals in NH2 [6]). Symons [9] has placed considerable doubt on the interpretation of the ESR spectrum assigned to the H2S- radical and these calculations support his conclusion (the inclusion of d orbit&s [l] do not seem to have the required [7] dramatic effect). There is an unaccountable discrepancy between our calculations and those from ref. [l] for H2S- and H2Sf. It seems that the H2S- results should be labelled H2Sf in ref. [l] and vice versa. The results as they stand [l] cannot be rationalised from sImpLe qualitative arguments. 505
Volume
4. number
8
---__
- ...__. -Ref. - .______.-. --
i’il
CHEMICAL
Comparison Radicaf
.._
-.H2S-?
[S.Tl
Table 1 of esperimental and theoretical h:rperfine .-__________---------------t Method gu, apt.
H2S’
UHFAA UHFAA RHF CI
H,SI 3 H2S *
Expt. UHFAA UHFAA RHF Cl
rI1 vi
111 I11
1 January
PHYSICS LETTERS
1970
coupling
constants -- -.--- -. ._______._.__.--_--._ .--.- _ Coupling constants (gauss) Heavy ntom Hydrogen __I_---.(=) 7.7 (+) 60.0
- 398.3333
- 398.2335
455-3 -4.03 -4.50
6.02 0.01 0.00
(-)24.2 -14.11 257.2 212.7
10.81 0.13 0.03
(-)23.9 -15.75
(1)19.5 14.82
0 1111 z+
NH$
Ill y1
Expt. UH FAA RHF
CH3
[II [I31 *
J.3H3_
[IdI
SH,I
r:] ll6I 1161
-55.7991
-25-F
CI
47.68
Espt. Uff FAA IiHF CI
-39.Si14
(-)23.0 -18.04 -21.13
(‘)41 .o 31.72 -30.45
Expt. L‘HFAX
-26.2508
(-)16.6 -17.22
(; )24.0 13.62
(-123.9 -22.26 -38.93 -11.9 -16.3
(4 110.3 8.16 80.59 IS.7 5.2
Espt. UIf FAX RIIF CI UH FAA RHF CI
-55.5249
--spin component. t Total energy nftcr :mnihilntion of quartet * This work. The geometry for H2S and H2S’ ws taken from
We conclude that the UHFAA method is capa-
ble of reasonably predicting the isotropic hyperfine coupling constants of heavy atoms as well as hydrogen atoms. Calculations on NaH’ [51 also support this conclusion.
REFERENCES [il D. B. Cook. A. Hinchliffe nnd P. Pnlmieri. Chem. Phys. Letters 3 (1969) 223. I2] D. B. Cook and P. Palmieri. Mol. Phys. 17 (1969)2’71. [3] S.Iiuzinagn, J. Chom. Phys. 42 (1963) 1293. [4] A.Vc~illnrd, Theorct. Chim. Actn 12 (1968) 405. [a] T. A. Ckston a~?d 13. Mc\%‘illinms, Trans. Faraday in-press. sot., [G] T. A. Claxton, to be published.
506
ref. (IO].
[‘if J_ E. Bennett,
B. Mile and A. Thomas. Chem. Commun. (3966) 182. [8] A. IIausmnnn, Z. Physik 192 (196(i) 313. ES]>I. C. R.Symons, Adwn. Chem. Ser. 82 (1968) 1. [lo] D. B. Cook and P. Pnlmieri, Chem. Whys. Letters
3 (1969) 219. [ll] T.Cole. J. Chem.
Phys. 35 (1961) 1169. [12] J. .J. Christiansen, W. Gordy and R. L. Morehouse, J. Gem. Phvs. 45 (1966) 1751: T-Cole, N. R. Davidson, H. M. McConnell and H. o I’ritchard, Itl[ol. Phvs. 1 (1958) 406: R.LV. Fcssenden ani R.H.SchuIer, J. Chcm. Phrs. 45 (1966) 1845. [13] RI. C. R. Symons nnd H. Wardale, Chem. Commun. (1967) 758. [14] V.t’L. Bjower~, E. L.Cochran, S.K. Foner and C.K. Jen, Ph>-s. Rev. Letters 1 (1958) 91. 115: M-C. R.Symons, Sature, in press. [Ziij B.T.Sutcliffle, J. Chem. Phys. 39 (1963) 3322.
AB
ZNZTZO
CHERIICALPHYSICSLETTERS
UHF
CALCULATIONS
OF
HYPERFINE
L &3xluary
COUPLING
1970
CONSTANTS
T. A. CLAXTON, D. McWILLIAMS and N. A. SMITH Depnrtment of Clren~isfry, The Ukversity, L.&ceder, UK
Received 29 October 1969 calculations using a minimal basis set of orbitals for the radicals H.-,S, H9S’, NHzi,
Ab iw?ioUIIF =+, cn3SCP ato6ic Recently is generally
and
NH7
orbital:
predict
the
h)Terfine
coupling
constants
to
all
nuclei
with
a consiCknt
rr&urac-
lf
are used.
[l] it has been suggested poor agreement between
that there the calcu-
lated hyperfine coupling constants to heavy nuclei and experiment. This was associated with the very strong dependence of the spin density at the nucleus with the orbital exponent of the 1s Slater type orbital. Firstly it is our view that the very good atomic self-consistent field orbitals. expressed as linear combinations of gaussian functions which are readily available for many atoms, should be used in the calculation of hyperfine coupling constants in preference to Slater type orbita!s. Secondly the very attractive proposition [1,2] to use a “mixed basis” is easily extended in principle to SCF orbitals if different size gaussian expansions of the SCF orbitals are used to achieve the same reduction in computer time that the “mixed basis” method achieves. We have done preliminary calculations on the following radicals; H2S-, H2S+, NH3+, CH3, BH3- and NH3, and have obtained significant differences from the results of Cook, Hinchliffe and Palmieri [l]. We have used the ab ittitio UHFAA method using the gaussian function expansions of the minimal basis set orbitals as given by Huzinaga [3] (nine s-type and five p-type) and Veillard [4] (twelve s-type and nine p-type) for the first and second row atoms respectively. The hydrogen 1s orbital was represented analogously us:ng a six term gaussian expansion suitably modified for different orbital exponents [3]. The hydrogen hyperfine coupling constants may be underestimated by as much as 10% due to inadequate representation of the hydrogen orbital by gaussian functions as described previously [5]. The results are collected in table 1, and it is stressed that the calculations are being further optimised by varying the orbital exponents of the hydrogen atom and bond lengths
until the energy is minimized. The hydrogen atom orbital qonent used in the calculation was 1.2. except for NH2 which has been partially optimised to have an orbital exponent close to 1.4 at an optimum angle of lO5O [S]. The bond lengths for NH3+, CH3, BH3- and NH2 were assumed to be 2 au. It is expected that optimisation will put the bond lengths in order r(NHsf) .; r(CH3) 5.r(BH3-) and the hydrogen orbital exponents, LY,in order [15] a(NH2-) > (u(CK3)> a(BH3-). Since the hydrogen coupling constant increases with increasing bond length and increasing orbital exponent in these radicaIs the discrepancies with the hydrogen coupling constants are readily rationalised. The variation of the heavy atom nuclei coupling con.stants with bond distance is less clearly defined, but ali the results, except for H2S- [‘i’] are in agreement with experiment. It may be significant that the heavy atom hyperfine coupling constants are all smaller than experiment which can be rationalised in terms of either an inadequate representation of the electron density at the nucleus of the gaussian expansion approximation to the SCF orbital (as already observed forthe hydrogen 1s orbital [5]) or a modification (contraction) of the SCF orbitals due to molecular formation (e. g. the hydrogen orbitals in NH2 [6]). Symons [9] has placed considerable doubt on the interpretation of the ESR spectrum assigned to the H2S- radical and these calculations support his conclusion (the inclusion of d orbit&s [l] do not seem to have the required [7] dramatic effect). There is an unaccountable discrepancy between our calculations and those from ref. [l] for H2S- and H2Sf. It seems that the H2S- results should be labelled H2Sf in ref. [l] and vice versa. The results as they stand [l] cannot be rationalised from sImpLe qualitative arguments. 505
Volume
4. number
8
---__
- ...__. -Ref. - .______.-. --
i’il
CHEMICAL
Comparison Radicaf
.._
-.H2S-?
[S.Tl
Table 1 of esperimental and theoretical h:rperfine .-__________---------------t Method gu, apt.
H2S’
UHFAA UHFAA RHF CI
H,SI 3 H2S *
Expt. UHFAA UHFAA RHF Cl
rI1 vi
111 I11
1 January
PHYSICS LETTERS
1970
coupling
constants -- -.--- -. ._______._.__.--_--._ .--.- _ Coupling constants (gauss) Heavy ntom Hydrogen __I_---.(=) 7.7 (+) 60.0
- 398.3333
- 398.2335
455-3 -4.03 -4.50
6.02 0.01 0.00
(-)24.2 -14.11 257.2 212.7
10.81 0.13 0.03
(-)23.9 -15.75
(1)19.5 14.82
0 1111 z+
NH$
Ill y1
Expt. UH FAA RHF
CH3
[II [I31 *
J.3H3_
[IdI
SH,I
r:] ll6I 1161
-55.7991
-25-F
CI
47.68
Espt. Uff FAA IiHF CI
-39.Si14
(-)23.0 -18.04 -21.13
(‘)41 .o 31.72 -30.45
Expt. L‘HFAX
-26.2508
(-)16.6 -17.22
(; )24.0 13.62
(-123.9 -22.26 -38.93 -11.9 -16.3
(4 110.3 8.16 80.59 IS.7 5.2
Espt. UIf FAX RIIF CI UH FAA RHF CI
-55.5249
--spin component. t Total energy nftcr :mnihilntion of quartet * This work. The geometry for H2S and H2S’ ws taken from
We conclude that the UHFAA method is capa-
ble of reasonably predicting the isotropic hyperfine coupling constants of heavy atoms as well as hydrogen atoms. Calculations on NaH’ [51 also support this conclusion.
REFERENCES [il D. B. Cook. A. Hinchliffe nnd P. Pnlmieri. Chem. Phys. Letters 3 (1969) 223. I2] D. B. Cook and P. Palmieri. Mol. Phys. 17 (1969)2’71. [3] S.Iiuzinagn, J. Chom. Phys. 42 (1963) 1293. [4] A.Vc~illnrd, Theorct. Chim. Actn 12 (1968) 405. [a] T. A. Ckston a~?d 13. Mc\%‘illinms, Trans. Faraday in-press. sot., [G] T. A. Claxton, to be published.
506
ref. (IO].
[‘if J_ E. Bennett,
B. Mile and A. Thomas. Chem. Commun. (3966) 182. [8] A. IIausmnnn, Z. Physik 192 (196(i) 313. ES]>I. C. R.Symons, Adwn. Chem. Ser. 82 (1968) 1. [lo] D. B. Cook and P. Pnlmieri, Chem. Whys. Letters
3 (1969) 219. [ll] T.Cole. J. Chem.
Phys. 35 (1961) 1169. [12] J. .J. Christiansen, W. Gordy and R. L. Morehouse, J. Gem. Phvs. 45 (1966) 1751: T-Cole, N. R. Davidson, H. M. McConnell and H. o I’ritchard, Itl[ol. Phvs. 1 (1958) 406: R.LV. Fcssenden ani R.H.SchuIer, J. Chcm. Phrs. 45 (1966) 1845. [13] RI. C. R. Symons nnd H. Wardale, Chem. Commun. (1967) 758. [14] V.t’L. Bjower~, E. L.Cochran, S.K. Foner and C.K. Jen, Ph>-s. Rev. Letters 1 (1958) 91. 115: M-C. R.Symons, Sature, in press. [Ziij B.T.Sutcliffle, J. Chem. Phys. 39 (1963) 3322.