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An .AB initio calculations of hyperfine coupling constants in HCO radical
CHEMICAL
PHYSICS
LETTERS
1 (1967)
217-218.
NORTH -HOLLAND
PUBLISHING
AN .AB lNlZ-70 CALCULATION OF HYPE&FINE CONSTANTS IN HCO RADICAL
COMPANY.
AhaTERDAM
COUPLING
A. HINCHLIFFE Sckool of fiIo2eculau Sciences_
The University
of Sussex.
BrigRfort.
England
and D. B. CXXX Department
of Chernistq~
The Univevsityy
Received
Sheffield 10. England
July 1967
The results of a non empirical calculation of hyperfine coupling constants in HCO are presented. in good a.greement wirithexperiment.
The formyl radical, HCO, has been prepared by Adrian et al. [Z]; the isotropic proton hyper-
fine coupling has the extremely large value of 137 gauss, and the 13~ isotropic hyperfine coupling is 134.7 gauss [2]. The gas phase geometry of the radical is known accurately: the bond lengths are r(CH) = 2.040 au, r(C0) = 2.268 au, and Hm = 120°. An SCF calculation has recently been reported for formaldehyde, using a similar molecular geometry (7(CH) = 1.00 au, r(C0) = 2.3 au, HCO = 1200) [3]. In this communication, we present the preliminary results of nc;n empirical UHF (Unrestricted Hartree Fock) calculations on formyl. The formaldehyde integrals* were taken to be an excellent approximation to the HCO integrals, with the exception of the nuclear attraction integrals, which were computed using numerical integration. A description of the UHF’ method has been given elsewhere [4]. In chemical language, the HCO radical possesses a CH u bond, a CO II bond, a CO u bond, 2 oxygen lone pairs, oxygen and carbon is cores, and au odd electron occupying an sp2 hybrid, lo-
calised on carbon. To retain this attractive picture as far as possible, we have transformed Newton’s nonorthogonal basis x to an orthogonal one $, 9 = xwus-+
= xv
where W Schmidt orthogonalises * Made available Newton.
(1)
all orbit&s
to us through the courtesy
of M.D.
against 1s orbitals U forms sp2 hybrids on carbon and oxygep, pointing in the appropriate directions, and S-H provides a LUwdin ES] symmetrical orthogonalisation. The normalised spin density, evaluated at the position of nucleus t2becomes, in matrix notation,
P(&) = ss
x(Z~) W=-
QW’x’&z)
i%
where x(Zn) iS the Value Gf the row x at nucLeus fz. After annihilation of the quartet spin function, P and Q are replaced by J and K respectively (41. The hyperfine coupling constant for nucleus n, A nr is
A,,= 142.77 g & P(l,) gauss
(3)
provided that p(Z,,) is given in units of atomic volume-1. The electronic g value is 2.0023, and the gn values used were lH: +5.5840;
13C: t1.40432;
170: -0.75720,
The UHF calculation was performed by repeated diagonalisations [4] and gave a total eZec&~zic energy of -138.82481 au after 44 cycles, when P and Q had converged to about 0.0001 in every element, on average. The mean values of S2 before and after annihilation of the quartet spin function were (S2)g)
= 0.762239;
(@}A&4
= 0.750085.
III table 1, we present the coupling constants before and after the single annihilation. The proton coupling constant is in exceLLent agreement with experiment, the “anmIhil.ated”
A. HINCHLIFFE
218
Hyperfine
TabIe 1 coupling constants (gauss) before annihilation. and experimental. before
1H 13C 170
ann.
This means, and after
after ann.
expt .
c133.95 +260.85 6.42
A137.0 +134.7
+154.58 +i86.44 - 12.50,
By transforming the integrals involved in the UHF calculation to various orthogonal bases and then making the 00 I?] approximation =
6ij6kZ[ii(kk_l
in
particular,
Ah = Qpii
that the relation
Q = 876 gauss
(5)
used to interpret proton hyperfine couplings in other work [8,9], should have a larger Q: in fact, the value of Q should be +1306 gauss for HCO and this gives improved agreement with experiment for the semi empirical calculations [8,9]. A more correct relation would be
value being the better one; ihe single annihilation has a significant effect on-the calculated coupling constant. The 170 coupling constant has not been observed experimentally - we predict that it will be small. and negatjve again, the single annihilation is quite important. The 13C coupling constant is in less good agreement with experimcmt, but is still quite acceptable. This kind of inaccuracy was also noted by Sutcliffe [6] for NH2, and is really inherent in the UHF method, for the spin density matrix is the differance of two matrices, each of which have large diagonal elements for the core electrons. A change of 0.0005 in the lsc spin density gives a change of 12 gauss in the coupling constant.
[ij(RZ]
and D. B. COOK
(4)
repeating the calculation and comparing the results with the full UHF calculation, it turns out that the CNDO procedure is approximSztely analogous to calculations performed using basis (1).
Ah = 876
(WUS-%)i2ieii
gaUSS
which shows that the Q of eq. (5) is not a constant but varies for protons in different environments. Fuller results along the lines outlined above will be published elsewhere.
REFERENCES [l)
F.J.Adrian. E.L.Cochran and V.A.Bowers. J. Chcm.Phys. 36 (1962) 1661. [a] F. J-Adrian. E. L. Cochran and V.A. Bowers. J. Chem. Phys. 44 (1966) 4626. [3] M.D. Newton and W. E. Pa!ke, J. Chem. Phys. 46 (1966) 2329. [4] A. T.Amos and G. G. Hall. Proc.Roy.Soc. A263 (1961) 483. 151 P-O. Lowdin, J. Chem. Phys. 18 (1955) 365. i6i B.T.Sutcliffe. J. Chem. Phys. 39. (196Q) 3322. (71 J.A.PopIe. D.P.Santry and G.A.Segal. J.Chem. Phya. 43 (1965) S129. [S] N. M.Atherton and A. Hinchliffe, Mol. Phys. 12 (1967) 349. 191 G.A. Petersson and A. D.McLachlan. J. Chem. Phys. 45 (1966) 628.
PHYSICS
LETTERS
1 (1967)
217-218.
NORTH -HOLLAND
PUBLISHING
AN .AB lNlZ-70 CALCULATION OF HYPE&FINE CONSTANTS IN HCO RADICAL
COMPANY.
AhaTERDAM
COUPLING
A. HINCHLIFFE Sckool of fiIo2eculau Sciences_
The University
of Sussex.
BrigRfort.
England
and D. B. CXXX Department
of Chernistq~
The Univevsityy
Received
Sheffield 10. England
July 1967
The results of a non empirical calculation of hyperfine coupling constants in HCO are presented. in good a.greement wirithexperiment.
The formyl radical, HCO, has been prepared by Adrian et al. [Z]; the isotropic proton hyper-
fine coupling has the extremely large value of 137 gauss, and the 13~ isotropic hyperfine coupling is 134.7 gauss [2]. The gas phase geometry of the radical is known accurately: the bond lengths are r(CH) = 2.040 au, r(C0) = 2.268 au, and Hm = 120°. An SCF calculation has recently been reported for formaldehyde, using a similar molecular geometry (7(CH) = 1.00 au, r(C0) = 2.3 au, HCO = 1200) [3]. In this communication, we present the preliminary results of nc;n empirical UHF (Unrestricted Hartree Fock) calculations on formyl. The formaldehyde integrals* were taken to be an excellent approximation to the HCO integrals, with the exception of the nuclear attraction integrals, which were computed using numerical integration. A description of the UHF’ method has been given elsewhere [4]. In chemical language, the HCO radical possesses a CH u bond, a CO II bond, a CO u bond, 2 oxygen lone pairs, oxygen and carbon is cores, and au odd electron occupying an sp2 hybrid, lo-
calised on carbon. To retain this attractive picture as far as possible, we have transformed Newton’s nonorthogonal basis x to an orthogonal one $, 9 = xwus-+
= xv
where W Schmidt orthogonalises * Made available Newton.
(1)
all orbit&s
to us through the courtesy
of M.D.
against 1s orbitals U forms sp2 hybrids on carbon and oxygep, pointing in the appropriate directions, and S-H provides a LUwdin ES] symmetrical orthogonalisation. The normalised spin density, evaluated at the position of nucleus t2becomes, in matrix notation,
P(&) = ss
x(Z~) W=-
QW’x’&z)
i%
where x(Zn) iS the Value Gf the row x at nucLeus fz. After annihilation of the quartet spin function, P and Q are replaced by J and K respectively (41. The hyperfine coupling constant for nucleus n, A nr is
A,,= 142.77 g & P(l,) gauss
(3)
provided that p(Z,,) is given in units of atomic volume-1. The electronic g value is 2.0023, and the gn values used were lH: +5.5840;
13C: t1.40432;
170: -0.75720,
The UHF calculation was performed by repeated diagonalisations [4] and gave a total eZec&~zic energy of -138.82481 au after 44 cycles, when P and Q had converged to about 0.0001 in every element, on average. The mean values of S2 before and after annihilation of the quartet spin function were (S2)g)
= 0.762239;
(@}A&4
= 0.750085.
III table 1, we present the coupling constants before and after the single annihilation. The proton coupling constant is in exceLLent agreement with experiment, the “anmIhil.ated”
A. HINCHLIFFE
218
Hyperfine
TabIe 1 coupling constants (gauss) before annihilation. and experimental. before
1H 13C 170
ann.
This means, and after
after ann.
expt .
c133.95 +260.85 6.42
A137.0 +134.7
+154.58 +i86.44 - 12.50,
By transforming the integrals involved in the UHF calculation to various orthogonal bases and then making the 00 I?] approximation =
6ij6kZ[ii(kk_l
in
particular,
Ah = Qpii
that the relation
Q = 876 gauss
(5)
used to interpret proton hyperfine couplings in other work [8,9], should have a larger Q: in fact, the value of Q should be +1306 gauss for HCO and this gives improved agreement with experiment for the semi empirical calculations [8,9]. A more correct relation would be
value being the better one; ihe single annihilation has a significant effect on-the calculated coupling constant. The 170 coupling constant has not been observed experimentally - we predict that it will be small. and negatjve again, the single annihilation is quite important. The 13C coupling constant is in less good agreement with experimcmt, but is still quite acceptable. This kind of inaccuracy was also noted by Sutcliffe [6] for NH2, and is really inherent in the UHF method, for the spin density matrix is the differance of two matrices, each of which have large diagonal elements for the core electrons. A change of 0.0005 in the lsc spin density gives a change of 12 gauss in the coupling constant.
[ij(RZ]
and D. B. COOK
(4)
repeating the calculation and comparing the results with the full UHF calculation, it turns out that the CNDO procedure is approximSztely analogous to calculations performed using basis (1).
Ah = 876
(WUS-%)i2ieii
gaUSS
which shows that the Q of eq. (5) is not a constant but varies for protons in different environments. Fuller results along the lines outlined above will be published elsewhere.
REFERENCES [l)
F.J.Adrian. E.L.Cochran and V.A.Bowers. J. Chcm.Phys. 36 (1962) 1661. [a] F. J-Adrian. E. L. Cochran and V.A. Bowers. J. Chem. Phys. 44 (1966) 4626. [3] M.D. Newton and W. E. Pa!ke, J. Chem. Phys. 46 (1966) 2329. [4] A. T.Amos and G. G. Hall. Proc.Roy.Soc. A263 (1961) 483. 151 P-O. Lowdin, J. Chem. Phys. 18 (1955) 365. i6i B.T.Sutcliffe. J. Chem. Phys. 39. (196Q) 3322. (71 J.A.PopIe. D.P.Santry and G.A.Segal. J.Chem. Phya. 43 (1965) S129. [S] N. M.Atherton and A. Hinchliffe, Mol. Phys. 12 (1967) 349. 191 G.A. Petersson and A. D.McLachlan. J. Chem. Phys. 45 (1966) 628.