INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY SYMP. NO. 8, 277-284 (1974)

An ab initio Study of the Electronic Structure and Isotropic Hyperfine Coupling Constants of

HCO, FCO, and HBF Using Different Gaussian Basis Sets

COLIN THOMSON AND DOUGLAS A. BROTCHIE Department of Chemistry, University of St. Andrews, St . Andrews KY16 9ST, Scotland.

Abstract

The equilibrium geometries of HCO, FCO, and HBF have been calculated by the LCAO-MO-SCF method for several Gaussian basis sets. The bonding in the molecules was discussed using the Mulliken popula- tion analysis, and isotropic hyperfine coupling constants calculated. Results for the latter are in fair agreement with experiment, and the geometry and coupling constants in the unknown HBF are predicted.

1. Introduction

Ab initio calculations of the isotropic hyperfine coupling constants of free radicals provide a severe test of the quality of the electronic wave function of the radical, and there have been several such calculations during the last few years [ 11. Atomic hyperfine coupling calculations seem to show that rather sophisticated wave functions, such as those obtained by the unrestricted Hartree-Fock method [2], or the various forms of the extended Hartree-Fock method [3], or wave functions including con- figuration interaction [4,5], are necessary in order to compute reliable spin densities at the nuclei. A review of recent ab initio work in this field has recently been given [l] .

However, for molecules, Schaefer and Rothenberg, in a detailed study of NO,[6], showed that it might be possible to use restricted Hartree-Fock (RHF) wave functions for qualitative calculation of isotropic hyperfine coupling constants, providing a large basis set was used. Subsequently, Green [7-91 investigated the use of the RHF and RHF + CI methods in a study of the spin densities in the 'X states of various diatomic molecules. Although RHF + CI calculations gave the most accurate results, the RHF method gave qualitatively reasonable spin densities. There have not been, however, any extensive studies of how the calculated spin densities depend on the basis set composition. In the present paper we report the results of such an investiga- tion of the triatomic radicals HCO, HBF, and FCO. The calculations on HBF have been briefly reported previously [lo]. The present paper deals primarily with ex- tensive calculations on HCO and FCO, but reference to the HBF results is made where comparisons are useful.

These three radicals form an interesting series. HCO has been extensively studied by spectroscopists [l 11 and has also been observed by electron-spin resonance [ 121

277 01974 by John Wiley & Sons, Inc.

278 THOMSON AND BROTCHIE

and infrared [13, 141 in matrix isolation experiments, and there have been numerous theoretical investigations including some ab initio calculations [ 15-17]. HBF, which is isoelectronic with HCO, has not been observed. FCO has been observed in matrix experiments [18, 191 but not in the gas phase, and its geometry is not ac- curately known.

We have therefore studied these three molecules, following our earlier work on unstable intermediates [20-241 with a view to determining how the computed properties and geometry vary with different quality basis sets.

2. Method of Calculation and Basis Sets

The calculations of the wave functions, energies, and other properties were carried out using the programmes I B M O L ~ ~ [21], I B M O L ~ [25], or ATMOL [26]. These pro- grammes solve the restricted Hartree-Fock (RHF) equations for openshell systems as formulated by Roothaan [27]. The basis sets were of Gaussian orbitals (GTO) centred on the atoms. The computations were carried out on an IBM 360/44 or an IBM 370/195.

The most extensive basis set explorations were done on HCO where both un- contracted and contracted sets were used. The basis sets and the sources of these are given in Table I, together with the contractions used. Basis set E is sufficiently large and flexible to give an energy within -0.005 hartree of the Hartree-Fock limit. The choice of the polarization function exponents used was based on the suggestions of Roos and Siegbahn [32] and the values used were a3d = 0.64 and 0.19 for carbon, a3d = 1.32 and 0.392 for oxygen, and cizp = 0.5 for hydrogen.

In the case of HBF and FCO, calculations were not carried out with the smallest and largest basis sets which were used for HCO.

The total energy was computed as a function of the angle ABC and the bond lengths R(AB) and R(BC) by successively minimising the energy with respect to the

TABLE I. Gaussian basis sets.

a b C B a s i s S e t Uncontracted Contracted Reference

"The notation used (a, b, c/d, e) refers to a-s-type, b-p-type, and c-d-type primitive Gaussians on

"a, b, c/d, e] refers to contracted Gaussians defined as in footnote a. 'All H-basis sets were taken from Huzinaga [31].

the first-row atom, and d-s-type and e-p-type primitive Gaussians on the hydrogen atom.

EQUILIBRIUM GEOMETRIES OF HCO, FCO, AND HBF 279

two bond lengths and the angle until a minimum value was obtained. Mulliken population analyses of the wave functions were carried out, and the unpaired electron density in the open-shell orbital was computed in order to calculate the isotropic hyperfine coupling constants.

3. Results

A. Energy Calculations and Geometry of the Radicals

The results of the calculations on HCO are given in Table 11, and for HBF [ 101 and FCO in Table 111. For HCO even the very small basis sets make reasonable qualitative predictions of the shape, despite the poor energy; a conclusion in accord- ance with the extensive work by Pople and coworkers, particularly on closed-shell molecules [33]. Most of the improvement in energy in going from a (95/4), basis to an (1 1, 7, 2/4, l), basis came from d-orbital participation, as shown in runs in which the d orbitals were deleted. The lowest energy obtained was 0.16 hartree lower than the previous best ab initio calculations [ 161. Quantitatively, the smaller basis sets (52), and (73), seem to overestimate the bond lengths by -0.1 bohr, and the bond angle is also a few degrees larger than experiment, but basis set E gives a n angle within 2” but bond lengths - 0.04 bohr too short. Our results for HBF and FCO are similar, and we can predict therefore that in the unknown HBF the angle HBF will be - 121” with bond lengths close to R(HB) = 2.21 bohr, and R(BF) = 2.46 bohr. In HBF the smallest basis set predicts the HB bond to be longer than the BF bond; an effect reversed with the larger basis sets. It might be remarked that a micro- wave study of HBF, gives bond lengths R(HB) = 2.24 bohr and R(BF) = 2.48 bohr [34]. The orbital energies in the three molecules, computed with the largest basis set used, are given in Table IV. The orders of the la” and 7a’ orbitals are inverted in HCO and HBF. Although Koopman’s theorem cannot be invoked for these open- shell species directly, we have shown previously that the eigenvalues obtained from

TABLE 11. Optimised geometries and energies for HCO (X’A‘) for various basis sets.

B a s i s Energy R (HC e” R ( C 0 )

A -110.0851 2.10 130 2.37

B - 112.4026 2.40 12 5 2.40

C -112.8523 2.33 128 2.39

D -113.1946 2.22 127 2.39

E -113.2783 2.10 12 5 2.18

- 123 2.22 Experiment 2.15-2.19

280

FCO

THOMSON AND BROTCHIE

HBF

B

C

D

-210.4338 2.59 125 2.42 -123.6788 2.60 122 2 .45

-211.4444 2 .70 126 2 .40 -124.3077 2.53 121 2 .61

-212.0693 2.50 126 2 .20 -124.6758 2 .25 121 2.50

B. Population Analysis and Bonding In the case of HCO we have examined the population analyses for each basis

set and observed large variations in the individual overlap and orbital populations

TABLE IV. Orbital energies in HCO, HBF, and FCO.

Orbi t a 1 HCO a b

HBF b

FCO

l a '

2a'

3a'

4a'

5a'

6a '

l a "

7a'

8a '

9a'

2a"

10a'

-20.616

-11.349

-1.4667

-0.825

-0.695

-0.596

-0.586

-0.390

~~ ~

-26.312

-7.706

-1.636

-0.786

-0.705

-0.596

-0.681

-0.385

~~

-26.402

-20.655

-11.501

-1.727

-1.461

-0.901

-0.771

-0.777

-0.722

-0.589

-0.567

-0.527

"Basis set E. bBasis set D.

EQUILIBRIUM GEOMETRIES OF HCO, FCO, AND HBF 28 1

TABLE V. Population analyses for HCO, HBF, and FCO (ABC).

fi (Debye)

9.27 5.32 8.43

“Basis set E. bBasis set D.

0.71 1.14

0.72 0.39 1 I, 0.25 0.95

between the different basis sets. For this reason we present only the gross atomic and overlap populations in Table V. However, it is clear that as the basis sets approach the largest we have used, sets D and E , there is a flow of electron density from H to C and from C to 0, leading to a substantial negative charge on 0 (Table V). This is true also in HBF and FCO. In each case the central atom is positively charged, but the H is almost neutral in HBF, and the fluorine is negatively charged in FCO. In the latter case the overlap population in the FC bond is very low, and the FC bond is substantially longer than the bond in CF, [35]. In both HCO and HBF, the overlap populations of the CO and BF bonds are quite different. This is probably partly accounted for by only a slight amount of x bonding in HBF compared to HCO. The dipole moments should not be very accurate since they are small, but experimental values are not available.

C. Isotropic HyperJine Coupling Constants

In HCO the unpaired electron occupies the 7a‘ orbital, which is mainly localized on carbon. The calculated hyperfine coupling constants with the largest basis set are a(’H) = 81.8G, a(I3C) = 143.56, and a(”O) = - 6.4G which compare with the experimental values aE(’H) = 137G and aE(13C) = 134.76 [19].

Table VI compares these values with those calculated by other workers, using both semiempirical and ab initio wave functions. The agreement with experiment for the RHF calculation is reasonable for the 13C and ”0 nuclei, but the proton coupling constant is only about half the observed value. The good agreement achieved by McCain and Palke [17] is somewhat suprising, since this was a minimal STO basis set calculation at the experimental geometry. The good agreement found in unre- stricted Hartree-Fock calculations with an assumed geometry [ 161 becomes poorer when the geometry is optimised, illustrating the sensitivity of these quantities to the geometrical parameters. One possible reason for our low a(’H)is that the hydrogen basis set is inadequate, and better agreement might be obtained if this were increased in size.

282

C

D

THOMSON AND BROTCHIE

167.7 421 .2 -2.62

196.8 290 .3 -13.13

TABLE VI. Calculated hyperfine coupling constants for HCO (X*A’).

Reference Method a ( H ) a ( C) a ( 0) 1 13 17

[ 361 Extended McLachlan 4 4 . 2 a 149 -4 5

1371 INDO 83.1 141.6 - 4 . 9

[ 151 Ab-init io UHF 133.9 200.8 - 6 . 4

[ 161 Ab-init io UHF 112.5 148.4 -0 .98

[ 171 Ab-init io RHF 140.6 114 .O - 6 . 6

T h i s work Ab-init io RHF 81.8 1 4 3 . 5 - 6 . 4

- Ex per imen t 137 134.7 -

“Values in gauss.

The calculated coupling constants for FCO are given in Table VII for three dif- ferent basis sets. As expected, the values are very sensitive to the basis set, but the agreement with experiment for the largest basis set is qualitatively similar to the results for HCO ; in particular the spin density on fluorine is about half the observed value. Even with this size basis, the results are very sensitive to the geometry of the radical, particularly a(19F) and ~ ( ‘ ~ 0 ) where the spin density is low.

Examination of the contributions to the spin density in HCO and FCO show that in HCO, the carbon s-orbital contribution in the 7a’ orbital is only about half the corresponding contribution in the 10a’ orbital in FCO, which parallels the large increase found for a(13C) in going from HCO to FCO.

However, the spin density on oxygen in both cases is low (- 0.03 in HCO; 0.06 in FCO), and though the absolute magnitudes are uncertain in view of the limita- tions of the population analysis, it is clear that these values are very much less than

TABLE VII. Hyperfine coupling constants for FCO (X’A’).

. C 7 0 ) 13

Basis a ( c)

B 1 8 9 . 5 a 268.3 1.39

Experiment 1 334 2 86 - “Values in gauss.

EQUILIBRIUM GEOMETRIES OF HCO, FCO, AND HBF 283

the value suggested by Cochran and coworkers of 0.28 [19], and the carbon spin density (0.72) is also higher than their value (0.53). Calculations with basis D on HBF give a('H) = 380 G, a("B) = 193 G, and a(19F) = 61 G. Our previous work on BF,[24] with a similar basis set gave calculated values of a(l0B) = 280 G and a(19F) = 190 G ; again rather similar relative magnitudes. Therefore we expect that the observed coupling constants in HBF should be approximately a('H) N 70-80 G, a("B) N 190 G, and a(19F) N 90-110 G. The proton coupling constant is thus predicted to be substantially less than in HCO, or in the isolectronic species HCN- (137 G) or HBO-(94 G ) .

4. Discussion

These calculations have examined the effect of basis set size on the molecular geometry of three triatomic radicals of C, symmetry. Basis sets of roughly minimal quality tend to overestimate the bond lengths, whereas the largest basis sets give geometrical parameters within N 2 % of experiment, and the predicted geometry for HBF should be this reliable. The isotropic hyperfine coupling constants are predicted well for the central atom, but the 'H or I9F coupling constants are about half the observed values. We predict the coupling constants in the as yet unobserved HBF to have the values quoted above.

It seems likely that despite its limitations, the RHF method will be of use for pre- dicting qualitatively the hyperfine coupling coefficients of unknown radicals, par- ticularly if the basis set is increased to give near HF accuracy in the wave function.

Acknowledgment

We are indebted to Dr. A. Veillard for providing a copy of I B M O L ~ from which I B M O L ~ ~ was developed, and also to Dr. E. Clementi for IBMOL version 5. The continued help of the staff of the University of St. Andrews Computing Laboratory is gratefully acknowledged. We also thank the S.R.C. for financial support (to D.A.B.), and for a grant of computer time on the IBM 370/195. Finally, we are indebted to both the Royal Society for a travel grant and the University of Florida for financial support which enabled one of the authors (C.T.) to present this paper at the 1974 Sanibel Symposium.

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