4102
J. Phys. Chem. 1991, 95, 4702-4708
Molecular Orbltal Studies of Hyperfine Coupling Constants in the H,CN and H(H0)CN Radicals Daniel M. Chipman,* Ian Carmichael, Radiation Laboratory,? University of Notre Dame, Notre Dame, Indiana 46556
and David Feller Molecular Science Research Center, Pacific Northwest Laboratory,$Richland, Washington 99352 (Received: October 9, 1990)
Isotropic magnetic hyperfine splittings have been evaluated for the closely related H2CN and H(H0)CN radicals from ab initio molecular orbital models. Uncertainties in the equilibrium geometries appear to have little effect on the carbon and nitrogen splittings but may affect the large methylene hydrogen splittings by up to several gauss. Vibrational averaging is estimated to provide corrections on the order of only 1 G or less at all nuclei. Direct, spin-polarization, and electron correlation effects all contribute about equally to the large methylene hydrogen splitting in each radical, as well as to the large difference in this splitting between the two radicals. The electron correlation contribution is the most difficult to calculate, and neither of the two distinct procedures utilized to study that effect provides a fully quantitative description at the limit of currently feasible calculations.
1. Introduction
When one of the hydrogens in the H2CN radical is substituted by a hydroxyl group, the large ESR hyperfine coupling constant (hfc) of -87 G experimentally observed' for the remaining methylene hydrogen undergoes a considerable drop down to -54 G. Various experimental measurements for a(H) in H2CN include values of 87.4 G (in an Ar matrix at 4.2 K2), 91 G (in solid HCN at 77 K3),89 G (in formamide at 77 K4),and 87.3 G (in aqueous solution a t r t " temperature5). The close similarity of these values found with different surroundings and at different temperatures argues against any large environmental effect, so theoretical studies in vacuo can meaningfully be applied. In recent calculationsS it was found that there is little change in geometry upon OH substitution, so it was concluded that the large drop in methylene hydrogen hfc must be due to more subtle electronic factors. However, the calculations underestimated the experimentally observed methylene hfc by about 338, so no more definitive statements could be made. In this work we reexamine these radicals with more extensive calculations in an attempt to obtain a more complete and quantitative theoretical understanding of this effect. A number of previous theoretical studies have been carried out on H2CN. Uncertainty in the equilibrium geometry has been highlighted by Bair and Dunning? whose Table X summarizes the results of 14 different semiempirical and a b initio determinations. Examination of that table shows the C N bond length to be quite sensitive to the method of calculation, with values as low as 1.10 A and as high as 1.36 A having been reported. The a b initio studies that attempted accurate description of electron correlation effects fall into a narrower but still significant range of 1.23 A (MBPT4/6-31G**') to 1.268 A (GVB-CI/[321(31I6) for the CN bond length. In light of this uncertainty, one purpose of the present work will be to examine the sensitivity of hfc to the assumed equilibrium geometry and, further, to determine whether vibrational averaging might provide significant corrections. Several previous theoretical determinations of the H2CN hfc have been reported. Most of these were limited to consideration of only direct and spin-polarization effects, as in unrestricted Hartree-Fock (UHF) calculations with and without partial spin annihilationgI0 and in restricted open-shell Hartree-Fock (ROHF) 'This research was supported in part by the Office of Basic Energy Sciences of the US. Department of Energy. This is Document No. NDRL-3316 of the Notre Dame Radiation Laboratory. $The Pacific Northwest Laboratory is operated for the U S . Department of Energy by Battelle Memorial Institute under Contract DE-AC06-76RLO 1830.
0022-365419 112095-4702502.50/0
plus single-excitation configuration interaction (SCI) determinations.5J0 In addition, one large-scale multireference single and double configuration interaction (MR SDCI) calculation has also been reported." In the latter study of 10 small radicals, the isoelectronic series H2CN, H2CO+,and H 2 B 0 stood out as being particularly difficult to describe, with errors in a(H) found to be 20-30% for this set as compared to 67 experimental' 87.3
a("N) 0.0 0.0 0.0 0.0 0.0 7.9 -26.0 -24.4 8.6 -25.1 8.1 --17.6 -2.3 -4.5 --23 5-24 25 6 (-)28.9 10.2 a(W)
0.0
'Total energy = -93.8497. bTotal energy = -93.8681. CTotalenergy = -93.8721. dTotal energy = -93.8747. eFrom ref 5. marizes the convergence behavior both with respect to decreasing the selection threshold and with respect to increasing the reference space size. ROHF+SDCI calculations already converge at a selection threshold of lod. For the multireference calculations a threshold of appears adequate for carbon and nitrogen, but hydrogen is not fully converged even at a threshold of 10". The M R ( 1 7 5 ) SDCI calculation seems to provide carbon and nitrogen couplings that are well converged with respect to enlarging the reference space. Hydrogen, on the other hand, increases 0.7 G between the MR(175) and MR(278) calculations, and indications are that it could well increase yet another 1-2 G with still larger reference spaces. The most notable features of Figure 1 are that the magnitudes of the couplings increase monotonically both as the selection threshold is decreased and as the size of the reference space increases, presumably ultimately converging to the full CI limit for the given basis. Thus, in cases where apparent convergence is not attained, the largest feasible calculations can be taken to give lower bounds to the magnitudes of the full CI couplings. It appears that this limit is nearly reached with the [421(21] basis in Figure 1 for carbon and nitrogen but may still be low by perhaps
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MO Studies of H2CN and H ( H 0 ) C N Radicals
68
TABLE V: Hyperfine Coupling Constants in gauss Calculated for the HICN Radical at the Optimum ROHF/[421121] Geometry Using the UHF-BasedQCISD(T) Metbod for Correlation Recovery basis 4’H) 4°C) o(I‘N)
t
/-
-261 L
-30
The Journal of Physical Chemistry, Vol. 95, No. 12, 1991 4707
I
10-8
1
I
IO-’
10-6
I
10-5
TE Figure 2. Convergence of HICN hfc in the FNO MR SDCI/[75321432] method as a function of configuration selection threshold TEand of the
reference space size. up to 3-4 G for hydrogen. These limiting values are in good agreement with experiment for carbon and nitrogen but are still much too small for hydrogen. We have carried out M R SDCI calculations on H2CN with a much larger basis set at a slightly different assumed equilibrium geometry obtained from an ROHF+SDCI/[43211321] optimization, as described earlier. It is seen in Table IV that the direct and spin-polarization contributions from ROHF and ROHF+SCI calculations with the [631141] basis at this new geometry are within 1 G of those obtained at the geometry corresponding to Table I, so this slight geometry change is not a significant factor. Comparison to larger basis ROHF and ROHF+SCI calculations in Table IV also shows hfc changes of less than 1 G, confirming that the [631141] basis is adequate for calculations at those levels of theory. Figure 2 shows the variation in the isotropic hyperfine values as a function of the CI selection threshold in several F N O MR SDCI/[7532)432] calculations. The largest reference space of 146 functions had CC?= 0.943 and produced 33 million single and double excitations before selection. Compared with the earlier M R SDCI study” on H2CN, the present work represents a far more extensive investigation of the effects of correlation recovery. The basis set has been increased from 68 to 148 functions, the reference space has been increased from 5 to 146 configurations, and the selection threshold has been decreased by at least an order of magnitude, from 1O-a to lo-’. The resulting number of selected configurations has jumped from around 21 000 to 450000 spinadapted configurations. As with the smaller basis MR SDCI studies, the hfc in most cases monotonically increase in magnitude with smaller selection thresholds and with larger reference spaces. The ROHF+SDCI hfc properties are well converged, and the MR(24) results appear to be nearly so. With the larger reference spaces, it was feasible only to perform calculations down to a IO-’ threshold. At that point the MR(83) result seems to be nearly converged, and in Table IV we show an estimate of the limiting values to the nearest gauss. The MR( 146) calculations, on the other hand, show large changes in passing from 10” to IO-’. This is reflected in Table IV by the fact that we only report bounds for the results of this
[42 112 1 ) [63 1141 J [742152] [852162J [7 441521 [74211521] [7441152I]
72.4 74.7 75.5 75.5 75.2 75.5 75.4
-28.9 -29.5 -27.9 -27.9 -28.2 -27.0 -27.8
9.2 9.6 9.0 9.0 9.3 8.8 9.3
experimentalu a From ref 5.
87.3
(-)28.9
10.2
largest calculation. This unusual change in convergence behavior as a function of reference space size has not previously been observed in the many studies of hfc that have been carried out on other radicals with this procedure. The ROHF+SDCI results are in poor agreement with experiment, while the MR(24)+SDCI and MR(83)+SDCI results are a little better. On the other hand, indications are that the MR(146)+SDCI results may approach much closer to experiment for all the nuclei. It can be concluded that a combination of very large reference space and very small selection threshold will be required to accurately treat H2CN by the MRCI approach. UHF-Based Methods for Correlation Recovery. The UHFbased QCISD(T) procedure attempts to include direct, spin-polarization, nondynamical, and dynamical electron correlation contributions by a somewhat different approach. As seen in Table I, it brings the calculated values for carbon and nitrogen very close to experiment for both rad cals. The hydrogen splitting is also substantially improved but is still about 15% below observation. The magnitude of this discrepancy greatly exceeds that found in calculations by this39and closely related28.Mtechniques on atoms and diatomic hydrides, an observation which prompted a more thorough exploration of basis set requirements for the present species. Further QCISD(T) results a t the ROHF/[421(21] geometry of H2CN from calculations using more complete basis sets are presented in Table V. The U H F results with these various basis sets are all within 1 G of the corresponding U H F results shown in Table I and so are not reported separately. The [421121] results are very close to those approached in Figure 1 for the M R SDCI method with this basis. This agreement suggests that these results are indeed close to the full CI limit for that basis. The [631141] basis set is just that designed for use in the previous ROHF+SCI calculations and is seen to produce little change in the computed spin densities. Results from a I7421521 basis set due to van Duijneveldt40 that is of slightly better than triple-< quality and augmented by two shells of five-component d functions4’ on the heavy atoms and two shells of p functions on the hydrogens are also displayed, and it can be seen that even this improvement engenders only small changes in the coupling constants. Addition of functions of higher angular momentum, f functions on the heavy atoms and d functions on hydrogens, to obtain a I742115211 basis produces even smaller shifts. Interestingly, for the heavy atoms the largest correlation corrections to the isotropic splitting are found with the most complete basis sets, whereas for the hydrogen coupling the opposite is true. The reduction due to correlation effects on a(H) of 9.5 G for the [421121] basis is diminished to 8.8 G for the largest basis set used. Addition to the [742152] basis of further shells of diffuse s and p functions on C and N and diffuse s functions on H to obtain an [852162] basis was also investigated and produced no change in the computed coupling constants. Calculations with additional diffuse and compact d shells on the heavy atoms to give a [744152] basis also resulted in only small shifts. The level of disagreement with experiment on the hfc at H is thus not alleviated much through (39) Carmichael, I. J . Phys. Chem. 1991, 95, 108. (40) van Duijneveldt, F. B. IEM Res. J . 1971, 945. (41) Lie, G. C.; Clementi, E. J . Chem. Phys. 1974.60, 1275.
4708 The Journal of Physical Chemistry, Vol. 95, No. 12, 1991 TABLE VI: Analysis of Correhtion Conretiom to tbe Hyperflw Coupling Colrturb in gauss Cakuhted for the H m Radical Using the QCISD(T)/[742(52]Method at the Optimum ROHFh421121] GeOlWhy
UHF doubles singles triples QCISD(T)
4W
a(W)
4'")
84.4 -26.5 16.6
24.9 -21.3
0.9
-65.1 57.8 -21.1 1.1
15.5
-27.9
5.8
4.5 9.0
basis set improvements effected here. For example, the 12.7-G shortfalls in the QCISD(T)/[631141] estimate of the hydrogen splitting is only slightly reduced, to 11.9 G, by employing the much larger [74411521] set. By way of contrast, the computed QCISD(T)/[74411521] values for the coupling at C and N are -27.8 and 9.3 G, respectively, within a few percent of the observed values. One possible explanation for this discrepancy lies in the extent of spin contamination in the UHF reference wave function, Sz(UHF) = 0.9472 for the [742152] basis set at the ROHF equilibrium geometry. In previous studies on atoms29and diatomic hydrides39it was found empirically and has been shown analyti c a l l ~ 'that, ~ if the sole spin contaminant is the state of the next higher spin multiplicity, then the QCISD wave function will be an essentially pure spin state. For H2CN however, annihilation of the quartet contribution leaves some residual spin contamination, s? = 0.7578, which is expected to persist even at the highest levels of correlation treated However, the good agreement with experiment obtained in calculations of the carbon and nitrogen coupling constants by this technique, as well as the good agreement of all the QCISD(T)/[421121] couplings with the full CI values estimated from MR SDCI/[421121] studies for H&N, argues against this explanation. As noted above, calculated values for the isotropic splitting due to the methylenic hydrogens are sensitive to the C N bond length employed. Some of our exploratory calculations were carried out at a geometry obtained by the UMP2/6-31G(d,p) method; viz. f C N = 1.217 A, f C H = 1.097 A, and 6HCH = 117.2'. While this short C N bond length leads to artifically high values for the coupling constants at hydrogen, it serves as a valuable check on the sensitivity of correlation corrections to molecular geometry. With the [421121] basis the UHFvalue for a(H) of 88.7 G is 5.8 G larger than that seen at the ROHF/[421(21] geometry that was used in most of our calculations. By contrast, the corresponding QCISD(T)/[421121] value for a(H) is 8.8 G larger than at the ROHF/[421)21] geometry. Assuming that the QCISD(T) procedure provides a reasonable estimate of the change in correlation correction to hfc with geometry, even if it does not give a fully quantitative value for the hfc itself, this indicates that the correlation correction to a(H) is not overly sensitive to geometry, varying only 3.0 G for this large displacement. ROHF+SCI/ [631141] calculations at this displaced geometry indicate the shift in a(H) due to direct plus spin-polarization effects to be 7.8 G, substantially larger than the 3.0-G shift due to correlation. This observation supports our use of the simpler ROHF+SCI method for qualitative exploration of geometric and vibrational effects. An analysis of the contributions to the correlation correction for the coupling constants in H2CN computed for the [742152] basis set, again at the ROHF/[421121] geometry, is presented in Table VI. The addition of amplitudes due to double replacements in the UHF determinant, giving the QCID model or, (42) Schlegcl, H.B. J . Phys. Chem. 1988, 92, 3075.
Chipman et al. equivalently, the coupled-cluster doubles (CCD) model, leads to a large decrease in the magnitude of the calculated unpaired spin density at each nucleus. Including the effect of single excitations, the QCISD model, results in a smaller shift in the opposite direction, though the value is surprisingly large at the hydrogens. The presence of triple replacements is accounted for perturbatively and is seen to be more than an order of magnitude smaller than these other corrections. As seen from Table I in calculations with the [631141] basis, the UHF estimate for the drop in hydrogen hfc upon OH substitution is only slightly improved upon the addition of electron correlation. However, the QCISD(T)/[631141] value at 29.4 G is much closer to the experimentally observed 32.9-G shift compared to that inferred from the results derived from spin-restricted models discussed above. Calculations with the larger [742152] basis set produce only a small improvement in the estimate of this shift placing our final value at 30.2 G, which is 8% below experiment.
6. Conclusion The large hfc values for the methylene hydrogens in H2CN and H(HO)CN, as well as their difference, arise from approximately equal contributions due to direct, spin-polarization and electron correlation effects. Studies on H2CN indicate that uncertainties in equilibrium geometry, particularly the CN bond length, affect these hfc by at most a few gauss and vibrational averaging affects the values only by about 1 G or less. The direct and spin-polarization contributions can be accurately obtained by relatively simple ROHF+SCI/[631141] calculations. Nondynamical electron correlation contributions lower the methylene hydrogen hfc by about 5 G in H2CN and about 2 G in H(HO)CN, leading to larger discrepancies with experiment. Both the ROHF- and UHF-based methods used here to obtain dynamical electron correlation contributions show corrections in the right direction, but neither is able to provide full quantitative agreement with experiment. The ROHF-based MR SDCI procedure for describing electron correlation appears to require a very large reference space before approaching the experimental hfc values. Unfortunately, increasing the size of the reference space also seems to require a decrease in the selection threshold to achieve convergence, and we have not been able to fully converge the largest MR( 146)+ SDCI calculations with our current computational resources. Yet higher order excitations, which would require still larger reference spaces, may be required to reach full quantitative agreement with experiment. The UHF-based QCISD(T) procedure for describing electron correlation gives results that appear to have nearly converged with respect to increasing basis set size. Assuming this to be the case, the remaining error in methylene hydrogen hfc of 12 G in H2CN and -9 G in H(H0)CN found with this approach must be largely due to yet higher order excitations in the wave function. These are also presumably necessary to clean up the remaining spin contamination and may require still larger basis sets for proper description. This work has shown that electron correlation effects are just as important as the direct and spin-polarization mechanisms for developing the methylene hydrogen hfc in these two radicals. But it has also been shown that it is not currently feasible to quantitatively obtain this contribution from either of two quite distinct state-of-the-art approaches for describing electron correlation, apparently because configurations corresponding to very high order excitations make important contributions. It must be concluded that this problem will pose a difficult challenge to quantum chemistry for some time to come.
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