108
J . Phys. Chem. 1991, 95, 108-111
is not required and so fewer simulations would be necessary. We can conclude from this analysis of the uncertainties in the estimates of the confidence intervals that the differences found between the parametric and Monte Carlo methods are indeed significant. In this paper, we treated an example in which only one parameter is transferred. For the Monte Carlo method, the extension to the case of several transferred parameters is immediate and needs no discussion. However, even if the distributions of all the parameters were normal, the extension using the parametric method becomes quite complicated. Equation 5 must be modified to include not only the contribution to the variance from the variances in each of the other transferred parameters but also the contribution of the covariances between pairs of the transferred parameters. In addition, the covariances between pairs of the adjustable parameters and between the adjustable and transferred parameters must be included as well. Thus, as the system becomes more nonlinear with more parameters both fixed and adjustable, the advantages of the Monte Carlo method over parametric statistics become greater. Conclusions Our studies of this example and of other systems not reported here lead us to believe that there is no simple a priori way of
determining when uncertainties in transferred parameters will have a significant effect on confidence intervals of parameters calculated in a second experiment and when parametric estimates of confidence intervals for the adjustable parameters used in the analysis of any experiment will be reliable. Although it is true that if the errors are sufficiently small, the nonlinearities are sufficiently mild, and the effects of covariances between parameters are included, the parametric method will give accurate estimates of the confidence intervals, we have not been able to quantify “sufficiently small” and “sufficiently mild” in order to determine a priori when parametric methods will work. We believe that the Monte Carlo method provides correct estimates of confidence intervals for parameters in practically all conceivable experiments because it constitutes a direct implementation of the definition of confidence intervals and, consequently, requires no assumptions about the linearity of the model, the distribution of the parameters, or the covariances between pairs of parameters. Any uncertainty in the Monte Carlo estimates can be reduced by performing enough simulations. Given the ubiquity of computer facilities and the ease of performing Monte Carlo calculations, it would seem that this approach is superior to parametric methods for the determination of confidence intervals.
Ab Initio Quadratic Configuration Interaction Calculations of Isotropic Hyperfine Coupling Constantst Ian Carmichael Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556 (Received: December 27, 1989; In Final Form: July 2, 1990)
Results are presented from quadratic configuration interaction (QCISD) calculationsof the isotropic component of the magnetic hyperfine coupling in the electronic ground states of the atoms B-F and of some radicals and radical cations derived from associated diatomic hydrides. Moderately large basis sets of contracted Gaussian functions are employed. Starting from unrestricted Hartree-Fock (UHF) reference spaces the unpaired spin density is determined by finite Fermi contact field perturbation theory. Comparison is made with previous values obtained by an approximate augmented coupled-cluster procedure in which both single and triple excitations are handled perturbatively. In all cases the QCISD predictions lie closer to the available experimentally observed hyperfine splittings.
Introduction I n many radicals and radical ions a simple spin-restricted single-configuration self-consistent-field molecular orbital picture of the electronic structure fails to indicate a nonzero contact spin density at a magnetic nucleus, although splittings due to that nuclear moment are readily observed in electron spin resonance spectra. For a long time the reliable and accurate prediction of isotropic hyperfine coupling constants of such species remained an elusive goal. Recently, however, substantial progress has been made along several fronts. Based on the above zero-order model, large scale multireference singles and doubles configuration interaction (MR-SDCI) calculations have yielded satisfactory results for a number of difficult cases, including the atoms, B-F,’but only with the adoption of very extensive Gaussian basis sets. Alternatively, using a spin-unrestricted (UHF) reference wave function, several techniques for the inclusion of further electron correlation, ranging from singles and doubles configuration interaction (CISD) to many-body perturbation theory (UMP4) and the closely related coupled-cluster doubles (CCD) method, have provided comparably accurate results, while employing a more modest description of the one-particle space.* These finite-field ‘Document No. NDRL-3255 from the Notre Dame Radiation Laboratory.
0022-3654/91/2095-0108$02.50/0
calculations of isotropic coupling constants were motivated by the quality of the results obtained by Sekino and Bartlett3 for a wide range of radicals using still smaller basis sets but with a more complete coupled-cluster singles and doubles correlation model (CCSD). For some especially troublesome cases, such as the electronic ground state of diboron, B2 X[3ZJ, the coupled-cluster methods, particularly when enhanced perturbatively to include the effects of replacements higher than double in the UHF determinant, (UCCD(ST)6) have given the more satisfactory account of the unpaired spin d e n ~ i t y . ’ , ~The . ~ best value from the UCCD(ST) procedureS for the isotropic splitting due to ”B of 13.6 M H Z , ~ which depended on a large contribution, 4.6 MHz, from amplitudes due to triples replacements in the UHF wave function, was in close accord with the experimental report of 15 MHz for this species isolated in a cryogenic neon m a t r i ~ . ~ More recently, the UCCD(ST) technique has been systematically applied to investigate the isotropic coupling constants of Feller, D.; Davidson, E. R. J . Chem. Phys. 1988, 88, 7580-7587. Carmichael, I. J . Phys. Chem. 1989, 93, 190-193. Sekino, H.; Bartlett, R. J. J . Chem. Phys. 1985, 82, 4225-4229. Knight, L. B., Jr.; Gregory, B. W.; Cobranchi, S. T.; Feller, D.; Davidson, E. R. J . Am. Chem. SOC.1987, 109, 3521-3525. (5) Carmichael, I. J . Chem. Phys. 1989, 91, 1072-1078. (6) Raghavachari, K. J . Chem. Phys. 1985, 82, 4607-4610.
0 1991 American Chemical Society
Isotropic Hyperfine Coupling Constants a series of diatomic hydrides and some of their radical cation^.^ While the overall level of agreement with the known experimental values was impressive, in the case of the I3C coupling constant in C H X [211,] there was a disappointing shortfall of about 10 MHz in the calculated result. The best prediction was 36.6 MHz, compared to the reported* gas-phase value of 46.8 (20) MHz from a microwave optical double resonance (MODR) study of the X-doubling spectrum of I3CH. The source of this deficiency appeared to reside in the perturbative treatment used to incorporate the effect of single replacements in the U H F determinant, since contributions from triple excitations were of negligible importance and basis set extensions provided little improvement. Satisfactory inclusion of the single excitations was made in the CCSD calculations of Sekino and Bartlett3 who also found little change upon noniterative inclusion of triple excitations. Recently? Pople et al. have developed an alternative electron correlation scheme, termed quadratic configuration interaction, QCISD when truncated in the space of single and double substitutions, which approximates the CCSD model, differing only in higher order terms. Here the QClSD model, together with its perturbative treatment of triples, QCISD(T), has been employed to reinvestigate the spin density distributions in the atoms, B-F, and the diatomic hydrides previously studied by the UCCD(ST) procedure. I n all cases the QCISD(T) predictions lie closer to the experimentally observed values and the source of this improvement may be traced to the fashion in which the effect of single excitations is now incorporated in the QCISD model, since the contribution from triple replacements remains essentially unchanged. Computational Details All calculations reported here were performed either with modified versions of the GAUSSIAN 86" or the GAUSSIAN 88" series of programs running on either a CONVEX C-120 or C-220 computer. As was found to be the case in the UCCD(ST) calculations on atoms,2 reliable results, with respect to small changes in exponents and contraction schemes, required the adoption of a basis set of triple-{qualityI2 including two shells of d-functions,I3 denoted TZP. On the hydrogen in the diatomic hydrides a roughly analogous contraction scheme may be written (8s2p)/[Ss2p]. The effect of the inclusion of diffuse s- and p-functions on both heavy atoms and hydrogen was tested. Calculations including further d-shells, both more compact and more diffuse, and f-shells on the heavy atoms and a single additional d-shell on hydrogen were also performed. The largest uncontracted basis set employed can be written ( 1 4s9p4d 1 f, 9s3pl d) in the hydrides and, when contracted to [8s5p4dl f, 6s3pld], is denoted ext. Five-component d-functions and seven-component f-functions were used throughout. The isotropic coupling constant, A,,, is proportional to the spin density per unpaired electron at the nucleus, the normalized Fermi contact splitting, Q(O)/n, Ai, = ( 8 ? r / 3 ) ( g , / g o ) g ~ P ~ Q ( O ) / n , (1) where gJg0 is the ratio of the isotropic g value for the atom to that of the free electron, here taken as unity, gN and PN are the nuclear rnagnetogyric ratio and the nuclear magneton, respectively, and ne is the number of unpaired electrons. The spin density at (7) Carmichael, I . J . Phys. Cfiem. 1990, 94, 5734-5740. (8) Steimle, T. C.; Woodward, D. R.; Brown, J. M. J . Chem. Phys. 1986, 85, 1276-1282. (9) Pople, J. P.; Head-Gordon, M.; Raghavachari, K. J . Chem. Phys. 1987, 87, 5968-5975. (IO) Frisch, M. J.; Binkley, J. S.;Schlegel, H. B.; Raghavachari, K.; Melius, C. F.;Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rolfing, C. M.; Kahn, L. R.;DeFrees, D. J.; Seeger, R.; Whiteside, R. A,; Fox, D. J.; Fleuder E. M.; Pople, J . A. GAUSSIAN 86; Carnegie-Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA, 1984. ( I I ) Frisch, M. J.; Head-Gordon, M.; Schlegel, H. B.; Raghavachari, K.; Binkley, J . S.;Gonzales, C.; DeFrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J . .I.P.;Fleuder E. M.; Topiol, S. Pople, J. A. GAUSSIAN 88; Gaussian Inc.: Pittsburgh, PA, 1988. (12) van Duijneveldt, F. B. IBM Res. J . 1971, 945-971. ( 1 3) Lie, G . C.; Clementi, E. J . Chem. Phys. 1974, 60, 1275-1 287.
The Journal of Physical Chemistry, Vol. 95, No. 1. 1991 109 TABLE I: Comparison with FCI Calculations of the Isotropic Solittin!? in the Nitrogen Atom basis/method
(9S5P) (10~5~) ( 1Os5pld)
UCCD(ST)b
QCISD(T)c
FCId
2.29 7.45 6.55
2.45 1.52 6.92
2.446 7.484 6.9 10
"Isotropic coupling constant in M H z for the 4S ground state of I4N. The experimental value is A,,(I4N) = 10.45 MHz. bAugmented coupled-cluster doubles model, ref 2. CQuadraticconfiguration interaction with fifth-order triples, present work. dFull CI, ref 15.
the nucleus is obtained by considering the energy shift, a E ( p ) / a p , induced by the application of a finite Fermi-contact field H'N = pQ(O) (2) to the Hamilt~nian.~ In practice this shift is calculated by a central difference approximation to the energy derivative. a E / d p = (E,, - E-,)/2p (3) A value of p = 0.0005 au proved sufficient to maintain numerical
accuracy while eliminating higher order contributions to the gradient. In the present coupled-cluster method, no configuration selection is employed and the effects of all double and simultaneous double excitations are considered. Corrections for the effect of single and triple replacements in the U H F determinant are then added perturbatively6 without allowing any relaxation of the doubles contribution. In the quadratic configuration interaction approach again no configuration selection is employed, other than the truncation in the space of single and double substitutions, to give the QCISD model. Here only the contribution from triple excitations is handled perturbatively. Similar noniterative corrections for the presence of triple substitutions have been proposed for the CCSD model.I4 In addition, for each of these approaches, the motion of all electrons is correlated, including those in the core, although the effect of core correlation is generally small as shown previously.' Results and Discussion The most stringent test of the quality of a method for calculating spin densities is comparison with the result of a full configuration interaction (FCI) treatment of the problem with the same basis set. For the nitrogen atom, Bauschlicher et al.I5 have provided FCI values for A,,(14N) for a number of small uncontracted Gaussian basis sets. It has previously been shown7 that the augmented coupled-cluster procedure produces results which follow the changes observed in the FCI predictions upon adding to a small s,p-basis set first a diffuse s-function and subsequently a polarizing d-function. In Table I this comparison is shown along with values derived from the present QCISD(T) treatment. In all cases the results from the QCISD(T) model lie even closer to the reported FCI values. The level of this agreement also prompted further study of the species previously considered by the UCCD(ST) approach. A similar path of basis set improvement was followed to that documented for previous calculations in atoms2 and diatomic hydride^.^ As was previously noted, stable results required a starting point of about triple-f quality. Smaller basis sets, such as the popular Dunning polarized double-{ description,I6 proved to be much too overcontracted to be suitable for the correlated calculation of atomic spin densities. As mentioned above, however, such a limited description of the one-particle space has been successfully employed3 in a study of the isotropic coupling in a number of molecular radicals using the more rigorous CCSD model. l 7 (14) Lee, Y . S.; Kucharski, S. A.; Bartlett, R. J. J . Cfiem. Phys. 1984,81, 5906-5912; Urban, M.; Noga, J.; Cole, S.J.; Bartlett, R. J. J . Cfiem. Phys. 1985, 83, 4041-4046. (15) Bauschlicher, C. W., Jr.; Langhoff, S. R.; Partridge, H.; Chong, D. P. J . Cfiem. Phys. 1988, 89. 2985-2992. (16) Dunning, T. H. J . Chem. Phys. 1970, 53, 2823-2833.
110 The Journal of Physical Chemistry, Vol. 95, No. 1, 1991 TABLE 11: Basis Set Dependency of Q(0)"in Atoms and Their Monohvdrides
CH[2nr1 basisb DZP TZP ext exptc
carbon I3Pl 0.01722 0.02864 0.03390 0.0346 (20)
DZP TZP ext exptC
nitrogen [4S] 0.1097 0.08847 0.09687 0.09705
DZP TZP ext exptC
oxygen [3P] 0.1263 0.1021 0.1045 0.1 14 (23)
C H 0.02679 -0.01408 0.03419 -0.01 344 0.03701 -0.01 303 -0.01289 (4) 0.0416 (18) NH['Z-] N H 0.1 120 -0.03205 0.1 140 -0.02984 0.1 184 -0.02944 0.1 190 (1 1) -0.02960 (28) OH1211il
0
H
0.08891 0.08486 0.08516 0.08441 (71)
-0.0 1744 -0.01 626 -0.01629 -0.01637 (1)
Isotropic spin density, Q(0) in au, from QCISD(T) model. bSee text for a description of these basis sets. For experimental references see text.
As noted previously, the most important extension of the TZP basis set is a more complete description of the d-space, except for the '70-coupling in OH where the addition of a diffuse s-function is equally necessary. However, such changes as were incurred by these extensions were generally small, approximately additive, and always acted to improve the level of agreement with known experimental results. Examples of the effect of basis sets enhancements are collected in Table 11 for the atoms C, N, and 0 and the corresponding neutral diatomic hydrides. Some caution is necessary when comparing with the reported experimental results for atoms. The form of the magnetic hyperfine Hamiltonian for atoms is well establishedI8 and the evaluation of matrix elements in an LS-coupled basis leads to terms both diagonal and off-diagonal in the total angular momentum, J . For the 2P states in B and F three hyperfine parameters are available. A3,2 and Al12 pertaining to the 2P3/2 and 2P,j2levels are reasonably accurately known; however, the off-diagonal or coupling term A3/2,1/2 is not. For boron, early ~ o r k 'reported ~ . ~ ~ the diagonal components at Al/2(11B)= 366.0765 (1 5) MHz and A, 2(11B)= 73.347 (6) MHz. While a subsequent study21 was abie to sharpen the precision of the upper-state value, much larger uncertainty remained in the coupling term, A3/2,i/2(I1B) = 16.44 (40) MHz. In fluorine the lower component was reported22at A,j2(19F)= 2009.99 ( I ) MHz together with a rough estimate of the coupling term, A3/2,1/2(I9F) = 446 ( I O ) MHz. Only later was the splitting in the upper component state resolved23and reported at AII2(l9F)= 102441.21 (3) MHz. Taken together with the conventional analysis of the magnetic hyperfine Hamiltonian, which allows the derivation of the relation 1 IO 16 = - F A l / 2 + TA3/2 - TA3/2,1/2 (4)
these values result in the isotropic coupling constants reported in Table 111. The uncertainties shown are dominated by t h e e r r o r in the off-diagonal components. For 3P atoms four hyperfine parameters are available experimentally, the diagonal constants, A2 and A , and two coupling In oxygen all four have been reportedZ3from terms A2,' and (17) Purvis,G. D., 111; Bartlett, R. J. J . Chem. Phys. 1982, 76, 191C-1918. (18) Abragam, A.; Pryce, M. H. L. Proc. R . Soc. (London) 1951, A205, 135-153. (19) Wessel, G. Phys. Reo. 1953, 92, 1581-1582. (20) Lew., H.; Title, R. S. Can. J . Phys. 1960, 38, 868-871. (21) Harvey, J. S. M.; Evans, L.; Lew, H. Can. J . Phys. 1972, 50, I7 19-1 727. (22) Radford, H. E.; Hughes, V . W.; Beltran-Lopez, V. Phys. Reo. 1961, 123, 153-160. (23) Harvey, J. S. M. Proc. R . Soc. (London) 1965, A285, 581-596.
Carmichael TABLE 111: Isotropic Splitting' in the Atoms B-F nucleus lstatel UCCD(ST)b OCISD(T)' "B [2P] 7.14 10.2 1 3 c [3P] 16.1 19.1 I4N [4S] 9.97 10.4 1 7 0 PI -30.6 -31.6 19F [2P] 292 299
exDtd 11.6 (7) (1 9.5) 10.45 -34.5 (69) 302 (18)
" A i min MHz. bAugmented coupled-cluster doubles model, ext basis set, ref 2. 'Quadratic configuration interaction with fifth-order triples, ext basis set, present work. dSee text for references.
a gas-phase magnetic resonance experiment as A2(I7O)= -218.569 (4) MHz, A1(I7O)= 4.738 (36) MHz, A2,1(170)= -126.6 (20) MHz, and A,,o(.170)= -91.7(72) MHz, with the largest uncertainty once again in the off-diagonal components. The contact spin density in this case is available from Ai,(,P)
1 = -AI 6
5
+ -A2 6
4 6
543
- ~ A l , -o g A z , l
(5)
In carbon only the diagonal constants are known,24AI(l3C) = 2.838 (17) MHz, A2(I3C) = 149.055 (10) MHz. Thecoupling terms have not been resolvedZ5and are instead taken from theory,26 so that an overall error estimate in the value of Ai,(13C) = 19.5 MHz so obtained is not readily available. However, as previously noted,2 interpolation among the results for the atoms B-F from various theoretical models allowed Macdonald and Golding2' to place AiW(l3C)= 21.4 MHz, reasonably close to the above value. Only in nitrogen is the isotropic hyperfine coupling constant accurately determined28at Ai,(14N) = 10.450929 12 (10) MHz. With these provisos the results from the present QCISD(T) procedure are seen to markedly improve the estimates previously obtained by the UCCD(ST) treatment for the isotropic hyperfine coupling in the atoms B-F as shown in Table 111. The form of the magnetic hyperfine Hamiltonian is also well-known for diatomic molecules, and the relations of Frosch and F ~ l e yallow ~ ~ the connection to be made with molecular parameters. The proton hyperfine splitting constants in C H have been measured30by a least-squares fit to several A-doubling transitions in the MODR spectrum of IZCH. Constraining these values to be unchanged in I3CH allowed Steimle et aL8 to locate and identify some of the same transitions in the heavier isotopomer. A similar least-squares treatment resulted in the isotropic coupling (denoted bF in ref 7) of AiS0(l3C)= 46.8 (20) MHz. More recently the deuterium coupling in CD has been The value obtained of Ai,o(2D)= -8.92 (37) MHz is in close accord with that expected from a simple scaling of the Ai,('H) result in 12CH by the ratio of the IH to 2D nuclear g factors. By use of the laser side-band technique in the submillimeter region, hyperfine structure was detected3*in the lowest rotational transitions of the vibrational and electronic ground state of the isoelectronic species NH'. Unfortunately the resolution available precluded the complete determination of the hyperfine parameters at both nuclei. Instead only certain linear combinations were reported and the isotropic component was not isolated. The detection of several zero-field rotational transitions in the electronic ground state of I4NH, and the resolution of the hyperfine structure was accomplished by van den Heuvel et The values ~
~~
(24) Wolber, G.;Figger, H.; Haberstroh, R. A,; Penselin, S.2.Phys. 1970, 236, 337-351. (25) Cooksy, A. L.; Saykally, R. J.; Brown, J. M.; Evenson, K . M. Asfrophys. J . 1986, 309, 828-832. (26) Schaefer, H. F., 111; Klemm, R. A.; Harris, F. E. Phys. Reo. 1968, 176, 49-58. (27) Macdonald, J. R.; Golding, R. M. Theor. Chim. Acfa 1978, 47, 1-16. (28) Hirsch, J. M.; Zimmerman, G. H.; Larson, D. J.; Ramsey, N. F. Phys. Rev. 1977, A16, 484-487. (29) Frosch, R. A.; Foley, H. M. Phys. Rev. 1952, 88, 1337-1349. (30) Brazier, C. R.; Brown, J. M. Can. J. Phys. 1984, 62, 1563-1578. (31) Brown, J. M ; Evenson, K. M. J. Mol. Specrrosc. 1988, 136.68-85. (32) Verhoeve, P.; ter Muelen, J. J.; Meerts, W. L.; Dymanus, A. Chem. Phys. L e f f . 1986, 132. 213-217.
The Journal of Physical Chemistry, Vol. 95, No. 1, 1991 111
Isotropic Hyperfine Coupling Constants
TABLE IV:
Isotropic Splitting in Some Diatomic Hydrides
molecule [state]
CH
[2n,]
N H t [211,]
N H [’E-]
OH+ [Q-] OH FH+
[2ni1
[2ni]
nucleus
I3C ‘H I4N ‘H I4N 1H ‘70 ‘H 170
’H I9F ’H
UCCD(ST)B QCISD(TY 36.6 -57.0 18.9 -72.3 18.0 -63.5 -49.3 -12.5 -49.1 -69.0 432 -67.3
41.6 -58.2 19.9 -75.2 19.1 -65.8 -50.9 -75.3 -5 1.6 -72.8 443 -69.5
exptd 46.8 (20) -57.67 (20) 19.22 (18) -66.23 (32) -75.83 (49) -51.17 (43) -73.2516 (68) 549 (96)
“ A i , in MHz. bAugmented coupled-cluster doubles model, ext basis set, ref 2. CQuadraticconfiguration interaction with fifth-order triples,
ext basis set, present work. dSee text for references.
TABLE V: Annlysis of the Correlation Contributions to the Density“ in CH X PlIJ and OH X fzlI,l method C H 0 UHF 0.09050 -0.01887 0.161 37 UCCD 0.029 17 -0.01280 0.07881 0.08291 UCCD(S) 0.033 86 -0.01302 0.081 08 UCCD(ST) 0.03260 -0.01277 0.07881 QCID 0.029 17 -0.01280 0.086 63 QCISD 0.038 30 -0.01 3 27 0.085 16 -0.01303 QCISD(T) 0.03701 exptb 0.0416 (18) -0.01289 (4) 0.08441 (71)
Isotropic Spin
H -0.024 17 -0.01535 -0.016 03 -0.01 5 44 -0.015 35 -0.01681 -0.01629 -0.01637 (1)
O Q ( 0 ) in au from ext basis set. bSee text for references.
Where the experimental values are unavailable, the present QCISD(T) estimates should provide a reliable guide. An analysis of the contributions from electron correlation within both the augmented coupled-cluster and quadratic configuration interaction models to the Fermi-contact spin densities in C H and O H is presented in Table V. The contribution from double replacements in the UHF determinant is the same in both cases, leading to the formally identical UCCD or QCID models, respectively. In the present approximate coupled-cluster approach, the effect of the inclusion of amplitudes due to single substitutions in the reference state is treated perturbatively, UCCD(S), as in eq 8 above. However, truncating the quadratic configuration interaction treatment in the space of both single and double substitutions leads to a modification of the doubles amplitude as well as the incorporation of single replacements in the QCISD result. Thus, from Table V, although it appears that the effect of single replacements on the heavy atom spin density is much greater in the QCISD model, for example, 0.00909 au versus 0.00499 au from the UCCD(S) model at carbon in CH, it must be remembered that the contribution from double substitutions has changed from the value inferred at the QCID level. The effect of triple replacements is handled perturbatively in both treatments, although different summations are necessary to avoid overcounting in the QCISD(T) approach. The triples contribution in the hydrides is small and similar in both models. For example, for the spin density at carbon in C H the UCCD(ST) triples give -0.001 27 au, while the QCISD(T) component is -0.001 12 au. In the atomic systems studied the QCISD(T) estimate of the effect of triple substitutions is much larger than the corresponding value from the UCCD(ST) model for boron, larger for carbon, essentially unchanged for nitrogen and oxygen, and only slightly smaller for fluorine.
obtained for Ai,(I4N) = 19.22 (18) MHz and Ai,(IH) = -66.23 (32) MHz improved the precision of those deduced from previous laser magnetic resonance (LMR) but the resolution was insufficient to reveal the effects of the nitrogen quadrupole moment. The availability of tunable submillimeter laser side-band radiation again allowed the detectionj5 of hyperfine structure in the lowest rotational transition of the isoelectronic OH+ X3Z- around ITHz. An analysis yielded Ai,(lH) = -75.83 (49) MHz. Larger error bars were given in the estimate subsequently reported36from a study of the four lowest rotational states of OH+ and OD+ by LMR spectroscopy in the far infrared. The line width precluded resolution of the deuterium splitting in OD+. The most recent, and most precise determination of the proton coupling in O H X2n appears to be the fitting3’ of previous farinfrared LMRSBand Zeeman effectj9 data to give Aiso(IH) = -73.2516 (68) MHz. Assuming this same splitting in I7OH led to an estimation of the coupling at oxygen of Ais0(170)= -51.17 (43) MHz. Lastly the fluorine hyperfine structure in HF’ X211 has been detected40 by direct laser absorption spectroscopy in a fast ion beam. The isotropic component was given as Ai,(I9F) = 549 (96) MHz, but the hydrogen hyperfine splitting was only partially resolved. Table IV collects these available experimental values of AiSo, with the error estimates provided by the original authors, in ground-state diatomic hydrides and shows a similar, if less draConclusions matic, improvement in the QCISD(T) results over the UCCD(ST) The recently developed quadratic configuration interaction estimates. Comparison with previous theoretical work was model for electron correlation has been applied in conjunction with presented elsewhere and will not be pursued here except to note finite-field perturbation theory to determine the isotropic hyperfine that the present estimates of isotropic coupling constants are coupling constants in a number of small radicals, for which a superior to those derived from a Slater-function based many-body perturbation theory treatment by Kristiansen and V e ~ e t h . ~ ~ single-determinant spin-restricted treatment yields a value of zero. The consistent incorporation of single replacements in the underlying UHF determinant leads to an improvement over previous (33) van den Heuvel. F. C.; Meerts, W. L.; Dymanus, A. Chem. Phys. Lett. results from an augmented coupled-cluster procedure in which 1982, 92, 215-218. this effect was treated perturbatively. Similar improvements (34) Wayne, F. D.; Radford, H. E. Mol. Phys. 1976, 32, 1407-1422. should also be available using the full CCSD model discussed (351 Bekoov. J. P.:Verhoeve. P.;Meerts. W. L.: Dvmanus. A. J. Chem. Phis. 1985. 82. 3868-3869. above. The values now obtained are in excellent agreement with ‘(36) Gruebele, M. H. W.; Muller, R. P.; Saykally, R. J. J. Chem. Phys. available experimental data. 1986, 84, 2489-2496. (37) Brown, J. M.; Kerr, C. M. L.; Wayne, F. D.; Evenson, K. M.; Radford, H. E. J. Mol. Spectrosc. 1981, 86, 544-554. (381 van Herwn. W. M.: Meerts. W. L.: Veseth. L. Chem. Phvs. Lett. 1985, 120, 247-251. (39) Leopold, K. R.; Evenson, K. M.; Comben, E. R.; Brown, J. M. J . Mol. Spectrosc. 1987, 122, 440-454. (40) Coe, J. V.; Owrutsky, J. C.; Keim, E. R.; Agman, N. V.; Hovde, D. C.; Saykally, R. J. J. Chem. Phys. 1989, 90, 3893-3902.
Acknowledgment. The research described herein has been supported by the Office of Basic Energy Sciences of the United States Department of Energy. (41) Kristiansen, P.; Veseth, L. J . Chem. Phys. 1986, 84, 2711-2719,
6336-6344.
