J . Phys. Chem. 1994, 98, 5896-5901
5896
Hyperfine Splitting in HOCO from ab Initio Calculation+ Ian Carmichael Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556 Received: February 7, 1994"
Results are reported from a n ab initio molecular orbital study of the isotropic hyperfine coupling, a, in trunsand cis-HOCO. Equilibrium radical structures are obtained from large-basis-set second-order Merller-Plesset perturbation theory (UMP2) calculations. Vibrational frequencies are predicted for the analogous deuterated species from scale factors determined by comparison with the results of similar calculations on, and the known experimental vibrational spectra of, various isotopomers of formic acid. The isotropic splittings due to the possible magnetic nuclei, IH, I3C, and 170,are then computed a t these optimized geometries. An extensive investigation of the basis-set dependence of the computed magnetic coupling constants is carried out at the unrestricted Hartree-Fock (UHF) and U M P 2 levels of theory. Further electron correlation effects on the calculated splittings are determined from the results of coupled-cluster (UCCD) and quadratic configuration interaction (UQCISD) treatments with moderately large basis sets. For the more readily observed couplings, u('H) and a(I3C), values of -4.7 and 533 M H z are obtained for the trans-isomer. Experimentally a(IH) = f 6 . 8 M H z is reported. [Sears et al. J . Chem. Phys. 1993, 98, 66241. Couplings in cis-HOC0 are predicted to be 77 M H z a t hydrogen and 608 MHz a t carbon.
Introduction The hydroxyformyl radical, HOCO, and its deuterated analog have, since their first gas-phase identification by Ruscic et al.,I been the subject of intensive investigation by a variety of highresolution spectroscopictechniques. TheobservationZof a portion of the rotational spectrum from the radical, produced by reacting chlorine atoms with formicacid, allowed the precisedetermination of the ground-state rotational parameters and provided estimates of a number of other important structural parameters. The v2 fundamental was detected3 in both isotopic species employing transient diode laser absorption spectroscopy subsequent to the photolysis of acetic acid with ultraviolet light. More recently, several further rotational 6-dipole transitions have been detected4 by far-infrared laser magnetic resonance techniques, considerably improving the precision of previous reports and allowing a partial characterization of the hyperfine parameters of the radical. An infrared difference-frequency laser spectroscopic study of the V I fundamental of the deuterated form has also just been r e p ~ r t e d . ~ HOCO is thought to be an intermediate in the most common reaction for atmospheric depletion of hydroxyl radicals, namely that with carbon monoxide, and the gas-phase chemistry of this process has been widely studied.6 Crossed-beam studies of the dynamics of this reaction in the single-collision regime have been interpreted' to include transient HOCO, and the thermochemistry of the radical has recently been c1arified.Q The species has also been implicated in the reverse reaction, that of carbon dioxide with hot hydrogen a t o m ~ . ~ J ~ Vibrational spectra for two isomeric forms of HOCO have been reported" following the vacuum-ultraviolet photolysis of water in a low-temperature CO matrix. The assignment of these spectra has recently been confirmed by the detection and analysis of a vibrational spectrum assigned to the trans-isomer in solid argon.l2 In these low-temperature (14 K) experiments the radical was formed by hydrogen abstraction from formic acid during codeposition with a beam of excited argon or discharge-induced fluorine atoms. Our own interest in hydroxyformyl arises from a completely different direction, further evidence of the ubiquitous nature of 'This is Document No. NDRL-3687 from the Notre Dame Radiation Laboratory. Abstract published in Advance ACS Abstracts, May 15, 1994.
this species and an indication of its widespread relevance. In the course of a joint experimental and theoretical study13 of the effect of pH on the ESR spectrum of the carboxyl radical anion, COL, in aqueous solution, results from a number of high-quality theoretical calculations on the structure and hyperfine splitting in the radical anion and its protonated forms were obtained. 13C splittings in COz- (336 MHz) and trans-HOC0 (521 MHz) were calculated, and it was pointed out that many of the coupling constants assigned in the literature to C02- were, in fact, severely perturbed by the nearby presence of protons or other counterions in the medium. Values of a(I3C) ranging from 342 MHz, from photolysis of TMPD in 3-methylpentane glass containing 13Cenriched carbon dioxide,I4 through 480 MHz, in X-irradiated single crystals of sodium hydrogen oxalate,15to 61 1 MHz, from y-radiolysis of CO adsorbed on alumina,I6 have been attributed to this species! The. last value presumably indicates strong interaction with neighboring aluminum cations, and indeed it has been theoretically demonstrated17 that complexation with alkali metal cations can considerably increase the 13C-coupling. In view of the central importance of the hydroxyformyl radical, and to afford support for the ongoing high-resolution studies, we felt it worthwhile to elaborate on our initial report of hyperfine splitting in this species and to present the results of some more recent calculations.
Computational Details The radical structures were optimized in large-basis-set calculations with the second-order unrestricted Mraller-Plesset perturbation theory (UMP2) procedure in which all electrons were correlated. Preliminary estimates were obtained with a supposed triple-{ split-valence basis set,l* written 6-3 1 lG(d,p) when augmented by five-component polarizing d-functions on carbon and oxygen and p-functions on hydrogen. At least for atoms, this basis set has been shownI9 to have characteristics more resembling a true double-{description of both the core and valence single-particle spaces. More thorough treatments were pursued by adding diffuse functions on the heavy atoms (denoted +), multiple polarization functions (2d on 0 and C, 2p on H), and higher angular momentum functions (seven-component f-shells on 0 and C, five-component d-shell on H) to give the largest basis set employed in the structural determination, denoted 6-31 l+G(2df,2pd).'"
0022-3654/94/2098-5S96$04.5~/0 0 1994 American Chemical Society
The Journal of Physical Chemistry, Vol. 98,No. 23, 1994 5891
Hyperfine Splitting in HOCO
TABLE 1: Optimized UMP2 Structures, Energetics, and Spin-SquaredExpectation Values' for Two Isomers of HOCO basis set 6-31 lG(d,p) 6-31l+G(2df,2dp) tram-HOC0 r(C=O)/A 1.182 1.181 1.344 1.342
r(c-oYA t9(OCO)/deg r(OH)/
0 (COH)/deg
E(UHF)/hartree E(UMP2)lhartree @(UHF)/ au 32(ASA) /au @(UMP2)/au r(C=O)/A
0.962
0.964
127.2
127.4 107.4 -188.201 37
106.3 -188.181 56 -188.748 59
0.7647 0.7502 0.7545 cis-HOC0 1.187 1.332
r(OH)/ @-OYA
0.971 130.4
-188.863 02
0.7650 0.7502 0.7546 1.186
1.330 0.972 130.9
t9(0CO)/deg O(COH)/deg 107.0 108.2 -188.200 60 E(UHF)/hartree -188.181 72 -188.746 03 -188.859 63 E(UMP2)lhartree 0.7633 S2(UHF)/au 0.7631 0.7501 S2(ASA)/au 0.7501 0.7544 0.7546 S2(UMP2)/au 0 S2 from UHF method, after (single-sided) quartet annihilation, S2(ASA), and from the UMPZ method, correlating all electrons. Preliminary calculations of the hyperfine coupling constants at the optimized radical geometries employed the DunningHuzinaga (9s5pld14sl p)/ [4s2pld12slp] double-{contraction21v22 and subsequently a much larger contraction (1 3s8p2d18s2p)/ [7s4p2d15s2p] due tovan Duijneveldt23with polarization functions taken from the work of Lie and Cleme11ti.2~ This basis set has been shown to be particularly suitable for the accurate recovery of Fermi contact interactions in small systems using the electron correlation techniques adopted in this w0rk.25-3~ At the lower levels of theory ( U H F and UMP2) the effects of further basis-set extensions were investigated. Multiple polarization functions, diffuse functions, and higher angular momentum functions were added to give the largest contracted basis set used in the spin density calculations, which may be written (14~9p4dlf19~3dld)/ [8~5p4dlf16~3pld]. The exponents chosen for these supplementary functions were as in earlier work.25 The unpaired spin densities at the nuclear positions were generally determined by finite (Fermi contact) field perturbation t h e ~ r y ,employing ~ ~ , ~ ~ coupled-cluster doubles (UCCD)33-34 and quadratic configuration interaction (UQCISD)35 techniques for the recovery of effects due to electron correlation. The effect of the inclusion in the correlated wave function of amplitudes due to triple replacements in the U H F reference state was also investigated in a single-step perturbative treatment, and results at this level of theory are denoted UQCISD(T).35 The isotropic coupling constants were obtained from thecalculated spin densities by scaling with known fundamental constants and the appropriate nuclear magnetogyric ratios. Most of the calculations were performed using modified versions of the Gaussian 88 and Gaussian 90 program s ~ i t e s 3 ~running ,3~ on Convex C- 120 or C-240 machines. The largest UMPZ studies, however, required the use of the Cray-2 supercomputer at the NERSC and were run using an unmodified version of Gaussian 92 (Release D2).38
Results and Discussion Radical Structures. Optimized structures and energies for the ground electronic 2A'state of the planar C, trans- and cis-isomers of HOCO obtained a t the UMPZ level of theory are reported in Table 1 . Little change in the geometrical parameters is seen upon basis-set improvements beyond the 6-3 1 lG(d,p) description.
TABLE 2: Vibrational Frequencies. and Relative Intensities' in Two Isomers of HOCO mode(symm.) computed freq re1 intens scaled freqb expt.c trans-HOC0 V I (a') 3888 53 3637 3602.9m v2 (a') 1921 76 1848 1843.6s v3 (a') 1272 100 1171 1211.2s v4 (a') 1122 26 1073 1064.6m vs (a') 623 2 610 552 38 522 515wm V6 (a") cis-HOC0 3495 3316 V I (a') 3736 14 1825 1797 v2 (a') 1896 100 1223 1261 v3 (a') 1329 1 1065 1088 v4 (a') 1113 64 605 620 vs (a') 617 11 607 44 574 V6 (a") a Frequenciesin cm-1 and relative intensities from UMP2/6-3 1lG(d,p) calculations. b Scaledby comparisonwith the known frequenciesof formic acid; see text. tram-HOC0 is isolated radical in a low-temperature argon matrix.'? cis-HOC0 is perturbed species in a low-temperature CO matrix." A gas-phase value of 1852.567 cm-I has recently been reported for ~2 in ~ a n s - H O C 0 . ~ The predicted structures are in reasonable accord with those found in the C I calculations of McLean and E l l i r ~ g e r however, ;~~ the C-0 bond lengths differ considerably from the values derived in multiconfiguration self-consistent-field (MCSCF) calculations byAoyagiandKatoNwitha [4s2pld12slp] basis set. For example, in the trans-form, the UMP2/6-3 11+G( 2df,2pd)-optimized value for the length of the carbonyl bond, r(C=O), is 0.020 A larger, while the (formally) singly-bonded C-O linkage is 0.013 A shorter, than those reported in the MCSCF study. Rotational constants computed from the present geometry are A = 167.98 GHz, B = 11.433 GHz, and C= 10.705 GHz, in excellent accord with those deduced from the observation of the gas-phase rotational spectrum for this species by Radford et aL2 For the cis-isomer the UMPZ calculation indicates A = 143.75 GHz, B = 11.703 GHz, and C = 10.822 GHz, and the differences between the results of the various theoretical approaches are again similar in this case. Table 1 also includes the optimized energies from which it can be seen that the trans-form is about 2 kcal mol-' more stable and is preferentially stabilized by the basis-set extensions by about 0.5 kcal mol-'. The expectation values of the spin-squared operator, for the underlying U H F wave function, those of singly-annihilated form (ASA), and those at the UMPZ level are also presented. It can be seen there is little spin contamination in the referencedeterminant and that thiscontamination is almost completely removed by single-sided (quartet) annihilation. The UMPZ estimates of 9 show little improvement over the U H F values, but the magnitudes of the residuals after annihilation suggest that the geometry optimizations will not be significantly distorted by the spin pollution. VibrationalSpectra. Calculated vibrational frequencies (cm-I) and expected infrared intensities, relative to the most intense absorption, are listed in Table 2 for both isomers. Theoretical results for the trans-species arecompared with recent argon matrix observations.12 A simple scale factor ( ~ 0 . 9 5 provides ) a reasonably close correlation between the calculated and observed values. Even closer accord can, however, by achieved by using modedependent scaling as suggested by h l a y and co-workers,41 and these scaledvalues are also included in Table 2. Here we compare frequencies from analogous MP2/6-3 1 lG(d,p) calculations with experimental observation of infrared absorption in various isotopomers of monomeric formic acid. The relevant data for formic acid have been summarized by Nakamoto and K i ~ h i d a . ~ ~ The scaled u2 value in trans-HOC0 is also in accord with the recent report of 1852.567 cm-1 for this mode in the gas phase, determined by transient diode laser spectroscopy.3 For the cisisomer of HOCO only an older work in which the radical was
s2,
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The Journal of Physical Chemistry, Vol. 98, No. 23, 1994
TABLE 3 Predicted Vibrational Frequencies. in Two Isomers of DOC0 mode(symm.) assignment trans-DOC0 cis-DOC0 OD stretch 2684 2576 u1 (a’) C=O stretch 1850 1831 YZ (a’) DOC bend 922 98 1 v3 (a’) 1112 1136 u4 (a’) C-0 stretch OCO bend 600 560 us (a’) 403 473 U6 (af’) torsion Frequencies in cm-l scaled from UMP2/6-31 lG(d,p) calculations based on comparison with formic acid and its deuterated analogs; see text. A gas-phasevalue of 2684.102 cm-1 has recently been reported for u1 in tran~-DOC0.~ Q
detected” in a low-temperature carbon monoxide matrix is apparently available. Observed frequencies were also assigned to trans-HOC0 in that work, and the effectiveness of matrix perturbations in reducing the OH stretching and HOC bending frequencies in that isomer has, more recently, been clearly demonstrated.12 Apparently these perturbations are also active in the cis-HOC0 spectrum, as is evidenced from the lack of consistency in the ratio between computed and observed frequencies. Similarly scaled vibrational frequencies for the deuterated species are reported in Table 3 to aid in the search for this isotopomer spectroscopically. The predicted values agree reasonably well with the observations of Milligan and Jacoxll in solid CO, despite the presence of perturbations due to hydrogen bonding. For trans-DOCO, v2 and v4 have been observedat 1841.7 and 1092.6 cm-1 in solid argon,12 and v1 at 2684.1 cm-I in the gas phase,5 in reasonable accord with the predictions offered in Table 3. The exact match with the reported 0-D stretch is, of course, coincidental. The greatest uncertainty (f10 cm-I) in the calculated values is expected in the DOC bending frequency, reflecting a corresponding uncertainty in the reported value for the analogous mode in DCOOD.42 The computed zero-point vibrational energies, taken from the scaled frequencies, lead to little change in the predicted relative stability of the species. A set of U H F wave function redeterminations stepping along the various normal mode directions indicate that there are no large changes in 32 so that the spin contamination is not expected to badly perturb the computed frequencies.43 It is also possible to gauge the appropriateness of using a singleconfiguration U H F reference space by examining the occupancy of the U H F (charge density) natural orbitals. Occupation numbers deviating substantially from 2.0 (for formally doubly occupied orbitals) or from 0.0 (for formally unoccupied orbitals) are indicative of the need for a multiconfiguration self-consistent field treatment mixing these functions.44 For both HOCO isomers a natural orbital analysis of the U H F wave function at the optimized geometry revealed no “filled” orbitals with occupation numbers less than 1.993 and, correspondingly, no “empty” orbital with occupation number greater than 0.003. Hyperfine Interactions. The natural orbital analysis also allowed the separation of direct (coming from the singly-occupied orbital) and spin polarization contributions to the U H F results for the Fermi contact spin density, which are presented in Table 4 fromcalculations with a small polarizeddouble-!:, [4s2pld12slp], basis set. The direct component is seen to dominate the electronnuclear coupling at carbon and the hydroxylic oxygen (denoted 02)in both species; this dominance is particularly pronounced in the trans-form. At the hydrogen and the carbonyl oxygen (denoted 01), however, substantial spin polarization contributions are present. At 01 in both species, the spin polarization term has the same sign and roughly the same magnitude as the direct contribution, resulting in a computed hyperfine splitting of about -65 MHz for both isomers. In cis-HOC0 the spin polarization reinforces the already large direct contribution to the unpaired
Carmichael
TABLE 4: Analysis of Contributions to a(UHF)* in HOCO nucleus contribution ‘3C ‘H ‘70, 1702 trans-HOC0 8.9 -34.0 -45.9 direct 594 spin polar. 33.8 -20.5 -30.9 2.5 total 628 -1 1.5 -64.9 -43.4 cis-HOC0 670 45.4 -39.1 -147 direct spin polar. 65.7 34.9 -26.8 -52.1 total 735 80.2 -66.5 -199 a Isotropic splitting in MHz from UHF/ [4s2pldl2slp] calculationsat the UMP2/6-3 1 l+G(2df,2pd)-optimized geometries. 0 1 is the carbonyl oxygen, 02 the hydroxylic site. TABLE 5: Basis-Set Effects on Computed a(UHF)* in trans-HOC0 nucleus basis set ”C ‘H 1701 1702 [4s2pld12slp] 628 -11.5 -64.9 -43.4 [ 7s4p2d15sZpl 614 -10.6 -66.5 -45.9 -66.4 -46.0 [7S4p4dl5S3Pl 614 -10.4 [7~4p2dlf15~2pld] 611 -10.7 -66.3 -45.5 [8sSp2d16s2p] 613 -10.5 -66.4 -46.1 [8~5p4dlf16~3pld] 61 1 -10.5 -66.2 -45.6 Isotropic coupling constant in MHz computed at the UMP2/63 1 l+G(2df,2pd)-optimized geometry. spin density at H, leading to a coupling constant at hydrogen of about 80 MHz. In the trans-species, however, the small direct term is offset by a larger spin polarization effect and the computed value for a(1H) is negative. It is known that the U H F method affords a reasonable description of the direct term. By way of comparison, a spinrestricted open-shell (ROHF) calculation (in which spinpolarization terms are not included) with the same basis set gives values for the coupling constants of a ( W ) = 604 MHz, a(lH) = 9.3 MHz, a(I7O1)= -32.0 MHz, and a(1702) = -44.3 MHz for trans-HOCO, in closeagreement with thecorresponding direct contributions displayed in Table 4. Note that the R O H F model necessarily predicts positive values for the unpaired spin density and that the negative couplings at the oxygen sites are simply a reflection of the sign of the magnetogyric ratio for the oxygen nucleus. Basis-set effects on the isotropic splitting in trans-HOCO, computed a t the U H F level, are explored in Table 5. The substantial improvement in the description of the single-particle space in going from the double-!: to the [7s4p2d15s2p] basis set leads to only modest decreases in the calculated spin density at C and H and similarly small increases (in magnitude) at the oxygen sites. Attempts to approach the U H F limit by adding multiple polarization functions, [7s4pg)5s&], higher angular momentum functions, [7s4p2da5s2pu], and diffuse functions, [&&2db2p], produced little further changes in the computed couplings. Thevalues obtained with the [8s5p4dlfl6s3pld]basis set are thus expected to be close to the limiting UHF values for isotropic coupling in trans-HOC0 at this geometry. For the cis-isomer, the results of a similar series of calculations suggest that the limiting U H F values for the corresponding coupling constants are a(I3C) = 705 MHz, a(IH) = 83.4 MHz, u(l7O1) = -66.3 MHz, and a(1702) = -196 MHz, respectively. As mentioned above, the hyperfine splitting, particularly at the carbon center, in these radicals is dominated by the so-called direct term arising from the electron in the formally singlyoccupied, highest-filled a molecular orbital. The relevant orbitals, loa1 (a),for both isomers are depicted in Figure 1 as contour plots in the molecular plane. No great differences are readily apparent. To illustrate the effect of the inclusion of spin polarization terms, the corresponding U H F spin density contours
Hyperfine Splitting in HOCO
The Journal of Physical Chemistry, Vol. 98, No. 23, 1994 5899 /
,--.
I \-#
- _H-
\
\
\
‘---*/
Figure 1. (a, Top) Highest occupied a-molecular orbital (loa’) in tramHOCO. Contours contain 90%, 7076, 50%, 30%, and 10% of the
probability from UHF/[8~5p4dlq6~3pld] calculations. Negative contours are dashed. (b, Bottom) Similar contours for the same orbital in cis-HOCO. are graphed in Figure 2. Contour levels (-0.01, -0.005, -0.0025, 4 . 0 0 1 25,0.0025,0.005,0.01,0.02, and 0.04 au) are specifically chosen to illustrate regions of negative spin density. It is evident that in the cis-isomer the hydrogen is located in a region of strongly positive spin density. On the other hand, in the trans-species, the hydrogen experiences an area of weakly negative spin density distribution. An abbreviated summary of basis-set effects on the computed coupling constants in correlated calculations on both isomers is presented in Table 6, which contains results from UMPZ calculations. Once again only relatively small changes (in magnitude) accompany the first improvement from the limited double-f description, and once again even smaller shifts ensue with further basis-set extensions. The results ascribed to the [8~5p4dlf16~3pld] basis set reported in Table 6 are also expected to be close to the UMPZ limiting values for the coupling a t the various nuclei in their respective species. A comparison of the U H F and UMPZ limiting values indicates that the inclusion of the effects of electron correlation a t the UMPZ level leads to a 10-1 2% reduction in the coupling at carbon from the U H F values in both cis- and trans-isomers. Almost no change is seen in the splitting due to the carbonyl oxygen despite the significant spin polarization contribution at that center, while at the hydroxylic oxygen the UMPZ procedure produces a 1520% increase (in magnitude) of the computed coupling constant. At the hydrogen site, however, electron correlation effects act differently. In trans-HOC0 the splitting is strongly reduced (in magnitude) from the UHF values; in the cis-isomer the effect is oppositely directed, leading to a slight decrease in the calculated value at the UMPZ level. The UMP2 procedure, of course, provides only a partial recovery of effects due to electron correlation. In particular only the effects of double replacements in the U H F reference determinant are considered, and indeed these are described incompletely. Double excitations provide the largest contribution to energy lowering in electron correlation schemes and often,
Figure 2. (a, Top) Spin density distribution in trans-HOC0 from UHF/
[8sSp4dlfl6~3pld]calculations. Negative contours (dashed lines) are at -0.01, -0.005, -0.0025, and -0.001 25 au, positive contours at 0.0025, 0.005, 0.01, 0.02, and 0.04 au. (b, Bottom) Similar contours for the UHF spin density in cis-HOCO. although not always, the dominant correlation correction contribution to U H F spin densities. An estimate of the penalty incurred in the computation of spin densities by the use of the second-order treatment of double excitations, implicit in the UMPZ method, is available from the results from small-basis-set calculations on trans-HOC0 presented in Table 7. A comparison with the UCCDvalues, in which the effect of double replacements through all orders is included, indicates that the UMPZ treatment underestimates the doubles correction at the carbon site and overestimates (in magnitude) the coupling a t the other nuclei for which spin polarization effects are more important. The overestimation is particularly pronounced a t the hydroxylic oxygen. The inclusion of the effect of amplitudes due to single replacements in the U H F determinant, and the concomitant relaxation of the doubles term, leads to results at the UQCISD level. At carbon and the hydroxylic oxygen the UMP2 estimates are fortuitously close to the computed UQCISD values. At hydrogen and the carbonyl oxygen such fortuitous cancellations do not occur and the discrepancy between the UMPZ and UQCISD values is greater than between the corresponding UCCD and UQCISD results. A similar picture emerges in the case of the cis-isomer, for which the results of contributions to correlated calculations with the double-c basis set are presented in Table 8. For both species, the inclusion of higher excitations (triples) by means of a single-step perturbative treatment leads to relatively small further changes in the computed coupling constants. However, for carbon the magnitude of the triples term is comparable, and oppositely directed, to that induced by the presence of single substitutions in the UQCISD model. The final
5900
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The Journal of Physical Chemistry, Vol. 98, No. 23, 1994
,.
TABLE 8: Correlation Contributions to Computed a Values* in cis-HOC0
H '
nucleus method (contribution)
13C
'H
UHF doubles singles triples UQCISD(T)
736 -94.1 13.0 -11.2 643
80.2 -7.3 0.5 1.5 74.8
1701 -66.5 -6.0 11.1 -1.3 -62.7
1702
-199 -18.6 -7.1 -5.6 -230
Isotropic splitting in MHz computed with the [4s2pld(2slp] basis set at the UMP2/6-3 1l+G(2df,2pd)-optimized geometry. (I
TABLE 9 Basis-Set Effects on UQCISD(T) Calculations of Isotropic Splittines* in HOCO nucleus basis set
'3C
'H
l7O1
trans-HOC0 -5.8 -4.7 cis-HOC0 643 74.8 608 76.8
[4s2pld12sl p] [7s4p2d15s2p]
557 533
[4s2pld12sl p] [7s4p2d15s2p]
-57.5 -57.4 -62.7 -61.0
1702
-60.8 -62.5 -230 -227
a Isotropic coupling constant in MHz computed at the UMP2/63 1 1+G(2df,2pd)-optimized geometries.
TABLE 1 0 Energy Separation in HOCO Isomers from Correlated Calculations* method
Figure 3. (a, Top) Spin density distribution in trans-HOC0 from UQCISD/ [7s4p2dlSs2p] calculations. Negative contours (dashed line) are at -0.01, -0.005, -0.0025, and -0.001 25 au, positive contours at 0.0025,0.005,0.01,0.02, and 0.04 au. (b, Bottom) Similar contours for the UQCISD spin density in cis-HOCO.
TABLE 6 HOCO
Basis-Set Effects on Computed a(UMP2)* in nucleus 'H
I7O1
trans-HOC0 [4s2pl d12s 1p] 564 -2.5 543 -1.3 [7s4p2d15s2p] [ 8 ~ 5 ~ 4 d l f 1 6 ~ 3 p l d ] 544 -0.2
-67.0 -66.0 -65.2
cis-HOC0 650 72.4 619 74.8 619 74.2
-74.9 -72.2 -71.5
basis set
1 3 c
[4s2pld12sl p] [7s4p2d15sZpl [8~5p4dltl6~3pld]
17o2
-55.1 -56.2 -54.2 -228 -225 -222
0 Isotropic coupling constant in MHz computed at the UMP2/631 l+G(2df,2pd)-optimized geometry.
TABLE 7: Correlation Effects on Computed a Values* in trans-HOC0 nu c1eus method
'3C
1H
170'
UHF UMPZ UCCD UQCISD UQCISD(T)
628 564 551 571 557
-11.5 -2.5 -4.6 -5.7 -5.8
-64.9 -67.0 -66.4 -55.7 -57.5
'TO2
-43.4 -55.1 -44.9 -57.3 -60.8
0 Isotropic splitting in MHz computed with the [4s2pld12slp] basis set at the UMP2/6-3 1l+G(2df,2pd)-optimized geometry.
table of computed coupling constants, Table 9, illustrates the effect of basis-set improvements at the UQCSID(T) level. Once again only relatively small changes ensue upon the substantial basis-set improvement between the [4s2pld12slp] and [7s4p-
UHF UMPZ UCCD UQCISD UQCISD(T)
trans-HOC0 (hartree) -188.213 -188.845 -188.842 -188.854 -188.877
87 88 96 64 23
cis-HOC0 (hartree) -188.213 -188.842 -188.839 -188.851 -188.874
18 60 99 86 23
A(cis-trans) (kcal mol-') 0.43 2.06 1.86 1.75 1.88
a Calculations with the [7s4p2d15s2p] basis set a t the UMP2/63 11+G(2df,2pd) geometry.
2d15s2pl descriptions. A comparison with the results of further basis-set extensions obtained in the U H F and UMPZ calculations suggests that the UQCISD(T)/ [7s4p2d15s2p] results should provide reasonable estimates of the actual isotropic coupling constants in these species. We note that Sears et a1.4 have reported a ('H) = f6.8 MHz for trans-HOCO. The present calculations suggest that the sign is indeed negative. Since the largest UQCISD(T) calculations should provide a reasonable estimate of the energy separation of the HOCO isomers, we conclude, in Table 10, with a summary of the effect of electron correlation on these energetics. Little change is evident beyond the UMPZ level. The UQCISD(T)/ [7s4p2dJSs2p]// UMP2/6-311+G(2df,2pd) value of 1.9 kcal mol-' confirms the relative stability of the trans-form.
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