Accurate ab Initio Quartic Force Fields and Thermochemistry of FNO

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J. Phys. Chem. 1994, 98, 11394-11400

11394

Accurate ab Initio Quartic Force Fields and Thermochemistry of FNO and ClNO Jan M. L. Martin* Limburgs Universitair Centrum, Department SBG, Universitaire Campus, B-3.590 Diepenbeek, Belgium, and University of Antwerp (UIA), Institute for Materials Science, Department of Chemistry, Universiteitsplein 1, B-2610 Wilrijk, Belgium

Jean-Pierre Franqois Limburgs Universitair Centrum, Department SBG, Universitaire Campus, B-3.590 Diepenbeek, Belgium

Renaat Gijbels University of Antwerp (UIA), Institute for Materials and Science, Department of Chemistry, Universiteitsplein 1, B-2610 Wilrijk, Belgium Received: May 30, 1994; In Final Form: August 17, 1994@

The quartic force fields of FNO and ClNO have been computed at the CCSD(T)/cc-pVTZ level. Using an “augmented” basis set dramatically improves results for FNO but has no significant effect for ClNO. The best computed force field for FWO yields harmonic frequencies and fundamentals in excellent agreement with experiment. Overall, the force fields proposed in the present work are probably the most reliable ones ever published for these molecules. Total atomization energies have been computed using basis sets of spdfg = 208.5 f 1 and 185.4 f 1 kcaymol for FNO and CINO, respectively. quality: our best estimates are DO The computed value for FNO suggests a problem with the established experimental heat of formation. Thermodynamic tables in JANAF style at 100-2000 K are presented for both FNO and ClNO.

Introduction The nitrosyl halides FNO and ClNO are of considerable interest as intermediates in the atmospheric depletion of ozone (see the introductions to refs 1 and 2). Of these, FNO is known as a challenging molecule to theoretical chemistry.2 The cubic force field of FNO has been detennined3s4from the sextic centrifugal distortion constants, together with SCF a b initio values for some off-diagonal constants. No quartic force field is known experimentally. A similar procedure has been performed for ClNO;5additionally, an older study by Mini et a1.6 presented quartic force constants as well as anharmonicity constants. FNO has been the subject of several theoretical studies. These include the SCF level cubic force constants mentioned above, cubic force fields at the MP2 and MP3 (second- and third-order Moller-Plesset theory7)levels,8 as well as the CISD (configuration interaction with all single and double excitations) level? Additionally there has been a semiempirical analysis of the force constants by Curtiss and Maroni’O and a series of papers by Francisco and co-workers2s11s12 in which the geometry and harmonic frequencies of FNO have been studied using many-body perturbation theory, coupled cluster methods,l3 and Becke-Lee-Yang-Parr (BLYP)14 density functional theory methods using larger basis sets. Finally, Lee1 performed coupled cluster geometry and harmonic frequency calculations of FNO and ClNO with a basis set of TZ2P (triple-[ plus two polarization functions) quality. For ClNO, besides the work of Lee,’ there are mainly the MP2 and MP3 cubic force fields by Bendazzoli et a1.8 The objective of the present paper is to obtain accurate ab initio force fields for both molecules. Past experiencefor H20,15 ~

* Author to

~~~~

~

~~~

~

whom correspondence should be addressed at Limburgs Universitair Centrum. E-mail: [email protected]. Abstract published in Advance ACS Abstracts, October 1, 1994. @

NHz,16 NH3,17 BH3,18 H2C0,19 CH4,20 N20, and C0221 has shown that errors on the order of less than 10 cm-’ are quite possible for first-row compounds if augmented coupled cluster methods and basis sets of at least spdf quality are used. As witnessed from our recent study of a number of sulfur compounds,22this pattern appears to be replicated for secondrow compounds as well. Additionally, we will present accurate calculated values for the total atomization energies of FNO and ClNO. Computational Methods All calculations were performed with the MOLCAS 2 package23interfaced with the coupled cluster program from the TITAN packagez4 running on an IBM RS/6000 model 365 workstation at the Limburgs Universitair Centrum (LUC). Electron correlation, like in our previous studies of this kind, was included at the CCSD(T) l e ~ e l , *which ~ - ~ ~is the coupled cluster with all single and double excitation (CCSD) augmented with a quasiperturbative estimate of the effect of triple excitations.25 The basis set used initially was Dunning’s correlation consistent polarized valence triple-f basis set,z9,30 which for firstrow atoms29 is a [4s3p2dlfl contraction of a (10s5p2dlf) primitive set and for second-row atoms30 is a [5s4p2dlfl contraction of a (15s9p2dlf) set. Additional calculations were performed with the “augmented” correlation consistent31polarized valence triple-l; (aug-cc-pVTZ)basis set on F and C1, which is obtained by adding one diffuse primitive of every angular momentum to the cc-pVTZ basis set. Finally, some calculations involved in the thermochemistry were performed with the ccpVQZ (correlation consistent polarized valence quadrupole-f) basis ~ e t ~ ~ ~ ~ ~ -represents w h i c h [5s4p3d2flg] (first row) and [6s5p3d2flg] (second-row) contractions of the (12s6p3d2flg) and (16sl lp3d2flg) basis sets, respectively-and a three-term additivity correction suggested by Martin32.33 which has a mean

0022-365419412098-11394$04.50/0 0 1994 American Chemical Society

Thermochemistry of FNO and ClNO

J. Phys. Chem., Vol. 98, No. 44, 1994 11395

TABLE 1: Computed Geometry and Harmonic Frequencies (cm-', expr' CCSDRZZP' CCSD(T)/TZ2Pi CCSD(T)/6-31lG(d)' CCSD(T)/6-31lG(2d)' CCSD(T)/6-31lG(2df)' BLYF'16-31 1G(2df)I2 CASSCF/6-31 lG(2d)" CCSD(T)/cc-pVTZ ditto aug(F)

+

A, deg) for FNO and Literature Values

m0

m

0

0 1

0 2

0 3

1.13 155(23) 1.132 1.137 1.144 1.142 1.142 1.144 1.142 1.14160 1.13623

1.51658(22) 1.498 1.536 1.502 1.512 1.486 1.566 1.523 1.49652 1.52461

109.9220(72) 109.9 110.0 110.2 110.1 110.2 110.7 110.0 110.165 109.856

1876.8 1887 1846 1869

775.5 808 772 795

522.9 560 520 522

1853.1 1879.4

804.3 772.6

549.3 524.5

absolute error of less than 0.5 kcal/mol for the total atomization energies of a number of reference molecules. Optimization was carried out by repeated multivariate parabolic interpolation, with the step length progressively reduced as convergence was approached. The force field was set up by central finite differences on a grid with step size 0.01 8, or rad. Thus computing the complete quartic force field of a nonlinear asymmetric triatomic requires 129 unique points in all. The intemal coordinate force field was then transformed to Cartesian coordinates using the INTDER program,34while the transformation to normal coordinates and the final spectroscopic analysis by standard second-order rovibrational perturbation were carried out using the SPECTRO program.37 Since neither FNO nor ClNO appears to exhibit any type of resonance at first sight, a perturbational treatment should be adequate. However, we have checked its validity by calculating the band origins for fundamentals, overtones, and two-quanta combination bands variationally using the vibrational selfconsistent field-configuration interaction (VSCF-CI) method of Romanowski et U Z . , ~ as~ implemented in a modified version of the POLYMODE program39running on an IBM RS/6000 at the LUC. For each reference state, the vibrational analog of the SCF problem is solved, and the vibrational analog of the CI matrix is constructed using the 'virtual mode' solutions for the excited states to preserve o r t h ~ g o n a l i t y .(This ~ ~ is exactly analogous to what is normally done in an electronic structure CI calculation.) Normal coordinates and the full nonrotating Watson Hamiltonian40were used; the n-mode basis set consist of all VSCF-oscillator products generated by allowing quantum numbers 0-6 in the NO stretch, 0-10 in the NX stretch, and 0-16 in the bend, with a maximum total quantum number of 18. Redoing the calculations in smaller basis sets showed that states with at most two quanta are converged to 0.1 cm-' or better for basis sets with maximum quantum numbers 6, 8, and 10 for the three modes and 12 overall, although some of the highly excited states are affected. For the latter, however, a potential of higher degree than quartic would be desirable anyway. Results and Discussion

A. FNO. Computed geometries and harmonic frequencies are given in Table 1, together with values from the literature. Anharmonic, rovibrational coupling, and centrifugal distortion constants are presented in Table 2. It is immediately obvious that the cc-pVTZ values are nowhere near the 10 cm-' or better accuracy that we have come to expect from CCSD(T)/cc-pVTZ frequency calculations. The NO stretch is low by 24 cm-', while the NF stretch is high by 29 cm-' and the bend high by 26 cm-'. Similar errors are seen in the fundamental^:^' -23, f 3 0 , and +25 cm-', respectively. This appears to suggest that the anharmonic portion of the potential is sound and that the problem lies chiefly in the geometry and harmonic frequencies (which are known to be

TABLE 2: Anharmonic, Rovibrational Coupling, and Centrifugal Distortion Constants for FNO in cm-' CCSD(T)/ cc-pVTZ 1820.8 795.7 v2 545.8 v3 1598.2 ZPE -17.226 XI 1 1.682 Xl2 -4.385 x22 2.720 x 1 3 -1.263 x 2 3 -2.149 x33 3.176 587 A, 0.400 523 Be 0.355 677 C, 0.013 214 ai, -0.009 190 a2~ -0.020 228 a3~ -0.000 382 alb 0.001 046 azb 0.002 985 a3b -0.000 227 al, 0.001 507 a2, 0.003 081 a3c 1 0 3 ~ ~ 0.000611 9 -0.001 249 1 lo3& 0.122 591 6 10' AK 1036~ 0.000 084 9 0.003 128 1 1036~ 1 0 7 ~ ~ -0.000 002 0.000 414 107aJK 1 0 7 ~ ~ , -0.014 728 1 0 7 ~ ~ 0.166 320 1074~ 0.000 001 0.000 085 1074~~ 0.018 008 1074~ v1

CCSD(T)I aug-cc-pVTZ 1846.3 763.5 521.1 1582.8 -17.392 1.340 -4.393 2.004 -1.959 -1.725 3.134 324 0.393 266 0.349 424 0.012 573 -0.010 019 -0.020 123 -0.000 617 0.000 938 0.002 821 -0.000 408 0.001 429 0.002 918 0.000 639 5 -0.001 111 3 0.122 282 7 0.000 087 5 0.003 241 0 -0.000 005 0.000 536 -0.015 887 0.170 829 0.000 001 0.000 128 0.019 460

expr' 1844.03" 765.Ma 521"

3.167 581(63) 0.396 844(6) 0.352 667(12) 0.013 12(13) -0.012 44(11) -0.020 68(21) -0.000 481(5) 0.001 00(1) 0.002 97(3) -0.000 299(3) 0.001 52(1) 0.003 04(3) 0.000 65(2) -0.001 179(37) 0.13 l(4) 0.000 089 8(27) 0.003 59( 11) -0.OOO 002 O(6) 0.000 523(28) -0.017 67(27) 0.209( 11) 0.OOO 001 05(10) 0.000 135(32) 0.020 6(22)

"Stephenson, C. V.; Jones, E. A. J. Chem. Phys. 1952, 20, 135.

far more sensitive to the level of theory than the higher derivatives). Comparison with the experimentallyderived cubic force field of Degli Esposti et aZ.: in which some constants were constrained to SCF ab initio values, reveals that the cubic constants are indeed basically in good agreement, while the quadratic ones are substantially off. There is actually a qualitative problem with the geometry, in that the CCSD(T)/cc-pVTZ level is expected to overestimate the bond distances by 0.003-0.007 8,33but that it actually seriously underestimates the NF bond distance. (The overestimate in the NO bond distance is also outside the expected range.) Similar results were obtained by Dibble and Francisco2 at the CCSD(T)/6-31lG(2df) level. The G/; diagnostic:* which has been proposed as an indicator for the importance of nondynamical correlation effects, is 0.022, which indicates that MP2 would do poorly but CCSD(T) results should not substantially be affe~ted.4~ (Actually, MP2 performs fairly well2 due to an obvious error compensation: 12-electron in 9-orbital CASSCF/6-31lG(2d) (complete active space SCW)

Martin et al.

11396 J. Phys. Chem., Vol. 98, No. 44, 1994 TABLE 3: Comparison of Perturbational and Variational Band Origins for Fundamentals, Overtones, and Combination Bands of FNO and ClNO FNO CWO state pert Val. pert V U 1846.3 763.5 521.1 3657.9 1518.3 1038.7 2611.2 2369.4 1282.7

1847.7 763.6 521.6 3665.4" 1518.4 1040.9 2611.2 2371.0 1284.2

1797.4 602.1 339.7 3560.2 1198.0 677.2 2399.6 2136.8 939.0

1798.6 601.6 339.7 3565.4' 1195.8 677.3 2399.3 2138.0 938.3

'

Close interaction with (1 12) state at 5235.4 cm-l. Close interactions with (052), (019), and (130) states at 4942.6,4949.5, and 4973.0

cm-l, respectively. calculations12produce a geometry in quite good agreement with experiment. Density functional results reported in the latter reference are competitive with MP2 results.'l) On the whole, the CCSD(T)/cc-pVTZ results are actually worse than those obtained by Lee1 at the CCSD(T)/TZ2P level. There, only the NO stretch is off (by an amount one expects at the CCSD(T)/TZ2P level), while the other two modes are in almost perfect agreement with experiment. This is almost certainly due to a fortunate error compensation between the effect off functions (which tend to contract bonds) and some other source of error. In order to find out what exactly this source is, we turn to a recent study by Martin and in which the basis set convergence of the geometry and harmonic frequencies of HF and H20 was investigated in great detail. It was revealed there that even a cc-pV5Z basis set (that is, one of spdfgh quality) failed to come closer than 10 cm-' to the experimentalharmonic frequency46of HF. The source of error there turned out to be the ionic character of HF: when a smaller cc-pVQZ basis set, augmented with spdf diffuse functions on F, was applied, almost perfect agreement with experiment was reached. A similarly augmented cc-pV5Z basis set changed that result by only about 1 cm-l, indicating that convergence had actually been reached. Now FNO has substantial ionic character as well. A CCSD(T)/aug-cc-pVQZ calculation on FNO is beyond our computational resources, and even a CCSD(T)aug-cc-pVTZ calculation would be problematic,but a CCSD(T) calculation with cc-pVTZ basis sets on {N,O} and an aug-cc-pVTZ basis set on F was quite feasible. As seen in Table 1, this results in a dramatic improvement. The harmonic frequencies are now in almost perfect agreement with experiment, with residual errors of f 2 . 6 , -2.9, and +1.6 cm-'. The fundamentals (Table 2) replicate this pattern, with errors of f 2 . 3 , -2.3, and f O . l cm-'. The bond angle is in almost perfect agreement with experiment, while the NO bond is too long by about 0.005 A, in agreement with the systematic correction of -0.006 8, suggested by Martin33for a double bond. Only the FN bond is rather overlong (+0.008 A), but this is to be expected for this type of weak and mostly ionic single bond. The fact that a change in the F basis affects all three vibrations, even the NO stretch, testifies to the significant coupling between vibrations that exists in FNO. A comparison between perturbational and variational band origins is given in Table 3 for all bands involving at most two quanta. It is immediately seen that the perturbational theory values agree very closely with the variational ones and that, in particular, second-order vibrational perturbation theory incurs errors in the fundamentals of only - 1.4, -0.1, and -0.5 cm-l.

TABLE 4: Computed and Experimental Internal Coordinate Force Constants of FNO in attojoule, A, and rada expt ref 4

CCSD(T)/cc-pVTZ CCSD(T)/cc-pVTZ+aug(F) ~

~~

2.369 235 7 1.929 946 4 F12 15.584 794 3 F22 0.264 340 3 F13 0.421 571 5 F23 1.950581 9 F 33 - 10.454 98 Fill -5.218 04 FZII -4.684 50 F221 -122.194 39 F122 -1.599 61 F~II -1.741 30 F321 -0.423 08 F322 -4.244 17 F33l -2.098 46 F332 -3.549 27 F333 62.558 46 Filii FZIII - 1.894 75 18.084 23 Fzzii 13.146 39 F2221 758.366 26 F2222 8.508 93 F~III 4.694 56 F3211 5.251 33 F3221 -4.608 71 F3222 7.051 00 FBII 8.135 29 F3321 -2.419 67 F3322 8.770 52 F3331 3.669 15 F3332 12.416 53 F3333

FII

2.135 461 8 1.889 166 3 16.005 238 1 0.256 213 6 0.388 785 8 1.851 163 7 -8.463 99 -5.233 75 -4.507 97 -125.427 75 - 1.45249 - 1.72696 -0.240 13 -4.131 41 -1.869 63 -3.413 01 44.483 76 2.004 17 15.341 92 13.503 86 780.862 55 7.980 52 4.875 93 4.687 61 -4.783 97 7.469 09 7.618 20 -2.914 07 8.731 27 3.193 49 11.59080

Internal coordinate definitions: SI = m; SZ=

'Constrained to SCF ab initio values.

2.133(11) 1.902(67) 15.912(24) 0.2358(30) 0.323(22) 1.8414(51) -9.06(17) -7.54(84) -5.34(51) - 136.9(23) - 1.394(26) -1.54' -0.61' -4.176(36) -1.88' -3.650(79)

NO;

S3 = OFNO.

The notable exception is the 2v1 overtone, which is underestimated by 7.5 cm-l. Inspection of the other eigenvalues of the vibrational Hamiltonian matrix reveals that the (1 12) state is only 11.6 cm-' lower in energy than the (200) state; under those circumstances the small but noticeable error seen in the perturbation theory result is unavoidable. On the whole, however, it appears that second-order perturbation theory is adequate for the present purpose. The quadratic force field (Table 4) is now in good agreement with the experimentally derived one of Degli Esposti et al? No fundamental changes are seen in the cubic force constants, confirming that the basis set effect that caused the geometry and harmonic frequency problems indeed had no substantial impact on the anharmonic portion of the force field. The quartic force constants are dominated by the diagonal quartic of the NO stretch. The only significant change between the cc-pVTZ and cc-pVTZ+aug(F) appears to be in the diagonal FN quartic, which is likely to be the most sensitive to basis set effects of the quartic force constants. No comparison with experiment is possible for the anharmonicity constants. However, since the agreement between the computed and experimental fundamentals is as good as that for the harmonic frequencies and no resonance effects of any importance are present, the Xu values given in Table 2 should be quite reliable. This conclusion is corroborated by the excellent agreement between computed and observed47fundamentals for FNI8O, where the small errors are again almost exactly the same as between the computed and experimentally derived4 harmonic frequencies. Agreement between the computed and experimentalrotational constants is of course somewhat adversely affected by the residual error in the geometry. The rovibrational constants involving the NO stretch appear to be quite sensitive to the level

Thermochemistry of FNO and ClNO

J. Phys. Chem., Vol. 98, No. 44, 1994 11397

TABLE 5: Computed and Experimental Spectroscopic Constants for HF and HCI re

we

a,

U&e

HF CCSD(T)/cc-pVTZ CCSD(T)/aug-cc-pVTZ CCSD(T)/cc-pVQZ CCSD(T)/aug-cc-pVQZ expP

0.917 24 0.920 96 0.916 22 0.9 17 69 0.916 81“

4177.4 4124.7 4162.3 4 141.8 4138.32“

88.51 87.18 89.55 89.49 89.88

0.772 81 0.765 82 0.787 56 0.787 82 0.798

CCSD(T)/cc-pVTZ CCSD(T)/aug-cc-pVTZ CCSD(T)/cc-pVQZ CCSD(T)/aug-cc-pVQZ expP

HC1 1.277 30 1.278 85 1.276 93 1.277 64 1.274 55b

3000.3 2991.0 2995.7 2989.5 2990.946b

53.44 53.55 52.36 52.14 52.8186

0.305 52 0.304 27 0.304 3 1 0.304 07 0.307 18

“Mechanical” re and w e are 0.916 80 A and 4138.77 cm-’, respectively.& “Mechanical” re and we are 1.274 54 8, and 2991.090 cm-’, re~pectively.~~

of theory. The high sensitivity of these constants to the reference geometry was previously noted by Alberts et ~ l .who , ~ computed the a! constants at the CISD/DZP level and observed quite radical changes when the experimental geometry was substituted for the computed one. It should be noted that the experimental values favor neither set of a! constants in particular and that the largest constants (i.e. those in the A direction) carry fairly large absolute uncertainties as well. The quartic centrifugal constants, on the other hand, agree as well as can be expected under these circumstances, given also the experimentaluncertainty. The same is true for the sextic centrifugal constants, which are dominated by @K, similarly as the quartic ones are dominated by AK. These conclusionsappear to hold for FN1*0as well. Summarizing, we can say that we probably calculated the first available accurate quartic force field and anharmonicity constants for FNO. B. ClNO. In order to determine whether an augmented basis set will be necessary for ClNO, we first perform some calculations on HCl with different basis sets. The results can be found in Table 5 . It is evident here that the erratic convergence pattern observed for “nonaugmented” basis sets in HF45is not replicated for HCl. This is undoubtedly related to the less polar character of the bond and to the lower electronegativity of chlorine. Since very satisfactory agreement with experimenP6 can evidently be obtained without augmented functions, they will not be used for ClNO. Computed geometries and harmonic frequencies are given in Table 6, together with the available calculated and experimental values from the literature. Agreement with experiment is quite within the realm of the expected for CCSD(T)/cc-pVTZ calculations. The NO stretch is low by 3.5 cm-’; the C10 stretch and the bend are high by 6.6 and 7.2 cm-’, respectively. Similar errors are seen for the fundamentals (Table 7). Previous CCSD(T)/TZ2P frequency calculations by Lee’ are in excellent agreement with experiment for the ClN stretch and the bend but underestimate the NO stretch by 32 cm-’. The geometry contains a nontrivial amount of experimental uncertainty. The bond angle is reproduced almost perfectly;

the error for the NO bond distance is in line with the expected overestimate of 0.006 A. The long C1N bond is overestimated by about 0.006 A, compared to 0.026 8, at the CCSD(T)/TZ2P level.’ We can therefore conclude that the geometry is satisfactorily handled as well. For this molecule, experimental anharmonicity constants are available. As seen in Table 7, they agree with our calculated values as closely as one can expect, given the fairly large experimental uncertainties in some of them. This appears to indicate that the anharmonic portion of the force field is quite well reproduced at this level of theory. This conclusion is corroborated by the rovibrational coupling constants. Given the residual error in the geometry, the calculated constants track the experimental ones as well as can be expected. The same is true for the centrifugal distortion constants, where the error is generally a couple of standard deviations on the experimental values. A comparison between perturbational and variational band origins can again be found in Table 3. Once more, very good agreement is seen for all bands with at most two quanta except 2v1, which is here in close interaction with the (052), (019), and (130) states, at -8.1, -1.4, and +22.5 cm-’ relative to the (200) band, respectively. (Given the relatively large error in the computed 0 3 , at least the second of these resonances is probably accidental.) For the fundamentals, perturbation theory incurs errors of only -1.2, +OS, and +O.O cm-’, respectively, herewith again justifying our perturbational treatment. Finally (Table 8), the cubic force field of Cazzoli et al. appears to be reproduced quite well. Note that, in that force field, several off-diagonal cubic constants were constrained to SCF ab initio values. The older force field by Mirri et al., in which no such constraints have been applied, exhibits significant differences (sometimes almost an order of magnitude) with both the computed and the Cazzoli et al. force fields. Therefore no great significance should probably be attached to the agreement (or lack thereof) between the quartic portion of Mirri et al. and that of the present work. In both cases, they are dominated by the large FZZZZanyway. C. Thermochemistry. Total and relative energies involved in the thermochemistry of FNO and ClNO are given in Table 9. The directly computed total atomization energies were adjusted for residual one-particle basis set incompleteness with the three-term correction proposed by Martin32s33

in which Nu,N,, and Np&represent the numbers of o bonds, n bonds, and electron pairs, respectively, and the coefficients are specific to the level of theory of the energy calculation as well as that of the reference geometry. (The coefficients involved here are repeated for convenience in Table 9.) Using the cc-pVQZ basis set from the cc-pVTZ reference geometry, this yields us best estimates of ED, of 213.0 and 189.4 kcdmol, respectively, for FNO and ClNO, with an expected average error of 0.5 kcal/m01.~~ With the smaller basis set, both values are lower by around 1 kcdmol, suggesting that

TABLE 6: Computed Geometry and Harmonic Frequencies (cm-’; expt6 expt5 CCSD/TZ2P1 CCSD(T)/TZ2P1 CCSD(T)/cc-pVTZ

A, dep) for ClNO and Literature Values

rN0

mcl

e

W1

w2

w3

1.135 710(68) 1.133 57(25)” 1.133 1.141 1.141 38

1.972 626(67) 1.974 53(25)” 1.967 2.001 1.981 69

113.405 3(34) 113.320(13)” 113.1 113.4 113.355

1835.6(2) 1835.6(2) 1850 1804 1832.1

603.2(2) 603.2(2) 626 602 609.8

336.4(2) 336.4(2) 352 338 343.6

Cazzoli et a1.: p 182 (text).

Martin et al.

11398 J. Phys. Chem., Vol. 98, No. 44, 1994 TABLE 7: Anharmonic, Rovibrational Coupling, and Centrifugal Distortion Constants for CMO in cm-1 expt CCSD(T)/cc-pVTZ - 17.281 0.04 -3.14 -0.3 1 -2.89 -1.13 1797.4 602.1 339.7 1386.6 2.876 208 0.190 063 0.178 282 0.022 211 -0.023 625 -0.016 972 -0.000 777 0.000 677 0.000 868 -0.000 613 0.000 873 0.000 865 0.000 195 0.134 751 -0.002 010 0.000 016 0.001 134 8.47 2.531 963 1.13496 - 1.090 243 7 3.022 2.757 8 1.025 946

ref 6

TABLE 8: Computed and Experimental Internal Coordinate Force Constants of ClNO in attojoule, A, and rada ~~

expt

ref 5 CCSD(T)/cc-pVTZ

- 17.80(3)

1.310 956 1 1.327 945 6 15.247 981 0 0.135 146 4 0.271 321 1 1.315 603 3 -4.204 83 -4.132 67 -2.985 82 .118.300 80 -0.603 72 -0.999 29 0.352 54 -2.398 20 -0.944 39 -2.153 90 9.223 09 6.652 95 6.994 97 12.709 08 732.160 58 2.245 17 2.733 46 1.500 67 -5.047 21 3.877 60 3.318 65 -3.408 11 4.713 35 0.870 26 5.694 33

-0.1(5) -2.60(25) -0.6(5) -4.3(5) -0.85( 10) 1799.7" 595.6" 330.9" [2.762 444Ib 0.190 827(2) 0.178 229 6(4) -0.026 532(7) -0.016 852(7) 0.000 737(10) 0.000 909( 10)

0.000 936(10) 0.000 919(10)

00.026 57(27) -0.017 Ol(17) -0.OOO 891(9) 0.000 735(7) 0.OOO 908(9) -0.OOO 700(7) 0.OOO 939(9) 0.OOO 903(9) 0.OOO 211(6) 0.146(4) -0.002 04(6) 0.OOO 016 7(5) 0.001 34(4) 8.67(77) 2.9(2) 1.37(7) -1.250(11) 3.229(57) 1.44(19)

a Jones, L. H.; Ryan, R. R.; Asprey, L. B. J . Chem. Phys. 1968,49, 581. Indirectly from geometry, which was determined from Be and C, for several isotopic species (see ref 5 for details).

further expansion of the basis set to cc-pV5Z would not greatly affect our proposed estimates. Combining these with computed zero-point energies (ZPEs) (Tables 2 and 7) yields DO values of 208.5 and 185.4 kcaV mol, which can be compared directly with experiment. From the experimental heats of formation at 0 K listed in the JANAF tables4*for the {F,N,O,Cl} atoms and the two species of interest, we find the experimental values Do(FN0) = 205.1 f 0.5 kcaY mol and DO(ClN0) = 187.2 f 0.2 kcaYmo1. While the discrepancy between theory and experiment for ClNO, although on the high side, is not implausible, the overshoot of 3.4 kcaY mol in the computed value for FNO suggests a problem with the experimental heat of formation. Lee' found deviations on the order of 3.5 kcavmol between computed and experimental reaction energies for a number of reactions involving FNO: he similarly concluded that an experimental error cannot be ruled out, arguing that this is not unusual for molecules involving bonds between several electronegative elements. (For example, the generally accepted heats of formation of HOF and cis-FONO were shown to be in error by x 3 and e 2 5 kcal/mol, respectively, by ab initio c a l c ~ l a t i o n s ? ~We ~ ~ ~therefore ) conclude that the experimental heat of formation is almost certainly in error. Since all the required data are available from the present calculations, we have set up the partition function and its first two moments using the hybrid analyticavdirect summation method described in detail in refs 15 and 51. For the temperature range 100(100)2000K, the heat capacity at constant temperature C,, the enthalpy H, the entropy S, and the free energy function [G(T) - &]/Tare displayed in JANAF style48

ref 6

ref 5b

-433) -1.93(30) -9.8(15) -116.2 -0.08(8) 1.30(15) 9.5(2.5) -1.76(2) -3.00(40) - 1.29 6(7) 0.3(8) 23(6) 53 689 -0.1(2) -1.5(3) -24( 19) -72 15(2) 30(6) 5(21) 1.7(3) 3.0(5) -13(6)

1.254(23) 1.44(8) 15.424(23) 0.1505(37) 0.417" 1.299(7) -4.20( 10) -5.55(55) -4.5(7) -120.3(59) -0.719(24) -0.948' 0.123' -2.503(39) - 1.101' -2.374(5 1)

Internal coordinate definitions: SI = mcl; S2 = mo; S3 = &w0. Table 10, set II. Constrained to SCF ab initio value.

TABLE 9: Energies Involved in Thermochemical Calculations on FNO and CMO CCSD(T)/cc-pVTZ N 0 F c1

FNO ClNO

CCSD(T)/cc-pVQZ

Total Energies (hartree) -54.514 488 -54.524 -74.973 822 -74.993 -99.620 299 -99.650 -459.671 757 -459.693 -229.428 825 -229.500 -589.443 539 -589.506

expP

589 411 187 248 791 215

Relative Energies (kcal/mol) 200.94 208.71 177.88 185.09 -0.706 -0.089 0.784 0.668 3.798 1.277 10.77 4.32 211.71 213.03 188.65 189.41 207.18 208.5 1 184.68 185.45

205.11 187.20

-

in Table 10, together with AC,, AH, AS, and log K for the reverse atomization reaction X(g) N(g) O(g) XNO (X = F, Cl). The electronic transition energies required for setting up the atomic partition functions were taken from the corresponding JANAF tables$* which could be reproduced to the accuracy displayed. The functions displayed for ClNO are proper weighted averages of computed functions for the 3 5 C N 0 and 37ClN0isotopomers; the low-abundance isotopes of N and 0 were simply accounted for by using the natural abundance atomic mass rather than the masses of the most abundant isotopes for the translational partition function. (The error

+

+

Thermochemistry of FNO and ClNO

J. Phys. Chem., Vol. 98, No. 44, 1994 11399

TABLE 10: JANAF-Style Thermochemical Tables for FNO and ClNO at a Pressure of 1 bar (0.1 ma) T, K C,, J/(Kmol) H",M/mol So, J/(Kmol) gefo, JI(Kmo1) AC,, JI(Kmo1) AlP,M/mol AS",J/(Kmol)

log Kf

FNO

100 200 298.15 300 400 500 600 700 800 900 lo00 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

33.623 37.390 41.712 41.783 45.106 47.687 49.785 5 1.522 52.969 54.187 55.223 56.120 56.908 57.613 58.254 58.848 59.405 59.935 60.446 60.943 61.432

3.332 6.857 10.747 10.824 15.176 19.821 24.698 29.766 34.992 40.352 45.824 51.392 57.044 62.771 68.564 74.420 80.333 86.300 92.319 98.389 104.508

208.470 232.750 248.516 248.774 261.272 27 1.626 280.511 288.320 295.298 301.609 307.373 312.679 317.597 322.180 326.473 330.513 334.329 337.946 341.387 344.668 347.807

175.147 198.465 212.471 212.694 223.332 231.984 239.349 245.798 25 1.557 256.773 261.549 265.959 270.060 273.895 277.499 280.900 284.121 287.182 290.098 292.885 295.553

100 200 298.15 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

35.008 40.818 44.812 44.870 47.546 49.643 5 1.420 52.946 54.258 55.391 56.382 57.262 58.056 58.786 59.468 60.116 60.740 61.348 6 1.947 62.544 63.142

3.362 7.159 11.376 11.459 16.087 20.950 26.005 31.226 36.588 42.071 47.661 53.344 59.110 64.953 70.866 76.845 82.888 88.993 95.158 101.383 107.667

218.652 244.728 261.833 262.110 275.406 286.248 295.460 303.504 310.662 317.120 323.008 328.424 333.441 338.117 342.498 346.624 350.523 354.224 357.748 361.113 364.337

185.025 208.935 223.676 223.912 235.187 244.348 252.117 258.896 264.928 270.373 275.347 279.929 284.182 288.153 291.880 295.393 298.718 301.875 304.883 307.754 310.503

-32.070 -28.735 -23.731 -23.646 - 19.594 - 16.456 -13.957 - 11.933 -10.276 -8.900 -7.744 -6.753 -5.892 -5.128 -4.439 -3.805 -3.215 -2.658 -2.126 -1.611 -1.109

-875.404 -878.489 -881.057 -881.102 -883.255 -885.051 -886.568 -887.858 -888.967 -889.922 -890.753 -891.478 -892.109 -892.659 -893.137 -893.549 -893.900 -894.193 -894.433 -894.619 -894.755

-192.549 -2 14.073 -224.592 -224.739 -230.960 -234.982 -237.752 -239.748 -241.228 -242.357 -243.233 -243.924 -244.473 -244.9 15 -245.269 -245.553 -245.780 -245.958 -246.094 -246.196 -246.265

447.200 218.253 142.624 141.672 103.276 80.185 64.763 53.729 45.442 38.990 33.823 29.591 26.062 23.074 20.512 18.290 16.344 14.628 13.101 11.735 10.505

-30.269 -23.781 -19.723 -19.669 -17.189 -15.144 - 13.271 - 11.572 -10.061 -8.728 -7.552 -6.506 -5.566 -4.707 -3.913 -3.167 -2.457 - 1.775 -1.113 -0.460 0.185

-778.716 -781.417 -783.531 -783.568 -785.404 -787.020 -788.439 -789.679 -790.759 -791.697 -792.510 -793.2 13 -793.814 -794.328 -794.758 -795.112 -795.393 -795.604 -795.749 -795.828 -795.841

-190.063 -209.062 -217.714 -217.838 -223.135 -226.749 -229.341 -231.258 -232.702 -233.808 -234.666 -235.336 -235.860 -236.272 -236.592 -236.835 -237.018 -237.146 -237.228 -237.27 1 -237.278

396.826 193.162 125.897 125.051 90.907 70.374 56.659 46.856 39.476 33.736 29.138 25.373 22.233 19.575 17.294 15.317 13.586 12.059 10.700 9.485 8.391

CLNO

incurred by this approximation is smaller than the smallest decimal place given.) There are fairly substantial differences between the present thermodynamic functions and the ones reported in the JANAF tables; these differences increase with temperature. For FNO (where the JANAF tables were computed using rigid-rotor, harmonic oscillator partition functions), the differences at 2000 K amount to +4.65 Jl(Kmo1) on C,, +3.85 kT/mol on H,and f 3 . 5 J/(Kmol) on S. The most important component of this difference is centrifugal distortion (+3.25 J/(Kmol) on C,,+2.7 kJ/mol on H, and +2.4 Jl(Kmo1) on S);the remainder goes to vibrational anharmonicity and rovibrational coupling. For ClNO-for which the published JANAF table includes vibrational anharmonicity-the corresponding differences at 2000 K amount to +4.3 J/(Kmol), 4-3.4 Hlmol, and +2.8 Jl(Kmol), respectively. Virtually all of this appears to be caused by centrifugal distortion, weighing in at +4.1 J/(Kmol), f 3 . 3 kJ/ mol, and +3.0 J/(K*mol),respectively. This again illustrates the point being made in ref 51 about the importance of centrifugal distortion effects in thermodynamic functions at elevated temperatures. Conclusions The quartic force fields of FNO and CWO have been computed at the CCSD(T)/cc-pVTZ level. Using an "aug-

mented" basis set dramatically improves results for FNO but has no significant effect for ClNO. The best computed force field for FNO yields harmonic frequencies and fundamentals in excellent agreement with experiment. Overall, the force fields proposed in the present work are probably the most reliable ones ever published for these molecules. Total atomization energies have been computed using basis sets of spdfg quality: = 208.5 f 1 and 185.4 & 1 kcaY our best estimates are DO mol for FNO and CWO, respectively. The computed value for FNO suggests a problem with the established experimental heat of formation. Thermodynamic functions in JANAF style at 100-2000 K are presented for both FNO and ClNO. The differences between the present and published JANAF values are mainly caused by neglect of centrifugal distortion. Acknowledgment. The authors gratefully acknowledge the support of the Science Policy Programming Services (DPWB) of the Prime Minister's Office for funds enabling the purchase of an IBM RS/6000 workstation [Grants NAP-48 (Characterization of Materials) and IT/SC-11 (Supercomputing)]. J.M. additionally acknowledges a Postdoctoral Researcher Fellowship of the National Science Foundation of Belgium (NFWO/FNRS), and the San Diego Supercomputer Center (SDSC) for a grant

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