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Density functional theory exploring the HONO potential energy surface
11 January 1999
Chemical Physics Letters 299 Ž1999. 334–344
Density functional theory exploring the HONO potential energy surface Branko S. Jursic
)
Department of Chemistry, UniÕersity of New Orleans, New Orleans, LA 70148, USA Received 5 August 1998; in final form 5 October 1998
Abstract The potential energy surface was carefully explored for the HONO molecular system with hybrid, gradient-corrected, and local spin density approximation. Computed geometries, relative energies, activation barriers, enthalpies of formation, and bond dissociation energies for this molecular species, as well as for related molecules, were calculated and compared with experimental and the complete basis set obtained values. The harmonic frequencies with the moment of inertia for all stationary points on the potential energy surface were calculated with both gradient-corrected and hybrid density functional theory methods. The reliability of the density functional theory method for exploring the small polar nitrogen system was discussed. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction There is considerable interest in exploring the structural and energetic properties of nitrous acid due to its presence in combustion as well as atmospheric chemistry. This compound is a well-known source of NOq electrophiles in organic synthetic chemistry w1x. Nitrous acid is very unstable in its pure form, but it is a well-known and important reagent in aqueous solutions and has been extensively investigated in the gas phase w2x. In the gas phase, equilibrium of the HONO decomposition with the formation of equimolar amounts of water, nitric oxide, and nitrogen ) Corresponding author. Fax: q1 504 280 6860; e-mail: [email protected]
dioxide can be reached. It was estimated that the enthalpy for this reaction is 38 kJr2 mol HNO 2 w2x. From microwave spectroscopy we know that in the gaseous phase nitrous acid is predominantly in the trans form. The structural parameters are r HO s ˚ r HO – N s 1.433 A, ˚ r NO s 1.177 A, ˚ aHON s 0.954 A, 102.18, aON O s 110.78 w2x. From the infrared data it was suggested that the cis form is only 0.5 kcalrmol higher in energy than trans-HONO. Although the HO–N bond should have a single-bond character, the rotational barrier is experimentally estimated to be 10.8 kcalrmol. We have previously demonstrated that density functional theory ŽDFT. methods are exceptionally accurate for computing structural parameters of small polar molecular systems w3–8x, their bond dissocia-
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 8 . 0 1 2 7 4 - 3
B.S. Jursicr Chemical Physics Letters 299 (1999) 334–344
tion energies w9–14x and, in some cases, isodesmic enthalpies of formation w15,16x. Furthermore, we have demonstrated that some of the DFT methods are highly accurate for the evaluation of the reaction activation barriers w17,18x. This particular chemical system, along with some other similar structures, were previously studied with highly accurate complete basis set ab initio methods w19x. Therefore, all structural and energetic properties of these molecular systems are well known, and these results will be used for the evaluation of the accuracy of three commonly used DFT methods used in exploring the potential energy surface ŽPES. of nitrous acid and the DFT applicability to larger organic molecular systems, which also includes the ONO molecular unit.
2. Computational methods All calculations were performed with the GAUSSIAN 94 computational package w20x. Three commonly used DFT methods are used: the B3LYP hybrid w21,22x, the BLYP gradient-corrected w22,23x, and SVWN local spin density approximation w24x. For all calculations, three gaussian-type basis sets Ž6-31GŽd,p., 6-311GŽ2d,2p., and 6-311GŽ3df,3pd.. were used. For their explanations see Ref. w25x.
3. Results and discussion As mentioned above, there are two isomers of HONO because the HO–N bond has a partially double-bond character. The isomers include cisHONO and trans-HONO. Structural parameters for the trans-HONO are available and they are listed in Table 1. Computed structural parameters for cisHONO, trans-HONO, as well as rotational transition state ŽTSr. for cis–trans isomerization are also presented in Table 1. In general, the hybrid B3LYP with a large basis set is accurate for the computed structural parameters of small chemical systems w9–14x. The computed geometries differ by less than 1% from the experimental values. This deviation is usually in the margins of the experimental error. The same is true for the trans-HONO geometry com-
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puted with the B3LYPr6-311GŽ2d,2p. theory level. The highest deviation between the experimental and the computed HONO structure is an estimated H–O ˚ and bond distance Žthe experimental value is 0.954 A ˚ .. Other values are almost the computed is 0.966 A identical to the experimental values. The BLYP gradient-corrected trans-HONO structure is slightly more off and SVWN produces the trans-HONO geometry that deviates the most from the experimental values ŽTable 1.. The structural parameters for the cis-HONO and of course, for the rotational HONO are not available. We believe that the B3LYPr6311GŽ2d,2p. computed geometries are the ones that are the most accurate. Therefore, the cis-HONO ˚ r HO – N s 1.390 structure should have r HO s 0.97 A, ˚ r NO s 1.180, aHON s 105.48 and a ONO s 110.98. A, The structure of the rotational HONO transition state is exactly what is expected on the basis of the general knowledge of the transition state theory. The dihedral angle is very close to 908 ŽTable 1.. Experimental data for the rotational barrier and the relative stability of the cis-HONO are available Ž10.8 kcalrmol. w2x. Total energies for the molecular species on the PES for the rotation around HO–NO bond are as listed in Table 1. This PES was previously explored with a highly reliable complete basis set ab initio method w19x. The estimated rotational barrier of 11.3 kcalrmol is only slightly higher than the experimental value. The DFT method estimates the rotational barrier to be slightly higher ŽTable 2.. The best estimate came from the most accurate density functional method with an extended basis set. Thus, the hybrid B3LYPr6-311GŽ3df,3pd. theory model estimates the same rotational barrier of 11.3 kcalrmol as the CBSQ method. An almost identical activation barrier was obtained with the same basis set, but now with the gradient-corrected BLYP density functional method ŽTable 2., while the local spin density DFT method overestimates the rotational barrier. All DFT methods suggest that the cis-HONO and trans-HONO have very similar energies. Actually, the B3LYPr6-311GŽ3df,3pd. estimates that their energy difference is zero, while the CBSQ estimates that the trans-HONO is slightly more stable ŽTable 2.. This is in agreement with both experimental data, as well as with the gradient-corrected BLYPr6-311GŽ3df,3pd. suggested preference ŽTable 2..
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Table 1 Structural parameters for trans-HONO and cis-HONO and rotational transition state structure computed with DFT methods Theory level trans-HONO B3LYPr6-31GŽd,p. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ3df,3pd. BLYPr6-31GŽd,p. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ3df,3pd. SVWNr6-31GŽd,p. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ3df,3pd. Experimental cis-HONO B3LYPr6-31GŽd,p. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ3df,3pd. BLYPr6-31GŽd,p. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ3df,3pd. SVWNr6-31GŽd,p. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ3df,3pd. TSr B3LYPr6-31GŽd,p. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ3df,3pd. BLYPr6-31GŽd,p. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ3df,3pd. SVWNr6-31GŽd,p. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ3df,3pd.
r HO ˚. ŽA
r HO – N ˚. ŽA
r NO ˚. ŽA
aHON Ž8.
aONO Ž8.
d HONO Ž8.
0.972 0.966 0.966 0.984 0.978 0.977 0.982 0.977 0.977 0.954
1.426 1.433 1.430 1.499 1.509 1.508 1.415 1.420 1.416 1.433
1.179 1.166 1.163 1.188 1.175 1.171 1.180 1.167 1.164 1.177
102.4 102.0 102.5 100.6 100.3 100.8 101.6 101.3 101.7 102.1
110.6 110.9 111.0 110.4 110.8 110.7 110.7 111.0 111.0 110.7
180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0
0.983 0.978 0.978 0.995 0.988 0.987 0.999 0.993 0.993
1.385 1.390 1.387 1.444 1.453 1.452 1.364 1.368 1.364
1.191 1.180 1.176 1.203 1.190 1.186 1.195 1.183 1.179
105.4 105.4 105.8 104.4 104.3 104.9 104.0 104.1 104.6
113.2 113.6 113.7 112.2 113.6 113.7 112.9 113.4 113.6
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.973 0.968 0.967 0.984 0.978 0.977 0.981 0.977 0.976
1.491 1.502 1.500 1.567 1.582 1.584 1.465 1.477 1.474
1.170 1.156 1.153 1.179 1.164 1.160 1.173 1.158 1.155
104.0 103.8 104.4 102.0 101.9 102.7 104.7 104.2 104.8
111.2 111.4 111.5 111.2 111.3 111.4 111.4 111.5 111.6
88.1 88.0 87.8 88.3 88.2 88.0 88.6 88.6 88.6
r, bond distances in angstrom; a, bond angles in degrees.
The computation of the enthalpy of formation directly from its building elements is a very important computational approach, because enthalpies of formation are broadly used throughout various research fields. Sometimes it is almost impossible to obtain enthalpies of formation for small nitrogen oxide derivatives due to their instability. Our best estimate of the enthalpy of formation for the transHONO comes from complete basis set ab initio studies w19x. The value is y18.4 kcalrmol at 0 K, which is 0.9 kcalrmol lower than the experimental value of y19.3 kcalrmol w26x. There is some evidence that for nitrogen oxide derivatives the experimental heat of formation should be corrected by
approximately 1–2 kcalrmol w27x. We believe that the enthalpy of formation for the trans-HONO should be y18.4 kcalrmol, as calculated with the complete basis set ab initio method w19x. To our surprise, the otherwise very accurate DFT method, hybrid B3LYP, estimated an enthalpy of formation that differed by 3–5 kcalrmol from this value. With the use of a higher basis set the estimated enthalpy of formation is closer to the expected value. Thus, D Hf at 0 K for trans-HONO is estimated with B3LYPr6311GŽ3df,3pd. to be y15.0 kcalrmol. Again, the best estimate comes from the gradient BLYPr6311GŽ3df.3pd.. The estimated enthalpy of formation is y18.5 kcalrmol at 0 K ŽTable 3.. Local spin
B.S. Jursicr Chemical Physics Letters 299 (1999) 334–344
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Table 2 Total energies Ža.u.. for cis-HONO, trans-HONO, and rotational transition state structure ŽTSr. with rotational barrier Ž D E, kcalrmol., and energy difference between cis-HONO and trans-HONO Ž D H, kcalrmol. Theory level
EŽ trans-HONO.
EŽ cis-HONO.
EŽTSr.
DE
DH
B3LYPr6-31GŽd,p. B3LYPr6-31GŽd,p. Ž0 K. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ2d,2p. Ž0 K. B3LYPr6-311GŽ3df,3pd. B3LYPr6-311GŽ3df,3pd. Ž0 K. BLYPr6-31GŽd,p. BLYPr6-31GŽd,p. Ž0 K. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ2d,2p. Ž0 K. BLYPr6-311GŽ3df,3pd. BLYPr6-311GŽ3df,3pd. Ž0 K. SVWNr6-31GŽd,p. SVWNr6-31GŽd,p. Ž0 K. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ2d,2p. Ž0 K. SVWNr6-311GŽ3df,3pd. SVWNr6-311GŽ3df,3pd. Ž0 K. CBSQ Ž0 K. CBSQ
y205.700306 y205.679926 y205.768695 y205.748356 y205.779541 y205.759216 y205.687712 y205.668611 y205.759099 y205.740010 y205.769435 y205.750343 y204.686947 y204.666894 y204.757087 y204.737085 y204.768206 y204.748206
y205.701723 y205.681317 y205.769291 y205.748987 y205.779495 y205.759228 y205.688060 y205.669008 y205.758667 y205.739693 y205.768183 y205.749243 y204.689374 y204.669408 y204.758629 y204.738758 y204.769238 y204.749387
y205.679002 y205.660743 y205.748156 y205.729938 y205.759521 y205.741275 y205.665077 y205.647915 y205.737483 y205.720342 y205.748655 y205.731447 y204.661101 y204.643178 y204.732281 y204.714407 y204.744159 y204.726254
14.3 12.9 13.3 12.0 12.5 11.3 14.4 13.2 13.3 12.1 12.3 11.2 17.7 16.5 16.5 15.3 15.7 14.5 11.3 10.9
y0.9 y0.8 y0.4 y0.4 0.0 0.0 y0.2 y0.2 0.3 0.2 0.8 0.7 y1.5 y1.6 y1.0 y1.0 y0.6 y0.7 0.5 0.5
Ž0 K., Sum of electronic and zero-point energies.
Table 3 Total energies Ža.u.. for hydrogen, oxygen and nitrogen molecules with estimated enthalpy of formation for trans-HONO Ž D Hf , kcalrmol. Theory level
EŽH 2 .
EŽN2 .
EŽO 2 .
D Hf
B3LYPr6-31GŽd,p. B3LYPr6-31GŽd,p. Ž0 K. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ2d,2p. Ž0 K. B3LYPr6-311GŽ3df,3pd. B3LYPr6-311GŽ3df,3pd. Ž0 K. BLYPr6-31GŽd,p. BLYPr6-31GŽd,p. Ž0 K. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ2d,2p. Ž0 K. BLYPr6-311GŽ3df,3pd. BLYPr6-311GŽ3df,3pd. Ž0 K. SVWNr6-31GŽd,p. SVWNr6-31GŽd,p. Ž0 K. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ2d,2p. Ž0 K. SVWNr6-311GŽ3df,3pd. SVWNr6-311GŽ3df,3pd. Ž0 K. CBSQ Ž0 K. CBSQ
y1.178539 y1.168366 y1.180013 y1.169940 y1.180034 y1.169985 y1.167912 y1.157901 y1.169601 y1.159707 y1.169611 y1.159726 y1.171246 y1.161567 y1.172710 y1.163124 y1.172728 y1.163159
y109.524129 y109.518532 y109.559893 y109.554338 y109.564553 y109.558970 y109.510648 y109.505327 y109.547371 y109.542086 y109.552102 y109.546778 y108.915140 y108.909656 y108.951860 y108.946401 y108.956657 y108.951168
y150.320038 y150.316259 y150.369073 y150.365344 y150.374583 y150.370808 y150.315425 y150.311969 y150.366327 y150.362917 y150.371111 y150.367664 y149.574307 y149.570555 y149.623899 y149.620203 y149.629527 y149.625786
y18.2 y12.7 y18.6 y13.1 y20.5 y15.0 y20.7 y15.7 y21.5 y16.4 y23.5 y18.5 y43.6 y38.1 y44.5 y39.0 y46.4 y40.9 y18.4 y20.0
Ž0 K., Sum of electronic and zero-point energies.
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density approximation should be avoided for computing the enthalpy of formation directly from the elements because the computed values differ by more than 20 kcalrmol from the expected value ŽTable 3.. In the solution, the heterolitic H–O bond dissociation energy is occurring easily due to strong solvation of both ions. In the gas phase, this process is energetically highly unlikely, and homolytic bond breaking with the formation of H and NO 2 radicals are predominate. This bond dissociation energy was estimated to be 76.4 kcalrmol at 0 K. None of the DFT methods generates exactly the same value, but the hybrid DFT method estimates a bond dissociation energy that is ; 3 kcalrmol below the CBSQ estimated values ŽTable 4.. Better agreement was obtained for the computed NO 2 heat of formation. Again the CBSQ computed value of 5.7 kcalrmol is lower than the experimental value of 8.6 kcalrmol. Our B3LYP computed value is somewhere between these to values. The best estimate, given by B3LYPr6-311GŽ3df,3pd., is 6.5 kcalrmol ŽTable 4.. Again, we have demonstrated that the hybrid DFT method produces reliable energies. The other
two DFT methods produce enthalpies of formation that substantially deviate from the experimental value ŽTable 4.. Let us now evaluate the heats of formation for the HO and NO radicals formed by the HO–NO bond breaking. Considering the fact that the radical is better stabilized by oxygen atoms than by hydrogen atoms, it is reasonable to expect that the HO–NO bond dissociation energy should be substantially smaller than the H–ONO bond dissociation energy. In fact, the CBSQ estimated bond dissociation energy is 48.5 kcalrmol. The hybrid B3LYP ab initio method computed bond dissociation energies are the closest to the CBS values. The best estimated value is 47.4 kcalrmol, which is only 1.1 kcalrmol below the CBSQ computed value ŽTable 5.. The enthalpies of formation for both HO and NO radicals are experimentally available. The value for OH is 9.3 kcalrmol w26x. The CBSQ computed enthalpy of formation is slightly higher Ž9.7 kcalrmol. while the B3LYPr6-311GŽ3df,3pd. is even higher Ž11.1 kcalrmol. ŽTable 1.. The other two DFT methods compute even higher HO enthalpies of formation. In
Table 4 Structural properties for NO 2 , total energies Ža.u.. for hydrogen radical and nitrogen dioxide with the H–ONO bond dissociation energy ŽBDE I . and the NO 2 enthalpy of formation Ž D Hf , kcalrmol. Theory level
r ˚. ŽA
a Ž8.
EŽH.
EŽNO 2 .
BDE I
D Hf
B3LYPr6-31GŽd,p. B3LYPr6-31GŽd,p. Ž0 K. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ2d,2p. Ž0 K. B3LYPr6-311GŽ3df,3pd. B3LYPr6-311GŽ3df,3pd. Ž0 K. BLYPr6-31GŽd,p. BLYPr6-31GŽd,p. Ž0 K. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ2d,2p. Ž0 K. BLYPr6-311GŽ3df,3pd. BLYPr6-311GŽ3df,3pd. Ž0 K. SVWNr6-31GŽd,p. SVWNr6-31GŽd,p. Ž0 K. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ2d,2p. Ž0 K. SVWNr6-311GŽ3df,3pd. SVWNr6-311GŽ3df,3pd. Ž0 K. CBSQ Ž0 K. CBSQ
1.203
133.8
1.195
134.1
1.191
134.4
1.224
133.1
1.216
133.5
1.211
133.7
1.202
133.8
1.193
134.1
1.189
134.3
y0.5002728 y0.5002728 y0.5021559 y0.5021559 y0.5021559 y0.5021559 y0.4954462 y0.4954462 y0.4975548 y0.4975548 y0.4975548 y0.4975548 y0.4939369 y0.4939369 y0.4961136 y0.4961136 y0.4961136 y0.4961136
y205.072205 y205.063384 y205.137751 y205.129025 y205.148727 y205.139880 y205.068881 y205.060668 y205.136636 y205.128513 y205.146621 y205.138370 y204.056931 y204.047982 y204.123773 y204.114913 y204.135070 y204.126090
80.2 73.0 80.8 73.5 80.7 73.5 77.4 70.6 78.4 71.5 78.6 71.8 85.4 78.4 86.1 79.1 86.0 79.1 76.4 77.7
6.2 7.6 7.1 8.5 5.1 6.5 1.2 2.5 2.1 3.4 0.3 1.7 y15.7 y14.2 y15.0 y13.5 y17.1 y15.5 5.7 5.0
r, N–O bond distance in NO 2 ; a, ONO bond angle in NO 2 ; Ž0 K., sum of electronic and zero-point energies.
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Table 5 Total energies Ža.u.. for hydroxy radical and nitric oxide with their heats of formation and HO–NO bond dissociation energy Theory level
EŽOH.
EŽNO.
D Hf ŽHO.
D Hf ŽNO.
BDE II
B3LYPr6-31GŽd,p. 3B3LYPr6-31GŽd,p. Ž0 K. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ2d,2p. Ž0 K. B3LYPr6-311GŽ3df,3pd. B3LYPr6-311GŽ3df,3pd. Ž0 K. BLYPr6-31GŽd,p. BLYPr6-31GŽd,p. Ž0 K. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ2d,2p. Ž0 K. BLYPr6-311GŽ3df,3pd. BLYPr6-311GŽ3df,3pd. Ž0 K. SVWNr6-31GŽd,p. SVWNr6-31GŽd,p. Ž0 K. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ2d,2p. Ž0 K. SVWNr6-311GŽ3df,3pd. SVWNr6-311GŽ3df,3pd. Ž0 K. CBSQ Ž0 K. CBSQ
y75.728482 y75.720066 y75.756862 y75.748418 y75.761153 y75.752680 y75.712256 y75.704196 y75.742350 y75.734254 y75.747240 y75.739091 y75.332730 y75.324478 y75.362388 y75.354138 y75.366926 y75.358636
y129.888155 y129.883618 y129.929501 y129.925023 y129.935522 y129.930991 y129.878985 y129.874746 y129.921803 y129.917619 y129.927430 y129.923188 y129.209462 y129.204979 y129.251624 y129.247189 y129.257717 y129.253227
13.1 14.0 11.1 12.1 10.1 11.1 18.5 19.3 16.1 17.0 14.5 15.4 25.1 26.1 22.5 23.5 21.5 22.5 9.7 9.9
21.2 21.2 22.0 21.8 21.4 21.3 21.4 21.3 22.0 21.9 21.4 21.4 22.1 22.0 22.8 22.7 22.2 22.1 20.3 20.3
52.5 47.8 51.7 47.0 52.0 47.4 60.5 56.3 60.0 55.3 59.5 53.3 90.8 86.2 89.8 85.2 90.1 85.6 48.5 50.0
Ž0 K., sum of electronic and zero-point energies; D Hf ŽHO., enthalpy of formation for HO in kcalrmol; D Hf ŽNO., enthalpy of formation for NO in kcalrmol; BDE II , HO–NO bond dissociation energy in kcalrmol.
the case of NO, it was experimentally estimated that its enthalpy of formation is 21.5 kcalrmol. The CBSQ estimated value is 1 kcalrmol lower. Our DFT generated enthalpy of formation for NO is actually closer to the experimental value than to the CBSQ value. For instance, the B3LYPr6311GŽ3df,3pd. estimates the enthalpy of formation for NO to be 21.3 kcalrmol, which is 0.2 kcalrmol below the experimental value ŽTable 5.. There is one other isomer of HONO that should be computationally explored, and it is the HNO 2 isomer. Structural parameters, total energy with the heats of formation, and the H–N bond dissociation energies are presented in Table 6. The geometry has ˚ r NO s 1.212 A, ˚ C 2v symmetry with r HN s 1.042 A, and a HN O s 115.8 ŽTable 6. as computed with the B3LYPr6-311GŽ3df,3pd. theory model. The CBSQ computed enthalpy of formation for HNO 2 is y10 kcalrmol. The hybrid DFT method computes an acceptable enthalpy of formation, but it is the BLYPr6-311GŽ3df,3pd. that computes the best HNO 2 enthalpy of formation ŽTable 6., which is the estimated value of y9.6 kcalrmol. The estimated H–N bond dissociation energy is 79.0 kcalrmol
with the B3LYPr6-311GŽ3df,3pd. computed value at 65.7 kcalrmol. The HONO can isomerize into the HNO 2 isomer through 1,2-hydrogen shift or into itself through 1,3-hydrogen shift. The DFT computed structural parameters for those two transition state structures; TS1 and TS2 are presented in Table 7. Both of the transition state structures are what would be expected on the basis of the transition state theory. The H–O bond distance is slightly longer than the H–N bond distance in TS1, indicating that the transition state TS1 is closer in geometry to HNO 2 than to HONO. This suggests that the activation barrier for the HNO 2 rearrangement into HONO is smaller than the reverse rearrangement. In fact, the HONO is 8.5 kcalrmol more stable than the HNO 2 . This is also confirmed with the B3LYPr6-311GŽ3df,3pd. calculation, generating the energy difference of 8.0 kcalrmol ŽTable 8.. The activation barrier for 1,2hydrogen shift through TS1 is estimated by the CBSQ to be 54.4 kcalrmol, which is in excellent agreement with the 55.2 kcalrmol computed with the B3LYPr6-311GŽ3df,3pd. theory level. Similar agreement between the CBSQ and B3LYP hybrid
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Table 6 Computed structural parameters, total energy Ža.u.. enthalpy of formation and H–NO 2 bond dissociation energy for HNO 2 Theory level
r1
r2
a1
a2
EŽHNO 2 .
D Hf
BDE III
B3LYPr6-31GŽd,p. B3LYPr6-31GŽd,p. Ž0 K. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ2d,2p. Ž0 K. B3LYPr6-311GŽ3df,3pd. B3LYPr6-311GŽ3df,3pd. Ž0 K. BLYPr6-31GŽd,p. BLYPr6-31GŽd,p. Ž0 K. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ2d,2p. Ž0 K. BLYPr6-311GŽ3df,3pd. BLYPr6-311GŽ3df,3pd. Ž0 K. SVWNr6-31GŽd,p. SVWNr6-31GŽd,p. Ž0 K. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ2d,2p. Ž0 K. SVWNr6-311GŽ3df,3pd. SVWNr6-311GŽ3df,3pd. Ž0 K. CBSQ Ž0 K. CBSQ
1.044
1.222
115.8
128.5
1.040
1.216
115.7
128.5
1.042
1.212
115.8
128.4
1.056
1.241
115.7
128.7
1.051
1.235
115.7
128.7
1.052
1.231
115.7
128.7
1.059
1.219
115.8
128.5
1.055
1.211
115.7
128.6
1.057
1.208
115.7
128.5
y205.689680 y205.667716 y205.757324 y205.735438 y205.768450 y205.746535 y205.676098 y205.655431 y205.746330 y205.725720 y205.756897 y205.736225 y204.684783 y204.663355 y204.754226 y204.732888 y204.765856 y204.744486
y11.5 y5.0 y11.5 y5.0 y13.5 y7.1 y13.4 y7.4 y13.5 y7.5 y15.6 y9.6 y42.2 y35.9 y42.7 y36.3 y45.0 y38.6 y10.0 y11.7
73.5 65.3 73.7 65.4 73.8 65.6 70.1 62.3 70.4 62.5 70.7 62.9 84.0 76.2 84.3 76.5 84.5 76.7 70.0 71.4
Ž0 K., sum of electronic and zero-point energies; D Hf , enthalpy of formation for HNO 2 in kcalrmol; BDE III , H–N bond dissociation energy for HNO 2 in kcalrmol.
Table 7 Structural parameters of TS1 and TS2 computed with DFT methods
ArI ArII ArIII BrI BrII BrIII CrI CrII CrIII
r1
r2
r3
r4
a1
a2
r5
r6
a3
a4
1.300 1.300 1.297 1.324 1.324 1.321 1.305 1.304 1.301
1.179 1.185 1.185 1.192 1.197 1.198 1.190 1.198 1.199
1.320 1.317 1.313 1.355 1.352 1.347 1.318 1.314 1.310
1.198 1.188 1.184 1.216 1.205 1.201 1.196 1.185 1.182
53.5 53.8 54.0 52.8 53.1 53.3 54.0 54.5 54.7
123.4 123.5 123.4 123.1 123.1 123.0 122.7 122.8 122.7
1.302 1.304 1.308 1.325 1.332 1.332 1.309 1.318 1.318
1.266 1.260 1.256 1.288 1.282 1.277 1.261 1.254 1.250
77.3 77.4 77.4 77.3 77.4 77.4 77.1 77.4 77.4
104.8 105.3 105.6 104.7 105.3 105.6 105.5 106.2 106.4
r, bond distances in angstrom; a, bond angles in degrees.
B.S. Jursicr Chemical Physics Letters 299 (1999) 334–344
341
Table 8 Total energies Ža.u.. for TS1 and TS2 with their activation energies and HNO 2 relative energy in regards to trans-HONO Theory level
EŽTS1.
EŽTS2.
D EI
D E II
DH
B3LYPr6-31GŽd,p. B3LYPr6-31GŽd,p. Ž0 K. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ2d,2p. Ž0 K. B3LYPr6-311GŽ3df,3pd. B3LYPr6-311GŽ3df,3pd. Ž0 K. BLYPr6-31GŽd,p. BLYPr6-31GŽd,p. Ž0 K. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ2d,2p. Ž0 K. BLYPr6-311GŽ3df,3pd. BLYPr6-311GŽ3df,3pd. Ž0 K. SVWNr6-31GŽd,p. SVWNr6-31GŽd,p. Ž0 K. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ2d,2p. Ž0 K. SVWNr6-311GŽ3df,3pd. SVWNr6-311GŽ3df,3pd. Ž0 K. CBSQ Ž0 K. CBSQ
y205.607339 y205.592315 y205.674520 y205.659653 y205.686295 y205.671323 y205.602358 y205.588375 y205.671922 y205.658094 y205.682666 y205.668739 y204.613758 y204.598662 y204.682495 y204.667586 y204.694550 y204.679559
y205.656025 y205.639731 y205.720088 y205.704034 y205.730242 y205.714142 y205.646416 y205.631229 y205.713126 y205.698170 y205.722227 y205.707222 y204.658261 y204.642128 y204.724001 y204.708136 y204.734533 y204.718616
58.3 55.0 59.1 55.7 58.5 55.2 53.6 50.3 54.7 51.4 54.4 51.2 45.9 42.8 46.8 43.6 46.2 43.1 54.4 54.5
27.8 25.2 30.5 27.8 30.9 28.3 25.9 23.5 28.8 26.3 29.6 27.1 18.0 15.5 20.8 18.2 21.1 18.6 28.9 28.8
6.7 7.7 7.1 8.1 7.0 8.0 7.3 8.3 8.0 9.0 7.9 8.9 1.4 2.2 1.8 2.6 1.5 2.3 8.5 8.3
Ž0 K., sum of electronic and zero-point energies; D E I , activation barrier for HONO rearrangement into HNO 2 in kcalrmol; D E II , activation barrier for HONO isomerization into ONOH in kcalrmol.
Table 9 Total energies Ža.u.. for water molecule with its enthalpy of formation, H–OH bond dissociation energy and enthalpy for 2HNO™ H 2 O q NO q N2 O reaction Theory level
EŽH 2 O.
D Hf ŽH 2 O.
BDE III
DH
B3LYPr6-31GŽd,p. 3B3LYPr6-31GŽd,p. Ž0 K. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ2d,2p. Ž0 K. B3LYPr6-311GŽ3df,3pd. B3LYPr6-311GŽ3df,3pd. Ž0 K. BLYPr6-31GŽd,p. BLYPr6-31GŽd,p. Ž0 K. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ2d,2p. Ž0 K. BLYPr6-311GŽ3df,3pd. BLYPr6-311GŽ3df,3pd. Ž0 K. SVWNr6-31GŽd,p. SVWNr6-31GŽd,p. Ž0 K. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ2d,2p. Ž0 K. SVWNr6-311GŽ3df,3pd. SVWNr6-311GŽ3df,3pd. Ž0 K. CBSQ Ž0 K. CBSQ
y76.419737 y76.398374 y76.452118 y76.430745 y76.459416 y76.438079 y76.398884 y76.378299 y76.433307 y76.412685 y76.441606 y76.420961 y76.050468 y76.029519 y76.084700 y76.063805 y76.092641 y76.071782
y50.9 y45.1 y54.9 y49.0 y57.7 y51.9 y45.9 y40.4 y50.5 y44.8 y54.2 y48.6 y57.8 y51.9 y62.8 y56.8 y66.0 y60.1 y55.9 y56.6
119.8 111.7 121.2 113.1 123.2 115.0 120.0 112.1 121.4 113.5 123.5 115.7 140.4 132.5 141.9 134.0 144.1 136.2 117.8 119.0
12.9 9.1 11.3 7.5 9.7 5.9 18.0 14.8 16.6 13.3 14.6 11.4 35.8 32.2 33.9 30.3 32.0 28.4 7.0 8.7
Ž0 K., sum of electronic and zero-point energies; D Hf ŽH 2 O., enthalpy of formation for H 2 O in kcalrmol; BDE III , H–O bond dissociation energy for water in kcalrmol; D H, enthalpy for 2HNO™ H 2 O q NO q N2 O reaction in kcalrmol.
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B.S. Jursicr Chemical Physics Letters 299 (1999) 334–344
Table 10 Harmonic vibrational frequencies Žcmy1 ., their IR intensities ŽkMrmol. in parentheses, and moment of inertial computed with B3LYPr6-311GŽ3df,3pd. for each minima on the PES for hydrogen addition to nitrogen dioxide NO 2
cis-HONO
trans-HONO
HNO 2
769.3 Ž6.6. 1401.1 Ž0.3. 1712.6 Ž355.7.
641.4 Ž27.6. 702.6 Ž88.8. 888.6 Ž263.9. 1344.4 Ž6.3. 1725.5 Ž177.9. 3594.0 Ž17.0.
590.3 Ž85.9. 622.7 Ž119.4. 830.2 Ž132.4. 1305.6 Ž168.1. 1793.5 Ž158.5. 3779.3 Ž70.2.
800.8 Ž25.5. 1063.5 Ž19.7. 1413.9 Ž48.0. 1518.3 Ž46.0. 1672.4 Ž348.7. 3150.7 Ž10.2.
21.14446 135.61603 156.76049
19.09587 143.10146 162.19733
16.66460 136.00608 152.67069
Moment of inertia Ža.u.. 7.41046 137.67477 145.08523
DFT methods were obtained for computing the activation barrier for the 1,3-hydrogen shift through TS2. The CBSQ computed activation barrier is 28.9 kcalrmol, while the B3LYPr6-311GŽ3df,3pd. is 28.3 kcalrmol ŽTable 8.. Considering that the less stable HNO 2 isomer is made through TS1 with an activation barrier around 55 kcalrmol, this isomerization is highly unlikely to occur in gas phase, while isomerization through TS2 is experimentally feasible, and the same HONO molecule is formed. As mentioned above, the enthalpy for the 2HNO ™ H 2 O q NO q N2 O decomposition reaction in the gas phase is 9.1 kcalr2 mol. It will be interesting to see if the DFT method can correctly estimate the enthalpy for this reaction. The experimental enthalpy of formation for water at 0 K is y57.1 kcalrmol w26x. The CBSQ estimates this enthalpy to be y55.9
kcalrmol ŽTable 9.. As in the case of nitrogen oxide built compounds, the hybrid DFT computes the best enthalpy of formation of the three applied DFT methods. The best estimate is y51.9 kcalrmol, computed with the B3LYPr6-311GŽ3df,3pd. theory model ŽTable 9.. The experimental H–O bond dissociation energy for water is 119 " 1 kcalrmol w26x. The SBSQ computed energy is slightly lower Ž117.8 kcalrmol, Table 9.. As we have already mentioned above, the most reliable DFT method is the B3LYP and the estimated bond dissociation energies are 2–3 kcalrmol lower than the CBSQ evaluated bond dissociation energies. That is also true for the H–O bond dissociation energy. The B3LYPr6311GŽ3df,3pd. evaluated bond dissociation energy is 115.0 kcalrmol ŽTable 9.. For the 2HNO™ H 2 O q NO q N2 O decomposition reaction, the CBSQ esti-
Table 11 Harmonic vibrational frequencies Žcmy1 ., their IR intensities ŽkMrmol. in parentheses, and moment of inertial computed with BLYPr6-311GŽ3df,3pd. for each minima on the PES for hydrogen addition to nitrogen dioxide NO 2
cis-HONO
trans-HONO
HNO 2
733.2 Ž5.3. 1302.5 Ž0.1. 1586.2 Ž266.0.
514.0 Ž68.2. 660.7 Ž76.9. 779.9 Ž186.5. 1254.5 Ž4.5. 1640.0 Ž178.4. 3464.7 Ž10.6.
510.5 Ž132.0. 570.2 Ž73.0. 741.6 Ž73.2. 1209.0 Ž137.3. 1716.4 Ž184.7. 3633.2 Ž47.9.
757.7 Ž20.7. 998.3 Ž19.9. 1318.6 Ž45.2. 1455.8 Ž37.2. 1544.4 Ž278.7. 2999.0 Ž26.2.
21.98596 144.20415 166.19012
20.26936 152.69172 172.96108
17.06299 140.49124 157.55423
Moment of inertia Ža.u.. 7.88058 141.71305 149.59363
B.S. Jursicr Chemical Physics Letters 299 (1999) 334–344
343
Table 12 Harmonic vibrational frequencies Žcmy1 ., their IR intensities ŽkMrmol. in parentheses, and moment of inertial computed by using 6-311GŽ3df,3pd. for three of the transition state structure on the PES for hydrogen addition to nitrogen dioxide TSr
TS1
TS2
BLYP
B3LYP
B3LYP
BLYP
B3LYP
BLYP
648.3i Ž87.2. 557.4 Ž124.0. 796.7 Ž152.6. 1078.0 Ž41.0. 1809.5 Ž203.4. 3767.6 Ž62.1. Moment of inertia Ža.u.. 21.61646 149.81713 165.66796
694.6i Ž77.4. 473.1 Ž106.8. 722.9 Ž118.2. 983.7 Ž37.0. 1743.7 Ž217.6. 3630.0 Ž41.8.
2086.3i Ž257.6. 507.5 Ž38.4. 704.6 Ž18.4. 1277.5 Ž174.2. 1631.2 Ž304.8. 2451.4 Ž28.8.
1915.5i Ž216.2. 506.3 Ž33.5. 641.2 Ž17.3. 1149.6 Ž153.5. 1517.1 Ž236.2. 2299.2 Ž11.1.
y1908.1i Ž177.1. 1025.4 Ž3.5. 1240.2 Ž66.8. 1300.8 Ž7.5. 1397.6 Ž334.8. 2102.9 Ž24.0.
1737.9i Ž158.4. 961.0 Ž1.7. 1177.7 Ž3.1. 1184.9 Ž53.5. 266.7 Ž266.7. 1968.1 Ž10.7.
22.60120 160.99465 177.59256
16.36148 141.23736 157.59883
17.11787 146.62907 163.74694
24.13850 114.23814 138.37664
24.98458 118.19684 143.18143
mates an endothermicity of 7.0 kcalrmol, which is slightly higher than the experimental value of 4.6 kcalrmol. In this case, the B3LYPr6-311GŽ3df,3pd. is actually closer to the experimental value Ž5.9 kcalrmol, Table 9.. For all stationary points on the H q NO 2 PES, the harmonic frequencies and moment of inertia were generated with the target being that they can be used for RRKM calculations. In some of our previous computational studies we have demonstrated that gradient-corrected BLYP density functional methods produce harmonic frequencies that are almost identical to the experimental values w28–30x. For the ground state, minima values are presented in Tables 10 and 11, and for transition state structures, the harmonic frequencies are presented in Table 12. All transition state structures have one imaginary frequency, which motion connects two minima on the PES for the H q NO 2 reaction.
4. Conclusion From an extensive DFT method exploring the PES for HONO chemical systems, it can be concluded that the complete basis set ab initio method is producing energies that are almost identical to the experimental values and in fact, in some cases, it was suggested that the experimental enthalpies of formation are 1–2 kcalrmol too high. The best agreement with experimental geometries, as well as
enthalpies of formation, enthalpies of reaction, bond dissociation energies, and reaction barriers were obtained with the hybrid B3LYP density functional method. While satisfied geometries can be obtained with a relatively modest basis set, such as 6-31GŽd,p. and 6-311GŽ2d,2p. for a more accurate evaluation of energies, a larger basis set, such as 6-311GŽ3df,3pd., is required. Computed energies with this theory model should be in the 2–3 kcalrmol range from the CBSQ ab initio or experimental values. Therefore, we are recommending the B3LYPr6-311GŽ3df,3pd. theory model as a reliable model for exploring the PES for chemical systems built from nitrogen, oxygen, and hydrogen. References w1x J. March, Advanced Organic Chemistry, Reaction Mechanisms, and Structure, 4th edition, Wiley, New York, 1992. w2x N.N. Greenwood, E. Earnshaw, Chemistry of the Elements, Pergamon Press, Oxford, 1984. w3x B.S. Jursic, Chem. Phys. Lett. 236 Ž1995. 206. w4x B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 365 Ž1995. 47. w5x B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 366 Ž1996. 97. w6x B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 389 Ž1997. 75. w7x B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 389 Ž1997. 251. w8x B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 418 Ž1997. 165. w9x B.S. Jursic, R. Martin, Int. J. Quantum Chem. 59 Ž1996. 495. w10x B.S. Jursic, J.W. Timberlake, P.S. Engel, Tetrahedron Lett. 37 Ž1996. 97. w11x B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 366 Ž1996. 103. w12x B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 370 Ž1996. 65. w13x B.S. Jursic, Int. J. Quantum Chem. 62 Ž1997. 291.
344 w14x w15x w16x w17x
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B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 422 Ž1998. 253. B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 391 Ž1997. 75. B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 417 Ž1997. 99. B.S. Jursic, Computing transition state structures with density functional theory methods, in: J.H. Seminario ŽEd.., Recent Developments and Applications of Modern Density Functional Theory, Elsevier, Amsterdam, 1996, p. 709. w18x B.S. Jursic, Int. J. Quantum. Chem. in press. w19x B.S. Jursic, Chem. Phys. in press. w20x GAUSSIAN 94, Revision B.3, M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P.
w21x w22x w23x w24x w25x
w26x w27x w28x w29x w30x
Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, Gaussian, Pittsburgh, PA, 1995. A.D. Becke, J. Chem. Phys. 98 Ž1993. 5648. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 Ž1988. 785. A.D. Becke, Phys. Rev. A 38 Ž1988. 3098. S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 Ž1980. 1200. J.B. Foresman, Æ. Frisch, Exploring Chemistry with Electronic Structure Methods, 2nd edition, Gaussian, Pittsburgh, PA, 1996. CRC Handbook of Chemistry and Physics, 67th edition, CRC Press, Boca Raton, FL, 1987. T.J. Lee, C.E. Dateo, J. Chem. Phys. 103 Ž1995. 9110. B.S. Jursic, Int. J. Quantum Chem. 64 Ž1997. 263. B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 394 Ž1997. 15. B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 428 Ž1998. 61.
Chemical Physics Letters 299 Ž1999. 334–344
Density functional theory exploring the HONO potential energy surface Branko S. Jursic
)
Department of Chemistry, UniÕersity of New Orleans, New Orleans, LA 70148, USA Received 5 August 1998; in final form 5 October 1998
Abstract The potential energy surface was carefully explored for the HONO molecular system with hybrid, gradient-corrected, and local spin density approximation. Computed geometries, relative energies, activation barriers, enthalpies of formation, and bond dissociation energies for this molecular species, as well as for related molecules, were calculated and compared with experimental and the complete basis set obtained values. The harmonic frequencies with the moment of inertia for all stationary points on the potential energy surface were calculated with both gradient-corrected and hybrid density functional theory methods. The reliability of the density functional theory method for exploring the small polar nitrogen system was discussed. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction There is considerable interest in exploring the structural and energetic properties of nitrous acid due to its presence in combustion as well as atmospheric chemistry. This compound is a well-known source of NOq electrophiles in organic synthetic chemistry w1x. Nitrous acid is very unstable in its pure form, but it is a well-known and important reagent in aqueous solutions and has been extensively investigated in the gas phase w2x. In the gas phase, equilibrium of the HONO decomposition with the formation of equimolar amounts of water, nitric oxide, and nitrogen ) Corresponding author. Fax: q1 504 280 6860; e-mail: [email protected]
dioxide can be reached. It was estimated that the enthalpy for this reaction is 38 kJr2 mol HNO 2 w2x. From microwave spectroscopy we know that in the gaseous phase nitrous acid is predominantly in the trans form. The structural parameters are r HO s ˚ r HO – N s 1.433 A, ˚ r NO s 1.177 A, ˚ aHON s 0.954 A, 102.18, aON O s 110.78 w2x. From the infrared data it was suggested that the cis form is only 0.5 kcalrmol higher in energy than trans-HONO. Although the HO–N bond should have a single-bond character, the rotational barrier is experimentally estimated to be 10.8 kcalrmol. We have previously demonstrated that density functional theory ŽDFT. methods are exceptionally accurate for computing structural parameters of small polar molecular systems w3–8x, their bond dissocia-
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 8 . 0 1 2 7 4 - 3
B.S. Jursicr Chemical Physics Letters 299 (1999) 334–344
tion energies w9–14x and, in some cases, isodesmic enthalpies of formation w15,16x. Furthermore, we have demonstrated that some of the DFT methods are highly accurate for the evaluation of the reaction activation barriers w17,18x. This particular chemical system, along with some other similar structures, were previously studied with highly accurate complete basis set ab initio methods w19x. Therefore, all structural and energetic properties of these molecular systems are well known, and these results will be used for the evaluation of the accuracy of three commonly used DFT methods used in exploring the potential energy surface ŽPES. of nitrous acid and the DFT applicability to larger organic molecular systems, which also includes the ONO molecular unit.
2. Computational methods All calculations were performed with the GAUSSIAN 94 computational package w20x. Three commonly used DFT methods are used: the B3LYP hybrid w21,22x, the BLYP gradient-corrected w22,23x, and SVWN local spin density approximation w24x. For all calculations, three gaussian-type basis sets Ž6-31GŽd,p., 6-311GŽ2d,2p., and 6-311GŽ3df,3pd.. were used. For their explanations see Ref. w25x.
3. Results and discussion As mentioned above, there are two isomers of HONO because the HO–N bond has a partially double-bond character. The isomers include cisHONO and trans-HONO. Structural parameters for the trans-HONO are available and they are listed in Table 1. Computed structural parameters for cisHONO, trans-HONO, as well as rotational transition state ŽTSr. for cis–trans isomerization are also presented in Table 1. In general, the hybrid B3LYP with a large basis set is accurate for the computed structural parameters of small chemical systems w9–14x. The computed geometries differ by less than 1% from the experimental values. This deviation is usually in the margins of the experimental error. The same is true for the trans-HONO geometry com-
335
puted with the B3LYPr6-311GŽ2d,2p. theory level. The highest deviation between the experimental and the computed HONO structure is an estimated H–O ˚ and bond distance Žthe experimental value is 0.954 A ˚ .. Other values are almost the computed is 0.966 A identical to the experimental values. The BLYP gradient-corrected trans-HONO structure is slightly more off and SVWN produces the trans-HONO geometry that deviates the most from the experimental values ŽTable 1.. The structural parameters for the cis-HONO and of course, for the rotational HONO are not available. We believe that the B3LYPr6311GŽ2d,2p. computed geometries are the ones that are the most accurate. Therefore, the cis-HONO ˚ r HO – N s 1.390 structure should have r HO s 0.97 A, ˚ r NO s 1.180, aHON s 105.48 and a ONO s 110.98. A, The structure of the rotational HONO transition state is exactly what is expected on the basis of the general knowledge of the transition state theory. The dihedral angle is very close to 908 ŽTable 1.. Experimental data for the rotational barrier and the relative stability of the cis-HONO are available Ž10.8 kcalrmol. w2x. Total energies for the molecular species on the PES for the rotation around HO–NO bond are as listed in Table 1. This PES was previously explored with a highly reliable complete basis set ab initio method w19x. The estimated rotational barrier of 11.3 kcalrmol is only slightly higher than the experimental value. The DFT method estimates the rotational barrier to be slightly higher ŽTable 2.. The best estimate came from the most accurate density functional method with an extended basis set. Thus, the hybrid B3LYPr6-311GŽ3df,3pd. theory model estimates the same rotational barrier of 11.3 kcalrmol as the CBSQ method. An almost identical activation barrier was obtained with the same basis set, but now with the gradient-corrected BLYP density functional method ŽTable 2., while the local spin density DFT method overestimates the rotational barrier. All DFT methods suggest that the cis-HONO and trans-HONO have very similar energies. Actually, the B3LYPr6-311GŽ3df,3pd. estimates that their energy difference is zero, while the CBSQ estimates that the trans-HONO is slightly more stable ŽTable 2.. This is in agreement with both experimental data, as well as with the gradient-corrected BLYPr6-311GŽ3df,3pd. suggested preference ŽTable 2..
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Table 1 Structural parameters for trans-HONO and cis-HONO and rotational transition state structure computed with DFT methods Theory level trans-HONO B3LYPr6-31GŽd,p. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ3df,3pd. BLYPr6-31GŽd,p. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ3df,3pd. SVWNr6-31GŽd,p. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ3df,3pd. Experimental cis-HONO B3LYPr6-31GŽd,p. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ3df,3pd. BLYPr6-31GŽd,p. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ3df,3pd. SVWNr6-31GŽd,p. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ3df,3pd. TSr B3LYPr6-31GŽd,p. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ3df,3pd. BLYPr6-31GŽd,p. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ3df,3pd. SVWNr6-31GŽd,p. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ3df,3pd.
r HO ˚. ŽA
r HO – N ˚. ŽA
r NO ˚. ŽA
aHON Ž8.
aONO Ž8.
d HONO Ž8.
0.972 0.966 0.966 0.984 0.978 0.977 0.982 0.977 0.977 0.954
1.426 1.433 1.430 1.499 1.509 1.508 1.415 1.420 1.416 1.433
1.179 1.166 1.163 1.188 1.175 1.171 1.180 1.167 1.164 1.177
102.4 102.0 102.5 100.6 100.3 100.8 101.6 101.3 101.7 102.1
110.6 110.9 111.0 110.4 110.8 110.7 110.7 111.0 111.0 110.7
180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0
0.983 0.978 0.978 0.995 0.988 0.987 0.999 0.993 0.993
1.385 1.390 1.387 1.444 1.453 1.452 1.364 1.368 1.364
1.191 1.180 1.176 1.203 1.190 1.186 1.195 1.183 1.179
105.4 105.4 105.8 104.4 104.3 104.9 104.0 104.1 104.6
113.2 113.6 113.7 112.2 113.6 113.7 112.9 113.4 113.6
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.973 0.968 0.967 0.984 0.978 0.977 0.981 0.977 0.976
1.491 1.502 1.500 1.567 1.582 1.584 1.465 1.477 1.474
1.170 1.156 1.153 1.179 1.164 1.160 1.173 1.158 1.155
104.0 103.8 104.4 102.0 101.9 102.7 104.7 104.2 104.8
111.2 111.4 111.5 111.2 111.3 111.4 111.4 111.5 111.6
88.1 88.0 87.8 88.3 88.2 88.0 88.6 88.6 88.6
r, bond distances in angstrom; a, bond angles in degrees.
The computation of the enthalpy of formation directly from its building elements is a very important computational approach, because enthalpies of formation are broadly used throughout various research fields. Sometimes it is almost impossible to obtain enthalpies of formation for small nitrogen oxide derivatives due to their instability. Our best estimate of the enthalpy of formation for the transHONO comes from complete basis set ab initio studies w19x. The value is y18.4 kcalrmol at 0 K, which is 0.9 kcalrmol lower than the experimental value of y19.3 kcalrmol w26x. There is some evidence that for nitrogen oxide derivatives the experimental heat of formation should be corrected by
approximately 1–2 kcalrmol w27x. We believe that the enthalpy of formation for the trans-HONO should be y18.4 kcalrmol, as calculated with the complete basis set ab initio method w19x. To our surprise, the otherwise very accurate DFT method, hybrid B3LYP, estimated an enthalpy of formation that differed by 3–5 kcalrmol from this value. With the use of a higher basis set the estimated enthalpy of formation is closer to the expected value. Thus, D Hf at 0 K for trans-HONO is estimated with B3LYPr6311GŽ3df,3pd. to be y15.0 kcalrmol. Again, the best estimate comes from the gradient BLYPr6311GŽ3df.3pd.. The estimated enthalpy of formation is y18.5 kcalrmol at 0 K ŽTable 3.. Local spin
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337
Table 2 Total energies Ža.u.. for cis-HONO, trans-HONO, and rotational transition state structure ŽTSr. with rotational barrier Ž D E, kcalrmol., and energy difference between cis-HONO and trans-HONO Ž D H, kcalrmol. Theory level
EŽ trans-HONO.
EŽ cis-HONO.
EŽTSr.
DE
DH
B3LYPr6-31GŽd,p. B3LYPr6-31GŽd,p. Ž0 K. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ2d,2p. Ž0 K. B3LYPr6-311GŽ3df,3pd. B3LYPr6-311GŽ3df,3pd. Ž0 K. BLYPr6-31GŽd,p. BLYPr6-31GŽd,p. Ž0 K. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ2d,2p. Ž0 K. BLYPr6-311GŽ3df,3pd. BLYPr6-311GŽ3df,3pd. Ž0 K. SVWNr6-31GŽd,p. SVWNr6-31GŽd,p. Ž0 K. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ2d,2p. Ž0 K. SVWNr6-311GŽ3df,3pd. SVWNr6-311GŽ3df,3pd. Ž0 K. CBSQ Ž0 K. CBSQ
y205.700306 y205.679926 y205.768695 y205.748356 y205.779541 y205.759216 y205.687712 y205.668611 y205.759099 y205.740010 y205.769435 y205.750343 y204.686947 y204.666894 y204.757087 y204.737085 y204.768206 y204.748206
y205.701723 y205.681317 y205.769291 y205.748987 y205.779495 y205.759228 y205.688060 y205.669008 y205.758667 y205.739693 y205.768183 y205.749243 y204.689374 y204.669408 y204.758629 y204.738758 y204.769238 y204.749387
y205.679002 y205.660743 y205.748156 y205.729938 y205.759521 y205.741275 y205.665077 y205.647915 y205.737483 y205.720342 y205.748655 y205.731447 y204.661101 y204.643178 y204.732281 y204.714407 y204.744159 y204.726254
14.3 12.9 13.3 12.0 12.5 11.3 14.4 13.2 13.3 12.1 12.3 11.2 17.7 16.5 16.5 15.3 15.7 14.5 11.3 10.9
y0.9 y0.8 y0.4 y0.4 0.0 0.0 y0.2 y0.2 0.3 0.2 0.8 0.7 y1.5 y1.6 y1.0 y1.0 y0.6 y0.7 0.5 0.5
Ž0 K., Sum of electronic and zero-point energies.
Table 3 Total energies Ža.u.. for hydrogen, oxygen and nitrogen molecules with estimated enthalpy of formation for trans-HONO Ž D Hf , kcalrmol. Theory level
EŽH 2 .
EŽN2 .
EŽO 2 .
D Hf
B3LYPr6-31GŽd,p. B3LYPr6-31GŽd,p. Ž0 K. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ2d,2p. Ž0 K. B3LYPr6-311GŽ3df,3pd. B3LYPr6-311GŽ3df,3pd. Ž0 K. BLYPr6-31GŽd,p. BLYPr6-31GŽd,p. Ž0 K. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ2d,2p. Ž0 K. BLYPr6-311GŽ3df,3pd. BLYPr6-311GŽ3df,3pd. Ž0 K. SVWNr6-31GŽd,p. SVWNr6-31GŽd,p. Ž0 K. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ2d,2p. Ž0 K. SVWNr6-311GŽ3df,3pd. SVWNr6-311GŽ3df,3pd. Ž0 K. CBSQ Ž0 K. CBSQ
y1.178539 y1.168366 y1.180013 y1.169940 y1.180034 y1.169985 y1.167912 y1.157901 y1.169601 y1.159707 y1.169611 y1.159726 y1.171246 y1.161567 y1.172710 y1.163124 y1.172728 y1.163159
y109.524129 y109.518532 y109.559893 y109.554338 y109.564553 y109.558970 y109.510648 y109.505327 y109.547371 y109.542086 y109.552102 y109.546778 y108.915140 y108.909656 y108.951860 y108.946401 y108.956657 y108.951168
y150.320038 y150.316259 y150.369073 y150.365344 y150.374583 y150.370808 y150.315425 y150.311969 y150.366327 y150.362917 y150.371111 y150.367664 y149.574307 y149.570555 y149.623899 y149.620203 y149.629527 y149.625786
y18.2 y12.7 y18.6 y13.1 y20.5 y15.0 y20.7 y15.7 y21.5 y16.4 y23.5 y18.5 y43.6 y38.1 y44.5 y39.0 y46.4 y40.9 y18.4 y20.0
Ž0 K., Sum of electronic and zero-point energies.
338
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density approximation should be avoided for computing the enthalpy of formation directly from the elements because the computed values differ by more than 20 kcalrmol from the expected value ŽTable 3.. In the solution, the heterolitic H–O bond dissociation energy is occurring easily due to strong solvation of both ions. In the gas phase, this process is energetically highly unlikely, and homolytic bond breaking with the formation of H and NO 2 radicals are predominate. This bond dissociation energy was estimated to be 76.4 kcalrmol at 0 K. None of the DFT methods generates exactly the same value, but the hybrid DFT method estimates a bond dissociation energy that is ; 3 kcalrmol below the CBSQ estimated values ŽTable 4.. Better agreement was obtained for the computed NO 2 heat of formation. Again the CBSQ computed value of 5.7 kcalrmol is lower than the experimental value of 8.6 kcalrmol. Our B3LYP computed value is somewhere between these to values. The best estimate, given by B3LYPr6-311GŽ3df,3pd., is 6.5 kcalrmol ŽTable 4.. Again, we have demonstrated that the hybrid DFT method produces reliable energies. The other
two DFT methods produce enthalpies of formation that substantially deviate from the experimental value ŽTable 4.. Let us now evaluate the heats of formation for the HO and NO radicals formed by the HO–NO bond breaking. Considering the fact that the radical is better stabilized by oxygen atoms than by hydrogen atoms, it is reasonable to expect that the HO–NO bond dissociation energy should be substantially smaller than the H–ONO bond dissociation energy. In fact, the CBSQ estimated bond dissociation energy is 48.5 kcalrmol. The hybrid B3LYP ab initio method computed bond dissociation energies are the closest to the CBS values. The best estimated value is 47.4 kcalrmol, which is only 1.1 kcalrmol below the CBSQ computed value ŽTable 5.. The enthalpies of formation for both HO and NO radicals are experimentally available. The value for OH is 9.3 kcalrmol w26x. The CBSQ computed enthalpy of formation is slightly higher Ž9.7 kcalrmol. while the B3LYPr6-311GŽ3df,3pd. is even higher Ž11.1 kcalrmol. ŽTable 1.. The other two DFT methods compute even higher HO enthalpies of formation. In
Table 4 Structural properties for NO 2 , total energies Ža.u.. for hydrogen radical and nitrogen dioxide with the H–ONO bond dissociation energy ŽBDE I . and the NO 2 enthalpy of formation Ž D Hf , kcalrmol. Theory level
r ˚. ŽA
a Ž8.
EŽH.
EŽNO 2 .
BDE I
D Hf
B3LYPr6-31GŽd,p. B3LYPr6-31GŽd,p. Ž0 K. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ2d,2p. Ž0 K. B3LYPr6-311GŽ3df,3pd. B3LYPr6-311GŽ3df,3pd. Ž0 K. BLYPr6-31GŽd,p. BLYPr6-31GŽd,p. Ž0 K. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ2d,2p. Ž0 K. BLYPr6-311GŽ3df,3pd. BLYPr6-311GŽ3df,3pd. Ž0 K. SVWNr6-31GŽd,p. SVWNr6-31GŽd,p. Ž0 K. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ2d,2p. Ž0 K. SVWNr6-311GŽ3df,3pd. SVWNr6-311GŽ3df,3pd. Ž0 K. CBSQ Ž0 K. CBSQ
1.203
133.8
1.195
134.1
1.191
134.4
1.224
133.1
1.216
133.5
1.211
133.7
1.202
133.8
1.193
134.1
1.189
134.3
y0.5002728 y0.5002728 y0.5021559 y0.5021559 y0.5021559 y0.5021559 y0.4954462 y0.4954462 y0.4975548 y0.4975548 y0.4975548 y0.4975548 y0.4939369 y0.4939369 y0.4961136 y0.4961136 y0.4961136 y0.4961136
y205.072205 y205.063384 y205.137751 y205.129025 y205.148727 y205.139880 y205.068881 y205.060668 y205.136636 y205.128513 y205.146621 y205.138370 y204.056931 y204.047982 y204.123773 y204.114913 y204.135070 y204.126090
80.2 73.0 80.8 73.5 80.7 73.5 77.4 70.6 78.4 71.5 78.6 71.8 85.4 78.4 86.1 79.1 86.0 79.1 76.4 77.7
6.2 7.6 7.1 8.5 5.1 6.5 1.2 2.5 2.1 3.4 0.3 1.7 y15.7 y14.2 y15.0 y13.5 y17.1 y15.5 5.7 5.0
r, N–O bond distance in NO 2 ; a, ONO bond angle in NO 2 ; Ž0 K., sum of electronic and zero-point energies.
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Table 5 Total energies Ža.u.. for hydroxy radical and nitric oxide with their heats of formation and HO–NO bond dissociation energy Theory level
EŽOH.
EŽNO.
D Hf ŽHO.
D Hf ŽNO.
BDE II
B3LYPr6-31GŽd,p. 3B3LYPr6-31GŽd,p. Ž0 K. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ2d,2p. Ž0 K. B3LYPr6-311GŽ3df,3pd. B3LYPr6-311GŽ3df,3pd. Ž0 K. BLYPr6-31GŽd,p. BLYPr6-31GŽd,p. Ž0 K. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ2d,2p. Ž0 K. BLYPr6-311GŽ3df,3pd. BLYPr6-311GŽ3df,3pd. Ž0 K. SVWNr6-31GŽd,p. SVWNr6-31GŽd,p. Ž0 K. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ2d,2p. Ž0 K. SVWNr6-311GŽ3df,3pd. SVWNr6-311GŽ3df,3pd. Ž0 K. CBSQ Ž0 K. CBSQ
y75.728482 y75.720066 y75.756862 y75.748418 y75.761153 y75.752680 y75.712256 y75.704196 y75.742350 y75.734254 y75.747240 y75.739091 y75.332730 y75.324478 y75.362388 y75.354138 y75.366926 y75.358636
y129.888155 y129.883618 y129.929501 y129.925023 y129.935522 y129.930991 y129.878985 y129.874746 y129.921803 y129.917619 y129.927430 y129.923188 y129.209462 y129.204979 y129.251624 y129.247189 y129.257717 y129.253227
13.1 14.0 11.1 12.1 10.1 11.1 18.5 19.3 16.1 17.0 14.5 15.4 25.1 26.1 22.5 23.5 21.5 22.5 9.7 9.9
21.2 21.2 22.0 21.8 21.4 21.3 21.4 21.3 22.0 21.9 21.4 21.4 22.1 22.0 22.8 22.7 22.2 22.1 20.3 20.3
52.5 47.8 51.7 47.0 52.0 47.4 60.5 56.3 60.0 55.3 59.5 53.3 90.8 86.2 89.8 85.2 90.1 85.6 48.5 50.0
Ž0 K., sum of electronic and zero-point energies; D Hf ŽHO., enthalpy of formation for HO in kcalrmol; D Hf ŽNO., enthalpy of formation for NO in kcalrmol; BDE II , HO–NO bond dissociation energy in kcalrmol.
the case of NO, it was experimentally estimated that its enthalpy of formation is 21.5 kcalrmol. The CBSQ estimated value is 1 kcalrmol lower. Our DFT generated enthalpy of formation for NO is actually closer to the experimental value than to the CBSQ value. For instance, the B3LYPr6311GŽ3df,3pd. estimates the enthalpy of formation for NO to be 21.3 kcalrmol, which is 0.2 kcalrmol below the experimental value ŽTable 5.. There is one other isomer of HONO that should be computationally explored, and it is the HNO 2 isomer. Structural parameters, total energy with the heats of formation, and the H–N bond dissociation energies are presented in Table 6. The geometry has ˚ r NO s 1.212 A, ˚ C 2v symmetry with r HN s 1.042 A, and a HN O s 115.8 ŽTable 6. as computed with the B3LYPr6-311GŽ3df,3pd. theory model. The CBSQ computed enthalpy of formation for HNO 2 is y10 kcalrmol. The hybrid DFT method computes an acceptable enthalpy of formation, but it is the BLYPr6-311GŽ3df,3pd. that computes the best HNO 2 enthalpy of formation ŽTable 6., which is the estimated value of y9.6 kcalrmol. The estimated H–N bond dissociation energy is 79.0 kcalrmol
with the B3LYPr6-311GŽ3df,3pd. computed value at 65.7 kcalrmol. The HONO can isomerize into the HNO 2 isomer through 1,2-hydrogen shift or into itself through 1,3-hydrogen shift. The DFT computed structural parameters for those two transition state structures; TS1 and TS2 are presented in Table 7. Both of the transition state structures are what would be expected on the basis of the transition state theory. The H–O bond distance is slightly longer than the H–N bond distance in TS1, indicating that the transition state TS1 is closer in geometry to HNO 2 than to HONO. This suggests that the activation barrier for the HNO 2 rearrangement into HONO is smaller than the reverse rearrangement. In fact, the HONO is 8.5 kcalrmol more stable than the HNO 2 . This is also confirmed with the B3LYPr6-311GŽ3df,3pd. calculation, generating the energy difference of 8.0 kcalrmol ŽTable 8.. The activation barrier for 1,2hydrogen shift through TS1 is estimated by the CBSQ to be 54.4 kcalrmol, which is in excellent agreement with the 55.2 kcalrmol computed with the B3LYPr6-311GŽ3df,3pd. theory level. Similar agreement between the CBSQ and B3LYP hybrid
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Table 6 Computed structural parameters, total energy Ža.u.. enthalpy of formation and H–NO 2 bond dissociation energy for HNO 2 Theory level
r1
r2
a1
a2
EŽHNO 2 .
D Hf
BDE III
B3LYPr6-31GŽd,p. B3LYPr6-31GŽd,p. Ž0 K. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ2d,2p. Ž0 K. B3LYPr6-311GŽ3df,3pd. B3LYPr6-311GŽ3df,3pd. Ž0 K. BLYPr6-31GŽd,p. BLYPr6-31GŽd,p. Ž0 K. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ2d,2p. Ž0 K. BLYPr6-311GŽ3df,3pd. BLYPr6-311GŽ3df,3pd. Ž0 K. SVWNr6-31GŽd,p. SVWNr6-31GŽd,p. Ž0 K. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ2d,2p. Ž0 K. SVWNr6-311GŽ3df,3pd. SVWNr6-311GŽ3df,3pd. Ž0 K. CBSQ Ž0 K. CBSQ
1.044
1.222
115.8
128.5
1.040
1.216
115.7
128.5
1.042
1.212
115.8
128.4
1.056
1.241
115.7
128.7
1.051
1.235
115.7
128.7
1.052
1.231
115.7
128.7
1.059
1.219
115.8
128.5
1.055
1.211
115.7
128.6
1.057
1.208
115.7
128.5
y205.689680 y205.667716 y205.757324 y205.735438 y205.768450 y205.746535 y205.676098 y205.655431 y205.746330 y205.725720 y205.756897 y205.736225 y204.684783 y204.663355 y204.754226 y204.732888 y204.765856 y204.744486
y11.5 y5.0 y11.5 y5.0 y13.5 y7.1 y13.4 y7.4 y13.5 y7.5 y15.6 y9.6 y42.2 y35.9 y42.7 y36.3 y45.0 y38.6 y10.0 y11.7
73.5 65.3 73.7 65.4 73.8 65.6 70.1 62.3 70.4 62.5 70.7 62.9 84.0 76.2 84.3 76.5 84.5 76.7 70.0 71.4
Ž0 K., sum of electronic and zero-point energies; D Hf , enthalpy of formation for HNO 2 in kcalrmol; BDE III , H–N bond dissociation energy for HNO 2 in kcalrmol.
Table 7 Structural parameters of TS1 and TS2 computed with DFT methods
ArI ArII ArIII BrI BrII BrIII CrI CrII CrIII
r1
r2
r3
r4
a1
a2
r5
r6
a3
a4
1.300 1.300 1.297 1.324 1.324 1.321 1.305 1.304 1.301
1.179 1.185 1.185 1.192 1.197 1.198 1.190 1.198 1.199
1.320 1.317 1.313 1.355 1.352 1.347 1.318 1.314 1.310
1.198 1.188 1.184 1.216 1.205 1.201 1.196 1.185 1.182
53.5 53.8 54.0 52.8 53.1 53.3 54.0 54.5 54.7
123.4 123.5 123.4 123.1 123.1 123.0 122.7 122.8 122.7
1.302 1.304 1.308 1.325 1.332 1.332 1.309 1.318 1.318
1.266 1.260 1.256 1.288 1.282 1.277 1.261 1.254 1.250
77.3 77.4 77.4 77.3 77.4 77.4 77.1 77.4 77.4
104.8 105.3 105.6 104.7 105.3 105.6 105.5 106.2 106.4
r, bond distances in angstrom; a, bond angles in degrees.
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Table 8 Total energies Ža.u.. for TS1 and TS2 with their activation energies and HNO 2 relative energy in regards to trans-HONO Theory level
EŽTS1.
EŽTS2.
D EI
D E II
DH
B3LYPr6-31GŽd,p. B3LYPr6-31GŽd,p. Ž0 K. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ2d,2p. Ž0 K. B3LYPr6-311GŽ3df,3pd. B3LYPr6-311GŽ3df,3pd. Ž0 K. BLYPr6-31GŽd,p. BLYPr6-31GŽd,p. Ž0 K. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ2d,2p. Ž0 K. BLYPr6-311GŽ3df,3pd. BLYPr6-311GŽ3df,3pd. Ž0 K. SVWNr6-31GŽd,p. SVWNr6-31GŽd,p. Ž0 K. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ2d,2p. Ž0 K. SVWNr6-311GŽ3df,3pd. SVWNr6-311GŽ3df,3pd. Ž0 K. CBSQ Ž0 K. CBSQ
y205.607339 y205.592315 y205.674520 y205.659653 y205.686295 y205.671323 y205.602358 y205.588375 y205.671922 y205.658094 y205.682666 y205.668739 y204.613758 y204.598662 y204.682495 y204.667586 y204.694550 y204.679559
y205.656025 y205.639731 y205.720088 y205.704034 y205.730242 y205.714142 y205.646416 y205.631229 y205.713126 y205.698170 y205.722227 y205.707222 y204.658261 y204.642128 y204.724001 y204.708136 y204.734533 y204.718616
58.3 55.0 59.1 55.7 58.5 55.2 53.6 50.3 54.7 51.4 54.4 51.2 45.9 42.8 46.8 43.6 46.2 43.1 54.4 54.5
27.8 25.2 30.5 27.8 30.9 28.3 25.9 23.5 28.8 26.3 29.6 27.1 18.0 15.5 20.8 18.2 21.1 18.6 28.9 28.8
6.7 7.7 7.1 8.1 7.0 8.0 7.3 8.3 8.0 9.0 7.9 8.9 1.4 2.2 1.8 2.6 1.5 2.3 8.5 8.3
Ž0 K., sum of electronic and zero-point energies; D E I , activation barrier for HONO rearrangement into HNO 2 in kcalrmol; D E II , activation barrier for HONO isomerization into ONOH in kcalrmol.
Table 9 Total energies Ža.u.. for water molecule with its enthalpy of formation, H–OH bond dissociation energy and enthalpy for 2HNO™ H 2 O q NO q N2 O reaction Theory level
EŽH 2 O.
D Hf ŽH 2 O.
BDE III
DH
B3LYPr6-31GŽd,p. 3B3LYPr6-31GŽd,p. Ž0 K. B3LYPr6-311GŽ2d,2p. B3LYPr6-311GŽ2d,2p. Ž0 K. B3LYPr6-311GŽ3df,3pd. B3LYPr6-311GŽ3df,3pd. Ž0 K. BLYPr6-31GŽd,p. BLYPr6-31GŽd,p. Ž0 K. BLYPr6-311GŽ2d,2p. BLYPr6-311GŽ2d,2p. Ž0 K. BLYPr6-311GŽ3df,3pd. BLYPr6-311GŽ3df,3pd. Ž0 K. SVWNr6-31GŽd,p. SVWNr6-31GŽd,p. Ž0 K. SVWNr6-311GŽ2d,2p. SVWNr6-311GŽ2d,2p. Ž0 K. SVWNr6-311GŽ3df,3pd. SVWNr6-311GŽ3df,3pd. Ž0 K. CBSQ Ž0 K. CBSQ
y76.419737 y76.398374 y76.452118 y76.430745 y76.459416 y76.438079 y76.398884 y76.378299 y76.433307 y76.412685 y76.441606 y76.420961 y76.050468 y76.029519 y76.084700 y76.063805 y76.092641 y76.071782
y50.9 y45.1 y54.9 y49.0 y57.7 y51.9 y45.9 y40.4 y50.5 y44.8 y54.2 y48.6 y57.8 y51.9 y62.8 y56.8 y66.0 y60.1 y55.9 y56.6
119.8 111.7 121.2 113.1 123.2 115.0 120.0 112.1 121.4 113.5 123.5 115.7 140.4 132.5 141.9 134.0 144.1 136.2 117.8 119.0
12.9 9.1 11.3 7.5 9.7 5.9 18.0 14.8 16.6 13.3 14.6 11.4 35.8 32.2 33.9 30.3 32.0 28.4 7.0 8.7
Ž0 K., sum of electronic and zero-point energies; D Hf ŽH 2 O., enthalpy of formation for H 2 O in kcalrmol; BDE III , H–O bond dissociation energy for water in kcalrmol; D H, enthalpy for 2HNO™ H 2 O q NO q N2 O reaction in kcalrmol.
342
B.S. Jursicr Chemical Physics Letters 299 (1999) 334–344
Table 10 Harmonic vibrational frequencies Žcmy1 ., their IR intensities ŽkMrmol. in parentheses, and moment of inertial computed with B3LYPr6-311GŽ3df,3pd. for each minima on the PES for hydrogen addition to nitrogen dioxide NO 2
cis-HONO
trans-HONO
HNO 2
769.3 Ž6.6. 1401.1 Ž0.3. 1712.6 Ž355.7.
641.4 Ž27.6. 702.6 Ž88.8. 888.6 Ž263.9. 1344.4 Ž6.3. 1725.5 Ž177.9. 3594.0 Ž17.0.
590.3 Ž85.9. 622.7 Ž119.4. 830.2 Ž132.4. 1305.6 Ž168.1. 1793.5 Ž158.5. 3779.3 Ž70.2.
800.8 Ž25.5. 1063.5 Ž19.7. 1413.9 Ž48.0. 1518.3 Ž46.0. 1672.4 Ž348.7. 3150.7 Ž10.2.
21.14446 135.61603 156.76049
19.09587 143.10146 162.19733
16.66460 136.00608 152.67069
Moment of inertia Ža.u.. 7.41046 137.67477 145.08523
DFT methods were obtained for computing the activation barrier for the 1,3-hydrogen shift through TS2. The CBSQ computed activation barrier is 28.9 kcalrmol, while the B3LYPr6-311GŽ3df,3pd. is 28.3 kcalrmol ŽTable 8.. Considering that the less stable HNO 2 isomer is made through TS1 with an activation barrier around 55 kcalrmol, this isomerization is highly unlikely to occur in gas phase, while isomerization through TS2 is experimentally feasible, and the same HONO molecule is formed. As mentioned above, the enthalpy for the 2HNO ™ H 2 O q NO q N2 O decomposition reaction in the gas phase is 9.1 kcalr2 mol. It will be interesting to see if the DFT method can correctly estimate the enthalpy for this reaction. The experimental enthalpy of formation for water at 0 K is y57.1 kcalrmol w26x. The CBSQ estimates this enthalpy to be y55.9
kcalrmol ŽTable 9.. As in the case of nitrogen oxide built compounds, the hybrid DFT computes the best enthalpy of formation of the three applied DFT methods. The best estimate is y51.9 kcalrmol, computed with the B3LYPr6-311GŽ3df,3pd. theory model ŽTable 9.. The experimental H–O bond dissociation energy for water is 119 " 1 kcalrmol w26x. The SBSQ computed energy is slightly lower Ž117.8 kcalrmol, Table 9.. As we have already mentioned above, the most reliable DFT method is the B3LYP and the estimated bond dissociation energies are 2–3 kcalrmol lower than the CBSQ evaluated bond dissociation energies. That is also true for the H–O bond dissociation energy. The B3LYPr6311GŽ3df,3pd. evaluated bond dissociation energy is 115.0 kcalrmol ŽTable 9.. For the 2HNO™ H 2 O q NO q N2 O decomposition reaction, the CBSQ esti-
Table 11 Harmonic vibrational frequencies Žcmy1 ., their IR intensities ŽkMrmol. in parentheses, and moment of inertial computed with BLYPr6-311GŽ3df,3pd. for each minima on the PES for hydrogen addition to nitrogen dioxide NO 2
cis-HONO
trans-HONO
HNO 2
733.2 Ž5.3. 1302.5 Ž0.1. 1586.2 Ž266.0.
514.0 Ž68.2. 660.7 Ž76.9. 779.9 Ž186.5. 1254.5 Ž4.5. 1640.0 Ž178.4. 3464.7 Ž10.6.
510.5 Ž132.0. 570.2 Ž73.0. 741.6 Ž73.2. 1209.0 Ž137.3. 1716.4 Ž184.7. 3633.2 Ž47.9.
757.7 Ž20.7. 998.3 Ž19.9. 1318.6 Ž45.2. 1455.8 Ž37.2. 1544.4 Ž278.7. 2999.0 Ž26.2.
21.98596 144.20415 166.19012
20.26936 152.69172 172.96108
17.06299 140.49124 157.55423
Moment of inertia Ža.u.. 7.88058 141.71305 149.59363
B.S. Jursicr Chemical Physics Letters 299 (1999) 334–344
343
Table 12 Harmonic vibrational frequencies Žcmy1 ., their IR intensities ŽkMrmol. in parentheses, and moment of inertial computed by using 6-311GŽ3df,3pd. for three of the transition state structure on the PES for hydrogen addition to nitrogen dioxide TSr
TS1
TS2
BLYP
B3LYP
B3LYP
BLYP
B3LYP
BLYP
648.3i Ž87.2. 557.4 Ž124.0. 796.7 Ž152.6. 1078.0 Ž41.0. 1809.5 Ž203.4. 3767.6 Ž62.1. Moment of inertia Ža.u.. 21.61646 149.81713 165.66796
694.6i Ž77.4. 473.1 Ž106.8. 722.9 Ž118.2. 983.7 Ž37.0. 1743.7 Ž217.6. 3630.0 Ž41.8.
2086.3i Ž257.6. 507.5 Ž38.4. 704.6 Ž18.4. 1277.5 Ž174.2. 1631.2 Ž304.8. 2451.4 Ž28.8.
1915.5i Ž216.2. 506.3 Ž33.5. 641.2 Ž17.3. 1149.6 Ž153.5. 1517.1 Ž236.2. 2299.2 Ž11.1.
y1908.1i Ž177.1. 1025.4 Ž3.5. 1240.2 Ž66.8. 1300.8 Ž7.5. 1397.6 Ž334.8. 2102.9 Ž24.0.
1737.9i Ž158.4. 961.0 Ž1.7. 1177.7 Ž3.1. 1184.9 Ž53.5. 266.7 Ž266.7. 1968.1 Ž10.7.
22.60120 160.99465 177.59256
16.36148 141.23736 157.59883
17.11787 146.62907 163.74694
24.13850 114.23814 138.37664
24.98458 118.19684 143.18143
mates an endothermicity of 7.0 kcalrmol, which is slightly higher than the experimental value of 4.6 kcalrmol. In this case, the B3LYPr6-311GŽ3df,3pd. is actually closer to the experimental value Ž5.9 kcalrmol, Table 9.. For all stationary points on the H q NO 2 PES, the harmonic frequencies and moment of inertia were generated with the target being that they can be used for RRKM calculations. In some of our previous computational studies we have demonstrated that gradient-corrected BLYP density functional methods produce harmonic frequencies that are almost identical to the experimental values w28–30x. For the ground state, minima values are presented in Tables 10 and 11, and for transition state structures, the harmonic frequencies are presented in Table 12. All transition state structures have one imaginary frequency, which motion connects two minima on the PES for the H q NO 2 reaction.
4. Conclusion From an extensive DFT method exploring the PES for HONO chemical systems, it can be concluded that the complete basis set ab initio method is producing energies that are almost identical to the experimental values and in fact, in some cases, it was suggested that the experimental enthalpies of formation are 1–2 kcalrmol too high. The best agreement with experimental geometries, as well as
enthalpies of formation, enthalpies of reaction, bond dissociation energies, and reaction barriers were obtained with the hybrid B3LYP density functional method. While satisfied geometries can be obtained with a relatively modest basis set, such as 6-31GŽd,p. and 6-311GŽ2d,2p. for a more accurate evaluation of energies, a larger basis set, such as 6-311GŽ3df,3pd., is required. Computed energies with this theory model should be in the 2–3 kcalrmol range from the CBSQ ab initio or experimental values. Therefore, we are recommending the B3LYPr6-311GŽ3df,3pd. theory model as a reliable model for exploring the PES for chemical systems built from nitrogen, oxygen, and hydrogen. References w1x J. March, Advanced Organic Chemistry, Reaction Mechanisms, and Structure, 4th edition, Wiley, New York, 1992. w2x N.N. Greenwood, E. Earnshaw, Chemistry of the Elements, Pergamon Press, Oxford, 1984. w3x B.S. Jursic, Chem. Phys. Lett. 236 Ž1995. 206. w4x B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 365 Ž1995. 47. w5x B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 366 Ž1996. 97. w6x B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 389 Ž1997. 75. w7x B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 389 Ž1997. 251. w8x B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 418 Ž1997. 165. w9x B.S. Jursic, R. Martin, Int. J. Quantum Chem. 59 Ž1996. 495. w10x B.S. Jursic, J.W. Timberlake, P.S. Engel, Tetrahedron Lett. 37 Ž1996. 97. w11x B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 366 Ž1996. 103. w12x B.S. Jursic, J. Mol. Struct. ŽTHEOCHEM. 370 Ž1996. 65. w13x B.S. Jursic, Int. J. Quantum Chem. 62 Ž1997. 291.
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