An ab initio and density functional study of nitrosomethane and its rearrangement products formaldonitrone and formaldoxime

THEO CHEM ELSEVIER

Journal of Molecular Structure (Theochem) 401 (1997) 141- I50

An ab initio and density functional study of nitrosomethane and its rearrangement products formaldonitrone and formaldoxime T. Vladimiroff Bldg. 3124, Armament

Engineering

Directorate,

US Army ARDEC,

Picatinny

Arsenal,

NJ 07806-5000,

USA

Received 26 July 1996; accepted 25 September 1996

Abstract Nitrosomethane is difficult to study experimentally, because it has a tendency to dimerize and rearrange to formaldoxime. However, theoretical methods, which are not bothered by these problem have not been extensively applied to these molecules. In this study, density functional theory is considered and results are compared to the more conventional SCF and MP2 methods. The same 6-3 1 lG** basis set is used throughout. Local, nonlocal and hybrid methods are employed. At the G2 level of theory the formaldonitrone is found to have comparable energy to nitrosomethane but the oxime form is found to be 12 kcal mol-’ lower. Geometry and vibrational frequencies are calculated for the stable species and compared to experiment and other calculations. The structures and energies of the transition states between these various stable forms of nitrosomethane are also reported. 0 1997 Elsevier Science B.V. Keywords:

Nitrosomethane; Formaldonitrone; Formaldoxime; Transition states; Density functional theory

1. Introduction The structure of nitrosomethane(NM) was determined by Turner and Cox [l] from the microwave spectra of ten isotopic species. An attempt by Luttke [2] to obtain the infrared spectrum of NM by dissociating the dimer in a heated cell resulted in the identification of only two vibrational frequencies. Difficulties were encountered due to the rapid tautomerization of this material. Some vibrational frequencies were deduced from the electronic spectra by Dixon and Kroto [3] and by Emsting et al. [4]. A complete IR spectrum has been reported by Barnes et al. [5] measured in an argon matrix at 20 K. One of these assignments has been brought into question by Dognon et al. [6] based on their scaled SCF/4-31G frequency calculations.

Since formaldoxime (FX) is stable in the gas phase it is more easily studied experimentally than NM. The gas phase structure was determined by Levine [7] using microwave spectroscopy. It was determined that the trans form is more stable. The infrared spectrum was studied by Califano and Luttke [8] but these authors concluded that the cis structure is more stable. This conclusion contradicted the work of Zumwalt and Badger [9] who also decided that the trans form is more stable based on their analysis of the third harmonic of the OH stretching region. Azman et al. [lo], examined the infrared spectra and performed normal coordinate analysis. High resolution IR spectra were obtained by Duxbury et al. [l l] and by Duxbury [ 121. The exact mechanism by which the isomerization of NM to FX takes place is not well understood.

0166- 1280/97/$17.00 0 I997 Elsevier Science B.V. All rights reserved PIi SO1 66- 1280(96)04876-2

142

T. Vladimiroff/Joumal of Molecular Structure (Theochem) 401 (1997) 14/L150

Adeney et al. [13] examined two pathways. The first involved the 1,3 intramolecular hydrogen shift and a subsequent rotation about the N-O bond to form the trans FX. The other path involved two successive 1,2 hydrogen shifts by way of the nitrone isomer. The energy barriers to both pathways were calculated to be rather high. The nitrone form has never been isolated, however, it was calculated to be stable and to lie about 10 kcal mol-’ above NM. Molecular geometries were determined at a fairly low level of theory using STO-3G and 4-31G basis sets and no correlation energy was included. Using these geometries, single point energy determinations were made using 6-3 1G ** basis sets and MP3 theory. More recently, formaldonitrone (FN) was studied by Altmann and Rzepa [ 141 as part of their investigation of carbonyl imines and FN and its protonated forms were studied by Strautmanis et al. [ 151. In the present work it was decided to reexamine some of these isomeric forms of nitrosomethane using larger basis sets and introduce correlation energy at the MP2 [ 161 level of theory. It was also decided to consider density functional methods as a less expensive alternative to many body perturbation theory. Density functional theory (DFT) [17] is becoming increasingly popular as a relatively inexpensive method of performing molecular calculations that go beyond the self-consistent field approximation. The problem is to determine an accurate functional relationship between the electron density and the exchange and correlation energy. The first approximation is to use the accurately known properties of the electron gas at constant density [ 18-201. Since it is obvious that the electron density in a molecule is not constant, several methods which employ gradient corrections have been devised [21-241. More recently hybrid methods have been introduced [25] which include part of the exact Hartree-Fock exchange energy. In this work the applicability of several DFT methods is also examined.

2. Computational details All the computations in this study were performed with the GAUSSIAN 94 [26] system of quantum chemistry programs. The moderate size 6-31 lG** [27] basis set was used throughout. Only five of the six possible

d functions were used. Electron correlation effects were introduced at the MP2 [ 161 level of theory. Molecular geometries were determined by minimizing the total energy using gradient techniques. The second derivative matrix was computed analytically. Three DFI methods were used in this work which can be characterized as local, nonlocal and hybrid. At the local spin density approximation the Dirac-Slater [ 181 exchange term was used along with VoskoWilk-Nussair’s parameterization [ 191 of the random phase approximation solution of the correlation energy of the homogeneous electron gas (SVWN). At the nonlocal level of approximation Becke’s exchange functional [21] was used in conjunction with the nonlocal correlation functional proposed by Lee, Yang and Parr [22] (BLYP). This nonlocal method was also employed in its hybrid form using the parameters determined by Becke [25] and designated as B3LYP. No further optimization of the three parameters was attempted.

3. Results and discussions The gas phase structure of NM as determined by Turner and Cox [l] is reported in Table 1 along with our calculated bond lengths and bond angles for the la’ ground state of this molecule. Structural parameters were also calculated in Refs. [6,13]. There have been several other theoretical studies of NM in the past but the thrust of these calculations has been to interpret its electronic spectra [28-311. Recently Bentley and Madden [32] published the structure of NM as part of their spin-trapping studies calculated at the MP2/6-31+G* level of theory. Their MP2 values are also included in Table 1. The MP2 results are in very good agreement with experiment although the Bentley and Madden [32] calculations Bredict an N=O bond length which is about 0.024 A too long. The local density functional method produces bond lengths which are too long for the bonds which involve hydrogen and too short otherwise. The bond angles are in reasonable agreement with experiment with the exception of the bond angle which involves the two out of plane hydrogens which is predicted to be too small by about 3”. The nonlocal DFT method predicts bond lengths which are uniformly too long and there is a one degree improvement in the bond

T. Vladimiroff/Journal

Table 1 Comparison

of experimental

and theoretical

RF-H,)

1.480 1.094 1.21 I 1.094

rms .I(N-C-f:,) .L(C-N-O) /(N-C-H,) ./(Ho-C-H,)

I Il.0 113.2 107.2 109.2

R(C-N) RGH,) R(N-0)

structural

parameters

1.464 1.083 1.168 1.084 0.028 1 Il.2 114.2 107.2 108.1 0.7

ITllS

Structure

(Theochem)

1.482 I.093 1.219 1.093 0.005 11 I.0 112.6 106.8 108.2 0.7

SVWN 1.457 1.102 1.202 1.103 0.016 111.7 113.6 106.7 106.1 I .9

Bond lengths are in A, bond angles are in deg. The subscript i indicates the in-plane hydrogen and the subscript o indicates the out-of-plane

angle involving the two out of plane hydrogens. The hybrid method shows an improvement in the bond length calculations which makes it almost as good as our MP2 results. There is only a slight improvement in the bond angles. There are experimental difficulties involved in obtaining gas phase vibrational spectra of NM due to its tendency to isomerize and dimerize. However, the infrared spectra have been obtained in a lowtemperature argon matrix by Barnes et al. [5]. Their

Table 2 Comparison

of experimental

and theoretical

frequencies

143

401 (1997) 141- 150

for nitrosomethane

MP2

SCF

[II

Exp.

of Molecular

for nitrosomethane

BLYP

MP2 [32]

B3LYP

1.511 I.099 1.219 1.101 0.019 I 11.6 113.4 106.5 107.3 1.2

1.475 1.093 1.235 I .094 0.014 I Il.4 112.X 106.8

I.487 1.092 1.202 1.094 0.007 111.4 113.6 106.7 107.5 1.1

0.5

hydrogen

measured frequencies and our calculated values are reported in Table 2. As can be expected the SCF frequencies are systematically high with a rms error of 246 cm-‘. A significant improvement is achieved by going to MP2 theory. The local density method achieves a further reduction in the root mean square error. The introduction of gradient corrections achieves a further small reduction in the error. The hybrid method does not produce a further improvement, however, this is not necessarily an indication of

(cm-‘)

Exp. [51

SCF

MP2

SVWN

BLYP

B3LYP

Ref. [6]

a’ 2991 2901 1549 1410 1348 967 870 574 a”

3280 3176 1967 1583 1531 1282 990 636

3195 3072 1567 1476 1396 1169 898 586

3065 2940 1655 1365 1279 1114 850 568

3045 2935 1550 1410 1313 1099 746 546

3126 3016 1673 1451 1368 1151 831 577

3151 3028 1563 1496 1368 1174 896 541

2955 1410 916 140 “146 h

3256 1583 1091 168

3181 1482 991 140

3039 1361 914 173

3014 1409 924 158

3100 1452 970 161

3052 1440 907 166

246 230

128 113

72 58

62 51

100 83

98 75

l7llS

mls c

a Taken from Ref. [29]. ’ Taken from Ref. [I]. ’ Root mean square error if 967 is changed to 1162 cm-‘.

144

Table 3 Comparison

T. Vladimiroff/Joumal of Molecular Structure (Theochem) 401 (1997) 141-150

of experimental

and theoretical

EXP. [71 R(C-N) R(N-0) R(C-H,)

1.276 I .408 I .085 1.086 0.956

RK-H,) R(O-H) rms L(C-N-O) L(H,-C-N) I(H,-C-N) QH-C-H) L(H-O-N)

110.2 121.8 115.6 102.7

structural

SCF

parameters MP2

1.247 1.362 I .079 1.074 0.940 0.029 112.3 122.4 117.3 120.4 104.7 2.0

for tram formaldoxime SVWN

1.281 1.394 1.089 1.083 0.96 0.008 110.6 122.3 116.2 121.4 101.8 0.7

BLYP

1.268 I.371 1.1 1.092 0.972 0.022 112.0 122.3 116.4 121.3 102.9 I .2

B3LYP

I.282 1.428 1.096 1.090 0.973 0.015 III.1 123.3 116.2 120.5 101.6 I .2

Bond lengths are in A, bond angles in deg. The subscript c indicates the hydrogen cis to the oxygen, and the subscript t indicates the hydrogen The molecule was found to be planar.

a poor theory. We only calculate the harmonic frequencies but compare them to experimental frequencies which have anharmonic contributions. Based on the work of Finley and Stephens [33], hybrid methods could be expected to yield better agreement if experimental harmonic frequencies were available for NM. Our calculations are not accurate enough to completely rule out the assignment made by Barnes et al. [5] of the 967 cm-’ band to the CH3 rocking mode, however our calculations definitely support the contention of Dognon et al. [6] that the proper assignment Table 4 Comparison

of experimental

Exp. d a’ 3650.3 3109.7 2913.2 1647 1410 1318 1166 892.5 530 a” 952.6 774. I 400 fIllS

a Experimental

and theoretical

frequencies

MP2 1431

1.268 I .399 I .089 1.083 0.963 0.007 111.6 122.8 116.6 120.6 102.7 1.1

1.283 I ,409 1.088 1.083 0.973 0.009 110.0 122.8 116.4 120.8 102.0 0.8

trans to the oxygen.

for this mode is the band at 1162 cm-‘. For all of our calculated frequencies the rrns error is reduced if this assignment is made. There have been numerous theoretical calculations on the structure of FX [ 13,34-421 with the latest being by McAllister and Tidwell [43] in their extensive study of substituent effects in isocyanates and imines. The structure of FX was determined by Levine [7] using microwave spectroscopy. The results of our calculations along with the experimental parameters determined by Levine [7] and the calculated MP2

for trans formaldoxime

(cm-‘)

SCF

MP2

SVWN

BLYP

B3LYP

4-31G [38]

4194 3383 3264 1917 1581 1495 1304 1080 583

3903 3299 3155 1675 1467 1362 1194 956 537

3132 3160 3013 1690 1380 1303 1142 969 527

3678 3135 3007 1621 1406 1306 1137 846 515

3830 3219 3090 1714 1451 1357 1182 926 536

3445 3323 1908 1602 1452 1300 927 550

1131 876 414

958 907 420

910 784 488

917 771 435

973 802 446

I190 872 395

250

121

52

28

80

226

frequencies

are from Ref.

[lo]. The frequencies reported to a tenth of a wavenumber are from Refs. [I I, 121.

T. Vludimiro~/JournaI

Table 5 Comparison

of theoretical

structure parameters

R(C-H,) R(N-H) L(C-N-O) I(N-C-H,) L(N-C-H,) L(C-N-H)

1.269 1.247 I .072 I.071 I.010 128.4 I 18.5 118.6 116.0

Structure (Theochem)

401 (1997)

145

141-150

for formaldonitrone BLYP

SVWN

MP2

SCF R(C-N) R(N-0) R(C-H,)

of Molecular

I.306 I.243 I.091 I .090 I .05 I 128.9 Ill.7 I IS.0 114.2

1.304 I.241 1.089 1.088 1.048 128.9 117.8 118.0 114.2

I .325 I.242 1.080 1.079 1.032 129.2 117.8 117.2 114.1

B3LYP 1.304 1.256 1.079 I.079 I .033 128.9 118.2 118.1 115.0

SCF [I51 I .269l I .2543 I .0704 I .0704 I .0099 128.33 I 18.47 118.89 116.52

Bond lengths are in A. bond angles in deg. This molecule was found to be planar

values of McAllister and Tidwell[43] are presented in Table 3. We note a slight improvement over the McAllister and Tidwell [43] MP2 computations using the larger basis set. The local density functional method seems to give results which are somewhat in between SCF and MP2 theory. The nonlocal and hybrid density functional methods give only a slight improvement for the geometric parameters of FX, with the B3LYP method giving the best bond lengths. Azman et al. [ 101 reported vibrational frequencies for FX in the gas phase and Duxbury et al. [l l] and Duxbury [ 121 analyzed some of the bands at high resolution. These data are summarized in Table 4 along with the results of our calculations. We could not find any recently published theoretical frequencies for this molecule so we include the calculations of Akagi et al. [38] obtained with a 4-31G basis set at Table 6 Comparison

of theoretical

vibrational

frequencies

for formaldonitrone

the SCF level of theory. The SCF results are too high with the rms deviation actually being smaller when the smaller basis set is used. The MP2 calculations produce a marked improvement over the SCF calculations. For FX the density functional methods also produce superior frequencies. Even the local method produces smaller rms deviations than the MP2 result. The nonlocal method is even better. For all the density functional approaches the hybrid method gives the worse results. To our knowledge, FN has not been isolated so that experimental data on this molecule have not been reported. However, several theoretical calculations have been performed on its energy and structure. Adeney et al. [13] reported the structure of this molecule at the SCF/4-31G level of theory and both Altmann and Rzepa [14] and Strautmanis et al. [15]

(cm-‘)

MP2

SVWN

BLYP

B3LYP

3647 3452 3325 I842

3373 3324 3224 1720

1650 1530 1385 II44 616 a”

1532 1486 I299 1087 577

3242 3106 3098 I677 1459 1427 1272 1049 568

3226 3102 3095 I600 I450 1401 I254 1031 578

3307 3263 3174 I674 1502 1451 I305 I075 577

II43 980 792

976 122 575

956 750 663

939 723 652

992 722 698

SCF a’

146

T. Vladimiroff/Joumal

of Molecular

Table 7 Relative energies of the various isomers of nitrosomethane negative (in kcal mol-‘)

Ref. [I31 SCF MP2 SVWN BLYP B3LYP G2

formaldonitrone

transformaldoxime

12.4 10.9 I .6 - I I.5 -4.6 -2.4 -0.9

-

Structure

(Theochem)

and related transition

-9.8 10.9 10.9 15.2 12.2 12.7 Il.9

401 (1997) 141-150

states to nitrosomethane;

lower energies are designated

tl

t2 “

t3

t4

70.7 82.6 62.8 46.5 55.4 60.8

2.6 2.6 3.8 6.9 4.6 4.3

65.2 70. I 56.3 39.5 47.2 51.4

49.0 64.9 48.6 31.2 38.9 44.1

as

*The energy of t2 is above the cis formaldoxime.

considered the 6-3 lG* level of Hartree-Fock theory. No higher order calculations were found. Our structural parameters for FN are presented in Table 5 along with the bond lengths and bond angles computed by Strautmanis et al. [15]. The vibrational frequencies are presented in Table 6. The accuracy of these calculations should be similar to the accuracy achieved in Tables l-4 for NM and FX. The energy of the nitrone form relative to NM is reported in Table 7. The best estimate of Adeney et al. [13] was that FN lies 12.4 kcal mol-’ above NM. Our SCF calculation gave 10.9 kcal mol-‘. However using MP2 theory the difference is still positive but only 1.6 kcal mol-‘. All of the density functional methods predict that the nitrone form is lower in energy. Since experimental energies are not available, it was decided to resolve this issue Table 8 Comparison

of theoretical

structural

parameters

for t I

SCF R(C-N) R(N-0) RF-H,)

R&-H) R(C-H’) &O-H,) I(C-N-O) L(N-C-H,) L(N-C-H) L(N-C-H’) L(N-O-H,) D(O-N-C-H,) D(O-N-C-H) D(O-N-C-H’)

a

by going to G2 [44] theory. Using this approach it was found that the nitrone form is 0.9 kcal mol-’ lower in energy than NM. Using this result along with the MP2 and hybrid density functional results it seems safe to say that these two forms of NM are comparable in energy and probably differ by less than a few kcal mol-’ . The mechanism by which NM rearranges to FX and possibly FN was examined next. As pointed out by Adeney et al. [ 131 two possible reaction pathways exist. Nitrosomethane could rearrange by a four center transition state (tl) to the cis FX and then rotate through a small potential barrier (t2) to the more stable trans form. Another possibility was to undergo a 1,2 intramolecular hydrogen shift to form FN involving transition state t3 and a subsequent 1,2

1.378 1.224 1.472 1.085 I .078 I .243 104.2 71.6 107.0 116.6 85.3 -6.8 74.9 157.4

Bond lengths are in A, bond angles in deg. The subscript m indicates the mobile hydrogen. a Dihedral angle.

MP2 1.373 1.284 1.438 1.093 I.086 1.322 103.8 74.8 110.2 118.1 81.9 -7.6 69.6 _ 155.7

SVWN 1.354 1.267 I.439 I.105 I.096 I.371 105.5 76. I 109.9 119.0 81.4 -8.0 67.3 .159.6

BLYP I.381 1.298 I.475 I.102 1.094 1.374 104.5 76.0 110.3 118.0 82.4 -7.7 69.6 158. I

B3LYP 1.366 1.268 I.445 1.096 1.087 1.332 104.5 75.0 109.6 118.5 82.3 -7.6 69.0 _ 158.4

SCF [I31 I .363 1.277 I .5 I2 I .083 1.069 I.318 104.4 75.0 I I I.3 118.1 -6.8 69.8 155.2

T. Vladimiroff/Journal

Table 9 Comparison

of theoretical

structural

parameters

R(C-N) R(N-0) R(C-H) R(C-H’) R(O-H) L(C-N-O) L(N-C-H) L(N-C-H’) L(N-O-H) D(O-N-C-H) D(O-N-C-H’) D(C-N-O-H)

a

for t2 MP2

SCF

147

of Molecular Structure (Theochem) 401 (1997) 141-150

1.241 1.382 I .082 I.076 0.943 113.9 123.1 117.3 107.6 -0.7 179.0 65.5

1.280 1.426 I.091 1.085 0.963 111.5 123.0 116.2 103.6 -0.4 179.0 71.2

SVWN 1.264 I .409 I.103 1.095 0.974 112.2 122.5 116.6 104.8 -0.8 178.5 77.8

BLYP I.278 1.469 1.098 I.094 0.977 I I I.6 123.8 116.3 103.8 -0.9 178.7 73.8

B3LYP I.266 1.433 I.091 I.086 0.966 112.4 123.4 116.7 105.0 -0.8 178.7 72.4

SCF [13] I.255 I.430 I .074 I.068 0.957 114.6 123.8 I 17.4 III.1 -1.1 178.3 54.3

Bond lengths are in A, bond angles in deg.

’ Dihedral angle. intramolecular shift to form trans FX by way of transition state t4. Adeney et al. [ 131 calculated the structure of transition states t 1-t4 at the STO-3G and the 43 lG/SCF level of theory. Their results along with our results are summarized in Tables 8-l 1, respectively. The geometry of tl was also determined at the HF/321G level of theory by Saito et al. [45]. The structure of these transition states is not known from experiment so that the calculated values can only be compared to each other. These calculations are in reasonable agreement, except for the fact that our Table IO Comparison

of theoretical

structural

parameters

SCF R(C-N) R(N-0) R(C-H) R(C-H’) R(C-H ,.) R(N-H,) I(C-N-O) L(N-C-H) L(N-C-H’) I(N-C-H,) L(C-N-H,) L(O-N-H,) D(O-N-C-H) D(O-N-C-H’) D(O-N-C-H,)

for t3 MP2

1.322 I .23 I 1.081 1.074 1.438 I.186

’

120.9 121.1 116.1 50.7 69.7 122.4 3.9 173.2 - 116.4

calculations for t4 indicate that this transition state is planar. Also, for the transition between cis and trans FX, the value of the torsional angle around the N-O bond from Ref. [13] was determined to be 70” @TO-3G) and 54” (4-31G). Our correlated calculations indicate an angle in the range of 7 1-78”. There is generally a good agreement that the energy of t2 is 2-5 kcal mol-’ above cis FX. In Table 7 the energies of the four transition states are summarized along with the best estimates from Ref. [13]. For our work the best energy estimates

1.393 I .234 I.093 I .086 1.407 1.213 121.1 120.7 113.0 51.3 64.9 126.6 5.6 164.4 - 119.1

Bond lengths are in ..k, bond angles in deg. The subscript m indicates the mobile hydrogen. a Dihedral angle.

SVWN 1.365 1.228 I.104 I.095 I .399 I .256 121.4 120.5 114.1 54.0 64.4 126.8 4.9 165.4 - 119.0

BLYP 1.392 1.254 I.100 I .092 I .43 1 I.259 120.9 120.8 114.3 53.0 65.1 125.0 5.4 165.4 - 117.4

B3LYP

SCF [13]

1.369 1.240 1.092 I .084 I .424 I.234 121.2 120.8 114.7 52.4 66. I 124.8 5.0 167.2 - 117.5

1.330 I.274 I .073 I.070 I .450 I.223 121.1 120.8 116.8 52.0 69.0 4.6 171.0 - 116.8

I48 Table 1I Comparison

T. VladimiroffFJoumal

of theoretical

structural SCF

R(C-N) R(N-0)

R(C-H) R(C-H’) R(O-H,) R(N-H,) L(C-N-O) L(O-N-H,) L(N-O-H,) L(N-C-H) L(N-C-H’) D(O-N-C-H) D(O-N-C-H’) D(O-N-C-H,)

’

parameters

of Molecular

Srruciure (Theochem) 401 (1997)

141- 150

for t4 MP2

I.243 1.366 1.079 1.074 1.266 1.102 125.3 60.6 49.3 118.7 119.5 0.0 180.0 180.0

I .289 1.360 1.088 1.080 1.296 I.1 16 125.2 62.2 49.6 117.6 118.3 0.0 180.0 180.0

SVWN I.274 1.361 1.098 1.090 1.286 I.138 124.9 61.2 50.8 117.8 118.8 0.0 180.0 180.0

BLYP I.288 1.410 1.094 1.088 1.302 1.140 124.8 60.3 49.5 118.8 118.6 0.0 180.0 180.0

B3LYP 1.272 1.384 I .088 1.081 I .287 1.127 125.0 60.6 49.7 118.4 119.0 0.0 180.0 180.0

SCF [13] 1.242 1SO7 I.075 1.071 1.275 I.126 123.0 55.7 46.8 119.8 120.4 0.3 - 179.8 - 152.0

Bond lengths are in A, bond angles in deg. The subscript m indicates the mobile hydrogen. aDihedral angle.

should be provided by the MP2 and the hybrid DFT method. Thus the energy for the four center transition state should be in the range of 60 to 63 kcal mol-’ as compared to the best energy computed in Ref. [ 131 of 70.7 kcal mol-‘. Our energy calculations for the transition state between NM and FN is in the range 5 l-56 kcal mol-' . The best estimate for Ref. [13] is 65.2 kcal mol-‘. The subsequent rearrangement to trans FX requires an energy in the range 44-49 kcal mol-’ by our calculations and was estimated to be 49.0 by Adeney et al. [13]. Our calculations indicate that the energy barriers should be lower than the previous estimates, however, our values are still higher than the experimental values. Batt and Gowenlock [46] measured the rate of isomerization of NM and determined a value of 29.1 kcal mol-’ for the activation energy. These workers were concerned about a heterogeneous contribution of the reaction rate. Subsequently, Benson and O’Neal [47] concluded that the activation energy should be more like 40 kcal mol-’ based on the assumption that the measured rate was within a factor 2-4 of the homogeneous rate and that the A-factor could be calculated by transition state methods. Benson and O’Neal [47] did not consider a two step path by way of FN. Both the calculations of Adeney et al. [13] and of this work agree that the path by way of FN involves a lower energy than the four center transition state. Also

the potential barriers would be more narrow, therefore they would be easier for the proton to tunnel through. So the question remains, why has there been no experimental evidence produced supporting the existence of FN? Barnes et al. [5] found that under low matrix to absorber ratios several bands (1598, 938, 736 cm-‘) were observed which could not be assigned to either the monomer or the cis or trans dimer of NM. These bands were assigned to cis-t-butyl nitrite. The method which predicted the frequencies with the lowest standard deviations in Tables 2, and 4 is BLYP. A glance at Table 6 indicates that FN is predicted to have frequencies by this method of 1600, 939 and 723 cm-’ which are in reasonable agreement with these observed bands and could be due to FN. The first two bands are predicted to be strong absorptions and the third band is predicted to be moderate.

4. Conclusions Nitrosomethane and its rearrangement products formaldonitrone and formaldoxime were studied using both ab initio and density functional methods. The structures of these molecules were most reliably reproduced using the MP2 theory. All of the DFT methods give better bond lengths than the SCF theory. Mixed results were observed for the bond angles with

T. Vladimiroff/Journal

of Molecular

the SCF results being quite good for nitrosomethane and worse than all of the DFf calculations for formaldoxime. For geometries, the hybrid B3LYP method was the best of all the DFT calculations and almost as good as MP2. For vibrational frequencies, all of the DFT methods were better than the MP2 results. Very good values were obtained for formaldoxime (where the gas phase vibrational frequencies are known) using the BLYP method which gives the smallest rms error. This may be fortuitous as pointed out before [33], but may still be useful in making assignments. Our calculations support the contention of Dognon et al. [6] that the proper assignment for the CH3 rocking mode is the band at 1162 cm-’ but they are not accurate enough to completely rule out the assignment made by Barnes et al. [S]. SCF and local DFT calculation are most misleading for the energy of formaldonitrone. The former predicting an energy of 11 kcal mol-’ higher than nitrosomethane and the latter predicting a value 11 kcal mol-’ lower. This is in contrast with the energy of formaldoxime where all of the computations are in fairly good agreement. Based on the G2, MP2 and hybrid calculations, our conclusion is that the energy of nitrosomethane should be above formaldonitrone by 1 t 3 kcal mol-‘. The energy of the transition states computed in this work should also have about the same accuracy. The estimated values would be tl (61 -+ 3 kcal mol-‘), t2 (3.5 -+ 2 kcal mol-‘), t3 (53 -+ 4 kcal mol-‘) and t4 (46 ? 3 kcal mol-‘). These values are still in substantial disagreement with the 40 kcal mol-’ estimate of Benson and O’Neal [47]. This may be due to a larger contribution to the heterogeneous reaction rate than assumed by Benson and O’Neal [47]. All of the theoretical calculations predict that formaldonitrone should be a stable species and according to our calculations its energy should be comparable to nitrosomethane. The energy of the various transition states indicate that the isomerization of nitrosomethane should go by way of the nitrone form. Thus it would be reasonable to expect that some formaldonitrone would be trapped in the argon matrix at 20 K. Our calculated vibrational frequencies for this species show that three of the vibrational frequencies assigned to cis-t-butyl-nitrite by Barnes and coworkers [5] could be attributed to formaldonitrone. This point could be clarified experimentally if an effort was made to specifically look for some of the formaldonitrone

Structure

(Theochem)

401 (1997)

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vibrational frequencies and if interference t-butyl-nitrite could be avoided.

149

from cis-

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