Ab Initio investigation of the structures and stabilities of CH2N2, CHFN2, and CF2N2 isomers: Important consequences of MP2 optimizations

Ab Initio Investigation of the Structures and Stabilities of CH,N,, CHFN,, and CF,N, Isomers: Important Consequences of MP2 Optimizations

Alexander I. Boldyrev* and Paul v.R. Schleyert Institut f u r Organische Chemie der Friedrich-Alexander Universitat Erlangen-Numberg, Henkestrasse 42, 8520 Erlangen, Germany

D. Higgins8 and Colin Thomson Department of Chemistry, University of St. Andrews, St. Andrews, Fve, Scotland KYl 69ST

Sofia S. Kramarenko Moscow Mendeleev Chemico-Technological Institute, 125820 Moscow, A-47, Miusskaja sq. 9, Russia

Received 5 August 1991; accepted 22 January 1992

A b initio calculations of the potential energy surfaces of CHzNz, CHFNz, and CFzNz at MP4SDTQ/6-31G*// MP2(fu11)/6-31G* reveal several surprising features. While diazomethane is more stable than diazirine, only the three-membered ring forms of the fluorine-substituted isomers are known experimentally. We find fluorodiazomethane and difluorodiazomethane not to be viable species: They have no barriers toward exothermic dissociation into Nz and CHF or CFz, respectively. In contrast, the three-membered ring isomers, fluorodiazirine and difluorodiazirine, have high barriers toward dissociation despite being high in energy. Diazomethane bends easily; a nonplanar C, minimum is found at MP2(fu11)/6-31G* but Czv symmetry is preferred at QCISD/6-31G*. 0 1992 by John Wiley & Sons, Inc.

INTRODUCTION

The most general route for the generation of carbenes involves the thermal decomposition of diazoalkanes, e.g., 1 and their three-membered ring isomers, diazirines, e.g., 2.',' Since carbenes

H

H /C=N=N H' 'N

\

1 2

are high energy species, the thermochemical driv- ing force for these reactions is provided by the formation of molecular nitrogen [eq. (l)]

X2CN2 +. X,C(singlet) + N2 (1)

In addition, singlet CF2 is strongly stabilized by the fluorine ~ubst i tuents .~ Hence, among carbene decomposition reactions, the exothermicity of eq. (1)

*Permanent address: Institute of Chemical Physics of the Russian Academy of Sciences, Kosygin str. 4, Moscow v-334, USSR.

?Author to whom all correspondence should be addressed. $Current address: Computing Service, University of Glasgow ,

Glasgow, Scotland G1 SSQQ.

with X = F is especially large. Experimental at- tempts to prepare both CF2N2 isomers have only led to difluorodiazirine (3). This suggests that 3 may be more stable than the unknown difluorodiazomethane, 4. If so, this would be opposite to the stability order of the parent compounds: diazomethane 1 is known to be more stable than diazirine 2 .1,2,4,5 Calculations

3 4

The present investigation was undertaken to an- swer the following questions:

1. Why has difluorodiazomethane eluded synthe-

2

sis? Is this due to thermodynamic or to kinetic problems? What are the relative stabilities of 1 vs. 2, 3 vs. 4, and 5 vs. 6? What about the related molecules, 7 vs. 8? (Recall that allene is more stable than its isomer, cyclopropene.)

Journal of Computational Chemistry, Vol. 13, No. 9, 1066-1078 (1992) 0 1992 by John Wiley & Sons, Inc. CCC 0192-8651/92/091066-13

CHZNZ, CHFNZ, AND CFzNp ISOMERS

F F

H /C=N=N

H' 'N

\

5 6

1067

12 13

METHODS OF CALCULATION

3.

4.

5.

7 8

How and to what extent do the fluorine substituents influence the energy of the CHFNz, CF2N2, and C3H2F2 isomers? If the relative energies of 3 vs. 4, 5 vs. 6 (as well as 7 vs. 8) really are inverted relative to 1 and 2, what are the reasons? What are the dissociation energies [eq. (l)]? How much are they affected by fluorine substitution? What are the lowest barriers for nitrogen loss from 1-6, assuming singlet states in all cases?

Our previous theoretical study compared the structures and energies of 3 and 4, as well as several additional CF2N2 isomers using semiempirical (MNDO) and ab initio (HFI3-21G) methods." At both these levels, difluorodiazomethane (4) was predicted not only to be between 150 (MNDO) and 41 (HF/3-21G) kcal/mol lower in energy than 3 but also to be the global minimum among all the CF2N2 isomers studied. In view of the apparent discrep- ancy with the experimental results (3 has been ~haracterized,~ but not 4), the present higher level theoretical examinations were initiated inde- pendently in Scotland and Erlangen. We present here a combined report of our results. These in- clude not only 3 and 4, but also 5-8 and three other CF2N2 isomers (9-11) from the previous study. lo

9 10 11

In addition, the stabilizing influence of gem-di- fluorosubstituents in 3, 4 and in the model compounds 7, 8, 1,l-difluorocyclopropane (12), and 2,2-difluoropropane (13) have been analyzed and compared with those in difluoromethane, CF2H2, and difluoropropane, (CH&CF2. l1

All calculations were carried out using the GAUS- SIAN12 and CADPAC13 programs on Microvax 11, CONVEX C210, and SCS40 computers. The stand- ard basis sets (e.g., 6-31G*) and procedure were used. The HF/6-31G* and MP2(fu11)/6-31G* geometries were optimized by force methods using analytical gradients. All stationary points on the HF/ 6-31G* and MP2(fu11)/6-31G* potential energy surfaces were characterized by analytical calculations of the HESSIAN force constant matrix and inspec- tion of the eigenvalues. The optimized geometries are given in Table I, and the total and relative energies of isomers as well as the number of imaginary frequencies in Table 11. Using the MP2(fu11)/6-3 l G * geometries, electron correlation corrections were probed in the frozen-core approx- imation by Moller-Plesset perturbation theory carried to second, third, and full fourth order14 with the 6-31G' basis set. The designations are, e.g., MP4SDTQ/6-3 lG*//MP2(fu11)/6-3 1G*, where // means "at the geometry of." Natural population analyses were performed with G82NBO. 1 5 3 1 6 Disso- ciation energies for CH2N2, CHFN2, and CFzNz into N2 and the corresponding carbene products are given in Table I11 and the vibrational frequencies and zero point energies (ZPE) are in Table IV. Our highest level [MP2(fu11)/6-31G*] frequencies and ZPEs were scaled by 0.94.lZb

RESULTS AND DISCUSSION

Diazomethane and the Effects of Fluorine Substituents

While diazomethane (1) in Czv and difluorodiazomethane (4) in CzV, and fluorodiazomethane (5) in C, symmetry are minima at HF/6-31G* (no imaginary frequencies), all are saddle points at MP2/6- 31G* (one imaginary frequency). Optimization of diazomethane at MP2/6-31G* gives a C, minimum with <C-N-N=178" bond and <H-C-N-N= 95.7" dihedral angles. While 1 is not planar, the energy difference between the minimum (C, configuration) and the inversion saddle point (CZv configuration) is very small (0.003 kcal/mol). Diazo- methane (1) can be said to be quasiplanar. The ground vibrational state of 1 lies above the barrier and the molecule has an average structure with CZv symmetry. With a larger basis set [QZ+P: ( 1 1 ~ 7 p l d / 5 s 4 p l d ) ~ , ~ + (5slp/3slp), at MP2(full)],

Tab

le I

. C

alcu

late

d st

ruct

ures

of

CH

7. C

HF.

CF7

. N7.

CH

rNr,

CH

FN7.

and

CF7

Nr

Spec

ies

Con

figu

ratio

n M

etho

d R

(N-N

) R

(N-C

) R

(C-H

) R

(C-F

) <N

NC

<N

CH

<N

CF

<FC

H

<HC

H

<FC

F <N

NC

H

<NN

CF

NZ

1 CH2

NN

(ts1)

2 5'

HF/

6-3 1

G*

MP2

/6-3

1G*

EXPT

a

HF/

6-31

G*

MP2

/6-3

1G*

EX

PT

~

HF/

6-31

G*

MP2

/6-3

1G*

EXPT

C

EX

PF

HF/

6-31

G*

MP2

/6-3

1G*

EXPT

e

MP2

/6-3

1G *

EX

PT

~

HF/

6-31

G*

MP2

/6-3

1G*

EXPT

f

HF/

6-31

G*

HF/

6-31

G *

MP2

/6-3

1Gf

EXPT

g

HF/

6-31

G*

MP2

/6-3

lG*

MP2

/6-3

1G*

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

1.07

8 -

1.13

-

1.09

768

-

1.15

0 1.

311

(1.1

39)

(1.3

00)

1.11

6 1.

281

1.15

0 1.

310

1.13

9 1.

300

1.07

8 1.

810

-

2.86

0

1.19

4 1.

446

1.25

6 1.

480

1.22

8 1.

482

1.11

1 1.

905

1.77

5 1.

147

2.26

4 2.

052

1.15

2 1.

337

-

-

1.09

7 1.

109

1.11

1.10

4 1.

121

1.12

9 -

-

-

-

-

-

-

1.07

7 (1

.077

) 1.

068

1.07

7 1.

077

1.09

1

1.07

4 1.

083

1.09

1.07

6

1.10

3

1.08

3

-

-

-

180.

0)

180.

0 18

0.0

180.

0

163.

4

65.6

64

.9

66.1

78

.9

85.1

1.36

7 17

0.0

116.

9)

117.

8 11

7.3

116.

9

93.9

118.

0 11

7.2

-

90.5

10

8.4

99.1

114.

4

-

-

-

-

102.

8 10

2.0

103.

06

104.

5 10

4.3

104.

34

104.

778

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

115.

5

103.

1 10

2.1

102.

4 -

-

-

-

-

-

-

-

-

-

125.

0 (1

26.2

) 12

4.3

125.

5 12

6.2

105.

4

118.

0 11

9.4

117

114.

8

105.

5

-

-

-

-

Tab

le I

. (c

ontin

ued)

8 "2,

Spec

ies

Con

figu

ratio

n M

etho

d R

(N-N

) R(

N-C

) R(

C-H

) R

(C-F

) <N

NC

<N

CH

<N

CF

<FC

H

<HC

H

<FC

F <N

NC

H

<NN

CF

N 0

HF/

6-31

G*

1.13

4 1.

256

1.06

4 1.

332

179.

8 12

3.1

118.

8 11

8.1

-

-

90.0

-9

0.0

MP2

/6-3

1G*

1.15

4 1.

303

1.07

5 1.

358

179.

4 12

2.3

117.

2 12

0.4

HF/

6-31

G*

1.21

4 1.

403

1.07

1.

335

64.4

12

2.5

117.

5 11

2.5

-

-

MP2

/6-3

1G*

1.28

2 1.

436

1.08

2 1.

358

63.5

12

1.8

116.

9 11

3.5

-

-

HF/

6-31

G*

1.12

6 1.

661

1.07

6 1.

321

79.3

11

5.5

110.

8 11

2.2

-

-

-46.

8 82

.0

HF/

6-31

G*

1.15

6 1.

231

-

1.30

5 18

0.0

-

123.

2 -

-

-

121.

6 -

1.33

4 18

0.0

MP2

/6-3

1G*

1.16

2 1.

285

-

-

90.0

-9

0.0

yg 5

cs

6

CS

(b3

)

4 C

ZV

107.

8 -1

04.5

$

108.

0 -1

04.6

U

c,

-

138.

8 -1

08.9

3

-

1.82

5 -

-

63.4

88

.1

101.

8 -

-

-

-

113.

5 -

116.

7 -

E 3

C2

V

HF/

6-31

G*

1.23

0 1.

375

-

1.31

3 63

.4

-

129.

5 -

-

-

-

-44.

3 ?2

-

-

-

-

MP2

/6-3

1G*

1.30

6 1.

407

-

1.33

8 62

.3

-

120.

9 -

109.

8 -

EXPT

h 1.

293

1.42

6 -

1.31

5 63

.0

-

120.

2 -

110.

7 -

-

107.

8

HF/

6-31

G*

1.14

1 1.

610

-

1.30

4 78

.6

-

119.

3 -

-

110.

4 -

1.78

0 -

1.30

4 62

.5

-

101.

3 -

-

111.

4 M

P2/6

-31G

* 1.

197

1.55

7 -

1.33

4 84

.2

-

117.

7 -

1.86

6 -

1.33

4 56

.1

-

98.9

-

-

-

-

(t.9

4)

cs -

-

-

-

-

-

-

-

-

-

Spec

ies

Con

figu

ratio

n M

etho

d R

(N-N

) R

(N-C

) R

(N-F

) R

(C-F

) <F

NN

<N

NC

<N

CF

9 C1

H

F/6-

3 lG

* 1.

187

1.37

3 1.

289

1.35

9 10

9.0

123.

4 10

6.3

MP2

/6-3

1G*

1.23

8 1.

264

1.32

3 1.

438

107.

0 15

6.1

118.

0

10

C1

HF/

6-3 l

G*

1.54

1 1.

357

1.21

1 1.

385

1.26

9 10

7.7

106.

6 M

P2/6

-31G

* 1.

675

1.37

5 1.

256

1.43

9 1.

305

106.

1 10

5.4

R(N

-N)

R(N

a-C

) R(

Nb-

C)

R(N

-F)

R(C

-F)

<FN

,Nb

<FN

aC

R(N

a-C)

R(

C-N

b)

R(F

-N)

< N,

CNb

< C

NaF

<

FN,F

11

cs

HF/

6-31

G*

1.38

5 1.

131

1.34

5 17

5.2

106.

5 10

4.0

MP2

/6-3

1GL

1.

395

1.18

1 1.

407

172.

8 10

4.0

103.

0 E

XP

T~

1.

386

1.15

8 1.

399

173.

9 10

5.4

102.

8

Dis

tanc

es a

re in

A, a

ngle

s in

degr

ees.

,D

ata

from

ref

. 19

a.

bDat

a fro

m r

ef.

19b.

C

Dat

a fro

m r

ef.

19c.

dD

ata f

rom

ref

. 20.

"D

ata

from

ref

. 21.

fD

ata

from

ref

. 22

. gD

ata

from

ref

. 23

. hD

ata f

rom

ref

. 24

.

Tab

le 1

1. C

alcu

late

d to

tal (

Eta

,, a.u

.) a

nd r

elat

ive

(AE

, kca

l/mol

) ene

rgie

s of

the

sta

tion

ary

poin

ts o

n th

e PE

S of

CH

2Ne,

CH

FNe,

and

CF2

N2 i

som

ers.

a

HF/

6-31

G//

MP2

(fu11

)/6-3

1G * /

/ M

P2/6

-31G

*//

MP3

/6-3

1G*/

/ M

P4/6

-31G

*//

HF/

6-3 l

G*

MP2

(f~1

1)/6

-3

1G *

MP2

(fu11

)/6-3

1G *

MP2

(fu11

)/6-3

1G*

MP2

(fu11

)/6-3

1G *

Spec

ies,

co

nfig

urat

ion

sym

met

ry

Eta,

A

E

Eta,

A

E

Eta,

A

E

Etot

A

E

Eta,

A

E

- 14

7.81

632

-246

.698

48

-345

.604

69

-

- 1

47.8

4378

(0)

- 14

7.81

190(

1)

- 1

47.8

3609

(0)

- 14

7.78

493(

1)

-

- 24

6.67

159(

0)

- 24

6.69

129(

0)

- 24

6.62

893(

1)

- 34

5.50

642(

0)

- 34

5.54

753(

0)

- 34

5.46

992(

1)

-345

.423

90

- 34

5.43

058

- 34

5.43

361(

0)

-

-

-

-

0.0

2.8b

4.8

19.7

b -

12.4

0.

0

43.6

b 25

.8

0.0

84.6

b

77.6

73

.4

71.5

- 1

48.2

3557

-247

.297

57

-346

.382

04

- 1

48.3

1059

8(0)

- 1

48.3

1059

4(1)

- 1

48.3

0022

(0)

- 1

48.2

3479

(1)

- 24

7.30

569(

0)

-247

.303

63(1

) - 24

7.32

392(

0)

C

- 34

6.30

324(

1)

- 34

6.34

9 15(

0)

- 34

6.28

425(

1)

-346

.221

12

-346

.250

58

- 34

6.24

146

-

-

-

0.0

0.00

3

6.5

0.5'

11.4

12

.7

0.0

28.9

0.

0

61.4

b 80

.3

61.9

67.6

- 1

48.2

2529

-

- 1

48.2

3399

-

-247

.284

88

-

-247

.284

51

-

-346

.366

84

-

-

-346

.357

18

-

-

-

-

- 14

8.29

878

0.0

- 1

48.2

9944

0.

0

No

barr

iers

to

addi

tion

are

foun

d at

thes

e le

vels

- 1

48.2

8906

6.

1 - 1

48.2

9431

3.

2 - 1

48.2

2427

0.

6'

- 1

48.2

2848

3.

5'

-247

.291

68

11.6

- 24

7.28

703

13.9

-2

47.2

8936

13

.1

-247

.288

26

13.2

-2

47.3

1019

0.

0 - 24

7.30

925

0.0

-247

.248

07d

23.1

' -2

47.2

4838

d 22

.7b

-346

.286

23

29.2

-3

46.2

8177

27

.3

-346

.332

69

0.0

-346

.325

36

0.0

-346

.268

26

61.9

' -3

46.2

5688

62

.gb

-

-

-

-

-

-

-

-

-

-

-

-

- 1

48.2

6676

- 24

7.32

937

- 34

6.41

308

-

- 1

48.3

3468

- 14

8.32

445

- 1

48.2

6420

- 24

7.33

193

-247

,330

76

-247

.348

18

-247

.289

3Zd

- 34

6.33

230

-346

.373

22

-346

.315

96

-

-

-

-

-

-

-

0.0

6.4

1.6'

10

.1

10.9

0.

0

25.1

b 25

.7

0.0

60.9

' -

-

-

"The

num

ber

of i

mag

inar

y fr

eque

ncie

s ar

e gi

ven

in p

aren

thes

es.

bBar

rier

for

CX

2('A

,) +

Nz

addi

tions

. T

he

TS c

ould

not

be

loca

ted,

des

pite

muc

h se

arch

ing,

at t

his

leve

l. dA

t HF/

6-31

G* g

eom

etry

.

CHZNz, CHF'NZ, AND CFzNz ISOMERS 1071

Table 111. Calculated and experimental energies for dissociation (kcalimol) of 1-6 into N2 and carbene products. Method la 2a 5 6 4 3

HF/6-3 lG* //HF/6-31G* 17.2 12.4 16.9 -4.5 -61.7 -35.9

MP3/6-31G*//MPZ(ful1)/6-3 l G * 41.1 37.9 1.6 15.5 -47.3b -20.0

MP2(f~11)/6-31G* //MP2(fu11)/6-3 1G * 47.1 40.6 5.1 16.5 -49.5' -20.6 MP2/6-31G*//MP2(f~ll)/6-31G* 46.1 40.0 4.3 15.9 -50.6b -21.4

MP4SDTQ/6-3 lG* //MP2(fu11)/6-3 1 G * 42.6 36.2 1.6 11.8 -50.7b -25.0 MP4SDTQ/6-3 lG* //MP2(fu11)/6-3 1G * + ZPE 36.4 28.9 -3.4 6.4 -54.1' -28.9 EXPT 62.lC 36.1-41. Id

52Be 50Bf

aExperimental dissociation energies of 1 and 2 into CH2('A1) and N2 calculated from the dissociation energies 1 and 2

bRelative energy of CF2NN(C%) with respect to CF2 + N2. CBased on AHfo(1) = 40 kcal/mo13* and AHfo(CH2) = 93 kcal/m01.~~ dBased on AHfo(2) = 61-66 kcal/m01.~~ eBased on AHfo(1) = 49.3 k~al/mol.~l fBased on AHY(1) = 51.3 kcal/m01.~~

into CH2(3BI) and N2 and the value of the singlet-triplet splitting in CH2 (9.1 kcal/m01)?~

the <C-N-N bond angle decreases slightly to 177.0' and the dihedral <H-C-N-N angle increases to 100.8". The inversion barrier also is a bit higher (0.06 kcal/mol). However, optimization of 1 at CISD/6-31G* and at QCISD/6-31G* give CZv minima. Like CaF2,17,18 diazomethane is a highly floppy molecule. A definitive solution to this prob- lem may require refined experimental and theoretical approaches. Experimental vibrational-rota- tional bands from a two-minima potential energy surface need to be considered. Theoretically, calculation of frequencies of the planar CZv structure at full-CI/DZ + P or at least at the reasonably large active space CASSCF/DZ + P level would be desir- able. Experimental data'9-21 for 1 were interpreted by assuming planar C2v symmetry. However, it was pointed out20 that "the higher-order centrifugal distortion constants have to be considered as fit- ting parameters which are necessary if all the mea- sured transition are to be included in the fit." This centrifugal distortion in diazomethane agrees with our quasilinear descriptions.

Diazomethane is stable thermodynamically with respect to dissociation into CH,('A,) + N, and CH2(3B,) + N,; however, our calculated dissociation energy at MP4/6-31G*//MP2(fu11)/6-31G* +ZPE is lower than the available experimental data (Table 111). The MP2(fu11)/6-31G* optimized geometries for both the C, and CZv configurations of 1 (Table I) agree within 0.001 A for bond lengths of 0.5" for valence angles (except for the <C-N-N angle). Both sets of calculated geometries are in good agreement with the experimental data (Table I). With a larger basis (QZ +P), all equilibrium bonds and angles are even closer to experiment, except the out-of-plane <C-N-N angle, which increases at this level. The frequencies calculated at MP2/6-31G* for the C, and CaV configurations of 1 are close. When scaled by 0.94 at MP-

2(full)/6-31G*, they agree with the experimental values. The exception is v6(bl), which is imaginary in the planar configuration. At MP2(fu11)/6-31G* vs(bl) is more than three times lower than experiment. But, the value of this frequency increases with larger basis sets and is closer to experiment. (A more detailed discussion of the nonplanarity of diazomethane and related systems will be pre- sented separately.22)

The ab initio potential energy surface for the dissociation of 1 into CH2('A1) + N2 was investi- gated ear lie^-?^-,^ Results at CI/STOSG are very poor because this molecule was found to be thermodynamically unstable and the barrier on the PES of the CHL('A1) + N, + CH,NN(l)('A,) addition reaction is 12 kcal/m01?~8~ At HF/DZ + P this PES has no barrier if the N, molecule approaches almost perpendicularly (93") to the CH2 plane with the C and N atoms nearly collinear (N-N-C angle 203 0 ) . 2 5

The CH2('A1) + N2 + 1 addition has a very small barrier (2.8 kcal/mol at HF/6-31G*, but this increases to 7.0 kcal/mol with the ZPE correction). The shortest distance R(C-N) in the transition structure (tsl) is 1.81 A ; Nz is almost perpendicular (94') to the CH2 plane, and the C-N-N angle is nearly linear, 180.6'. Analysis of the vector of the imaginary frequency v6(bl) confirms that this configuration is the saddle point on the dissociation pathway. We do not understand why this barrier was not located earlier25 since DZ+P basis sets usually give very similar results to 6-31G*. But, when correlation energy is included [i.e., at MP2(fu11)/6-31G*] no activation energy for this N2 + CH2('A1) addition is found. This agrees with the experimental observation that this addition proceeds efficiently even at 20 K.1gc,27

Geometry optimization of 5 at MP2/6-31G* in C1 symmetry also gives a nonplanar structure

1072 BOLDYREV ET AL.

Table IV. Calculated and experimental frequencies (cm-') of CH2, CHF, CF2, N,, 1-6, and 9-11.

HF/6-3 lG* MP2(f~11)/6-3 IG * MP2(f~11)/6-3 l G * Species Configuration Symmetry unscaled unscaled scaled by 0.94 EXPT

1'

2

CS

CS

c z v

3193 (126) 1565 (0) 3130 (62)

11.3

3060 (173) 1573 (20) 1332 (208)

8.5

1390 1295 729

4.9

2759 3.9

3388 (9) 2309 (777) 1589 (63) 1322 (15) 666 (13) 453 (1)

3518 (0) 1249 (4)

21.6 594 (164)

- - - - - - - - -

3167 2727 1542 1223 291 3451

3247 1145 245

19.4

3320 (11) 2002 (48) 1654 (1)

1098 (0) 1176 (27) 985 (27)

3428 (28) 1262 (7)

23.0

3298 2413 1514 1107 597 6721

3440 1145 519

1181 (4)

20.1

3002 1499 3086

2883 1483 1261

1282 1180 667

2180

3279 241 1 1467 1188 573 95i

3412 1139 45 1

3277 2410 1467 1185 573 139

3411 1142 451

10.8

8.0

4.5

3.1

19.9

20.1 - - - - - - - - -

3220 1605 1512 1507 1021 1039 837

3345 1176

21.2

3045 2018 1439 1042 341 312i

3161 850 239

17.3

2822 1409 2901

2710 1394 1185

1205 1109 62 7

2049

3082 2266 1379 1117 539 89i

3207 1071 424

3080 2265 1379 1114 539 131

3206 1073 424

10.2

7.6

4.2

2.9

18.7

18.9 - - - - - - - - -

3027 1509 1421 994 960 977 787

3144 1105

2862 1897 1353 979 32 1 2931

2971 799 225

19.9

16.3

2806= 1353" 2865"

2643b 1403b 1182b

10.0

7.5

1224' 1112' 665'

235@

3077' 2102' 1413e 1170' 564e 406e

3185e 1109' 421'

19.2

[3077]'

[1413]" [1170]'

(5641' [406Ie

[3 1851' [1109]' [421]'

19.2

4.3

3.4

[2102]'

- - - - -

-

- - -

3020' 1626' 1459' 991f

967' 807'

3132' 1125f

-

- - - - - - - - -

CHZNZ, CHFNZ, AND CFzNz ISOMERS 1073

Table IV. (continued)

HF/6-3 1G * MP2(f~11)/6-3 1G * MPZ(fu11)/6-3 1G * Species Configuration Symmetry unscaled unscaled scaled by 0.94 EXPT

5

5'

6

C1

CS

CHF . . N z ( t ~ 3 ) C1

4

3 CZ"

3513 (19) 2171 (447) 1613 (86) 1367 (25) 1192 (174) 684 (7) 266 (5) 604 (4) 509 (50)

17.0 - - - - - - - - -

3436 (15) 1937 (62) 1514 (27) 1376 (115) 1147 (94) 576 (18)

1218 (0) 1085 (18) 552 (4)

18.4

3367 2296 1439 1261 1082 719 418 368 880i

15.7

2188 (20) 1659 (424) 930 (65) 513 (3)

1509 (309) 670 (9) 207 (5) 457 (7) 319 (1)

12.1

1918 (142) 714 (320) 910 (19) 549 (10) 502 (0) 277 (10) 628 (15) 547 (1 78) 542 (14)

13.3

3380 2350 1432 1234 1098 650 262 522 3971

3283 2384 1383 1199 1092 692 530 465 251

3301 1534 1386 1223 1044 520

1086 958 497

15.6

16.1

16.5 - - - - - - - - -

2271 1513 825 42 5

1404 642 221 415 482i

1576 243 818 498 450 140 556 306 487

11.0

11.5

3177 2209 1346 1160 1032 611 246 49 1 373i

3085 2241 1300 1127 1026 650 498 437 236

3103 1442 1303 1150 981 489

1021 90 1 467

14.7

15.2

15.5 - - - - - - - - -

2135 1422 776 400

1320 603 208 390 4531

1481 1168 769 468 423

1079 523

1228 458

10.4

10.8


Table IV. (continued)

HF/6-31G* MP2(fu11)/6-31Gt MP2(f~11)/6-31G* Species Configuration Symmetry unsealed unsealed sealed by 0.94 EXPT

11

CF2 * Nz(ts) cs

2649 1280 1212 983 710 685 544 3 13 232

2176 1351 746 576 419

1086i 1397 407 347

12.3

10.6

1930 1225 756 535 422 785i

1275 384 295

9.8

1814 1152 711 503 397 73%

1199 361 277

9.2

2244h 1024h 891h 841h 618h 577h 457h 25Bh 190h 10.1

IR intensities are given in parentheses. aData from ref. 27. bData from ref. 29. CData from ref. 43. dData from ref. 44. eData from ref. 45. 'Data from ref. 46. gData from ref. 47. hData from ref. 4.

with a <C-N-N=170.0" bond angle as well as with <H--C-N-N=112.7' and <F-C-N-N= - 112.8' dihedral angles. At MP4SDTQ/6-31G*// MP2(fu11)/6-31G* +ZPE, 5 is thermodynamically unstable (Table 111). Starting from 5, a search for a transition structure at MP2(fu11)/6-31G* led only to the CHF('A1) + N2 dissociation products. At our most sophisticated MP4SDTQ/6-31G*//MP2(fu11)/6- 31G* +ZPE level, 5 is indicated not to be a viable chemical species.

While optimization of difluorodiazomethane (4) at HF/6-31G* gives (misleadingly) a local minimum, 4 is highly unstable thermodynamically with respect to dissociation into CF2 and N2 (see Table 111). Indeed, geometry optimization of difluorodiazomethane at MP2(fu11)/6-31G* (C, symmetry) leads directly to dissociation products CF, + Nz. No barrier is encountered. Hence, 4 also is not a viable chemical species.

Diazirine and the Effects of Fluorine Substitutes

Both at HF/6-31G* and at MP2(fu11)/6-31G*, diazirine (2), difluorodiazirine (3), and fluorodiazirine (6) are all minima (no imaginary frequen-

cies; see Table 11). Our best estimate indicates the relative energy of 2 to be is 7.5 kcal/mol above 1 [MP~SDTQ/~-~~G*//MP~(~U~~)/~-~IG* +ZPE]. We found 2 to be thermodynamicaliy stable toward dissociation into either CH2(3B1) and N2 or CH2('A1) and N2. While the CH2('Al) + N2 pathway leading to the formation of 2 is characterized by a barrier (tsz) of 19.7 kcal/mol at HF/6-31G*, this is reduced sharply with electron correlation to 1.6 and 5.0 kcal/mol at MP~SDTQ/G-~~G*//MP~(~UI~)/~-~~G* without and with ZPE, respectively. This result contradicts the earlier conclusions, based on lower level computation^?^-^^ The calculated frequencies for 2 at MP2(full)/6-31G* scaled by 0.94lZb agree well with the experimental values (Table IV).

At all correlated levels, fluorodiazirine (6) is lower in energy than its dissociation products, CHF + N2. The dissociation is exothermic at our best level [6.4 kcal/mol, MP4SDTQ/6-31G*//MP- 2(fu11)/6-31G* + ZPE]. Fluorodiazirine (6) may be observable experimentally because of the high potential barrier. We were able to compute a barrier (ts3) of 43.6 kcal/mol at only HF/6-31G*, but single point data indicated that the energy barrier due to correlation will be 23-25 kcal/mol lower (Table 11). Calculated frequencies at MP2(full)/6-31G* of 6

CHZNZ, CHFNZ, AND CFZNZ ISOMERS 1075

(scaled by 0.94, Table IV) may help identification of matrix isolated species.

Difluorodiazirine (3) is much higher in energy than its dissociation products CF2 + N2 [by 28.9 kcal/mol at MP4SDTQ/6-3 lG*//MP2(full)/G- 3 lG* + ZPE]. Nevertheless, 3 is well known experimentally. Its equilibrium geometry and vibrational frequencies have been determined.4 The persist- ence of this species is due to the large dissociation barrier (ts4) 34.2 kcal/mol at MP4SDTQ/6-31G*// MP2(fu11)/6-31G* + ZPE. The bond lengths calculated at MP2(fu11)/6-31G* for 3 differ from experiment by less than 0.02 A ; the valence angles vary by 1 O . These are the largest discrepancies between calculated equilibrium geometries at MP2(fu11)/6- 31G* and experimental data of all the systems considered here. The most pronounced effects of electron correlation on bond distances (0.06 A ) are found in 3. The calculated and experimental frequencies are very close (Table IV).

Other CF2N2 Isomers

The HF/6-31G* and MP2(fu11)/6-31G* optimized geometries of 9, 10, and 11 are qualitatively similar to those obtained previously at HF/3-21G. lo The MP2(fu11)/6-31G* geometry for difluorocyanamide

(1 1) agrees with the experimental s t r~c ture . '~ In particular, the degree of bending at the amino nitrogen and at carbon are reproduced satisfactorily.

The relative ordering of the energies of the isomers is of even greater interest. Both HF/6-31G* and MP2(fu11)/6-31G* predict difluorodiazirine (3) to be the most stable CF2N2 isomer. A polarized basis set is necessary to describe these molecules adequately. Difluorocyanamide (1 l), the only other isomer known, has the second lowest energy at HF/6-31G* followed by (10). In contrast, at MP- 2(fu11)/6-31G* the cyclic isomer 10 is predicted to be more stable than isomer 11.

Comparisons of CH2N2-CHFN2-CF2N2 Series

Dissociation energies (Table 111) in the diazomethane series decrease by 39.8 kcal/mol in going from 1 to 5 and by a further 50.7 kcal/mol from 5 to 4 (the latter is not a minimum on the PES, but included for discussion purposes). In the diazirine series, the dissociation energies decrease by 22.5 kcal/mol from 2 to 6 and by 35.3 kcal/mol from 6 to 3. The trends in dissociation energies in both series are due to decreasing relative stability of the triplet with respect to the singlet state in the CH2- CHF-CF2 set. The dissociation energies into triplet

Table V. energy differences of the dissociation products (kcal/mol).

Experimental and calculated (in parentheses) dissociation energies (AEdiSs) and experimental triplet-singlet

Reaction

No. A B AEdiss AAEdiss AST(A) AST(B) CAST(A+B)

1. CHz=CHz - C H Z ( ~ B ~ ) + CH2(3B1) + 173.3 5 la 0.0 2 . CHF=CHz - CHF('A1) + CHZ(~BI) + 156.0 5 7a + 17.3 5 7 3. CFz=CHz - CFz('AI) + CHz(3B1) +130.0 ? 2.4" +43.3 2 2.4 4. CHF=CHF - CHF('A1) + CHF('Al) +129.2 ? 7" +44.1 2 7 5. CHF=CFz - CHF('A1 + CFZ('A1) +97.2 2 7a +76.1 ? 7 6. CF2=CFz - CFz('Al) + CF2('A1) +72.1 * 2.4" + 101.2 ? 2.4

8. CHF=N=N CHF('A1) + NZ('Z,+) (-3.4)e + 176.7 9. CFz=N=N - CFz('A1) + Nz('C +) (-54.1)" +227.4

10. CHz=C=O - CH2(3BI) + CO(lf+) +77.Zf + 96.1 11. CHF=C=O - CHF('A') + CO(lC+) (+41.8)f +131.5 12. CFz=C=O - CFz('A1) + CO('C+) (+l.O)f + 172.3 13. c-C~HG - CHZ(~BI) + CHZCHz('A1J +92.7a +80.6 14. 12 CFz('A1) + CHZCHz('AlJ +50.0" + 123.3

16. 6 -* CHF('A1) + N2('Cg+) (+6.5)' + 166.8

7. CH2=N=N --t C H Z ( ~ B ~ ) + N2('2g+) +41.7-53.0' + 131.6-120.3

15. 2 - C H Z ( ~ B ~ ) + NZ('C,+) +27-+32h + 146.3-+ 141.3

17. 3 CFz('A1) + NZ('&+) (-27.5)' +200.8 aData from ref. 30. bData from ref. 48. 'Data from refs. 38, 41, and 42. dData from ref. 44. eCalculated at MP4SDTQ/6-31G*//MP2(full)/6-3lG* (see Table 111). 'Calculated at MP4SDTQ/6-31G*//MP2(full)/6-3lG*; data from ref. 28. BData from refs. 49 and 50. hData from ref. 40. 'Calculated at MPZ(fu11)/6-31G*.

0.0 +11.4b +50.0b +11.4 +11.4 +50.0

0.0 +11.4 +50.0

0.0 $11.4 +50.0

0.0 +50.0

0.0 +11.4 + 50.0

0.0 0.0 0.0

+11.4 +50.0 +50.0

+ 170.5[3rIg]d + 170.5[3rI,] + 170.5[3rIg] + 139.2[311r]d + 139.2[311r] + 139.2[3rIr] + 101.5g + 101.5

+ 143.5[32,+] + 143.5[3C,+] + 143.5[32,,+]

0.0 +11.4 +56.7 +22.8 +68.1

+ 113.4 + 170.5 + 181.9 +220.5 + 139.2 + 150.6 + 189.2 + 101.5 + 151.5 + 143.5 + 154.9 + 193.5


HF/6-3 lG* / / HF/6-3 1G* MP2(full)/ 6-3 1G*

MP2(f~11)/6-31G*/ /

-4.6

F

CH,F + -+ CH,+ A -13.1

-9.9 --+ CH,+ CH,F + N N A -11.3

+7.9 CH,F + CH,=N=N - CH, + CHF=N=N

CH,F, + CH,=CH, - CH, + CF,=CH,

CH,F, + CH,=C=CH, + CH, + CF,=C=CH,

CH,F, + CH,=N=N - CH, + CF,=N=N

CH,F,+ CH,=C=O -+ CH,+ CF,=C=O

F F

+7.3

-4.5

+7.0

+24.2

+31.9

+27.4

+26.9

A CH,F,+ + CH,+ -2.8 -4.3

F F

CH,F, + A - CH, + & -13.0 (11)

-6.4 -7.9

CH,=CF, + CH,=C=CH, - CH,=CH, + CF,=C=CH,

CH,=CF, + CH,=N=N - CH,=CH, + CF, =N=N

CH,=CF, + CH,=C=O - CH,=CH, + CF, =C=O

CH,=CF,+ + CH,=CH,+ x F F

n

+11.4

+28.6

+36.6

+1.7 (16)

-8.5

- CH,=CH,+ XN -2.0 A N CH,=CF, +

N N

Scheme 1. have been taken from the l i t e r a t ~ r e . ~ ~ . ~ ~

Isodesmic reaction energies for fluorine transfer reactions. Ab initio data for many reference molecules

CXz and N2 fragments are approximately the same along the series. The variation in the singlet-triplet excitation energies in the CH2-CHF-CF2 set mainly determines the trends in the dissociation energies of 1-6.

The barriers for the CX2('A1) + Nz addition reac-

tions giving diazirine (2), fluorodiazirine (6), and difluorodiazirine (3) increase sharply. The barriers can be regarded as arising from the need for pro- motion of an electron in CX2 from the carbon lone pair into the p,,(C) orbital and in N, either from a lone pair into a Tf-orbital (combination with ex-

CHZN,, CHFWZ, AND CFzNz ISOMERS 1077

cited CX2 then leads to the diazomethanes) or from a .r,-orbital into a <-orbital (leading to the diazirines). Hence, the singlet-triplet separations along the CX, series again set the trend (see Tables I1 and V).

Double-Bond Dissociation Energies Trend in CX2N2, CX2C0, CX2CX2, and CX2(CH2),

The change with increasing fluorine substitution in the dissociation energies of CX2N2 (into CX2 and N,), of CXzCO (into CX, and CO), of CX,CX2 (into CX, and CX,), and of CX2(CH2), (into CX2 and CH,CH,) in their ground states can be approx- imated by the sum of the triplet excitation energies of both fragments. The data in Table V proves to be approximately true.

Isodesmic reactions (Scheme 1) may be used to evaluate and compare the influence of fluorine substitution on the stabilities of diazomethane and diazirine, as well as other reference molecules. The calculated energies of reactions (2)-(4), (lo)-( la), and (16)-(18) show that transfer of one and two fluorine atoms from CH3F, CH2F2, and CH2=CF2 to cyclopropane, cyclopropene, and diazirine are exothermic, whereas the transfer of fluorines to allene, diazomethane, and ketene [see eqs. (5 ) , (7)- (9), and (13)-(15)] are endothermic. This helps understand why fluorodiazirine and difluorodiazirine are more stable than fluorodiazomethane and difluorodiazomethane, whereas diazomethane is more stable than is isomer, diazirine. Such effects of fluorine substitution have been discussed exten- sively in the l i t e r a t~ re .~O-~~

EFFECTS OF MP2 OPTIMIZATION

We found several important consequences of MP2(fu11)/6-31G* optimizations. At MP2(full)/ 6-31G*, the planar forms of diazomethane (l), fluorodiazomethane ( 5 ) , and dif luorodiazometh- ane (4) all have one imaginary frequency (transition structures). In contrast, all these species have planar minima (no imaginary frequencies) at HF/ 6-31G*; and 1 is planar at CISD/6-31G* and at QCISD/6-31G* as well.

In contrast to the HF/6-31G* CX,('A,) + N2 results, additions to give 1, 4, and 5 have no barriers at MP2(fu11)/6-31G * . Since difluorodiazomethane (4) is unstable thermodynamically toward dissociation into CF, and N2 and there is no dissociation barrier, 4 cannot be expected to exist as a viable species. MP2(fu11)/6-31G* optimization sharply reduces the barriers found at HF/6-31G* for the CX,('A,) + Nz additions: from 19.7 to 0.5 kcal/mol for 2 and from 84.6 to 61.4 kcal/mol for 3.

CONCLUSIONS

The main conclusions of this study are:

1.

2.

3.

4.

5.

Diazomethane (l), fluorodiazomethane ( 5 ) , and difluorodiazomethane (4) do not have planar minima at MP2(fu11)/6-31G*, although 1 is planar (C,,) at CISD/6-31G* and at CQISD/6-3lG*. The CH2('A1) + N2 -+ 1, CHF('A') + N2 -+ 5 , and CF2(lA1) + N2 + 4 addition pathways have no barriers at MP2(fu11)/6-31G*. Fluorodiazomethane (5) and difluorodiazo-meth- me (3) and not viable species. Their energies are higher than the products: CHF + Nz by 3.4 kcall mol, and CF, + Nz by 54.1 kcal/mol [at MP4SDTQ/6-31G*/ /MP2(full)6-31G* + ZPE], respectively, and there are no barriers to dissociation. Of course, entropy also favors dissociation. While difluorodiazirine (4) is higher in energy [ 28.9 kcal/mol at MP4SDTQ/6-3 lG* / /MP2(full)/ 6-31G* + ZPE] than the dissociation products CF2 + N,, 3 is stable due to the high dissociation barrier i34.2 kcalimol at MP4SDTQ/6-31G*//MP- 2(fu11)/6-31G* + ZPE]. Fluorodiazirine (6) is only 6.4 kcal/mol more stable than the CHF + N2 products, but the dissociation barrier CHF + N, to give 6 is quite high [25.1 kcal/mol at MP4SDTQ /6-31G * / /HF/6-3 1 G* 1. Diazirine (2) is more stable than the CH2 + N2 products by 28.9 kcal/mol [at MP4SDTQ/6-3 1G * //MP2(full)/ 6-31G* +ZPE]. The barrier [5.0 kcal/mol at MP4SDTQ/6-31G*//MP2(fu11)/6-31G* +ZPE] for the reverse reaction, the CH2('Al) + Nz addition to give 2, is quite low. When more fluorines are present, the trend in stability of the CX2Nz set toward dissociation, as well as the increase of the barriers for the CH2 + N2 -+ 2 , CHF + N, -+ 6, and CF, + Nz +

3 additions, are related to the increase in the singlet-triplet excitation energies along the CH2-CHF-CF, series.

A.I.B. thanks the Alexander von Humboldt Foun- dation for the award of a Fellowship. The Deutsche Forschungsgemeinschaft, the Fonds der Chemischen Industrie, and the Convex Computer Corporation provided financial support at Erlangen. We thank Profes- sor T. Tidwell for information and a preprint of related work.

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Documents

Ab Initio investigation of the structures and stabilities of CH2N2, CHFN2, and CF2N2 isomers: Important consequences of MP2 optimizations