AB initio studies of hydrogen exchange and abstraction in the H + CH4 system

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‘CHEMUL

PHYSICS LET~R$

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STUDIES OF’iiYhROGEN EitiHANtiE ABSTRkTION IN THE-H + Cl& SY !3EMi

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-..1Febi~.197i :

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AND

. S. EHRENSON and M.D.. NEWTON Department of Chemirrry, ~Brookhaven Xational Laboratory, Upton, New York,11973, USA

..:

Received ‘:

..

29 November

_, .&iergies

product

and ojtimal geometries have been computed in the UHF LCAO MO GTO framework for reactant and likely inteimediate structures in the exchange znd abstraction r&ctions ofH + CH4. The effects

df

addition of polarization functions to both the hydrogen and carbon basis sets have been evaluate&

.. F&,.ieactions if thermal and hot hydrogen atom

@tapes with methane are of considerable experimental and theoretical interest, both for their own sake and some siniple because they are p&entially archetypes,for channels

of radical abstraction

and exchange

in higher

homolog and substituted hydrocarbons. Work on the .two principal charinels of reaction.for methane has recently been.surveyed.[ l] . The essentially thermoneut&abstraciion reaction, H’ + CHq + HH’.+ CH3 +.0.3 kcal/mole, ;. ‘.

(1)

:

has y activation energy of = 12 kcal/mole &d has been studied u&g thermal protons [2, 31 . Exchange, ,‘..

H’+CH,

+CH3H’+H,

(2)

on the other hacd, has not been observed in the thermal. .iegion but.‘is repq.rted to htive a threshoId energy of = 35 kc~l/molc (for T. + CD,, tritium produced in ri+clear recQii and photochemical processes [4] ). Stereoch.emical donsiderations are important in reasoning ab~ut.thd&r&ction pathways, particularly ._&,rsactj& (_) wlieie the.reactants &nd products are indisting&shable.exce$t for isoibpic differences. -.. .-,The’ab,i&o calculqtidns reported here have, a&drdin$y;been direkted tcjwards elucidating the ,. ,

197 1

.‘.

details of intermediate structuies along likely reaction pathways, with considerations of stereochemical as well as energetic factors in mind. All energy-structure caiculations presented are of the LCAO MO.type, empldying extended gaussiantype orbital (GTO) basis sets; the smallest set used was the so-called 4-3 1G basis [.5] (two basis functidns for each valence atomic orbital@. For certain configurations, this basis was.supplemented with CT0 pol+a+n functions (2p for hydrogen and 3d for carbon)rf. Most of the calculations on the open shell CHs system, were carried out in the unrestricted Hartree-Fock (UHF) framework and the spin expectation value (U*>) monitored. For comparison, many of the calculations were also examined in the restricted (RHF) framework (tS2) constrained to be 0.75)ZfS. The most

,abstraction

plausible stereochemistry fur low energy is approach of the incoming H’atom along

a CH bond of methane, with subsequent departure of . f Extensive calculations

with as basis for small hydrides .have beenreported by Lathan et al. [6] : $4 Eoth the 2p’md 3d polarization functions we!e given

exponents,of 0.75. The sensitivity of tkniethane

total

energy to hydrdgenic 2p and.caFbon 3d exponents has previously been,examined by R+enberg ,ad Schaefer I : ‘.,.

(c) c, SUBSTITUTION

Fig. 1. Perspective

drawiws

of the energy optimized intermediate structures (4-3 lG, UHF level) for the abstraction tion channels of the H’ + CH4 reactions considered.

and substitu-

in the opposite direction along this axis, maintaining CT,, symmetry throughout (see fig.. 1a). This is known as the axial attack mode [IO] _Off-axis attack &ould be less favorable, since it leads,to structures : which bear resemblance in the extreme to those postulated (vide infra and ref. [l]) as intermediates in substitution (i.e., the C, structures), and, hence, are expected to be higher in energy. We have therefore examined theaxial attack pathway as a model for abstraction at & near the threshold energy of k 12 k&/mole. Fig. 2 represents the: potential energy surface’ obtained for the ati& abstraction w,ith the 4-3 lG

HH’

1.36 / 1.28 l.ZOi

I

, 1.08

-. 1.24

:

1.40

1.56

:

1.72

big. 2. me potisi’tid energy surface for abstraction at the. 4-3 1G level; ‘llie cooidinates &e’principal geometri&vaiiants~.,:

iin A); optimization implicit. Numerical a&+em-.‘sntour

,.I.

,,. oi the~tikining 2 degees 6f frydoG.’ @ues in kca.I/mole.are foi iRe saddle: @Et :f lines‘show~. Cotit& tin6 sepa.@jOn

_ y.$+$e l?,‘n&ber 1, _. : ..’ ‘_,,.. ,._. -:

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.,

,CilEMICAL PHYSICS,LETTERS

.’ I

.,basis,To~‘en&gies &ere calculated for 68 individual sparining~crucial H’H and CH ranges (the “:othcr 2 degrees:b&g optimized inall cases), and 1296 ‘:&h&&re ge’nerr$d.for the surface by polynomial ‘i&rpola~on~ IeSng to a predicted Lqdd!e point .: &sition,at rfi$ = 0.93, A, rCS = 1.38 A and a barrier “height of 25~.0~kcat/mole‘.with respect to the reactants, H + CH4: pi loc+iosi and height of the saddle point were sub&quentIy verified by a quadratic fit in ttio ‘dimensions based on mlcuhited energies in the immedi‘.ate v@nity of the interpdmd siddie point. The other geometric parameters representing the saddle point configuration are ~C+r,etiyl = 1.077 A and Q,, = .;. t Polynomials of order n-1 were fit to n points in each ’ st&.tres

(HI-l’-first and then CH) dimension and interpolation performed to yield as closely as possible an equally spaced grid.

1 Febfiary 197i

-j’;

103.6”; ,Qveiall, reaCtion (I) is predicted to be ‘ij 4.5 kcal/mole exothkrmic.~ , i When 2p polarization functions on-hydrogen were 1: included in a similar searching scheme, the predicted ” saddle point occurred at essentially the same geometry ‘. = 1.37 A) and with essentially @Hi’ 7 0.93 A, rC‘CH the same barrier (24.2 k&/mole higher than H + CHq)Roth CH, and CE$ were stabilized by =9 kcal/mole. ‘Ihe exothermicity. of reaction (1) dropped slightly to ,; 3.2 kcal/mole. Reaction (2), where formally identical particles are exchanged, has historically been assumed also to proceed along an axial attack pathway, but through a transition state similar to %2 reactions, i.e., Walden inversion [I 1, 121. The direction of attack is opposite to that for abstraction,

toward

the rear, or carbon

end,

Table 1

Structure and energy results computed for the H’ + CH4 exchange reactiona)

Symmetry B&is r1

r2

.

c s b,

D3h 4-31G

+2PH

+3+

+2~~,3dc

f2PH

l.320c) (1.320$

l-378,4 (1.309)

1.317

1.198

1.187

(1.320)

1.074 (1.079)

1.077 (1.080)

1.077

1.081

1.083

(1.077)

1.092,o (1.096)

1.100

(1.077)

105.1, 1 (103.8)

104.1

72.6,9

73.7

86.2

86.0

-to.S39s.

(73.1)

.

td,

4-31G

1.401 (1.329)

.b

,ti(kcal/mole)

+2PH

1.452 (1.342)

e-

Got (au)

4-31G

C4v

-. -40.5520 (-40.5350) :

54.6 (65.3) 0.846

-40.5674

-4os734

(-40.5516)

(40.5499)

(-40.5597)

54.3 (64.2)

(64.8)

54.9 (63.5)

(?.a34

0.811

-4OJ162.1 (-IO.s046)

-4OS3Sl

-4o.s200

77.1,2

74.6

74.7

71.8

(84.4) 0.827.

S

0.805

0.803

0.195

a) AU distances in A, angIei in degrees, energies as indicated. AE is the energy relative to separated H + CH+ See fgs. lb- Id for parameter I&elk. Bold face parameter values indicate energy optimization carried out with respect to this parameter. With two or more such degrees of freedom, cycling to internal consistency with optimization was accomplished. Values in parentheses .: undei rrram’entrfes-r&efor the RHF framework calculations.‘The RHF energy-optimized geometries were based on the RHF. method proposed by SegA [ 201. Using these optimal geometries, the total energies were then recalculated with the Roothaan ,- ‘. &F $ocedure to facilitate comparison with the calculations using 3d orbit&, since the latter calcuhrtions employed the .. Rdbthaan method [8,9]_ The ;wo RHP methc,Is lead to slightly different total energies.‘with the Roothaan energies being the

:‘::l&rer_ :i.., I .,:: .. b)Ititti entry for~the~etlipsedconformation, the second, following the commas are’for the staggered conformation. Only terminal ;digiis which &urge frtiin the eciipsed values are shown. )‘.o),The ?r::v&e of:l_32,A w&.estimated from RHF results *th the smaller basis sets. The opurnh UHF va!ue is expected,to be ‘.i, d*+&i larger., -. I ; .‘ ..,, ,..: ‘.. ‘, ._ : ..,. ;....-i I, .. ..,. I., ” : .,;.... .-_, ,,’ .. “. ._‘l ,, ., ,‘. ;.,2& --,,: .,-:(.:;._ ;I;, ‘ ;‘ , ..,, ; .: .” ..;.,..‘..I y; .,:“:,, ;: ‘., _..’ -, -. :. :,.“ ‘ .. “;..y .,,;. b : “_ \ ;. “,, ,,,. ., .’ -. -.: .-: ,,_,\.;‘ ,,,‘ _.: I.- ::.c_ _;,,,> : ,. .. : .. ’_ : :, _.,. .:i_;;iz.:,-.I ,. ,_., _._ .._.. _‘; _ 1. ,: 1 ‘. i

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..: ‘._ .:: _I ...\ t-y

Volume 13, number 1.

‘CHEMICAL PHYSICS LETTERS

:

:

lFhW.1972

.‘, Tabie 2 1 .,: NormaI-mode analysis of the vibrations of the D,b structure ofCHsa) Symmefzy

F-matrix elements mdyne/A

coordinates

..Fll F22

F12 A: Symmetry Rj; Wkms)/JiR.G &Ah4 + A@24 -ADIS - aB25

F33

+ Ah4

F44

-

F34

E’ Symmetry R sa;(2Ad1 - ad2 &b; (Adz - A&)@ R 6a;D(2AB14 -

A&4

aSss)I&-

ad3,lJT

-

M34

+ 2Ai31s - A&s - &W/X= - AP34 + AP25 - APss)/2 &,;Dh%4 R,,:

dt2A ‘%!3 - A@412-

R,b;dWlz E” Symmetry Raa:D(2@14 -2AS15

R,b;D(APz.a

A&13)1&-

1.72 0.29

F77

0.39

0.39

F56

FSS

where A, = 4n2c2wi,

0.26

basis sets with D = 1.425A = rlr d = and wn are the frequencies

this pathway would be akompanied bjl inversion is particularly noteworthy. While the reaction under consideration is not susceptable to any direct experiFental test of this implication, supposedly related hydrogen exchange processes involving substituted akanes have been characterized by almost complete retention of. configuration [ 131. Tkis suggests that. alternative exchange pathways in methane should be appears in the off-axis

...’

0.10

-0.11 -0.01.

0.26

A1334 - AS25 + Ah)/2

lb). Table 1 presents details of results obtained on klculations of this type of structure. The stereochemical implication that exchange by

:

-1.60 0.15

6.07

- A@24 - Ah + M,, + AP35)/-

transition state for exchange via Walden inversion (fig.

_

-1.49 0.14 -0.78

0.30

F67

of a CH bond axis of methane. Again C3v symmetry is assumed to be maintained, that is, up to the point where the axial hydrogens are equally displaced from the carbon (which lies in the plane of the equatorial. hydrogens). At this pgint we have a Djh trigonal bipyramid, which is the proposed structure of the

examined., ” A plausible alteinatiie

6.i6 1.00

Fss

F5.7

a) For the energy optimized structure using the 4-31G and all Q’S = 120’ (L HbCHbj. See fig. lb. b) Units of mdyne/A-‘amu-‘,

6.10 1.06. 0.55

F66

- A~1s)/fi

-

,.

:

1.074 A = rz, all B’s = 90” (LHaCHb)

of the nqrmal modes.

approach of H’ toward a methane _-

hydrogen, cuhninating in ‘the formation of a C, structure, as shown in fig lc. Exchange is accomplished by departure of the

hydrogen with identical environment to that of H’ in the,intermediate, along a path identical to that followed by H’ in its approach_ Stereochen&try suggests retention of configuration in the absence of any rearrangements of the Cs structure [ 141. Distance and angle parameters as well as energies for both the staggered (fig. Ic) an’d eclipsed forms of the C, structure are to be found in table 1, along with those of h third possibility,.a CH, structure with’Cav symmetry (fig. Id), which represents an intermediate in a pseudorotation prbcess leading to racemikion, [1,15]. The results obtained using the 9-3lG basis reveal eat thk ‘pathway through the .D3, structure invojyes ! barrier height !t least 20 kcaj/mole less than those -’ occurring in the other exc&nge.processes donsideredr In order to ascertain’whbther the’&,, structure truly ‘- :, .:. ... . ., : : _ zjl, :’ ‘.., ‘. .‘.. ,_. .‘. :. .., .,

._ ,.V+une

.i_._ ..:.

13,ntimber 1

: _-

.

:

‘.

.

CHEMSCALPHYSICSLETTERS

:

-represents a saddle poiirt; we have carried out a normal ,-.:-mode arialysis of.its vibrat’idns.,Table 2 contains the ‘, ‘pertinent data for the optimal structure obtained in the,IjHF framework following standard prescriptions -. for symmetry coordinates [ 16, 173 _In accord.with bur’assumpiion; all force constants with the exception of.that corresponding to the vibration associated with .the Walden inversion motion are positive and the frequency w3 = (X3/4r2c2)‘A is imaginary, as it should be if D3,., is a local .maximum with respect to the rqaction coordinate. It is also of interest relating to the questidn of pseudorotation (DJh + C4,) that the ,vibration modes corresponding to R2, R, and R, are relatively soft. Only equatorial bond displacement modes are stiff, but they would enter only as very smali displacements in the process. Addition of 2p polarization functions to the basis set for hydrogen improves the total energy of all po!yatomic species in tire UHF framework as follows: -lM(C4v)I% l~(C,)I>~(DSh)I =&(CH4) I. Thus the Dgh pathway process, while remaining the most favored energeticqy with barrier essentially unchanged by addition .of the 2p polarization functions, is somewhat less favored than was the case in the absence of polarization functions. The inclusion of hydrogenic 2p functions also leads to an appreciable shortening of the equilibrium length of several CH bonds (i.e., those denoted r1 in fig. 1). In order to test further the importance of polarization functions, WChave carried out calculations for the DSl-,’ structure including both 2p orbitals on H and 3d orbitals on carbon [7] ..The large amount of com.puter time involved in calculations with this expanded basis precluded a total geometry optimization, and we have assigned the values r1 =1320Aand r2 = 1.077.& These v&l& are similar to the optimal DSh distances obtained for smaller basis sets in the RI-IF approximation (first two columns of tabie I)?. Althsugh the addition of 3% functions clearly lowers the .(?-I5 total energy, we find that, as was true for 2pH functions alone, the D3h barrier is essentially unaffected.‘One.should note, however, that both the ‘? Since

1 F&u&y 1972

vibr&ibnal modes inyolvir?gthe axial CHbonds are

.-quit& soft (table i), it is expectid that the Dgh energy .-,_ obt&&
reactant CHd and the intermediate D3h structure have. relatively high symmetry. One might expect 3k functions to lower the barrier sigrrificantly-in other pathways in which the intermediate has lesssymmetry (9. C4, or C,), thus allowing the 3darbitals to participate more extensively in the molecular orbit&. TIltis expectation is supported by the results of Dedieu and Veillard [ 181 where polarization functions were found to stabilize the lower symmetry species (C,, CH3 F) re!ative to the higher symmetry species (D3, CHSF,), the reaction of interest being the SN2 exchange of fluoride in the F- ‘%CH3F reaction. As a final comment on polarization functions, we note that inclusion of 3dC functions by themselves (column 3, table I), lowers the D,, total energy about the same amount as inclusion of just the 2pII functions (column 2, table 1). Most of the discussion so far has dealt with the unrestricted approximate Hartree-Fock (UHF) results. Table 1 indicates that relaxation of the spin restriction ieads to appreciable departures from pure doublet states. Correspondingly;we find that the unrestricted energies for the various CHS structures are significantly lower than their restricted counterparts; i.e., the calculated barriers for the three exchange pathways are =7-10 kcal lower in the UHF framework. The equilibrium lengths of the weaker CH bonds in the saddle point configurations are also seen to be somewhat longer at the UHF level. One consequence of the extra flexibility in the UHF framework is that polarization functions are seen to be somewhat less important at this level, than is the case for the RHF calculations. The.differences between UHF and RHF results also underscore the limitations of the single configuration framework in representing the CI-IS energetics. Our UHF results can be considered as providing a level intermediate between the RHF single configuration model, and more elaborate configuration interaction (CI) calculations. CI calculations on the CH, system have recently been reported by Morokuma and Davis [ 191. In summary, we have presented the-results of approximate Hartree-Fock calculations for various channels of hyhrogen exchange on methane, and discussed preliminary irtdications that more e,xtensive calculations would make the channels which allow stereochemical retention or racemization (by pseudorotation of thaDXh dirOUgh c4v type StNCtI&S

Volume, 13. number 1

CHEMICAL PHYSICS LEtiERS

the energetic

sense, or, on the other, whether geometric (or steric) factors are sufficient to make the two paths dynamic:

ally competitive, is difficult to answer at the present time. Moreover, the related questions from..the experimental point of view of the iack of information,on.exchange with thermal protons, and the propriety of extrapolation of stereochemical information from heavier more complicated contribute to uncertainty

; ‘.

:i Fe!&+_

. . ,.

1372. :

.’ : /3] M.J..’Kurylo aird’R.R. Timtr~ons, J. Chem. Phys. 50 (1959) . 5076. ,[41 C.C Chow and F.S. Rowland, J. Chem. Phys 50,(1969) -.” 5133 and referen& therein. [S] R. Dithfield, W-3. Hehre and J.A. PopI&. Jl Cbem. Phys. 54 (1971) 724;. [6] W-A. Lathan, W.J. Hehre, L:A. Curtissand J.A. Pople, to be published. [7] S. Rothenborg arid H.F.Schaefer III, J. Chem. Phys 54 (1.971) 2764. [S) C.C.J. Roothaan, Rev. hIod. Phys. 32 (1960) 179. [9]‘S. Rothenberg, P. Kolhnan, M.E. Sch%artz, E.F. Hayes and L.C. Allen, Intern. J. Quantum Chem. 3s (1970) .. 715: [ 101 R. Wolfgang, Accounts Chem. Res. 2 i1969) 248. 111 f E. Gorin, W:Kau.rmann, J. Walter and H: Eyring, J. Chem. Phys. 7 (1939) 633. [ 121 D.L. Bunker and M. Patteugill, Chem. Whys Letters 4 (1969) 315; J. Chem. Fhys. 53,(1970) 3041. [ 131 C.F. Palino and F.S. Rowland, J. Phys. Chem. 75 (197 1) 1299 and ieferences therein, [ 141 S. Ehrenson, Chem. Phys. Letters 3 (1969) i8.5. [IS] F.H. Westheimer, Accounts Chem. Res. 1 (1968) 70. [ 161 J.S; Zioniek and C.B. Mast, J. Chem. Phys. 21 (1953)

[14]) more [l]., or by, rearrangement of C;‘&nctures competitive with Walden inversion. Whether, on the one hand, more elaborate computations will demon-

strate that they. are truly competitive’in

’’

substrates’to methane.also in interpretation Of all

results. It is a pleasure for us to acknowledge receipt of results on the H + CH4 system from Professor K. Morokuma prior to publication, and for conversations with him concerning these studies.

862. [17] P.C. Haarhoff and C.W.F.T. Pistorius, 2. Naturforsch.

References

14a (1959) 972. [ 181 A. Dediec and A. Veillard, Chem. Phyr Letters’S’(1970) 328. [ I9 ] K. Morokuma and R.E: Davis, to be published. [20] G.A. SeSaJ, J. Chem. Phys. 52 (1970) 3530.

[l] R.E. Weston Jr. and S. Ehrenson, Chem. Phys. Letters 9 (1971) 351. [2] R.N. Walker, J. Chem. Sot. (1968) 2391A.

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