Potential energy curve in the trans—cis isomerization of glyoxal

V&&29,

nitiber

+EMICAL+I~ICS

L

1 Novaber

LEVERS

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PbTErVrlAiENERGYCURVEINT~E.~~~§-CISISOMERLZATIQNOF

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1974

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GiYOXAL

Keqneti R,.SUNJ$?ERG and Lap M. CHEUNG

Am& Lnboratory-USdEC.and

Departknt

:

of &emisfry,

I&a Store University, Ames, IhuoSOO5~0. UXA

Received 21 June 1974

A series of Hartree-Fock calculations on glyoxal for the irons, ciri and five inte&ediate values of the diyedrat angle are presented. The molecule geometry is optimized ot each point. The’energy’for the,‘&zns-cir isomerita~ion is 4.77 kcal!moie and the energy barrier is 7.22 kcal/mole. Moment of inertia for the rotation of one of the aldehyde groups about the carbonLab& bond is calculated:

I. Introduction

The-molecular’strricture of trhns-gIyoxa1 was determined from electron diffraction data by Kuchitsu et al. il], and the microwave spectmand structure of the cis configuration were reported by Durig et al. [2]. These data suggest that the geometry of the molecule undergoes some distortion as the dihec@ angle (0) varies from 0” (rrans) to 180” (iis). In one of thesepapers [2] it is suggested that this vtiiation might be of importance in understanding the barrier, :’ : Two calcuiations on glyoxal are in the rec.ent literature. The first, by Pincelli et al.. [3]; is a HartreeFock calculation; the calculation for the rrans configuration used the known geometry and the calculation .forthe cis configuration used the rrans structural :. . .. p’arameters with h dihedral angle of 18C”. The cii_imzs energy difference h this calculation ‘tias greater ‘, by. about a factor of-two than the’reported value-of ,. ,Currie and &say [4]:The second calculation, bjl Ha [S], used a.standard geometry for both the cis ‘,..1 and trans configurations, and with the Hartiee-Foc& approxiination ,quite’&curately reproduced the: ,.,Currie-@say energy difference; it also quite, rea- ” ‘: .- sonably predicted the dipole moment,of the cis con-’ :. ::. .figuration reported m ref. [2], as did the first.cal~ :: -- v &]at,ion;.

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!n &is paper the authors report’s series-bf Ha&& ;.Fock calculatioiis~on glyoxal: ‘+e calcul&ns’oPti-

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‘mize the molecular’geometry for the tram. cti, and five intermediate valuesof 8. It was found that the cis-rrans energy difference was a compromise between the values reported in refs. .[3,, 51, and it was found that the variation of the geometry had a substantiai effect on’the ‘moment of inertia for the rotation of one of.the aldehyde groups about the carbon-carbon bond.

2. Baslsset Even-tempered cartesian gaussian atomic orbitals [6] were used in the.calculations. The bases for oxy gen, carbon arrd-hydrogen were (9sSp/3sZp), (6s4p/3s2p) and (4s/2s), respectively. The eventempered parameters for oxygen and carbon were :determined by optimiz& the Hattree-Fock energy of carbon monoxide whiIe those for hydrogen were determined from formaldehyde [7]. Contraction coefficients were obtained by the scheme given in ref. [7]. -’ -1 .. ‘. ‘_’

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~3.@rtlrn@ation of the geometry . ,.

molecular geometry of. .carried out in ‘.-’ three srages]_Wer&s&ned &iqgeomet&s used by Ha. : .. a3 aninitial approximation to tie molecuIar geometry The optin-&ation of.&

. . . .. I the cir mnd
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49

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.“hliie-29,,numb&‘1 ,.

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CHEMIC+L

PHYSICS LETTERS

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of the.& and _transspecies, and we then optimized Ah~se geometries in the following manner: ,;;(l j Keeping R,,--, , RCO, LCCH and LCCO constant,

;

the total energy was evaluated for tllee,points.at and near the initial v-Sue of RcC. A parabpla was fit.ted to these points, and the minimum predicted by the para,bola was taken to define the optimum value of&c. .. (2) Ke@g

LCCH and LCCO fixed and using the’

value of R,, from step 1, the total energy was evaluated-for six points at and near themitial values of ‘.. Ra and&. A’quadratic surface was fitted to these six points, and the minimum predicted by this surface was taken to define, the optimum values of. ;kH

and&.

ferenl.‘ in&two configurations. .The changes in RRC_j, RCO, and LCCH are all about an order’of magnitude ‘,Iless than the changes in the RCC and LCCO ‘variables. .- ,Thus we optimized only RCC and LCCO m the varioiis@auc/~e configurations-calculated: The parti.. cular .vaIues of.the minor parameters were chosen in the fclhowi& ways: for 8, = 15” and 0. = 16.5” the ‘values fcr the pans andcis configuratiorrs were used respectively; for 0 =.65”, 8 = go”, and 8‘= 115” the minor parameters were taken to be the averages of ‘value:;for the Vatis and ci,r species. The optimizations of R,---- and KC0 in the ghdze configurations were made in a matier much like the trommd cis optimizations; only much less work was invol&j_

... (3) Using the values,of RCC, RcH, and R,, predieted by steps 1 ‘and 2, the total energy was evaluated. for Six points at and near the initial vahres’of LCCfi and LCCO; As histep 2, a quadratic surface was fitted to these:points, and the minin&n predicted by this surface was, taken to define ari optimized, set of structural parameters for the_molecule at the value of the dihedral angle-considered. In executing this procedure we found that the : ’ &$ural parameters predicted differed considerably from the parameters assumed initiahy. The procedure was then executed again; the values’from this calcula‘tion differed only slightl,y~from those determined by t&e fnst optimjtitjon, and these later values are displayed in table 1. .-An examination of the structural parameters for the cis and Iram configurations showed that R,, and LCCO were the only parameters that, are very dif-

1

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The final results are displayed in table 1,

4. The barrier The absolute and relative energies are reported as .a function of the dihedral angle in tables 2 and 3. The barrier energy, EB ,‘was interpolated by a seven-term cosine series of the form \ ‘6 -, J% = c b; 9, > n=O @Js:l=(2i7)-“Z

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.n=O;

c0s(dj,

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Table 1

Structural

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RcC

parameters

and moment

LCCH

RCO

RCH

of inertiaa)

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0. ‘-15 65 90’ 115 105. 180

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‘ob) -!BOc)

2.8607 2.8665 2.8808 i.Bs73 2.880s 2;8805 2.8802 2.883 .:2.844

2.0473 2.0473 2.0416 2.0476 2.0476 2.0479 2.a479

2.2675 2.2675 282650 2.2650 2.2650 2.2626 2.2626

2.120 __

2.290

115.8? 1X.8? 115.9:; 115.9:) 115.93 115.99 115.99 112;2

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LCCO We@

-IX 10-4

120.78 120.88 121.56 122.08 122.29. 122.19 -122.19

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8.9996 8.9821 8.8442 8.7522 8.7148 8.7150 8.7150

121.2 123.9

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Vdlume29,number

1

CHEFlICAL

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Wed 0 .lS ,’ 65 99 115 165 180

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PHYSICS L5l.hRS

I November

1974

Table 2 Absolute energies

ET

EK.

E ee

EN

Eh’e

-226.32460 -226.32389 -226.31584 ,-226.31335 -226.31368 -226.31684 -226.31705

226.14106 226.14126 226.14272 226.q332 226.13027 226.12550 226.12265

183.20693 183.15043 183.27524 183.45281 183.89545 184.64978 184.70002

102.64413 102.58OOO 102.67557 iO2.82974 103.25769 103.98953 104.03960

-738.31673 -738.19557 -738.40937. -738.72922 -739.59709 --741.08164 -741.17932

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1+ ETIEK ti.2 x E.1 x 7.7 x 8.0 x a;1 x 85 x 8.6 x

104 lo4 lo+ 10-4 104 104 lo4

T+e 3 Relative energies 0 @W

AE

AEK

AEee

AEN

A&e

'0 15 65 90 115 165 180

0.0 0.00071 0.00876 0.01125 0.01092 0.00776 0.00755

0.0 0.00020 0.00166 -0.00774 -0.01079 -0.01556 -0.01841

0.0. .-0.05654 0.06831 0.24588 0.68852 1.44285 1.49309

0.0 -0.06413 0.03144 0.18561 0.61356 1.34540 1.39547

0.0 -0.12116 -0.09264 -0.4L249 -1.28036 -2.7649 L -2.86259

sive and attractive terms as suggested, by Fink and Men [S], we define

TabIe4 Fourier coefficients

n

EB. bn

I, bn

0 1 2 3 .4 c

0.01865 -0.00596 -0.00663 -0.00067 o.coo13 -0.oaoo6 0.00001

220770.00 2442.52 869.12 -27.82 -48.81 107.23 62.52

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AEA = AEN,

,

AER = AEK + AEN + AER ,

1

r.4-

1

1

The

coefficients are displayed in table 4; the function is graphically displayed in fig. 1. We should note that the Fourier expansion of EB tells us that the barrier can be represented by the form 2

:

.’ V,{l-cos(nO)};

EB=c n=l

- Bcl -120 -60

is was suggested by Durig et al. in ref. [2]. If

one attempts td partition the barrier into repul-

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The structura\p&sneter$

in table 1 &n be used

to calculate the moment of inertia for the rotation of

the aldchqide group about the carbon-carbon bond. of that,mom&nt are reported in table 1. ‘. Th&:e moments can be Fourier analysed in the’ same manner as the energy barrier; the Fourier coefficients are r,ep:pbrtedin table 4, and the fiinction is displayed kaphicallji in fi& 2. The values

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repulsive’according to &h&her the attractive or rep&-’ We’term in the ba&er is dominan:. In going ,from .: %VISto gauche and cis to gauche we tabulate hEA : -and +??R us& the flatis and cis energies as references for the two pidcesses. Th&g, values are recorded in tabIe g’aong with the a&gmqent as to wethe; the .‘.bar& piocess i.s:attractive or repulsive. .. The ,conclusions agree in a’gen&l way with those : $ut by Ha in.ref.-[S] ;exit?pt that we find a region in the fmtis tdgauche region where the ba:rierIprocess ; Is si&ificarrtly attractive. 1x1r&f_ [8], Fink and Men pointed out that the’ attractive ar?d repulsiie cdmponents of such a barrier .. re+r~ act &fphasa;‘&is is seeqto be true for oyr glyotil calculation evsqtonsidering the unexpected reverbal of the &r&r character in goir?g from rr&s .: to&&he. Thehkight of this barrierpredicted.by *is calculation is.7.22 kcal/mole,and the c[s-pans energy,diJf&ence is 4.77 kcal/inole. In the calculation by ’ pincelk et aL[3], i$ese values were reported to be 7.84 and 6.46 kcaljmole, respec$vely. The values reported by &[5] were 6.22 for tile barrier height and,Z%J9 foi’the cis-&z~~s energy difference. CleaIrly ‘these calculatiorq are in essential agreement as regards -the barrier h&&t, although Sour calculations the, barrier maz&nLu$ is reported at a dihedral &-@a of %p iat&& than the 90’ value used in refi. [3,5]. The : CiSAram energy differerice we report is essentially a ’ I’&mpiomise b&w&n i&e results of Fir&& et al. and

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:- “’ 1,Novembe; 1974

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.’ -.+nd co&i&r the vie\Qpdint ,adApted by’Ha in ref. [j]. ::We defrpe the barrier character as attractive or

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CHEMICALPHYSICS LE’ITERS

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Volume 29;number

1

CHEMICAL PHYSICS LETTERS

It is seen that the moment changes by about three percent, and it is a function that char&es rather.rapidly’with the dihedral angle; faster at any rate than the veq.kmooth barrier might lead one to expek. As a general criticism of the geometries obtained ,by this calculation it is worth noting that they behave in a reasonable and consistent manner. As oqe rotates from pans t,o cis the large CO

groups are brought into proximity; this IeadS one to expect the C-C bond distance to increase and the X00 angle to increase; both these ,effects are reasonable distortions to compensate the repulsion generated by bringing the CO groups closer together. The distortion actually very well compensates for these effects. If’one defines total steric potential AES = LIE,, +

AE, + AENe ,

then this total is seen to be only slightly Iarger than the barrier itself. The actual barrier is recovered by

the drop in the kinetic energy as one goes from V&S to .cis, and this is a reasonable response to the generally increasing length of the TIelectron cloud created by the two conjugated I! bonds on the CO groups. The information gained in barrier analysis by the optimization of the geometry during the rotation C;LI~ be significant in some molecules [93; in this analysis we fiid that what compromise between theory and experiment as regaids the cir;-_tra/is energy difference

tie obtained geometry.

1 November 1974 was due to the optimization

of the

Acknowledgement

The authors thank Professor Glen Russel and Mr. Chit Chung for suggesting the problem arld Professor Klaus Ruedenberg for supporting the research.

References [l] K. Kuchitsu, T. Fukuyama and T. hforino. J. hfoL Struct. 1 (1968) 463; ,[2] J.R.,Ducig, CC. Tong (1972) 4425. (31 V. Pincelli, B. Cadioli (1971) :73. [4] G.N. Currie and DA.

4 (1969) 41.. and Y.S. Li, J. Chem. Phys. 57 and D-T. David, J. hZoL Sttuct

9

Ramsay. Can J. Phys. 49 (L971)

- _ 317. [5] T.-K. Ha, J. MoL Struct. 12 (1972) 171. [6] K. Ruedenberg,

R.C. Raffenetti and R.D. Bzdo, Energy Structure and Reactivity, Proceedings OF the 1972 Boulde; Conference on Theoretical Chemistry (Wiley, New York, 1973) p. 164. [7] RD. Bardo and K. Ruedenberg, J. Chem. Phys. 60 (1974) 918. [8] W.H. Fink and L.C. Alkn, J. Chem. Ehys. 46 (1967)

2261. 191 T.H. Dunning Jr. and N.W. Winter, Chem. Phys. Letters 11 (1971) 194.