Electronic structure of some peroxy radicals

Journal of Molecular Structure, 27 (1975) 97-104 0 Elsevier Scientific Publishing Company, Amsterdam -

ELECTRONIC! STRUCTURE

STANISLAV

97 Printed in The Netherlands

OF SOME PEROXY

BISKUPIG and LADISLAV

RADICALS

VALKO

Department of Pkys~c~l Chemistry, Slovak Technicaf U~~ve~~ty, ~ra~~~vff fCtechostovakiaJ (Received 6 May 1974)

ABSTRACT The semiempirical SCF-INDO method with the annihilation procedure of Amos and Snyder was applied to the all-valence electron systems of several peroxy radicals. The components of the electronic g-factor tensor were theoretically calculated_ The minimization of the total energies of peroxy radicals with respect to the geometrical parameters yielded the equiiibrium O-O bond length and the X-O-O valence angle. INTRODUCTION

The question of the structure and reactivity of peroxy radicals is of central interest in physical chemistry, because many reactions involve peroxy radicals as key intermediates in the gas and liquid phase oxidation of the hydrocarbons Furthermore, they play an important role in biological processes connected with the oxidation of living systems. In spite of the great significance of peroxy radicals there is a relatively small number of papers dealing with the interpretations of their electronic structure. These studies have, however, been almost entirely confined to the simplest peroxy radicals, i.e. hydroperoxy radical 11, 21 and fluoroperoxy radical [ 3,4, 51. The hydroperoxy radical has recently been the subject of investigations by the ab initio method [63 in both the ground and the lowest excited state. In the case of FOO’ radical the study was oriented to the ~terpretation of ESR chmacteristics [43 and their calculation was also carried out [5]. The only paper dealing with the study of the alkylperoxy radicals is from Yamamota et al. 173, whose conclusions are made on the basis of the EHT method. In this paper through the semiempirical SCF (INDO) method, the calculation of electronic structure of some simple radicals such as a IIOO’, FOO’, CHsOO’, CH&H&O; CH&H&H200’ was performed including the spin density, the components of the electronic g-factor tensor and equ~b~um geometrical parameters. METHOD

QF CALCULATIQN

The unrestricted INDO-MO

scheme was described in ref. 8 and here we

summarize only the pertinent details concerning of the g-tensor components

calculations. The components of the electronic g-factor tensor were carried out to second order by the Stone equation [9], in which we consider the gauge invariance s”b =g,6,

+ Ag*

(a, b=x,y,z)

(1)

where ge is the g factor of the free electron (2.00232) Ag* can be written

and for the deviations

(2)

where z; is the a component of angular momentum about atom k, and Skis the spin-orbit coupling constant for the kth atom. The E,. - En energy differences in eqn. (2) represent the excitation energies, from which in the framework of unrestricted SCF methods the most important are (i) the transition of p electron from doubly occupied to half-filled molecular orbital, and (ii) the excitation of an unpaired arelectron to a previously higher unoccupied molecular orbital. The particular excited states we can describe by the following antisymmetrized wave functions: %--W = M&W&

- - - G@vf.

*j-.+j =

- - * @vLe- - - g-,

ltw’:

w:

Using wave functions function Xl&= I$$ I&$@

- - 1Lrp_1@I

$7

(3)

(4)

(3) and (4) in addition to the ground state wave

- _ _ $5@ c c---

3/f-

1v$Y

(5)

for the excitation energies we obtain the following relations: I$+,.= < *+,I:&

=

(6)

- Jf’iP+ ZC/$

=+-ef q--Q=<

q-+r> - < ‘Eg&=I ‘kg>

~r_+@lur+j>--~g “-E;-Ei

Jtiw+ 4;

Iszwp (7)

where ef, e,“, #, $are orbital energies for 0 and 01electrons, ca, qr@ are known as Coulomb integrals and c, K/ exchange integrals for the corresponding

electrons. In the calculation of spin densities we used the spin annihilation procedure of Amos and Snyder [lo].

99 RESULTS AND DISCUSSION

Equilibrium geometrical

parameters

Molecular structure of many radicals have not been obtained and the calculations are often carried out with the assumed molecular structures. In this paper the minimization of the total energies of peroxy radicals with respect to the geometrical parameters yielded the equilibrium Q-O bond length and the L X-0-0 valence angle. The H-O, F-O, C-O, C-C and C-H bond lengths used were the same as in ref. 11: rHo = 1.05 A, rFo = 1.19 a, rco = 1.44 a, ?-co= 1.54 A and r,, = 1.093 A, and ail remaining valence bond angles for the “saturated” part of the compounds studied were assumed to be tetrahedral (109.5” ) with staggered conformations in the case of C2H500’ and n-C3H700’. Calculated equilibrium bond lengths and valence bond angles are listed in Table 1 which also shows some general trends. The O-O bond lengths of the different peroxy radicals are almost identical, being independent of the nature of the group X. Thus the calculations suggest that the valence L X-O-O bond angles slightly increase in going from HOO’ to n-C3H700’, and the magnitude is influenced by the X group bonded on the O-O’. TABLE

1

Calculated interatomic distances and bond angles in some peroxy radicals Radical

L X-O-O

FOO’ HOO’ CH,OO’ C,H,OOn-C,H,OO’

109.9 111.4 112.5 114.0 114.5

(deg)

roo(Aj 1.195 1.190 1.195 1.197 1.199

Spin density

The distribution of the unpaired electron over the molecular framework can be quite useful in analyzing the electronic structure and reactivity of peroxy radicals as weII as for theoretical prediction of the form of ESR spectra. In the great majority of peroxy radicaIs the unpaired spin is almost entirely concentrated in apt orbital built, to a first approximation, from Zp, orbit& on the terminal and central oxygen atoms of the O-O’ group. The calculated spin densities corrected with respect to the spin annihilation procedure are listed in Table 2. In the great majority of peroxy radicals the spin density on the terminal oxygen atom is to be 79% and 21% on the central oxygen atom. Some general trends can be observed by comparing the series of alkylperox: radicals. The calculated spin density only slightly increases on the terminal

100

TABLE2 Calculatedspin densities Radical

Atom

Total spin density on atom

1

0.7950

2 3

0.2121 -0.0070

1

0.7961 0.2039

2 3

0.0055 0.7921 0.2062 -0.0051 0.0036 -_,0.0004 0.0036 0.7942

0.2044 -oo.oo53 0.0036 0.0036 -0.0001 -0_0001 - 0.0004 - 0.0001

b,

1

0.7949

2 3 4 5 6 7 8 9 10 11 12

0.2035 -00.0052 0.0037 0.0037 0.~000 -0.0001 -0.0001 -0.0003 0.0000 -0.0001 0.0000

oxygen atom, i.e. 0.7921 for the methyfperoxy radical to 0.7949 for n-propylperoxy

radical.

Shimizu et al. [lZj calculated by the use of EHT method for the HOO’ radical that the value of spin density was 0.3114 on the central oxygen atom, white Adrian et dl. [Z] gave 0.290. In our calculations we obtain a reasonable value 0.2121 on the central oxygen atom. The ESR spectra of the different peroxy radicals ROO’ are striking in that they are almost identical, being independent of the nature of the group R,

101

and showing no hyperfine interaction with the protons in this group. This indicates that the free electron occupies an orbital that is confined almost entirely to the O-O’ region of the radical and is unaffected by the substituent group. Since the reactivity of radicals in terms of activation energy is determined principally by the orbital of the free electron it follows, all peroxy radicals will have similar activation energies in bond-forming reactions [ 133 _ g

tensor

In the calculation of the components of electronic g-factor tensor, it is necessary to estimate not only the spin distribution, but also the excitation energies from the 0 orbitals to the odd 7~* orbital. In the present investigations, these quantities were calculated according to eqn. (2) and the Cartesian coordinate system for the particular peroxy radicals were chosen as in Fig. 1. The constants of spin-orbital interactions used in our calculation are [14] cc = 28 cm-’ , co = 151 cm-’ and SF= 270 cm-‘. It is concluded from the present study that the most important contributions for the Agab correspond from the w-r* and ~+rr* excited states, which is remarkable in the case of HOO’ radical (Table 3, excitations 6+7 and 4+7). The calculated principal components of electronic g-factor tensor are tabulated in Table 4. The origin of the deviation, in general, of the principal g factor in FOO’, HOO’ and alkylperoxy radicals, from the free spin value (2.00232) is reasonably well understood [15]_ The g shifts are associated with spin-orbit interactions between the ground state and excited states of the radical, and the deviation is proportional to Ag=k

&

(8)

where k is the proportionality constant, 5 is spin-orbit coupling constant and AE is the energy difference between the ground and excited states. From this relation it follows that the deviation in Ag becomes inversely proportional to the energy separation. We suggest that the 6+7 excitation which corresponds to excited states involving the lone-pair orbital of the oxygen atom and the antibonding molecular orbital, i.e. n(2pyO)+* transitions give the dominant contribution to Agxx in the O-O bond direction (Table 3). To this transition corresponds relatively low excitation

i.e. Eh7 = 1.741 eV.

Fig. 1. Cartesian coordinate system for studied peroxy radicals.

energy,

102

TABLE3 Contribution of excited configurations to g tensor of the hydroperoxy radical Excited configuration

Energy (eW

g”

gyy

1+7 2-7 3+7 4+7 6-+7

37.768 20.374 12.753 8.001 1.741 8.559 9.781

0 0 102 75 17076 0 0

131 22 191 3095 284 0 0

17254

3723

7-+8 7+9 Total

iP

P(x

-143

4 2 140 -482 2201 0 0

-364

1864

0

0 0 0

-2210

106)

TABLE4 CakuIated excitation energies n-w* (E,) and X* +(first unoccupied MO) (E,) and calculated principal (diagonalized) values of g tensor of some peroxy radicals Radical

EL (ev)

FOO’ HOO’ CH,OO’ C,H,OO-

2.364 1.741 1.835 2.219

n-C,H,OO'

2.368

z_, (ev) 7.323 8.559 9.965

2.01583 2.001983 2.01764

2.00517 2.00579 2.00442

2.00232 2.00196 2.00232

11.085 11,284

2.01484 2.01388

2.00433 2.00408

2.00705 2.00213

The excitation from the O-O o-bonding orbital to the odd antibonding orbital (excitation 4-+7) with the energy separation E4+ = 8.001 eV makes a most important contribution to AgYY. The contribution to Aga in the direction perpendicular to the molecular plane is determined by the excitation of free electron from zr*antibonding molecular orbital to the higher virtual molecular orbital. The magnitude of Agz is negligibly small, thus g” - ge (Table 4). The dependence of calculated g tensors on the radical structure should be examined in the present theoretical study. The calculated value of gxx depends considerably on the L H-O-O angle (Fig. 2). On the other hand, the angular dependence of gyy and gz is negligibly small (Table 5). It is of particular interest that, as the valence angle L H-O-O increases, the gM component first rapidly decreases until it reaches an energy minimum, then increases monotonically. Figure 3 shows the results of plotted calculated excitation energies _F: _* versus valence bond angle t H-0-O. It may be seen that the correlation between g= component and excitation energy is quite reasonable. It is important to investigate the g-tensor components for other peroxy ?T* molecular

103

2.023 9

xx

2.022 -35.928

2.02-l -35.930

2.020

2.0% -35.932

Fig.2.Angulardependencesofthetotal radical.

energy(Et,_,t)andthegXXcomponentforHOO-

TABLE5 Angulardependenceoftheg-tensorcomponents L H-O-O

(deg)

99 102 105 108 111 114 117

&?=

P

g”

2.022413 2.021426 2.020701 2.020191 2.019859 2.019676 2.019636

2.005919 2.005894 2.005865 2.005832 2.005796 2.005757 2.005716

2.001997 2.001990 2.001981 2.001971 2.001958 2.001941 2.001921

Q H-O-O:

Fig. 3.PlotofE _+excitation radical.

energyversustheL

HO0

valence bondanglefor

HOO'

104

radicals in order to make clear the relation between the g factor and the electronic structure of the alkylperoxy radicals. In the present investigation, the g-tensor components have been calculated and as a result the deviation of Ag- from the free spin value is expected to be large and decreases with the increasing number of the carbon atoms in the alkyl group. Thus we have been led to the conclusion that the changes in the increasing excitation energies r-r+-+ and n*+(unoccupied MO’s) in order from CH300’ to n-C3H700’ are largely responsible for this observation (Table 4). The small decrease can be seen also in the case of g YYcomponent, while g” component remains very near to the free spin value. One unsatisfactory point remains in this study. The molecular structure in the excited state was assumed to be the same as that of the ground state.

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