Evolution of electronic distribution during chemical reactions

Journal of Molecular Structure, 103 (1983) 269-273 THEOCHEM Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

EVOLUTION OF ELECTRONIC

DISTRIBUTION

DURING CHEMICAL

269

REACTIONS*

R. DAUDEL Centre de Ml@canique Ondulatoire 75940 PARIS CEDEX

Apoligu&e

du C.N.R.S.

23, rue du Maroc

19 (FRANCE)

ABSTRACT The loge theory is used to follow the evolution of the electronic distribution of molecules during chemical reactions. It is shown that loge theory orovides a process to precise the positions of the arrows which are currently used by chemists.

INTRODUCTION Arrows actions.

are currently But usually,

used to represent

these arrows

are not drawn after precise

quantum

the electronic

performs

distribution

electron

mechanical

cess to follow

and indistinguishable.

the reorganization

during chemical

pure intuitions.

calculations

evolutions

showing

along the reaction

In fact it is not easy to do such calculations trons are delocalized

transfers

are drawn by following

because

a priori,

But the loge theory

of the electronic

re-

They

how reallv path. the elec-

orovides

clouds of molecules

a pro-

during

collisions. The purpose

of this oaper is to show how this can be done. It is mainly based 1 on a theory I developed with various colleagues and a work done by Professor 2 Leroy and coworkers .

LOGE THEORY First of all, I must recall some main features Let us take the example Consider

of the BH molecule.

a sphere of arbitrary

tom. From a good wave function calculate

the probability

r centered

Pn of finding

trons in this sphere R. Figure ties PO(Q),

radius

associated

concerning

at the nucleus

with this molecule

a certain

of the boron a-

it is oossible

of the various 3 of the radius r.

*Dedicated to Professor Kenichi Fukui in honour of the award of the 1981 Nobel Prize in Chemistry.

0166-1280/83/$03.00

oroblem.

to

number _? (and only -n) of elec-

1 shows the variation

PI(n)... PC(") as a function

the lose theory.

It is a six electron

0 1983 Elsevier Science Publishers B.V.

probabili-

1.6 r

0.0 0.0

1.0

2.0

3.0 r-w

4.0

5.0

Fig.2

Fig. 1. Variation mission

as a function

of r of the probabilities

Pn (reproduced

by per-

from ref. 1)

Fig. 2. Missing

information

function

and fluctuation

of the number

of electrons

in the sphere. (reproduced

by permission

It is seen that only P2, reaches probabilities electrons

loge.

tom itself

value

(near one). The other

is the onlv Leading event. The sphere centered

and corresponding

to the maximum

two

at the

value of P2 is said to be a two-

(r = 0.7 a.u.) As such a loge is also found in the free boron a-

it is called a boron core loge.

The concept function

an important

remain above 0.5 for all value of r. It is said that finding

in the sphere

boron nucleus electron

from ref. 1)

of loge can be precised

I associated

It is known that

to a distribution

by

introducing

the missing

of probabilities

information

Pi.

: -1

I = ci Pi log2 Pi

In our case each Pi is a function of r, therefore The figure 2 represents

the variation

ximum amount of information

I is also a function

of I as a function

on the localizability

of r. To obtain

of electrons

of r. the ma-

we must minimized

271 the missing

information

nimum is obtained maximum

function.

when

r = 0.7 a.u. that is to say exactlv

value. The partition

ves the most possible

It is seen on figure 2 that a non trivial mi-

of the soace which

amount of information

when P2 reaches

corresponds

its

to tne core loge gi-

on the localizabilitv

of the elec-

trons. The figure 2 also shows the variation electrons minimum

inside of the sphere.

ducing a portion

X of the number of

It is seen that this fluctuation

value when the sphere coincide

To go further we can divide

of the fluctation

also reaches

a

with the core loge (r = 0.7 a.u.).

the molecular

space into three volumes

by intro-

of cone of angle a. thti summit of the cone being at the boron

nucleus and it axis the BH line (figure 3).

Fio. 3 Three

loge partition

We can calculate

of the molecular

again the missing

three volume partition.

It reaches

space of BH.

information

its minimum

function

value for

associated

with that

:

r = 0.7 a.u. CL = 73" Then, finding

two electrons

in each of the three corresponding

loges is the lea-

ding event. Therefore

the region inside the cone is said to be a two-electron

-the BH bond loge. The region outside A bond loge appears loge cores in which

to be a region of the space extended

the fluctuation

LOGES AND MOST LOCALIZED Unhappily

Happily

of a good partition

two atomic

is minimized.

of a molecular to establish

space into loges

a bridge between

orbitals.

it has been shown that the various

with a molecule

between

of the number of electrons

joh. For that reason it is useful

loges and localized

;

ORBITALS.

the calculation

is a difficult

bond loge

the cone is said to be the lone pair lose.

lie mainly

in the various

most localized

loges.

orbitals

associated

272 Furthemore coincide

the centroids

Therefore

the centroids

of the regions much.

EVOLUTION

OF ELECTRONIC

As a consequence, centroids

of charge of th? most localized

of the molecular

fluctuate

Such studies

DISTRIBUTION

to the addition

PATH.

the reorganization

the collision

of the

of two molecules,

We shall present

by Leroy and coworkers.'

because

substituents

donators

electron

activate

to substituted

ethylenes.

This

:

activate

the ethvlene,

zed molecular

orbitals

(reproduced

It appears

electron

dona-

This figure

of the centroids

that the electronic becomes

this reorganization

locali-

of diazomethane

to

from ref. 2) reorganization small

only starts when the distance

(2.25 a.u.)

leads to electron

to the nearest

is represented

diazomethane,

of charge of the most

along the path of the cycloaddition

NC bond of the diazomethane This transfer

groups desactivate

,

by permission

the two molecules

Furthermore

withdrawing

it.

Figure 4 shows the evolution

transfer

going from the

CH2 group of the ethylene

molecule.

by an arrow on figure 5.

gives an explanation

of the effect

of substituents

on the reac-

of both reagents.

It is seen for example transfer

do not

its reactivitv.

2) on the contrary

tivities

during

of diazoalkanes

interesting

1) electron withdrawing

ethylene,

give an idea

path.

is oarticularly

electron

orbitals

almost

of their results.

It is related

tors diminish

to follow

orbitals

orbitals

the number of electrons

ALONG A REACTION

it seems interesting

have been performed

here an example

between

space in which

of charqe of localized

along the reaction

example

of charge of the most localized 4 of charqe of the loges.

with the centroids

is enhanced

withdrawing

group.

that if the substituant

and the reaction

activated.

R is a donor the electron The reverse

is true if R is a

273

R.2A

R.5A

l.PYRAZOLINE

R.225A

Fig. 4 Evolution

of centroids

Figure 5. Explanation

of charge during a cycloaddition.

of the effect of substituents

(reproduced

by permission

from ref. 2)

REFERENCES For a review see : R. Daudel, The New World of Quantum Chemistry, B. Pullman and R. Parr (ed) Reidel (Pub.) 1976 , 33-56. G. Leroy, M. Sana, L. A. Burke and H.T. Nguyen, Quantum Theory of Chemical Reactions, Vol. I R. Daudel, A. Pullman, L. Salem and A. Veillard (ed) Reidel (Pub) 1980, 91-144. R. Daudel, R.F.W. Bader, M.E. Stephens and D.S. Borrett J. Can. Chem. -52 (1974) 1310. R. Daudel, M.E. Stephens, L.A. Burke and G. Leroy, Chemical Physics Letters -52 (1977) 426.