The e. s. r. signal observed on dissolving the solid in pyridine was the sam e as that found for the other solids and was thus assig n ed to DPNO,
No o ther signal was detected fo r any of th ese sy stem s,
d) D ecom position of Bensenediazonium A cetate
The p rep aratio n of this unstable solid is describ ed elsew here in this th esis. Using a concentration of about 25 mg. /m l. in benzene and mod, 1.27 gauss a wealc broad 1:1:1 trip le t was
detected. On reducing the mod. to 0.41 gauss the hyperfine com ponents of the b ro ad peaks w ere reso lv ed and showed the typical stru c tu re of the DPNO spectrum and the following
m easu rem en ts w ere m ade in gauss: (l)a .- = 10.07, (6) a ^ N o, p-H-„=1,88
and (4) ^ = 0.84. A lso A F = -0.12, giving g - 2.0057
THEORETICAL CALCULATIONS
McLACHLAN MOLECULAR ORBITAL CALCULATIONS
a) Introduction 108
b) C om puter P ro g ram m e 110
c) Choice of M olecular O rbital P a ra m e te rs 111
d) C alculated Spin Density D istributions for N itroxide R adicals
(i) Phenylnitroxide 117
(ii) D iphenylnitr oxide 117
(iii) (N~Phenylacetam ido)phenylnitroxide 120
II CNDO SELF-CONSISTENT FIELD THEORY
CALCULATIONS
a) Introduction 127
b) C om puter P ro g ram m e 130
c) V ariation of R adical G eom etry to Find the M inimum E nergy Configuration
(i) H^NO. 131
(iii) HC«0 132 (iv) H^C=CH 132 (v) C 6»5 133 (vi) H NC=0 133 (vii) HgC=NO- 133 (yiii) HN=NO- 133 (ix) PhNO’ 134 (x) PhNO"'" 134 (xi) PhCH=NO- 135 (xii) PhN=NO- 136
I McLACHLAN MOLECULAR ORBITAL CALCULATIONS
a) Introduction
It is now well estab lish ed that the hyperfine splitting from a rin g proton in the e. s. r, spectrum of m o st aro m atic fre e rad icals in solution is re la te d to the unpaired spin density in
58 the TT -o rb ital at the adjacent carbon atom by the M cConnell equation
Among se v e ra l m ethods developed to account for tlie spin distribution over the carbon atom s in a rad ical, two in p a rtic u la r have found w idespread use.
The f ir s t is the sim ple Huckef m olecular o rb ital m ethod,
which neglects the o -o rb itals as being lo calised and non-
in teracting, and re g ard s the “fT-orbitals as a lin e a r com bination of the available 2p^ atom ic o rb itals. The re su ltan t unpaired
electro n spin d istribution gives a successful account of the sp ectra of m any altern an t hydrocarbon ions. However, because the
m o lecu lar o rb ital wave function m akes no allow ance fo r the co rrelatio n of electrons the m ethod is unable to account fo r tîie negative spin densities which n. ui. r, studies have shown to occur
128 in rad icals such as the pyrene negative ion.
altliough allowing for negative spin densities, is also both laborious and inflexible.
57
The M cLachlan theory com bines the b est of both these m ethods to provide a straig h tfo rw ard technique fo r predicting spin density distributions, the b asis of which is outlined below.
In a rad ical the conventional single determ inant wave
function with one unpaired electron and Zn o th er electrons
p aire d in n m o lecu lar o rb itals is le ss useful than fo r a closed shell system , because the m otions of the electrons of c and P spins a re affected in d ifferent ways by the odd electron.
To allow fo r this effect and the re su ltan t negative spin densities, two types of wave function can be used. One type uses the
conventional determ inant with a sm all adm ixture of excited
configurations, while the oth er uses a single determ inant vdth 57
different o rb itals fo r a and p spins. M cLachlan was able to
show that the fo rm e r leads to n early the sam e 'tr-e le c tro n spin distribution as tlie la tte r, if the sm all adm ixture of excited
states is reg ard ed as a p ertu rb atio n of the Hiickel m o lecu lar o rb itals.
Thus the spin density in M cLachlan’s m ethod is given by /> r ~ C ro^ K S q
mutual polar is ability of atom s r and s, and X is a n u m erical
constant which can be adjusted to give the b est fit with experim ent, but is often set at 1.2.
The p ertu rb atio n can be reg ard ed as a sm all additional a ttrac tiv e term acting, within the Hiickel fram ev/ork, on those electrons with spin p a ra lle l to the odd electron.
The calculation thus produces spin densities approxim ating to those from fie m o re rigorous self-co n sisten t field theory.
Identical densities a re p red icted fo r positive and negative ions, and the approxim ation holds fo r neu tral altern a n t rad icals giving negative spin densities w here the Hiickel densities a re zero or sm all. Although not contained in the orig in al theory, the spin density distributions fo r rad icals containing heteroatom s have been successfully calculated using the Me Lachlan m ethod,
b) Com puter Projs^ramme
The calculations w ere p erfo rm ed on an IBM 1620 com puter, 129
using a p ro g ram m e w ritten by D. H. Levy in F o rtra n II, fo r an IBM 7090 and m odified fo r the 1620 by Dr. C, Thomson, The p rogram m e calculates both Hiickel and Me Lachlan spin densities from input data consisting of tlie constant X and the n o n -zero
c) Choice of M olecular O rbital P a ra m e te rs
It is usual to express the Coulomb (c.) and resonance
130 131 (Py) in teg rals in te rm s of the values ap p ro p riate to benzene. '
a = a + h p X C X C “ C ‘, P xy - k p xy c -c '
w here h^^ and a r e the MO p aram eters in the Pauling
approxim ation.
F o r the Ph-N-O* frag m en t of arylnitroxides the p a ra m e te rs
re q u ired a re 1)^^, ly , ^KO norm al ranges of
131
these have been liste d by S treitw eiser as follows: h ^ = 1.5,
1.0 < h ^< 2 ,0 , 0 .6 < k _ < 0 ,8 and 0 .7 < k _ < % .2 . In additionJN<J OJN
the effect of s te ric hindrance preventing p lan arity in the ra d ic al can be taken into account by considering the resonance in teg ral
as a term cos 0 , w here 0 is tZie angle of tw ist and is the
jpesonance in,teg3?a3.jbotwo3n the planar sy stem and the substituent. Two quite different sets of values have been used for
Me Lachlan calculations on nitroxide rad icals with equal su ccess.
132 , , 13
Deguchi et a l . and also Kikuchi and Someno u sed the
following values fo r calculations perfo rm ed on phenylnitroxide {PNG}
0 8 1 0
On the o ther hand Ays cough and 5 a rg e n t^ ^ found it
n ec essary to employ a value of outside the lim its m entioned
by S treitw eiser, The p a ra m e te rs they used a re as follows: X « 1.2, h ^ =5 1.5, h^ - 1.0-1.8, = 1.6, k ^ ^ » 1.05-1.2,
In view of this d isag reem en t in the choice of k ^ ^ , it was decided to c a rry out calculations on both phenylnitroxide (PNC) and diphenylnitroxide (DPNO) in an attem pt to find a common se t of p a ra m e te r values for the Ph-N-O* fragm ent, which could then be used fo r the (N -phenylacetam ido)phenylnitroxide (PAPN) rad ical.
Phenylnitroxide
Below a re liste d the hyperfine coupling constants for PNO 133
found by Kikuchi and Someno, together with the experim ental
H
spin densities fo r the protons assum ing a value of 23,7 gauss,
a ^ - 8.81 gauss a ^ ^ ^ = 11.71 gauss
a o - H = a „ ~ 2.92 gauss p - M (ejcp. ) - 0,123^
the PNO rad ical for values of ranging from 0.6 to 2.0, with the rem aining p a ra m e te rs fixed at the following values:
X ~ 1*2, hj^ “ 1.5, h ^ ~ 1*0, - 1*2.
F ro m this table and from Fig. 33, which shows the change in the ratioyo(para) ^ (o rth o ) with variatio n of it is c le a r that the experim entally observed equivalence of the ortho
and p a ra positions is p red icted fo r values of about 0.5 and 1
.
6.
1.5