Multivariate regression with substituent shift increments. IV. 2-(4-X-phenyl)-1,3-dihydro-2H-isoindole-1,3-diones and 3-(4-X-phenyl)-3,4-dihydro-2H-1,3-benzoxazine-2,4-diones

Article abstract of DOI:10.1135/cccc19991709

Two series of para disubstituted benzenes were studied: 2-(4-X-phenyl)-1,3-dihydro-2H-isoindole-1,3-diones (1) and 3-(4-X-phenyl)-3,4-dihydro-2H-1,3-benzoxazine-2,4-diones (2). Their ¹H and ¹³C chemical shifts were correlated with substituent shift increments (SSI) a_j and z_j, respectively. For ¹³C chemical shifts, all four z_j values, z_j, z_o, z_m, and z_p, were used to check the assignment and to find out possible variables for improvement of regression equations. Significant deviations from plain additivity were observed in the case of δ_H3 and δ_C3 chemical shifts. This can be explained by changes in diamagnetic anisotropy contribution induced by different twist of 4-substituent from the benzene plane caused by variable substituent in position 1.

Full text of DOI:10.1135/cccc19991709

Multivariate Regression
1709
MULTIVARIATE REGRESSION WITH SUBSTITUENT SHIFT INCREMENTS.
IV. 2-(4-X-PHENYL)-1,3-DIHYDRO-2H-ISOINDOLE-1,3-DIONES AND
3-(4-X-PHENYL)-3,4-DIHYDRO-2H-1,3-BENZOXAZINE-2,4-DIONES+
a,
b
c1
c2
Miroslav HOLÍK *, Zdeněk FRIEDL , Karel WAISSER and JiříG REGOR
a
Department of Theoretical and Physical Chemistry, Faculty of Science, Masaryk University,
CZ-611 37 Brno, Czech Republic; e-mail: holik@chemi.muni.cz
Faculty of Chemistry, Technical University Brno, CZ-612 00 Brno, Czech Republic;
e-mail: friedl@fch.vutbr.cz
Department of Inorganic and Organic Chemistry, Pharmaceutical Faculty, Charles University,
CZ-501 65 Hradec Králové, Czech Republic; e-mail: waisser@faf.cuni.cz., gregor@faf.cuni.cz
b
c
1
2
Received July 13, 1999
Accepted August 16, 1999
Dedicated to Professor Otto Exner on the occasion of his 75th birthday.
Two series of para disubstituted ben zen es were studied: 2-(4-X-ph en yl)-1,3-dih ydro-
2H-isoin dole-1,3-dion es (1) an d 3-(4-X-ph en yl)-3,4-dih ydro-2H-1,3-ben zoxazin e-2,4-dion es
(2). Th eir 1H an d 13C ch em ical sh ifts were correlated with substituen t sh ift in crem en ts (SSI)
aj an d zj, respectively. For 13C ch em ical sh ifts, all four zj values, zi, zo, zm, an d zp, were used
to ch eck th e assign m en t an d to fin d out possible variables for im provem en t of regression
equation s. Sign ifican t deviation s from plain additivity were observed in th e case of δH3 an d
δC3 ch em ical sh ifts. Th is can be explain ed by ch an ges in diam agn etic an isotropy con tribu-
tion in duced by differen t twist of 4-substituen t from th e ben zen e plan e caused by variable
substituen t in position 1.
Key w ord s: Substituen t sh ift in crem en ts; NMR spectroscopy, 1H an d 13C; Substituen t effects;
Lin ear regression ; Proportion ality relation sh ip; Ph th alim ides; Ben zoxazin es.
It is believed th at in 1,4-X,Y-disubstituted ben zen es with a variable
substituen t X an d a fixed substituen t Y, possibly con tain in g m ultiple
bon ds, th e twist an gle between th e ben zen e rin g an d th e plan e of Y
substituen t is reflected by a slope ρ in th e Ham m ett equation an d is th ere-
fore con stan t1 . However, we h ave sh own 2–6 th at th e m ost probable expla-
n ation of ch em ical sh ifts in th e n eigh bourh ood of substituen t Y is th e
+ For Part III see ref.20
Collect. Czech. Chem. Commun. (Vol. 64) (1999)

1710
Holík, Friedl, Waisser, Gregor:
ch an ge of its diam agn etic an isotropy or van der Waals con tribution due to
variation of th e twist an gle with th e substituen t X. Th e ch an ge of th e twist
in m olecules with th e ch an ge of th e substituen t can be observed also in th e
4
m agn itude of th e J couplin g con stan ts of th e ben zyliden e type7.
An effect of diam agn etic an isotropy of m ultiple bon d or arom atic rin g on
th e sh ieldin g of n uclei is m ore pron oun ced in 1H th an 13C NMR spectro-
scopy. Th us, in 1,4-disubstituted ben zen es th e m ost affected NMR sign al
sh ould be th at of H atom in meta position to a variable X substituen t. For
its ch em ical sh ift we can write accordin g to th e additivity rule Eq. (1).
δm = 7.27 + ao(Y) + am(X) ,
(1)
wh ere am an d ao are substituen t sh ift in crem en ts (SSI) obtain ed from spectra
of m on osubstituted ben zen es8.
δm = b0(Y) + b1 am(X) + ε
(2)
Equation (2) can be used for an alysis of ch em ical sh ifts of 1,4-disubstituted
ben zen es with a fixed substituen t Y an d a variable substituen t X; it h as
1
been used for ch eckin g correctn ess of H NMR sign al assign m en t9 an d for
estim atin g2–6 values of slopes b1. Accordin g to th e m agn itude of b1 value
th e in vestigated cases can be rough ly divided in to th ree categories:
1. b1 ≈ 1
No essen tial ch an ge in th e con form ation of group Y, from th e viewpoin t of
diam agn etic an isotropy, is caused by exch an gin g on e X substituen t for an -
oth er.
δm = 7.621 + 0.978 am + ε
n = 23
(3a)
Th e value 0.978 statistically (95%) in sign ifican tly differen t from on e was
obtain ed for 4-substituted ben zon itriles10. Also th e slope 1.009 foun d for
5-(p-X-ph en yl)tetrazoles11 was n ot sign ifican tly differen t from on e.
δm = 8.179 + 1.009 am + ε
n = 10
(3b)
Collect. Czech. Chem. Commun. (Vol. 64) (1999)

Multivariate Regression
1711
2. b < 1
In th e substan ces wh ere th e dih edral an gle between th e ben zen e rin g an d
th e plan e of substituen t Y decreases with th e in creasin g don or ch aracter
(DID) of th e substituen t X, i.e., n itro derivative is m ore twisted th an am in o
on e, slope b sign ifican tly differs from on e. Th us, th e down field sh ift of Hm
NMR sign al caused by a decrease in th e electron den sity on Hm atom is par-
tially com pen sated by a decrease in th e diam agn etic an isotropy con tribu-
tion of substituen t Y wh ich sh ifts th e sign al upfields.
δm = 7.654 + 0.303 am + ε
n = 7
(3c)
Th e slope value (0.303) in 2-(4’-substituted ben zyliden e)[3]ferrocen o-
ph an e-1,3-dion es12 con siderably differs from un ity an d even larger decrease
was observed in th e case of 4-substituted N-ben zyliden ean ilin es2,13; Hm
ch em ical sh ifts bein g alm ost un affected by substitution .
δm = 7.075 + 0.053 am + ε
n = 7
(3d)
3. b > 1
Wh en th e twist an gle between th e ben zen e rin g an d th e substituen t Y de-
creases with decreasin g don or ch aracter (DDD) of th e substituen t X, i.e., n i-
tro derivative is less twisted th an am in o on e, th en an in crease in
diam agn etic an isotropy con tribution supports th e electron ic effect an d th e
slope of regression equation (2) is larger th an on e. Th is effect was observed5
for 1-(4-X-ph en yl)-2,6-dim eth yl-4-pyridon es
δm = 7.235 + 1.275 am + ε
n = 7
(3e)
an d 2-(4-X-ph en yl)-1,3-dih ydro-2H-isoin dole-1,3-dion es (1); both slopes be-
in g sign ifican tly differen t from on e.
δm = 7.452 + 1.252 am + ε
n = 7
(3f)
Collect. Czech. Chem. Commun. (Vol. 64) (1999)

1712
Holík, Friedl, Waisser, Gregor:
A sign ifican ce of fitted param eters in m ultivariate regression was tested by
th e Studen t t-test by com parin g tested value divided by correspon din g stan -
dard deviation with critical t-value for respective n um ber of freedom s an d
con fiden ce level (n orm ally 95%), Eq. (3g).
b − β
t =
≥ t ( 0. 05 , n – p )
(3g)
sb
With β = 0 it tests statistical im portan ce of correspon din g variable, with β = 1
it tests a sign ifican ce of deviation of slope from on e.
In 13C NMR spectra th e effect of diam agn etic an isotropy is less pro-
n oun ced th an in 1H NMR an d electron ic effects m ay prevail. With m ulti-
variate regression 14 of 13C ch em ical sh ifts on four 13C SSI, Eq. (4), a
prelim in ary in sigh t in to th e electron ic effects actin g in 1,4-disubstituted
ben zen es h as been obtain ed in th e followin g way14
:
δC = b0 128.5 + b1 zi + b2 zo + b3 zm + b4 zp + ε .
(4)
For Y group actin g as electron don or:
δC1 correlates with zi an d zm (–b3)
δC3 correlates with zm an d zp (–b4) .
If Y acts as electron acceptor:
δC1 correlates in addition to zi also with zo (+b2) and zp (–b4)
δC3 correlates in addition to zm also with zo (–b2) and zp (±b4) .
In th e case of m ore com plicated substituen t Y, like in th e m en tion ed
4-pyridon es an d N-ph en ylph th alim ides (1), δC1 correlated sign ifican tly
with all SSI, i.e., zi, zo, zm, an d zp; th e δC3 gave sign ifican t slopes with zm an d
zp its sign depen din g probably on a m ixture of several effects.
Now we h ave a larger series of 2-(4-X-ph en yl)-1,3-dih ydro-2H-iso-
in dole-1,3-dion es (1) an d a sim ilar series of 3-(4-X-ph en yl)-3,4-dih ydro-
2H-1,3-ben zoxazin e-2,4-dion es (2) an d we can repeat som e calculation s
with m ore con fiden ce an d m ake oth er to support previous fin din gs14.
Collect. Czech. Chem. Commun. (Vol. 64) (1999)

Multivariate Regression
1713
EXPERIMENTAL
Preparation s
2-(4-Substituted ph en yl)-1,3-dih ydro-2H-isoin dole-1,3-dion es (1)5,18 were prepared by
refluxin g equim olar am oun ts (50 m m ol) of ph th alic an h ydride an d respective 4-substituted
an ilin e in toluen e (100 m l) con tain in g trieth ylam in e (0.8 m l). Th e reaction s were carried out
wh ile rem ovin g water for 3 h , crude reaction m ixtures were filtered h ot th rough a silica gel
colum n an d recrystallized from toluen e. All com poun ds gave satisfactory elem en tal an alyses
an d sh arp m eltin g poin ts.
7
8
O
O
5
6
9
X
N
X
N
10
1
4
1
4
11
8
5
6
12O
2
3
2
3
7
O
O
1
2
NMe2
OMe
F
h
H
a
b
c
d
e
f
NMe2
OMe
F
g
h
i
H
a
b
c
d
e
f
CF3
CF3
i
CN
CN
j
Cl
k
l
COOMe
COMe
NO2
Cl
j
COOEt
NO2
Br
Br
k
Me
t-Bu
m
Me
g
3-(4-Substituted ph en yl)-3,4-dih ydro-2H-1,3-ben zoxazin e-2,4-dion es were prepared15–17 by
addin g eth yl ch loroform ate (5.2 g, 48 m m ol) dropwise to a stirred solution of th e respective
4-substituted salicylan ilide (40 m m ol) in dry pyridin e (20 m l) cooled with ice. Th e prepared
m ixture was h eated on a steam bath for 1 h an d th en poured in to 140 m l of 5% h ydroch lo-
ric acid. Next day th e product was filtered off, suspen ded in 5% potassium h ydroxide solu-
tion , th orough ly stirred, filtered off an d recrystallized from eth an ol in yields of 55–65%.
NMR Measurem en ts
Spectral m easurem en ts were don e on a Bruker Avan ce DRX-500 spectrom eter at 500 (1H)
an d 125 (13C) MHz, respectively. Sam ples were m easured at con cen tration 0.1 m ol dm –3 in
CDCl3 (1) or DMSO-d6 (2) an d ch em ical sh ifts were stan dardized on TMS (1H) or on th e cen -
tral peak of th e solven t used19 13C): CDCl3 δ 76.91 an d DMSO-d6 δ 39.56. Digital resolution
(
was 0.0002 an d 0.007 ppm in 1H an d 13C NMR spectra, respectively. Ch em ical sh ifts are col-
lected in Table I (1) an d Table II (2).
Calculation s
All calculation s were carried out with double precision on a PC with Pen tium -S/150 MHz
processor with 32 MB RAM. Stan dard subroutin es were used for lin ear regression an d sign i-
ficance testing; for assignment a multivariate regression program ASSIGN was used20. The semi-
empirical calculation s at th e AM1 level21 were perform ed un der full geom etry optim ization .
Collect. Czech. Chem. Commun. (Vol. 64) (1999)

1714
Holík, Friedl, Waisser, Gregor:
Collect. Czech. Chem. Commun. (Vol. 64) (1999)

Multivariate Regression
1715
Collect. Czech. Chem. Commun. (Vol. 64) (1999)

1716
Holík, Friedl, Waisser, Gregor:
RESULTS AND DISCUSSION
1H NMR Spectra of 1 and 2
1
For th e regression an alysis of H ch em ical sh ifts of sign als assign ed to h y-
drogen atom s ortho, δH , an d meta, δH , to variable substituen t X, th e fol-
m
lowin g m odel equationo, Eq. (5), was used.
δH = b0 7.27 + b1 aj + εj ,
(5)
j
wh ere aj is correspon din g SSI variable8 an d εj is statistical error. Ch em ical
sh ifts δH in both series 1 an d 2 sh ow regular additive beh aviour (see Eqs
(6a) an d o(6b)). Th e subscripts in paren th eses are correspon din g stan dard de-
viation s; if sm aller th an 0.01 th e value is substituted by 0.01).
δH (1) = 1.028(0.01) + 0.975(0.01) ao + εo
(6a)
o
sy = 0.457
r = 0.9990
n = 13
δH (2) = 1.034(0.03) + 0.978(0.05) ao + εo
(6b)
o
sy = 0.482
r = 0.9863
n = 11
On th e oth er h an d, regression an alysis of ch em ical sh ifts δH in both series
m
1 an d 2 afforded slope value, b1, sign ifican tly larger th an on e (see Eqs (7a)
an d (7b)).
δH (1) = 1.026(0.01) + 1.246(0.03) am + εm
(7a)
m
sy = 0.167
r = 0.9965
n = 13
δH (2) = 1.028(0.01) + 1.330(0.10) am + εm
(7b)
m
sy = 0.188
r = 0.9758
n = 11
Collect. Czech. Chem. Commun. (Vol. 64) (1999)

Multivariate Regression
1717
Th e slope b1 (1) for th e larger set (Eq. (7a)), 1.246, does n ot differ from th e
value obtain ed form erly5, 1.252 (Eq. (3f)). Th is m ean s, th at it does n ot de-
pen d on th e n um ber of m easurem en ts (com poun ds). Th e residuals from Eq.
(6a), εm, were tran sform ed to “jackkn ife” residuals, wh ich can h elp to detect
outliers in data. In order to en h an ce a n um erical value of residual wh ich
sh ould belon g to a probable outlier, th e plain residuals, i.e., differen ces be-
tween experim en tal an d calculated values, ε, are tran sform ed to “jackkn ife”
residuals, εjk, usin g Eq. (7c).
n − p − 1
n − p − ε 2n
ε
ε jk = ε n
,
wh ere ε n
=
(7c)
se 1 − hi
wh ere se is stan dard error of estim ate an d hi is th e correspon din g diagon al
elem en t of a tran sform ation m atrix H = X(X′X)–1X′. If εj > 0.2 (n – p) th en
th e correspon din g yi value is con sidered as suspicious an d th e regression
sh ould be repeated with out it. Th e “jackkn ife” residual for F derivative
sh owed value 2.74 an d th e correspon din g δH (F) datum can be suspected as
in fluen tial. Om ittin g th is m easurem en t th em regression equation (Eq. (7d))
was obtain ed.
δH (1) = 1.026(0.01) + 1.243(0.02) am + εm
(7d)
m
sy = 0.174
r = 0.9980
n = 12
It is clear th at n eith er th e n um ber of m easurem en ts n or th e presen ce of
outlier is respon sible for th e slope b1(1) larger th an on e.
In order to support our idea th at th is in crease is due to th e ch an ge in dia-
m agn etic con tribution of th e Y group (see above), th e geom etries of th ree
substan ces 1 (X = NH2, H, NO2) were calculated by sem iem pirical AM1
m eth od wh ich was developed for th e calculation of m olecular con form a-
tion s an d electron ic properties21. Th e results of calculation s (len gth of
C
aryl–N bon d in Å, dih edral an gle in degrees between th e an ilin e ben zen e
rin g an d th e plan e of N=C–H atom s are given ), X = NO2, 1.406, 25.36; X =
H, 1.412, 29.26; X = NH2, 1.413, 30.76, are in agreem en t with our in terpre-
tation of th e con form ation al ch an ges in duced by th e ch an ge in th e
substituen t X. Wh en com parin g b1(1) = 1.246 with b1(2) = 1.330 it was
tem ptin g to attribute th e in crease in th e latter case to th e differen t geom e-
try of th e six- an d five-m em bered rin gs. However, th e in spection of “jack-
Collect. Czech. Chem. Commun. (Vol. 64) (1999)

1718
Holík, Friedl, Waisser, Gregor:
kn ife” residuals of Eq. (7b) revealed th at εjk(NMe2) = 2.09 an d 1a derivative
can be suspected as outlier. After leavin g it out (see Eq. (7e)), th e lower
value of b1 (1.232) was obtain ed.
δH (2) = 1.030(0.01) + 1.232(0.10) am + εm
(7e)
m
sy = 0.161
r = 0.9768
n = 10
13C NMR Spectra of 1 and 2
As th e first step in an alyzin g 13C NMR spectra of both series, th e program
ASSIGN20 was used to ch eck th e sign al assign m en t. Th is program uses Eq.
(4) for fittin g all ch em ical sh ifts of arom atic carbon atom s with all corre-
spon din g SSI , i.e. zi, zo, zm, an d zp. Th e bj values obtain ed were tested by th e
Studen t t-test for th e statistical sign ifican ce on th e 95% con fiden ce level.
Th e sign ifican t values are in Table III.
Wh ile th e regression with all SSI is advan tageous from th e viewpoin t of
th e best fit for sign al assign m en t, for th e an alysis of data on ly th ose vari-
ables are relevan t wh ich possess statistically sign ifican t slope values. Th ere-
fore, each data set (i.e. ipso, ortho, etc.) was an alyzed in depen den tly.
Ch em ical Sh ifts of C1 (ipso to X) Atom s
In th e series 1, th e regression of δC1 with correspon din g SSI, i.e., zi, is given
in Eq. (8a).
δ
C1(1) = 0.993(0.01) + 1.005(0.01) zi + ε
(8a)
sy = 14.86
r = 0.9992
n = 13
However, “jackkn ife” residuals suggest th at th e value for m eth yl derivative
could be an outlier: εjk(Me) = 2.44 > 0.2 11.
After leavin g th is m easurem en t out alm ost sam e equation (Eq. (8b)) was
obtain ed.
Collect. Czech. Chem. Commun. (Vol. 64) (1999)

Multivariate Regression
1719
δC1(1) = 0.992(0.01) + 1.006(0.01) zi + ε
(8b)
sy = 15.52
r = 0.9995
n = 12
Neith er param eters b were ch an ged n or th e stan dard deviation sy decreased;
we can con clude th at th e value for th e Me derivative is n ot an outlier. Th en
th e rem ain in g SSI values, each in dividually or in pairs, were tested as possi-
ble oth er explan atory variables but all tests were n egative. Statistical sign ifi-
can ce of addition of an oth er explan atory variable in to a regression can be
tested by a partial F-test Eq. (8c)
SRp − SRp+1
F =
n − p ≥ F
,
(8c)
(
)
0. 05 , 1 , n − p
SRp+1
wh ere SRp is th e sum of squares of residuals for regression with p param eters
an d SRp+1 th e sam e quan tity for regression with p + 1 param eters.
On ly wh en all of th em were taken (like in ASSIGN program ) th en th e re-
sult of F-test was positive.
TABLE III
Regression param eters, correlation coefficien ts, an d stan dard deviation of data calculated by
program ASSIGN usin g four SSI as explan atory variables
Com -
poun d
Catom
b0
b1
b2
b3
b4
sy
r
1
2
3
4
1
2
1
2
1
2
1
2
0.995
0.998
1.005
1.002
0.983
1.003
1.027
1.053
1.024
1.030
0.101
0.128
1.012
1.003
–0.465
–0.615
–0.117
–0.124
0.041
0.081
–0.071
0.100
0.867
0.961
0.9999
0.9999
0.9996
0.9993
0.9693
0.9646
0.9973
0.9983
14.86
15.61
6.79
7.45
0.84
0.86
4.87
5.36
0.910
1.211
Param eters b were calculated accordin g to Eq. (4); on ly th ose sign ifican t by th e Studen t t-test
at th e 95% level are given .
Collect. Czech. Chem. Commun. (Vol. 64) (1999)

1720
Holík, Friedl, Waisser, Gregor:
F-test = 20.79 > F(0.05, 3, 8) = 4.07 an d also > F(0.01, 3, 8) = 7.59
In th e series 2, th e regression of δC1 with correspon din g SSI, i.e., zi, is
given in Eq. (8d).
δ
C1(2) = 0.995(0.01) + 0.993(0.01) zi + ε
(8d)
sy = 15.61
r = 0.9991
n = 11
Also in th is series, th e “jackkn ife” residuals suggest th at th e value for
m eth yl derivative could be outlier: εjk(Me) = 2.06 > 0.2 9.
An d again , n o im provem en t was ach ieved after leavin g th is m easurem en t
out (Eq. (8e)).
δ
C1(2) = 0.994(0.01) + 0.993(0.01) zi + ε
(8e)
sy = 16.45
r = 0.9994
n = 10
Sm all im provem en t in regression can be obtain ed again on ly with all th e
oth er SSI values as explan atory variables.
F-test = 16.16 > F(0.05, 3, 6) = 4.76 an d also > F(0.01, 3, 6) = 9.78 .
Ch em ical Sh ifts of C2 (ortho to X) Atom s
Th e results from th e ASSIGN program (Table III) suggest th at besides th e zo
also th e zp variable can be used in regression with δC2. In th e series 1, th e re-
gression of δC2 with zo is given in Eq. (9a).
δ
C2(1) = 1.005(0.01) + 1.023(0.01) zo + ε
(9a)
sy = 6.79
r = 0.9993
n = 13
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Multivariate Regression
1721
From “jackkn ife” residuals th e value for th e dim eth ylam in o derivative
cam e out as a possible outlier: εjk(NMe2) = 2.80 > 0.2 11.
After leavin g th is m easurem en t out a sligh t im provem en t was ach ieved
(Eq. (9b)):
δ
C2(1) = 1.005(0.01) + 1.007(0.01) zo + ε
(9b)
sy = 5.87
r = 0.9995
n = 12
Th is reduced series was tested by th e F-test for th e addition of zp variable to
th e regression equation ; th e test was n egative.
F-test = 4.12 < F(0.05, 1, 9) = 5.12
Wh en th is test was perform ed on th e origin al data it was positive at th e
95% con fiden ce level but n egative at th e 99% on e. Th e n ecessity to im -
prove th e regression in cludin g zp variable can be evoked by th at sligh tly
outlyin g value for th e NMe2 derivative. An an alogous situation was ob-
served in series 2.
δ
C2(2) = 1.003(0.01) + 1.039(0.02) zo + ε
(9c)
sy = 7.45
r = 0.9984
n = 11
Th e “jackkn ife” residuals poin ted out th at again th e value for th e
dim eth ylam in o derivative could be an outlier: εjk(NMe2) = 2.81 > 0.2 9.
δ
C2(2) = 1.003(0.01) + 1.013(0.02) zo + ε
(9d)
sy = 6.45
r = 0.9989
n = 10
The conclusion m ade on the series 1 data is supported by those of the series 2.
Addition of zp variable is n ot n ecessary.
F-test = 4.89 < F(0.05, 1, 7) = 5.59
Collect. Czech. Chem. Commun. (Vol. 64) (1999)

1722
Ch em ical Sh ifts of C3 (meta to X) Atom s
Holík, Friedl, Waisser, Gregor:
Th e results from th e ASSIGN program (Table III) suggest th at besides th e zm
also th e zp variable can be used in regression with δC3. In th e series 1, th e re-
gression of δC3 with zm, is given in Eq. (10a).
δ
C3(1) = 0.983(0.01) + 1.005(0.17) zm + ε
(10a)
sy = 0.84
r = 0.8790
n = 13
Due to a very sm all susceptibility of th e experim en tal data (sy = 0.84) to th e
ch an ge in substituen t X it was n ecessary to an alyze th is depen den ce m ost
carefully. As a suspected outlier we selected th e NO2 derivative: εjk(NO2) =
2.80 > 0.2
tain ed.
11. After leavin g correspon din g data out Eq. (10b) was ob-
δ
C3(1) = 0.983(0.01) + 1.10(0.13) zm + ε
(10b)
sy = 0.86
r = 0.9329
n = 12
Regardless of wh eth er th e NO2 derivative was retain ed or left out th e F-test
for addition of zp variable to th e regression was positive.
F-test = 26.18 > F(0.05, 1, 10) = 4.96 an d also > F(0.01, 1, 10) = 10.04 for n = 13
F-test = 18.62 > F(0.05, 1, 9) = 5.12 an d also > F(0.01, 1, 9) = 10.56 for n = 12
In clusion of zp variable led to th e better fit, Eq. (10c) or (10d).
δ
C3(1) = 0.983(0.01) + 0.893(0.10) zm – 0.069(0.01) zp + ε
(10c)
sy = 0.84
r = 0.9681
n = 13
δC3(1) = 0.983(0.01) + 0.951(0.09) zm – 0.055(0.01) zp + ε
(10d)
sy = 0.86
r = 0.9787
n = 12
Collect. Czech. Chem. Commun. (Vol. 64) (1999)

Multivariate Regression
1723
Sim ilar beh aviour was observed in series 2. However, in th is case th e NMe2
derivative was a suspected outlier. Th e data in cludin g th e NMe2 derivative
gave Eq. (11a) an d th ose with out th e NMe2 com poun d gave Eq. (11b).
δ
C3(2) = 1.004(0.01) + 0.949(0.26) zm + ε
(11a)
sy = 0.86
r = 0.7778
n = 11
εjk(NMe2) = 2.67 > 0.2
9
δC3(2) = 1.005(0.01) + 0.997(0.19) zm + ε
(11b)
sy = 0.85
r = 0.8761
n = 10
Sin ce in both cases th e F-test allowed to add explan atory variable zp to th e
regression th e Eqs (11c) an d (11d) were calculated.
F-test = 37.08 > F(0.05, 1, 8) = 5.32 an d also > F(0.01, 1, 8) = 11.26 for n = 11
F-test = 15.96 > F(0.05, 1, 7) = 5.59 an d also > F(0.01, 1, 7) = 12.25 for n = 10
δC3(2) = 1.004(0.01) + 1.216(0.12) zm + 0.097(0.02) zp + ε
(11c)
sy = 0.84
r = 0.9643
n = 11
δC3(2) = 1.004(0.01) + 1.192(0.12) zm + 0.084(0.02) zp + ε
(11d)
sy = 0.85
r = 0.9639
n = 10
Collect. Czech. Chem. Commun. (Vol. 64) (1999)

1724
Ch em ical Sh ifts of C4 (para to X) Atom s
Holík, Friedl, Waisser, Gregor:
Th e ASSIGN program (Table III) sh ows th at on ly th e zp variables correlate
with δC4. In th e series 1, th e regression of δC4 with zp is given in Eq. (12a).
δ
C4(1) = 1.025(0.01) + 0.922(0.03) zp + ε
(12a)
sy = 4.87
r = 0.9951
n = 13
After excludin g th e NO2 derivative as possible outlier: εjk(NO2) = 5.57 > 0.2
11, we obtain ed Eq. (12b).
δ
C4(1) = 1.027(0.01) + 0.958(0.01) zp + ε
(12b)
sy = 4.83
r = 0.9989
n = 12
In both cases th e F-test sh owed n on -im portan ce of oth er explan atory vari-
ables.
It was sh own th at in 1,4-disubstituted ben zen es th e secon d order regres-
sion 22 of δC4 with σI an d σR con stan ts23 can give electron dem an d of th e Y
substituen t.
2
δC4 = 131.912(0.25) + 3.859(0.61)σI + 18.602(1.01)σR – 5.200(2.65)σR + ε (12c)
sy = 4.87
r = 0.9967
n = 13
2
Th e slope at th e σR variable, b3, is sign ifican t on ly at th e 90% level. Th ere-
fore, th e electron dem an d value η = b3/b2 = –0.279 is sign ifican t also at th is
level. If th e suspected outlier NO2 is left out, Eq. (12d) gives b3 param eter at
th e 95% level an th e calculated η is m ore probable: b3/b2 = –0.158.
δC4 = 131.773(0.12) + 4.647(0.31)σI + 19.754(1.01)σR – 3.125(1.26)σR2 + ε (12d)
sy = 4.83
r = 0.9993
n = 12
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Multivariate Regression
1725
From th e com parison of th is η datum with th ose for com m on substitu-
en ts22 it follows th at th e ph th alim ido group in 1 can be regarded as a weak
electron acceptor.
For series 2 th e equation correspon din g to (12a) reads (13a).
δ
C4(2) = 1.053(0.01) + 0.986(0.02) zp + ε
(13a)
sy = 5.36
r = 0.9977
n = 11
Sin ce n o outlier was suspected th e regression with σ con stan ts23 h ad th e
form of Eq. (13b).
2
δC4 = 135.202(0.36) + 4.159(0.82)σI + 17.538(1.31) σR – 7.604(3.36)σR + ε (13b)
sy = 5.36
r = 0.9959
n = 11
Th e b3 param eter was again sign ifican t on ly at th e 90% level. Neverth eless,
th e n egative η value, b3/b2 = –0.433, allowed to classify th e substituen t Y in
series 2 also as an electron acceptor.
CONCLUSIONS
Th orough testin g of regression param eters an d residuals obtain ed from th e
correlation of 1H an d 13C NMR ch em ical sh ifts in 1,4-disubstituted
ben zen es 1 an d 2 with substituen t sh ift in crem en ts aj an d zj, respectively,
sh owed th at ch em ical sh ifts in th e meta position to variable X substituen t,
i.e. in th e ortho position to fixed substituen t Y, are sen sitive to con for-
m ation al ch an ges con cern in g th e ben zen e rin g an d th e plan e of Y
substituen t. Th is effect is m ost pron oun ced in 1H ch em ical sh ifts causin g a
sign ifican t in crease in correspon din g slope values over on e. In 13C NMR
sh ifts th e variable wh ich reflects th is con form ation al ch an ge can be substi-
tuted by th e SSI value for th e para position sin ce th e electron den sity on C4
is decisive for th e bon d order an d twist an gle of th e substituen t Y. However,
1
th is effect is n ot so clear as in th e case of H ch em ical sh ifts an d th e reason
for th e sign of th e correspon din g slope m ay con sist in a differen t space in -
Collect. Czech. Chem. Commun. (Vol. 64) (1999)

1726
Holík, Friedl, Waisser, Gregor:
terval (an d th erefore in diam agn etic an isotropy field) aroun d th e C=O bon d
in wh ich th e carbon Cm can m ove.
The autors wish to thank Dr S. Böhm from Department of Organic Chemistry, Prague Institute of
Chemical Technology for kind performing semiempirical AM1 calculations and Dr O. Humpa for mea-
surement of NMR spectra.
REFERENCES
1. Craik D. J., Brownlee R. T. C., Sadek M.: J. Org. Chem. 1982, 47, 657.
2. Holík M., Běluša J., Břicháček J.: Collect. Czech. Chem. Commun. 1978, 43, 610.
3. Holík M., Potáček M., Švaříček J.: Collect. Czech. Chem. Commun. 1978, 43, 734.
4. Holík M., Pavéska P., Mlynárik V.: J. Mol. Struct. 1984, 114, 15.
5. Holík M., Matějková B.: Collect. Czech. Chem. Commun. 1990, 55, 261.
6. Holík M.: Chemom. Intell. Lab. Syst. 1993, 19, 225.
7. Haslinger E., Wolschann P.: Org. Magn. Reson. 1977, 9, 1.
8. Beeby J., Sternhell S., Hoffmann-Ostenhof T., Pretsch E., Simon W.: Anal. Chem. 1973,
45, 1571.
9. Holík M.: Org. Magn. Reson. 1977, 9, 491.
10. Exner O., Buděšínský M.: Collect. Czech. Chem. Commun. 1991, 56, 2234.
11. Ciarkowski J., Kaczmarek J., Grzouka Z.: Org. Magn. Reson. 1979, 12, 631.
12. Solčániová E., Toma Š., Sališová M., Liptaj T.: Org. Magn. Reson. 1983, 21, 429.
13. Perez C., Schleinitz K.-D., Gründemann E.: Z. Chem. 1982, 22, 260.
14. a) Holík M.: Collect. Czech. Chem. Commun. 1996, 61, 713; b) Holík M.: J. Mol. Struct.
1999, 482–3, 345.
15. Waisser K., Kubicová L., Klimešová V., Odlerová Ž.: Collect. Czech. Chem. Commun. 1993,
58, 2977.
16. Wagner G., Singer D., Weuffen W.: Pharmazie 1966, 21, 161.
17. Einhorn A., von Bagh A.: Chem. Ber. 1910, 43, 322.
18. a) Grandmougin E., Lang A.: Chem. Ber. 1909, 42, 4014; b) Forbes E. J., Stacey M.,
Tatlow J. C., Wragg R. T.: Tetrahedron 1960, 8, 67; c) Bogert T. M., Wise L. E.: J. Am.
Chem. Soc. 1912, 34, 693; d) Yamamoto T., Kurata Y.: Can. J. Chem. 1983, 61, 86;
e) Gabriel S.: Chem. Ber. 1878, 11, 2260.
19. Levy G. C., Cargioli J. D.: J. Magn. Reson. 1972, 6, 143; Günther H.: NMR Spectroscopy,
Basic Principles, Concepts, and Applications in Chemistry, 2nd ed., p. 532. Wiley, New York
1995.
20. Holík M., Friedl Z., Marchalín Š.: Collect. Czech. Chem. Commun. 1999, 64, 1696.
21. Dewar M. J. S., Zoebisch E. G., Healy E. F., Steward J. J. P.: J. Am. Chem. Soc. 1985, 107,
3902.
22. Holík M.: Magn. Reson. Chem. 1992, 30, 189.
23. Hansch C., Leo A., Taft R. W.: Chem. Rev. 1991, 91, 165.
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