Electrophilic aromatic substitution: a free-electron approach

Volume

77. number

CHEMICAL

2

ELECTROPHILIC

AROMATIC

tiszl6 VON SZENTPALY Itrstrtut fur Theoretrsclre Clrenrre

PHYSKS

SUBSTITUTION

Umverarat

Recened 7 August 1980, m final form

Snrrtgart

15 October

LEITERS

1.5 Januaq

A FREE-ELECTRON

D- 7000 Stutrgart

1981

APPROACH

FRG

1980

Free-electron superdelocahzabdlty mdlcesare mtroduced to ratlonnhze the partul rate factors for electrophlhcaromatic substltutlons The corrclatlon coeffkent r = 0 975 for eghteen posItIons on polycychc aromatIc hydrocarbons IS compnrable to r = 0 979 of CND0/2 calculations For the fist time, n model wthout ekphc~r electron repuklon gwes rl rrnctwity mdev of predIctwe value PredIctIons are gwen for some unmeasured rate factors

1. Introduction

of free-electron

superdelocalizabilities

Recently, a modified free-elecrron model (MFE) [ 1,2] has been very successful m calculatmg the n-band positrons m the photoelectron spectra of aromatlc hydrocarbons [l] and biolo@cal molecules [2] In this paper, the free-electron model serves to calculate the parhal rate factors for electrophdlc aromatic substrtutrans. Various mdrces, e g locahzahon energres [3], freevalences [4,5] and superdelocalizablhtres [6], have been proposed to correlate reactivity with molecular structure. For alternating hydrocarbons these mdlces are interdependent and their relationshIps have been drscussed by several authors [7-91 The superdelocahzabihty Index Introduced by Fuku~ et al [6] IS easdy evaluated, smce the reactivity 1s descr?bed m smgle-atom parameters of the fundamental molecular skeleton and It 1s not necessary to carry out separate locahzatlon energy calculations for every fragment denved from the u-complex constderrd Unfortunately, HMO superdelocahzabrhtres give mediocre correlatlonq with large standard errors m the partial rate factors comparable to calculations usmg HMO locahzatlon energies. Superdelocahzabdhes based on free-electron (FFMO) calculations have not yet been reported. Their mtroductron In this paper is~ustlfied by the fact that the FEMO and HMO models are mathematically isomorphic molficatlons of exh other [ IO- 161 Dls352

cussmg this Isomorphlsm, Ruedenbergand Ham [ 14,l S] have presented a modified LCAO model wh~h IS almost Identrcal with the simple FEMO network. model [ 17-191 For purely cychc alternating hydrocarbons, such a modified LCAO model yields almost the same close correlation kvlth the photoelectron spectra as the MFE model [ 1,2] Further, the approximate atom populations [ 141 of the free-electron and the modlfied LCAO models are ldentlcal and the exact atom populatrons very sumlar for such molecules [ 14,151 Smce the concept of superdelocahzablhty IS not hmrted to a specific LCAO model, rt IS reasonable to test free-electron (FE) superdelocahzabdltres as a reactlvlty mdex for aromatlc substltutlons. The electrophdlc FE superdelocahzabrhty SL of the pth carbon atom m an even hydrocarbon with 212 atoms is denved analogously to Its HMO counterpart [6] It IS proportlonal to

(1) ’ IS the contrlbu tron of the lth n-orbital to the pc&latlon of the pth atom The energy hfference eNB - E, between a non-bondmg orbItal [ 14, p 18941 and the,th orbrtal IS expressed by

2C

ENB - E, = (fi*/%72*0*)[(n/2)2

- K/q ,

(2)

with K, = 2nDIAl, A, bemg the de Broghe wavelength of the jth free-electron orbltal, D = 1.40 A the average

0 009--2614/81/0000-0000/S

02.50

0 North-Holland

Pubhshing

Company

Volume

77, number

CHlNIC4L

7

PHYSICS

CC bond length and t>z* the effecuve electron mass [I]. Smce the lmear correlatlon wth the logar1tlim of the partial rate factors logf(p) IS of the kmd ,

(3)

It IS converuent to omit the factor fi2/21il”DZ Thus, the electrophdlc FE superdelocahzablhty Introduced as

IS

logf(p)

= LJ+ 6$(P)

LlI-l-ERS

(4)

Wlth a constant D = 1 40 A, the c,; may be represen ted (a) By D” tnnes the Lalue of the/t11 FE orbIta at atom p, such qf(p)D’ are tabulated [ Is] For atoms where substltut!on can occur, they fulfil the populatlon theorem for al ternan t hydrocarbons. 1e

(5)

nnd discussion

Table 1 contams the exact free-electron contrlbutlons S$, to the atom populations calculated by eq (7) The $(p)D’ and K values have been taken from refs [Is,-( S] TlIe two derslons of FE superdelocnllzabIlltIes S,‘($(p)) =-Y:(p) dnd S:@Q,;) =SL(p) are compded together with the corresponding HLlO values SF m table 3- The Ilnedr correldtlons wth the euperlmental logj-values for protlodctrltlatlon according to (3) yield tile followng regressIon Ilnes and correlation coefficlen ts I logf,,,(S~)=-1253+2’08S~.

(b) By the 1ntegrJted

density

logf4,

($)

=

logf&.S~)= p-D/1

These alternat:ves do not east for the HMO model, where only (J) IS possible, since the orbltals are not euphcltly gwen it IS of Interest whether alternawe(b) accountmg for the exact free-electron dlstnbutlon mlproves the correlation with experiment Fortunately, It IS not necessary to carry out the integration to obtam the contrlbutlon au,; Its dlffereme to $(p)D’ IS [ 141

6a,; -

b;(p)D2

X [G’;(q) + $0

= (1 + K,-’ sm

K,)(?

- ?Ol’(p)] D” ,

(7)

q and Y bemg the nelghbour atoms to p On the evpenmttntal side, the protlodetrltlatlon of trltlum-labelled aromatlc hydrocarbons m tnfluorodcetlc actd [20,2 I] has become the standard method for measurmg isotope-exchange rates of polycycllc

aromatlc hydrocdrbons

dnd

has ylelded the lxgest

body of quantltatwe data on electropluhc aromatlc substltutlon [20--261 These data are especially suitable for comparison wth MO calculations because the

-891

r = 0 975, + 164O.S;

-S74+

1228S;‘.

I = 0 956. I =Os)-Fl

The calculated log j values are collected III table 3 and plotted versus the observed IoyJm figs I and 2 Tile standard errors SE(logf) dnd the correlation coefficwnts J are compared wth those of other calculatwns m table 4 Both versions of FE superdelocallr~b!htws are clearly super lor to the corresponding HhlO Index It IS rspeclally satlsfymg that the SL mdek, using the exact FE contnbutlons 6~,‘~ (6). IS dlstlnctly prcfera-

ble to the Sf Index wth its dpproumiatc contrlbutlons A comparison wth SCF calculations (table 4) reveals that the SL Index CND0/2 mdlces

sin K,)_”

1981

stew hmdrance IS neghglble for the Isotope ewhangc reactlons. whereas It can play a major role m mtratlon. for example [23] Therefore the calculated FE and HMO superdelocah7abd~tles ~111 be correlated wth the loganthms of the partial rate factors for protlodetntlatlons according to eq. (3)

2 Results

S,F(p)=,g k,‘,/[(Ir/2) - hf]

15 January

IS about

as relldble

,IS the PPP and

For the first tune It IS shown that a model wth utlplrtrr electron repulsion [ I ] IS able to gwe a remarkably good reactwty Index Concermng the adequacy of an effectwe mass t12* to allow for mipliclt electron repulsion, It should be mentIoned that the MFE model can be represented as a smlphtied version [27] of the Pople SC’F method [X3] This IS shown along slmrlar lmesas for HMO [X3,29] Certamly, lfan fxpkrr form of repulsion were needed, It would be useless to replace Huckel MOs by FE MOs Therefore. thus study (1) mvahdates the common assumption [X,30]

353

Volume 77, number

Table 1 The exact free-electron I

CHEMICAL

2

contnbutmns

60,;

to the populatton

6

15 January

PHYSICS LETTERS

1981

at atom p

&’

benzene

anthracene

naphthalene

p=l

p=l

p=2

p=1

p=2

p=9

0.1667 0 3045 0 0288

0 OS09 0 0711 0.1455 0 0201 0 1612

0.0909 0 1757 0 0395 0 1186 i) 0766

0 0625 0 0822 0.0198 0 0788 0 1485 0.0151 0.08 15

0.0625 0 1234 0.1191 0 0203 0 0509 0 0761 0 0492

0 0625 0.0025 0 0921 0.1293 0 0034 0.0138 0 1728

phenanthrene

1 2 3 4 5 6 7

p=l

p=2

p=3

p=4

p=9

00625 0 0935 0.0045 0 0944 0 0991 0 0409 0 0937

0 0625 0.1328 0 0504 0 1116 0 0121 0 1177 0 0144

0 0525 0 1220 0 0942 0 0152 0 0991 0 0191 0.0888

0 0625 0 0696 00518 0 0687 0 0991 0 0949 0 0434

0 0625 0 0563 0.2218 0 0044 0.0309 0 0236 0 1417

12

I; ooz

1

@0

m2

tetracene

pyrene

p=l

p=2

p=

12

0 0476 0.075 1 0 0341 0.0473 0.0106 0 1114 0.0118 0.1041 0.0469

0 0476 0 0946 0 0929 0 0118 0 0902 0 0333 0 0542 0.0438 0 0327

0 0476 0 0132 0 0467 0.0954 0 0498 0.0352 OOll2 0 0503 0.1266

p=l

p=2

p=4

0 0526 0.‘066 0 0210 0.0743 0 0857 0 0016 0.0260 0.1201

0.0526 0.1397 0.0019 0 1644 0.0104 0.006 1 0.1088 0.0203

0 0526 0 0065 0 1482 0 0609 0 0266 0.0988 0.0260 0.0706 Table to be contmued

354

on next page

77. number 2

Volume Table

CHEMICAL

PHYSICS

1.5 January

LETTERS

1981

1 (contmued)

perylene

trlphenylene

coronene

p=l

p=3

p=3

p=2

p=l

p=l

1

00476

2 3 4 5 6 7 8 9

0.0398 0 0695 0 0099 0.0942

0 0476 0 1694 0 0003 0.0805 0 0317 0 0382 0 0391 0.0640 0 0303

0 0417 0.0736 0 0298 0 0500 0 0707 0 0292 00112 0 0646 0 0298 0 0868

0 0417 0 0610 0.0762 0 1069 0 0248 0 0362 0.0580 0 0484 0 0284 0 0229

0 0 0 0 0 0 0 0 0 0

0 0333 0 0788 0 0121 0 0556 00511 0 0275 0 0785 0 0244 0 0274 @ 0123 0 0107 0 0789

00411 0 1048 0 0329 0 0504

10

0417 0340 0818 0763 0102 0884 0635 0132 0066 0730

11 12

Table 2 Freeelectron

and Huckel superdelocahzabltles

Hydrocarbon

Posltlon

s,F

s;

SH e

benzene naphthalene

1 1 2 1 2 9 1 2 12 1 2 3 4 9 1 2 4 1 2 3 2 1 1

0 621 0 723 0.666 0 769 0 700 0 919 0 798 0 725 1 025 0 720 0 667 0 680 0 706 0 737 0821 0 669 0751 0 704 0.674 0 857 0 686 0 824 0.749

0621 0 748 0.658 0 800 0 690 0 995 0831 0 715 1 126 0 743 0 658 0.679 0 721 0.753 0853 0 632 0 769 0 719 0 668

0 833 0 994 0 873 1 073 0 922 1 312 1 122 0961 1504 0 977 0 860 0 893 0 939 0.997 1115 0 828 1026 0 928 0.875 1 195 0 856 I117 0991

anthracene

tetracene

phennnthrene

pyrene

triphenylene

perylene coronene

0.911 0 644 0.864 0.764

that exphcit conslderatlon of electron repulsion IS needed III deahng with the reactlvrtres of even alternatmg hydrocarbons, (2) provides strong evidence that, for even alternants, the FE wavefunctlons are much more adequate than the Huckel orbltals In order to understand the SUCC~S of FE superdelocahzabihties, two chfferences between the FEMO and HMO models should be &scussed separately. (a) HMO assumes a constant /3 between all nezghbouring carbon atoms, whereas, m LCAO terms, the branching concht1ons for FEMOs [ 171 are equivalent to the mtroductlon of another two related resonance bonds connected Integrals 0, and flJJ, representing with one and two branchmg pomts J of the carbon skeleton. Note, that PJ and pJJ are not new parameters, they are related [ 141 to p by P,=($)“‘P,

P,,=$P-

(8)

(b) In the FEMO models, the Functions @,(x) are exphcltly and continuously gven, whereas orzly coefficients cIp at the nuclei are obtamable with HMO. The me&ocre performance of HMO superdelocahzabdlties IS due to these factors. The comparison between SF, sf and SL provides a diagnostic Insight, enabhng us to separate the two steps (a) and (b)

Volume Table 3 Observed

77, number

CHEMICAL

2

and calculated

partial rate factors

Hydrocarbon

benzene naphthalene anthracene

phenanthrene

pyrene

tilphenylene perylene coronene ‘1 Refs

b, Ref

[22-263

PosItIon

1 1 2 1 2 9 1 2 3 4 9 1 2 4 1 2 3 1

for protlodetntlation

m anhydrous

2.0

FEMO (S,F)

FELIO (SE)

HMO (S,H)

CNDO/Z b,

0 00

0 89

3.14 1 89 4 16 2 64 7 45 3 07 191 2 19 2 77 3 45 5 31 1 95 3 76 2 72 2 06 6 11 3 12

1 28 3 36 1 89 4 21 2 41 7 41 3 28 1 89 2 23 2 92 3 44 5 08 1 46 3 71 2 89 2 05 6 03 3 62

1 49 3 47 1 98 4 43 2 58 7 37 3 26 1.82 2 22 2 79 3 50 4 95 142 3 86 2 65 2 00 5 93 3 43

0 15

3 06 2 18 3 90 3 05 7 10 2 96 2 24 2 59 2 91 3 21 5 90 1 91 3 15 2 79 2.13 6 21 3 87

2 87 1.70 4 10 2 81 6 46 3.15 2 09 2 53 2.73 3 43 5 57 1 70 3 76 2 93 2 65 6 68 -

[23]

4.0

5.0

7.0

7.5

-

7.0

-

6.5

-

6.0

-

-5.0 0

-

24.5

-

214-o

-

8 J3.5

-

3.0

-

2.5

-

2.0

-

6.0

Fig 1. Correlation of FEhlO parti rate factors obtamed by SE calculations with observed park11 rate factors for protlodetrltition 356

at 70°C

obs a)

5.5

3-o

CF-&OOH

1981

log f

SF e

1-O

15 January

PHYSICS LC-l-fERS

I?g 2. Correlation of HhlO partial rate factors obtamed by .S$ calcuiatlons with ooserved partial rate factors for protlodetrltiation

Volume

77, number

Table 4 Standard different

CHEMICAL

2

errors SE(logf) models

and

correlation

coefficients

SE(logf)

r

Ref

(S,T)

0 38

0 975

this work

(S&,

0 50

0 9.56

this work

0 63

0941

thts work

r of

PHYSICS

15 January

LETTERS

Table 5 Partial ra.fe factors

Posit Ion

Hydrocarbon Model k EM0 FEMO

_-

H hl0

(S,H,

HhlO

(L+)

0 73

0 893

1231

HMO

-

040

0 966

(231

CND0/2

0 37

0 979

r231

PPP

0 39

0 912

-___1731

w(Lw)

preduxcd

(a) The difference between SL’ rend SE corresponds to the mtroductlon of the smaller resonance integrals for the bonds c,onnected with branchmg pomts, smce approximate c;~ v&es are used for both mdlces (b)The Improvement obtamed by proceedmg from Si to SF mdlces represents the superlorlty of the exact FE distnbutlon over the approximate one The contributions of both (a) and (b) are of comparable unportance (table 4) Thus comparison has a beanng on the proposltlon to draw different regression lines for different positlon types [23,30]. Obviously such hnes tend to comtide by proceedmg from SF to SL Contrary to earher suggestions [X3,30] it 1s concluded that, for HMO, a cksectlon mto different regression hnes IS tzof due to the tack ofexpkvt electron repulsion, but rather to the inherent HMO deticiencies discussed under (a) and (b). Regarding all-valence-electron SCF models, It should be recalled that MINDO/Z and HMO calcutatlons were equally poor m their correlation with the reactlvltles of arylethyt acetates [3 l] _Thus exphcit electron reputslon does not necessarily lead to improved correlation \vlth chenucal reactivity

3. Predictions With the correlation coefficient r = 0.975, a pre&ctive utdlty must be attributed to the FE superdelocahzablhty index Sz_ Thus, the logfvalues nre calculated for tetracene and perylene. The only logfdetermined experunentally [22] is that of the position 3 of perylene. The log f predicted by the SF, Sz and SF indices are given m table 5. There are considerable dlfferences in the predictlons

tctraccne

perylene -_-

1 2 12 1 2

b> dlffercnt

1981

models

log f I-CM0

FCXIO

(SL-)

ts;,

HMO (SF)

481 3 17 9 81 5 37 2 32

4 2 9 5 1

5 3 9 4 1

72 82 56 26 66

04 06 73 86 77

The partial rate factors m substttutions with other electrophlllc reagentscan be ratlonahred and predlcted by cahbrntmg eq (3) via relevant expenmental data The magmtude of the slope shouid be a measure of how the transition state resembles tile reaction mtermediate Some data are given In refs [X.32,33] However, the slopes for n:tratlon and chlormatlon should be fitted to more recent experiments

Xeferences 1’1 L von Szcntpnly,

Chem Phys Letters 67 (1979) 63 L von Szentpat>, J hlol Struct 60 (1980) 391 t:; G W Wheland, J Am Chem Sot 64 (1942) 900 DIscussIons Faraday Sot 2 (1947) 9, J I41 C A Coulson, Chum Phys 45 (1948) 243 R Jacques, Xl Jean, C Sandorfy and C tst R Dsudel. VroeLmt, J Chum Phys 46 (1949) 249 and C Nagatn, Bull Chem Sot ICI I; l-uhu~. T Yonezawa Japan 27 (1954) 423, J Chcm Phys 27 (1957) 1?47_

ISI

C A Coulson and H C Longuet-Hlggns, A191 (1947) 39 K I uhu~, T Sonezawa and C Nagata,

PI

26 (1957) 831 I Samuel,Compt

t7t

Rend

Acad

S-1

Proc Roy Sot J Chem

(Pans)

249

Phys (1959)

1893 IlO1

H H Jaffe, J Chem Phys 20 (1952) 1646.21 (1953) 1287 Proc Phys Sot (London) A66 (1953) t111 C A Coulson, 652 Proc CambrIdge Phll Sot 49 (1953) 650 t121 J S Crlfflth, \V Scherr,J Chem Phys 21 (1953) f131 M RuedenbergandC t141

1565,22 (1954) 151. K Ruedenberg, J Chem

1151 N S Hamnnd

K Rucdenberg,

Phys

22 (1954) J Chem

Phls

1878 29 (19.58)

1199 of physics, Vol 37 Part 2, ed 11‘51 J R Platt, EncyclopedIa S Flugge (Sprmger. Berhn, 1961) Helv Chum Acta 32 (1949) 2247, Angew iI71 H Kuhn. Chem 62 (1950) 389 357

Volume [ 181 [19] 1201 [21] [22]

[ 231 (241 [2.5]

358

77, number

2

CHEhIICAL

PHYSICS LETTERS

H H Perkampus, Z. Naturforsch. 7a (1952) 594 C W. Scherr. J. Chem. Phys. 21 (1953) 1582 C Eabom and R Taylor, J. Chem Sot. (1961) 247 R Baker, C Eabom and J A Sperry, J Chem Sot. (1962) 2382 A. Strertwreser Jr, A Lewrs, J Schwager, R W Frsh and S Labana, J Am Chem Sot 92 (1970) 6.529. A Strertwreser Jr , PC. Movery, R G Jesarhs and A Lewrs. J. Am. Chem. Sot 92 (1970) 6529 R Baker,C Eabom and R Taylor, J.Chem Sot Perks II (1972) 97 R. Taylor, rn Comprehenswe chenucal kinetrcs. VoL 13, eds C H. Bamford and C F H. Trpper (Elsevrer, Amsterdam. 1972) table 159

15 January

1981

[ 251 H V. Ansell, BIM. Huschler and R Taylor, J. Chem Sot Perkm ll(l977) 353 [27] L van Szentpaly, to be pubhshed [ 28 ] J-A Pople, Trans Faraday Sot. 49 (195 3) 1375. 1291 M J S. Dewar. The MO theory of orgamc chemrstry (McGraw-Hrll. New York, 1969) p 94. [ 301 C. Prirktiyr, Z. DoleJsek and R. Zahradnik, Collection Czech Chem Commun 33 (1968) 1211 [ 3 11 J N. MurrelI, W. Schmrdt and R. Taylor, J Chem. Sot. Perkm II (1973) 179 [ 321 A Strertwieser Jr., hlolecular orbrtal theory for organrc chermsts OVdey, New York, 1961) pp_ 323 ff 1331 L. Ahschuler and E Berlmer. J Am Chem. Sot 88 (1966) 5837