bond lengths and bond orders in benzenoid hydrocarbons and related systems: a comparison of valence...

ELSEVIER

THEO CHEM

Journal of Molecular Structure (Theochem) 427 (1998) 25-37

Bond lengths and bond orders in benzenoid hydrocarbons and related systems: a comparison of valence bond and molecular

orbital treatments

Rudolf Kiralj a+*, Biserka Kojib-ProdiC”, Sonja NikoliC b, Nenad Trinajstib b

“X-ray Laboratory, Rudjer BoSkoviC Institute, P.O.B. 1016, HR-10001 Zagreb, Croatia bTheoretical Chemistry Group. Rudjer BoSkoviC Institute, P.O.B. 1016, HR.10001 Zagreb, Croatia

Received 24 October 1996; accepted 15 April 1997

Abstract

Bond length-bond order relationships for carbon-carbon, carbon-nitrogen and carbon-oxygen bonds in benzenoid hydrocarbons, azabenzenoids and picrate-like systems are reinvestigated and discussed. The novel relationships between bond lengths and bond orders, computed by valence bond (VB) and molecular orbital (MO) methods were established using regression analyses. The applicability of both methods to predict the bond lengths in conjugated systems is compared. The theoretical curves based on harmonic potentials and the results of regression analyses reveal no preference for VB or MO.

0 1998 Elsevier Science B.V.

Keywordy: Azabenzenoids; Benzenoid hydrocarbons; Bond orders; Bond length-bond order relationships; Picrate-like systems

1. Introduction

Pauling used valence bond (VB) calculations of bond lengths in benzenoid hydrocarbons to demon-

strate its agreement with molecular orbital (MO) calculations for predicting geometries of conjugated systems [I]. In addition to the Pauling formula for predicting bond lengths from n-bond order, based on the harmonic potential [l], there are other linear regression bond length-bond order equations using

Pauling n-bond orders [2-41. Related equations are likewise available within the MO theoretical frame- work which are based on the Hiickel MO or self- consistent field (SCF) MO r-bond orders [4-91.

* Corresponding author. E-mail address: [email protected]

Very extensive calculations based on a LCAO-MO-

SCF approach were performed for benzenoid hydrocarbons [lo], polyenes and polyphenyls [ 111, cyclooctatetraene and related compounds [ 121, and fulvalenes [ 131. However, these analyses published almost thirty years ago were based on limited and less accurate data. These days, Cambridge Structural

Database [14] is a rich source of experimentally determined molecular geometries from X-ray and neutron diffractions. These data can be used for various classes of compounds with good estimates of bond lengths accompanied with their standard deviations.

In this work, the reinvestigation of bond length- bond order relationships of carbon-carbon, carbon- nitrogen and carbon-oxygen bonds in benzenoid

0166-1280/98/$19.00 0 1998 Elsevier Science B.V. All rights reserved PII SOl66-l280(97)00176-0

26 R. Kirdj et al./Journal of Molecular Structure (Theochem) 427 (1998) 25-37

benzene pyrldme napbthalcne isoqumoline anlhracene acrldlne

k ’ g X=N. Y=C phenvlthndine XZC. Y=N 7.8.dibezoqumoline

chrysene

pyrene

3.4.benzopyrene pcrylenc I .2.54-dibenzanlhracene I .2LWd~benzacr~dme

I .I*-benzbisanthrene lctrabenzohcptaccne

hexabenzo(h-. ef, hl. fl. no. yr)coroncnc

benzdl. 2. 3.hc4. 5. 6.h’c’)dicoronene

Scheme 1. Structural formulae with bond numbering of benzenoid hydrocarbons and azabenzenoids

R. Kiralj et al./Journal of Molecular Structure (Theochem) 427 (1998) 25-37 21

hydrocarbons, azabenzenoids and picrate-like systems

are reported. Our interest in revising the bond length-bond order

relationships was motivated by our work on the struc-

ture determination of a variety of benzenoid hydrocarbons and related systems [15]. The possibility of forming K.. . T interactions between various aromatic systems has led to use some of these compounds as DNA intercalators. Quite a number of these aromatic

compounds such as proflavine, elipticin, 3,5,6,8-tetra- methyl-N-methyl-fenantrolinium cation are efficient

as DNA intercalators. For this type of molecules antiviral, antitumor and antibiotic properties were

recognized [ 16,171; among them daunomycin, actino-

mycin and others are in a wide use [ 181. Knowledge of the chemical bond character in these systems is of great importance for understanding the nature of ?r-interactions with DNA.

Bond orders, calculated by the variants of VB (Pauling r-bond orders, Pauling bond numbers) and

MO methods (Hi.ickel MO and SCF MO a-bond orders), were used to compare applicability of the VB and MO models for predicting the bond lengths in benzenoid hydrocarbons and related systems. The experimental bond lengths were taken from crystal

structures (Cambridge Structural Database, the April release 1996 [ 141 including our own recent data [ 151) and they were used to establish novel bond length- bond order relationships.

Regression equation coefficients and correlation coefficients depend on the selection criteria of the set: quality of the crystallographic data (R factor limit, a presence of disorder and geometry deviations due to various errors), and geometrical and hybridi- zation characteristics (planarity and substitution of

hydrocarbon molecules, their participation in the metal or r-complexes or the organometallic com-

pounds). The Pauling set of benzenoid hydrocarbons derived from 1980 [l] is smaller than those of Hemdon [2], and Hemdon and Pirkinyi [3]. At present, more accurate experimental data are available and larger sets can be used in the analysis. Our set of benzenoid hydrocarbons [ 151 was extracted from the crystallographic structures [14] with R 5 0.07 (excluding disordered structures and highly distorted molecules). The planar, unsubstituted and uncharged molecules in their crystal structures, molecular complexes and clathrates and solvates were

selected. In this paper the set is extended by two

new crystal structures of benzenoid hydrocarbons [4]. The Pauling set [ 11, our set [ 151 and the extended set of benzenoid hydrocarbons (Scheme 1) are analy- sed in terms of Pauling, Coulson (Hiickel MO) and SCF MO x-bond orders.

This work on improving carbon-carbon bond length-bond order relationships in benzenoid hydrocarbons is also extended to the carbon-carbon and the carbon-oxygen bonds in picrate-like systems

[ 151, and to the carbon-carbon and carbon-nitrogen bonds in the planar azabenzenoids (Scheme 1) [15].

2. Methods

The MINP 2.0 program [ 191 was used to create the input files for molecular mechanics MM3(92)

[20]: the experimental bond lengths were used for the planar molecules. The SCF n-bond orders were calculated by the VESCF procedure [21] for the conjugated systems (incorporated in MM3(92) [20]). The experimental data were not available for 1,2,8,9_dibenzanthracene. Therefore, the values of the bond lengths were obtained from the Pauling

theoretical curve relating bond lengths and bond

orders (Eq. (4)). Pauling, Coulson, SCF MO and VESCF r-bond

orders, and Pauling bond numbers were correlated with experimental bond lengths using statistical package Stat WorksrM for Macintosh [22]. Two types of unweighted correlations were performed:

(i) linear regression:

d=a+bp (1)

(ii) second-order polynomial regression:

d=a+bp+cp2 (2)

where d is the experimental bond length in A, p is the Pauling r-bond order (or in some cases the Pauling bond number), and a, b and c are regression coefficients. The experimental bond lengths are correlated with those calculated by the regression Eq. (1) and (2):

dexp = a + P&t, (3)

where CY and /3 are regression coefficients. The theoretical curve for carbon-carbon bonds

is the Pauling curve [l] based on the harmonic

28 R. Kiralj et al/Journal of Molecular Structure (Theochem) 427 (I 998) 25-3 7

Table 1

Pauling bond numbers ’ n and VESCF s-bond orders ~ysscr, experimental ’ and calculated b bond lengths (in A) for the Pauling set of

benzenoid hydrocarbons

Molecule Bond n PVESCF d w d “B dMo

Benzene

Naphthalene

Anthracene

Pyrene

Perylene

1,14-Benzbisanthrene

a

a

b

C

d

a

b

:

e

t

f

e

f

h”

i

;

C

d

e

f

t

:

e

f

g a

b

C

d

f

g h

i

j k I

m

n

0

P

9 r

S

1 SO0 0.666 1.397 1.394 1.400

1.333 0.518 1.401 1.423

1.667 0.794 1.372 1.370

1.333 0.494 1.423 1.423

1.333 0.616 1.412 1.423

1 so0 0.633 1.396 1.394 1.408

1.250 0.543 1.434 1.439 1.427

1.250 0.42 I 1.431 1.439 1.436

1.750 0.841 1.364 1.360 1.374

1.250 0.448 1.417 1.439 1.428

1.800 0.868 1.357 1.354 1.378

1.200 0.389 1.448 1.450 1.426

1.400 0.636 1.414 1.410 1.419

1.400 0.559 1.434 1.410 1.413

1.600 0.744 1.384 1.379 1.390

1.400 0.580 1.395 1.410 1.405

1.600 0.744 1.395 1.379 1.391

1.400 0.564 1.408 1.410 1.411

1.200 0.367 1.459 1.450 1.434

1.883 0.881 1.346 1.351 1.361

1.167 0.366 1.440 1.458 1.445

1.333 0.576 I .423 1.423 1.415

1.500 0.633 1.403 1.394 1.401

1.500 0.668 1.390 1.394 1.394

1.333 0.430 1.424 1.458 1.445

1.322 0.612 1.421 1.424 1.417

1.339 0.498 1.398 1.421 1.427

1.610 0.782 1.369 1.378 1.383

1.390 0.538 1.415 1.412 1.418

1.558 0.753 1.394 1.385 1.391

1.322 0.487 1.428 1.424 1.429

1.120 0.270 1.471 1.470 1.461

1.533 0.705 1.400 1.389

1.467 0.603 1.390 1.399

1.400 0.603 1.420 1.410

1.133 0.354 1.460 1.467

1.867 0.889 1.350 1.347

1.133 0.344 1.470 1.467

1.233 0.483 1.440 1.443

1.633 0.731 1.370 1.375

1.367 0.522 1.400 1.416

1.300 0.592 1.420 1.429

1.333 0.494 1.430 1.423

1.667 0.783 1.370 1.370

1.333 0.536 1.430 1.423

1.667 0.75 1 1.360 1.370

1.300 0.483 1.430 1.429

I.033 0.282 1.490 1.494

1.400 0.507 1.400 1.410

1.133 0.379 1.470 1.467

1.467 0.658 1.410 1.399

R. Kiralj et al./Journal of Molecular Structure (Theochem) 427 (I 998) 25-3 7 29

Table 1 (contwrued)

Molecule Bond n PWXF d exp dve d MO

t 1.300 0.42 1 1.430 1.429

u 1.300 0.553 1.440 I.429 Tetrabenzoheptacene a 1.809 0.871 1.340 1.353 1.360

b 1.191 0.383 1.440 1.453 1.400

c 1.182 0.617 1.410 1.414 I.400

d 1.427 0.583 1.420 1.406 I.390

e 1.573 0.716 1.360 1.383 1.380

f 1.427 0.616 1.400 1.406 1.380 g 1.573 0.690 1.390 1.383 1.390

h 1.382 0.560 1.420 1.414 1.400

i 1.236 0.389 1.430 1.442 1.400

] 1.045 0.280 1.480 1.490 1.420

k I .227 0.427 I.460 I.444 1.410

1 1.727 0.798 1.360 1.363 1.380

m 1.273 0.447 1.420 1.443 1.400

n 1.227 0.527 1.420 1.444 1.410

0 1.500 0.628 1.380 1.394 1.390

a 1.322 0.61 1 1.420 1.424 1.425 b I.339 0.498 1.420 1.42 I 1.422

C 1.610 0.782 1.369 1.378 1.377

d 1.390 0.539 1.402 1.412 1.402

% 1.558 1.322 0.487 0.75 1 1.385 1.433 1.385 1.424 1.395 1.43 1

g 1.120 0.275 1.468 1.470 1.469 h 1.322 0.493 1.433 1.424 1.43 1

I 1.558 0.737 1.385 1.385 1.398 ] 1.390 0.564 1.383 1.412 1.394

k 1.558 0.736 1.391 1.385 1.397

I 1.120 0.279 1.462 1.470 1.468

m 1.322 0.493 1.432 1.424 1.43 1

n 1.322 0.604 I.432 1.424 1.43 1

a Pauling bond numbers and experimental bond lengths are taken from Refs. [ 1,25,26].

’ The calculated bond lengths for VB theory are derived from the Pauling equation (4). and for MO theory are taken from Refs. [I .lO].

Quaterrylene

potential: 3. Results and discussion

A=&-(d, -dd)(kdlksPP)lC(kdlks)PP+ 11 (4)

where pP is the Pauling r-bond order, d, and dd are single and double carbon-carbon bond lengths,

respectively, k, and kd are corresponding force constants. Eq. (4) is also used for Pauling bond numbers n [23] which are related to the Pauling bond orders by n = pp + 1. The analogous curve for carbon-nitrogen bonds is established using the following data for bond lengths d, = 1.469 A and dd = 1.279 A [24], and for the force constants k, = 5.3 x 1O-8 N A-’ and kd = 10.0 x lo-’ N A-’ (parameters defined in MM3(92) [20]).

VB resonance-theoretical and VESCF r-bond

orders, and experimental and calculated bond lengths for the Pauling set of benzenoid hydrocarbons [ 1,25,26] are listed in Table 1.

Our sets of benzenoid hydrocarbons, azabenzenoids and picrate-like systems, previously described in terms of linear bond length-Pauling and Coulson x-bond order relationships [ 151, are now presented (excluding picrate- like systems which are only discussed here) in terms of SCF MO [27] and VESCF r-bond orders (Table 2).

The extended set of benzenoid hydrocarbons includes data for hexabenzo[bc,eLhi,kl,no,qr]coronene

30

Table 2

R. Kiralj et al./Journal of Molecular Structure (Theochem) 427 (I 998) 25-3 7

Experimental bond lengths a d (in A), and SCF MO b psCF and VESCF p”~s,-~ r-bond orders of benzenoid hydrocarbons and azabenzenoids

MOleCUle Bond d P SCF PVESCF c MOkCUlC Bond d PSCP PVESCF c PVESCF d

Benzenoid hydrocarbons

Benzene

Naphthalene

Anthracene

Tetracene

Triphenylene

Pyrene

Perylene

a a

b

d

a

b

d

c d

g h

a

b

d

g a b

d

b

d

e

g h

k

a

b

d

e

a

b

d

e

g

1.390(9)

I .407(2)

1.371(2)

I .422(2)

I .420(2)

I .395(3)

I .432(3)

I .428(3)

1.353(4)

1.418(5)

1.338(5)

I .422(7)

1.413(7)

1.414(4)

1.349(S)

1.381(9)

I .376(4)

l.391(7)

I .454(6)

I .442(2)

1.405(2)

1.388(2)

l&l(2)

1.434(2)

1.349(2)

1.415(2)

I .469(g)

I.41 l(9)

I .405(9)

1.385(10)

1.390(11)

1.402(2)

I .437(2)

I .33 l(2)

1.417(2)

1.417(2)

1.415(2)

1.361(2)

1.392(2)

1.370(2)

I .409(2)

I .453(2)

I .347(4)

I .429(4)

1.417(3)

I .400(4)

I .380(5)

I .423(3) I .426(2)

1.411(2)

I .359(3)

I .393(2)

I .384(2)

I .429(2)

1.471(2)

0.667

0.513

0.799

0.486

0.627

0.632

0.55 I 0.414

0.844

0.447

0.870

0.387

0.642

0.552

0.750

0.575

0.749

0.556

0.368

0.539

0.539

0.708

0.492

0.377

0.865

0.413

0.318

0.367

0.599

0.713

0.616

0.702

0.437

0.842

0.426

0.639

0.525

0.77 I

0.550

0.769

0.529

0.410

0.885

0.360

0.578

0.633

0.669

0.42 I

0.623

0.490

0.790

0.530

0.757

0.480

0.278

0.666

0.518

0.794

0.494

0.616

0.633

0.543

0.42 I

0.84 I

0.448

0.868.

0.389

0.636

0.559

0.744

0.580

0.744

0.654

0.367

0.541

0.532

0.724

0.467

0.369

0.875

0.387

0.317

0.639

0.596

0.717

0.61 I

0.678

0.445

0.831

0.438

0.601

0.553

0.748

0.571

0.747

0.558

0.418

0.881

0.366

0.576

0.633

0.668

0.430 0.612

0.498

0.782

0.538

0.753

0.487

0.270

COrO”C”e

Quaterrylene

Pyridine

Isoquinoline

Acridine

Phenanthridine

a

b

C

d

a

b

c

d

e

f

8 h

i

j k

I

m

”

a

b

C

a

b

C

d

e

f

8 h

I j k

a

h

C

d

e

f

8 h

a

b

C

d

;

8 h

i

j k

I

m

”

0

1.424 0.455

I.420 0.655

1.414 0.462

1.372 0.821

I .420(4)

1.417(4)

I .367(4)

1.401(4)

I .382(4)

1.431(4)

1.468(4)

I .43 l(4)

I .383(4)

I .383(4)

I .389(4)

I .462(4)

I .429(4)

I .43 I(4)

azabenzenoids

1.336(3)

1.381(3)

I .377(3)

1.388

1.324

I.410

I.410

1.416

1.359

I.411

1.364

I.418

I .42 I

I.343

I.350

I.429

1.425

1.364

I .399

1.345

1.436

I.385

I .296(3)

I .432(3)

1.415(3)

I .406(3)

1.381(3)

I .403(3)

1.374(3)

I .408(3)

I .447(3)

I.41 l(3)

I .377(3)

1.401(3)

I .373(3)

1.406(3)

1.418(3)

0.667 0.666

0.667 0.666

0.486 0.494

0.627 0.616

0.486 0.494

0.799 0.794

0.513 0.518

0.799 0.794

0.486 0.494

0.486 0.494

0.799 0.794

0.55 1 0.543

0.414 0.42 I

0.844 0.841

0.447 0.448

0.844 0.841

0.414 0.42 I

0.632 0.633

0.387

0.642

0.552

0.750

0.575

0.749

0.556

0.368

0.556

0.749

0.575

0.750

0.552

0.642

0.389

0.636

0.559

0.744

0.580

0.744

0.564

0.367

0.564

0.744

0.580

0.744

0.559

0.636 0.636

0.441

0.647

0.467

0.816

0.61 I

0.498

0.782

0.539

0.75 I

0.487

0.275

0.493

0.737

0.564

0.736

0.279

0.493

0.604

0.663

0.66 I

0.669

0.504

0.797

0.476

0.621

0.502

0.788

0.526

0.788

0.502

0.483

0.799

0.63 I

0.537

0.417

0.842

0.446

0.842

0.419

0.637

0.856

0.391

0.642

0.548

0.754

0.568

0.754

0.55 I

0.377

0.554

0.752

0.570

0.752

0.549

R. Kiralj et al./Journal of Molecular Structure (Theochem) 427 (I 998) 25-37 31

Table 2 (continued)

MOl~Cld~ Bond d P SCF PVESCF c MOlCCUlC Bond d PSCP PVESCF c PVESCF d

1,2.5.6-Dibenzanthracene a

b

k

m

d

e

B

h

m

3,4-Benzopyrene

d

e

f

m

0

P

q

w

1.391(2)

1.426(2)

1.438(2)

1.338(2)

1.436(2)

1.413(2)

1.412(2)

1.360(2)

1.403(2)

1.373(2)

1.406(2)

1.455(2)

1.397(2)

1.429(7)

1.388(9)

1.412(9)

1.367(X)

1.410(10)

1.414(9)

1.414(g)

1.367(9)

1.366(10)

1.409(9)

1.394(10)

1.469(8)

1.430(10)

1.406(S)

1.378(13)

1.401(12)

1.414(12)

1.434(12)

1.342(13)

1.447(12)

1.444(11)

1.361(12)

1.419(12)

1.410(11)

1.425(12)

1.374(14)

1.397(14)

1.364(13)

1.419(12)

1.435(12)

1.395(11)

1.423(11)

1.352(12)

1.441(12)

1.418(11)

1.412(12)

1.376(14)

1.419(11)

0.638

0.577

0.362

0.883

0.365

0.641

0.569

0.737

0.590

0.735

0.572

0.346

0.643

0.617

0.684

0.543

0.326

0.904

0.321

0.457

0.762

0.488

0.622

0.493

0.792

0.523

0.789

0.502

0.456

0.672

0.420

0.853

0.407

0.603

0.578

0.718

0.434

0.639 P 1.397(3)

0.572 7,8-Dibenzoquinoline a 1.388(10) 0.870

0.367 b 1.375(10) 0.387

0.879 C 1.419(10) 0.642

0.369 d 1.441(10) 0.552

0.636 e 1.341(10) 0.750

0.573 f 1.391(10) 0.575

0.733 g 1.329(10)

0.592 h 1.383(10)

0.732 I 1.431(10) 0.368

0.578 j 1.350(10) 0.556

0.345 k 1.439(10) 0.749

0.646 I 1.389(20) 0.575

0.462 In 1.330(10) 0.750

0.679 ” 1.409(10) 0.552

0.418 0 1.419(10) 0.642

0.852 P 1.420(10) 0.387

0.412 I-Azatriphenylene a 1.464(2) 0.318

0.636 b 1.404(2) 0.637

0.541 C 1.376(2)

0.759 d 1.342(2)

0.562 e 1.3X7(2) 0.616

0.758 f 1.36X(2) 0.713

0.545 g 1.395(2) 0.559

0.392 h 1.459(2) 0.318

0.487 I 1.407(2) 0.599

0.805 j 1.372(2) 0.713

0.613 k 1.387(2) 0.616

0.686 I 1.377(2) 0.713

0.540 m 1.397(2) 0.599

0.329 ” 1.408(2) 0.637

0.901 0 1.462(2) 0.318

0.325 P 1.405(2) 0.637

0.453 4 1.399(2) 0.599

0.762 r 1.373(2) 0.713

0.489 s 1.391(2) 0.616

0.616 t 1.362(2) 0.713

0.500 ” 1.397(2) 0.599

0.787 1,2,8.9-Dibenzacridine a 1.350(6)

0.526 b 1.419(U) 0.577

0.785 C 1.455(6) 0.346

0.509 d l.427(7) 0.641

0.455 e 1.411(13) 0.572

0.671 f 1.399(10) 0.735

0.424 !z 1.408(9) 0.590

0.850 h 1.377(11) 0.737

0.413 I 1.434(9) 0.569

0.602 j 1.419(11) 0.365

0.576 k 1.367(9) 0.883

0.719 I 1.463(9) 0.361

0.441 m 1.388(8) 0.640

0.868

0.389

0.636

0.559

0.744

0.580

0.367

0.564

0.744

0.580

0.744

0.559

0.636

0.389

0.317

0.639

0.611

0.717

0.596

0.317

0.596

0.717

0.611

0.717

0.596

0.639

0.317

0.639

0.596

0.717

0.611

0.717

0.596

0.571

0.347

0.634

0.579

0.732

0.593

0.732

0.574

0.371

0.878

0.368

0.640

0.397

0.863

0.397

0.642

0.543

0.737

0.552

0.757

0.541

0.374

0.554

0.752

0.569

0.753

0.550

0.639

0.396

0.322

0.656

0.564

0.739

0.574

0.745

0.571

0.322

0.590

0.722

0.604

0.722

0.591

0.642

0.322

0.644

0.588

0.724

0.602

0.725

0.588

0.641

0.567

0.342

0.639

0.576

0.735

0.589

0.736

0.571

0.366

0.881

0.364

0.643

a Estimated standard deviations and notation of bond lengths were taken from Ref. [ 151. ’ SCF MO x-bond orders are taken from Ref. [27].

’ VESCF T-bond orders for carbonpcarbon bonds are calculated for benzenoid hydrocarbons and also used for analogous carbon-carbon

bonds in azabenzenoids.

d VESCF r-bond orders for carbon-carbon bonds are calculated for azabenzenoids.

32 R. Kiralj et al./Journal of Molecular Structure (Theochem) 427 (1998) 25-37

Table 3

Experimental bond lengths d (in A), and Pauling pp, Coulson pc, SCF MO ’ psCF and VESCF pVEsCF r-bond orders of hexa-

benzo[bc, ef, hi, kl, no, qr]coronene and benzo[ 1,2,3-bc:4,5,6-b’c’ldicoronene

Molecule Bond d PP PC

Hexabenzo[bc, ef, hi, kl, no, qrlcoronene a 1.417(2) 0.400 0.542

b 1.446(2) 0.200 0.488

: 1.417(2) 1.458(2) 0.400 0.100 0.547 0.413

; 1.398(2) 1.376(2) 0.500 0.500 0.613 0.667

Benzo[ 1,2,3-bc:4,5,6-b’c’ldicoronene

6

1.417(2) 0.300 0.538

1.364(2) 0.700 0.743

: I .422(2) 1.415(2) 0.300 0.400 0.540 0.535

; 1.419(2) 1.365(2) 0.300 0.700 0.535 0.478

g 1.424(2) 0.300 0.530

h 1.412(2) 0.400 0.529

i 1.413(2) 0.300 0.561

j 1.379(2) 0.700 0.664

k 1.432(2) 0.300 0.512

1 1.478(2) 0.000 0.411

m 1.420(2) 0.400 0.547

n 1.42 l(2) 0.300 0.519

0 1.429(2) 0.300 0.526

P 1.422(2) 0.300 0.521

4 1.422(2) 0.400 0.538

a Experimental bond lengths, Pauling, Coulson and SCF MO s-bond orders were taken from Ref. [4].

PSCF PVESCF

0.583 0.592

0.395 0.371

0.589 0.329 0.597 0.313

0.636 0.667 0.639 0.667

0.485 0.468

0.800 0.815

0.488 0.617 0.469 0.649

0.479 0.806 0.460 0.822

0.474 0.456

0.611 0.643

0.507 0.488

0.775 0.776

0.476 0.460

0.287 0.269

0.619 0.645

0.481 0.465

0.479 0.457

0.482 0.463

0.615 0.645

and benzo[ 1,2,3-bc:4,5,6-b’c’ldicoronene [4] and VESCF r-bond orders for these molecules (Table 3).

The second-order polynomial regression is per-

formed for the Pauling bond numbers and r-bond orders. The regression coefficients and regression

parameters are given in Table 4. The parameters for correlation between the experi-

mental and calculated bond lengths obtained using Eq. (4) are given in Table 5.

3.1. The Pauling set of benzenoid hydrocarbons

The bond length-Pauling bond number dependence (Table 1) is defined by the Pauling theoretical curve (Eq. (4)), linear regression straight line, and second-order polynomial regression curve. Both regression curves approximate the Pauling curve (Eq. (4)) reasonably well (with the largest deviation 0.026 A for n = 1.0). The linear regression equation in terms of Pauling a-bond orders (d/A = 1.478

- 0.166 pr) is comparable with those of Hemdon [2], Hemdon and Parkinyi [3], Goddard et al. [4],

with large differences of the b coefficients (within the limits of three standard deviations 3~).

The linear correlation between the experimental bond lengths and VESCF n-bond orders (Table 1) is in agreement to those of Goddard et al. [4] and Dewar and Gleicher [6] and (within the 30 limits).

In general, bond lengths in benzenoid hydrocarbons are well reproduced [l] by VB and MO methods. A comparison of the experimental bond lengths with those computed by these two methods reveals certain differences between them. The VB method (Eq. (4)) seems to be slightly more appropriate than MO [ 1, lo] by producing a better linear fit of data, and the regression and correlation coefficients are closer to the ideal values (VB: CY = 0.082, /3 = 0.940, r = 0.944; MO: (Y = -0.140, fi = 1.101, r = 0.838). But the weak point of VB is the clustering of experimental bond lengths

Tab

le

4

Reg

ress

ion

anal

yses

re

sults

of

bon

d le

ngth

-bon

d or

der

rela

tions

hips

fo

r ca

rbon

-car

bon,

ca

rbon

-nitr

ogen

an

d ca

rbon

-oxy

gen

bond

s in

ben

zeno

id

hydr

ocar

bons

, az

aben

zeno

ids

and

picr

ate-

like

syst

ems

Dat

a se

t C

lass

of

mol

ecul

es

Bon

d R

egre

ssm

co

effi

cien

ts

Qua

lity

para

met

ers

Paul

ing

set

Ben

z.

hydr

ocar

bons

c-

c R

ef.

[I]

Our

set

Ref

. [I

S]

Ben

z.

hydr

ocar

bons

c-

c

Aza

benz

enoi

ds

c-c

C-N

Ext

ende

d

set

h

Picr

ate-

like

syst

ems

c-c

c-o

Ben

z. h

ydro

carb

ons

C-C

n 82

I .

644(

g)

- 0.

I66

(7)

n 82

I .

8 I8

(54)

0.

41 l

(76)

PV

CS

CP

82

I .

522(

6)

- 0.

192(

10)

PP*

124

I .464

(3)

- 0.

143(

6)

PP

12

4 I .

467(

5)

0.15

7(25

)

PC*

I IO

1.

591(

7)

- 0.

315(

12)

PS

CF

96

1.

510(

S)

0. I

80(9

)

PV

ES

CF

12

4 I.

508(

5)

- 0.

176(

9)

PP

* 77

I .

462(

6)

- 0.

143(

13)

PP

77

I .

478(

12)

-

0.22

6(54

)

PC

* 77

1.

571(

14)

- 0.

283(

23)

P S

CP

77

I .

497(

IO

) 0.

161(

16)

PV

ExF

r 77

I .

499(

IO

) -

0.16

4(16

)

PVES

CF

77

I .49

7( 1

0)

0.16

1(16

)

PP

* II

I .

444(

IO

) -

0.18

4(18

)

PP

II

1.

432(

22)

- 0.

132(

91)

PY

ES

CP

II

I .49

3( 1

3)

- 0.

219(

19)

PP

* 27

1.

497(

11)

- 0.

2 12

(25)

PP

27

1.

501(

14)

0.24

7(79

)

PP

' IO

I .

326(

5)

-0.1

98(1

8)

PP

14

7 I .

464(

4)

- 0.

132(

8)

PP

14

7 I .

456(

l)

0.08

9(32

)

PC

133

1.50

1(7)

-

0. I

72(

12)

PSU

II9

1.51

2(5)

-

0.18

2(8)

PVES

CF

147

1.50

8(S

) 0.

175(

8)

0.94

3

0.08

5(26

) 0.

950

0.91

5

0.89

8

0.01

5(27

) 0.

898

0.92

8

0.90

4

0.88

0

0.78

3

0.09

5(60

) 0.

791

0.82

0

0.75

9

0.76

4

0.75

8

0.95

9

0.05

3(89

) 0.

961

0.96

6

0.86

2

0.05

2( I

1 I )

0.

863

0.96

8

0.80

6

- 0.

048(

34)

0.80

8

0.78

0

0.90

8

0.88

3

0.00

9

0.00

8

0.01

I

0.01

0

0.01

0

0.00

8

0.01

I

0.01

4

0.01

3

0.01

2

0.01

I

0.01

7

0.01

6

0.01

5

0.00

6

0.00

7

0.00

7

0.01

5

0.01

5

0.00

7

0.01

3

0.01

3

0.01

6

0.01

0

0.01

I

0.00

6

0.00

6

0.00

6

0.00

6

0.00

6

0.00

6

0.00

6

0.00

6

0.00

6

0.00

6

0.00

6

0.00

5

0.00

5

0.00

5

0.00

7

0.00

7

0.00

8

0.00

5

0.00

5

0.00

5

0.00

5

0.00

5

- -

- 0.

01 I

0.

003

0.99

8 64

7

0.01

0 0.

00 I

0.

999

367

0.01

3 -

0.00

1 1.

001

410

0.01

4 -

0.00

2 I.

001

508

0.01

4 0.

003

0.99

8 25

3

0.01

1 -

0.00

1 I .

ooo

668

0.01

3 -

0.00

3 I.

002

420

0.01

5 -

0.00

1 I.

000

417

0.01

9 1o

m5

1.00

0 II

9

0.01

8 -

0.00

4 I .

003

62

0.01

7 0.

0003

1.

000

I54

0.02

0 0.

003

0.99

7 10

2

0.01

9 -

0.00

07

I .oo

o I0

5

0.02

0 0.

002

I.00

1 IO

1

0.00

9 -

0.00

2 1.

002

104

0.01

0 0.

006

0.99

6 48

0.00

8 0.

0002

I.

000

I28

0.02

I

0.00

1 1.

000

74

0.02

I

0.00

I

0.99

9 35

0.01

I

0.00

1 0.

999

II8

0.01

8 0.

002

0.99

9 26

8

0.01

8 0.

0002

1.

000

136

0.01

9 0.

001

1.00

0 20

4

0.01

3 -

0.00

4 I.

003

549

0.01

4 0.

0002

I.

000

511

’ Pa

ulin

g pp

, C

ouls

on

pi,

SCF

MO

psc

r an

d V

ESC

F pV

EsC

F r-

bond

or

ders

.

h R

egre

ssio

n co

effi

cien

ts

a, b

and

c

are

coef

fici

ents

of

reg

ress

ion

equa

tions

d

= a

+ b

p or

d =

a +

bp

+ c

p’;

d i

s a

bond

le

ngth

in

2

,p

is a

bon

d nu

mbe

r or

r-

bond

or

der,

r is

a

corr

elat

ion

coef

fici

ent.

’ A

vera

ge

abso

lute

de

viat

ion

6 (i

n A

) of

cal

cula

ted

from

ex

peri

men

tal

bond

le

ngth

s,

d A

vera

ge

estim

ated

st

anda

rd

devi

atio

n o

of e

xper

imen

tal

bond

le

ngth

s (i

n A

).

’ St

anda

rd

erro

r of

est

imat

e s

(in

A)

and

F r

atio

.

’ Reg

ress

ion

para

met

ers

of t

he e

quat

ion

dex

p =

a +

@d

,,,,.

g V

ESC

F T

-bon

d or

ders

fo

r be

nzen

oid

hydr

ocar

bons

(s

et

from

R

ef.

[ 151

) an

d fo

r I ,2

,8,9

_dib

enza

nthr

acen

e ar

e ta

ken

for

CC

bo

nds

in a

zabe

nzen

oids

.

h O

ur

set

(Ref

. [1

5])

is e

xten

ded

by l

itera

ture

da

ta

for

hexa

benz

o[hc

, ef

,f‘,

hi,k

l,no.

qrl

coro

nene

an

d be

nzo[

1,2,

3-bc

:4,5

$b’c

’]di

coro

nene

(R

ef.

[4])

an

dpv,

,,,

r-bo

nd

orde

rs

for

thes

e m

olec

ules

.

* Pr

evio

usly

pu

blis

hed

(Ref

. [ 1

51).

34 R. Kiraij et al./Journal of Molecular Structure (Theochem) 427 (1998) 25-37

Table 5

The comparison between the experimental and calculated bond lengths a (in A)

Data set Class of Bond Quality parameters

molecules

type order 6b UC (Y d bd

Pauling set, Ref. [I] Benz. hydrocarbons c-c n 0.008 0.056 0.959

Our set, Ref. [ 151 Benz. hydrocarbons c-c PP 0.012 0.006 0.246 0.821

Azabenzenoids CC PP 0.014 0.006 0.227 0.833

C-N PP 0.009 0.005 - 0.018 1.017

Picrate-like systems c-c PP 0.016 0.007 - 0.008 1.055 Extended set ’ Benz. hydrocarbons c-c PP 0.015 0.005 0.358 0.745

a Pauling r-bond orderspr and bond numbers n in equations: d= 1.504- [0.313(n- 1)]/[0.84n+0.16] and d= 1.504-[0.313p]/[O.84p+ l]

for C-C bonds and d = 1.469 - [0.358p]/[O.887p + l] for C-N bonds; d is a bond length in A.

b Average absolute deviation 6 (in A) between the calculated and experimental bond lengths.

’ Average estimated standard deviation e of experimental bond lengths (in A).

d Regression parameters of the equation dexp = cy + fld,,,,. ’ Our set (Ref. [15]) is extended with hexabenzo[bc, ef, hi,kl, no,qr]coronene and benzo[1,2,3-bc:4,5,6-b’c’ldicoronene (Ref. [4]).

depending on the Pauling r-bond orders: there are more than four bond lengths (a = + 0.001 A) with

the same bond number, which is graphically observed as columns of points (Fig. 1 (a), Table 1: five entries for n = 1.500; six entries for n = 1.400; seven entries for n = 1.322 and 1.333). The simple Pauling resonance theory (in which the unexcited KekulC structures with unit weights are used and the excited Dewar-type structures excluded) cannot distinguish

aromatic bonds with similar but not identical chemi-

cal environments, and clustering cannot be avoided [2,3,23,28]. Pauling performed VB refinement of the

bond numbers for perylene and quatenylene [l] by including the first-excited Kekule structures which differentiated a-bond orders of particular bonds. However, the clustering effect is not observed in the case of VESCF n-bond orders.

3.2. Our set of benzenoid hydrocarbons

This set [ 151, although larger than the Pauling set,

shows almost identical curves of linear and second- order polynomial regressions (Table 4: the largest deviation ( > 3~) from the Pauling curve is 0.040 A at pp = 0.0). The linear regression equation is in better agreement with equations from the literature [2-41 than one of the Pauling set. However, the regression curves (Table 4) are in better agreement with the experimental bond lengths than the Pauling theoretical curve (Eq. (4)) (Table 5). Our set also exhibits the clustering of experimental data (Fig. l(b): six

entries for pp = 0.200, 0.250, 0.400, 0.444; seven entries for pp = 0.500, ten entries for pp = 0.667, 27 entries for pp = 0.333).

The regression analysis with Coulson r-bond orders [ 151 exhibits linear fit (Table 4) and agrees with analogous Herndon and Pirkinyi equation [3] (within 3~). However, these results cannot be compared with those obtained by Goddard et al. [4] and

Coulson and Golebiewski [5]. Linear regression equations using SCF MO [27]

and VESCF r-bond orders (Table 2) are almost identical (Table 4) and in agreement with the equations reported in the literature [4,6]. Therefore, it

appears that the molecular mechanics MM3(92) pro- gramme [20] can be used for computing of r-bond orders of the SCF quality.

3.3. The set of azabenzenoids

3.3. I. Carbon-carbon bonds The linear and second-order polynomial regres-

sions (Table 4) deviate from the Pauling curve (Eq. (4)) (maximum deviation 0.042 A for pp = 0.0). The ldexp - d,,,,I differences for VB approaches

are in the same range (Tables 4 and 5). The linear equation is comparable to those in the literature [2-41. It is also in accord with our previously derived equations for the set of benzenoid hydrocarbons [15]. The azabenzenoid set (Table 2, Fig. l(c)) shows very pronounced clustering of the experimental data (five entries for pp = 0.200 and 0.556;

R. Kiralj et al./Journal qf Molecular Structure (Theochem) 427 (1498) 25-37

I

. .

. I

q l I .

q q .I II

q I . -a’ .

. I

. . .

I. .

0. q .’ I

q .

o :J,oP . .

q 07 ,- q 0.

.

N

.

I.

. .

I l

I. -

I q

n --

. , .:: I.

da% n

-a

35

36 R. Kiralj et al./Journai of Molecular Structure (Theochem) 427 (1998) 25-37

seven entries for pp = 0.600; 11 entries for pp = 0.444; 15 entries for pp = 0.400).

A related regression based on Coulson n-bond

orders [ 151 is also linear (Table 4) and shows the same characteristics as observed for benzenoid hydro-

carbons (preceding paragraph). The regression analyses based on three types

of SCF a-bond orders (SCF MO and VESCF bond orders for the analogous hydrocarbons, and VESCF bond orders for the azabenzenoids) are

almost identical (Table 4) and in agreement with equations reported in the literature [4,6] (within 3~).

3.3.2. Carbon-nitrogen bonds

Linear and second-order polynomial regression curves reproduce the theoretical curve (Eq. (4)) reasonably well (Table 4) (maximum deviation within 3~: 0.037 A for pp = 0.0). Both regression equations

and the theoretical curve are in agreement with the experimental values. No clustering effect is detected (Tables 4 and 5).

The linear correlation based on VESCF r-bond orders (Table 4) differs from that one of Dewar and Gleicher [6].

3.4. The set of picrate-like systems

3.4. I. Carbon-carbon bonds

Linear and second-order polynomial regression curves reproduce the theoretical curve (Eq. (4)) reasonably well (maximum deviation at pp = 1.0 is 0.049 A) (Table 4). Quality parameters in Table 4 indicate that these two types of regressions are equally applicable. The clustering effect is observed for 10 entries for pp = 0.500.

3.4.2. Carbon-oxygen bonds

The small set of data (ten bonds, [15]) exhibits linearity in the 0.0-0.5 range ofpp orders (Table 4) and the clustering effect (five bond lengths with pp = 0.0).

3.5. The extended set of benzenoid hydrocarbons

Our set of benzenoid hydrocarbons [ 151 enlarged by two molecules [4] contains the largest number of data (147 bonds). The clustering effect is highly pronounced (Fig. l(d)) (six entries for pp = 0.250,

0.444; seven entries for pp = 0.200; nine entries

for pp = 0.300, 0.500; ten entries for pp = 0.400, 0.667; 27 entries for pp = 0.333). Linear and secon-

d-order polynomial regressions (Table 4) agree well

with the Pauling curve (Eq. (4)) (with maximum 0.048

A at pp = 0.0). The linear equation is in agreement with the literature reports [2-41 (within 3~).

The linear regression analysis based on the Coulson r-bond orders (Table 4) differs from those of Goddard et al. [4] and Coulson and Golebiewski [5]. However, it is similar to that

of Herndon and PgrkHnyi [3] (within 3~). The results from regression analyses including SCF

MO and VESCF r-bond orders (Table 4) are in accord with those based on the literature equations [4,6] (within 3~).

4. Conclusions

The present analysis of bond length-bond order relationships using valence bond and molecular orbital methods includes larger experimental data sets and more chemically distinctive bonds than previous reports [l-4]. The obtained results can be

summarized as follows.

Carbon-carbon, carbon-nitrogen and carbon-

oxygen bond lengths in benzenoid hydrocarbons, azabenzenoids and the picrate-like systems are described fairly well by the VB approach.

The novel linear bond length-bond order relationships are proposed. The second-order polynomial regression curves and the theoretical curves for carbon-carbon and carbon-nitrogen bonds are applicable as well as the linear equations.

Linear regression equations based on the MO (Coulson and SCF MO and VESCF) r-bond orders fit the data as well as the VB-related equations (in terms of regression quality parameters). The Coulson and SCF MO r-bond orders for benzenoid hydrocarbons are used for analogous azabenzenoids, but somewhat lower quality regressions are achieved. Calculation of VESCF r-bond orders using MM3(92) [20] for azabenzenoids supports such an approximation. MM3(92) [20] reproduces well the SCF MO r-bond orders in benzenoid hydrocarbons.

R. Kiralj et al./Journal qf Molecular Structure (Theochem) 42 7 (1998) 25-3 7 37

The simple Pauling VB approach has a disadvan-

tage: experimental bond lengths are clustered due to their dependence on the same Pauling r-bond

orders. This phenomenon is observed in almost all benzenoid systems in this study, and also in the

literature [1,4]. The same trend of data clustering is not observed in the MO approaches. The clustering phenomenon is a consequence of exclusion of

Dewar and excited KekulC structures which also contribute to the bond orders. The influence of the heteroatom on the carbon-

carbon bond length cannot be estimated for the sets of benzenoid hydrocarbons, azabenzenoids

and picrate-like systems (the differences are within the 3a limits). The average difference of carbon- carbon bond lengths in azabenzenoids and chemi-

cally analogous carbon-carbon bond lengths in

benzenoid hydrocarbons is 0.013 A [ 151. Too large standard deviations of the b correlation

coefficients overshield fine differences in the chemical bond character. More pronounced r-bond character detected in benzenoid hydrocarbon sets than that reported in the literature [2-41 (including non-benzenoid systems like graphite, ethylene and butadiene) might not be reliable. Larger sets of more accurate data are needed to

observe such fine structural details. The largest differences between linear regression coefficients for three benzenoid hydrocarbon sets are observed (within the 3u limits) when

Pauling and Coulson r-bond orders are used. This can be explained by different criteria for extraction of experimental data and their quality, number of bonds, and method of calculation used. It may be expected that any new structure would affect the regression analysis. Thus no regression equation should be used as an absolute criterium for the structural investigation, especially without a consideration of standard deviations and regression quality parameters.

Acknowledgements

This work was supported by the Ministry of Science and Technology of Croatia through grants No. 00980608 and No. 00980606.

References

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[3] W. C. Hemdon and C. Pirkinyi. J. Chem. Educ., 53 (1976)

689.

(41 R. Goddard, M. W. Haenel, W. C. Hemdon, C. Kriiger and M.

Zander, J. Am. Chem. Sot., I 17 (I 995) 30.

[5] C. A. Coulson and A. Golebiewski, Proc. Phys. Sot. (London),

78 (1961) 1310.

[6] M. J. S. Dewar and G. J. Gleicher, J. Chem. Phys.. 44 (1966)

759.

[7] M. J. S. Dewar and de Llano, J. Am. Chem. Sot.. 91 (1969)

789.

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bond lengths and bond orders in benzenoid hydrocarbons and related systems: a comparison of valence...

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