Not esSelf-consistent Methods ill H~~kel & Extended H~'ckelTheories: Part II - Application to pi-EJection Systems]

A. K. MUKHOPADHYAY & N. G. MUKHERJEE*Chemistry Department, University College of Science.

Calcutta 700 009

Received 15 November 1980; revised 29 December 1980;accepted 7 January 1981

A self-consistent procedure for the Huckel theory, developedearlier [Int. J. quantum Chem., 19(1981),515)] has been used forthe calculation of 'vertical ionisation potentials of some alternantand non-alternant hydrocarbons and dipole moments of the non-alternants. The results show that the values are consistentlybetter than those obtained by the conventional c.l-technique.

IN an earlier paper', a self-consistent procedure forthe Huckel and extended Huckel theories based

on a suggestion of Harris", was developed. A similarmethod had been developed earlier by Kalman",Our method differed from that of Kalman in tworespects: (i) we used original Mulliken approxima-tion for the off-diagonal elements of the hamiltonianmatrix instead of using the exsin approximation intro-duced by Kalman and (ii) we accelerated the conver-gence using a steepest descent techniques. Timeconsuming repeated orthogonal non-orthogonaltransformations were also avoided thereby. As theconvergence of the method seemed very good, intro-duction of any more sophistication like conjugategradient technique etc. into the method was deemedunnecessary. In. what follows we apply the methodfor the calculation of vertical ionisation potentials ofsome alternant and non-alternant hydrocarbons anddipole moments of the non-alternant hydrocarbons.The self-consistent approach in the Huckel and exten-ded H uckel theories has received less attention thanit deserved, and has sometimes been used ratherincompetently''.

Nowadays there are many advanced methods 8,11-13available for the calculation of pi-electronic structuresof large neutral and ionised molecules. Our aim hereis not to show any superiority of our method overthese. The prime motivation of this paper is to seethe result of introduction of a true self-consistentnature in the naive Huckel.theory with a sound theo-retical basis.

It is to be noted that the ionisation potential (lk)is not given as the negative of orbital energy (Ek)obtained by the diagonalisation of the self-consistenthamiltonian F. Instead, from the definition, we have

I» = Ecauon - Emolecule= Trli.T/t, +H ... (1)

tPaper under reference 1 may be considered as Part Iof the series.

where H is the Huckel hamiltonian matrix (afterw-correction and assuming small overlap so thatclosed and open shell operators are almost equal) andthe LCAO co-efficients of the kth orbital, from whichan electron has been removed to create the cationhave been collected in column Ts: Again-, '

F=H+D ... (2)

where DM,= -[wi(S'R)iI+Wk(S'R)kk]SikS;} = J( SH for i =1= i

= Si1, otherwise S being the overlap matrix.Hence expression (1) can be simplified to

. .. (3)

The proposed method has been applied for thecalculation of ionisation potentials and dipole-.moments of some pi-electron systems. Since neitherthe conventional eo-technique nor the SCF w-techni-que developed earlier by us5 include the overlapcharge, 0ur aim is to see if the present method givesvalues better than those obtained earlier or approachthe pPp14 values. It has been found for larger systemsthat the steepest descent method is faster and lesstime consuming than the direct diagonalisation pro-cedure.

In Tables 1and 2 are given the ionisation potentialsof some alternants and non-alternants respectivelycalculated by the present method and by methodsavailable in literature. For a particular molecule thesame geometry" has been used for all the methodsof calculation. Two sets of calculations for thealterriants have been made using the present method.In one, a fixed overlap of 0.25 has been taken betweenthe neighbours and no overlap between the non-neighbours. In the other, actual overlaps (usingSlater orbitals with orbital exponent 1.625 forcarbon) between atomic orbitals have been used.For non-alternants actual overlaps only have beenconsidered. The values of at and K are those used byKrishna and Gupta-, i.e. - 9.40 eVand 2.0 respecti-vely in all the calculations. As only carbon 2pz orbi-tals are involved, a single w-value has been used fora particular set of calculations. w-Values for differentsets are included in Tables 1 and 2. Vertical ionisa-tion potentials obtained by the second procedure,i.e. considering actual overlaps are decidedly betterthan those obtained by the pure Huckel or by consider-ing a fixed overlap and are quite near to those ob-tained by SCF MO method", The IP's obtained byKrishna and Gupta 4 are of course better than ours .Their results are even better than SCF MO resultsand are within allowable errors of experiment. Itis however unfortunate that Krishna and Gupta-did not optimise F in the proper way.

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INDIAN J. CHEM •• VOL. 20A, AUGUST 1981

TABLE 1- IONIZATIONPOTENTIALOF SOMEALTERNANTHYDROCARBONS

[Values in eV]

Molecule Huckel Set 1 Set 2 Krishna SCF MO Expl. valueConstant Slater orbital & Gupta' (ref. 7) (ref. 7)overlap overlap

(~ =-1.095) (w = -1.95)

Ethylene 11.2799 9.5279 9.781 10.56 10.14 10.56Butadiene 10.65 8.900 9.101 . 9.15 9.02 9.18 .Benzene 1039 9.381 9.36 9.38 9.35 9.38Naphthalene 10.65 8.779 8.728 8.31 8.45 8.26Anthracene 10.28 8.41 8.36 7.72 7.83 7.55Phenanthrene 10.63 8.74 8.666 8.19 8.28 8.03Styrene 10.73 8.88 8.886 8.73 8.71 8.86Biphenyl 10.80 8.895 8.752 8.31 8.45 8.30

TABLE2 - IONIZATIONPOTENTIALOF SOME NON-ALTERNANTHYDROC~ONS

Molecule[Values in eV]

Present method SCF MO(ref. 8)

9.10*9.148.88

AzuleneAcepleiadyleneNaphth [cdef azulene

8.4278.338.204

Molecule(,Values in eV]

Present method SCF MO(ref, 8)

8.87

8.92

Pentaleno [def] heptalene 8.122

Cyclohept[bc]acenaphthylene 8.22

*Experimental value of only one compound, namely azulene, is definitely known" as 7.72.

TABLE 3 - DIPOLE MOMENTSOF SOME NON-ALTERNANT HYDROCARBONS

[Values in Deleye]

Molecule Huckel w-technique SCF Present SCFMO Explmethod w-technique method value

(w = -1.0) (c.l = -1.4) (w = -1.95) (ref. 8)

Azulene 6.41 4.70 1.99 1.826 1.79 1.0 (ref. 9)Acepleiadylene 8.47 6.89 5.30 3.469 1.15 0.5 (ref. 10)Naphth [cde] azulene 5.93 4.53 3.64 3.412 1.71Pentaleno [dell heptalene 5.74 4.45 3.40 2.98 1.68Cyclohept [bc] acenaphthylene 4.37 3.47 2.67 2.48 0.60

In Table 3 are given the dipole moments of somenon-alternants calculated using the present methodand other available methods. It is evident fromTable 3 that the dipole moments are consistentlybetter than those obtained by the conventional w-tech-nique and they are even better than those obtainedby self-consistent w-technique.

It is therefore hoped that the present methodwould give fairly good results for properties relatedto charge density distributions when adapted for aniterative extended Huckel method and be quite usefulfor very large molecular systems, where even semi-empirical all valence-electron calculations arestill regarded uneconomical. Further work on theselines is in progress.

Thanks are due to the Centre of Computer Science,University of Calcutta, for computer facility. One ofus (A.K.M.) wishes to thank the UGC, New Delhifor a teacher fellowship.

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