Vohnne 57, number 1 CHEMICAL PHYSICS LETTERS 1 July 1978

NOTE ON THE INDO GEOMETRY OPTIMIZATION OF BIPEIENYL

Peter SCHARFEI?IBERG Institut jiiii Wirkstofforschung der Akzdemie der Wissenschaften der DDR. 1136 Berlin, Germany

and

Ch. JUNG Sektion Chemie der Humboldr-UniversitZt zu Berlin. DDR-I 08 Berlin, Germany

Received 12 April 1978

Recently ptzblished results of Raya and Dannenberg concerAng the biphenyi mckcule show some inadequacies. Our recalculation gives contrary results, which are in qualitatively good agreement with some CNDO/Z calculations presented recently. Consequently, implications discussed by Rayez and Dannenberg are not justified and they are in contrast to our experience with CNDO/Z geometry optimizations

1. introduction

The authors of ref. [I] report on INDQ calcula- tions of geometries of biphenyl for different confor- mations, i.e. several frozen angles of twist_ Each phe- nyl ring is assumed to be planar. An inversion centre follows as the most essential symmetry element from the symmetrical varied geometry parameters (see ta- ble I of ref. Cl]), and additionally a reflection plane for the planar qonformation, obviously identical with the molecular plane. Thz fact is also expressed in the resulting optimized geometries (see table 2 of ref.111).

Thus a molecular model constructed on the basis of the given data is of such kind that atom C, shows a distance of approximately 0.18 A from the Cl-Cl. axis as does atom C,..

However, a higher symmetry should be assumed in agreement with spectroscopic data [2,3] and should be conserved along the path of mhknization of the molecular energy - planar: D, orrhogonak Dad, nonorthogonal and nonplanar twisted: D2 - as we stressed recently in connection with CNDO/2 geom- etry.optimizations of biphenyl [4,5] _

2. Method

Basic principles of the geometry optimization method used have been sufficiently described else- where [4-6]_ One of us (ch J.) recently expanded the underlying semi-empirical LCAO MO SCF pro- gramrne for INDO calculations, and here we employ- ed the standard INDO version [7] with reference to ref. [I]_ All of the explki$Iy used internal group co- ordinates are collected ia table 1. The first partials of the molecular INW energy with respect to these co- ordinates must be calculated explicitly, and this has been done for effectiveness by means of analytical formulas, in order to be able to implement Fletcher’s quasi-Newton minimization method 183. Coordinates and minimization algorithm together are sufficient to conserve automatically all above-mentioned symme- tries during the run of the geometry optimization [9].

3. Results and discussion

CNDO/Z and INDO estimations of the twist angle of biphenyl are incorrect. (For experimenti results see ref. [ 141.) This is a well-known fact for semirigid

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CHEMICAL PHYSICS LETTERS 1 July 1978

Table 1 Complete set of intemal group coordinates used for the gt+ ometry optimization of the biphenyl molecule

Distances/bond-/ Set of atoms whose position change dihedral a&es is implied by coordinate changes

cr’-cr C,,C~,C~,C~.C~.C~.H~,H~,H~J~S.H~ C,--c6; LCr’crce C,,He Cr’-~s;~Crcr’Ce’ Cs,,He’ c~-cz;Lcl~clc2 C2rH2 c,~-c2*;Lc~c~~c2~ Cy&*

C~-C5;LCIc~CS =5&i cL*-cs*; Lc1cI*c$j. Cs.,Hs* c,-c3;Lc~‘c1c3 C,& C,*-C3*; LCrCrC3’ C3’.H3* c15c4 C4=H4 c. *-c4* * C4.&4* C6-H6;LCxC6H6;

el*cIc6H6 H6 Q-H& LC1’C6’&5’;

6CrClnC6&* H6* C,-H2;rcC1C2H2;

kGC2H2 H2 c2r--H2*; tqc2’H2’;

+5CtClQHa* H+* Cs-Hs; ~C~csHs H5 CsGls.; ,K&j*Hs, Hs’ C3-Hs; LC1c3H3 H3 C3~-H3*;LC~~,c3’~3’ K3*

C4-H4 % c4*-H4* =s*

molecular models [lO,l 11, but here the validity of this statement has been shown with respect to opti- mized, i.e. relaxed models too. Notwithstanding all the other strtlctural data seem to be satisfactory com- Dared with experimental results [12,133. The shape of the phenyl-phenyl distance as a function of tor- sion is similar for the CNDO/2 and INEO method - the causes have been discussed in detail in ref. [S J.

A semirigid standard geometrical model [7,5] has

f"- 1 1201

Fig_ 1. Calculated molecular structu~ of the planar, ortho- gonal, and 40°-twisted biphenyl molecule as well as the (lNDO-1 equilibrium geometry (61.8”-twisted); for the phe- nyl-phenyl distance see table 2. The ortho-hydrogen atotns projected 0.006 A out of the phenyl plane in the 40’ con- formation, and 0.0016 A in the equiliirium geometry, re- spectively_

its INDO potential minimum at 80” with an extreme- ly low barrier of 2.9 J/mole compared with the ortho-

gonal (90°-twisted) conformation of this model. Si- multaueous variation of twist angle and phenyl- phenyl distance results in an energy minimum due to 79O and 1 A6424 A, respectively_ It should be men- tioned that we reported on a quite similar shape of the C!NDO/Zpotential for the torsion of nitroben- zene [S]. However, the inclusion of all the remaining molecular degrees of freedom in the optimization sbified the miniium to the orthogonal conformation

Table 2 Calculated phenyl-phenyl distance and relative energy of the optimized structures as a function of the twist angle (planar: e=O”)

0 1.46438 11.5929 20 1.46291 7.1751 40 1.46045 1.4397 61.8 1.45972 C!.O 90 X.45983 0.2374

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Voluale 57, number 1 CHEMICAL PHYSICS LETTERS 1 July 1978

$2 (PLANAR) I ORTHOGONALI

Fig_ 2. Relative energy of the biphenyl molecule versus angle of internal rotation (Erel = E + 235900.4’704 kJ/mole).

of nitrobenzene, whereas the behaviour of biphenyl under INDO geometry optimization is contrary.

Semirigid twist of the equilibrium structure from 6 1.8” to 90” gives 0.26 15 kJ/mole as an upper bound to the respecti;re energy barrier, which can be obtain- ed after complete relaxation of the biphenyl molecule kept at the 90°-twisted position_ We want to empha- size that such a marginal barrier, particularly with re- gard to the shape of the potential in the range from 40” to 90” may be anything (say an artefact, possibly) but that it can be accepted to be significant or far more realistical than other results [ 10,11,4,5]. Natu- rally, any conclusion like “qualitative correct estima- tion of torsional angle” should be questionable.

Neither the shape of the phenyl-phenyl distance function nor the potential curve (fig. 2) nor the mo- lecular structures (fig. 1) of our calculations are in agreement with the results of Rayez and Dannenberg [ 11. The conservation of symmetry elements and the well-balanced accuracy of the geometry optimization of different conformations require the greatest atten- tion. This is necessary because many small erroneous contributions in the calculation of a larger molecule possibly not only cause quantitative but perhaps also qu&tative shifts of the results. The choice of internal group coordinates like those given in table 3 as an ex- ample guarantees the conservation of an inversion centre but breaks initial D2-symmetry. Nevertheless, a careful optimization yields in very good approxima- tion the more stable D2-symmetry, as we found with CNDO/2 calculations (unpublished results). The fim- damentals of symmetry making and breaking are sub- ject of ref. [9].

Table 3 Internal group coordinates which cause conservation of an in- version centre but no: the conservation of an initial D2- symmetry in connection with steepest descent lie miuimiza- tion techniques. The coordinates of the hydrogen atoms can be chosen nearly arbitrarily, but they have to be independent of each other and independent of the coordinates contamed in the table and have to conserve at least the inversion centre

Distances/bond-/ Set of atoms whose position change dihedral angles is implied by coordinate changes

c1-c~;.K~C~c~ C~~C~,C~,CSF~:HZ,H~.H~.HS.H~ C1*-C& LC~C~‘Cg Cz’,C3’,C4~,C5,,C6~H2~J13,,H4~,Hs0,H~~ C2-C3;LC1C2C3 C~.C~.CS,C~,H~.H~.HS.H~ C,*-C& LC1*C#C5* C2~,C3~,C4~IC5’,H2’.H3,,H4~.Hs~

c3-c4; LCZC3C4 C~.CS.CS.H~.HS.H~ c5’-c4’; LC6’CS*C4# C~~,C~~,C~~,H~Y,H~~,H~~ c4-c5; LC3C4C5 Cd6rHd6 c4*-c3*; LC5C4C3~ C~~,C~~.HZ~.H~~ cs -c6 ; Lc4c5c6 C6.H6 C3*-C2*; LC4C&2# C2*,H2r

We performed the calculations on a BESM6 com- puter of the Academy of Sciences by means of a ge- ometry optimization programme, written in FORTRAN [15].

References

[l] J-C. Rayez and JJ. Dannenberg, Chem. Phys. Letters 41(1976) 492.

[2! A. d’Annibale, L. Lunazzi, A.C. Boicelli and D. Mac- ciantelli, J. Chem. Sot. Perkin Tranr II (1973) 1396.

[3j L. LeGaIl and Sb Suzuki, Chem. Phys Letters 46 11977) 467.

141 P. Scharfenberg and H. Sklenar, Proceedings of a sym- posium held in SUN (1976), to be published.

[S] P. Scharfenberg, J. MoL Struct, submitted for publica- tion

161 P. Scharfenberg, Theoret. Chim. Acta, to be published. 171 J.A. Pople and D-L Beveridge, Approximate molecular

orbital theory (McGraw-Hill, New York, i970). [ 81 R. Retcher, FORTRAN-Subroutines for Miiation

WAO9A), Harwell(l972). [9] P. Scharfenberg, Theoret. Chim. Acta, submitted For

publication. [lo] B. Tinland, Them-et Chim. Acta ll(l968) 452. Ill] 0. Gropen and H.M. Seip, Chem. Phys. Letters 11

(1971) 445. [12] J. Trotter, Acta Cryst. 14 (1961) 1135. 1131 G-B. Robertson, Nature 191 (1961) 593. (141 0. Bastiansen, Acta Chem. Stand. 3 (1949) 408. [ 151 P. Scharfenberg, BIENE2 - EmProgramm zur Bestimmung

der Gleichgewichtsgeometrie grosser Molekeln, Beti (1975).

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