INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, VOL. XIII. 635-639 (1978)

Additivity Model for Calculations of UHF Spin Densities in Some Aza- Aromatic Radical Anions

K. K. SHARMA Department of Chemistry, Zakir Hussain College, Ajmeri Gate, Delhi-6, India

Abstracts

The additivity model suggested by Moss et al. has been applied for predicting spin densities in aza-aromatic radical anions. The core-resonance integrals (&) have been evaluated using Linder- berg’s relation. The spin-density values calculated using the additivity model, have been found to be in good agreement with unrestricted Hartree-Fock (UHF) spin-density values.

Le modtle d’additivitt propost par Moss et al. a t t t employ6 pour prtdire des densitCs de spin dans des anions radicaux aza-aromatiques. Les integrales de rtsonance du coeur (&) ont e t t caicultes par la relation de Linderberg. Les valeurs de la densitt de spin obtenues par ce rnodtle s’averent &tre en bon accord avec les valeurs calcultes par la mtthode UHF.

Das von Moss et al. vorgeschlagene Additivitatsmodell ist zum Vorhersagen von Spindichten in aza-aromatischen Radikalanionen angewandt worden. Die Rumpfresonanzintegrale (&,) sind mittels der Linderberg’schen Relation berechnet worden. Die mit diesem Modell berechneten Spindichtewerte stimmen mit den von der UHF-Methode erhaltenen Werten wohl iiberein.

Introduction

The additivity model suggested by Moss et al. has been applied for predicting the spin-density distributions in methyl-substituted radical anions [ 1-31. ESR data for a large number of aza-aromatic radical anions are available in the literature [4-91 and the observed splitting constants can be interpreted in terms of spin-density distributions in these systems. The purpose of this paper is to present a theoretical study [2] of spin-density distributions in the aza-aromatic radical anions.

Calculation Method

The unrestricted Hartree-Fock (UHF) nethod of Snyder and Amos [ lo] has been employed in this paper. The spin densities and charge densities were obtained after annihilation of the quartet spin component from the UHF wave functions. All molecules were assumed to be planar, and the C-C and C-N distances within the ring were taken equal to 1.40 and 1.34 A, respectively.

Valence-state ionization potentials and electron affinities were taken from the work of Hinze and Jaffe [ l l ] . Resonance integrals (&) for various bonds were obtained using Linderberg’s relation [12]. According to this relation the gradient of the overlap is related to the resonance integral by the relation,

@ 1978 John Wiley & Sons, Inc 0020-7608/78/0013-0635 $01.00

636 SHARMA

The effective nuclear charges for various atoms were obtained from the work of Mulliken et al. [ 131. The starting density matrices used for the self-consistent iterations procedure were obtained by employing the parameters of Streitwieser [14]. Topologies of the studied systems are given in Figure 1. All calculations reported in this paper were done on IBM 360144.

r m

P m Figure 1 . Topology of systems studied.

Results and Discussion

Cavalieri et al. [15] have found that the changes in proton splittings caused by aza-substitution obey an additivity relationship, i.e., aza-substitutions at positions i and j produce a change in the splitting at position k equal to the sum of the effects obserired at k in radicals that are substituted only at i or only at j . Since the proton splitting is proportional to the spin density, one would expect additivity of the spin-density values. For a nitrogen substituted at position 1 of the naphthalene radical anions, changes in the spin densities at the 2, 3, 4, 5 , 6, 7, and 8 positions are represented by b, c, d, e , f, g, and h, respecttvely. Similarly for a nitrogen substituted at position 2 of the naphthalene anion, the changes in the spin densities at 1, 3 ,4 , 5, 6, 7, and 8 positions are represented by a', c', d', e ' , f ' , g', and h', respectively. Expressions resulting from an additivity of spin- density values for quinoline and isoquinoline radical anions are given in Table I along with calculated spin-density values. Using UHFAA spin-density values in naphthalene radical anion (a = 0.2145 and p = 0.0485) and the expressions given in Table I, it is possible to estimate the parameters. Table I1 lists these values. The expressions resulting from an additivity model for some di- and tetra-aza-substituted naphthalene radical anions are given in Table 111. Using these expressions and the parameter values given in Table 11, spin-density values for various positions in these systems can be estimated and they are given under I in Table 111. The estimated spin-density values obtained by the additivity model seem to be in good agreement with the UHFAA values given under I1 in Table 111.

CALCULATIONS OF UHF SPIN DENSITIES 617

TABLE I. Spin densities in the radical anions of quinoline and isoquinoline.

System Position Expression for pi P*

Isoquinoline

Quinoline 2 3 4 5 6 7 8 1 3 4 5 6 7 8

b + P c + P d + a e + a f + P g + P h + a a ' + a C ' + P

d ' + P e ' + a f + P g ' + P h'+a

0.128 0.028 0.337 0.189 0.012 0.064 0.123 0.312

-0.015 0.134 0.136 0.119

-0.012 0.261

TABLE 11. Calculated parameter values.

Parameter Value

b 0.0796 C -0.0205 d 0.1225 e -0.0255 f -0.0365 g 0.0155

a' 0.0975 C' -0.0635 d' -0.0805 e' -0.0785 f' 0.0705

h' 0.0465

h -0.0915

g' -0.0605

Recently [9] it has been shown that a one-parameter relationship is fairly satisfactory for predicting nitrogen splittings and one might expect the p N values to be adequately described by an additivity model. Let the spin density at position 1 of quinoline be A and let D, E, and H represent the changes produced in this spin-density value by aza-substitution at the 4, 5 , and 8 positions, respectively. The spin-density values in a -substituted naphthalene anions are given by the expressions in Table IV. The values of the parameters are given in the footnote of this table. Using these parameter values the spin-density ( A + D + E + H ) at position 1 of 1,4,5,8-tetra-aza-naphthalene (VI) anion can be predicted to be 0.183. This is in good agreement with the UHFAA value of 0.175.

638 SHARMA

TABLE 111. Spin density of aza-aromatic radical anions"

Pi Expression for

System Positionb Pi I i1

I

111

IV

V

2 p + b + c 0.108 0.116 5 a + e i h 0.098 0.114 6 P + f + g 0.028 0.030

2 P + b + f 0.092 0.084 3 P + c + g 0.044 0.047 4 a + d + h 0.246 0.240

2 P + b + s 0.144 0.129 3 P + e + f a.014 0.005 4 a + d + e 0.312 0.299

1 a + a ' + e ' 0.235 0.228 3 P + c ' + g ' 0.075 0.038 4 a i d ' + h' 0.181 0.162

1 a + a ' + h' 0.359 0.362 3 P + C ' + f 0.056 0.027 4 a + d ' + e ' 0.056 0.101

VI 2 P + b + c + g + f 0.098 0.094

a Values given under I were obtained using an additivity model, those under I1 were obtained from UHFAA calculations.

See Figure 1.

TABLE IV. Spin-density values.

Naphthalene Expression for derivative PN PN

1-aza A 0.162 1,4-diaza A + D 0.257 1,Sdiaza A + E 0.152 1,8-diaza A + H 0.098 2-aza B 0.135 2,6-diaza B + F 0.133 2,7-diaza B + G 0.035

D = 0.095. E = -0.010. F = -0.064

CALCULATIONS OF UHF SPIN DENSITIES 639

The present study indicates that the additivity model satisfactorily predicts the spin-density values in aza-aromatic radical anions.

Acknowledgments

The author is grateful to Professor R. P. Mitra and Dr. N. K. Ray for their valuable help.

Bibliography [ l ] R. E. Moss, N. A. Ashford, R. G. Lawler, and G. K. Fraenkel, J. Chem. Phys. 51, 1765 (1969). [2] K. K. Sharma, “Unrestricted Hartree-Fock study of T-electron spin density and charge density

[3] K. K. Sharma, Int. J. Quant. Chem. 11, 753 (1977). [4] F. Garson and W. L. F. Aromaergo, Hel. Chirn. Acta 48, 112 (1965). [5] J. C. M. Henning, J. Chern. Phys. 44, 2139 (1966) and references therein. [6] C. L. Talcott and R. J. Meyers, Mol. Phys. 12, 549 (1967). [7] E. T. Strom, G. A. Russell, and R. Konaka, J. Chem. Phys. 42, 2033 (1965). [8] L. Lunazzi, A. Magnini, G . F. Pedulli, and F. Taddei, J. Chem. SOC. B, 163 (1970). [9] K. K. Sharma, Ind. J. Chern. A 15, 371 (1977).

distributions in some conjugated systems,” Ph.D. thesis, Delhi University, 1973.

[lo] L. C. Snyder and A. T. Amos, J. Chem. Phys. 42,3670 (1965). Ill] J. Hinze and H. H. Jaffe, J. Amer. Chem. SOC. 84, 540 (1962). [12] J. Linderberg, Chern. Phys. Lett. 1, 39 (1967). [13] R. S. Mulliken, C. A. Rieke, D. Orloff, and H. Orloff, J. Chem. Phys. 17, 1248 (1949). [ 141 A. Streitwieser, Molecular Orbital Theory for Organic Chemists (Wiley, New York, 1962),

[15] P. D’oro Cavaiieri, R. Danieli, G. Maccagnani, G. F. Pedulli, and P. Palmieri, Mol. Phys. 20, p. 135.

365 (1971).

Received May 24, 1977 Revised. January 23 , 1978 Accepted for publication February 23, 1978