No abstract

The triplet instability problem associated with the random-phase approximation (RPA) is well known. It arises from the fact that for the ground state of many systems there exists an unrestricted H F solution that is of lower energy than the restricted H F solution on which RPA equations are based. When RPA calculations are carried out using a model Hamiltonian like that of Pariser, Parr, and Pople, (PPP) the triplet instability problem can be very conveniently studied by continuously changing the values of semiempirical parameters upon which the model Hamiltonian depends. In fact, since the pioneering work of Ball and McLachlan [ 1 1 on ethylene molecule, such a study has been made by a number of workers [2-41. In ethylene, because of the extraordinary simplicity of the problem, the effect of semiempirical parameters on its various molecular quantities can be studied by means of simple analytical expressions. This is, however, not possible for larger systems for which extensive computations are needed. Recently, Guha Niyogi et al.[5] have extended the work of Ball and McLachlan [ 11 to a number of hydrocarbons. All these parametric studies are generally made up to a point at which the H F ground state starts becoming triplet unstable. If one goes beyond this point, several interesting features appear. It is the purpose of the present paper to report these aspects of the RPA triplet calculation of conjugated hydrocarbons taking ethylene, trans-butadiene, hexatriene, and benzene as the test molecules.Exactly the same method of calculation as employed by Guha Niyogi et al.[5] has been followed here.The resonance integral, / 3, is taken to be the dominating variable parameter. The one-center electron repulsion integral, y c~ is set equal to 1 1 .I 3 eV and the two-center repulsion integrals are evaluated using the approximations due to Mataga and Nishimoto (MN) [6], Ohno [7], and Matsuoka and Ito ( M I ) [8].As pointed out earlier, we have concentrated our attention to the 0 values lying in the range 0 Q 1/31 < I/3:I, where is the value of 0 at which the RPA triplet energy becomes zero.Considering ethylene, one can easily calculate that in the PPP modelwhere SCI refers to C I calculations taking only singly excited configurations into account, and K = (414214142). It follows from these equations that the SCI and RPA solutions become triplet unstable when 1/31 Q K / 2 and 1/31 Q K , respectively. Moreover, the RPA solution attains its minimum value at the point where the SCI solution starts becoming triplet unstable. Equation'(2) further indicates that triplet instability in RPA solution also occurs at 0 = 0. The RPA eigenvalue equation can be written in the form

AbstractsSinglet-singlet transition energies, oscillator strengths, triplet energy levels, and the ground state correlation energy of a number of conjugated hydrocarbons have been calculated by the simple random-phase approximation (RPA) within the framework of the Pariser-Parr-Pople (PPP) model. The effect of semi-empirical parameters in such calculations has been examined in detail. A set of parameters has been deduced from these parametric studies which is found to yield results for the singlet spectra of the molecules in excellent agreement with experiment. It is, however, not possible to treat the triplet states using these same parameters, since they produce triplet instabilities in all the molecules. The triplet instability problem associated with semi-empirical RPA calculations has been discussed in detail.Des Cnergies de transition singulet-singulet, des forces d'oscillateur, des niveaux triplets et I'inergie de corrklation de I'Ctat fondamental d'un nombre d'hydrocarbures conjuguCs ont Ctk calculCs par I'approximation des phases altatoires (RPA) dans le cadre du modele de Pariser-Parr-Pople. L'effet des parametres semi-empiriques a CtC examin6 en dttail. De ces Ctudeson a obtenu un nombre de paramttres, qui donnent des resultats pour les spectres singulet en accord excellent avec I'exptrience. 11 n'est pas possible, cependant, d'ernployer les m&mes paramttres pour les Ctats triplets, puisqu'ils produisent des instabilitts dans toutes les molicules. Les problimes d'instabilitt associes aux calculs de type RPA semi-empirique ont t t t discutCs en dbtail.Ubergangsenergien von Singulett-Singulett-Typ, Oszillatorenstarken, Triplettenergieniveaus und Korrelationsenergien fur den Grundzustand einer Reihe von konjugierten Kohlenwasserstoffen sind mittels der einfachen "Random-Phase-Approximation" (RPA) im Rahmen des Pariser-ParrPople'schen Modells berechnet worden. Der Einfluss der semi-empirischen Parameter auf solche Berechnungen ist eingehend untersucht worden. Eine Reihe von Parametern ist von diesen Studien erhalten worden, die Resultate fur die Singulett-spektren in sehr guter Ubereinstimmung mit den Experimentaldaten geben. Es ist aber nicht moglich die Triplettzustande mit denselben Parametern zu behandeln, weil sie Triplettinstabilitaten in allen Molekulen erzeugen. Das mit semi-empirischen RPA-Berechnungen zusammenhangende Triplettinstabilitatsproblem ist ausfiihrlich diskutiert worden.

26) It has been generally considered that intersystem crossing occurs from the lowest excited state of a given spin multiplicity. The present discussion disagrees with this general concept, because the present photoreaction scheme Includes Intersystem crossing from higher energetic excited states. However, some discussions similar to the present one have also been reported for the photochemistry of transition metal complexes: for example G.

No abstract