Pertubation theory

McCoy A B and Siebert E L 1996 Canonical Van VIeck pertubation theory and its applications to studies of highly vibrationally excited states of polyatomic molecules Dynemics of Moiecuies end Chemicei Reections ed R E Wyatt and J Z H Zhang (New York Dekker) p 151... 

Values from coupled HF pertubation theory (76-77) for H-0 and from solid-state... 

Table 9 Magnetic susceptibility results calculated using SCF pertubation theory. The units are 10 5 J T 2 mol-1 throughout. The origin of the vector potential was taken either as the centre of mass or at the starred atom...

Stell, G., Rasaiah, J., and Narang, H. (1972) Thermodynamie pertubation theory for simple polar fluids. J. Mol. Phys. 23, 393-406. 

The more recent 1992 Maslen et al. force field for benzene (153) was computed by evaluating analytic derivatives through quartic terms at the SCF level. The DZP basis set was used in these studies. The derivatives were evaluated at the equilibrium geometry determined at the MP2 (Moller-Plesset second-order pertubation theory) level using a larger basis set, TZ2P (triple-zeta plus double polarization). It is significant that a complete ab initio force field at the quartic level has been computed for benzene. 

Close to the nuclei the nuclear charge attraction is opposed by a rapid increase of the kinetic energy and Ashcroft s potentials simulate this rather well. Using pertubation theory similar to that discussed in the context of the resolvent method, one finds that the surface energy behaves as ... 

Such models can be classified in semi-empirical methods (9-13), corresponding states approaches (14-17), pertubation theories (18-20) and equation of state models (21-28), of which the latter were shown to be well able to correlate experimental solubilities in the nearcritical region. 

Unfortunately in pertubation theory we run into trouble at an early stage. Consider the triangle diagram contributions to the amplitudes of Fig. 9.3 shown in Fig. 9.4. Gauge invariance requires... 

In real systems, nonrandom mixing effects, potentially caused by local polymer architecture and interchain forces, can have profound consequences on how intermolecular attractive potentials influence miscibility. Such nonideal effects can lead to large corrections, of both excess entropic and enthalpic origin, to the mean-field Flory-Huggins theory. As discussed in Section IV, for flexible chain blends of prime experimental interest the excess entropic contribution seems very small. Thus, attractive interactions, or enthalpy of mixing effects, are expected to often play a dominant role in determining blend miscibility. In this section we examine these enthalpic effects within the context of thermodynamic pertubation theory for atomistic, semiflexible, and Gaussian thread models. In addition, the validity of a Hildebrand-like molecular solubility parameter approach based on pure component properties is examined. 

A third class of new polymer integral equation theories have been proposed by Kierlik and Rosinberg. Their work is an extension of a density functional theory of inhomogeneous polyatomic fluids to treat the homogeneous phase. The Wertheim thermodynamic pertubation theory of polymerization is employed in an essential manner. Applications to calculate the intermolecular structure of rather short homopolymer solutions and melts have been made. Good results are found for short chains at high densities, but the authors comment that their earlier theory appears to be unsuited for long chains at low to moderate (semidilute) densities. ... 

Studies in Perturbation Theory. XIII. Treatment of Constants of the Motion in Resolvent Method, Partitioning Technique, and Pertubation Theory... 

The potential energy surface for the isomerization reaction, corresponding to the migration of around N2 (NNH - " HNN), was calculated by ab initio techniques (MO SCF and MPPT(3) (third-order Moller-Plesset pertubation theory)). A cyclic C2V structure was located at the peak of the calculated barrier of 192 kJ/mol [4, 5]. 

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