Multistate perturbative methods

Some of the more important aspects of the theory behind the method are described in the review. In particular, the choice of the zeroth-order Hamiltonian is discussed together with the intruder-state problem and its solution. A generalization of the method to a multistate perturbation approach is suggested. Problems specifically related to spectroscopic applications are discussed, such as the choice of the active space and the treatment of solvent effects. 

Figure 6.8 shows the variation in rotational viscosity ( y ) with time t. The most remarkable feature of the result in (6.56) is that, as a function of time, the square of the amplitude of the rotational viscosity y q ) oscillates sinusoidally (Fig. 6.8). After rising to a maximum of [ (t-Tc)-kK ]Y 2, it drops back to zero. Since, (6.56) is obtained by comparing (6.55) with (6.45), the maximum value allotted to ( y ) must not exceed one, else the perturbative method will be invalid and hence, (6.56). This result is highly surprising. At times t = where n = 1, 2, 3... the FLC molecules certain to have almost infinite rotational mobility resulting into zero rotational viscosity as evident from Fig. 6.8. Therefore, the applied field should not keep for a longer period of time but it should turn off after an interval of time for maximizing the chances to produce finite rotational torque on the FLC director and as a result to obtain the system with finite rotational viscosity. Once the field is turned off, this reduced viscosity seems to produce a finite but weaker torque at the memory state and thereby, promotes multistability and resolution in the memory states as proposed earlier.

An alternative way to approach the problem is to start out with a hxed MR function, and develop a perturbation theory on it. This is thus an MRPT of the unrelaxed or contracted coefficients variety. The SSMR-based perturbation theories based on contracted description using CAS [43-48] have been widely used as efficient methods to treat quasi-degeneracy. There are usually two ways in which the virtual functions are handled they can be contracted functions themselves or they can be simpler CSFs. Multistate versions of the contracted variety has also been suggested [46]. An SS-based CC formulation of the. frozen variety has been developed [38], where a wave operator is used to generate the exact state by its action on the entire MR function. 

All the SAPT methods considered so far have used a single operator projecting onto a specific subspace c a b- The HS perturbation theory, introduced by Hirschfelder and Silbey [50], follows a different, multistate philosophy. It performs a perturbation expansion for a primitive func-... 

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