Single-reference theory, relationship

This chapter, therefore, encompasses two extremes of excited-state theories within the single-reference, linear-response framework One that aims at high and controlled accuracy for relatively small gas-phase molecules such as EOM-CC and the other with low to medium accuracy for large molecules and solids represented by CIS and TDDFT. We aim at clarifying the mutual relationship among these excited-state methods including the two extremes, while delegating a more complete exposition of EOM-CC to the next chapter contributed by Watts. 

The Cn-kij A) terms are easy to determine. The zero-body term, Cq a)i equals 1 the one-body term, C mA)-> equals Ti the two-body term, C2(mA), equals T2 + if rriA > 2 the three-body term, Cz rnA) equals riT2 + if rriA = 2 and Ts + T1T2 + if rriA > 3, etc. The coefficients, Eq. (27), define the generalized moments of CC equations (for a discussion of the relationship between the method of moments of Krylov [99] and the single-reference CC theory, see Ref. [100]). They are readily available for the basic CC approximations, such as CCSD (the rriA = 2 case). As pointed out in our original work [11,30], the generalized moments represent the most fundamental quantities... 

The relationship between single-reference Brillouin-Wigner perturbation theory and its Rayleigh-Schrodinger counterpart is well known, but for completeness we include a brief account of the single-reference case in Section 4.4.1 before turning to the multi-reference case in Section 4.4.2. 

The AutoShielding Potential (ASP) theory has shown an exponential relationship for the Polyani (Verb. Dtsch. Phys. Ges. (1914) 16 1012) sorption potential — defined as the reversible work required to achieve the equilibrium pressure, P, in a closed system. This is conveniently expressed for the single vapor component with respect to the liquid sorbate reference pressure, P(0), at a given temperature, T,... 

The results of calculations of electrooptic properties for 1,2 and 3 are presented in Table3.6. Due to the computational limitations, MP2 results are presented only for single component (x) of /x, a, / and 7. Since rotationally invariant hyperpolarizabilities are more suitable for structure-property relationships analysis, one have to select reliable level of theory for calculations of a, (3 and 7. The values of axx, (3xxx and Yxxxx calculated at the MP2 level of theory may serve as a reference data. Based on the results presented in Tables 3.3 and 3.6 the following ordering of axx values can be observed a > It is worth noticing, that PM6 model... 

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