Coupled-cluster wave functions, derivatives energy

Such a basis set combines well with coupled-cluster wave functions to tend to converge in a consistent and predictable manner towards limits of the basis set and the theory. Calculation of the rotational g tensor and magnetizability involved use of rotational London orbitals [10]. Optimization, first order in derivatives of energy with respect to internuclear distances, yielded all reported geometric stmctures of... 

Koch H, Jdrgen H, Jensen A, Jorgensen P, Helgaker T, Scuseria GE, Schaefer III HF (1990) Coupled cluster energy derivatives. Analytic Hessian for the closed-shell coupled cluster singles and doubles wave function Theory and applications. J Chem Phys 92 4924-4940... 

H. Koch, H. J. Aa. Jensen, P. j0rgensen, T. Helgaker, G. E. Scuseria, and H. F. Schaefer, /. Chem. Phys., 92, 4924 (1990). Coupled-Cluster Energy Derivatives. Analytic Hessian for the Closed-Shell Coupled-Cluster Singles and Doubles Wave Functions Theory and Applications. 

Coupled cluster response calculaAons are usually based on the HF-SCF wave-function of the unperturbed system as reference state, i.e. they correspond to so-called orbital-unrelaxed derivatives. In the static limit this becomes equivalent to finite field calculations where Aie perturbation is added to the Hamiltonian after the HF-SCF step, while in the orbital-relaxed approach the perturbation is included already in the HF-SCF calculation. For frequency-dependent properties the orbital-relaxed approach leads to artificial poles in the correlated results whenever one of the involved frequencies becomes equal to an HF-SCF excitation energy. However, in Aie static limit both unrelaxed and relaxed coupled cluster calculations can be used and for boAi approaches the hierarchy CCS (HF-SCF), CC2, CCSD, CC3,... converges in the limit of a complete cluster expansion to the Full CI result. Thus, the question arises, whether for second hyperpolarizabilities one... 

Frequency-dependent response functions can only be computed within approximate electronic structure models that allow definition of the time-dependent expectation value. Hence, frequency-dependent response functions are not defined for approximate methods that provide an energy but no wave function. Such methods include MoUer-Plesset (MP) perturbation theory, multiconfigurational second-order perturbation theory (CASPT2), and coupled cluster singles and doubles with non-iterative perturbative triples [CCSD(T)]. As we shall see later, it is possible to derive static response functions for such methods. 

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