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In order to circumvent the problem of spin contamination in unrestricted Hartree-Fock based coupled cluster (CC) calculations, we present a new method of calculation for certain classes of open-shell systems. The approach ensures that the proper spin component of the resulting correlated wave function is projected out in the energy evaluation by the use of a reference function constructed from suitably chosen restricted open-shell Hartree-Fock or other orbitals. This single-reference open-shell spin-restricted CC method is applied to the calculation of ionization potentials in the N2 molecule, and it is shown that highly accurate results can be obtained in a 5s4pld basis. The mean error for all the principal ionization potentials of N2 compared to experiment is 0.45%.

A multireference coupled-cluster (MRCC) formulation for the direct calculation of excitation energies and ionization potentials is presented. The reference space connects a set of p–h excited determinants built from all the set of active particles and holes in the model space. This model space is incomplete, requiring a Fock-space approach and the postulate of a ‘‘universal’’ wave operator to arrive at a linked diagram expression for the effective Hamiltonian Heff, whose eigenvalues are the excitation energies for the problem. Use of a normal-ordered exponential cluster ansatz allows one to construct, hierarchically, the CC equations for the p–h model space starting from the ground state. We present an extension of an earlier formulation for excitation energies that allows us to have both active and inactive particles and holes in our method. Numerical applications are reported for the prototypical small molecules CO and N2.

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Weyl's theory for a singular second-order differential equation and the complex scaling method of Balslev and . Combes are combined to obtain a stable method for describing the continuous spectrum. The method obtained can be viewed as an extension of the Siegert method. The theory is applied to a model potential earlier used by Moiseyev et al.The experimental development of laser spectroscopy, electron scattering, and in particular, the high-frequency deflection technique, ' have lead to a considerable interest in the theory of the spectral continuum and more specifically in quasibound states and resonances in the vibrational continua of molecules. The simultaneous development of complex scaling in terms of the Aguilar-Balslev-Combes (ABC) theory' ' for dilatation analytic operators has opened a field of new ideas. Methods of this type are important for the understanding of a complete, nonisolated system. One of the first applications of the ABC theory in the study of resonances was reported by Bain, Bardsley, Junker, and Sukumar. ' They used a modified variational principle to obtain the complex eigenvalue of the complex-rotated Hamilton-ian. The position of the resonance as a function of the dilatation angle was studied numerically. One of the difficulties of the application of this method is its basis-set dependence. This problem was to some extent solved utilizing the existence of the complex virial theorem Weyl's theory for a singular second-order differential equation' has earlier proven to be an efficient tool in the analysis of the continuous spectrum. ' In the numerical applications made so far (see, e.g. , Hehenberger et al. ' and Ref. 8) one makes use of the numerical information of the Green's function or the Weyl-Titchmarsh m function on the real axis, A Siegert state" can then only be obtained via analytic continuation based on the previously mentioned numerical data.In this report we present a synthesis of Weyl's theory and the theory of complex scaling. The step to "go into" the complex plane appears, in fact, quite natural if the details of Weyl's theory are considered. In contrast to previous techniques which one way or another were based on the numerical dependence of the resonance so-y' (x)+~2[a -q(x)]y(x} = 0.(l)For simplicity we will only consider one equation here. Extensions to the case of coupled equations are easily incorporated in the present formulation, but this will be reported elsewhere. Putting~gg, where g is a complex scale factor with 0~argy & v/4, we obtain the transformed equation, 2 2 y'"(x) +~" [e(q)q"(x)]y"(x) = O.In order to emphasize the g dependence, we will write Eq. (2) as a differential equation with the real variable x belonging to the interval ( -, +~) and the parametric dependence on g indicated by a suffix. We assume that g above is consistent with (2) limq"(x}= q"(+~) = const&~. lutions on the dilatation angle 8 = argy, we employ a direct numerical integration of the Siegert' solution on the higher-order Riemann sheet. As a consequence, the dependence of the...

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