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Towards a spin-adapted coupled-cluster theory for high-spin open-shell states
1.See, for example, J. F. Stanton and J. Gauss, Adv. Chem. Phys. 125, 101 (2003).
5.See, for example, R. J. Bartlett, in Modern Electronic Structure Theory, Part II, edited by D. R. Yarkony (World Scientific, Singapore, 1995), p. 1047.
6.G. D. Purvis, H. Sekino, and R. J. Bartlett, Collect. Czech. Chem. Commun. 53, 2203 (1988).
14.X. Li and J. Paldus, in Recent Advances in Computational Chemistry, Recent Advances in Coupled-Cluster Methods, Vol. 3, edited by R. Bartlett (World Scientific, Singapore, 1997), p. 183.
16.M. Nooijen, Int. J. Mol. Sci. 3, 56 (2002).
17.L. Adamowicz, J. P. Malrieu, and V. Ivanov, Int. J. Mol. Sci. 3, 550 (2002).
24.The term “CC expectation value” is used for all expressions based on the corresponding energy derivative formulas. For further details concerning the evaluation of the spin expectation value in the CC theory, we refer to Ref. 8.
25.J. Paldus (private communication).
26.For recent examples concerning the use of automatic programing tools, see M. Kállay and P. R. Surján, J. Chem. Phys. 113, 1359 (2000);
27.This is due to the fact that our cluster operator does not commute with and yields spin eigenfunction only when applied to the reference state. In particular, the repeated application of thus does not produce a spin eigenfunction.
30.The space spanned by the single and double excited determinants is not a closed subspace for the operator. For this reason, triple excitations with one spin flip, quadruple excitations with two spin flips, etc., must be also considered when defining, for example, doubly excited CSFs. For a detailed discussion in the case of doublet states, see Ref. 28.
33.As discussed in Ref. 23, the PSA-CC approximation can be derived from the SR-CC scheme via a linearization of the projected spin equations. However, fulfillment of the linearized spin equation is equal to setting to zero.
34.See, for example, R. Paunz, Spin Eigenfunctions (Plenum, New York, 1979).
35.For further details, see M. Heckert, Diploma thesis, Universität Mainz, 2002.
37.G. Herzberg, Molecular Spectra and Molecular Structure, Electronic Spectra and Electronic Structure of Polyatomic Molecules Vol. III (Van Nostrand, New York, 1966);
37.K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure, Constants of Diatomic Molecules Vol. IV (Van Nostrand, New York, 1979).
40.T. H. Dunning, J. Chem. Phys. 97, 1007 (1989).
41.J. Gauss, in Encyclopedia of Computational Chemistry, edited by P. v. R. Schleyer, N. L. Allinger, T. Clark, J. Gasteiger, P. A. Kollmann, H. F. Schaefer, and P. R. Schreiner (Wiley, New York, 1998), p. 615ff.
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