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30
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33646852587
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For general reviews of the Fock space approach,see the articles in
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(1991)
Theor. Chim. Acta
, vol.80
, pp. 427
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37
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36549100024
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Excitation energies obtained in EOM-CC calculations are equivalent to those calculated using coupled-cluster linear response theory[
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(1990)
J. Chem. Phys
, vol.93
, pp. 3333
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Koch, H.1
Jo/rgensen, P.2
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41
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85038141193
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In cases where nondynamical correlation effects are important, direct methods such as EOM-CCSD and the multireference Fock space CC approach should be more reliable than the single-configuration QRHF-CC and TD-CC methods since the latter approaches are intrinsically biased towards the reference configuration. In direct methods, there is no such bias and these methods therefore provide a more balanced treatment for problems of this type. This point has been discussed in some detail in a recent paper on the Fock space approach[
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(1992)
J. Chem. Phys
, vol.95
, pp. 6224
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Stanton, J.F.1
Bartlett, R.J.2
Rittby, C.M.L.3
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42
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85038143939
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Strictly speaking, it is only the truncation of the vector which causes the method to be inexact.
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44
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85038146961
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In order to retain consistency with the normal CC treatment of the ground state, the R; vectors should be normalized to unity
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45
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0001334147
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P. S. Zalay and R. J. Bartlett, J. Chem. Phys, (in press). The functional form of the ground state CC energy and its potential advantage for property calculations had previously been noted by Arponen
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(1983)
Ann. Phys. (N.Y.)
, vol.151
, pp. 311
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Arponen, J.S.1
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46
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85038136900
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This expression applies equally well to transitions between two excited states.
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47
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85038145391
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Here, we make an implicit distinction between the actual reduced one-particle density matrix of ground state CC theory [formula omitted] and the “relaxed” or “effective” one-density (see Ref. 11, for example), which includes all effects of orbital relaxation. Only the former type of density matrix is considered in this paper.
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49
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85038144955
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In Ref. 13, the H matrix elements are designated as [formula omitted] while the intermediates used in solving the CCSD equations are denoted as [formula omitted]
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50
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85038131056
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To save disk space, the terms involving [formula omitted] may be handled differently from the rest. As discussed in Ref. 13, the contractions between [formula omitted] and the trial vectors may be broken down into three terms, each of which involves one contribution to the [formula omitted] amplitudes. If carried out in this fashion, no non-Hermitian [formula omitted] type quantities need to be stored on disk, and the ordered lists may exploit the intrinsic permutational symmetry of the bare Hamiltonian integrals. This results in negligible computational overhead and a significant reduction in the demand for disk storage.
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51
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85038149425
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We have not mentioned the [formula omitted] and [formula omitted] matrix elements in this context because the former vanish when the T amplitudes obey the CC equations and consequently need not be stored.
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54
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85038149547
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Although H contains a number of three- and higher-body operators, only a few of the three-body terms contribute to the EOM-CCSD equations. These are not listed in Table I, but their explicit spin-orbital representation can be extracted from Eqs. (31) and (32) by considering only the t amplitudes and antisymmetrized two-electron integrals.
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57
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85038133057
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ACES H, an ab initio program system, authored by J. F. Stanton, J. Gauss, J. D. Watts, W. J. Lauderdale, and R. J. Bartlett. The package also contains modified versions of the MOLECULE Gaussian integral program of J. Almlof and P. R. Taylor, the ABACUS integral derivative program of T. U. Helgaker, H. J. A. Jensen, P. Jo/rgensen, and P. R. Taylor, and the PROPS property integral package of P. R. Taylor
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60
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85038143728
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It should be pointed out that partitional EOM (Ref. 25) and the coupled-cluster linear response theory (Ref. 26) has previously been applied to calculate transition energies for these systems. Since the latter gives excitation energies identical to those obtained in the EOM-CC approximation, the energies listed in the first column of Table III have been previously presented in the literature but not the dipole strengths or AEL values
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61
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85038132794
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The ground state CCSD density matrix is of course non-Hermitian, and the approximate natural orbital basis is therefore biorthogonal. Nevertheless, to calculate the AEL values listed in this paper we have simplified matters by symmetrizing the ground and excited state density matrices. This should make essentially no difference to the numerical values of the AEL
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78
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0001017742
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(1989)
J. Chem. Phys
, vol.90
, pp. 4617
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Algranati, M.1
Feldman, H.2
Kella, D.3
Malkin, E.4
Miklazky, E.5
Naaman, R.6
Vager, Z.7
Zajfman, J.8
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84
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85038142044
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In the limit of an exact calculation, the two approaches are of course equivalent, but the symmetric strategy still requires the summation of an infinite series of terms.
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