CCSDT correlation

The HF level as usual overestimates the polarity, in this case leading to an incorrect direction of the dipole moment. The MP perturbation series oscillates, and it is clear that the MP4 result is far from converged. The CCSD(T) method apparently recovers the most important part of the electron correlation, as compared to the full CCSDT result. However, even with the aug-cc-pV5Z basis sets, there is still a discrepancy of 0.01 D relative to the experimental value. 

CCSD(T) instead of CCSDT amounts to no more than 10 % of the total triples correction and 1 % of the total correlation energy, thus fulfilling our requirement for an acceptable approximate triples theory. 

The prerequisites for high accuracy are coupled-cluster calculations with the inclusion of connected triples [e.g., CCSD(T)], either in conjunction with R12 theory or with correlation-consistent basis sets of at least quadruple-zeta quality followed by extrapolation. In addition, harmonic vibrational corrections must always be included. For small molecules, such as those contained in Table 1.11, such calculations have errors of the order of a few kJ/mol. To reduce the error below 1 kJ/mol, connected quadruples must be taken into account, together with anhar-monic vibrational and first-order relativistic corrections. In practice, the approximate treatment of connected triples in the CCSD(T) model introduces an error (relative to CCSDT) that often tends to cancel the... 

The CCS, CC2, CCSD, CC3 hierarchy has been designed specially for the calculation of frequency-dependent properties. In this hierarchy, a systematic improvement in the description of the dynamic electron correlation is obtained at each level. For example, comparing CCS, CC2, CCSD, CC3 with FCI singlet and triplet excitation energies showed that the errors decreased by about a factor 3 at each level in the coupled cluster hierarchy [18]. The CC3 error was as small as 0.016 eV and the accuracy of the CC3 excitation energies was comparable to the one of the CCSDT model [18]. 

Urban M, Noga J, Cole SJ, Bartlett RJ (1985) Towards a full CCSDT model for electron correlation. J Chem Phys 83 4041 1046... 

FCI energies of the ground state and several excited states (3 12+, 2 ll, and 2 2A states) were obtained by Olsen et al. [66] in 1989 using a DZP basis set augmented with diffuse functions. These data have been used as tests for a wide variety of EOM/FR-CC methods, including CCSD [20, 24], CCSDT-la [44], CC3 [45], CCSDT-3 [46], and CCSDt [52], Later Hirata et al. [49] obtained FCI results with the 6-31G basis set. Shiozaki et al. [57] have obtained FCI results with the augmented correlation-consistent polarized valence double-zeta (cc-pVDZ) and valence triple-zeta (aug-cc-pVTZ) sets. 

D. Feller, J.A. Sordo, A CCSDT study of the effects of higher order correlation on spectroscopic constants. 1. First row diatomic hydrides, /. Chem. Phys. 112 (13) (2000) 5604-5610. 

The exponential ansatz given in Eq. [31] is one of the central equations of coupled cluster theory. The exponentiated cluster operator, T, when applied to the reference determinant, produces a new wavefunction containing cluster functions, each of which correlates the motion of electrons within specific orbitals. If T includes contributions from all possible orbital groupings for the N-electron system (that is, T, T2, . , T ), then the exact wavefunction within the given one-electron basis may be obtained from the reference function. The cluster operators, T , are frequently referred to as excitation operators, since the determinants they produce from fl>o resemble excited states in Hartree-Fock theory. Truncation of the cluster operator at specific substi-tution/excitation levels leads to a hierarchy of coupled cluster techniques (e.g., T = Ti + f 2 CCSD T T + T2 + —> CCSDT, etc., where S, D, and... 

M. Urban,. Noga, S. J. Cole, and R. J. Bartlett,/. Chem. Phys., 83,4041 (1985). Towards a Full CCSDT Model for Electron Correlation. 

CCSDT Model for Electron Correlation. CCSDT-n Models. 

The variation at the CCSD(T) level is shown in Table 11.3, with the change relative to-the MP2 level given as A values. Additional correlation with the CCSD(T) method gives only small changes relative to the MP2 level, and the effect of higher-order correlation diminishes as the basis set is. enlarged. For HoO the CrSD(T) method is virtually indistingable from CCSDT. ... 

The equations for the cluster coefficients and the correlated energy in a CCSDT model were given in operator form in Section III [cf. Eqs. (80)— (83)] this form is, of course, not amenable to calculations. In Section V the time-independent techniques discussed in Section IV are applied to evaluate the requisite matrix elements in terms of cluster coefficients and one- and two-electron integrals over the spin-orbital basis. 

The expressions for the matrix elements obtained in the preceding section, together with Eqs. (80)-(83), enable us to write implicit equations determining the cluster coefficients and the correlated energy in terms of the cluster coefficients and the one- and two-electron integrals over the spin-orbital basis. We may write Eq. (80), the projection of the Schro-dinger equation for the CCSDT wave function on the singly excited space, as... 

Following the pair correlation approach of Sinanoglu,4 Cizek2 introduced the coupled-pair many-electron theory (CPMET) method, which takes into account only double excitation clusters T2. In the present paper we prefer our more systematic nomenclature for different versions of the CC method, consistently used in our previous papers. Thus the original Cizek approach will be denoted CCD (CC doubles), while its linearized version will be denoted as LCCD. By including in the CC equations single excitation clusters T, we arrive at the CCSD method, exploited in a series of papers by Bartlett and co-workers.9-11 We will also consider the linearized version of the CCSD method, LCCSD,15 the full CCSDT model that includes effects of triple excitation clusters T3, and the CCSDTQ model that also considers T. ... 

Table 17 summarizes tire results of a benchmark study for the convergence of Atj for neon with the correlation treatment in a series of CC methods from [39], Whereas CCSf) yields results still ca. 3% too low (orbital-relaxed) or 1.4% too high (orbital-unrelaxed), the CCSDT results differs from the FCI limit by only 0.002 a.u. or a0.1%. Thus CCSDT provides for the Cotton-Mouton effect of Ne results which aie converged within approximately 0.1%. 

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