Coupled-cluster doubles theory

The ab initio HF calculations reported below have been performed with the GAUSSIAN 76 [26] program package. The atomic basis sets applied are a minimal (STO-3G [26]) one, a split valence (6-31G [26]) one, a split-valence one plus a set of five d-functions on carbon (6-31G [26]), and one with an additional set of p-functions on hydrogen (6-31G [26]). The correlation energy has been computed using Mpller-Plesset many body perturbation theory of second order (MP2) [27], the linear approximation of Coupled Cluster Doubles theory (L-CCD)... 

Harmonic and cubic force fields of Sis were calculated using coupled-cluster (CC) theory (25) and a correlation-consistent basis set. Specifically, the CC singles and doubles (CCSD) method (24) was used in conjunction with the cc-pVTZ basis set (25) developed by Dunning and co-workers. The force... 

Noga, J., Kedzuch, S., Simunek, J., Ten-no, S. Explicitly correlated coupled cluster F12 theory with single and double excitations. J. Chem. Phys. 2008, 128, 174103. 

The single-reference coupled cluster (CC) theory [1-5] has become a standard computational tool for studying ground-state molecular properties [6-10]. The basic approximations, such as CCSD (coupled cluster singles and doubles approach) [11-15], and the noniterative CCSD[T] [16,17] and CCSD(T) [18] methods, in which the cleverly designed corrections due to... 

In spite of the method s present utility and popularity, the quantum chemical community was slow to accept coupled cluster theory, perhaps because the earliest researchers in the field used elegant but unfamiliar mathematical tools such as Feynman-like diagrams and second quantization to derive working equations. Nearly 10 years after the essential contributions of Paldus and Cizek, Hurley presented a re-derivation of the coupled cluster doubles (CCD) equa-... 

Various approximations of Eq. (6), the exact wave function in the coupled-cluster formalism, have been discussed in the chemical literature. In particular, Cizek s coupled-pair many-electron theory (CPMET),5 also referred to as coupled-cluster doubles (CCD) by Bartlett,8 has re-... 

Another possibility is to increase the order of PT while restricting the excitation level of the intervening intermediate states. This is most easily done when the excitations are limited to doubles, yielding the rath order MBPT with doubles, or DMBPT(n). In fact, in this case, the summation can be carried out to infinite order, yielding the DMBPT(oo) method [27]. However, this result can be easily seen to be equivalent to the linear version of coupled-cluster (CC) theory that is restricted to two-body amplitudes, namely, to the L-CPMET (linear coupled-pair many-electron theory) or, more succinctly, to L-CCD (linear CC with doubles) in current terminology. 

Among the methods which guarantee adequate inclusion of the electron correlation effects, the coupled cluster (CC) theory is one of the most effective [4, 5, 33, 39, 59, 65, 79]. The first CC calculations of molecular properties related to the interaction of the molecule with the electric field date back to the first years of using the CC theory in molecular calculations [6, 14], However, the CC calculations, even those performed with the standard approach which includes single and double excitations from the reference wave function (CCSD), involve significant computational cost. 

As the next step in handling the correlation problem in larger molecules, the coupled-cluster doubles (CCD), also called coupled-pair many-electron theory (CPMET), introduced into the electronic correlation problem by Cizek, was first applied to smaller molecules and then to the nucleotide bases using localized orbitals. 

Coupled cluster response theory, 27 Coupled cluster single-double (CCSD), 10 C-PCM method, viii... 

QCISD(T) = quadratic Cl including single, double, and triple excitations, UCCD(ST) = coupled-cluster doubles method based on the unrestricted Hartree-Fock method and corrected for single and triple replacements, MC SCF = multiconfiguration SCF, MRD Cl = multireference singles and doubles Cl, MBPT= many-body perturbation theory, SD Cl = singles and doubles Cl. 

Abstract Recent extensions of the coupled-cluster (CC) theory to molecular solutes described with the Polarizable Continuum Model (PCM) are summarized. The recent advances covered in this review regard (1) the analytical gradients for the PCM-CC theory at the single and double excitation level and (2) the analytical gradients for the PCM-EOM-CC theory at the single and double excitation level for the descriptions of the excited state properties of molecular solutes. As coupled-cluster is the top level that quantum mechanical (QM) calculations on molecules can presently be performed, and the PCM model gives an effective description of the solute-solvent interaction, these computational advances can be profitably used to study molecular processes in condensed phase, where both the accuracy of the QM descriptions and the influence of the environment play a critical role. 

In the following, the theory of Kutzelnigg s linear R12 functions shall be presented and analyzed in the framework of the coupled-cluster doubles (CCD) method, To illustrate the ideas and approximations employed in the linear R12 methods, it is sufficient to consider the CCD model, as the corresponding CCD-R12 theory exhibits all properties of the R12 theories. It is a relatively simple matter to include singles (CCSD) or even triples (for example in the CCSD(T) method), and CI-R12-type wave functions or MPn-R12 energies require essentially the same computational procedures as the CCD-R12 approach. 

In previous publications we have described the application of the linked-diagram-based methods, many-body perturbation theory and coupled-cluster double-excitation theory, for the computation of potential energy surfaces, electronic excitation energies, and molecular properties. Here we report details of potential energy surface features for two species commonly found in flames formyl radical, HCO, and hydrogen nitroxide, HNO. In particular, we... 

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