Coupled Cluster Singles And Doubles Method Research Articles

The integral-direct coupled cluster singles and doubles model

An efficient and highly vectorized implementation of the coupled cluster singles and doubles (CCSD) model using a direct atomic integral technique is presented. The minimal number of n6 processes has been implemented for the most time consuming terms and point group symmetry is used to further reduce operation counts and memory requirements. The significantly increased application range of the CCSD method is illustrated with sample calculations on several systems with more than 500 basis functions. Furthermore, we present the basic trends of an open ended algorithm and discuss the use of integral prescreening.

First row benchmark tests of the parametrized configuration interaction with parameter X (PCI-X) scheme

A recently suggested scheme termed parametrized configuration interaction with parameter X (PCI-X) for scaling the correlation energy has been applied on a benchmark test consisting of 32 first row molecules. Several different methods like Mo/ller–Plesset second-order perturbation theory (MP2), modified coupled pair functional method (MCPF), averaged coupled pair functional method (ACPF), coupled cluster singles and doubles (CCSD), and CCSD with a perturbational estimate of triple excitations [CCSD(T)] have been tested using systematically chosen basis sets ranging from double zeta (DZ) to very large atomic natural orbital (ANO) sets containing several sets of d and f functions. For each method and basis set the scaling parameter is optimized. The scaling does in all cases lead to large, sometimes dramatic, improvements of the results. Typically, using a single reference state method like MCPF the average absolute deviation compared to experiments for the benchmark goes from an unscaled value of about 20 kcal/mol down to about 2 kcal/mol. For MCPF and similar methods no improvement of the results is obtained going beyond the DZ+polarization (DZP) level. Significant improvements due to scaling occurs even at the highest level using the CCSD(T) method and the largest basis set. For medium size basis sets the present scaling is far superior to the extrapolation schemes used in the Gaussian-1 and -2 (G1 and G2) theories.

Gauge-invariant calculation of nuclear magnetic shielding constants at the coupled–cluster singles and doubles level

The gauge-including atomic orbital (GIAO) method for the gauge-invariant calculation of nuclear magnetic shielding constants has been implemented at the coupled-cluster singles and doubles (CCSD) level. A brief description of the theory and its computational requirements is provided. Finally, the GIAO–CCSD method is applied to calculate nuclear shielding constants of N2O with two different basis sets, the larger of which contains 153 contracted Gaussian functions.

Coupled-cluster methods with noniterative triple excitations for restricted open-shell Hartree–Fock and other general single determinant reference functions. Energies and analytical gradients

A new, noniterative triples correction to the coupled-cluster singles and doubles (CCSD), method, for general single determinant reference functions is proposed and investigated numerically for various cases, including non-Hartree–Fock (non-HF) reference functions. It is correct through fourth-order of perturbation theory for non-HF references, and unlike other such methods, retains the usual invariance properties common to CC methods, while requiring only a single N7 step. In the canonical Hartree–Fock case, the method is equivalent to the usual CCSD(T) method, but now permits the use of restricted open-shell Hartree-Fock (ROHF) and quasirestricted Hartree–Fock (QRHF) reference determinants, along with many others. Comparisons with full configuration interaction (FCI) results are presented for CH2, CH2+, CH3, NH2, and SiH2. The paper also reports the derivation and initial computational implementation of analytical gradients for the ROHF-CCSD(T) method, which includes unrestricted Hartree–Fock (UHF) CCSD(T) and RHF-CCSD(T) as special cases. Applications of analytical gradients are presented for HOO, the CN radical, which is highly spin contaminated at the UHF level, and HCO, the latter with several large basis sets. With these developments of analytical gradients, these highly accurate generalized CCSD(T) methods can be widely applied.

Nuclear spin–spin coupling constants evaluated using many body methods

In nuclear spin–spin coupling constant determinations, correlation corrections to the Fermi contact term are significant. In this paper we report the coupling constants calculated for the HD and HF molecules obtained by the infinite-order coupled cluster singles and doubles (CCSD) methods and MBPT(4). These are in good agreement with the experimentally estimated value for the Fermi-contact term. In addition, it is well known that the coupled perturbed Hartree–Fock (CPHF) scheme fails for multiply bonded molecules because the closed shell Hartree–Fock solution is triplet unstable. A CCSD method using ordinary nonrelaxed SCF orbitals is presented in order to circumvent this problem, and illustrated by application to the C2H4 molecule. It is shown that CCSD results based upon ordinary SCF orbitals include effectively all the effect of orbital relaxation and reproduce the experimental values for most of the coupling constants. Unlike previous results, the 3J(H–H) constant is positive in agreement with experiment.