Samuel J. Cole

Towards a full CCSDT model for electron correlation

Coupled cluster models for electron correlation which include the effects of single, double, and triple excitation operators are analyzed. An alternate version of the approximate CCSDT‐1 method is implemented. In this version, the full CCSDT cluster operator eT1+T2+T3 is preserved in the creation of single and double excitation coefficients, but in calculation of triple excitation coefficients only the T2 operator is used. We also present a theoretical analysis of the simplest improvement for the evaluation of the contribution of triples beyond that obtained with fourth‐order MBPT. In this approximation, an MBPT(4)‐like calculation of the triples energy is evaluated with converged CCSD T2 coefficients. This is found to offer a good approximation to the converged CCSDT‐1 results.

A theoretical study of the water dimer interaction

We have performed a study of the water dimer interaction using larger basis sets and higher levels of theory than have been previously applied to this system. For the minimum geometry we have used spdf basis sets containing up to 212 orbitals. Our most accurate SCF interaction energy for the minimum is −3.73±0.05 kcal/mol. We have shown that this energy can be reproduced to within 0.1 kcal/mol using much smaller basis sets containing proper (diffuse) exponents. Accounting for the basis set superposition error is shown to be essential. We computed the dispersion energy with neglect of the intramolecular correlation using basis sets of various sizes. The best value obtained in a large spdf basis set with exponents which optimize this quantity is −1.93 kcal/mol and it is expected to be accurate to 0.1 kcal/mol or better. Using some of these basis sets we have performed supermolecular many‐body perturbation theory (MBPT) and coupled‐cluster (CC) calculations including triple excitations. We have shown that if...

Comparison of MBPT and coupled cluster methods with full CI. II. Polarized basis sets

Results from many‐body perturbation theory (MBPT) and coupled‐cluster (CC) calculations relative to a single reference function are compared with recent full CI results for Ne, F, F−, HF, H2O, and NH2. MBPT results include second through fourth order, while CC results are reported for the CCSD, CCSD+T(CCSD), and CCSDT‐1 methods. The basis sets used are of double‐zeta plus polarization quality or better. HF, H2O, and NH2 are studied at several displaced geometries. Agreement to within 0.3 kcal/mol is found between infinite order CCSDT‐1 results and full CI at the equilibrium geometries, while finite‐order MBPT(4) is still quite good. For FH, CCSDT‐1 relative to an incorrectly separating RHF reference is still accurately described all the way to the separated atom limit. At 2.0 Re, only the CCSDT‐1 method obtains satisfactory agreement with full CI, having an average error of 3.6 kcal/mol, while MBPT(4) has an average error of 13.1 kcal/mol.

The quartic force field of H2O determined by many‐body methods. II. Effects of triple excitations

Ab initio coupled cluster and many‐body perturbation theory methods that include triple excitation effects are applied to the determination of the quartic force field of the water molecule using an extended Slater‐type basis set. Predictions of fundamental, overtone, and combination vibrational frequencies, rotational constants, and vibration–rotation coupling constants are reported for H2O and its isotopomers. The best predicted harmonic frequencies for the stretching modes of H2O are accurate to 3 cm−1, while the bending mode has an error of 28 cm−1. The mean absolute error for all frequencies reached by two quanta is 0.6%, while the anharmonic constants xi j have a mean absolute error of less than 3%. The important role of triple excitation effects in the surface determination is discussed, and is compared with the effects of quadruple excitations.

Singlet-triplet energy gap in methylene using many-body methods☆

Abstract Many-body methods are applied to the singlet-triplet energy gap in: CH 2 in a variety of basis sets. The best result obtained with a coupled-cluster method that includes effects of triple excitations is 10.1 kcal/mol in a basis set of 74 contracted Gaussian orbitals. The best full fourth-order MBPT result is 11.5 kcal/mol, demonstrating a residual infinite-order effect of 1.4 kcal/mol.

Correlated calculation of the interaction in the nitromethane dimer

The interaction energy of the nitromethane dimer at several separations between the monomers was calculated using fourth‐order many‐body perturbation theory (MBPT), with single, double, and quadruple (SDQ) excitations included. The self‐consistent field (SCF) counterpoise (CP) correction, and second‐order dispersion energy were also computed. A double‐zeta plus polarization basis was used. The monomers were oriented so that a hydrogen atom on each monomer could form a hydrogen bond with an oxygen on the other monomer. An interaction energy of 3.57 and 5.04 kcal/mol was found at the SCF and SDQ‐MBPT(4) levels of theory, respectively. The CP‐corrected SCF energy added to the second‐order dispersion energy gives an interaction energy of 5.62 kcal/mol.