A study of Be2 with many-body perturbation theory and a coupled-cluster method including triple excitations

Abstract

The unusual potential energy curve for the 1∑+g ground state of Be2 is investigated using many-body perturbation theory (MBPT) and coupled-cluster (CC) methods. The curve, which has a ∼2 kcal/mol inner minimum at ∼2.6Å and a van der Waals minimum at ∼5.0 Å, is very difficult to describe accurately with even high-level ab initio correlated methods. To resolve uncertainties in previous MBPT/CC studies, we have generalized CC theory to include effects of triple excitations. The present calculations are compared with recent full CI results to assess the relative importance of different contributions of electron correlation. MBPT (4) is found to be qualitatively correct, but to slightly exceed the correct full CI binding energy, while CC theory even with triple excitations, has no inner minimum. The latter follows from CC theory being exact for separated Be atoms (with frozen core) but to have a 1% correlation energy error in the binding region. Yet this 1% accounts for the ∼2 kcal/mol inner well. The possibility of the remaining 1% arising from connected quadruple excitations T4 is discussed.

The CC3 model: An iterative coupled cluster approach including connected triples

“…In the first approach, simplifications are introduced in the CCSDT amplitudes equations, and iterative methods are used to solve the amplitude equations. [4][5][6] In the other and more popular approach, the lowest-order perturbation energy contributions from connected triples are added to the CCSD energy. [6][7][8][9] The CCSD energy is correct through fourth order except for one fourth-order contribution from connected triples.…”

Multireference coupled-cluster method using a single-reference formalism

“…The electronic non-relativistic hamiltonian, in coordinate representation, written in terms of atomic units is; (17) where the indices i and j are over the N electrons, the index A is over the M nuclei, ZA is the charge on the A'th nucleus and rij is the radial distance between the i'th electron and the j'th electron. Combining the 25 first two terms into a one electron operator, f, this can be written in second quantized formalism as;…”

A Critical Assessment of Coupled Cluster Method in Quantum Chemistry

“…The foregoing account of T 3 clusters corresponds to CCSDT-1 [241] or CCSDT-la [242], which are still n7 procedures (for each iteration). When the h(')(1,3) term is also accounted for, the method is referred to as CCSDT-lb [17,242].…”