Natural Linear-Scaled Coupled-Cluster Theory with Local Transferable Triple Excitations: Applications to Peptides

The natural linear-scaled coupled-cluster (NLSCC) method (Flocke, N.; Bartlett, R. J. J. Chem. Phys. 2004, 121, 10935) is extended to include approximate triple excitations via a coupled-cluster with single, double, and triple excitation method (CCSDT-3). The triples contribution can potentially be embedded in a larger singles and doubles region. NLSCC exploits the extensivity of the CC wave function to represent it in terms of transferable natural localized molecular orbitals (NLMOs) or functional groups thereof that are obtained from small quantum mechanical (QM) regions. Both occupied and virtual NLMOs are local because they derive from the single-particle density matrix. Noncanonical triples amplitudes are avoided by applying the unitary localization matrix to the canonical CC wave function for a QM region. A generalized NLMO code interfaced to the ACES II quantum chemistry software package provides NLMOs for the relevant number of atoms in a given functional group. Applications include linear polyglycine and the pentapeptide met-enkephalin, which was chosen as a more realistic three-dimensional system with nontrivial side chains. The results show that the triples contributions are quite large for aromatic bonds suggesting an interesting active space method for triples in which different bonds require different excitation levels. The NLSCC approach recovers a very large percentage (>99%) of the CCSD or CCSDT-3 correlation energy. Highly accurate electronic structure methods, such as coupledcluster (CC) and configuration interaction (CI), are troubled by the task of including all possible permutations of one, two, three, etc. electrons among a large number of single-particle basis functions. The excitation operator, T, which accomplishes this is oftentimes truncated after the two-particle piece, T ) T1 + T2 + T3 + ... ≈ T1 + T2, where TN is an N-particle excitation operator, leading to singly (S) and doubly (D) excited determinants. Both the CCSD and CISD methods scale as O(o 2 V 4 ), where o and V are respectively the number of occupied and virtual orbitals, but only the exponential ansatz, unique to CC theory, additionally includes disconnected parts of triple and quadruple excitations. These disconnected triple and quadruple excitations, like T1T2 and T2T2, respectively, make truncated CC converge to the full CI (FCI) much more quickly than truncated CI, thus making CC the method of choice for high-level applications to medium-sized molecules. The remaining pieces of the triple excitation manifold are said to be connected and may be required for ≈1 kcal mol -1 accuracy in the energy and similar accuracy in other properties. The necessity of connected triples is understood from an order-by-order comparison with many-body perturbation theory (MBPT) in which it is found that the triply excited manifold is dominated by connected T3 as opposed to T1T2 or T1 . This is in contrast to the dominant term in the quadruply excited manifold which is disconnected T2 as opposed to connected T4. These connected contributions are not obtained until explicit inclusion of T3 as in CCSD(T), CCSDT-x (x ) 1a, 1b, 2, 3), or CCSDT. These methods scale as noniterative O(o 3 V 4 ), iterative O(o 3 V 4 ), and iterative O(o 3 V 5 ), respectively, making these CC methods, without modification, prohibitive for large molecules. The exponential ansatz used in CC theory makes it a size-extensive method, which is a necessary condition for a system with a large number of electrons. For large molecules, a size-inextensive linear ansatz, for example as in truncated CI, would give a vanishing correlation energy