Fragment-Based Excitonic Coupled-Cluster Theory for Large Chemical Systems

Abstract

Accurate energetic modeling of large molecular systems is always desired by chemists. For example, ligand-protein binding simulations and enzymatic catalysis studies all involve with a small energy difference. The energetic accuracy depends largely on a proper handling of electronic correlations. Molecular mechanics (MM) methods deliver a parameterized Newtonian treatment to these problems. They show great capability in handling large calculations but give only qualitatively good results. Quantum mechanics (QM) methods solve Schrödinger equations and exhibit much better energy accuracy, though the computational cost can be prohibitive if directly applied to very large systems.

Fragment-based methods have been developed to decompose large QM calculations into fragment calculations. However, most current schemes use a self- consistent field (SCF) method on fragments, in which no electronic correlation is accounted for. The super-system energy is computed as a sum of fragment energies plus two-body corrections and, possibly, three-body corrections (a "body" is a fragment). Higher order corrections can be added.

Nevertheless, many problems require the treatment of high order electronic correlations. The coupled-cluster (CC) theory is the state-of-the-art QM method for handling electronic correlations. The CC wavefunction contains correlated excitations up to a given truncated level and coincidental excitations for all possible electronic excitations. It is a brilliant way of including more electronic correlations while maintaining a low-order scaling. In the proposed excitonic coupled-cluster (X-CC) theory, substantial modifications have been made to allow CC algorithms to act on the collective coordinates of fragment fluctuations to obtain super-system energy.

The X-CC theory is designed to achieve accurate energetic modeling results for large chemical systems with much improved affordability and systematic improvability. The test system used in this work is a chain of beryllium atoms. A 30-fragment X-CCSD(2) calculation delivered matching accuracy with traditional CCSD method. An X-CCSD(2) calculation on a chain of 100 bonded fragments finished in 7 hours on a single 2.2 GHz CPU core. The X-CC scheme also demonstrates the ability in handling charge transfer problems. Due to the use of fluctuation basis in the test cases, the excitonic algorithms can be easily generalized to inhomogeneous systems. This will be investigated in future work.