Algorithm for analytic nuclear energy gradients of state averaged DMRG-CASSCF theory with newly derived coupled-perturbed equations.

We present an algorithm for evaluating analytic nuclear energy gradients of the state-averaged density matrix renormalization group complete-active-space self-consistent field (SA-DMRG-CASSCF) theory based on the newly derived coupled-perturbed (CP) DMRG-CASSCF equations. The Lagrangian for the conventional SA-CASSCF analytic gradient theory is extended to the SA-DMRG-CASSCF variant that can fully consider a whole set of constraints on the parameters of multi-root canonical matrix product states formed at all the DMRG block configurations. An efficient algorithm to solve the CP-DMRG-CASSCF equations for determining the multipliers was developed. The complexity of the resultant analytic gradient algorithm is overall the same as that of the unperturbed SA-DMRG-CASSCF algorithm. In addition, a reduced-scaling approach was developed to directly compute the SA reduced density matrices (SA-RDMs) and their perturbed ones without calculating separate state-specific RDMs. As part of our implementation scheme, we neglect the term associated with the constraint on the active orbitals in terms of the active-active rotation in the Lagrangian. Thus, errors from the true analytic gradients may be caused in this scheme. The proposed gradient algorithm was tested with the spin-adapted implementation by checking how accurately the computed analytic energy gradients reproduce numerical gradients of the SA-DMRG-CASSCF energies using a common number of renormalized bases. The illustrative applications show that the errors are sufficiently small when using a typical number of the renormalized bases, which is required to attain adequate accuracy in DMRG's total energies.

A novel ring-shaped reaction pathway with interconvertible intermediates in chitinase A as revealed by QM/MM simulation combined with a one-dimensional projection technique.

Substrate-assisted catalysis (SAC), a mechanism of chitin hydrolysis by chitinases belonging to the glycoside hydrolase family 18 (GH18), has been studied experimentally and theoretically for several decades. However, the detailed reaction mechanism in chitinase A (ChiA) remains unclear at the atomic level. In this study, we investigated glycosylation, the first step of SAC, of ChiA obtained from Serratia marcescens (SmChiA), using QM/MM simulations combined with a one-dimensional projection (ODP) technique, which enabled us to explore the multi-dimensional free energy surface efficiently. The results showed that the reaction proceeds via a novel ring-shaped concerted reaction pathway with interconvertible intermediates, viz. oxazolinium ion and oxazoline, which have not been fully identified in previous studies. We also compared this chitin hydrolysis mechanism in SmChiA with that in SmChiB reported previously. The computational protocol developed in this study could also be applicable for elucidating complicated reaction mechanisms in other enzymes.