Improved constrained optimization method for reaction-path determination in the generalized hybrid orbital quantum mechanical/molecular mechanical calculations

Abstract

The nudged elastic band (NEB) and string methods are widely used to obtain the reaction path of chemical reactions and phase transitions. In these methods, however, it is difficult to define an accurate Lagrangian to generate the conservative forces. On the other hand, the constrained optimization with locally updated planes (CO-LUP) scheme defines target function properly and suitable for micro-iteration optimizations in quantum mechanical/molecular mechanical (QM/MM) systems, which uses the efficient second order QM optimization. However, the method does have problems of inaccurate estimation of reactions and inappropriate accumulation of images around the energy minimum. We introduce three modifications into the CO-LUP scheme to overcome these problems: (1) An improved tangent estimation of the reaction path, which is used in the NEB method, (2) redistribution of images using an energy-weighted interpolation before updating local tangents, and (3) reduction of the number of constraints, in particular translation/rotation constraints, for improved convergence. First, we test the method on the isomerization of alanine dipeptide without QM/MM calculation, showing that the method is comparable to the string method both in accuracy and efficiency. Next, we apply the method for defining the reaction paths of the rearrangement reaction catalyzed by chorismate mutase (CM) and of the phosphoryl transfer reaction catalyzed by cAMP-dependent protein kinase (PKA) using generalized hybrid orbital QM/MM calculations. The reaction energy barrier of CM is in high agreement with the experimental value. The path of PKA reveals that the enzyme reaction is associative and there is a late transfer of the substrate proton to Asp 166, which is in agreement with the recently published result using the NEB method.

Single‐ended transition state finding with the growing string method

“…TS finding methods typically fall into one of two categories: single‐ended and double‐ended methods . Single‐ended methods operate on a single chemical structure and attempt to locate a TS by systematically adjusting the structure until it reaches the TS.…”

Reliable and efficient reaction path and transition state finding for surface reactions with the growing string method

“…The algorithms designed to locate TSs and RPs are usually classified as single‐ended or double‐ended . Single‐ended methods start from a single initial state and refine it systematically to locate a TS.…”

Projected Hybrid Orbitals: A General QM/MM Method

“… 20 , 21 , 30 , 31 , 46 Ten-no and co-workers further extended the GHO method with a restricted hybridization (RH) scheme, 47 and used it to study excited states, 51 NMR magnetic shielding tenors, 52 circular dichroism spectra, 53 and reaction paths. 54 A main difference between the LSCF and GHO method, however, is the way the boundary atom is recognized in SCF optimizations; three bonds from the boundary atoms are optimized in the LSCF method, whereas just one covalent bond is part of the SCF procedure. Thus, the error caused by the boundary approximation on the QM region may be minimized in the GHO method.…”