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.

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