CLQA method

The approximate third energy derivatives calculated as in Eq (9) from successive force constants along the path can then be used to augment the LQA step. The result is called the corrected LQA (CLQA) method [7]. 

The CLQA method for determining the MEP has been compared to the LQA method, the Euler method, and the quadratic and cubic Taylor series methods on an ab initio MCSCF potential energy surface for the reaction. 

Neither the CLQA method nor the higher order implicit algorithms suggested by Gonzalez and Schlegel were included in this study. 

Sun and Ruedenberg obtained improved performance by using 3c, as the midpoint of the integration range rather than the start. Page and Mclver also developed the CLQA method, a correction to the LQA method involving a component of the third derivatives. "... 

The LQA, CLQA, and GS methods yield the exact tangent and curvature vectors along the path in the limit of infinitesimal step size, whereas the first-order methods reproduce only the tangent. The GS and CLQA methods also give the correct curvature vector at the transition structure, but the LQA method does not. 

Fourth-order Runge-Kutta and various predictor-corrector methods have been used successfully for reaction path following, especially on analytical potential energy surfaces. Page and Mclver have extended the LQA and CLQA methods... 

CLQA = corrected local quadratic approximation DDRP = dynamically defined reaction path DRP = dynamic reaction path ES = Euler stabilization method GS = Gonzalez and Schlegel method IMK = Ishida-Morokuma-Kormomicld method LQA = local quadratic approximation MB = Miillar-Brown method MEP = minimum energy path ODE = ordinary differential equations SDRP = steepest descent reaction path VRl = valley-ridge inflection. 

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