Nuclear hessians are routinely calculated in the course of quantum chemical analyses to verify the nature of stationary points (SP's) on potential energy surfaces. Hessians are also calculated as inputs to eigenvector-following transition state (TS) optimization methods. However, hessian costs typically scale one power of system size higher than gradients, and can be prohibitive for large systems. Though the full hessian is typically calculated for SP search and characterization, one usually needs only the lowest eigenmode(s). This can be accomplished by a finite difference realization of the Davidson method, which only requires first derivatives of the energy. Quasi-Newton methods such as the partitioned-rational function optimization (P-RFO) are ideally suited since the lowest eigenvectors of the P-RFO updated hessian constitute the initial subspace of the Davidson method for characterizing SP's. Depending on whether the optimizer is looking for a minimum or TS, the approach iteratively calculates the lowest one or two eigenvalues, respectively. Similarly, this technique can be combined with interpolation methods that determine TS guess structures, such as the freezing string method (FSM), to generate approximate hessian matrices in lieu of full hessians as input to P-RFO for TS optimization. Since the rate of convergence is approximately independent of system size, this approach achieves significant cost savings relative to the full hessian. Moreover, the combination of these techniques � FSM for TS guess generation, Davidson-based approximate hessian construction, P-RFO for TS search, and TS characterization with the Davidson method - permits automation of the process of TS search and characterization beginning with the reactant and product. The finite-difference Davidson method is therefore a viable alternative to full hessian calculation for SP characterization and search when analytical hessians are prohibitive or not available. Analogously, it can also be used to calculate the lowest eigenvalue of the electronic hessian for wavefunction stability analysis, particularly when exact hessians are not available.

Size�independent, hessian�free technique for stationary point search and characterization on a potential energy surface

248th National Meeting (2014)

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