Rational Function Optimization

The Rational Function Optimization (RFO) expands the function in terms of a rational approximation instead of a straight second-order Taylor series (eq. (14.3)). 

In the Partitioned Rational Function Optimization (P-RFO), two shift parameters are employed. 

Lowest Unoccupied Molecular Orbital (MRCI) methods, 122 Partitioned Rational Function Optimization Quadmpole moment, 236 ... 

A. Heyden, A. T. Bell, and F. J. Keil, Efficient methods for finding transition states in chemical reactions comparison of improved dimer method and partitioned rational function optimization method, Journal of Chemical Physics, vol. 123, p. 224101, 2005. 

Ratiaal functiaal ptimizatin. The rational functional optimization or RFO (Baneijee et al. 1985 Baker 1986, 1987) is another method that develops from the Newton-Raphson procedure. Essentially, Equation (47) is rearranged and modified into a rational functional ... 

The shift parameter can be used to ensure that the optimization proceeds downhill even if the Hessian has negative eigenvalues. In addition, it can be chosen such that the step size is lower or equal to a predefined threshold. Popular methods using a shift parameter are the rational function optimization (RFO) [48] and Trust Radius (TR) methods [49, 50]. A finer control on the step size and direction can be achieved using an approximate line search method, which attempts to fit a polynomial function to the energies and gradients of the best previous points [51]. 

The principal optimization algorithm in PQS, both for minima and transition states, is the eigenvector following (EF) algorithm developed in 1986 (Baker 1986). It is based on the Rational Functional Optimization (RFO) approach of Simons and coworkers (Banerjee et al. 1985) which was found at the time to provide the best recipe for determining the shift parameter, A. In this approach, the energy on the PES following a step h is written as (see O Eq. 10.1) ... 

BFGS = Broyden - Fletcher - Goldfarb - Shanno DFP = Davidson-Fletcher-Powell EF = eigenvector following GDIIS = geometry optimization by direct inversion of the iterative subspace LST = linear synchronous transit QST = quadratic synchronous transit RFO = rational function optimization. 

The rational function optimization (RFO) method of controlling the step size involves minimizing a rational polynomial approximation of the surface ... 

CPR = conjugate peak refinement GDIIS = geometry direct inversion in the iterative subspace GE = gradient extremal LST = linear synchronous transit LTP = line then plane LUP = locally updated planes NR = Newton-Raph-son P-RFO = partitioned rational function optimization QA = quadratic approximation QST = quadratic synchronous transit SPW = self-penalty walk STQN = synchronous transit-guided quasi-Newton TRIM = trust radius image minimization TS = transition structure. 

In the partitioned rational function optimization (P-RFO) the energy is approximated by a rational function instead of a second-order Taylor series ... 

Rational Function Optimization (RFO), 320 Rayleigh-Schrodinger perturbation theory,... 

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