Systematic determination of MCSCF equilibrium and transition structures and reaction paths

Abstract

The restricted step optimization algorithm is applied to potential energy surfaces calculated from multiconfiguration self-consistent-field wave functions. Equilibrium and transition-state geometries are determined by iteratively solving a set of level-shifted Newton–Raphson equations. At each geometry the molecular gradient and Hessian are calculated analytically, and a first-order prediction of the wave function at the next geometry is obtained by combining the geometrical derivatives of the wave function with the geometrical step vector. The usefulness of this prediction is discussed and illustrated by test calculations. The numerical accuracy which is required in the wave function and its geometrical derivatives in order to maintain quadratic convergence in the optimization of the molecular geometry is analyzed. It is demonstrated that the Newton–Raphson step vector and the wave function prediction may be determined without calculating the molecular Hessian explicitly. Sample calculations are carried out for the potential energy surfaces of diazene (N2H2) and the diazenyl radical (N2H). Equilibrium geometries are determined in less than five iterations and the optimization of transition states requires typically ten iterations.

The Dalton quantum chemistry program system

“…Minima can be determined using first-order (quasi-Newton) and second-order (Newton) methods 41. Dalton also has several first- and second-order methods for determining saddle points (transition states), including mode following42 and image minimization 43. Geometry optimizations may be performed for excited states44,45 and core-ionized states 46.…”

An efficient density-functional-theory force evaluation for large molecular systems

“…To summarize, DALTON geometry optimizations are carried out in redundant internal coordinates 41,43 using the quasi-Newton method with the Broyden-Fletcher-GoldfarbShanno ͑BFGS͒ updating formula 53 and the initial Hessian proposed by Lindh et al 54 The steps are determined by the level-shifted trust-region method. 55 At each iteration, the root-mean-square of the gradient, its maximum absolute element, the root-mean-square of the step vector, and its maximum absolute element in internal coordinates are determined; for a chosen threshold parameter ⑀ ͑typically 10 −4 ͒, convergence is declared if these four quantities are smaller than ⑀, 5⑀, 3⑀, and 15⑀, respectively.…”

Single-root multireference Brillouin-Wigner coupled-cluster theory. Rotational barrier of the N2H2 molecule

“…Needless to say, the true trans± cis isomerization path for the N 2 H 2 molecule is not via double bond rotation but as in-plane inversion or via partial dissociation into a N 2 H radical [45]. Using di erent theoretical methods it was found that the double bond rotation is not favourable isomerization pathway since the energy barrier about 67 kcal mol -1 is too high [45].…”