This section describes one of the most important features of any quantum chemical software package; locating equilibrium geometries and transition structures of molecules. In DALTON this is done using either second-order trust-region optimizations [22] (energies, gradients and Hessians are calculated) or a variety of first-order methods [23] (only energies and gradients are calculated). These methods have been implemented for Hartree-Fock, Density Functional Theory, MCSCF and various Coupled-Cluster wave functions. For other non-variational wave functions--such as CI--the program can only do first-order geometry optimizations using a numerically calculated gradient. This will be invoked automatically by the program in case of a non-variational wave function. Some comments connected to such geometry optimizations are collected in Sec. 7.3.
For historical reasons, DALTON actually contains two different modules for exploring potential energy surfaces: *WALK which is a pure second-order module and *OPTIMIZE which contains both first- and second-order methods. While there is a lot of overlap between the two modules, certain calculations can only be done using one or the other of the two. The main strength of *WALK is it's robustness, while *OPTIMIZE focuses more on speed and efficiency. For regular optimizations of minima and transition states, the recommended module is *OPTIMIZE.
One of the strengths of the DALTON program package is the stable algorithms for locating first-order transition states. As described below, this can done by one of three algorithms in *WALK: by trust-region second-order image surface minimization [24], by gradient extremal walks [25], or by following a specific mode [26] (all requiring the calculation of the Hessian at every point). These options will be discussed in more detail below. The *OPTIMIZE module also contains the stable second-order trust-region image surface minimization (using analytical or approximate Hessians), as well as a partitioned rational function method [27].
Another feature of the DALTON program system is the options for calculating essential information about the potential energy surface so that subsequent molecular dynamics analysis can be made. There are two options for doing this in the program: One can either follow an Intrinsic Reaction Coordinate (IRC) [25], or solve Newton's equations for the nuclei under the potential put up by the electrons [28]. Whereas the first option can be used for modeling the immediate surroundings of a molecular reaction path, the second will give a precise description of one molecular trajectory. Chemical reactions may thus be monitored in time from an initial set of starting conditions. The program will automatically generate a complete description of the energy distribution into internal energies and relative translational energies. By calculating a large number of trajectories, a more complete description of the chemical reaction may be obtained [29].
Please note that for geometry optimizations using the Self-Consistent Reaction Field model, certain restrictions apply, as discussed in Sec. 15.2.1.