Generalized Internal Coordinates for Creative Exploration of Interatomic Geometries

We have implemented the concept of generalized internal coordinates (GICs) which can be applied to diverse molecular systems, allowing for the inclusion of nontraditional geometric parameters (other than regular bonds and angles) with no further implementation effort. The GICs can be generated automatically from initial connectivity information and/or by parsing the user-provided input. They can be customized for specific purposes using symbolic algebra and basic mathematical operations (such as +, -, ×, ÷, sqrt, etc.). The analytical first- and second-order derivatives with respect to Cartesian coordinates are built automatically to provide for the seamless integration of such GICs into geometry optimization, potential energy surface searching and scans, and normal-mode analysis in terms of internal coordinates, all without further coding. Our algorithm allows the user to create compound internal coordinates that are functions of other coordinates, as well as special-purpose coordinates for specific classes of problems. The GICs can be constrained to specific values or to an interval of values, or they can be conditionally constrained based on the values of other coordinates. Several examples are provided to demonstrate both the efficacy of GICs and the range of new possibilities that they create.