Developments in biochemistry and materials sciences have led to increasing interest in the reactivity of large chemical systems, presenting theoretical and computational challenges that can be addressed with hybrid methods such as ONIOM. Here, we show that the diagonalized ONIOM Hessian can be partitioned/deconstructed into contributions from the individual subcalculations-indicating the curvature of their potential energy surfaces (PESs)-without increasing the computational cost. The resulting pseudofrequencies have particular application in the study of transition structures and higher-order saddle points with ONIOM, where we find that an imaginary frequency may result from combining subcalculations for which the corresponding vibrational frequencies are all real. Two cycloaddition reactions, including functionalization of a 150 atom (5,5) single-walled carbon nanotube, demonstrate how this analysis of pseudofrequencies allows identification of critical points where further exploratory work should be carried out to ensure that the ONIOM PES correctly approximates the target.

We investigate the performance of Our own N-layered Integrated molecular Orbital and molecular Mechanics (ONIOM) hybrid computational method applied to Diels–Alder reactions of bromo-2(H)-pyran-2-ones, combining the B3LYP/6–31G(d) method with a variety of low-level methods. We show that ONIOM is able to reproduce full B3LYP calculations, including the prediction of the stereoselectivity, which requires accurate potentials. We focus on the various ways in which the performance and potential errors of ONIOM can be analyzed, and show that the best method combination depends on the property one is interested in.

We demonstrate that the ONIOM method can be used to optimize a conical intersection between the ground and first excited-state potential energy surfaces of previtamin D (precalciferol), with excitation localized in a small part of the molecule: the hexatriene chromophore. These calculations were up to 100 times faster with little loss of accuracy compared to a full non-ONIOM Target calculation. The most accurate ONIOM method combination was CASSCF/4-31G//ROHF/STO-3G(Triplet): in comparison to the Target (CASSCF/4-31G), bond lengths and angles in the hexatriene model region were calculated to within 0.02 A and 0.7 degrees , respectively, and the energy difference between the conical intersection and nearest associated S 1 minimum to within 0.5 kcal x mol (-1). All of the low-level methods selected produced accurate geometries, including the UFF molecular mechanics and AM1 semiempirical methods, suggesting a cheap and efficient way of initially optimizing conical intersections geometries. Furthermore, ONIOM allows for an assessment of the localization of excited states, providing some fundamental insight into the physical processes involved.

In this article, we compare and contrast the RASSCF, ONIOM and MMVB electronic structure methods for calculating relaxation paths on potential energy surfaces of the excited states of large molecules, and for locating any resulting conical intersections at which nonadiabatic decay can take place. Each method is treated here as an approximation to CASSCF, which we choose as our reference level of theory, but which becomes prohibitively expensive computationally for large molecules. Both MMVB and ONIOM are hybrid computational methods – combining different levels of theory in an energy plus derivatives calculation at a particular molecular geometry – but they differ fundamentally in that MMVB is a hybrid-atom method, whereas ONIOM is a hybrid-molecule method. We explain this distinction through four representative applications: the photostability of pyracylene (studied with CASSCF, RASSCF, MMVB); large geometry changes in the singlet excited states of triangulene (studied with MMVB); a model for interstitial nickel defects in a synthetic diamond lattice (studied with ONIOM CAS:UFF); and the photochemical [4 + 4] cycloaddition of cyclohexadiene to naphthalene (studied with ONIOM CAS:MMVB). We show that each method is more appropriate for a particular type of photochemical problem. This article is part perspective, part review, and contains new results for three multi-state or photoinduced processes in complex systems.