Understanding the properties of electronically excited states is a challenging task that becomes increasingly important for numerous applications in chemistry, molecular physics, molecular biology, and materials science. A substantial impact is exerted by the fascinating progress in time-resolved spectroscopy, which leads to a strongly growing demand for theoretical methods to describe the characteristic features of excited states accurately. Whereas for electronic ground state problems of stable molecules the quantum chemical methodology is now so well developed that informed nonexperts can use it efficiently, the situation is entirely different concerning the investigation of excited states. This review is devoted to a specific class of approaches, usually denoted as multireference (MR) methods, the generality of which is needed for solving many spectroscopic or photodynamical problems. However, the understanding and proper application of these MR methods is often found to be difficult due to their complexity and their computational cost. The purpose of this review is to provide an overview of the most important facts about the different theoretical approaches available and to present by means of a collection of characteristic examples useful information, which can guide the reader in performing their own applications.

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calculations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of diabatization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully variational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on standard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview.

High level ab initio calculations ranging from coupled cluster methods including explicitly correlated approaches to standard second order Møller–Plesset theory using spin scaling (SOS-MP2) have been performed on sandwich and slipped parallel dimer structures of a series of quasi one-dimensional acenes and on two-dimensional sheets containing the pyrene to coronene series encircled with two layers of benzene rings. Sandwich (graphitic AA type) and slipped parallel (AB type) structures were considered and, within the given symmetry restrictions, full geometry optimizations were performed. Basis set superposition effects have been considered. The computed geometries show a significant biconcave deviation of the two-dimensional sheets from planarity with the central intersheet C⋯C distances considerably smaller that van der Waals distances. The computed intersheet binding energy per carbon atom extrapolated for N → ∞ of −74.3 meV (1.713 kcal mol⁻¹) per atom agrees quite well with an experimental defoliation energy of −52 meV (1.199 kcal mol⁻¹) per atom (−67 meV (1.545 kcal mol⁻¹) per carbon atom without corrections for H binding contributions) for polyaromatic hydrocarbons (PAHs) from graphite. A limited investigation of density functional theory (DFT) calculations using empirical dispersion contributions has been performed also showing a significant underbinding character of the D3 method. For most of the DFT variants investigated the graphene sheet models retain a quasi-planar structure in strong contrast to the aforementioned SOS-MP2 results.