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When is an acene stable? The pronounced multiradical character of graphene nanoribbons of different size and shape was investigated with high‐level multireference methods. Quantitative information based on the number of effectively unpaired electrons leads to specific estimates of the chemical stability of graphene nanostructures.

An efficient and general method for the analytic computation of the nonandiabatic coupling vector at the multireference configuration interaction (MR-CI) level is presented. This method is based on a previously developed formalism for analytic MR-CI gradients adapted to the use for the computation of nonadiabatic coupling terms. As was the case for the analytic energy gradients, very general, separate choices of invariant orbital subspaces at the multiconfiguration self-consistent field and MR-CI levels are possible, allowing flexible selections of MR-CI wave functions. The computational cost for the calculation of the nonadiabatic coupling vector at the MR-CI level is far below the cost for the energy calculation. In this paper the formalism of the method is presented and in the following paper [Dallos et al., J. Chem. Phys. 120, 7330 (2004)] applications concerning the optimization of minima on the crossing seam are described.

The COLUMBUS program system is a collection of Fortran programs for performing general multireference single-and double-excitation configuration interaction (MRSLICI) wave function optimization based on the graphical unitary group approach. The program system also includes integral generation, SCF and MCSCF orbital optimization, integral transformation, and wave function analysis programs. The original program system was written in 1980 to 1981. Since that time, it has evolved into one of the most popular MRSDCI program systems used in the computational chemistry community. The discussion of this evolution will include the exploitation of efficient matrix-matrix and matrix-vector product computational kernels, the use of generally contracted symmetry-adapted orbital basis sets, general Hamiltonian diagonalization procedures, energy-based internal walk selection, flexible DRT specification, improved coupling-coefficient evaluation methods, coupled-pair functional and multireference CPF capabilities, and density matrix construction. The numerous versions of the program system that are maintained at different sites and on different computers are now in the process of being merged. The source code for this combined version will be made available to the computational chemistry community. The source code for a specific computer may be generated from the source code for another computer by a single pass through a simple filter utility that is included with the program system. The directly supported computers will initially include various models of VAX, Cray, FPS, IBM, CDC, and ETA machines with the addition of other machines shortly thereafter. The ongoing developments of the COLUMBUS system that are discussed include a new method for computing analytic energy gradients for MRSDCI wave functions. This effective-density-matrix based method avoids the "coupled perturbed MCSCF" solutions for each coordinate direction, avoids the transformation of any derivative-integral quantities from the AO to the MO basis, avoids the transformation of the coupling coefficients from the MO to the AO basis, allows a subset of the MCSCF doubly occupied orbitals to be frozen in the CI wave function, and allows the MRSLXI wave function to be generated from general reference CSFs that are not necessarily related to the MCSCF expansion CSFS.

The COLUMBUS Program System allows high-level quantum chemical calculations based on the multiconfiguration self-consistent field, multireference configuration interaction with singles and doubles, and the multireference averaged quadratic coupled cluster methods. The latter method includes size-consistency corrections at the multireference level. Nonrelativistic (NR) and spin-orbit calculations are available within multireference configuration interaction (MRCI). A prominent feature of COLUMBUS is the availability of analytic energy gradients and nonadiabatic coupling vectors for NR MRCI. This feature allows efficient optimization of stationary points and surface crossings (minima on the crossing seam). Typical applications are systematic surveys of energy surfaces in ground and excited states including bond breaking. Wave functions of practically any sophistication can be constructed limited primarily by the size of the CI expansion rather than by its complexity. A massively parallel CI step allows state-of-the art calculations with up to several billion configurations. Electrostatic embedding of point charges into the molecular Hamiltonian gives access to quantum mechanical/molecular mechanics calculations for all wave functions available in COLUMBUS. The analytic gradient modules allow on-the-fly nonadiabatic photodynamical simulations of interesting chemical and biological problems. Thus, COLUMBUS provides a wide range of highly sophisticated tools with which a large variety of interesting quantum chemical problems can be studied. C 2011 John

The method for the analytic calculation of the nonadiabatic coupling vector at the multireference configuration-interaction (MR-CI) level and its program implementation into the COLUMBUS program system described in the preceding paper [Lischka et al., J. Chem. Phys. 120, 7322 (2004)] has been combined with automatic searches for minima on the crossing seam (MXS). Based on a perturbative description of the vicinity of a conical intersection, a Lagrange formalism for the determination of MXS has been derived. Geometry optimization by direct inversion in the iterative subspace extrapolation is used to improve the convergence properties of the corresponding Newton-Raphson procedure. Three examples have been investigated: the crossing between the 1(1)B1/2(1)A1 valence states in formaldehyde, the crossing between the 2(1)A1/3(1)A1 pi-pi* valence and ny-3py Rydberg states in formaldehyde, and three crossings in the case of the photodimerization of ethylene. The methods developed allow MXS searches of significantly larger systems at the MR-CI level than have been possible before and significantly more accurate calculations as compared to previous complete-active space self-consistent field approaches.