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WIREs Comput Mol Sci
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Columbus—a program system for advanced multireference theory calculations

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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. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 191‐199 DOI: 10.1002/wcms.25

Figure 1.

Graph describing an MR‐CISD expansion for a state with N = 2a + b = 7 electrons and spin S = b/2 = ½ (top node). The different levels (i = 1, … , n) of the graph correspond to the n orbitals, five of which (levels i = n − 4, … , n) are internal. Each distinct strictly ascending path from the origin (i = 0) to the top (i = n) describes one of the CSFs of the expansion in terms of cumulative spin‐coupling of the orbitals. The eight distinct paths confined to the heavy lines describe the eight reference configurations, a CAS based on the three active orbitals (i = n − 4, n − 3, n − 2). The inset shows the four possible modes of spin‐coupling each orbital, described by the different slopes of the corresponding lines and identified by the step number d = 0, 1, 2, 3. The d values 0 and 3 refer to empty and double occupied orbitals, respectively, d = 1 and d = 2 correspond to low‐spin and high‐spin, respectively. The partial state obtained after the coupling of orbital i has Ni = 2ai + bi electrons and spin Si = bi/2. The Δ values indicate changes in respective values due to the four coupling cases.

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Figure 2.

COLUMBUS module structure and available program execution paths.

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Figure 3.

Evolution of potential energy computed at the MRCIS level for a typical adenine dynamics trajectory. At each time step the energies of states S0–S3 are shown. The crosses indicate the active electronic state determining at this point the dynamics within the surface‐hopping scheme.

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