COLUMBUS Program System Research Articles

Spin-density calculation via the graphical unitary group approach

In this work we discuss the calculation of the spin-density matrix from fundamental spin principles as implemented in the COLUMBUS Program System employing the graphical unitary group approach (GUGA). First, a general equation for the spin-density matrix is derived in terms of the one-and two-particle reduced density matrices, quantities that are spin-independent and readily available within the GUGA formalism. Next, the evaluation of this equation using the Shavitt loop values is discussed. Finally, the spatially resolved counterpart of the spin-density matrix, the spin distribution, is calculated for the phenalenyl radical and structures produced by heteroatoms with mono- and di-substitutions. The physical meaning of the spin-density along with its computational description using various methods is discussed putting special emphasis on negative contributions to the spin-density and their quantification via a spin-promotion index.

Local Electron Correlation Treatment in Extended Multireference Calculations: Effect of Acceptor-Donor Substituents on the Biradical Character of the Polycyclic Aromatic Hydrocarbon Heptazethrene.

The implementation of a local correlation (LC) treatment of multireference (MR) configuration interaction approaches within the COLUMBUS program system is reported. The LC treatment is based on the weak pairs approximation of Sæbø and Pulay (Ann. Rev. Phys. Chem. 1993, 44, 213) and a geometrical analysis of Walter et al. (Chem. Phys. Lett. 2001, 346, 177). The removal of simultaneous single excitations out of the weak pairs is based on the reference doubly occupied space only, leading to a straightforward program implementation and a conceptual simplicity in terms of well-defined localized orbitals. Reductions of up to an order of magnitude in the configuration space expansion and in computer time for the Davidson diagonalization step are found. The selection of the active and the virtual orbital spaces is not affected by this procedure. This treatment is successfully applied to the singlet biradical heptazethrene and its different acceptor-donor substituents: 4,12-dicyanoheptazethrene, 4,12-diaminoheptazethrene, and 4-amino-12-cyanoheptazethrene. Simultaneous insertion of pairs of donor and acceptor groups increases the biradical character; for push-pull substitution, this effect is significantly smaller. In addition, results obtained from spin-corrected unrestricted density functional theory calculations are supported by our MR calculations.

Columbus—a program system for advanced multireference theory calculations

AbstractThe 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.25This article is categorized under: Software > Quantum Chemistry

The nonadiabatic deactivation paths of pyrrole

Multireference configuration interaction (MRCI) calculations have been performed for pyrrole with the aim of providing an explanation for the experimentally observed photochemical deactivation processes. Potential energy curves and minima on the crossing seam were determined using the analytic MRCI gradient and nonadiabatic coupling features of the COLUMBUS program system. A new deactivation mechanism based on an out-of-plane ring deformation is presented. This mechanism directly couples the charge transfer 1pipi* and ground states. It may be responsible for more than 50% of the observed photofragments of pipi*-excited pyrrole. The ring deformation mechanism should act complementary to the previously proposed NH-stretching mechanism, thus offering a more complete interpretation of the pyrrole photodynamics.

Analytic evaluation of nonadiabatic coupling terms at the MR-CI level. II. Minima on the crossing seam: formaldehyde and the photodimerization of ethylene.

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.

Solvent effects in electronically excited states using the continuum solvation model COSMO in combination with multireference configuration interaction with singles and doubles (MR-CISD)

An implementation of the COSMO continuum solvation model into the MCSCF and MR-CISD programs of the COLUMBUS program system is reported. Equilibrium solvation and non-equilibrium solvation models for the treatment of electronic excitations have been used. Solvatochromic effects have been computed for a representative set of n-π* and π-π* states of formaldehyde, acrolein and pyrazine using several solvents ranging from some with apolar character to water. Agreement with experimental shifts is good within the limits of a continuum model.

Cope Rearrangement of 1,5-Hexadiene: Full Geometry Optimizations Using Analytic MR-CISD and MR-AQCC Gradient Methods

Full geometry optimizations within given molecular symmetries have been performed on the chair and boat forms involved in the Cope rearrangement of 1,5-hexadiene using highly correlated methods (MR-CISD and MR-AQCC) and extended basis sets. These optimizations are based on analytic gradient procedures developed within the COLUMBUS program system and are the first ones for the Cope rearrangement, which have been carried out at a multireference, post-CASSCF level. By comparison of MR-CISD and MR-AQCC results, the importance of size-extensivity corrections is clearly demonstrated. Computed energetic stabilities with respect to 1,5-hexadiene and bis-allyl are in good agreement with experimental data. Only a single saddle point for the chair form of C2h symmetry is found in contrast to CASSCF results, but in agreement with CASPT2N and MRMP2 investigations. Thus, we confirm these previous results showing that the mechanism of the Cope rearrangement of 1,5-hexadiene is concerted via an aromatic transition state.

Reducing I/O costs for the eigenvalue procedure in large-scale configuration interaction calculations.

Several aspects of the matrix diagonalization method used for CI calculations in the COLUMBUS Program System are discussed, including a linear basis-contraction algorithm and the use of a nonorthogonal expansion basis. Both of these features significantly reduce the I/O requirements during the iterations.

An ab initio study of the f–f spectroscopy of americium +3

The levels associated with the lowest F7 and D5 terms of Am+3 have been calculated using ab initio spin–orbit configuration interaction techniques. A series of configuration interaction calculations were carried out that include significant amounts of single and double excitations and with two different pseudopotentials available in the literature. Double and single excitations from the 6s, 6p, and 5f subshells are all important in the determination of the level energies. A comparison of the two examined pseudopotentials with increasing amounts of electron correlation indicates that both yield results in qualitative agreement with experiment. More importantly, though, it is estimated that both are in significant quantitative error relative to experimental results, even for very large configuration interaction calculations. The calculations were performed using the new parallel spin–orbit configuration interaction component to the COLUMBUS Program System.

Geometry optimization of excited valence states of formaldehyde using analytical multireference configuration interaction singles and doubles and multireference averaged quadratic coupled-cluster gradients, and the conical intersection formed by the 1 1B1(σ-π*) and 2 1A1(π-π*) states

Extended MR-CISD (multireference configuration interaction singles and doubles), MR-CISD+Q (multireference configuration interaction singles, doubles, and quadrupole), and MR-AQCC (multireference averaged quadratic coupled clusters) calculations have been performed on the following valence states of formaldehyde: 1 1A1 (planar ground state), 1 1A2 and 1 1A″ (planar and nonplanar n-π* state), 1 1B1 and 2 1A1 (planar σ-π* and π-π* states) and their nonplanar counterparts 2 1A′ and 3 1A′. Full geometry optimizations have been performed using analytic gradient techniques developed for the MR-CISD and MR-AQCC methods as implemented into the COLUMBUS program system. Basis set extrapolation techniques have been used for the determination of high-accuracy geometries and adiabatic excitation energies. Harmonic vibrational frequencies have been computed also. Agreement between calculated and available experimental data is very good. Especially for the σ-π* and π-π* states experimental information is extremely scarce and our results provide reliable predictions. The major new result of our work is the finding that for the 2 1A1(π-π*) state the structure optimized under planarity constraints is only a saddle point and not a minimum. This fact is the result of a conical intersection between the σ-π* and π-π* states (1 1B1 and 2 1A1). The final result is that neither on the 2 1A′ nor on the 3 1A′ surface a stationary minimum can be assigned to the π-π* state.

High-level multireference methods in the quantum-chemistry program system COLUMBUS: Analytic MR-CISD and MR-AQCC gradients and MR-AQCC-LRT for excited states, GUGA spin–orbit CI and parallel CI density

Development of several new computational approaches within the framework of multi-reference ab initio molecular electronic structure methodology and their implementation in the COLUMBUS program system are reported. These new features are: calculation of the analytical MR-CI gradient for excited states based on state-averaged MCSCF orbitals, the extension of the MR-ACPF/AQCC methods to excited states in the framework of linear-response theory, spin–orbit CI for molecules containing heavy atoms and the development of a massively-parallel code for the computation of the one- and two-particle density matrix elements. Illustrative examples are given for each of these cases.

Ab initio determination of americium ionization potentials

The first three ionization potentials of americium are calculated using ab initio spin–orbit configuration interaction techniques. These results are favorably compared to available experimental and previous theoretical work. The lowest two ionization potentials are accurately determined using wave functions constructed as simple single and double substitutions from a self-consistent field reference configuration with scalar relativistic effects included through an averaged relativistic pseudopotential. A determination of the third ionization potential to comparable accuracy requires inclusion of the spin–orbit operator and significant intermediate coupling with a resulting configuration expansion length in excess of 1.9 million double-group adapted functions. The solution to this problem was achieved by application of a new parallel spin–orbit configuration interaction component to the COLUMBUS Program System. A decomposition of the ionization potential calculation into parts either sensitive or largely insensitive to the spin–orbit operator is favorably tested, leading to hybrid calculations of improved accuracy.

A general multireference configuration interaction gradient program

An efficient and general method for the computation of analytic energy gradients and energy response properties for general MRCI (multireference configuration interaction) and ACPF (averaged coupled pair functional) wave functions is presented. This methodology includes a general approach, based on successive orbital transformations, for the inclusion of the effects of various orbital resolution (canonicalization) constraints. Initial implementation in the columbus Program System demonstrates, particularly for large-scale multireference wave functions, that the additional computational effort required for the energy gradient is a small fraction of that required for the energy. For polyatomic molecules, the computational resources required for the energy gradient do not depend explicitly on the number of constituent atoms. This combination of features represents a major step forward in the computation and characterization of molecular potential energy surfaces.

The COLUMBUS Standard Integral File Structure: A proposed interchange format

AbstractThe integral file structure used in the COLUMBUS Program System is described. This file structure is proposed for use as an interchange format for the exchange of information between various electronic structure codes. Access to the integral and density matrix arrays stored in the file structure is simplified by a supporting subroutine library. This library is portable across various computers and is readily available to programmers from the COLUMBUS distribution files. This library provides for the efficient processing of individual records, including the use of asynchronous I/O and the vectorized processing of packed orbital labels. The individual arrays are identified in a self‐defining and extensible manner, allowing for the addition of new integral types as demanded by the application. The format of the individual records is also self‐defining, allowing for the use of various packing and data compression methods within each record without burdening the calling program with unnecessary complications.

A progress report on the status of the COLUMBUSMRCI program system

The COLUMBUS program system is a collection of Fortran programs for performing general multireference single- and double-excitation configuration interaction (MRSDCI) 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 MRSDCI wave function to be generated from general reference CSFs that are not necessarily related to the MCSCF expansion CSFs.