Ron Shepard

Analytic evaluation of nonadiabatic coupling terms at the MR-CI level. I. Formalism

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.

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.

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.

Comparison of the convergence characteristics of some iterative wave function optimization methods

The convergence properties of several iterative methods for the optimization of orbitals and configuration mixing coefficients in multiconfigurational electronic wave functions are compared. All of the iterative methods considered here are derived from corresponding approximate energy expressions. These energy expressions are discussed within the context of their suitability for the calculation of noninfinitesimal wave function corrections. A method based on the partitioned orbital Hessian matrix and which uses an approximate super‐CI secular equation for the wave function corrections is shown to posses second‐order convergence and to have the largest radius of convergence of the methods analyzed in detail in this work for several molecular examples. Particular attention is given to convergence properties for excited states, where the differences between these methods are most significant.

The Multiradical Character of One- and Two-Dimensional Graphene Nanoribbons

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.

Columbus-a program system for advanced multireference theory calculations

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.

A MASSIVELY PARALLEL MULTIREFERENCE CONFIGURATION INTERACTION PROGRAM : THE PARALLEL COLUMBUS PROGRAM

A massively parallel version of the configuration interaction (CI) section of the COLUMBUS multireference singles and doubles CI (MRCISD) program system is described. In an extension of our previous parallelization work, which was based on message passing, the global array (GA) toolkit has now been used. For each process, these tools permit asynchronous and efficient access to logical blocks of 1‐ and 2‐dimensional (2‐D) arrays physically distributed over the memory of all processors. The GAs are available on most of the major parallel computer systems enabling very convenient portability of our parallel program code. To demonstrate the features of the parallel COLUMBUS CI code, benchmark calculations on selected MRCI and SRCI test cases are reported for the CRAY T3D, Intel Paragon, and IBM SP2. Excellent scaling with the number of processors up to 256 processors (CRAY T3D) was observed. The CI section of a 19 million configuration MRCISD calculation was carried out within 20 min wall clock time on 256 processors of a CRAY T3D. Computations with 38 million configurations were performed recently; calculations up to about 100 million configurations seem possible within the near future.

Multireference configuration interaction treatment of potential energy surfaces: symmetric dissociation of H2O in a double-zeta basis

Abstract Multiconfiguration SCF and multireference CI calculations have been performed for the H 2 O molecule in a double-zeta basis for four symmetric geometries, for comparison with full CI results. Unlike single-reference results, the energy errors are almost independent of geometry, allowing unbiased treatments of potential energy surfaces.

Toward high‐performance computational chemistry: II. A scalable self‐consistent field program

We discuss issues in developing scalable parallel algorithms and focus on the distribution, as opposed to the replication, of key data structures. Replication of large data structures limits the maximum calculation size by imposing a low ratio of processors to memory. Only applications which distribute both data and computation across processors are truly scalable. The use of shared data structures that may be independently accessed by each process even in a distributed memory environment greatly simplifies development and provides a significant performance enhancement. We describe tools we have developed to support this programming paradigm. These tools are used to develop a highly efficient and scalable algorithm to perform self‐consistent field calculations on molecular systems. A simple and classical strip‐mining algorithm suffices to achieve an efficient and scalable Fock matrix construction in which all matrices are fully distributed. By strip mining over atoms, we also exploit all available sparsity and pave the way to adopting more sophisticated methods for summation of the Coulomb and exchange interactions.

Toward high-performance computational chemistry: I. Scalable Fock matrix construction algorithms

Several parallel algorithms for Fock matrix construction are described. The algorithms calculate only the unique integrals, distribute the Fock and density matrices over the processors of a massively parallel computer, use blocking techniques to construct the distributed data structures, and use clustering techniques on each processor to maximize data reuse. Algorithms based on both square and row‐blocked distributions of the Fock and density matrices are described and evaluated. Variants of the algorithms are discussed that use either triple‐sort or canonical ordering of integrals, and dynamic or static task clustering schemes. The algorithms are shown to adapt to screening, with communication volume scaling down with computation costs. Modeling techniques are used to characterize algorithm performance. Given the characteristics of existing massively parallel computers, all the algorithms are shown to be highly efficient for problems of moderate size. The algorithms using the row‐blocked data distribution are the most efficient.