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. © 1997 by John Wiley & Sons, Inc.     

The parallel implementation of configuration-selecting multireference configuration interaction method

We report on a scalable implementation of the configuration-selecting multireference configuration interaction method for massively parallel architectures with distributed memory. Based on a residue driven evaluation of the matrix elements, this approach allows the routine treatment of Hilbert spaces of well over 10⁹ determinants, as well as the selective treatment of triple and quadruple excitations with respect to the reference space. We demonstrate the scalability of the method for up to 128 nodes on the IBM-SP2 and for up to 256 nodes on the Cray-T3E. We elaborate on the specific adaptation of the transition residue-based matrix element evaluation scheme that ensures the scalability and load balancing of the method. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1559–1570, 1999     

A multireference direct CI program based on the symmetric group graphical approach

Specific features of an SGGA-based multireference direct CI program working in large internal spaces are discussed. In particular, advantages resulting from the explicit separation of the orbital and the spin spaces are explored. Concepts allowing for the efficient creation of a flexible and symmetry-adapted CI basis, for the high-speed generation of the coupling coefficients and for structuring a simple permutation driven algorithm to handle the orbital space are briefly discussed.Alexander von Humboldt Fellow 1985/87     

The direct configuration interaction method for general multireference expansions: Symmetric group approach

A computer implementation of the direct configuration interaction method formulated within the symmetric group approach is discussed. The formulation allows for an open-shell as well as for a multiconfigurational reference state. The number of all necessary formulas, derived by a computer for each integral type rather than for the individual integrals, is lower than in the currently existing techniques, including the unitary group approach. The logical structure of a general program for singly and doubly excited configurations is outlined. The efficiency of the symmetric group approach is demonstrated on a recently developed program, restricted to one reference state only.     

New perspectives in multireference perturbation theory: the n-electron valence state approach

The n-electron valence state perturbation theory (NEVPT) is a form of multireference perturbation theory which is based on a zero order reference wavefunction of CAS-CI type (complete active space configuration interaction) and which is characterized by the utilization of correction functions (zero order wavefunctions external to the CAS) of multireference nature, obtained through the diagonalization of a suitable two-electron model Hamiltonian (Dyall’s Hamiltonian) in some well defined determinant spaces. A review of the NEVPT approach is presented, starting from the original second order state-specific formulation, going through the quasidegenerate multi-state extension and arriving at the recent implementations of the third order in the energy and of the internally contracted configuration interaction. The chief properties of NEVPT—size consistence and absence of intruder states—are analyzed. Finally, an application concerning the calculation of the vertical spectrum of the biologically important free base porphin molecule, is presented.     

Accuracy of energy extrapolation in multireference configuration interaction calculations

The accuracy of extrapolation procedures in conjunction with energy-based configuration selection in CI calculations is examined. The normally high accuracy of such extrapolation can deteriorate in multireference CI calculations when configuration functions of low weight are included in the root (reference) set. This is due to the inadequacy of second-order energy contribution estimates for the very large number of discarded low-contribution functions generated as single and double excitations from the minor members of the root set. The problem may be overcome by increasing the number of configurations included in the zero-order function used for the energy contribution estimation process. Illustrative results are presented for excited states of the H₂O molecule and the H₂O⁺ ion.     

A numerical test on the size consistency of some multireference configuration interaction approaches

The size consistency of selected multireference CI approaches is tested on two model problems, namely seven non-interacting H₂ molecules at their equilibrium bond length r_e or at 2r_e and seven non-interacting Ne atoms. I n all cases the results obtained from the two-class CIPSI method (which is an multireference MP2 procedure) are suprisingly good. The three-class CIPSI algorithm (which is an approximation of MR-SDCI) is much superior to SDCI, especially when the selection introduces the largest quadruply excited components. The implication of size-consistency error on dissociation energies is discussed.     

Nonadditivity and the stability of Ag3. A multireference configuration interaction study

Variational (?30 000 determinants) and perturbational (?3.5 million determinants) Localized Multireference Configuration Interaction (LMRCI) calculations includingf polarization functions are made to study the role played by the three-body terms in the stabilization energy of three selected geometries of the silver trimer: linear, equilateral and a Jahn-Teller obtuse triangle conformation. A comparative analysis of the relative stability of these geometries is done through a many-body decomposition of the interaction energy. Like in Cu₃, the most symmetrical arrangement (i.e. an equilateral triangle) is found to be less stable than the obtuse triangle because it has the highest three-body repulsion energy. The absolute minimum is the obtuse triangle having a Jahn-Teller stabilization energy of 328 cm^?1. Unlike Cu₃, the linear geometry is found to be less stable than the equilateral by 1282cm^?1. Results show again the importance of three-body terms in the total interaction energy of these trimers.     

A multireference configuration interaction method based on the separated electron pair wave functions

A multireference configurational interaction method based on the separated electron pair (SEP) wave functions, SEP‐CI approach, has been developed as an approximation to the traditional CASSCF method. It differs from the CASSCF method in that active orbitals are obtained from the SEP wave function without further optimization in the subsequent CI calculations, and the active space is automatically constructed according to the occupation coefficients of SEP natural orbitals. These features make the present SEP‐CI method computationally much less demanding than the CASSCF method. The applicability of the SEP‐CI method is illustrated with sample calculations on the insertion reaction of BeH₂ and dissociation energies of LiH, BH, FH, H₂O, and N₂. © 2005 Wiley Periodicals, Inc. J Comput Chem 27: 39–47, 2006     

Full configuration interaction algorithm on a massively parallel architecture: Direct-list implementation

A parallel full configuration interaction (FCI) code, implemented on a distributed memory MPP computer, has been modified in order to use a direct algorithm to compute the lists of mono- and biexcitations each time they are needed. We were able to perform FCI calculations on the ground state of the acetylene molecule with two different basis sets, corresponding to more than 2.5 and 5 billion Slater determinants, respectively. The calculations were performed on a Cray-T3D and a Cray-T3E, both machines having 128 processors. Performance and comparison between the two computers are reported and discussed. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 658–672, 1998     

A configuration interaction study of the water molecule and interpretation of the walsh diagram

Large scale ab initio SCF and CI calculations are used to investigate the bond angle dependence of the energy and one-electron properties of the water molecule. The SCF wave functions are used to reinvestigate the Hellmann-Feymann force interpretation of Walsh diagrams. The results are much closer to the ideas of Walsh than those obtained by Coulson and Deb.     

Photochemistry of ethylene: a multireference configuration interaction investigation of the excited-state energy surfaces

Multireference configuration interaction with singles and doubles (MR-CISD) calculations have been performed for the optimization of conical intersections and stationary points on the ethylene excited-state energy surfaces using recently developed methods for the computation of analytic gradients and nonadiabatic coupling terms. Basis set dependence and the effect of various choices of reference spaces for the MR-CISD calculations have been investigated. The crossing seam between the S0 and S1 states has been explored in detail. This seam connects all conical intersections presently known for ethylene. Major emphasis has been laid on the hydrogen-migration path. Starting in the V state of twisted-orthogonal ethylene, a barrierless path to ethylidene was found. The feasibility of ethylidene formation will be important for the explanation of the relative yield of cis and trans H2 elimination.     

Generalization of analytic energy derivatives for configuration interaction wave functions

This paper takes the form of a review including some original contributions. A fresh derivation of analytic energy derivative expressions for configuration interaction (CI) wave functions is presented. In this method the CI energy is described by _IJC_IC_J(H _IJ-_IJE) so that the orthonormality condition is explicitly included therein. In the sequence of differentiations up to fourth order it will be demonstrated that each derivative may be expressed in terms of (H _IJ-_IJE) and its derivatives in a symmetric way with respect to the interchange of differential variables. In a similar manner, the CI variational condition may be described in an equation which explicitly includes the normalization condition. It is shown that the differentiation of the modified variational condition produces the coupled perturbed configuration interaction (CPCI) equations in directly soluble and compact forms. The necessary formulae for the energy derivatives up to fourth order and the CPCI equations up to second order are explicitly given.     

A regionally contracted multireference configuration interaction method: general theory and results of an incremental version

This work proposes to take benefit of the localizability of both occupied and virtual inactive molecular orbitals (MOs) in the context of complete active space singles and doubles configuration interaction (CAS-SDCI). The doubly occupied MOs are partitioned into blocks, or regions, corresponding to a subset of adjacent bonds and lone pairs. The localized virtual MOs are attributed to these regions from a spatial criterion. Then a series of limited post-CAS-CI calculations is performed, using the same reference space, one for each block, and then one per pair of blocks. From these independent CI calculations contracted external functions are defined for each block or for each pair of blocks, and for each state. A general multistate formalism is proposed, the CI matrix being expressed in the space defined by the CAS and the contracted functions. Preliminary numerical studies, resting on the evaluation of single-block and two-block contributions to the dynamical correlation energy of each state, are presented. Provided that size-consistency corrections are taken into account the results of the procedure are shown to be in excellent agreement with those of the nonpartitioned post-CAS-CI. The computational benefits of this evidently parallelizable procedure are underlined.     

Convergence property of multireference many-body perturbation theory analyzed by the use of a norm of effective Hamiltonian

Summary It is proposed to use a norm of anth order effective Hamiltonian, for analyzing the convergence property of the multireference many-body perturbation theory (MR-MBPT). The utilization of the norm allows us to employ only (1) asingle number for all the states that we are interested in, and (2) values which decreases from thepositive side to zero as the ordern of the perturbation increases. This characteristic features are in contrast to those in the usually used scheme whereseveral numbers, namely, the eigenvalues of the target states, should be used and they mayoscillate around exact eigenvalues. The present method has been applied to MR-MBPT calculations of the (H₂)₂, CH₂, and LiH molecules based on the multireference versions of Rayleigh-Schrödinger PT, Kirtman-Certain-Hirschfelder PT, and the canonical Van Vleck PT; and following features are found: (1) the above three versions of the perturbation theories have essentially the same convergence property judged from the lowering of the norm; (2) the lower order truncation of the perturbation series gives reasonable solutions; (3) the norm decreases irrespective of the perturbation expansion being convergent or divergent for the first several orders (up to about the sixth order).     

A multireference perturbation theory study on the vertical electronic spectrum of thiophene

The vertical electronic spectrum of the thiophene molecule is investigated by means of second and third order multireference perturbation theory (NEVPT). Single-state and quasi-degenerate NEVPT calculations of more than 25 singlet excited states have been performed. The study is addressed to the theoretical characterization of the four lowest-energy valence states, as well as the 3s, 3p and 3d Rydberg states. In addition, the excitation energies of two and valence states are also reported. For almost all the excited states, coupled cluster calculations (CCSD and CCSDR(3)) have been also carried out, using the same geometry and basis set used for the NEVPT ones, in order to make the comparison between the results of the two methods meaningful. A remarkable accordance between the NEVPT and CC excitation energies is found. The present results, over all, confirm the experimental assignments but, above all, represent an important contribution to the assignments of some low-energy states, valence and Rydberg, for which a firm interpretation is not available in the literature.     

A flexible correlation group table (CGT) method for the relativistic configuration interaction wavefunctions

A generalized correlation group table (CGT) method is described for the relativistic configuration interaction (RCI) wavefunctions of molecules containing heavy atoms. In this method first four keywords are defined and two properties are discussed in terms of spectroscopic states and double group theory. These definitions and properties are then used to summarize six principles to stipulate the relationship among relativistic states, nonrelativistic states, as well as RCI configurations. The definitions, properties, and principles comprise the generalized CGT method, which facilitates the classification and assignment of the RCI wavefunctions, and thus, provide a general technique for complex systems containing several open shells. Finally, the techniques are exemplified with a few computational models.     

On the role of parallel architecture supercomputers in time-dependent approaches to quantum scattering

Summary Results of our initial study of the use of parallel architecture super-computers in solving time-dependent quantum scattering equations are reported. The specific equations solved are obtained from the time-dependent Lippmann-Schwinger integral equation by means of a quadrature approximation to the time integral. This leads to a modified Cayley transform algorithm in which the primary computational step is a matrix-vector multiplication. Implementation has been carried out both for the MasPar MP-1 and the NCUBE 6400 parallel machines. The codes are written in a modular form that greatly facilitates porting from one machine architecture to another. Both parallel machines prove to be more powerful for this application than the serial architecture VAX 8650. Specific analysis of machine performance is given.Ames Laboratory is operated for the U.S. Department of Energy by Iowa State University under Contract No. 2-7405-ENG-82. This research was supported by the Division of Chemical Sciences and Applied Mathematical Sciences, Office of Basic Energy SciencesR.A. Welch Predoctoral Fellow under R.A. Welch Foundation Grant E-608Supported in part under National Science Foundation Grant CHE89-07429     

Accurate spectroscopic constants of the lowest three electronic states in halonitrenes with multireference configuration interaction

Internally contracted multireference configuration interaction (icMRCI) calculations of the ground state (X³Σ⁻), the first excited state (a¹Δ) as well as the second excited state (b¹Σ⁺) have been performed for a series of halogenated nitrenes NXs (X = Cl, Br, and I). Accurate spectroscopic constants of these lowest three electronic states of each NX were obtained in this work using MRCI methods with aug‐cc‐pVXZ (X = T, Q, 5) basis sets and complete basis set (CBS) limit. In addition, various corrections, including the Davidson correction, scalar relativistic effect, core‐valence correlation, and spin‐orbit coupling effect, have been studied in calculating spectroscopic constants, especially for heavy‐atom nitrenes. Comparisons have been made with previous computational and experimental results where available. The icMRCI + Q calculations presented in this work provide a comprehensive series of results at a consistent high level of theory for all of the halogenated nitrenes.