Direct Configuration Interaction Method Research Articles

Theoretical study of the I++I− mutual neutralization reaction

We have computed the cross sections of the mutual neutralization reaction between ${\mathrm{I}}^{+}$ and ${\mathrm{I}}^{\ensuremath{-}}$ for a collision energy varying from 0.001 eV to 50 eV. These cross sections were obtained using the adiabatic potential energy curves of the ${\mathrm{I}}_{2}$ system computed with a direct relativistic multireference configuration interaction method and a semiclassical approach (i.e., Landau-Zener surface hopping). We report the cross sections towards the following neutral states: $\text{I}(^{2}P_{3/2})+\text{I}{(}^{2}{P}_{3/2})$, $\text{I}{(}^{2}{P}_{3/2})+\text{I}{(}^{2}{P}_{1/2})$, $\text{I}{(}^{2}{P}_{1/2})+\text{I}{(}^{2}{P}_{1/2})$, and $\text{I}(5{p}^{4}6s)+\text{I}{(}^{2}{P}_{3/2})$. We also discuss the cross sections towards the following two excited ionic states: ${\text{I}}^{\ensuremath{-}}{(}^{1}{S}_{0})+{\text{I}}^{+}{(}^{3}{P}_{0})$ and ${\text{I}}^{\ensuremath{-}}{(}^{1}{S}_{0})+{\text{I}}^{+}{(}^{3}{D}_{2})$. The results of these calculations are in qualitative accordance with recent experimental measurements conducted in the Double ElectroStatic Ion Ring ExpEriment (DESIREE) in Stockholm. These results can be used to model iodine plasma kinetics and thus to improve our understanding of the latter.

Fundamental peak disappears upon binding of a noble gas: a case of the vibrational spectrum of PtCO in an argon matrix.

Anharmonic vibrational state calculations were performed for PtCO and Ar-PtCO via the direct vibrational configuration interaction (VCI) method based on CCSD(T) energies and CCSD dipole moments at tens of thousands of grids, to get insights into the anomalous effect of a solid argon matrix on the vibrational spectra of PtCO. It was shown that, through the binding of Ar to PtCO via a strong van der Waals interaction, the Pt-C-O bending fundamental level drastically loses the infrared intensity although the corresponding overtone band shows a relatively large intensity. The origin of this phenomenon was analyzed based on the dipole moment surfaces and electron densities around the equilibrium structure. The present computations have solved the inconsistency between the gas-phase and the matrix-isolation experiments for PtCO.

Björn Olof Roos (1937–2010)

Björn Roos was one of the most prominent theoretical chemists of the 20th and early 21st century. His membership in the International Academy of Quantum Molecular Sciences (IAQMS) honored perhaps more the IAQMS than it honored Björn Roos himself. Also, he was an active member of the Bureau of that Academy, in addition to important positions of trust in Sweden. Björn was a Ph.D. student of Inga Fischer-Hjalmars, who in turn had studied with Charles Coulson. It is interesting to ask whether his combination of intellectual rigor and sense for the physical and chemical facts can be partially derived from his academic ancestry. He started with semiempirical methods but switched to ab initio method development in 1968. After only a few years, in 1972, he had his first permanent achievement, the direct Configuration Interaction (CI) method. The Complete Active Space method followed in 1980 and CASPT2 in 1990. His scientific oeuvre is discussed by others in this volume. As a scientist, he only improved with age. One must record here his last “heat” with heavy-element chemistry, when he introduced relativistic terms in the MOLCAS package, single-handedly developed basis sets, and ran a number of classical applications. Perhaps, the crowning achievement was the understanding of the chemical bond in U2, published in Nature in 2005. His last papers are still appearing posthumously. Björn's scientific competence and intellectual discipline had as their vehicle an outspoken personality. This made his surrounding a magic circle that was free of any pretensions or ambiguities. We miss his sardonic laughter. Björn's last decade was shadowed by cancer. He is missed by his wife Ingela, and by five children from two marriages.

Björn O. Roos: 1937–2010. Mentor, colleague, innovator

Björn O. Roos: 1937–2010. Mentor, colleague, innovator

Generalization of the direct configuration interaction method to the hartree-fock interacting space for doublets, quartets, and open-shell singlets

Generalization of the direct configuration interaction method to the hartree-fock interacting space for doublets, quartets, and open-shell singlets

Direct configuration interaction and multiconfigurational self-consistent-field method for multiple active spaces with variable occupations. I. Method

In order to reduce the number of ineffective configurations in a priori generated configuration spaces, a direct configuration interaction method has been developed which limits the electron occupations of orbital groups making up a total active space. A wave function is specified by first partitioning an active space into an unrestricted number of orbital groups and second by providing limiting values, in the form of minima and maxima, for the electron occupancies of each group. The configuration interaction problem corresponding to all possible determinants satisfying these conditions is solved in a fully direct manner by the use of Slater–Condon expressions in conjunction with single and double replacements. This configuration interaction approach, termed occupation restricted multiple active space-configuration interaction, has also been linked with orbital optimization programs to produce the occupation restricted multiple active space-self consistent field method.

Direct configuration interaction and multiconfigurational self-consistent-field method for multiple active spaces with variable occupations. II. Application to oxoMn(salen) and N2O4

In a previous paper, a new direct configuration interaction method for multiple active spaces with variable occupations was described. The present article illustrates how this method may be applied to the oxoMn(salen) complex and the N2O4 molecule. In the first application it is shown how complete-active-space self-consistent-field wave functions of the oxoMn(salen) system may be approximated by a drastically reduced number of configurations with negligible loss of accuracy in terms of energetics. In the second application, to N2O4, it is demonstrated how the fully optimized reaction space wave function may be approximated and also how the recovery of dynamic correlation effects may be achieved. The best predictions of the structure (rNN=1.743 Å, rNO=1.189 Å, ∠(ONO)=134.4°) and binding energy (De=16.0 kcal/mol) are both in very good agreement with experiment (rNN=1.756, rNO=1.191, ∠(ONO)=134.46°, De=16.3 kcal/mol).

Identification of deadwood in configuration spaces through general direct configuration interaction

In order to identify ineffective and, hence, superfluous configurations in algorithmically generated configuration spaces, a direct configuration interaction (CI) method has been developed for determining completely general configurational expansions based on arbitrary determinantal configuration lists. While based on the determinantal ordering scheme of Knowles and Handy, our direct CI algorithm differs from previous ones by the use of the Slater–Condon expressions in direct conjunction with single and double replacements. A full, as well as a completely general selected, CI program has been implemented. With it, full configuration spaces of Ne, C2, CO and H2O with up to about 40 million determinants have been investigated. It has been found that, in all cases, fewer than 1% of the configurations in a natural-orbital-based configuration expansion reproduce the exact results within chemical accuracy.

Generalized doubly symbolic formulation for integral-driven direct configuration interaction method

A direct configuration interaction (CI) scheme using the generalized double symbolism both for the external space and for the internal space is proposed in an integral-driven context. The reason why the double symbolism is used in the present formulation is that the main target is in investigating large molecular systems. The integrals, configuration state functions, and energy expressions are systematically classified in terms of the orbital labels and their mutual relations. Various types of CI wavefunctions can be set up flexibly. The resulting structure of integral processings in the sigma vector construction is complicated. The number of unique loop types for two-electron integrals is 1325. Because the parallel architecture is gaining importance in the recent computational platforms, the parallelism is also addressed.

Direct CI method in restricted configuration spaces

A configuration interaction (CI) method in restricted CI (RCI) space obtained by imposing inequality-type restrictions on the occupancies of groups of molecular orbitals (MOs) was studied. The direct CI approach in such space was analyzed, and some recommendations concerning practical implementation of the RCI method are given. The corresponding program has been written in FORTRAN 77 for an IBM 486 DX personal computer and has been used for electronic structure calculations on transition metal complexes using a valence MO basis with the INDO approximation. © 1996 by John Wiley & Sons, Inc.

Generalized doubly symbolic formulation for integral-driven direct configuration interaction method

Generalized doubly symbolic formulation for integral-driven direct configuration interaction method

Symmetric group graphical approach to the direct configuration interaction method

AbstractAn approach to the configuration interaction method based on symmetric groups (SGA) is developed. The formalism is an alternative of the unitary group approach (UGA). In many aspects the present formulation seems to be superior to UGA. In particular, in SGA the orbital and the spin parts of the configuration state functions may be processed separately. In consequence its graphical formulation is much simpler and the coupling constant expressions are more compact than the UGA analogs. A special emphasis is put on direct CI implementations. In addition to formulas for coupling constants, explicit expressions allowing for separation of external and internal space contributions are also presented.

A diagrammatic construction of the direct configuration interaction method

A simple diagrammatic formalism useful for describing and comparing theories of electronic structure is described. The formalism is applied to derive the direct singles and doubles configuration interaction (CI) method. The resultant equations have the form of an iterative perturbation theory and execute more rapidly on a computer than conventional CI. Examples are given of the convergence of the method.

The alchemy configuration interaction method. I. The symbolic matrix method for determining elements of matrix operators

The symbolic matrix method which gives compact representation and efficient determination of expressions for the Hamiltonian and other matrix operators arising in configuration interaction (CI) calculations is presented. With this method, the computing and storage requirements for matrix expressions become insignificant compared to the total requirements of a CI calculation. The efficiency is achieved by taking advantage of analogies between expressions of different matrix elements to reduce drastically the number of expressions determined explicitly. The symbolic matrix method is completely general, unrestricted by the type of operators considered, or by the choice of n-particle basis. It can take full advantage of any point group symmetry, and the ordered interacting spaces to reduce the dimension of the n-particle basis. In addition, the method provides a basis for a general direct CI method which will be presented in a forthcoming paper. A comparison with the graphical unitary group approach is provided.

Large scale N-fermion calculations

The direct configuration interaction method for open-shell N-electron systems is described. The method is based on the theory of the symmetric group of particle permutations.

The inclusion of high-order replacements in configuration interaction calculations. Application to H 3O + inversion barrier

It is shown that some triple- and quadruple-replacement configurations may be added to the usual list of single- and double-replacement configurations in the Roos direct configuration interaction method for closed-shell systems. Calculations on He 2 can give correct dissociation to two He atoms. The effect of these replacements on the inversion barrier of H 3O + is also reported.

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.

Application of unitary group methods to configuration interaction calculations

A computational approach to the direct configuration interaction method is described. The method is formulated using the calculus of the generators of the unitary group. The simple structure of the generator matrices within the harmonic excitation level scheme is exploited to give a computational method that is competitive with traditional approaches. A new scheme for basis set truncation in the case of partial configuration interaction is devised employing orbital populations. It is also shown that the block structure of the generator matrices leads to the definition of a new order parameter for perturbation methods which is both effective and convenient.

Generalization of the direct configuration interaction method to the Hartree–Fock interacting space for doublets, quartets, and open-shell singlets. Applications to NO2 and NO2−

The direct configuration interaction method, including all Hartree–Fock interacting single and double replacements of a single root function, has been generalized to a wide class of systems. Programs capable of handling closed-shell singlets and open-shell doublets, triplets, quartets, and singlets in a routine fashion are described. The open-shell singlet presents some particular difficulties which have been overcome, and thus it appears that the direct CI method can be a fairly general and quite automatic approach to the electron correlation problem. The versatility of these programs is illustrated by applications to the vertical electronic spectra of NO2 (doublet and quartet spin states) and of NO2− (closed-shell singlet, open-shell singlet, and triplet spin states).

Coupling constants in the direct configuration interaction method

A general algorithm of evaluation of the coefficients of molecular integrals (coupling constants) appearing in the direct configuration interaction method is derived. The configurations are assumed to be spin-adapted antisymmetrized products of orthonormal orbitals. No limitation is imposed either upon the reference state (the number of the singly occupied orbitals may be arbitrary) or upon the excitation multiplicity.