A programmable spin-free method for configuration interaction

In this note a method is presented for quick implementation of configuration interaction (CI) calculations in molecules. A spin-free Hamiltonian for anN electron system in a spin stateS, expressed in terms of the generators for the unitary group algebra, is diagonalized over orbital configurations forming a basis for the irreducible representation [2^1/2N-S 1^2S ] of the permutation group S _N . It has been found that the basic algebraic expressions necessary for the CI calculation involve a limited category of permutations. These have been displayed explicitly. On leave from the Indian Institute of Technology, Bombay, India.     

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. Received: 19 December 2000 / Accepted: 9 May 2001 / Published online: 11 October 2001     

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.     

Internally contracted multiconfiguration-reference configuration interaction calculations for excited states

Summary The calculation of electronically excited states with the internally contracted multiconfiguration-reference configuration interaction (CMRCI) method is discussed. A straightforward method, in which contracted functions for all states are included in the basis, is shown to be very accurate and stable even in cases of narrow avoided crossings. However, the expense strongly increases with the number of states. A new method is proposed, which employs different contracted basis sets for each state, and in which eigensolutions of the Hamiltonian are found using an approximate projection operator technique. The computational effort for this method scales only linearly with the number of states. The two methods are compared for various applications.Dedicated in honor of Prof. Klaus Ruedenberg     

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.     

Core and valence electrons in atoms and ions: configuration interaction calculations

Summary The partitioning of ground-state atoms or ions into inner spherical cores with radius _b and outer valence regions extending from _b to infinity is explored with the help of the expression for the valence-region energy (where T ^v and V ^v are, respectively, the kinetic and potential energies of the valence electrons N ^v found beyond the boundary surface defined by _b) using also the appropriate expression for E ^ion, the energy of the ion left behind after removal of the valence electrons. E ^v and E ^ion are meaningful only for discrete numbers, N ^c, of electrons assigned to the core, namely, when the exchange integrals, K ^cv, between N ^c and N ^v total (or at least closely approach) 0, i.e., for N ^c = 2 e or N ^c = 2 and 10 e for the first- or second-row elements, respectively.Part of the projected Ph.D. dissertation of N. D.     

Superoperator method for calculating configuration interaction,including doubly excited configurations

A superoperator algorithm that had been proposed previously [Teor. Éksp. Khim.,11, No. 1, 3 (1975)] for taking all doubly excited configurations into account has been worked out in detail for singlet states and has been realized numerically in theab initio version of STO-4G. The method does not require the construction of the configuration interaction matrix. This matrix is replaced by superoperators, which are rules for the transformation of the variational parameters, stacked, in a transition-type matrix. Calculations have been performed for small molecules of the second period, and also for linear chains of hydrogen atoms (for h₁₄, 1275 configurations were taken into account), for which additivity of the correlation energy is observed in the approximation that was used.Presented at Conference on Quantum Chemistry, Dnepropetrovsk, September, 1983.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 4, pp. 385–391, July–August, 1985.     

A comparison of variational and non-variational internally contracted multiconfiguration-reference configuration interaction calculations

Summary The internally contracted multiconfiguration-reference configuration interaction (CMRCI) method and several non-variational variants of this method (averaged coupled pair approximation (ACPF), quasidegenerate variational perturbation theory (QD-VPT), linearized coupled pair many electron theory (LCPMET)) have been employed to compute potential energy functions and other properties for a number of diatomic molecules (F₂, O₂, N₂, CN, CO) using large basis sets and full valence CASSCF reference wavefunctions. In most cases the variational CMRCI wavefunctions yield more accurate spectroscopic constants than any of the employed non-variational methods. Several basis sets are compared for the N₂ molecule. It is found that atomic natural orbital (ANO) contractions led to significant errors in the computedr _e , _e , andD _e values.     

On the invariance of the configuration interaction energy with respect to orbital rotations

Summary The invariance of the configuration interaction (CI) energy with respect to orbital rotation is considered. The inclusion of all spin couplings versus only those from the first-order interacting space is considered. A definition for the analog of a second-order CI calculation when inactive electrons are present is proposed.     

Multi-component molecular orbital study of isotope effects on lithium hydride molecules with the configuration interaction scheme

The multi-component molecular orbital method, which can take account of the quantum effect of the electrons and nuclei, is applied to the calculation of lithium hydride isotope species with the configuration interaction (CI) scheme. The optimum basis set functions for quantum nuclei are proposed by the fully variational procedure under single electronic–single nuclear excitation CI level. The average internuclear distances and dipole moments for isotopic lithium hydride molecules calculated with small basis functions are reasonable agreement with the corresponding experimental values.     

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.     

Implementation and use of a direct, partially integral-driven non-Dyson propagator method for molecular ionization

The Green's function ADC(3) scheme has been for many years a successful method to predict theoretically the ionization (and electron affinity) spectrum of molecules. However, a dramatic enhancement of the method's power has come only recently, with the development of an approximation method to the one-particle Green's function which does not make direct use of the Dyson equation. In the present work, we present an efficient computer implementation of this novel approach, with first comparative tests demonstrating its enormous computational advantage over the conventional approach.     

Configuration interaction: Molecular orbitals for accurate calculations on diatomics

A procedure is developed to construct an optimum set of molecular orbitals (MO's) to be used in large scale configuration interaction expansion for diatomics. The set is optimum in the sense that a significant energy improvement can be obtained for a relatively short wavefunction expansion. Application of this methodology to the ground state of the LiH molecule gave an energy of –8.06345 a.u. for an expansion with 1852 terms obtained from a set with 16-, 12-, and 6-type MO's.     

A method of incorporating quadruple correction in the scheme of multi-reference singly and doubly excited configuration interaction — a CSF based coupled pair approximation

Summary We develop an approximate size consistent method within a framework of the multi-reference configuration interaction scheme. The Rayleigh-Schrödinger perturbation theory is employed with a specific selection of the unperturbed part of the electronic Hamiltonian. The second order energy is obtained by a set of equations similar to the quasidegenerate variational perturbation theory of Cave and Davidson. The approximate fourth order energy is obtained by solving a set of equations similar to the coupled electron pair approximation (CEPA). The method has been tested for two simple systems, BeH₂ and N₂, and the results are quite encouraging.     

Configuration space partitioning and matrix buildup scaling for the vibrational configuration interaction method

The accurate computation of anharmonic vibrational states for medium to large molecules is a requirement for the detailed understanding of nonlinear multidimensional infrared spectra and the dynamical information encoded in them. The vibrational configuration interaction (VCI) method constitutes a particularly promising tool in this respect. It is generally hampered though by its unfavorable scaling with respect to system size. We analyze the scaling behavior of several well‐known as well as some new approximate VCI schemes in detail, which are complementary to the class of configuration selection schemes developed recently. We find that the combination of a configuration space partitioning, possibly based on configuration selection, with energetic thresholding and resonance screening provides an efficient scheme for the reduction of computational effort involved in VCI calculations while at the same time maintaining sufficient accuracy for the vibrational energies. © 2012 Wiley Periodicals, Inc.     

Subspace effective potential theory for configuration interaction

In this article we present an approach which combines the configuration interaction methodology and orbitals derived via single particle equations with a local potential V_eff, the variational parameters of which are determined by minimizing the so‐called subspace functional instead of the traditional single energy functional . In this way ground and excited states orbitals are put on equal footing. The V_eff is restricted to have the form of a model potential expressed in terms of the external potential. One of the advantages of the present direct mapping formulation, is that the effective potential, V_eff, has the symmetry of the external potential. Applications are focused mainly on excited states of the HeH and BeH molecules having spatial and spin symmetries as those of the ground one. © 2016 Wiley Periodicals, 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 practical valence bond method: a configuration interaction method approach with perturbation theoretic facility

The previously developed valence bond configuration interaction (VBCI) method (Wu, W.; Song, L.; Cao, Z.; Zhang, Q.; Shaik, S., J. Phys. Chem. A, 2002, 105, 2721) that borrows the general CI philosophy of the MO theory, is further extended in this article, and its methodological features are improved, resulting in three accurate and cost-effective procedures: (a) the effect of quadruplet excitation is incorporated using the Davidson correction, such that the new procedure reduces size consistency problems, with due improvement in the quality of the computational results. (b) A cost-effective procedure, named VBCI(D, S), is introduced. It includes doubly excited structures for active electrons and singly excited structures for inactive pairs. The computational results of VBCI(D, S) match those of VBCISD with much less computational effort than VBCISD. (c) Finally, a second-order perturbation theory is utilized as a means of configuration selection, and lead to considerable reduction of the computational cost, with little or no loss in accuracy. Applications of the new procedures to bond energies and barriers of chemical reactions are presented and discussed.     

On the configuration interaction method for singlet states

The direct CI method, which avoids explicit calculation of the Hamiltonian matrix, is presented in a new form. The method is linked with Davidson's algorithm for iterative evaluation of the ground state eigenvector. The viability of the method is indicated by the test calculations on water which are described.     

Application of the direct configuration interaction method to the ground state of O2

The Direct Configuration Interaction Method, originally due to Roos [1], has been implemented using the method of Lucchese and Schaefer [2], for open shell systems. As in the closed-shell case, the method is very efficient. Results are presented for a part of the potential energy curve of the O₂ ^3– _g ground state electronic configuration, together with several properties.