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.     

Excited states in the multireference state-specific coupled-cluster theory with the complete active space reference

The recently proposed multireference state-specific coupled-cluster theory with the complete active space reference has been used to study electronically excited states with different spatial and spin symmetries. The algorithm for the method has been obtained using the computerized approach for automatic generation of coupled-cluster diagrams with an arbitrary level of the electronic excitation from a formal reference determinant. The formal reference is also used to generate the genuine reference state in the form of a linear combination of determinants contracted to a configuration with the spin and spatial symmetries of the target state. The natural-orbital expansions of the one-electron configuration inferaction density matrix allowed us to obtain the most compact orbital space for the expansion of the reference function. We applied our approach in the calculations of singlet and triplet states of different spatial symmetries of the water molecule. The comparisons of the results with values obtained using other many-particle methods and with the full configuration interaction results demonstrate good ability of the approach to deal with electronic excited states.     

Emploi d'une méthode de perturbation-variation pour l'étude de la polarisation de spin dans les radicaux libres aromatiques

A perturbation method has been used to deal with the problem of the interaction of configuration in the free aromatic radicals. We have considered only the mono-excitated configurations which are responsible for the specific effects due to the spin polarization; the corresponding wave functions are built up with the set of molecular orbitals LCAO SCF (occupied and virtual) of the ground-state configuration. We thus obtain a good distribution of spin densities on the rings of the studied radicals: the benzyl and the methylene-naphthyls radicals. The spin density on the extracyclic carbon remains too large as in the case of the SCF representation. This may be explained by the shape of the molecular orbital occupied by the unpaired electron in the SCF configuration, and the structure of the method used which disregards the excitated configurations involving this orbital.     

Symmetric group graphical approach to the direct configuration interaction method

An 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.     

Application of the unitary group approach to evaluate spin density for configuration interaction calculations in a basis of S2 eigenfunctions

We present an implementation of the spin‐dependent unitary group approach to calculate spin densities for configuration interaction calculations in a basis of spin symmetry‐adapted functions. Using S² eigenfunctions helps to reduce the size of configuration space and is beneficial in studies of the systems where selection of states of specific spin symmetry is crucial. To achieve this, we combine the method to calculate U(n) generator matrix elements developed by Downward and Robb (Theor. Chim. Acta 1977, 46, 129) with the approach of Battle and Gould to calculate U(2n) generator matrix elements (Chem. Phys. Lett. 1993, 201, 284). We also compare and contrast the spin density formulated in terms of the spin‐independent unitary generators arising from the group theory formalism and equivalent formulation of the spin density representation in terms of the one‐ and two‐electron charge densities.     

Effect of Configuration Interaction on the G Values for Trigonally Distorted Octahedral Low Spin d5 System

The g values for trigonally distorted octahedral low spin d⁵ system is calculated, including configuration interaction. An appropriate set of five-electron wave functions is employed. The portion of the g values calculated here without including configuration interaction is identical with that of Griffith and Hill.     

Electron correlation studies: Rumer basis approach

A technique for the configuration interaction (CI) study of many-electron systems is developed based on Rumer spin-coupling scheme for the antisymmetrized configuration state functions (CSF). Incorporating a new graphical approach, the primitive configurations have been generated in blocks of definite ionocities to permit ready association of possible spin functions with each of the primitive configurations. Simple as well as extended Hubard model Hamiltonians have been studied to test the efficiency of the method. Procedures have been incorporated to calculate various correlation functions using the spin-adapted CSFs without invoking explicit expansions in terms of slater determinants. © 1996 John Wiley & Sons, Inc.     

Local configuration interaction: An efficient approach for larger molecules

The first full implementation of the localized configuration interaction technique at the variational CI, CEPA-2 and variational CEPA levels is described. Timings are presented for a double-zeta plus polarization calculation on butadiene. The restriction of the correlation space to local basis functions results in a spectacular enhancement of the efficiency of the CI loop. The loss in the correlation energy is only a few percent; we argue that most of the loss is due to the exclusion of intramolecular basis set superposition artifacts.     

On the evaluation of spin–orbit coupling matrix elements in a spin‐adapted basis

In the present article, we outline a simple scheme for generating configuration interaction matrix elements for spin–orbit interactions in molecules. The procedure leads to a close parallelism with spin‐free permutation‐group approaches. Unitary shift operators were successfully used on the orbital space to generate the matching permutations necessary to evaluate the required matrix elements. The procedure is adequately illustrated using examples. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 23–27, 1999     

Full configuration interaction approach to the few-electron problem in artificial atoms

We present a new high performance configuration interaction code optimally designed for the calculation of the lowest-energy eigenstates of a few electrons in semiconductor quantum dots (also called artificial atoms) in the strong interaction regime. The implementation relies on a single-particle representation, but it is independent of the choice of the single-particle basis and, therefore, of the details of the device and configuration of external fields. Assuming no truncation of the Fock space of Slater determinants generated from the chosen single-particle basis, the code may tackle regimes where Coulomb interaction very effectively mixes many determinants. Typical strongly correlated systems lead to very large diagonalization problems; in our implementation, the secular equation is reduced to its minimal rank by exploiting the symmetry of the effective-mass interacting Hamiltonian, including square total spin. The resulting Hamiltonian is diagonalized via parallel implementation of the Lanczos algorithm. The code gives access to both wave functions and energies of first excited states. Excellent code scalability in a parallel environment is demonstrated; accuracy is tested for the case of up to eight electrons confined in a two-dimensional harmonic trap as the density is progressively diluted up to the Wigner regime, where correlations become dominant. Comparison with previous quantum Monte Carlo simulations in the Wigner regime demonstrates power and flexibility of the method.     

Correlation energy extrapolation by intrinsic scaling. I. Method and application to the neon atom

Remarkably accurate scaling relations are shown to exist between the correlation energy contributions from various excitation levels of the configuration interaction approach, considered as functions of the size of the correlating orbital space. These relationships are used to develop a method for extrapolating a sequence of smaller configuration interaction calculations to the full configuration-interaction energy. Calculations of the neon atom ground state with the Dunning's quadruple zeta basis set demonstrate the ability of the method to obtain benchmark quality results.     

Contributions of the electronic spin and orbital current to the CoCl(4) (2-) magnetic field probed in polarised neutron diffraction experiments

Polarised neutron diffraction experiments conducted at 4.2 K on Cs(3)CoCl(5) crystals have been analysed by using a four-dimensional model Hilbert space made of ab initio n-electron wave functions of the CoCl(4) (2-) molecular ion. Two spin-orbit mixing coefficients and several configuration interaction coefficients have been optimized by fitting calculated magnetic structure factors to experimental ones, to obtain the best ensemble density operator that is representable in the model space. A goodness of fit, χ(2), less then 1 has been obtained for the first time for the two experimental data sets available. In the present article, the optimized density operators are used to calculate the magnetic field densities that are the genuine observables probed in neutron diffraction experiments. Density maps of such observables are presented for the first time and numerical details are provided. The respective contributions of spin density and orbital current to the magnetic field density are analyzed.     

The analysis of electron pair distribution functions in molecules

Electron pair distribution functions are analyzed for a variety of SCF+CI wavefunctions, for a range of simple molecules. The statistical correlation between electrons of like spin introduced by the antisymmetry requirement on the many-electron wavefunction is contrasted with the manner in which unlike-spin electron correlation is introduced through the inclusion of configuration interaction.     

Quantum Monte Carlo study of ground and first excited state of C,N, O,F, and Ne atoms using Slater-Jastrow-Backflow wave function

All-electron fixed-node diffusion quantum Monte Carlo energies of the two lowest-lying states of C, N, O, F, and Ne atoms are reported. The Slater-Jastrow form is used as the trial wave function. We will use single- and multideterminant wave functions as the Slater part. The single-determinant wave function has been computed by the Hartree-Fock method and the multideterminant wave functions have been computed by the complete active space self-consistent field, configuration interaction with single and double excitation, configuration interaction with single, double, triple, and quadruple excitation and second-order configuration interaction. For the ground- and first excited states, the multideterminant wave functions have computed more than 99% of the correlation energy. Significant improvements have been achieved using the backflow transformations and up to 99.8% of the correlation energy has been recovered. A very good agreement with the experimental data has been obtained for the excitation energies.     

Long-range interactions in H-He:ab initio potential,hyperfine pressure shift and collision-induced absorption in the infrared

Summary The collisional complex H-He, with both atoms in their electronic ground-states, is treated as a molecule in self-consistent field (SCF) and multi-reference configuration interaction (MR-CI) calculations to determine interaction energy, dipole moment and spin density as function of internuclear separation. A basis set tailored for long-range interactions was used and the basis set super-position errors were controlled. The resulting functions are analyzed and presented in analytical form, in terms of exchange and damped dispersion contributions. For all three properties there is full agreement with the accurately known long-range coefficients, but the dipole moment function shows rather large overlap effects even at large distances which obscure higher-order dispersion coefficients. The well depth of 22.56 µE_h is significantly deeper than most recentab initio calculations and model potentials have suggested, but our number corroborates existing semi-empirical values. Likewise, the calculated spin density variations are more pronounced than recent work has suggested. The resulting hyperfine pressure shift of H atoms in a helium buffer gas is in very good agreement with experiment, except for temperatures of the order of 1 K. Infrared absorption continua associated with the induced dipole moment are evaluated for their astrophysical interest.Dedicated to Prof. W. Kutzelnigg on the occasion of his 60th birthday     

Efficient methods for configuration interaction calculations

Advanced techniques are developed to provide efficient economic treatment of the large scale eigenvalue problem posed when configuration interaction is carried out on SCF basis sets of moderate size. When the characteristic properties of the hamiltonian matrix are examined in light of the type of solution required, partitioning of the configuration space is shown to result in an expansion of the problem about a limited core of states, where the small but cumulative interactions of vast regions of the remaining space are reduced to the form of an effective potential. With proper selection of the core, the evaluation of this potential can be readily and accurately truncated to a level involving minimum expenditure in time and effort. In particular only diagonal elements and a strip of the full CI matrix are required to achieve an accuracy of 1 – 5 kcal/mole with complete treatment for configuration spaces of order tens of thousands. In addition, a close look at current theory on the generation of matrix elements between spin symmetry adapted configurations leads to simplified expressions where the matrix elements are derived in the form of a weighted sum of molecular integrals in which the weighting coefficients represent the integrated value of the wavefunctions over spin coordinates. For typical cases of low multiplicity and limited numbers of open shells the list of unique parameters needed to generate all weights are shown to be readily stored as a program library. Actual times for matrix element generation are believed to be an order of magnitude faster than current techniques. Practical demonstration of the accuracy and efficiency of the method is provided by calculations on formaldehyde, water, and ethylene.     

Spin-free approach for evaluation of electronic matrix elements using character operators of ℒN

A spin-free method is presented for evaluating electronic matrix elements over a spin-independent many-electron Hamiltonian. The spin-adapted basis of configuration state functions is obtained using a nonorthogonal spin basis consisting of projected spin eigenfunctions. The general expressions for the matrix elements are given explicitly, and it is demonstrated how the matrix elements may be obtained simply from the knowledge of the irreducible characters of the permutation group ℒ_N. The presented formulas are very general and may be applied in connection with both spin-coupled valence bond studies and in conventional configuration interaction (CI) methods based on an orthonormal orbital basis. © 1996 John Wiley & Sons, Inc.