Correlation energy extrapolation by intrinsic scaling. II. The water and the nitrogen molecule

The extrapolation method for determining benchmark quality full configuration-interaction energies described in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] is applied to the molecules H(2)O and N(2). As in the neon atom case, discussed in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] remarkably accurate scaling relations are found 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. The method for extrapolating a sequence of smaller configuration-interaction calculations to the full configuration-interaction energy and for constructing compact accurate configuration-interaction wave functions is also found to be effective for these molecules. The results are compared with accurate ab initio methods, such as many-body perturbation theory, coupled-cluster theory, as well as with variational calculations wherever possible.     

Configuration-interaction energy derivatives in a fully variational formulation

A configuration-interaction energy function (Lagrange) which is variational in all variables, including the orbital rotational parameters, is constructed. When this Lagrangian is used for obtaining configuration-interaction derivatives, all the important simplifications which occur for derivatives of variational wave functions carry over in a straightforward way. In particular, the state and orbital rotational response parameters obey the 2n+1 rule and the Lagrange multipliers obey the somewhat stronger 2n+2 rule. The simplifications which are normally obtained by invoking the Handy-Schaefer technique are automatically incorporated to all orders. Simple expressions for energy derivatives up to third order are presented. The relationship between the numerical errors in the variational parameters and the errors in the calculated energy derivatives is discussed.     

Configuration interaction calculations on the nitrogen molecule

A contracted Gaussian basis set capable of describing about 63% of the correlation energy of N₂ has been used in a detailed configuration-interaction calculation. Second-order perturbation theory overestimated the correlation energy by 23–50% depending on how H⁰ was chosen. Pair-pair interaction affects the correlation energy by about 20% while quadruple excitations have an 8% effect.     

New iterative scheme for a simultaneous calculation of m first eigenstates of a real symmetric matrix

A new iterative scheme for a simultaneous calculation of the m lowest eigenvalues together with their eigenvectors has been derived for a real symmetric matrix. The scheme is based on the orthogonal gradient method and is easy to use for large-scale configuration-interaction calculations of electronic wave functions. A variant of the scheme deals with nonorthogonal basis functions, which are particularly simple in the case of the bonded-function method of Boys.     

Ab initio multireference configuration-interaction theoretical study on the low-lying spin states in binuclear transition-metal complex: magnetic exchange of [(NH3)5Cr(mu-OH)Cr(NH3)5]5+ and [Cl3FeOFeCl3]2-

The magnetic exchange interaction behavior and energy spectrum of low-lying spin states are investigated by using ab initio multireference configuration-interaction method for the representative binuclear transition-metal complexes [(NH(3))(5)Cr(mu-OH)Cr(NH(3))(5)](5+) and [Cl(3)FeOFeCl(3)](2-). Our calculations for the nonmodeling real title complexes found that under the appropriate basis sets and active space, ab initio method at multireference configuration-interaction level of theory is able to give accurate energy spectrum of low-lying spin states within reachable computation demand nowadays and the deviation of magnetic exchange interaction to Lande interval rule can be described by the biquadratic correction in terms of Heisenberg spin Hamiltonian. As a methodology comparison, density-functional theory combined with broken-symmetry approach provides an alternative yet efficient approach to produce accurate numerical results, but there are dependences on the particular chosen exchange-correlation functionals and system dependent. The spin population analyses at complete active space self-consistent-field level of the theory provide an instructively understanding and prediction for the magnetic interaction mechanism.     

Calculation of molecular electronic spectra by projected-unrestricted Hartree–Fock theory

This paper is concerned with a new application of projected-unrestricted Hartree–Fock theory, namely, the calculation of electronic spectra for symmetric molecules. The excited electronic state is represented by a single determinant whose unrestricted nature allows for orbital rearrangement relative to the self-consistent ground state. The self-consistent calculation must be followed by spin projection to obtain appropriate spin eigenstates. It was necessary to develop modified procedures for portions of the spin projection calculation because our method of constructing the wave functions produces degeneracies among the natural orbitals. Illustrative calculations using the all-valence-electron INDO approximations produced results which compared favorably with configuration-interaction treatments. The method described here should be most useful, however, in conjunction with ab initio calculations using flexible basis sets.     

The low-lying electronic states of YCu

The spectroscopic constants for the singlet and tripletstates of YCu below about 15 000 cm⁻¹ are determined using an internally contracted multireference configuration-interaction approach. These calculations are calibrated by studies of fewer states using higher levels of correlation treatment and/or basis sets. The computed T_c values and radiative lifetimes are in reasonable agreement with experiment. The calculations confirm the previous experimental assignment for all but one state, where theory helps resolve between two possible assignments.     

SAC-CI general-R study of the ionization spectrum of HCl

The valence ionization spectrum of HCl is studied by symmetry-adapted-cluster configuration-interaction general-R and SD-R methods. The general-R method describes well the peak positions and intensities of seven satellite lines observed below the double ionization threshold. The twinning shake-up states due to the (4σ)⁻¹ state and the Rydberg states of HCl⁺ are correctly reproduced. Received: 26 June 1998 / Accepted: 9 September 1998 / Published online: 8 February 1999     

Calculation of Vertical Ionization Potentials of Oxygen Difluoride,Difluoramine, and Difluoromethane by Local Density Approximation

The vertical ionization potentials of OF₂, HNF₂, and CH₂F₂ were computed by the deMon density functional program. The results are compared with earlier calculations and with experiment. The average absolute deviation of the 21 computed ionization potentials of the outer valence electrons from experiment is 0.44 eV, which compares well with 0.37 eV for frozen-orbital configuration-interaction calculations. Although this performance is not as good as perturbation corrections to Koopmans' theorem, the computation requirements are much less demanding.     

Simple test of the utility of modified Hartree-Fock orbitals: The He atom

A method proposed recently for the generation of modified Hartree-Fock virtual orbitals has been tested by performing a simple configuration-interaction calculation for the ground state of the He atom. A very compact truncated basis set was constructed by using an a priori criterion based on the probability density within the region of the occupied orbital. The best results were obtained by making the virtual orbital energies more positive.     

Generalized brillouin theorem for multiconfigurational SCF theories

The matrix elements of the total Hamiltonian between a multiconfigurational SCF wave function and some well-defined linear combinations of excited Slater determinants are equal to zero. By means of this generalized Brillouin theorem it is possible to estimate the improvements to be expected from a subsequent configuration-interaction treatment. The expression of the effective potential for the orbitals can be also derived in the frame of a given multiconfigurational theory. As an example, the case of the CMC-SCF method recently suggested [9] is examined.     

Analytic calculation of the diagonal Born-Oppenheimer correction within configuration-interaction and coupled-cluster theory

Schemes for the analytic calculation of the diagonal Born-Oppenheimer correction (DBOC) are formulated and implemented for use with general single-reference configuration-interaction and coupled-cluster wave function models. Calculations are reported to demonstrate the convergence of the DBOC with respect to electron-correlation treatment and basis set as well as to investigate the size-consistency error in configuration-interaction calculations of the DBOC. The importance of electron-correlation contributions to the DBOC is illustrated in the computation of the corresponding corrections for the reaction energy and activation barrier of the F + H2 --> FH + H reaction as well as of the atomization energy for trans-butadiene.     

A study of the ground state wave function of carbon monoxide

A large configuration-interaction calculation has been performed to determine the wave function, energy, and molecular properties of CO. The most important configurations were used to obtain the natural geminals and their occupation numbers. A pair-energy approach to the correlation energy was attempted with results which differ significantly from the configuration-interaction results.     

Elastic scattering of low-energy electrons by N2 including the effect of target electronic correlation

A procedure to use configuration-interaction (CI) target wave-functions in the electron–molecule collision theory is applied to study the elastic e⁻–N₂ scattering in the (5–20) eV incident energy range. Correlated static and exchange contributions to the interaction potential are presented. Two different atomic basis sets are used. Differential cross sections (DCS) obtained by using Hartree–Fock or CI wave-functions are presented and compared. In the CI case, single and double, and single, double and triple excitations are considered. The effect of electron correlation is analyzed in all the cases. The continuum wave-functions were obtained via the Schwinger variational iterative method. The influence on the DCS of both the size of the atomic basis set and the inclusion of higher-order excitations in the CI calculation is discussed.     

Ab initio Hartree–Fock and configuration-interaction treatment of the interaction between two nickel atoms

The interaction between two nickel atoms in the configurations (3d)⁸(4s)² and (3d)⁹ (4s)¹ has been calculated using ab initio methods (Hartree–Fock and configuration interaction). The results of the calculations compare favorably with the optical spectrum. The discrepancy between the calculated and the experimental dissociation energy is discussed, and a new estimate of the dissociation energy is given. The configuration-interaction calculations show that the interaction between the two nickel atoms is of a very complex nature. In spite of this the binding can be interpreted in a simple way. The bond is minly due to the 4sσ_g molecular orbital while the 3d orbitals of the two nuclei are exchange coupled.     

Intermediate neglect of differential overlap spectroscopic studies on lanthanide complexes

Summary The Intermediate Nelgect of Differential Overlap model for spectroscopy has been extended to lanthanide complexes by including spin-orbit coupling. The method uses atomic spectroscopy and model Dirac-Fock calculations on the lanthanide atoms and ions to obtain ionization potentials, Slater-Condon factors and basis sets. The spin-orbit interaction strength, (nl), is acquired from atomic spectroscopy, and only one-center terms are formally included. Calculation then proceeds using one open-shell operator for all sevenf-orbitals initially assumed degenerate to generate starting non-relativistic molecular orbitals for the subsequent configuration-interaction and spin-orbit calculation.Calculations are performed on the monoxides La, Ce, Gd, and Lu where there are ample experimental assignments. In general, the results are quite good, suggesting that the calculated energies, oscillator strengths and spin-orbit splittings can be used with success in assigning spectra, even in those cases wherejj-coupling is of intermediate strength.     

Full configuration interaction benchmark calculations for transition moments

Full configuration-interaction (FCI) calculations have been performed for the ã ¹A₁–b¹B₁and ã ¹A₁–(2)¹A₁transitions in CH₂ and for selected dipole and quadrupole transitions in BeO. The FCI transition moments are compared to those obtained from correlation treatments that truncate the n-particle expansion. The state-averaged MCSCF/SOCI and FCI results agree well, even for BeO, where the CASSCF level nonorthogonal transition moment differs from the state-averaged CASSCF transition moment.     

Calculation of ground- and excited-state potential energy curves for barium-rare gas complexes in a pseudopotential approach

Adiabatic potential curves for the ground state and several low-lying excited states of the barium atom interacting with Ne, Ar, Kr and Xe have been obtained from valence ab initio configuration-interaction calculations. Atomic cores are replaced by scalar-relativistic l-dependent pseudopotentials, while core-polarization potentials are used for describing correlation contributions of the rare-gas atoms and the Ba²⁺ cores. Implications of the resulting potential curves for the interpretation of experimental data are discussed, together with first applications of the curves for calculating absorption profiles of the (6s ²)¹S→(6p)¹P Ba transition. Received: 7 April 1998 / Accepted: 27 July 1998 / Published online: 12 October 1998     

An Ab Initio calculation of the spin dipole-dipole parameters for methylene

The electron spin dipole-dipole interaction in CH₂ has been calculated as a function of bond angle with configuration-interaction wave functions built from contracted gaussianlobe basis functions. The values D = 0.781 cm^?1 and E = 0.050 cm^?1 were obtained for the spin dipole-dipole contribution to these parameters for the best CI wave function at the equilibrium geometry. The angular dependence of D shows that the assumption of perfect orbital following is not valid. Based on previous estimates of the spin-orbit contribution to D, the total D is estimated to be 0.9 ± 0.1 cm^?1 which is higher than the current experimental value 0.76 ± 0.02 cm^?1.