Form Of Configuration Interaction Research Articles

Extraction of a One-Particle Reduced Density Matrix from a Quantum Monte Carlo Electronic Density: A New Tool for Studying Nondynamic Correlation

In this work, we present a method to build a first order reduced density matrix (1-RDM) of a molecule from variational Quantum Monte Carlo (VMC) computations by means of a given correlated mapping wave function. Such a wave function is modeled on a Generalized Valence Bond plus Complete Active Space Configuration Interaction form and fits at best the density resulting from the Slater-Jastrow wave function of VMC. The accuracy of the method proposed has been proved by comparing the resulting kinetic energy with the corresponding VMC value. This 1-RDM is used to analyze the amount of correlation eventually captured in Kohn-Sham calculations performed in an unrestricted approach (UKS-DFT) and with different energy functionals. We performed test calculations on a selected set of molecules that show a significant multireference character. In this analysis, we compared both local and global indicators of nondynamic and dynamic correlation. Moreover, following the natural orbital decomposition of the 1-RDM, we also compared the effective temperatures of the corresponding Fermi-like distributions. Although there is a general agreement between UKS-DFT and VMC, we found the best match with the functional LC-BLYP.

Geminal-based configuration interaction

The antisymmetrized geminal power (AGP) wave function has a long history and considerable conceptual appeal, but in many situations its accuracy is wanting. Here, we consider a form of configuration interaction (CI) based upon the AGP wave function and take advantage of its killing operators to construct an excitation manifold. Our geminal CI reduces to standard single-determinant-based CI in the limit in which AGP reduces to a single determinant. It substantially improves upon AGP in the reduced BCS Hamiltonian, which serves as a prototype for the kinds of strong pairing correlations relevant in Bardeen-Cooper-Schrieffer-style superconductivity. Moreover, our geminal CI naturally generalizes to add correlation to more general geminal-based wave functions than AGP.

A new method of solving the many-body Schrödinger equation

A method of solving the Schr\"{o}dinger equation based on the use of constant particle-particle interaction potential surfaces (IPS) is proposed. The many-body wave function is presented in a configuration interaction form, with coefficients depending on the total interaction potential. The corresponding set of linear ordinary differential equations for the coefficients was developed. To reduce the computational work, a hierarchy of approximations based on interaction potential surfaces of a part of the particle system was worked out. The solution of a simple exactly solvable model and He-like ions proves that this method is more accurate than the conventional configuration interaction method and demonstrates a better convergence with a basis set increase.

Valence photodetachment of Li−and Na−using relativistic many-body techniques

The multiconfiguration Tamm-Dancoff technique (MCTD) is applied to study photodetachment of negative ions of lithium and sodium. A cusplike structure is found in the photodetachment cross section just below the first detachment-plus-excitation threshold of Li${}^{\ensuremath{-}}$ (Li 2$p$), and of Na${}^{\ensuremath{-}}$ (Na 3$p$), in qualitative agreement with existing theoretical and experimental results. The current work emphasizes the importance of correlation in the form of configuration interaction in the photodetachment process and demonstrates the utility of MCTD in dealing with highly correlated systems.

Transitions in C II, N III, and O IV

We present oscillator strengths and transition probabilities between levels belonging to 2s 22p, 2s2p 2, 2p 3, 2s 23l (l=0,1,2) configurations for each of C II, N III, O IV and, in the case of C II only, the 2s 24p and 2s 25p configurations. The wavefunctions are of configuration interaction form, and the radial functions have been optimized using the code CIV3 to represent both spectroscopic orbitals and correlation effects.

Accurate multichannel continuum states by a general configuration interaction expansion in a B-spline basis: application to He photoionization

We report theoretical calculations of the total and partial cross section and asymmetry parameter for He photoionization up to the N = 3 threshold. Multichannel continuum wavefunctions are obtained via a least squares solution of the Schrödinger equation employing a basis set expansion based on a primitive B-spline radial basis and a general configuration interaction form. This allows use of a mixed full CI and close-coupling expansion in a completely general approach to improve correlation description in the continuum channels. The present algorithm correctly describes the full range of phenomena encountered with full details and a remarkable accuracy both on non-resonant cross sections and resonance structures. An accuracy of better than 0.001 Mb is estimated both on total and partial cross sections, also Fano resonance parameters compare very well with the best methods available based on Hylleraas type wavefunctions and complex coordinate rotation.

Transitions in Fluorine-Like Ions

We present oscillator strengths of transitions between the states belonging to the 2s22p5, 2s2p6, 2s22p43l (l = 0, 1, 2) configurations in fluorine-like ions in the range 10 ≤ Z ≤ 33. A summary of the leading percentage compositions is given for 18 ≤ Z ≤ 33. The wave functions are of configuration interaction form and the radial functions have been optimized using the code CIV3 to represent both spectroscopic orbitals and correlation effects.

Configuration interaction of states of the quasi-one-electron type

A study has been made of quasi-one-electron models defined by one-electron variational operators: antisymmetrized degree* of geminal (ADG), the extended Hartree-Fock method (EHF), and one-particle amplitudes of spin pairing (OASP). A generalization has been proposed in the form of configuration interaction of corresponding states. It has been shown that the OASP, EHF, and ADG are algebraically equivalent to exactly the same many-electron construction related to condensation of different types of spin excitons. A matrix scheme of calculation has been developed, through which variational solutions can be obtained and a configuration interaction calculation can be performed for all three models within the framework of a single program. The method has been applied to the π-states of short polyenes, where it has succeeded in account for 90% of the correlation energy.

Local Permutational Symmetry and the Separated-Atom Limit

Local permutational symmetries are shown to supply approximate quantum numbers for a system composed of approximately localized subsystems. Local permutational symmetries associated with simple valence-bond wavefunctions in the separated-atom limit are studied and in certain cases are found to yield a nonphysical combination of local permutational symmetries. This nonphysical behavior can be avoided by use of a certain suitable form of configuration interaction or by a projection with either an appropriate chemically canonical matric basis element or a generalized structure projector.

Configuration Mixing in the N=4 Electron Isoelectronic Sequence*

The theoretical central-field-approximation predictions for the 3P and 1P terms of the 1s2 2s3p configuration in the N=4 electron isoelectronic sequence are in violent disagreement with observation. Correlation effects in the form of configuration interaction have been included by considering the mixing among nine odd configurations. Even though the terms are displaced considerably, they remain quite pure, and after configuration mixing the agreement between theory and observation is good. In order to show the use of such theoretical calculation, weighted oscillator strengths for the 2s2 1S1–2s3p1P1, 3P1 transitions are also computed.