General Configuration Interaction Research Articles

Calculating the distance from an electronic wave function to the manifold of Slater determinants through the geometry of Grassmannians

The set of all electronic states that can be expressed as a single Slater determinant forms a submanifold, isomorphic to the Grassmannian, of the projective Hilbert space of wave functions. We explored this fact by using tools of Riemannian geometry of Grassmannians as described by Absil et. al [Acta App. Math. 80, 199 (2004)], to propose an algorithm that converges to a Slater determinant that is critical point of the overlap function with a correlated wave function. This algorithm can be applied to quantify the entanglement or correlation of a wave function. We show that this algorithm is equivalent to the Newton method using the standard parametrization of Slater determinants by orbital rotations, but it can be more efficiently implemented because the orbital basis used to express the correlated wave function is kept fixed throughout the iterations. We present the equations of this method for a general configuration interaction wave function and for a wave function with up to double excitations over a reference determinant. Applications of this algorithm to selected electronic systems are also presented and discussed.

Frozen-density embedding employing configuration interaction as a subsystem method

ABSTRACT We report the implementation of a general configuration interaction (CI) implementation combined with frozen-density embedding (FDE). The implemented direct CI algorithm for ground and excited states covers all truncated CI schemes ranging from CI singles (CIS) to full CI (FCI) and also the complete active-space (CAS) ansatz to treat molecules in which dynamic and static correlation effects dominate, respectively. Combining this general CI ansatz with FDE enables to study environment effects upon molecular properties, required to obtain a balanced description of correlation and environment effects. In the framework of the uncoupled FDE (FDEu) scheme, the implementation allows to combine truncated CI schemes, e.g. CI singles doubles triples quadruples (CISDTQ), embedded in water molecules computed using second-order Møller–Plesset perturbation theory (MP2) and density-functional theory (DFT), also denoted CISDTQ-in-MP2-in-DFT.

To Be or Not to Be: Demystifying the 2nd-Quantized Picture of Complex Electronic Configuration Patterns in Chemistry with Natural Poly-Electron Population Analysis.

We provide a didactic introduction to 2nd-quantized representation of complex electron-hole (e/h) excitation patterns in general configuration interaction wave functions built from orthonormal local orbitals of natural atomic orbital or natural bond orbital (NBO) type. Such local excitation patterns of chemically oriented basis functions can be related to the resonance concepts of valence bond theory, and quantitative evaluation of the associated excitation probabilities then provides an alternative assessment of resonance "weighting" that may be compared with those of NBO-based natural resonance theory. We illustrate the usefulness of anticommutation relations in deriving Pauli-compliant expressions for allowed excitation patterns, showing how the exciton-like promotions φλ → φν (creating an e/h excitation with h in φλ and e in φν ) impose strict constraints on associated e/h-probabilities (requiring, e.g., that the e-probability for an electron "to be" or "not to be" in φν must be rigorously linked to the complementary h-probabilities in φλ ). Specific examples are presented of the quantum Boolean logic for four or six local spin-orbitals, with emphasis on Natural Poly-Electron Population Analysis (NPEPA) evaluation of VB-type covalent and ionic contributions in conventional 2-center bonding, resonance weightings in 3-center hydrogen bonding, and general characteristics of higher-order m-center bonding motifs for m > 3. Numerical results are presented for methylamine, acrolein, and water dimer to illustrate current NPEPA implementation in the NBO program. © 2019 Wiley Periodicals, Inc.

Weighted f-values, A-values, and line strengths for the E1 transitions among 3d 6, 3d 54s, and 3d 54p levels of Fe III

Weighted oscillator strengths, weighted radiative rates, and line strengths for all the E1 transitions between 285 fine-structure levels belonging to the 3d 6, 3d 54s, and 3d 54p configurations of Fe III are presented, in ascending order of wavelength. Calculations have been undertaken using the general configuration interaction (CI) code CIV3. The large configuration set is constructed by allowing single and double replacements from any of 3d 6, 3d 54s, 3d 54p, and 3d 54d configurations to nl orbitals with n ⩽ 5 , l ⩽ 3 as well as 6p. Additional selective promotions from 3s and 3p subshells are also included in the CI expansions to incorporate the important correlation effects in the n = 3 shell. Results of some strong transitions between levels of 3d 6, 3d 54s, and 3d 54p configurations are also presented and compared with other available calculations. It is found that large disagreements occur in many transitions among the existing calculations.

Convergent multichannel continuum states by a general configuration interaction expansion in a B-spline basis: application to photodetachment

We report the theoretical calculation of the total and partial cross section and asymmetry parameter for 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 (CI) form. This allows the 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 remarkable accuracy both on nonresonant cross sections and resonance structures. An accuracy of better than 0.01 Mb is estimated on both the total and partial cross sections, except for the shape resonance. In addition, Fano resonance parameters compare very well with the best methods available based on Hylleraas-type wavefunctions and complex coordinate rotation.

A determinantal approach to spin-orbit configuration interaction

A general configuration interaction (CI) algorithm incorporating one- and two-electron spin-orbit operators is presented. The algorithm is determinant based and enables the use of highly vectorized non-relativistic algorithms in the most operation-intensive part. Excitations between α and β spin orbitals are avoided in the time consuming parts by performing separate S + and S − operations. The relativistic CI expansions are often very large, so the algorithms require only the presence of segments of vectors in memory. Double-group symmetry is fully accounted for and time-reversal symmetry is exploited for both even and odd numbers of electrons.

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.

A method of generating an effective orbital set for configuration interaction calculations

It is proposed that early stages of multiconfiguration self-consistent field (MCSCF) type calculations can be exploited to generate good orbital sets for use in the general configuration interaction (CI) calculation.

An efficient method for the evaluation of coupling coefficients in configuration interaction calculations

A new method for evaluating one-particle coupling coefficients in a general configuration interaction calculation is presented. Through repeated application and use of resolutions of the identity, two-, three- and four-body coupling coefficients and density matrices may be built in a simple and efficient way. The method is therefore of use in both multiconfiguration SCF (MC SCF) and multireference configuration interaction (MRCI) calculations. Examples show that the approach is efficient for both these applications.

The use of projection operators in the configuration interaction problem

Matrix elements of the many-particle Hamiltonian, for atomic, molecular, or nuclear wave function calculations, can be reduced from quadratic to linear forms by the use of totally antisymmetric basis functions which result from applying projection operators to single determinants. The projection operators select components with definite transformation properties under symmetry operations of the invariance group of the Hamiltonian. It is shown that the projected functions need to be known only up to an undetermined numerical factor in order to determine matrix elements between the corresponding normalized functions. A method is given for constructing such projected determinants from any orthonormal set of totally antisymmetric functions with the same transformation properties under the symmetry group. To complete the presentation of a self-contained, practicable, and reasonably efficient method for evaluating the general configuration interaction matrix element, a minimal set of linear equations are stated which determine the transformation coefficients that completely reduce the representation of an arbitrary symmetry group.