Configuration Interaction Model Research Articles

Theoretical study on molecular charge populations of 1D π-stacked multimers in neutral and electron oxidation states

Abstract We theoretically investigated molecular charge populations of 1D π-stacked multimers consisting of π-conjugated molecules in the neutral and electron oxidation states based on the valence-bond (VB) theory. Qualitative analysis for a π-stacked trimer model based on the VB mixing diagram suggested that the inner monomer site tends to be more positively charged than the outer sites in the monocationic π-stacked trimer. Spatial expansion of each molecular site orbital toward the stacking direction is predicted to enhance the difference of positive charge populations between the inner and outer monomers. In contrast, an opposite tendency for the site charges was expected in the dicationic π-stacked trimer, primarily due to the hole–hole Coulomb repulsions. To generalize the results of the trimer to π-stacked N-mers, 1D N-site VB configuration interaction models were constructed considering the orbital expansion effects between the sites. We examined how the number of monomers (N), stacking distance (R), and characteristic orbital exponent for the monomers (ζ) affected the molecular charge populations in the monocationic and dicationic π-stacked N-mers through the parameters χij characterizing the orbital expansion effect. The results are expected to help establish design strategies for novel electronic functional materials based on discrete stacks of π-conjugated molecules.

Variational quantum eigensolver for closed-shell molecules with non-bosonic corrections.

The realization of quantum advantage with noisy-intermediate-scale quantum (NISQ) machines has become one of the major challenges in computational sciences. Maintaining coherence of a physical system with more than ten qubits is a critical challenge that motivates research on compact system representations to reduce algorithm complexity. Toward this end, the variational quantum eigensolver (VQE) used to perform quantum simulations is considered to be one of the most promising algorithms for quantum chemistry in the NISQ era. We investigate reduced mapping of one spatial orbital to a single qubit to analyze the ground state energy in a way that the Pauli operators of qubits are mapped to the creation/annihilation of singlet pairs of electrons. To include the effect of non-bosonic (or non-paired) excitations, we introduce a simple correction scheme in the electron correlation model approximated by the geometrical mean of the bosonic (or paired) terms. Employing it in a VQE algorithm, we assess ground state energies of H2O, N2, and Li2O in good agreement with full configuration interaction (FCI) models respectively, using only 6, 8, and 12 qubits with quantum gate depths proportional to the squares of the qubit counts. With the adopted seniority-zero approximation that uses only one half of the qubit counts of a conventional VQE algorithm, we find that our non-bosonic correction method reaches reliable quantum chemistry simulations at least for the tested systems.

Origin of Ferromagnetic Exchange Coupling in Donor–Acceptor Biradical Analogues of Charge-Separated Excited States

A new donor-acceptor biradical complex, TpCum,MeZn(SQ-VD) (TpCum,MeZn+ = zinc(II) hydro-tris(3-cumenyl-5-methylpyrazolyl)borate complex cation; SQ = orthosemiquinone; VD = oxoverdazyl), which is a ground-state analogue of a charge-separated excited state, has been synthesized and structurally characterized. The magnetic exchange interaction between the S = 1/2 SQ and the S = 1/2 VD within the SQ-VD biradical ligand is observed to be ferromagnetic, with JSQ-VD = +77 cm-1 (H = -2JSQ-VDŜSQ·ŜVD) determined from an analysis of the variable-temperature magnetic susceptibility data. The pairwise biradical exchange interaction in TpCum,MeZn(SQ-VD) can be compared with that of the related donor-acceptor biradical complex TpCum,MeZn(SQ-NN) (NN = nitronyl nitroxide, S = 1/2), where JSQ-NN ≅ +550 cm-1. This represents a dramatic reduction in the biradical exchange by a factor of ∼7, despite the isolobal nature of the VD and NN acceptor radical SOMOs. Computations assessing the magnitude of the exchange were performed using a broken-symmetry density functional theory (DFT) approach. These computations are in good agreement with those computed at the CASSCF NEVPT2 level, which also reveals an S = 1 triplet ground state as observed in the magnetic susceptibility measurements. A combination of electronic absorption spectroscopy and CASSCF computations has been used to elucidate the electronic origin of the large difference in the magnitude of the biradical exchange coupling between TpCum,MeZn(SQ-VD) and TpCum,MeZn(SQ-NN). A Valence Bond Configuration Interaction (VBCI) model was previously employed to highlight the importance of mixing an SQSOMO → NNLUMO charge transfer configuration into the electronic ground state to facilitate the stabilization of the high-spin triplet (S = 1) ground state in TpCum,MeZn(SQ-NN). Here, CASSCF computations confirm the importance of mixing the pendant radical (e.g., VD, NN) LUMO (VDLUMO and NNLUMO) with the SOMO of the SQ radical (SQSOMO) for stabilizing the triplet, in addition to spin polarization and charge transfer contributions to the exchange. An important electronic structure difference between TpCum,MeZn(SQ-VD) and TpCum,MeZn(SQ-NN), which leads to their different exchange couplings, is the reduced admixture of excited states that promote ferromagnetic exchange into the TpCum,MeZn(SQ-VD) ground state, and the intrinsically weaker mixing between the VDLUMO and the SQSOMO compared to that observed for TpCum,MeZn(SQ-NN), where this orbital mixing is significant. The results of this comparative study contribute to a greater understanding of biradical exchange interactions, which are important to our understanding of excited-state singlet-triplet energy gaps, electron delocalization, and the generation of electron spin polarization in both the ground and excited states of (bpy)Pt(CAT-radical) complexes.

Geometric interpretation for coupled-cluster theory. A comparison of accuracy with the corresponding configuration interaction model.

Although coupled-cluster theory is well-known for its accuracy, the geometry associated with the manifold of wave functions reached by the coupled-cluster Ansatz has not been deeply explored. In this article, we look for an interpretation for the high accuracy of coupled-cluster theory based on how the manifold of coupled-cluster wave functions is embedded within the space of n-electron wave functions. We define the coupled-cluster and configuration interaction manifolds and measure the distances from the full-configuration interaction (FCI) wave function to these manifolds. We clearly observe that the FCI wave function is closer to the coupled-cluster manifold that is curved than to the configuration interaction manifold that is flat for the selected systems studied in this work. Furthermore, the decomposition of the distances among these manifolds and wave functions into excitation ranks gives insights into the failure of the coupled-cluster approach for multireference systems. The present results show a new interpretation for the quality of the coupled-cluster method, as contrasted to the truncated configuration interaction approach, besides the well-established argument based on size extensivity. Furthermore, we show how a geometric description of wave function methods can be used in electronic structure theory.

Precision calculation of isospin-symmetry-breaking corrections to T=1/2 mirror decays using configuration-interaction framework built upon multireference charge-dependent density functional theory

We present systematic study of isospin impurities ($\alpha_{\rm ISB}$) to the wave functions of $T=1/2$, $11\leq A \leq 47$ mirror nuclei and the isospin-symmetry-breaking (ISB) corrections ($\delta_{\rm ISB}^{\rm V}$) to their ground state vector $\beta$-decays using, for the first time, multi-reference charge-dependent density functional theory (MR-DFT) that includes strong-force-rooted class-III interaction adjusted to correct for the Nolen-Schiffer anomaly in nuclear masses. We demonstrate that, unexpectedly, the strong-force-rooted isovector force gives rise to a large systematic increase of $\alpha_{\rm ISB}$ and $\delta_{\rm ISB}^{\rm V}$ as compared to the results obtained within MR-DFT that uses Coulomb interaction as the only source of ISB. This, in turn, increases a central value of the $V_{\rm ud}$ element of the CKM matrix extracted from the $T=1/2$ mirrors bringing it closer to the value obtained form the purely vector superallowed $0^+ \to 0^+$ transitions. In order to compute the value of $V_{\rm ud}$, we performed precision calculation of the Fermi matrix elements in $A=19, 21, 35$, and 37 mirror nuclei using DFT-rooted configuration-interaction model that includes all relevant axially-deformed particle-hole configurations built upon Nilsson orbitals originating from the spherical $sd$ shell. Our calculations yield $|V_{\rm ud}|=0.9736(16)$.

Electronic Structure of Lr+ (Z = 103) from Ab Initio Calculations

The four-component relativistic Dirac–Coulomb Hamiltonian and the multireference configuration interaction (MRCI) model were used to provide the reliable energy levels and spectroscopic properties of the Lr+ ion and the Lu+ homolog. The energy spectrum of Lr+ is very similar to that of the Lu+ homolog, with the multiplet manifold of the 7s2, 6d17s1 and 7s17p1 configurations as the ground and low-lying excited states. The results are discussed in light of earlier findings utilizing different theoretical models. Overall, the MRCI model can reliably predict the energy levels and properties and bring new insight into experiments with superheavy ions.

Electronic structure of Rf+ (Z=104) from ab initio calculations

We report calculation of the energy spectrum and the spectroscopic properties of the superheavy element ion: Rf^+. We use the 4-component relativistic Dirac-Coulomb Hamiltonian and the multireference configuration interaction (MRCI) model to tackle the complex electronic structure problem that combines strong relativistic effects and electron correlation. We determine the energies of the ground and the low-lying excited states of Rf+, which originate from the 7s^26d^1, 7s^16d^2, 7s^27p^1, and 7s^16d^17p^1 configurations. The results are discussed vis-\`a-vis the lighter homologue, Hf^+ ion. We also assess the uncertainties of the predicted energy levels. The main purpose of the presented calculations is to provide a reliable prediction of the energy levels and to identify suitable metastable excited states that are good candidates for the planned ion-mobility-assisted laser spectroscopy studies.

Mirror energy differences in T=1/2f7/2 -shell nuclei within isospin-dependent density functional theory

Background: Small asymmetry between neutrons and protons, caused by the differences in masses and charges of the up and down constituent quarks leads to the isospin symmetry breaking. The isospin non-conservation affects broad range of observables from superallowed Fermi weak interaction to isospin-forbidden electromagnetic rates. Its most profound and cleanest manifestation are systematic shifts in masses and excitation energies of mirror atomic nuclei. Purpose: Recently, we constructed the charge-dependent DFT that includes class II and III local interactions and demonstrated that the model allows for very accurate reproduction of Mirror and Triplet Displacement energies in a very broad range of masses. The aim of this work is to further test the charge-dependent functional by studying Mirror Energy Differences (MEDs) in function of angular momentum $I$. Methods: To compute MEDs we use DFT-rooted no core configuration interaction model. This post mean-field method restores rotational symmetry and takes into account configuration mixing within a space that includes relevant (multi)particle-(multi)hole Slater determinants. Results: We applied the model to $f_{7/2}$-shell mirror pairs of $A=43$, $45$, $47$, and $49$ focusing on MEDs in low-spin part (below band crossing) what allowed us to limit the model space to seniority one and three (one broken pair) configurations. Conclusions: We demonstrate that, for spins $I\leq 15/2$ being subject of the present study, our model reproduces well experimental MEDs which vary strongly in function of $I$ and $A$. The quality of model's predictions is comparable to the nuclear shell-model results by Bentley et al. Phys. Rev. C 92, 024310 (2015).

Electron scattering studies of BF and BF2

The present article reports calculated elastic, differential, momentum transfer and excitation cross section for electron scattering from BF and BF2 radicals using the ab initio R-matrix method. The calculations are performed with complete active space—configuration interaction and static exchange models for both targets to yield scattering cross sections and resonance parameters. Elastic and momentum transfer cross sections are also calculated using the spherical complex optical potential method to cover a wide energy range. The total ionization cross section is also reported from ionization threshold to 5 keV. The calculated cross sections for these neutral species are important for BF3 plasma and are reported for the first time to the best of our knowledge except ionization.

Theoretical Molecular Design of Phenanthrenes for Singlet Fission by Diazadibora-Substitution

Based on the valence configuration interaction (VCI) model and quantum chemical calculations, we theoretically investigate the potential of diazadibora-substituted phenanthrenes [(BN)2-phenanthrenes] as novel singlet fission (SF) chromophores. (BN)2-substitution to phenanthrene is performed to exhibit a captodative effect, which is found to enhance both diradical character and exchange integral. These enhanced parameters induced by (BN)2-substitution are shown to bring energetically favorable SF with high triplet excitation energies. In order to reveal the relationship between diradical character and positions replaced by (BN)2, analyses based on the VCI model, odd-electron density, and resonance structures are conducted. Accordingly, a concrete design principle, which is inherent in and is understandable from the topology of (BN)2-phenanthrene, is presented. Furthermore, design strategies to fine-tuning of the diradical character are newly demonstrated based on the additional introduction of π-donor and π-acceptor. The present results provide feasible candidate molecules and novel design strategies toward the discovery of bright SF chromophores for the application to efficient organic solar cells.

Vibrational Coupled Cluster Computations in Polyspherical Coordinates with the Exact Analytical Kinetic Energy Operator.

We present the first use of curvilinear vibrational coordinates, specifically polyspherical coordinates, in combination with vibrational coupled cluster theory. The polyspherical coordinates are used in the context of both the adaptive density-guided approach to potential energy surface construction and in the subsequent vibrational coupled cluster calculations of anharmonic vibrational states. Results obtained based on the polyspherical coordinate parametrization are compared to results obtained with the use of rectilinear vibrational coordinates, namely, normal coordinates and hybrid optimized and localized coordinates for the formaldehyde molecule. This comparison is carried out with the full vibrational configuration interaction model, using the respective fully coupled potential energy surfaces and untruncated kinetic energy operators. The polyspherical coordinates are shown to facilitate an acceleration of convergence for truncated methods when compared to the use of normal coordinates. We furthermore report on calculations on the hydrogen peroxide molecule in the polyspherical coordinate parametrization. The polyspherical vibrational coordinates are shown to perform very well, even for truncated methods, especially when considering the difficulty that rectilinear vibrational coordinates can exhibit in treating complicated internal molecular motion.

Artificial Neural Networks Applied as Molecular Wave Function Solvers.

We use artificial neural networks (ANNs) based on the Boltzmann machine (BM) architectures as an encoder of ab initio molecular many-electron wave functions represented with the complete active space configuration interaction (CAS-CI) model. As first introduced by the work of Carleo and Troyer for physical systems, the coefficients of the electronic configurations in the CI expansion are parametrized with the BMs as a function of their occupancies that act as descriptors. This ANN-based wave function ansatz is referred to as the neural-network quantum state (NQS). The machine learning is used for training the BMs in terms of finding a variationally optimal form of the ground-state wave function on the basis of the energy minimization. It is relevant to reinforcement learning and does not use any reference data nor prior knowledge of the wave function, while the Hamiltonian is given based on a user-specified chemical structure in the first-principles manner. Carleo and Troyer used the restricted Boltzmann machine (RBM), which has hidden units, for the neural network architecture of NQS, while, in this study, we further introduce its replacement with the BM that has only visible units but with different orders of connectivity. For this hidden-node free BM, the second- and third-order BMs based on quadratic and cubic energy functions, respectively, were implemented. We denote these second- and third-order BMs as BM2 and BM3, respectively. The pilot implementation of the NQS solver into an exact diagonalization module of the quantum chemistry program was made to assess the capability of variants of the BM-based NQS. The test calculations were performed by determining the CAS-CI wave functions of illustrative molecular systems, indocyanine green, and dinitrogen dissociation. The simulated energies have been shown to converge to CAS-CI energy in most cases by improving RBM with an increasing number of hidden nodes. BM3 systematically yields lower energies than BM2, reproducing the CAS-CI energies of dinitrogen across potential energy curves within an error of 50 μEh.

Spectroscopic Signatures of Resonance Inhibition Reveal Differences in Donor-Bridge and Bridge-Acceptor Couplings.

The torsional dependence of the ground state magnetic exchange coupling (J) and the corresponding electronic coupling matrix element (HDA) for eight transition metal complexes possessing donor-acceptor (D-A) biradical ligands is presented. These biradical ligands are composed of an S = 1/2 metal semiquinone (SQ) donor and an S = 1/2 nitronylnitroxide (NN) acceptor, which are coupled to each other via para-phenylene, methyl-substituted para-phenylenes, or a bicyclo[2.2.2]octane ring. The observed trends in electronic absorption and resonance Raman spectral features are in accord with a reduction in electronic and magnetic coupling between D and A units within the framework of our valence bond configuration interaction model. Moreover, our spectroscopic results highlight different orbital mechanisms that modulate coupling in these complexes, which is not manifest in the ferromagnetic JSQ-B-NN values. The work provides new detailed insight into the effects of torsional rotations which contribute to inhomogeneities in experimentally determined exchange couplings, electron transfer rates, and electron transport conductance measurements.

Thermal evaporation of pyrene clusters.

This work presents a study of the thermal evaporation and stability of pyrene (C16H10)n clusters. Thermal evaporation rates of positively charged mass-selected clusters are measured for sizes in the range n = 3-40 pyrene units. The experimental setup consists of a gas aggregation source, a thermalization chamber, and a time of flight mass spectrometer. A microcanonical Phase Space Theory (PST) simulation is used to determine the dissociation energies of pyrene clusters by fitting the experimental breakdown curves. Calculations using the Density Functional based Tight Binding combined with a Configuration Interaction (CI-DFTB) model and a hierarchical optimization scheme are also performed in the range n = 2-7 to determine the harmonic frequencies and a theoretical estimation of the dissociation energies. The frequencies are used in the calculations of the density of states needed in the PST simulations, assuming an extrapolation scheme for clusters larger than 7 units. Using the PST model with a minimal set of adjustable parameters, we obtain good fits of the experimental breakdown curves over the full studied size range. The approximations inherent to the PST simulation and the influence of the used parameters are carefully estimated. The derived dissociation energies show significant variations over the studied size range. Compared with neutral clusters, significantly higher values of the dissociation energies are obtained for the smaller sizes and attributed to charge resonance in line with CI-DFTB calculations.

Toward scalable many-body calculations for nuclear open quantum systems using the Gamow Shell Model

Drip-line nuclei have very different properties from those of the valley of stability, as they are weakly bound and resonant. Therefore, the models devised for stable nuclei can no longer be applied therein. Hence, a new theoretical tool, the Gamow Shell Model (GSM), has been developed to study the many-body states occurring at the limits of the nuclear chart. GSM is a configuration interaction model based on the use of the so-called Berggren basis, which contains bound, resonant and scattering states, so that inter-nucleon correlations are fully taken into account and the asymptotes of extended many-body wave functions are precisely handled. However, large complex symmetric matrices must be diagonalized in this framework, therefore the use of very powerful parallel machines is needed therein. In order to fully take advantage of their power, a 2D partitioning scheme using hybrid MPI/OpenMP parallelization has been developed in our GSM code. The specificities of the 2D partitioning scheme in the GSM framework will be described and illustrated with numerical examples. It will then be shown that the introduction of this scheme in the GSM code greatly enhances its capabilities.

Exciton effects on the nonlinear optical properties of the endohedral La@C82 complex

Using the Hartree–Fock single-excitation configuration interaction (CI) model, we calculated the second-order and third-order nonlinear polarizability of the La@C82 molecule. Obtained results indicate that the third-order nonlinear polarizability $$ \gamma $$ is much larger than the second-order nonlinear polarizability $$ \beta $$ and linear polarizability. Also, our results show that the $$ \gamma $$ value of the La@C82 molecule is much larger than those of the C60 and C70 molecules. The spectral shapes of the third-order nonlinear polarizability tensor, the second-order nonlinear polarizability tensor and linear polarizability of the C82 molecule turn out to be determined mainly by the geometrical distributions of the pentagons in the fullerene structures.

Effect of Coulomb interaction on the second-order nonlinear optical and magneto-optical properties of the endohedral La@C82 crystal with spatial dispersion

Using the Hartree-Fock single-excitation configuration interaction (CI) model, the second- order nonlinear optical dielectric tensor, refractive index, reflectivity, circular dichroism (CD), birefringence coefficient (θ) and the effects of spatial dispersion of the simple cubic (sc) phase of the La@C82 crystal are calculated. It is shown that the intermolecular polarization interaction has significant effects on the nonlinear properties of the endohedral fullerenes, and that, in some contrast to other organic species, nondipolar contributions to this interaction are important. The spectral shapes of the second-order nonlinear dielectric tensor of the La@C82 crystal turn out to be determined mainly by the geometrical distributions of the pentagons in the fullerene structures. Our results on the effect of spatial dispersion show that the nonlinear refractive index and reflectivity of the La@C82 crystal in the energy range 0.3–6 eV have sharp structures in each band.

Electron impact scattering study on chlorobenzene

ABSTRACTIn this article, we report a detailed theoretical study on electron interactions with chlorobenzene with incident energies ranging from 0.1 to 5000 eV. Due to this wide range of impact energy, we are able to investigate a variety of processes and report data on resonances, differential cross-sections (DCS), momentum transfer cross-sections (MTCS), rate coefficient, vertical electronic excitations, dissociative electron attachment (DEA), total ionisation cross-sections and total scattering cross-sections (TCS). In order to compute the total scattering cross-sections, we have employed the ab-initio R-matrix method via Quantemol-N for the lower energy range (0.1 eV to 20 eV) and Spherical Complex Optical Potential (SCOP) beyond threshold energy of the target to 5000 eV. The R-matrix calculations are performed using a close-coupling method with the aid of 34 target states, 1667 configuration state functions, and 233 channels employing Configuration Interaction (CI) model. The present study reports evidence for electron scattering resonances through analysis of eigenphase diagrams fitting them to Breit-Wigner profile at low energies below the ionisation threshold.

Gamow-Teller response in the configuration space of a density-functional-theory–rooted no-core configuration-interaction model

The atomic nucleus is a unique laboratory to study fundamental aspects of the electroweak interaction. This includes a question concerning in medium renormalization of the axial-vector current, which still lacks satisfactory explanation. Study of spin-isospin or Gamow-Teller (GT) response may provide valuable information on both the quenching of the axial-vector coupling constant as well as on nuclear structure and nuclear astrophysics. We have performed a seminal calculation of the GT response by using the no-core-configuration-interaction approach rooted on multi-reference density functional theory (DFT-NCCI). The model treats properly isospin and rotational symmetries and can be applied to calculate both the nuclear spectra and transition rates in atomic nuclei, irrespectively of their mass and particle-number parity. The method is applied to compute the GT strength distribution in selected $N\approx Z$ nuclei including the $p$-shell $^8$Li and $^8$Be nuclei and the $sd$-shell well-deformed nucleus $^{24}$Mg. In order to demonstrate a flexibility of the approach we present also a calculation of the superallowed GT beta decay in doubly-magic spherical $^{100}$Sn and the low-spin spectrum in $^{100}$In. It is demonstrated that the DFT-NCCI model is capable to capture the GT response satisfactorily well by using relatively small configuration space exhausting simultaneously the GT sum rule. The model, due to its flexibility and broad range of applicability, may either serve as a complement or even as an alternative to other theoretical approaches including the conventional nuclear shell model.

P,T -odd and magnetic hyperfine-interaction constants and excited-state lifetime for HfF+

Parity- and time-reversal-symmetry violating interaction constants required for the interpretation of a recent measurement (arXiv:1704.07928 [physics.atom-ph]) of corresponding symmetry violations in the $\Omega=1$ (${^3\Delta}_1$) science state of the HfF$^+$ molecular ion are reported. Using a relativistic four-component all-electron multi-reference configuration interaction model the nucleon-electron scalar-pseudoscalar interaction constant is determined as $W_S = 20.0$ [kHz]. An updated result for the electron electric-dipole-moment effective electric field of $|E_{\text{eff}}| = 22.7 \left[\frac{\rm GV}{\rm cm}\right]$ is obtained. Further results of relevance in the context of the search for leptonic charge-parity violation such as magnetic hyperfine interaction constants and electronic $G$-tensor for HfF$^+$ are presented.