Cluster Configuration Interaction Research Articles

Challenges in the Use of Quantum Computing Hardware-Efficient Ansätze in Electronic Structure Theory.

Advances in quantum computation for electronic structure, and particularly heuristic quantum algorithms, create an ongoing need to characterize the performance and limitations of these methods. Here we discuss some potential pitfalls connected with the use of hardware-efficient Ansätze in variational quantum simulations of electronic structure. We illustrate that hardware-efficient Ansätze may break Hamiltonian symmetries and yield nondifferentiable potential energy curves, in addition to the well-known difficulty of optimizing variational parameters. We discuss the interplay between these limitations by carrying out a comparative analysis of hardware-efficient Ansätze versus unitary coupled cluster and full configuration interaction, and of second- and first-quantization strategies to encode Fermionic degrees of freedom to qubits. Our analysis should be useful in understanding potential limitations and in identifying possible areas of improvement in hardware-efficient Ansätze.

The excited states of azulene: A study of the vibrational energy levels for the lower ππ*-valence states by configuration interaction and density functional calculations, and theoretical studies of the Rydberg states.

A new vacuum ultraviolet absorption (VUV) spectrum of azulene vapor has been obtained by using a synchrotron radiation source. The onset of the ultraviolet spectrum, previously reported by Sidman et al., has been analyzed in detail by Franck-Condon (FC) and Herzberg-Teller (HT) methods. The photoelectron spectral profile identifies the 3px-Rydberg state 00 band to be 131cm-1 from the VUV maximum. Excited state energy levels were calculated by three independent methods: the wide scan VUV spectrum was correlated with symmetry adapted cluster configuration interaction calculations. The low energy portion of the spectrum was studied by both time dependent density functional theoretical methods (TDDFT) and multi-reference multi-root CI (MRD-CI). Equilibrium structures were determined for valence states at the TDDFT level. Rydberg states were determined by both TDDFT and MRD-CI. The FC + HT analyses were performed on the TDDFT wave-functions. The HT intensity profiles are generally low in intensity, relative to the FC ones; however, HT is dominant in the second singlet state (S2, 11A1). As a result, numerous non-symmetric modes, their overtones, and combination bands show considerable intensity in that band. Energies obtained from use of extremely diffuse s-, p-, d-, or f-character functions enabled realistic extrapolation to the IE1 for many Rydberg states (RS). The lowest RS (3b13s) based on IE2 lies at 4.804eV with a quantum defect of 0.714. Differentiation between valence and RS is readily made using the second moments of the charge distribution.

Geometric, electronic and spectral properties of germanium and Eu-doped germanium clusters

This study explored the geometric, electronic, and spectral properties of germanium and Eu-doped germanium clusters and compared their simulated PES spectra. The stability of Gen and EuGen nanoclusters was examined with density functional theory using FHI-aims as a software package. Symmetry-adapted cluster-configuration interaction general-R (SAC-CI-General-R) method and the SDD basis set were adopted to determine ionization energies and calculate their intensities. Natural bond orbital (NBO) calculations were performed to determine the effective molecular orbitals in the ionization and study the electron density on the nanoclusters. The shape of molecular orbitals (MO) involved in the ionization process for each structure was displayed and interpreted. The analyses of binding energies showed that increasing the size of nanoclusters leads to more stability for nanoclusters. Ionization energy and the photoelectron spectrum of these clusters indicated that Eu as an impurity reduces ionization energy and shifts the ionization processes towards infrared wavelengths. Interestingly, pure and doped clusters followed a similar pattern in terms of an increase/decrease in the first ionization energy compared to n-1 and n + 1 clusters.

Investigation on the electronic structures of thiamine and related compounds: Free base or salt?

We report the simulated photoelectron spectra of thiamine free base, thiamine and thiamine diphosphate (ThDP) in the gas phase. The structures of eighty conformers of thiamine (vitamin B1) were optimized by DFT method at the B3LYP/6-31+G(d) level. Then population ratios (PRS) with Boltzmann distribution equation were calculated using Gibbs free energy and the stable conformers were obtained. The ionization energies of these conformers were determined by two high-level computational methods. General-R-symmetry adapted cluster-configuration interaction (general-R-SAC-CI) method and electron-propagator theory (EPT) method were used to obtain vertical valence ionization energies (IP). To characterize the nature of ionization processes about different spectral bands, the natural bonding orbital (NBO) method was used to obtain orbital electron densities. The electron correlation was taken into account with SAC-CI method and MOs shapes and ionization assignments given for each spectral band. Results for ThDP show that spectra of two conformers are different: oxygen lone pair ionizations appear at higher ionization energies in the spectrum of conformer II while giving rise to the first ionization band in conformer I. The validity of Koopmans’s approximation was considered for each ionization band and the role of electron correlation was attributed to breaking down of this approximation. The implications of electronic structure results for biological activity of thiamin are discussed. Comparison with the earlier work using aerosol thermodesorption method suggests that free base was present in their photoionization spectra in addition to the deprotonated cation.

The ionized states of 6,6-dimethylfulvene; the vibrational energy levels studied by photoionization, configuration interaction and density functional calculations

A new synchrotron-based photoionization spectrum of 6,6-dimethylfulvene shows significant vibrational fine structure (VFS), in contrast to previous studies; this was successfully analysed by Franck-Condon (FC) methods. The sequence of ionic states in the range 7 to 19 eV has been determined by both symmetry adapted cluster configuration interaction and density functional methods, especially using the long-range corrected version of the Becke three-parameter hybrid functional (B3LYP) using the Coulomb-attenuating method (CAM-B3LYP). Both lead to reliable theoretical values for both the calculated vertical and adiabatic ionization energies. The FC profile for the lowest ionization energy (IE1, X2A2) shows extensive VFS which is analysed successfully. The second IE (A2B1) shows truncated structure owing to overlap with IE1.

Electronic Couplings and Electrostatic Interactions Behind the Light Absorption of Retinal Proteins.

The photo-functional chromophore retinal exhibits a wide variety of optical absorption properties depending on its intermolecular interactions with surrounding proteins and other chromophores. By utilizing these properties, microbial and animal rhodopsins express biological functions such as ion-transport and signal transduction. In this review, we present the molecular mechanisms underlying light absorption in rhodopsins, as revealed by quantum chemical calculations. Here, symmetry-adapted cluster-configuration interaction (SAC-CI), combined quantum mechanical and molecular mechanical (QM/MM), and transition-density-fragment interaction (TDFI) methods are used to describe the electronic structure of the retinal, the surrounding protein environment, and the electronic coupling between chromophores, respectively. These computational approaches provide successful reproductions of experimentally observed absorption and circular dichroism (CD) spectra, as well as insights into the mechanisms of unique optical properties in terms of chromophore-protein electrostatic interactions and chromophore-chromophore electronic couplings. On the basis of the molecular mechanisms revealed in these studies, we also discuss strategies for artificial design of the optical absorption properties of rhodopsins.

Photoionization of zwitterionic liquids

The electronic structures of three zwitterionic liquids (Zw-IL) have been studied using high-level ab initio method: equation-of-motion coupled-cluster (IP-EOM-CCSD) method. This method was found to match experimental UV photoelectron spectrum (UPS) of related N-methylimidazole better than Outer-valence Green’s Function (OVGF) method or Symmetry Adapted Cluster-Configuration Interaction (SAC-CI) method. Zw-IL gas phase photoelectron spectra have been simulated in the valence ionization regions based on the vertical ionization energies calculated. Valence ionizations have been attributed to specific molecular orbitals to specific functional groups The calculated electronic structures and valence ionization energies of Zw-ILs can be related to their polarizability which in turn influences the AC conductivity. AC conductivity is one of the principal properties of Zw-ILs which makes them very useful as electrolyte materials in lithium ion batteries or electric capacitors.

Potential-energy curve for the a3Σu+ state of a lithium dimer with Slater-type orbitals

We report state-of-the-art ab initio calculations of the potential energy curve for the $a^3\Sigma_u^+$ state of the lithium dimer conducted to achieve spectroscopic accuracy ($<$1cm$^{-1}$) without any prior adjustment to fit the corresponding experimental data. The nonrelativistic clamped-nuclei component of the interaction energy is calculated with a composite method involving six-electron coupled cluster and full configuration interaction theories combined with basis sets of Slater-type orbitals ranging in quality from double- to sextuple-zeta. To go beyond the nonrelativistic Born-Oppenheimer picture we include both the leading-order relativistic and adiabatic corrections, and find both of these effects to be non-negligible within the present accuracy standards. The potential energy curve developed by us allowed to calculate molecular parameters ($D_e$, $D_0$, $\omega_e$ etc.) for this system, as well as the corresponding vibrational energy levels, with an error of only a few tenths of a wavenumber ($0.2-0.4\,$cm$^{-1}$). We also report an ab initio value for the scattering length of two $^2S$ lithium atoms which determines the stability of the related Bose-Einstein condensate.

Structural and electronic properties of Gen and EuGen-1 nanoclusters: A full potential DFT study

In this work, the stability, structure and electronic properties of the nanoclusters of germanium (Gen) and europium atom doped germanium clusters (EuGen-1) with n=2 to 12, 15 and 20 were investigated. First, the stability of nanoclusters such as Gen and EuGen-1 was addressed using FHI-aims as a software package based on the density functional theory. Then the lowest-energy structures were selected for calculating the first vertical ionization with the symmetry adapted cluster-configuration interaction General-R (SAC-CI-General-R) method. The results of this research show that there is a good agreement between calculation and experiment ionization potential for Gen nanoclusters. Generally, the analyses of binding energies show that increasing the size of nanoclusters leads to more stability for nanoclusters. The most stable nanoclusters for EuGen can be created with exchanging the Eu atom in the most stable Gen+1 nanoclusters, but there is an exception for n=11 case. Here, the second difference in energy (∆2E) and gap energy are computed for the stable nanoclusters. The results of ionization energy and second difference in energy confirm that Ge7 and Ge10 also EuGe8 and EuGe10 have the most stability.

Excitation of hydrated Li+ and Na+ to their dissociative states: The effect of hydrogen bond on the dissociation of LiO and NaO bonds and the comparison of the TD-DFT and SAC-CI excited dissociative states.

In this work, the ground and excited dissociative potential energy curves of hydrated Li+ and Na+ ions with different structures, containing two, three, and four M-O bonds (M=Li and Na), have been calculated. The vertical energies for the excitation of the clusters to their dissociative states were calculated. The scanning of the potential surfaces was performed in the direction of two normal vibrational modes related to the symmetric and asymmetric stretching of M-O bonds. The difference in the arrangement and number of water molecules around the alkali cation made it possible to study the effect of the hydrogen bond network on the dissociation of M-O bonds. Two different methods including the time-dependent density functional theory (TD-DFT) and direct-symmetry adapted cluster-configuration interaction (direct-SAC-CI) were used for calculating the potential energy curves, separately to compare the TD-DFT method with a correlative computational method such as SAC-CI. The TD-DFT method predicted the charge transfer from water molecules to alkali cation during the dissociation of clusters in the gas phase while the electrostatic field of water blocked this charge transfer. For some clusters, it was found that the change of the theoretical method from the TD-DFT to SAC-CI creates changes in the states of fragments obtained from the dissociation and charge transfer.

Extensive Quantum Chemistry Study of Neutral and Charged C4N Chains: An Attempt To Aid Astronomical Observations

Many molecular species can presumably still be observed in space if they are adequately characterized chemically. In this paper, we suggest that this could be the case of the neutral (C$_4$N$^0$) and anion (C$_4$N$^-$) cyanopropynylidene chains, which were not yet identified in space although both the neutral (C$_3$N$^0$ and C$_5$N$^0$) and anion (C$_3$N$^-$} and C$_5$N$^-$) neighboring members of the homologous series were observed. Extensive data obtained from quantum chemical calculations using density functional theory (DFT), coupled cluster (CC), and quadratic configuration interaction (QCI) methods for all charge and spin states of interest for space science (doublet and quartet neutrals, triplet and singlet anions, and singlet and triplet cations) are reported: e.g., bond metric and natural bond order data, enthalpies of formation, dissociation and reaction energies, spin gaps, rotational constants, vibrational properties, dipole and quadrupole momenta, electron attachment energies ($EA$) and ionization potentials ($IP$). The fact that (not only for C$_4$N but also for C$_2$N and C$_6$N) the quantum chemical methods utilized here are able to excellently reproduce the experimental $EA$ value -- which is often a challenge for theory -- is particularly encouraging, since this indicates that theoretical estimates of chemical reactivity indices (which are key input parameters for modeling astrochemical evolution) can be trusted. The presently calculated enthalpies of formation and dissociation energies do not substantiate any reason to assume that C$_4$N is absent in space. To further support this idea, we analyze potential chemical pathways of formation of both C$_4$N$^0$ and C$_4$N$^-$, which include association and exchange reactions.

Interactions and charge-transfer dynamics of anAl+ion immersed in ultracold Rb and Sr atoms

Atomic clocks based on an Al$^+$ ion sympathetically cooled by a laser-cooled alkaline-earth ion have achieved unprecedented accuracy. Here, we investigate theoretically interactions and charge transfer dynamics of an Al$^+$ ion immersed in an ultracold gas of Rb and Sr atoms. We calculate potential energy curves and transition electric dipole moments for the (Al+Rb)$^+$ and (Al+Sr)$^+$ ion-atom systems using coupled cluster and multireference configuration interaction methods with scalar relativistic effects included within the small-core energy-consistent pseudopotentials in Rb and Sr atoms. The long-range interaction coefficients are also reported. We use the electronic structure data to investigate cold collisions and charge transfer dynamics. Scattering of an Al$^+$ ion with alkali-metal or alkaline-earth-metal atom is governed by one potential energy curve whereas charge transfer can lead to several electronic states mixed by the relativistic spin-orbit coupling. We examine the branching ratios resulting from the interplay of the short- and long-range effects, as well as the prospects for the laser-field control and formation of molecular ions. We propose to employ the atomic clock transition in an Al$^+$ ion to monitor ion-atom scattering dynamics via quantum logic spectroscopy. The presented results pave the way for the application of atomic ions other than alkali-metal and alkaline-earth-metal ones in the field of cold hybrid ion-atom experiments.

Electronic and vibrational structure in the S0 and S1 states of corannulene.

Corannulene is a nonplanar aromatic hydrocarbon also known as a buckybowl. Its electronic and vibrational structure has been investigated by analyzing its fluorescence excitation spectrum and dispersed fluorescence spectrum in a supersonic jet. Its spectral features are in keeping with the expectation, confirmed by some previous results, that it has fivefold or C5v symmetry. The observed prominent vibronic bands in the S1 ← S0 transition have been assigned to e1 and e2 bands on the basis of theoretical calculations so that the S1 state was assigned to 1E2. The symmetry adapted cluster configuration interaction calculation supports this assignment of the S1 electronic state, although the time-dependent density functional theory calculation suggests that the S1 state is 1A2. It has also been shown that the normal coordinates for strong vibronic bands mainly include out-of-plane vibrational motion. The rotational envelopes are well explained by taking account of the Coriolis interaction between the degenerate vibrational and rotational levels. The mechanism of bowl-to-bowl inversion is also discussed with the results of theoretical calculations regarding the barrier to inversion and metastable conformation.

Multiferroic properties of melanothallite Cu2OCl2

Here we report on $P\text{\ensuremath{-}}E$ hysteresis loop measurements that unravel the ferroelectric nature of melanothallite ${\mathrm{Cu}}_{2}{\mathrm{OCl}}_{2}$, a new multiferroic material with high critical temperature. Its spin structure was investigated by polarized and unpolarized neutron scattering experiments which reveal a cycloidal magnetic structure with vector chirality (magnetic polarity) that can be inverted by opposite poling of the sample with an inverted electric field. This shows that ${\mathrm{Cu}}_{2}{\mathrm{OCl}}_{2}$ is a spin-induced ferroelectric material. Finally, we show that the ferroelectric properties of ${\mathrm{Cu}}_{2}{\mathrm{OCl}}_{2}$ are driven by the inverse Dzyaloshinskii-Moriya interaction mechanism which is also able to predict the observed direction of the ferroelectric polarization properly. The origin of the noncollinear spin structure in melanothallite are competing AFM-FM exchange couplings which we estimate from a combined ab initio $+$ cluster configuration interaction calculation.

Exploring response of Li2 molecule to external electric field: A DFT and SAC-CI study

Quantum chemical calculations are performed using Gaussian16W Software to theoretically investigate the response of Li2 molecule to external electric field. Ground state properties of Li2 molecule in the presence of electric field are modelled using Density Functional Theory(CAM-B3LYP/[6-311++G(3df,3pd)]) while excited states are modelled using Symmetry Adapted Cluster Configuration Interaction theory and 6-311++G∗∗ basis set. The effect of external electric field on ground state properties including structural (bond length, total energy, harmonic vibrational frequency and rotational constant), electronic (dipole moment and polarizability) and thermodynamic (vibrational contribution to partition function, thermal energy, entropy and specific heat capacity) properties is reported. External electric field modifies the charge distribution within the molecule and hence its molecular properties. Potential energy curves and transition dipole moments of 22 states (13Singlet + 9Triplet) are also reported. The computed parameters agree well with the experimental data wherever the later is available.

The low-lying electronic states of HfO2− and HfO2: A symmetry adapted cluster–configuration interaction (SAC-CI) study

The low-lying doublet states of the HfO2− anion and low-lying triplet excited states of the HfO2 molecule were studied using the SAC-CI method. The vertical excitation spectrum of HfO2− was calculated. Four valence-bound states (X2A1, 12B1, 22A1, and 12B2(II)) and one dipole-bound state (2A1(DB)) of HfO2− were found. The vertical electron detachment energies (VDEs) from the ground electronic state of HfO2− to the triplet excited states of HfO2 were obtained. These VDEs were compared with previous photoelectron spectra of HfO2−, and possible candidate states for the unassigned bands were found. The equilibrium geometries of the valence-bound states of HfO2− and some selected triplet excited states of HfO2 were optimized. The adiabatic relative energies of these electronic states were obtained. Density functional theory (BPW91) was also applied to compute some electronic states of HfO2− and HfO2 for comparison.

High accuracy theoretical investigations of CaF, SrF, and BaF and implications for laser-cooling.

The NL-eEDM collaboration is building an experimental setup to search for the permanent electric dipole moment of the electron in a slow beam of cold barium fluoride molecules [NL-eEDM Collaboration, Eur. Phys. J. D 72, 197 (2018)]. Knowledge of the molecular properties of BaF is thus needed to plan the measurements and, in particular, to determine the optimal laser-cooling scheme. Accurate and reliable theoretical predictions of these properties require the incorporation of both high-order correlation and relativistic effects in the calculations. In this work, theoretical investigations of the ground and lowest excited states of BaF and its lighter homologs, CaF and SrF, are carried out in the framework of the relativistic Fock-space coupled cluster and multireference configuration interaction methods. Using the calculated molecular properties, we determine the Franck-Condon factors (FCFs) for the A2Π1/2→X2Σ1/2 + transition, which was successfully used for cooling CaF and SrF and is now considered for BaF. For all three species, the FCFs are found to be highly diagonal. Calculations are also performed for the B2Σ1/2 +→X2Σ1/2 + transition recently exploited for laser-cooling of CaF; it is shown that this transition is not suitable for laser-cooling of BaF, due to the nondiagonal nature of the FCFs in this system. Special attention is given to the properties of the A'2Δ state, which in the case of BaF causes a leak channel, in contrast to CaF and SrF species where this state is energetically above the excited states used in laser-cooling. We also present the dipole moments of the ground and excited states of the three molecules and the transition dipole moments (TDMs) between the different states. Finally, using the calculated FCFs and TDMs, we determine that the A2Π1/2→X2Σ1/2 + transition is suitable for transverse cooling in BaF.

The Intriguing Case of the One‐Photon and Two‐Photon Absorption of a Prototypical Symmetric Squaraine: Comparison of TDDFT and Wave‐Function Methods

AbstractWe face the challenging description of the excited states responsible for one photon (OPA) and two photon (TPA) absorption in squaraine dyes, adopting both time‐dependent density functional theory and a large variety of post Hartree Fock methods, including coupled cluster and adiabatic diagrammatic construction methods (ADC, to the second and third order), symmetry adapted cluster configuration interaction (CI), CASSCF including second‐order perturbative corrections (PT2) with standard CASPT2 recipe and according to n‐electron valence PT2 (NEVPT2) approach, and an additional multireference CI with PT2 corrections (CI‐MRPT2). We selected a small prototypical symmetric squaraine dye for which these accurate computations are feasible and experimental data are available. We show that while all methods reasonably reproduce the OPA spectrum, an acceptable description and assignment of the states responsible for TPA is only possible through ADC(3) and multireference calculations, due to the strong involvement of double‐excitations. The nature of ground state and OPA and TPA states is investigated with a rigorous reading of the CASSCF wavefunctions in terms of localized molecular orbitals on the donor and acceptor fragments, showing that these states arise from a balance of many different contributions including biradical configurations, local excitations and charge‐transfer states where both side aromatic rings and the carbonyls of the squarylium moiety act as donors.

Theoretical study of the low-lying electronic states of iron hydride cation.

Both FeH and FeH+ are predicted to be abundant in cool stellar atmospheres and proposed to be molecular components of the gas phase interstellar medium (ISM). However, experimental and simulated data for both species are lacking, which have hindered astronomical detection. There are no published laboratory data for the spectroscopy of FeH+ in any frequency regime. It is also not established if FeH+ possesses salient multireference character, which would pose significant challenges for ab initio modeling of geometric and spectroscopic properties. With a set of high-level coupled cluster and multireference configuration interaction computations, a study of the electronic structure of the ground state and seven excited states of FeH+ was carried out. An X5Δi electronic ground state of FeH+ is found, in agreement with previous theoretical studies. Including corrections for spin-orbit coupling and anharmonic vibrational effects, the Ω = 3, ν = 0 spin ladder of the A5Πi electronic state lies 872 cm-1 higher in energy than the Ω = 4, ν = 0 spin ladder of the ground state. Combined with previous work in our laboratory, the ionization energy of FeH is computed to be 7.4851 eV. With modern multireference configuration interaction and coupled cluster methods, spectroscopic constants (re, Be, ωe, ωexe, αe, and D¯e) for several bound excited states (A5Πi, B 5Σi +, a 3Σr -, b3Φi, c3Πi, d3Δr, and 7Σ+) were characterized. This study will lead efforts to identify FeH+ in the ISM and help solve important remaining questions in quantifying metal-hydride bonding.

Theoretical study of the absolute inner-shell photoionization cross sections of the formic acid and some of its hydrogen-bonded clusters.

Inner-shell absolute photoabsorption and photoionization cross sections of the formic acid, HCOOH, and its small hydrogen-bonded clusters, i.e., (HCOOH)2, HCOOH2 +, HCOHOH+, and HCOOH·H3O+, were calculated at the time-dependent density functional theory (TDDFT) level, and the results were used to analyze the effect of the formic acid clustering on the carbon and oxygen K-edge photoionization cross sections. The discrete electronic pseudospectra obtained with square-integrable (L2) basis set calculations were used in an analytic continuation procedure based on continued fraction functions to obtain the photoabsorption cross sections. Symmetry adapted cluster configuration interaction calculations on the small formic acid clusters have also been performed at the oxygen K-edge to assign the discrete transitions and ionization potentials in support to the TDDFT results.