Pair Orbitals Research Articles

Local, expressive, quantum-number-preserving VQE ansätze for fermionic systems

We propose VQE circuit fabrics with advantageous properties for the simulation of strongly correlated ground and excited states of molecules and materials under the Jordan–Wigner mapping that can be implemented linearly locally and preserve all relevant quantum numbers: the number of spin up (α) and down (β) electrons and the total spin squared. We demonstrate that our entangler circuits are expressive already at low depth and parameter count, appear to become universal, and may be trainable without having to cross regions of vanishing gradient, when the number of parameters becomes sufficiently large and when these parameters are suitably initialized. One particularly appealing construction achieves this with just orbital rotations and pair exchange gates. We derive optimal four-term parameter shift rules for and provide explicit decompositions of our quantum number preserving gates and perform numerical demonstrations on highly correlated molecules on up to 20 qubits.

One-to-One Correspondence between Reaction Pathways and Reactive Orbitals.

The one-to-one correspondence between reaction pathways in the potential energy theory and reactive orbitals in the electronic theory for reactions is presented. In this study, the reactive orbital energy method is applied to the intrinsic reaction coordinates of the global reaction route map generated by an automated reaction path search method. The reactive orbital energy method specifies the pairs of occupied and unoccupied reactive orbitals driving chemical reactions and determines whether the reactions are electron transfer-driven or dynamics-driven. Surprisingly, it is found that the reactive orbital pairs are determined one by one for the electron transfer-driven reaction pathways from an identical molecule. The reactive orbital energy method is also found to provide the sophisticated interpretations of reactions for the electronic motions. This one-to-one correspondence is expected to trigger the unification of the potential energy theory and the electronic theory for reactions that have been independently developed.

Spectroscopic signatures of gate-controlled superconducting phases

We investigate the tunneling conductance of superconductor-insulator-normal metal (SIN) and superconductor-insulator-superconductor (SIS) heterostructures with one superconducting side of the junction that is electrically driven and can exhibit $\pi$-pairing through a modification of the surface inversion asymmetric couplings. In SIN tunneling we find that the variation of the electrically driven interactions generally brings an increase of quasi-particles in the gap due to orbitally polarized depaired states, irrespective of the inter-band phase rearrangement. The peak of SIN conductance at the gap edge varies with a trend that depends both on the strength of the surface interactions as well as on the character of the gate-induced superconducting state. While this shift can be also associated with thermal effects in the SIN configuration, for the SIS geometry at low temperature the electric field does not yield the characteristic matching peak at voltages related with the difference between the gaps of the superconducting electrodes. This observation sets out a distinctive mark for spectroscopically distinguishing the thermal population effects from the quantum gate-driven signatures. In SIS the electrostatic gating yields a variety of features with asymmetric peaks and broadening of the conductance spectral weight. These findings indicate general qualitative trends for both SIN and SIS tunneling spectroscopy which could serve to evaluate the impact of gate-control on superconductors and the occurrence of non-centrosymmetric orbital antiphase pairing.

Spectroscopic and quantum chemical study on a non-linear optical material 4-[(1E)-3-(5-chlorothiophen-2-yl)-3-oxoprop-1-en-1-yl] phenyl4-methylbenzene-1-sulfonate

Chalcone derivatives are known for their characteristic non-linear optical efficiency. In the present work, the relation between the molecular structure and non-linear optical properties of a synthesized chalcone derivative 4-[(1E)-3-(5-chlorothiophen-2-yl)-3-oxoprop-1-en-1-yl] phenyl4-methylbenzene-1-sulfonate (4TPMS) have been investigated by combined experimental and theoretical approaches. The title compound 4TPMS was characterized by spectroscopic techniques viz. Raman, FT-IR, UV-vis, and 1H NMR. Further, the experimental findings were validated by quantum chemical computations. The crystalline geometry of 4TPMS was optimized to energy minima by employing density functional theory (DFT) with B3LYP/6-311++G(d,p) approximation level. Harmonic vibrational frequencies were calculated and the spectral assignments have been done by potential energy distribution (PED) analysis. Significant non-linear optical (NLO) responses of chalcone are mainly caused by charge delocalization between lone pair and antibonding molecular orbitals within the molecule. Hence, natural bond orbital (NBO) was performed to analyze the charge delocalization along with the stability of the molecule. The population analysis based on Charges from Electrostatic Potentials using a Grid based method (CHELPG) was employed to understand the electrophilic/nucleophilic reaction sites.Moreover, the time-dependent density functional theory (TD-DFT) was employed to predict the energies, absorption wavelengths (λmax) and oscillator strengths (f) of the electronic transitions. The TD-DFT calculation successfully reproduces the experimental UV-Vis spectrum of 4TPMS. The chemical shifts observed in 1H-NMR and the calculated GIAO shielding tensors also showed good agreement. A vibrational contribution to the NLO activity and the effect of charge delocalization on the NLO response were illustrated by comparing the similar kind of chalcone derivatives.

CO2 separation of a novel Ultem‐based mixed matrix membrane incorporated with Ni2+‐exchanged zeolite X

AbstractIn this study, polyetherimide (Ultem) was chosen as a polymeric matrix, and micron‐sized Ni2+‐exchanged nano‐porous NaX zeolite was selected as an inorganic filler to fabricate novel mixed matrix membranes (MMMs) for CO2 separation. Fabricated membranes were evaluated by Differential scanning calorimeter, Fourier transform infrared spectroscopy, X‐ray diffraction, scanning electron microscopy, and energy dispersive X‐ray. The influences of filler loading (0–5 wt.%) and feed pressure (2–10 bar) on gas separation properties were surveyed. CO2/N2 ideal selectivity of 3 wt.% NiX loaded MMM (optimum MMM) was increased to 34 (about 36%) compared to 25 for the pristine membrane. Furthermore, CO2 permeability was improved by about 45%, from 1.3 Barrer for the pure membrane to 1.88 Barrer for MMM containing 3 wt.% functionalized filler. These improvements originate from a combination of the inherent surface diffusion mechanism of zeolite X and reversible reaction between free orbitals of transition metal ions (Ni2+) and electron pairs of CO2 molecules. © 2021 Society of Chemical Industry and John Wiley & Sons, Ltd.

Control of chaotic behavior in the dynamics of generalized Bonhoeffer-van der Pol system: Effect of asymmetric parameter

The effect of the asymmetric parameter in the dynamics, both of the forced Duffing van der Pol (DVdP) system and of the forced generalized Bonhoeffer-van der Pol (BVdP) system is investigated, namely the possibility for these systems to execute dynamics chaos even for large values of this asymmetric parameter. We have shown that the dynamics of the associated non dissipative and unforced system can be interpreted by means of an effective energy potential which may exhibit a two-hump or a two-well configuration according to the magnitude of the parameters of the system. In the two-well configuration, a pair of pulses of different amplitudes describing homoclinic orbits useful in the prediction of irregular dynamics for the associated forced system are analytically derived as well as the expression of the single pulse describing the single homoclinic orbit in the case of two-hump configuration and which leads to a kink-antikink pair (heteroclinic orbits) in the absence of the asymmetric parameter. By means of the Melnikov theory, the conditions for the existence of the transverse intersection of stable and unstable orbits or dynamics chaos are also derived. In the particular case for which the system can exhibit a pair of homoclinic orbits, the presence of the asymmetric parameter induces two types of domains among which a more favorable domain for the existence of chaotic behavior. In both cases, the asymmetric parameter reduces the domain range in which the system can execute regular dynamics and consequently increases its domain of a possible dynamics chaos. The accuracy of these analytical results is checked through the bifurcation diagrams and the corresponding Lyapunov exponents resulting from numerical simulations. It appears that the background properties of the unforced system, namely its capacity to exhibit autonomous oscillations and the stability of its equilibrium points which are closely connected to the magnitude of the asymmetric parameter, influence the accuracy of the analytical predictions.

Cover Picture

This cover picture shows the design and synthesis of N‐heterocyclic carbenes bearing a nido‐C2B9 carborane ligand as the backbones. In this work, gold(I) complex was prepared to prove the imidazolium salts could serve as carbene ligands and the computational analyses revealed high‐lying lone pair orbitals of these ligands, predicting their strong σ–donating abilities. More details are given in the article by Xiao et al. on page 2410—2416.image

Basis set truncation corrections for improved frozen natural orbital CCSD(T) energies

A number of approaches are proposed and assessed to reduce the frozen natural orbital (FNO) truncation error of coupled-cluster singles and doubles with perturbative triples [CCSD(T)] energies. The diagrammatic energy decomposition method of Irmler and Grüneis [J. Chem. Phys. 151, 104107 (2019)] is extended to the FNO truncation correction of the particle-particle ladder (PPL) term in the case of closed- and open-shell molecular systems. The approach is tested for reaction, interaction, and atomization energies, and it is found the most robust for a wider range of FNO truncation thresholds outperforming the commonly employed additive MP2 correction. We also show that the linear extrapolation (LE) of FNO-CCSD(T) energies as a function of second-order Møller–Plesset (MP2) energies provides the best correlation energies and most balanced energy differences with tighter FNO thresholds, but it lacks systematic error compensation that would be required for the better performance with looser FNO thresholds. Further insight is gained from a diagrammatic and spin-component decomposition based analysis. Moreover, orbital (pair) specific energy decompositions are utilised to introduce size-consistent variants of the promising PPL and LE FNO corrections and their analogues for (T), which are also readily applicable in the context of popular local correlation methods.

N‐Heterocyclic Carbenes with a Nido‐C2B9 Carborane Backbone

Main observation and conclusionThe steric and electronic properties of N‐heterocyclic carbenes (NHCs) can be modified by the exocyclic substituents at the nitrogen atoms, by 1—3 atoms’ replacements of the five‐membered imidazolium skeleton and by the changes of the backbones. Herein, we report the usage of nido‐C2B9 carborane anions as the backbones of NHCs. Stirring the mixture of secondary amino o‐carboranes (1b—1e), triethyl orthoformate and HBF4∙Et2O results in the unexpected cage‐opening of o‐carboranes to afford the nido‐C2B9 carborane anions supported N‐heterocyclic carbene precursors (4b—4e). Deprotonation of 4b with sodium hexamethyldisilazide at −78 oC affords the N‐heterocyclic carbene ligand, which was used to form an Au(I) NHC complex (5). DFT calculations revealed a high‐lying lone pair orbitals of the carbene ligands, predicting their strong σ‐donating abilities.

Magnetic Field-Induced "Mirage" Gap in an Ising Superconductor.

Superconductivity is commonly destroyed by a magnetic field due to orbital or Zeeman-induced pair breaking. Surprisingly, the spin-valley locking in a two-dimensional superconductor with spin-orbit interaction makes the superconducting state resilient to large magnetic fields. We investigate the spectral properties of such an Ising superconductor in a magnetic field taking into account disorder. The interplay of the in-plane magnetic field and the Ising spin-orbit coupling leads to noncollinear effective fields. We find that the emerging singlet and triplet pairing correlations manifest themselves in the occurrence of "mirage" gaps: at (high) energies of the order of the spin-orbit coupling strength, a gaplike structure in the spectrum emerges that mirrors the main superconducting gap. We show that these mirage gaps are signatures of the equal-spin triplet finite-energy pairing correlations and due to their odd parity are sensitive to intervalley scattering.

Synthesis of novel benzohydrazide and benzoic acid derivatives: Crystal Structure, Hirshfeld surface analysis and DFT computational studies

New series of benzohydrazide/benzoic acid derivatives were synthesized (4a-b and 5a-b) and subjected to solid-state characterization by NMR spectroscopic measurements. The molecular and crystal structures of 4a and 5a have also been examined by single-crystal X-ray crystallography were reveal that naphthalene frameworks are close to planarity. Besides, the dihedral angle between the mean plane of the naphthalene ring system and the phenyl ring is 2.26(7) and 78.87(8)° for 4a and 5a, respectively. The molecules are linked through N—H⋯O and C—H⋯O hydrogen bonds, forming chains parallel to the ab plane in benzohydrazide and O—H⋯O contacts in benzoic acid. The sheets are further stacked through C—H⋯π interactions resulting in the formation of a 3D supramolecular network. Hirshfeld surface analysis has also been performed to investigate intermolecular interactions in the solid-state; the most important contributions for the crystal packing are from H⋯H, C⋯H/H⋯C, and O⋯H/H⋯O interactions. Additionally, DFT calculations with the B3LYP/6-311G (d, p) level of the theory have been used to analyze the Mulliken atomic charges, molecular electrostatic potential map, and non-linear optical properties of the compounds were produced using the optimized structures. Moreover, the natural bond orbital analysis is conducted to explore the interactions among different orbital and lone pairs taking place within the compounds. The energy framework calculations suggest that the contacts formed between molecules are largely dispersive.

Two-orbital quantum discord in fermion systems

A simple expression to compute the quantum discord between two orbitals in fermion systems is derived using the parity superselection rule. As the correlation between orbitals depends on the basis chosen, we discuss a special orbital basis, the natural one. We show that quantum correlations between natural orbital pairs disappear when the pairing tensor is zero, i.e. the particle number symmetry is preserved. The Hartree-Fock orbitals within a Slater determinant state, a Hartree-Fock-Bogoliubov quasiparticle orbitals in a quasiparticle vacuum, or the ground state of a Hamiltonian with particle symmetry and their corresponding natural orbitals are some relevant examples of natural basis and their corresponding states. Since natural orbitals have that special property, we seek for the quantum discord in non-natural orbital basis. We analyze our findings in the context of the Lipkin-Meshkov-Glick and Agassi models.

Modeling Ultrafast Electron Dynamics in Strong Magnetic Fields Using Real-Time Time-Dependent Electronic Structure Methods.

An implementation of real-time time-dependent Hartree–Fock (RT-TDHF) and current density functional theory (RT-TDCDFT) for molecules in strong uniform magnetic fields is presented. In contrast to earlier implementations, the present work enables the use of the RT-TDCDFT formalism, which explicitly includes field-dependent terms in the exchange–correlation functional. A range of current-dependent exchange–correlation functionals based on the TPSS functional are considered, including a range-separated variant, which is particularly suitable for application to excited state calculations. The performance of a wide range of propagator algorithms for real-time methods is investigated in this context. A recently proposed molecular orbital pair decomposition analysis allows for assignment of electronic transitions, providing detailed information about which molecular orbitals are involved in each excitation. The application of these methods is demonstrated for the electronic absorption spectra of N2 and H2O both in the absence and in the presence of a magnetic field. The dependence of electronic spectra on the magnetic field strength and its orientation relative to the molecule is studied. The complex evolution of the absorption spectra with magnetic field is rationalized using the molecular orbital pair decomposition analysis, which provides crucial insight in strong fields where the spectra are radically different from their zero-field counterparts.

LOCAL COORDINATES FOR COMPLEX AND QUATERNIONIC HYPERBOLIC PAIRS

AbstractLet $G(n)={\textrm {Sp}}(n,1)$ or ${\textrm {SU}}(n,1)$ . We classify conjugation orbits of generic pairs of loxodromic elements in $G(n)$ . Such pairs, called ‘nonsingular’, were introduced by Gongopadhyay and Parsad for ${\textrm {SU}}(3,1)$ . We extend this notion and classify $G(n)$ -conjugation orbits of such elements in arbitrary dimension. For $n=3$ , they give a subspace that can be parametrized using a set of coordinates whose local dimension equals the dimension of the underlying group. We further construct twist-bend parameters to glue such representations and obtain local parametrization for generic representations of the fundamental group of a closed (genus $g \geq 2$ ) oriented surface into $G(3)$ .

Improved accuracy and transferability of molecular-orbital-based machine learning: Organics, transition-metal complexes, non-covalent interactions, and transition states.

Molecular-orbital-based machine learning (MOB-ML) provides a general framework for the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. The application of Nesbet's theorem makes it possible to recast a typical extrapolation task, training on correlation energies for small molecules and predicting correlation energies for large molecules, into an interpolation task based on the properties of orbital pairs. We demonstrate the importance of preserving physical constraints, including invariance conditions and size consistency, when generating the input for the machine learning model. Numerical improvements are demonstrated for different datasets covering total and relative energies for thermally accessible organic and transition-metal containing molecules, non-covalent interactions, and transition-state energies. MOB-ML requires training data from only 1% of the QM7b-T dataset (i.e., only 70 organic molecules with seven and fewer heavy atoms) to predict the total energy of the remaining 99% of this dataset with sub-kcal/mol accuracy. This MOB-ML model is significantly more accurate than other methods when transferred to a dataset comprising of 13 heavy atom molecules, exhibiting no loss of accuracy on a size intensive (i.e., per-electron) basis. It is shown that MOB-ML also works well for extrapolating to transition-state structures, predicting the barrier region for malonaldehyde intramolecular proton-transfer to within 0.35 kcal/mol when only trained on reactant/product-like structures. Finally, the use of the Gaussian process variance enables an active learning strategy for extending the MOB-ML model to new regions of chemical space with minimal effort. We demonstrate this active learning strategy by extending a QM7b-T model to describe non-covalent interactions in the protein backbone-backbone interaction dataset to an accuracy of 0.28 kcal/mol.

Saddle-center and periodic orbit: Dynamics near symmetric heteroclinic connection

An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same level of a Hamiltonian, and two non-symmetric heteroclinic orbits permuted by the involution. This is a codimension one structure; therefore, it can be met generally in one-parameter families of reversible Hamiltonian systems. There exist two possible types of such connections depending on how the involution acts near the equilibrium. We prove a series of theorems that show a chaotic behavior of the system and those in its unfoldings, in particular, the existence of countable sets of transverse homoclinic orbits to the saddle periodic orbit in the critical level, transverse heteroclinic connections involving a pair of saddle periodic orbits, families of elliptic periodic orbits, homoclinic tangencies, families of homoclinic orbits to saddle-centers in the unfolding, etc. As a by-product, we get a criterion of the existence of homoclinic orbits to a saddle-center.

Interpretation of Exchange Interaction through Orbital Entanglement

Recently, the analysis of single-orbital entropy and mutual information has been introduced as a tool for the investigation of contributions to the exchange (J) coupling between open-shell metal ions [Stein et al. J. Phys. Chem. Lett. 2019, 10, 6762-6770]. Here, we show that this analysis may lead to an incorrect interpretation of the J-coupling mechanism. Instead, we propose an orbital-entanglement analysis that is based on the two-electron density and that provides a coherent picture of the contributing exchange pathways, which seems fully consistent with the available J values. For this purpose, we used a prototypical bis-μ-oxo binuclear manganese complex ([Mn2O2(NH3)8]4+) and demonstrated that its antiferromagnetism (J < 0), calculated by using the active space composed of all valence pO and dMn orbitals, correlates well with the largest elements in the differential low-spin vs high-spin entanglement map. These elements correspond to interactions between the pairs of dMn orbitals mediated by the oxo-bridging out-of-plane p orbitals, representing the π superexchange pathway. We also show that the reduction of active space to manifold of the singly occupied magnetic orbitals does not lead to discrepancy between the calculated J values and entanglement maps. This contrasts to analysis of mutual information, which suggests the "direct" dMn-dMn interactions to play a dominant role for the J coupling, irrespective of the size of active space as well as of the antiferromagnetism expected. The failure is attributed to the large contribution of spin entanglement contained in the mutual information of the low-spin state, which may be regarded as the origin of the different complexity of its wave function and electron density.

Photophysical investigation of maleimide units substituted [5]carbohelicene derivatives: Absorption, emission, ECD and CPL spectral-shapes

[5]Carbohelicene derivatives are generally unable to show chirality due to the easily occurred racemization. While stable chirality could be achieved by introducing bulky substituents. To understand the substituent effect on the optical properties, we present a systematic study on the chiroptical properties of two [5]carbohelicene derivatives (HeliIm and MeO-HeliIm) from pure electronic level to vibrational analysis. Electronic calculations show that the introduction of methoxy (MeO-HeliIm) promotes the electron transfer and causes narrower Molecular Orbital (MO) gaps of key orbital pairs with respect to HeliIm. This leads to the relative shift of the spectra between HeliIm and MeO-HeliIm. The vibrationally resolved spectra nicely captured the vibronic features and also correctly reproduced the different signs of chiroptical spectra, in nice agreement with the experiment. They show that Franck-Condon (FC) contribution is of vital importance in the reproduction of the experimental spectral shapes. However, Herzberg-Teller (HT) moderately improves the performance of the vibrationally resolved spectra. What is more, HT modes play a unique role in the analysis of the different optical properties. Finally, it is highlighted that the typical vibration of out-of-plane-deformation of methyl in MeO is responsible for causing the different transition processes.

Global dynamics for a class of new bistable nonlinear oscillators with bilateral elastic collisions

How to model non-smooth dynamical systems and study its non-smooth global dynamics by developing analytical methods is now an important topic. In this paper, a new bistable nonlinear oscillator with bilateral elastic constraints and a three-piecewise nonlinear restoring force is established to study the perturbation of viscous damping and an external harmonic excitation. A five-piecewise linear approach to the restoring force can transform the original dimensionless dynamical equations into a two-dimensional piecewise-defined Hamiltonian systems, separated by four switching manifolds with symmetrical characteristic and subjected to damping dissipation and a periodic excitation. The geometrical structure of the unperturbed system has a pair of symmetrical piecewise-defined homoclinic orbits and each of them transversally and continuously crosses two switching manifolds. The analytical Melnikov method is extended here to fit the theoretical framework for analyzing homoclinic bifurcations and chaotic dynamics for non-smooth oscillators with multiple switching manifolds. A global perturbation technique is presented to calculate the distance between the stable and unstable manifolds and derive the Melnikov function in the form of piecewise-integration. A major innovation here is no need to extend the vector filed near the switching manifolds and carry out rigorous perturbation analysis with geometrical intuition to derive the Hamilton energy differences of trajectories involving infinite time. The developed Melnikov function can be directly used to detect the parameter threshold of homoclinic chaos in the bistable nonlinear oscillator under bilateral elastic collision. Finally, the effectiveness of the Melnikov analysis for homoclinic chaos is verified by simulations.

Quantifying electron-correlation effects in small coinage-metal clusters via ab initio calculations.

We investigate many-electron correlation effects in neutral and charged coinage-metal clusters Cun, Agn, and Aun (n = 1-4) via ab initio calculations using fixed-node diffusion Monte Carlo (FN-DMC) simulations, density functional theory (DFT), and the Hartree-Fock (HF) method. From very accurate FN-DMC total energies of the clusters and the HF results in the infinity large complete-basis-set limit, we obtain correlation energies in these strongly correlated many-electron clusters involving d orbitals. The obtained bond lengths of the clusters, atomic binding and dissociation energies, ionization potentials, and electron affinities are in satisfactory agreement with the available experiments. In the analysis, the electron correlation effects on these observable physical quantities are quantified by relative correlation contributions determined by the difference between the calculated FN-DMC and HF results. We show that the correlation contribution is not only significant for the quantities related to electronic structures of the coinage-metal clusters, such as electron affinity, but it is also essential for the stability of the atomic structures of these clusters. For example, the electron correlation contribution is responsible for more than 90% of the atomic binding energies of the small neutral copper clusters. We also demonstrate the orbital-occupation dependence of the correlation energy and electron pairing of the valence electrons in these coinage-metal clusters from the electron correlation-energy gain and spin-multiplicity change in the electron addition processes, which are reflected in their ionization potentials and electron affinities.