Ground State Energy Of Electron Research Articles

Molecular electronic structure calculation via a quantum computer

Quantum computers can be used to calculate the electronic structure and estimate the ground state energy of many-electron molecular systems. In the present study, we implement the Variational Quantum Eigensolver (VQE) algorithm, as a hybrid quantum–classical algorithm to calculate the ground state energy of the molecules such as H3+, OH−, HF and BH3 in which the number of qubits has an increasing trend. We use the parity transformation for fermion to qubit encoding and the Unitary Coupled Cluster for Single and Double excitations (UCCSD) to construct an ansatz. We compare our quantum simulation results with the computational chemistry approaches including Full Configuration Interaction (FCI), as benchmark energy and Unrestricted Hartree–Fock (UHF), as a common computational method. Our results show that there is a good agreement between molecular ground state energy obtained from VQE and FCI. Moreover, the accuracy of the ground state energies obtained from VQE in our work is higher than the previously reported values. This work aims to benchmark the VQE algorithm to calculate the electronic ground state energy for a new set of molecules that can be good candidates for molecular simulation on a real quantum computer.

Fragmentation of Multiply Charged C10H8 Isomers Produced in keV Range Proton Collision

The dissociation of multiply charged C10H8 isomers produced in fast proton collisions (velocities between 1.41 and 2.4 a.u.) is discussed in terms of their fundamental molecular dynamics, in particular the processes that produce different carbon clusters in such a collision. This aspect is assessed with the help of a multi-hit analysis of daughter ions detected in coincidence with the elimination of H+ and CHn+ (n = 0 to 3). The elimination of H+/C+ is found to be significantly different from CH3+ loss. The loss of CH3+ proceeds through a cascade of momentum-correlated dissociations with the formation of heavy ions such as C9H5+, C9H52+ and C7H3+. The structure of such large fragment ions is predicted with the help of their calculated ground state electronic energies and the multi-hit time-of-flight (ToF) correlation between the second and third hit fragments if detected. Furthermore, we report experimentally the super-dehydrogenation of naphthalene and azulene targets, with evidence of complete dehydrogenation in a single collision.

Electronic Structure, Spectroscopy, Cold Ion–Atom Elastic Collision Properties, and Photoassociation Formation Prediction of the (MgCs)+ Molecular Ion

In this paper, we extensively study the electronic structure, interactions, and dynamics of the (MgCs)+ molecular ion. The exchanges between the alkaline atom and the low-energy cationic alkaline earths, which are important in the field of cold and ultracold quantum chemistry, are studied. We use an ab initio approach based on the formalism of non-empirical pseudo-potential for Mg2+ and Cs+ cores, large Gaussian basis sets, and full-valence configuration interaction. In this context, the (MgCs)+ cation is treated as an effective two-electron system. Adiabatic potential energy curves and their spectroscopic constants for the ground and the first 20 excited states of 1,3Σ+ symmetries are determined. Furthermore, we identify the avoided crossings between the electronic states of 1,3Σ+ symmetries. These crossings are related to the charge transfer process between the two ionic limits, Mg/Cs+ and Mg+/Cs. Therefore, vibrational-level spacings and the transition and permanent dipole moments are presented and analyzed. Using the produced potential energy data, the ground-state scattering wave functions and elastic cross-sections are calculated for a wide range of energies. In addition, we predict the formation of a translationally and rotationally cold molecular ion (MgCs)+ in the ground-state electronic potential energy through a stimulated Raman-type process aided by ion–atom cold collision. In the low-energy limit (<1 mK), elastic scattering cross-sections exhibit Wigner law threshold behavior, while in the high-energy limit, the cross-sections act as a function of energy E go as E−1/3. A qualitative discussion about the possibilities of forming cold (MgCs)+ molecular ions by photoassociative spectroscopy is presented.

Effect of pressure in tuning the physical properties of MAX phase Zr2AN (A = In, Ga): A DFT scheme

The coexistence of metals and ceramics properties has made the MAX phase materials different from other three-dimensional materials. This study investigates several physical properties such as the structural, mechanical, and optoelectronic features of the pressure-induced Zr2AN (A = In, Ga) MAX phase via the density functional theory (DFT) insight. The lattice parameter c is greater than a (=b) as it is layered along the z direction. The electronic ground state energy and the applied pressure are inversely related. The elastic stiffness constants of the hexagonal crystal system have a positive and linear correlation with increasing pressure. The band structure reveals that both structures are electrically conductive at 0–50 GPa pressure range. The PDOS reveals the contribution of the Zr-4d orbital at the Fermi level. The optical parameters in the visible range point to possible optoelectronics and various technological applications.

A Ground-State Dual-Descriptor Strategy for Screening Efficient Singlet Fission Systems.

Exploration of singlet fission (SF) materials is vital for enhancing the photoelectric conversion efficiency of photovoltaic devices, and the development of an effective screening means is in great demand. In this work, we for the first time propose a promising dual-descriptor strategy to predict the SF energetics (ΔESF) from ground-state electronic properties, the gap (GapHL) and exchange energy (KHL) between the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO), where GapHL plays a dominant role and KHL acts as a correction. This strategy is statistically verified through exploring the effect of N-doping on the electronic/energetic properties of the N-doped tetracene derivatives and isomers. Several rules of thumb are suggested, and the reliability of this strategy is validated by comparison with experiments. This work proposes a novel strategy for exploring SF chromophores with insights into the SF energetics from ground-state properties and certainly has fundamental interest and generality in exploring efficient SF-capable materials.

Benchmarking First-Principles Reaction Equilibrium Composition Prediction.

The availability of thermochemical properties allows for the prediction of the equilibrium compositions of chemical reactions. The accurate prediction of these can be crucial for the design of new chemical synthesis routes. However, for new processes, these data are generally not completely available. A solution is the use of thermochemistry calculated from first-principles methods such as Density Functional Theory (DFT). Before this can be used reliably, it needs to be systematically benchmarked. Although various studies have examined the accuracy of DFT from an energetic point of view, few studies have considered its accuracy in predicting the temperature-dependent equilibrium composition. In this work, we collected 117 molecules for which experimental thermochemical data were available. From these, we constructed 2648 reactions. These experimentally constructed reactions were then benchmarked against DFT for 6 exchange-correlation functionals and 3 quality of basis sets. We show that, in reactions that do not show temperature dependence in the equilibrium composition below 1000 K, over 90% are predicted correctly. Temperature-dependent equilibrium compositions typically demonstrate correct qualitative behavior. Lastly, we show that the errors are equally caused by errors in the vibrational spectrum and the DFT electronic ground state energy.

Quantum Many-Body Theory from a Solution of the N-Representability Problem.

Here we present a many-body theory based on a solution of the N-representability problem in which the ground-state two-particle reduced density matrix (2-RDM) is determined directly without the many-particle wave function. We derive an equation that re-expresses physical constraints on higher-order RDMs to generate direct constraints on the 2-RDM, which are required for its derivation from an N-particle density matrix, known as N-representability conditions. The approach produces a complete hierarchy of 2-RDM constraints that do not depend explicitly upon the higher RDMs or the wave function. By using the two-particle part of a unitary decomposition of higher-order constraint matrices, we can solve the energy minimization by semidefinite programming in a form where the low-rank structure of these matrices can be potentially exploited. We illustrate by computing the ground-state electronic energy and properties of the H_{8} ring.

First-Principles Investigation of Electronic and Related Properties of Cubic Magnesium Silicide (Mg2Si)

We present results from ab initio, self-consistent calculations of electronic, transport, and bulk properties of cubic magnesium silicide (Mg2Si). We employed a local density approximation (LDA) potential to perform the computation, following the Bagayoko, Zhao, and Williams (BZW) method, as improved by Ekuma and Franklin (BZW-EF). The BZW-EF method guarantees the attainment of the ground state as well as the avoidance of over-complete basis sets. The ground state electronic energies, total and partial densities of states, effective masses, and the bulk modulus are investigated. As per the calculated band structures, cubic Mg2Si has an indirect band gap of 0.896 eV, from Γ to X, for the room temperature experimental lattice constant of 6.338 Å. This is in reasonable agreement with the experimental value of 0.8 eV, unlike previous ab initio DFT results of 0.5 eV or less. The predicted zero temperature band gap of 0.965 eV, from Γ to X, is obtained for the computationally determined equilibrium lattice constant of 6.218 Å. The calculated value of the bulk modulus of Mg2Si is 58.58 GPa, in excellent agreement with the experimental value of 57.03 ± 2 GPa.

The van der Waals interactions in systems involving superheavy elements: the case of oganesson (Z = 118).

This work presents a study involving dimers composed of He, Ne, Ar, Kr, Xe, Rn, and Og noble gases with oganesson, a super-heavy closed-shell element (Z = 118). He-Og, Ne-Og, Ar-Og, Kr-Og, Xe-Og, Rn-Og, and Og-Og ground state electronic potential energy curves were calculated based on the 4-component (4c) Dirac-Coulomb Hamiltonian and were counterpoise corrected. For the 4c calculations, the electron correlation was taken into account using the same methodology (MP2-srLDA) and basis set quality (Dyall's acv3z and Dunning's aug-cc-PVTZ). All calculations included quantum electrodynamics effects at the Gaunt interaction level. For all the aforementioned dimers the vibration energies, spectroscopic constants (ωe, ωexe, ωeye, αe, and γe), and lifetime as a function of the temperature (which ranged from 200 to 500 K) were also calculated. The obtained results suggest that the inclusion of quantum electrodynamics effects reduces the value of the dissociation energy of all hetero-nuclear molecules with a percentage contribution ranging from 0.48% (for the He-Og dimer) to 9.63% (for the Rn-Og dimer). The lifetime calculations indicate that the Og-He dimer is close to the edge of instability and that Ng-Og dimers are relatively less stable when the Gaunt correction is considered. Exploiting scaling laws that adopt the polarizability of involved partners as scaling factors, it has also been demonstrated that in such systems the interaction is of van der Waals nature (size repulsion plus dispersion attraction) and this permitted an estimation of dissociation energy and equilibrium distance in the Og-Og dimer. This further information has been exploited to evaluate the rovibrational levels in this symmetric dimer and to cast light on the macroscopic properties of condensed phases concerning the complete noble gas family, emphasizing some anomalies of Og.

Quantum Monte Carlo: Reduction of time‐step error with the wave function correction method

AbstractWe compare the accuracy and precision of the wave function correction method to that of traditional diffusion quantum Monte Carlo (traditional DQMC) simulations. Direct calculation of corrections to trial wave functions reduces time step error for Be and Ne electronic ground state energies when compared to traditional DQMC results. The fixed‐node method is utilized for these fermionic systems, so error due to incorrect node locations is not addressed. This correction DQMC method achieves more accurate energies at larger time steps, promising decreased computational cost to reach a given accuracy. For an optimized Be trial wave function, the statistical uncertainty per unit of computational effort is also reduced relative to traditional DQMC. Correction DQMC utilizes walker feed integrals and growth factors, as reported previously. We illustrate the method in a simple harmonic oscillator example, and we report high accuracy energies for Be and Ne at several time steps.

Accurately Determining the Phase Transition Temperature of CsPbI3 via Random-Phase Approximation Calculations and Phase-Transferable Machine Learning Potentials

While metal halide perovskites (MHPs) have shown great potential for various optoelectronic applications, their widespread adoption in commercial photovoltaic cells or photosensors is currently restricted, given that MHPs such as CsPbI3 and FAPbI3 spontaneously transition to an optically inactive nonperovskite phase at ambient conditions. Herein, we put forward an accurate first-principles procedure to obtain fundamental insight into this phase stability conundrum. To this end, we computationally predict the Helmholtz free energy, composed of the electronic ground state energy and thermal corrections, as this is the fundamental quantity describing the phase stability in polymorphic materials. By adopting the random phase approximation method as a wave function-based method that intrinsically accounts for many-body electron correlation effects as a benchmark for the ground state energy, we validate the performance of different exchange-correlation functionals and dispersion methods. The thermal corrections, accessed through the vibrational density of states, are accessed through molecular dynamics simulations, using a phase-transferable machine learning potential to accurately account for the MHPs’ anharmonicity and mitigate size effects. The here proposed procedure is critically validated on CsPbI3, which is a challenging material as its phase stability changes slowly with varying temperature. We demonstrate that our procedure is essential to reproduce the experimental transition temperature, as choosing an inadequate functional can easily miss the transition temperature by more than 100 K. These results demonstrate that the here validated methodology is ideally suited to understand how factors such as strain engineering, surface functionalization, or compositional engineering could help to phase-stabilize MHPs for targeted applications.

DeePKS-kit: A package for developing machine learning-based chemically accurate energy and density functional models

We introduce DeePKS-kit, an open-source software package for developing machine learning based energy and density functional models. DeePKS-kit is interfaced with PyTorch, an open-source machine learning library, and PySCF, an ab initio computational chemistry program that provides simple and customized tools for developing quantum chemistry codes. It supports the DeePHF and DeePKS methods. In addition to explaining the details in the methodology and the software, we also provide an example of developing a chemically accurate model for water clusters. Program summaryProgram Title: DeePKS-kitCPC Library link to program files:https://doi.org/10.17632/x54bnz5vxk.1Developer's repository link:https://github.com/deepmodeling/deepks-kitLicensing provisions: LGPLProgramming language: PythonNature of problem: Modeling the energy and density functional in electronic structure problems with high accuracy by neural network models. Solving electronic ground state energy and charge density using the learned model.Solution method: DeePHS and DeePKS methods are implemented, interfaced with PyTorch and PySCF for neural network training and self-consistent field calculations. An iterative learning procedure is included to train the model self-consistently.

Quantum expectation-value estimation by computational basis sampling

Measuring expectation values of observables is an essential ingredient in variational quantum algorithms. A practical obstacle is the necessity of a large number of measurements for statistical convergence to meet requirements of precision, such as chemical accuracy in the application to quantum chemistry computations. Here we propose an algorithm to estimate the expectation value based on its approximate expression as a weighted sum of classically-tractable matrix elements with some modulation, where the weight and modulation factors are evaluated by sampling appropriately prepared quantum states in the computational basis on quantum computers. Each of those states is prepared by applying a unitary transformation consisting of at most N CNOT gates, where N is the number of qubits, to a target quantum state whose expectation value is evaluated. Our algorithm is expected to require fewer measurements than conventional methods for a required statistical precision of the expectation value when the target quantum state is concentrated in particular computational basis states. We provide numerical comparisons of our method with existing ones for measuring electronic ground state energies (expectation values of electronic Hamiltonians for the lowest-energy states) of various small molecules. Numerical results show that our method can reduce the numbers of measurements to obtain the ground state energies for a targeted precision by several orders of magnitudes for molecules whose ground states are concentrated. Our results provide another route to measure expectation values of observables, which could accelerate the variational quantum algorithms.

Spherical quantum dot in modified Kratzer–Coulomb potential: study of optical rectification coefficients

We consider the effects of quantum dot radius, confinement potential depth and controllable effective mass on the optical rectification coefficient (ORC) in spherical quantum dots, which is confined with Modified Kratzer–Coulomb Potential (MKCP). Using the Nikiforov–Uvarov method and compact density matrix theory, the ground state energy, ORC and wave function of electrons under the combined action of many factors are calculated. The results show that they affect the optical rectification response from different angles, including the position of peak and formant.

Chemistry beyond the Hartree–Fock energy via quantum computed moments

Quantum computers hold promise to circumvent the limitations of conventional computing for difficult molecular problems. However, the accumulation of quantum logic errors on real devices represents a major challenge, particularly in the pursuit of chemical accuracy requiring the inclusion of electronic correlation effects. In this work we implement the quantum computed moments (QCM) approach for hydrogen chain molecular systems up to H_6. On a superconducting quantum processor, Hamiltonian moments, langle H^prangle are computed with respect to the Hartree–Fock state, which are then employed in Lanczos expansion theory to determine an estimate for the ground-state energy which incorporates electronic correlations and manifestly improves on the direct energy measurement. Post-processing purification of the raw QCM data takes the estimate below the Hartree–Fock energy to within 99.9% of the exact electronic ground-state energy for the largest system studied, H_6. Calculated dissociation curves indicate precision at about 10mH for this system and as low as 0.1mH for molecular hydrogen, H_2, over a range of bond lengths. In the context of stringent precision requirements for chemical problems, these results provide strong evidence for the error suppression capability of the QCM method, particularly when coupled with post-processing error mitigation. While calculations based on the Hartree–Fock state are tractable to classical computation, these results represent a first step towards implementing the QCM method in a quantum chemical trial circuit. Greater emphasis on more efficient representations of the Hamiltonian and classical preprocessing steps may enable the solution of larger systems on near-term quantum processors.

Machine learning based prediction of the electronic structure of quasi-one-dimensional materials under strain

We present a machine learning based model that can predict the electronic structure of quasi-one-dimensional materials while they are subjected to deformation modes such as torsion and extension/compression. The technique described here applies to important classes of materials such as nanotubes, nanoribbons, nanowires, miscellaneous chiral structures and nano-assemblies, for all of which, tuning the interplay of mechanical deformations and electronic fields is an active area of investigation in the literature. Our model incorporates global structural symmetries and atomic relaxation effects, benefits from the use of helical coordinates to specify the electronic fields, and makes use of a specialized data generation process that solves the symmetry-adapted equations of Kohn-Sham Density Functional Theory in these coordinates. Using armchair single wall carbon nanotubes as a prototypical example, we demonstrate the use of the model to predict the fields associated with the ground state electron density and the nuclear pseudocharges, when three parameters - namely, the radius of the nanotube, its axial stretch, and the twist per unit length - are specified as inputs. Other electronic properties of interest, including the ground state electronic free energy, can then be evaluated with low-overhead post-processing, typically to chemical accuracy. We also show how the nuclear coordinates can be reliably determined from the pseudocharge field using a clustering based technique. Remarkably, only about 120 data points are found to be enough to predict the three dimensional electronic fields accurately, which we ascribe to the symmetry in the problem setup, the use of low-discrepancy sequences for sampling, and presence of intrinsic low-dimensional features in the electronic fields. We comment on the interpretability of our machine learning model and discuss its possible future applications.

Comprehensive structural {single crystal X-raydiffraction, spectroscopic & DFT computational simulation} and biological {in vitro DNA binding & antibacterial} studies of polymeric copper(Ⅱ)-based imidazole drug entity

A polymeric tetrakis N-imidazole copper(II) sulphate complex [Cu(imidazole)4(SO4)]n1, was synthesized and thoroughly characterized by various spectroscopic techniques, elemental analysis and single crystal X-ray crystallography. X-ray diffraction analysis confirmed that polymer complex 1 crystallized in a monoclinic C2/c space group possessing the lattice constants, a = 9.2213(1) Å, b = 17.6062(3) Å, c = 10.5710(2) Å, α = γ = 90˚ and β = 93.561˚ (1) per unit cell. Hirshfeld surface and DFT calculations were executed to simulate the electronic ground state energies in gas phase which showed that the HOMO and HOMO–1 were distributed on the axially coordinated SO42– moiety and considerable amount of electron density was present on Cu(II). Absorption and emission spectroscopic techniques were used to investigate the binding interaction of the copper(II) imidazole complex with the therapeutic target ct-DNA. The results suggested that the complex 1 binds to the ct-DNA through an electrostatic mode. The gel electrophoresis experiments of 1 were carried out with plasmid pBR322 which revealed that the polymer complex could unwind the plasmid DNA at 30 μM micromolar concentration via discernible oxidative cleavage pathway. Molecular docking studies were also carried out to support the results of DNA binding experiments. In addition, the antimicrobial potential of polymer complex was evaluated against various key pathogens viz., B. subtilis, E. coli, K. pneumonia and S. aureus. Antibiofilm behaviour of the complex 1 was examined against E. coli and S. aureus. The results demonstrated that 1 could act as an active antibacterial agent as it inhibited the bacterial growth in agar plates very efficiently.

A Spectroscopic Validation of the Improved Lennard-Jones Model.

The Lennard–Jones (LJ) and Improved Lennard–Jones (ILJ) potential models have been deeply tested on the most accurate CCSD(T)/CBS electronic energies calculated for some weakly bound prototype systems. These results are important to plan the correct application of such models to systems at increasing complexity. CCSD(T)/CBS ground state electronic energies were determined for 21 diatomic systems composed by the combination of the noble gas atoms. These potentials were employed to calculate the rovibrational spectroscopic constants, and the results show that for 20 of the 21 pairs the ILJ predictions agree more effectively with the experimental data than those of the LJ model. The CCSD(T)/CBS energies were also used to determine the parameter of the ILJ form, related to the softness/hardness of the interacting partners and controlling the shape of the potential well. This information supports the experimental finding that suggests the adoption of for most of the systems involving noble gas atoms. The He-Ne and He-Ar molecules have a lifetime of less than 1ps in the 200–500 K temperature range, indicating that they are not considered stable under thermal conditions of gaseous bulks. Furthermore, the controversy concerning the presence of a “virtual” or a “real” vibrational state in the He molecule is discussed.

Dipole and generalized oscillator strengths-dependent electronic properties of helium atoms immersed in a plasma

Atoms subjected to extreme environmental conditions are of fundamental importance due to the modification of their electronic properties. In this work, we study the helium atom when immersed in a plasma environment. In order to describe the plasma medium, we use two models when solving the Schrodinger equation in a restricted Hartree–Fock approach: the Debye–Huckel screened (DHS) potential and a more general exponential-cosine screened Coulomb (ECSC) potential. The plasma length parameter, $$\lambda $$ , in both model potentials characterizes the plasma screening effects which cause an increase or decrease in the electronic properties of the helium atom. We report results for the total electronic ground state energy, orbital energy, dipole oscillator strengths, generalized oscillator strengths (GOS), mean excitation energy, electrostatic dipole polarizability, and electronic stopping cross section. We find that the ECSC plasma model produces a less bound system than the DHS plasma model at the same value of the screening length, $$\lambda $$ . However, the ECSC model potential has a stronger dipole transition from the 1s to the 2p and 3p states than the DHS model potential. Also, the ECSC potential predicts a higher static dipole polarizability than the DHS model potential, with a consequent lower mean excitation energy. We also find a larger GOS for the ECSC than for the DHS for the same momentum transfer at the same value of the screening length, $$\lambda $$ . Consequently, the ECSC mode potential produces a larger electronic stopping cross section than the DHS for the same $$\lambda $$ and projectile velocity. In the limit of $$\lambda \rightarrow \infty $$ , we have excellent agreement with the free helium properties. These quantitative values for the electronic properties would be useful for the investigations of the atomic structure and collisions of helium atoms immersed in plasmas.

Chemical Energetics and Atomic Charges Distribution of Variably Sized Hydrated Sulfate Clusters in the light of Density Functional Theory

Among the ions classified in the Hofmeister series, the firstly ranked divalent sulfate anion has the strongest hydrating and water-structure making propensity. This unique characteristic actually makes it kosmotropic which causes water molecules to interact each other and contributes to gain structural stability of its hydrated clusters [SO42−(H2O)n]n = 1−40. In this study, few variably sized microhydrated sulfate clusters [SO42−(H2O)n]n = 1−4, 16 are considered separately, and inquired their chemical energetics and atomic charge distributions through ab initio based theoretical model. The main objective of this insight is to specify and interpret their thermodynamic stabilities, binding energies, and specific bonding and electronic interactions quantum mechanically. An in-depth analysis of their change in relative ground state electronic energy with respect to hydration number indicates stronger affinity of the sulfate ion towards water molecules while attaining structural stability in any aqueous type solutions. The mathematically determined values of their binding energy (DE) almost holds up the same with this structural stability order: [SO42−(H2O)16] > [SO42−(H2O)4] > [SO42−(H2O)3] > [SO42−(H2O)2] > [SO42−(H2O)], as reliable as experimentally and molecular dynamics simulation predicted trend. Moreover, the Mulliken derived partial atomic charges feature qualitative charge distribution in them which not only depicts electronic interactions between the specific atoms but also exemplifies the involvement of central sulfate units in hydrogen bond formation with surrounding water molecules.