Value Of Ground State Energy Research Articles

Quantum synergy in peptide folding: A comparative study of CVaR-variational quantum eigensolver and molecular dynamics simulation

One of the technological fields that is developing the fastest is quantum computing in biology. One of the main problems is protein folding, which calls for precise, effective algorithms with fast computing times. Mapping the least energy conformation state of proteins with disordered areas requires enormous computing resources. The current study uses quantum algorithms, such as the Variational Quantum Eigensolver (VQE), to estimate the lowest energy value of 50 peptides, each consisting of seven amino acids. To determine the ground state energy value, Variational Quantum Optimisation (VQE) is first utilised to generate the energy values along with Conditional Value at Risk (CVaR) as an aggregation function is applied over 100 iterations of 500,000 shots each. This is contrasted with 50 millisecond molecular dynamics-based simulations to determine the energy levels and folding pattern. In comparison to MD-based simulations, the results point to CvaR-VQE producing more effective folding outcomes with respect to sampling and global optimization. Protein folding can be solved to get deep insights into biological processes and drug formulation with improving quantum technology and algorithms.

First-principles calculations to investigate structural, electronic, and optical properties of AgWO4 and PdWO4 tungstate materials for optoelectronic applications

The optoelectronic devices play a crucial role in our daily lives by seamlessly integrating optics and electronics, enabling technologies like smartphones, solar cells, and optical communication. Solar cells have been very vital in terms of providing sustainable and clean energy. Conventional Perovskite-based solar cells possess limitations like stability and toxicity. Recently, ABO4-type materials have gained attention in optoelectronic devices due to their structural stability and suitable optoelectronic properties for solar cell applications. The structural, electronic, and optical properties of AgWO4 and PdWO4 have been explored using the first principal simulations in line with density functional theory (DFT) using WIEN2K simulation software. The Perdew-Burke-Ernzerhof Generalized-Gradient-Approximation (PBE-GGA) is acclimated to optimize the geometry of both materials under consideration. Trans-Balha modified Becke-Johnson approximation (TB-mBJ) approximation is implemented to study materials' optoelectronic properties. Structural analysis revealed the stable structure of AgWO4 and PdWO4 in the monoclinic phase with increasing lattice parameters and decreased unit cell volume upon replacement of Ag with Pd cation on the A site. Both materials ' negative values of ground state energies indicate the stability of both compounds. Upon analysis of the band structure of AgWO4 and PdWO4, it is found that both materials possess a band gap of 1.34eV and 0.73eV,respectively, signifying that both materials under consideration are semiconductors, with a potential for a controlled flow of electrical charges, coming up with promising various optoelectronic applications. Optical characteristics were explored and examined in depth in the framework of hypothetical dielectric constant. It has been discovered that the dielectric function has a broad span of energy integrity when it comes to its dielectric function. Materials with narrow bandgaps and excellent UV light absorption were found suitable for optoelectronic and solar cell applications.

Analytical estimate of effective charge and ground-state energy of beryllium atom utilizing variational method

In this paper, we present an analytical procedure to determine the effective charge and ground-state energy of a four-electron beryllium atom. The procedure followed is based on a variant of variational technique using modified hydrogenic one-electron wave function to calculate effective charge in 1s and 2s states of beryllium atom. The effective charge in 1s state is 3.68609 and in 2s state is 1.82362. Further, we have used these values in non-relativistic Hamiltonian with interaction terms to calculate the ground-state energy of beryllium atom. The estimated value of ground-state energy (− 14.3423 au) is in good agreement with the experimental results and with other theoretically obtained values. The calculated results without using any computationally intensive technique are the essence of this research work.

Exotic topological point and line nodes in the plaquette excitations of a frustrated Heisenberg antiferromagnet on the honeycomb lattice

A number of topological nodes including Dirac, quadratic and three-band touching points as well as a pair of degenerate Dirac line nodes are found to emerge in the triplet plaquette excitations of the frustrated spin-1/2 J1–J2 antiferromagnetic Heisenberg honeycomb model when the ground state of the system lies in a spin-disordered plaquette-valence-bond-solid phase. A six-spin plaquette operator theory of this honeycomb model has been developed for this purpose by using the eigenstates of an isolated Heisenberg hexagonal plaquette. Spin-1/2 operators are thus expressed in the Fock space spanned by the plaquette operators those are obtained in terms of exact analytic form of eigenstates for a single frustrated Heisenberg hexagon. Ultimately, an effective interacting boson model of this system is obtained on the basis of low energy singlets and triplets plaquette operators by employing a mean-field approximation. The values of ground state energy and spin gap of this system have been estimated and the validity of this formalism has been tested upon comparison with the known results. Emergence of topological point and line nodes on the basis of spin-disordered ground state noted in this investigation is very rare on any frustrated system as well as the presence of triplet flat band. Evolution of those topological nodes is studied throughout the full frustrated regime. Finally, emergence of topological phases has been reported upon adding a time-reversal-symmetry breaking term to the Hamiltonian. Coexistence of spin gap with either topological nodes or phases turns this honeycomb model an interesting one.

First principles investigation of structural, vibrational and thermal properties of black and blue phosphorene

In this investigation, structural, dynamical and thermal properties of black and blue phosphorene (P) are presented through the first principles calculations based on the density functional theory (DFT). These DFT calculations depict that due to the approximately same values of ground state energy at zero Kelvin and Helmholtz free energy at room-temperature, it is expected that both structures can coexist at transition temperature. Lattice dynamics of both phases were investigated by using the finite displacement supercell approach. It is noticed on the basis of harmonic approximation thermodynamic calculations that the blue phase is thermodynamically more stable than the black phase above 155 K.

Numerical exact diagonalization of singularity in the ground state of two-dimensional hydrogen atom

With the development of computing technology, numerical exact diagonalization method plays a vital role in modern computational condensed matter physics, especially in the research area of strongly correlated electron systems: it becomes a benchmark for other numerical computational techniques, such as quantum Monte Carlo, numerical renormalization group, density matrix renormalization group, and dynamic mean field theory. In this paper, we first numerically exactly diagonalize the three-dimensional hydrogen atom with the combination of finite-difference method, and find that the numerical wave function of ground state is in good agreement with the analytical calculations. We then turn to discuss the space dimension confinement hydrogen system, two-dimensional hydrogen atom, and notice that the numerical wave function is no longer in agreement with the analytical calculation, where the ground state wave function has a numerical singularity as radius approaches to zero. Compared with the case of the three-dimensional hydrogen atom, this issue mainly comes from the nature of space dimension confinement. To resolve such an issue of numerical singularity in two-dimensional hydrogen atom, we need to construct a new discrete and normalized Bessel function as a basis to study the ground state behavior of dimension confinement system based on the framework of Lanczos-type numerical exact diagonalization. The constructed normalized Bessel basis is orthogonal and discrete, and thus becomes suitable for practical calculation. Besides, these prominent properties of such a Bessel basis greatly reduce the complexity and difficulty in practical calculation, and thus makes computing work efficient. In addition, Lanczos-type numerical exact diagonalization method can extremely speed up the process of solving the eigenvalue equation. As a result, such a high efficient calculation of our method demonstrates the consistence between numerical and analytical ground state energy value, and the corresponding wave function with enough truncated basis number. Since this kind of numerical singularity occurs in many space dimension confinement systems, our finding for constructing a new discrete Bessel basis function may be helpful in studying the quantum systems with numerical singularity behaviors in wavefunctions in future. On the other hand, it should be pointed out that the Bessel basis is incorporated into the linear augment plane wave method in the density functional theory to study the electronic band structure of the condensed material and obtain high accurate results, especially in the theoretical prediction of topological insulators and in experimental realization as well.

Temperature Effect of Hydrogen-Like Impurity on the Ground State Energy of Strong Coupling Polaron in a RbCl Quantum Pseudodot

We study the ground state energy and the mean number of LO phonons of the strong-coupling polaron in a RbCl quantum pseudodot (QPD) with hydrogen-like impurity at the center. The variations of the ground state energy and the mean number of LO phonons with the temperature and the strength of the Coulombic impurity potential are obtained by employing the variational method of Pekar type and the quantum statistical theory (VMPTQST). Our numerical results have displayed that Open image in new window the absolute value of the ground state energy increases (decreases) when the temperature increases at lower (higher) temperature regime, Open image in new window the mean number of the LO phonons increases with increasing temperature, Open image in new window the absolute value of ground state energy and the mean number of LO phonons are increasing functions of the strength of the Coulombic impurity potential.

The study of electronic, elastic, magnetic and optical response of Zn1-xTixY (Y = S, Se) through mBJ potential

To explore the structural, electronic, magnetic and optical properties of Zn1-xTixY (Y=S, Se) alloys, in the composition range 0 ≤ x ≤ 1, we have applied full-potential linearized augmented plane wave plus local orbital (FP-LAPW + lo) scheme, which is based on the density functional theory (DFT). Structural optimizations have been done in ferromagnetic (FM) and antiferromagnetic (AFM) phase by using Wu–Cohen generalized gradient approximation (WC-GGA), whereas recently developed modified Becke and Johnson (mBJ) potential was employed to study electronic and optical properties. The lower value of ground state energy and negative enthalpy of formation confirm stability in the FM phase. Due to the spin polarization of electrons in the Ti-d orbital, origin of half-metallic ferromagnetism has been expressed by the calculated band structures, electronic density of states (DOS) and magnetic moments. We also have calculated the exchange splitting energy Δx (d), crystal field energy (ΔEcrystal = Et2g−Eeg) and exchange constants (N0α and N0β). The negative value of exchange constant (N0β) and large splitting of 3d-states of Ti show that the down spin potential is more effective than up spin. Finally, the results of optical parameters such as complex dielectric constant ε (ω), refractive index n (ω), normal incident reflectivity R (ω), absorption coefficient ɑ (ω), optical conductivity σ (ω) and optical loss factor L (ω) are discussed in the energy range 0–14 eV. Moreover, we have verified the Penn's model by showing the inverse relation between the static dielectric constant and the optical band gap. The direct relation between static dielectric constant and static refractive index has been observed by increasing the composition of Ti. The calculated parameters provide valuable theoretical information for optical and spintronics device applications.

Two-electron impurity in the parabolic quantum dot: Uncertainty relation and perturbation approach

Two-electron impurity states in parabolic confinement have been investigated. We have estimated the ground-state energy value, using the Heisenberg uncertainty relation. Using variational methods the ground state energy and wave function of the single-electron impurity problem have been achieved. The dependence of ground-state energy and Coulomb electron–electron interaction energy correction on the QD size is studied. The dependence of the state exchange time on the QD radius has been calculated. It has been shown that the presence of the impurity leads to the appearance of negative values of the energy of the system on the one hand, and to the saturating character of the state exchange time.

Application and foundation on inversion lattice potential of gold and silver

How to construct an accurate interatomic potential function is an important and basic problem in the simulation procedure. Using first-principles method, the single atom energies in different lattice constants are calculated to achieve the ground state curves of Au and Ag. These energies are calculated in the Perdew and Zunger form of the local-density approximation ultra-soft pseudo potentials. The cut-off energies of the plane wave bases of Au and Ag are set to be 320 eV and 300 eV respectively, which are sufficient for their full converge. The Brillouin zone is all sampled with a 12×12×12 Monkhorst-Pack mesh of k points for Au and Ag. Allowable error in total energy is smaller than 1×10-6 eV per atom. The lattice cohesive energies in different lattice constants are calculated to achieve the lattice energy and atom distance curves after subtracting the value of ground state energy from each of these energy. Then the accurate inversion potential curves are obtained according to the Chen-Möbius inversion theory and self-compiled program. Based on the fitting consequences of inversion potential curves, using different potential function formulas, a double exponential potential function to fit the inversion potential is presented. This function provides the accurate formulas and parameters for the following research. Moreover, the phonon spectra and the densities of states of Au and Ag are calculated respectively by using the inversion potential data, the embedded atom method (EAM) potential theory and first principles method to verify the reliability of the inversion potential. The comparison of the results among the three methods shows that the tendencies of these curves are similar. But they still have some deviations especially in the range of high frequency. However these curves indicate that the inversion potential can reasonably reflect the interaction between atoms. Meanwhile, the inversion potential method has great advantage in calculation quantity compared with the EAM potential method. The inversion method needs less time in calculation. In addition, the thermal expansion coefficients, the elastic moduli and the Grüneisen constants of Au and Ag are also calculated based on the fitting formulas and parameters. The results agree well with the experimental data, which implies that these inversion potentials are effective and accurate.

Relativistic calculations of ground states of single-electron diatomic molecular ions

We have performed relativistic calculations of ground-state energies for a series of single-electron homonuclear dimers A 2 (2Z−1)+ with nucleus charge Z = 1, 2, 10, 20, 30, 40, 50, 60, 70, 80, 90, 92, and 100 and internuclear distances R = 2/Z. The work involves the Born-Oppenheimer approximation and the single-electron two-center Dirac Hamiltonian, which describes the interaction between an electron and two immovable point charges. Analysis of the convergence process and comparison with data presented in other works for H 2 + and Th 2 179+ dimers shows that the relative error of the obtained results is on the order of 10−11–10−12. High-accuracy values of ground-state energies for some dimers other than Z = 1 and 90 have been obtained in this work for the first time.

Ground state energy and scaling behaviour of spin gap in the XXZ [formula omitted] antiferromagnetic chain in longitudinal staggered field

The ground state energy and the spin gap of a spin-12 Heisenberg antiferromagnetic XXZ chain in the presence of longitudinal staggered field (hz) have been estimated by using Jordan–Wigner representation, exact diagonalization and perturbative analysis. All those quantities have been obtained for a region of anisotropic parameter (Δ) defined by 0≤Δ≤1. For Δ=0, the exact value of ground state energy is found for finite values of hz. The spin gap is found to develop as soon as the staggered field is switched on. The magnitude of spin gap is compared with the field induced gap measured in magnetic compounds CuBenzoate and Yb4As3 when Δ=1. The dependence of spin gap on both Δ and hz has been found which gives rise to scaling laws associated with hz. Scaling exponents obtained in two different cases show excellent agreements with the previously determined values. The variation of scaling exponents with Δ can be fitted with a regular function.

How to spoil a good basis set for Rayleigh-Ritz calculations

For model quantum mechanical systems such as the harmonic oscillator and a particle in an impenetrable box, we consider the set of exact discrete spectrum functions and define the modified basis set by subtraction of the ground state wavefunction from all the other wavefunctions with some real weights. It is demonstrated that the modified set of functions is complete in the space of square integrable functions if and only if the series of the squared weights diverges. A similar, but nonequivalent criterion is derived for convergence of Rayleigh-Ritz ground state energy calculations to the exact ground state energy value with the basis set extension. Some numerical illustrations are provided which demonstrate a wide variety of possible situations for model systems.

Optical properties of nano-multi-layered quantum dot: oscillator strength, absorption coefficient and refractive index

In this paper, the exact solution of Schrodinger equation for multi-layered quantum dot (MLQD) within the effective mass approximation and dielectric continuum model is obtained with finite and infinite confining potential (CP). The MLQD is a nano-structured semiconductor system that consists of a spherical core (GaAs) and a coated spherical shell (Ga $$_{1-x}$$ Al $$_{x}$$ As) as the whole dot is embedded inside a bulk material (Ga $$_{1-y}$$ Al $$_{y}$$ As). Using the obtained energies, wave functions and taking advantage of numeric calculations, the oscillator strength, refractive index and absorbtion coefficient change associated with intersubband electronic transition from the ground state to the first allowed excited state are investigated for different CPs (both finite and infinite) and shell thicknesses. The results show that all values of ground state energy for large core dot radius approach the same value (the energy of bulk material) independent of CPs and shell thicknesses. Also it is shown that the optical properties are strongly affected by the changes in CPs and shell thicknesses.

Accurate modeling of the influence of back gate bias and interface roughness on the threshold voltage of nanoscale DG MOSFETs

An accurate 2-D analytical model regarding the influence of back gate bias Vbg on the threshold voltage of double gate (DG) MOSFETs for a wide range of geometric dimensions and gate materials is presented. The threshold voltage Vt and its variation have been determined with different geometric dimensions taking into account several effects such as quantum mechanical effects and the surface roughness effect for various back gate bias conditions. Our theoretical calculations rely on the solution of 2-D Poisson’s equation while numerical simulation results are obtained from the numerical device simulator ATLAS. The shift in Vt due to quantum effects and the surface roughness-induced effect has been calculated by employing the accurate value of ground state energy computed using variational approach for a finite rectangular quantum well as exists in a real DG MOS structure. Our investigations show that Vt increases with increasing negative Vbg and exhibits significant enhancement due to quantum effects and the surface roughness effect particularly for channel thickness below 5nm. The margin of accuracy has been verified by comparing our analytical and simulation results with reported simulation and experimental data for various devices.

Combined effect of Debye plasma environment and external electric field on hydrogen atom

We consider weakly coupled plasmas, characterized by Debye–Huckel model potential, and an external electric field along z-axis. Due to plasma environment the energy levels of atom are shifted up, bound states are merged to continuum. For external electric field the excited energy levels also split up; degenerate energy eigenvalues become nondegenerate. In the presence of external electric field, energy levels are shifted up and down, except ground state. The ground state energy value is shifted only down. Therefore, it is very interesting to study the combined effect of plasmas and external electric field on a simple atom (hydrogen). To calculate the energy levels and the corresponding states, we expand the wave function in terms of linear combination of the basis functions. The basis is generated by hydrogenic wave functions. Here, we estimate various plasma surroundings and electric field strengths. We observe converged results for the basis size 45, with angular momentum states up to eight.

Ab initiocoupled-cluster and configuration interaction calculations forO16using theVUCOMinteraction

Using the ground-state energy of {sup 16}O obtained with the realistic V{sub UCOM} interaction as a test case, we present a comprehensive comparison of different configuration interaction (CI) and coupled-cluster (CC) methods, analyzing the intrinsic advantages and limitations of each of the approaches. In particular, we use the importance-truncated (IT) CI and no-core shell model (NCSM) schemes with up to 4-particle-4-hole (4p4h) excitations, with and without the Davidson extensivity corrections, as well as the size extensive CC methods with a complete treatment of one- and two-body clusters (CCSD) and a noniterative treatment of connected three-body clusters via the completely renormalized correction to the CCSD energy defining the CR-CC(2,3) approach, which are all capable of handling larger systems with dozens of explicitly correlated fermions. We discuss the impact of the center-of-mass contaminations, the choice of the single-particle basis, and size-extensivity on the resulting energies. When the IT-CI and IT-NCSM methods include the 4p4h excitations and when the CC calculations include the 1p1h, 2p2h, and 3p3h clusters, as in the CR-CC(2,3) approach, we observe an excellent agreement among the different methodologies, particularly when the Davidson extensivity corrections are added to the IT-CI energies and the effects of the connected three-body clusters aremore » accounted for in the CC calculations. This shows that despite their individual limitations, the IT-CI, IT-NCSM, and CC methods can provide precise and consistent ab initio nuclear structure predictions. Furthermore, the IT-CI, IT-NCSM, and CC ground-state energy values obtained for {sup 16}O are in reasonable agreement with the experimental value, providing further evidence that the V{sub UCOM} two-body interaction may allow for a good description of binding energies for heavier nuclei and that all of the methods used in this study account for most of the relevant particle correlation effects.« less

Modelling of threshold voltage and subthreshold slope of strained-Si MOSFETs including quantum effects

In this paper, the threshold voltage and subthreshold slope of strained-Si channel n-MOSFETs are determined, taking into account quantum-mechanical effects, and the effect of bandgap narrowing due to heavy channel doping and the effect of surface roughness at the Si/SiGe heterointerface for ultra thin channels. Quantum-mechanical effects have been incorporated by considering three components, (1) the modified subband energy of 2D inversion layer charges at the silicon dioxide–silicon interface, (2) the increased effective oxide thickness and (3) the altered value of ground state energy due to surface roughness. The analytical results of threshold voltage and threshold voltage difference are presented with reference to unstrained-Si channel for strained-Si MOSFETs by employing poly-Si gate and titanium nitride gate, the work function of which can be varied over a wide range. In addition, we have predicted the dependence of threshold voltage on different values of oxide thickness, channel doping concentration, and on the molar content, x, of Ge in the Si1−xGex virtual substrate. When compared with the theoretical data of Nayfeh et al our analytical results agree more closely with our experimental results and also with measured and simulated data of threshold voltage for a wide range of devices available in the literature. Furthermore, we have calculated the subthreshold slope of strained-Si channel MOSFETs for different amounts of Ge in the SiGe layer.

A Quasi-physical Algorithm for the Structure Optimization in an Off-lattice Protein Model

In this paper, we study an off-lattice protein AB model with two species of monomers, hydrophobic and hydrophilic, and present a heuristic quasi-physical algorithm. First, by elaborately simulating the movement of the smooth solids in the physical world, we find low-energy conformations for a given monomer chain. A subsequent off-trap strategy is then proposed to trigger a jump for a stuck situation in order to get out of the local minima. The algorithm has been tested in the three-dimensional AB model for all sequences with lengths of 13–55 monomers. In several cases, we renew the putative ground state energy values. The numerical results show that the proposed methods are very promising for finding the ground states of proteins.

Structural stability analysis of Wigner crystal with Gaussian and Yukawa-type positive background

Calculations of the ground-state energies of Wigner crystals having simple cubic (sc), body-centered cubic (bcc), face-centered cubic (fcc), diamond, and perovskite structures and (hence) the analysis of relative stability of Wigner crystals of various different structures are reported. The positive background is represented by a periodic array of Gaussians and Yukawa-type distribution. The effects on stability of the perturbation due to the underlying lattice have been demonstrated. Among the structures, the bcc lattice still remains the most stable known arrangement and the Yukawa-type background leads to a lower ground state energy value compared to a Gaussian type. The calculations are done for the range of the density parameter rs corresponding to low densities for the above two cases. The range of low-density region favorable for Wigner crystallization is found to be above rs=20. The role of correlation energy is suitably taken into account. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001