Fock Theory Research Articles

Molecular modeling analyses of functionalized cellulose

AbstractFunctionalization of cellulose with nanomaterials and functional groups is essential for enhancing its properties for specific applications, such as flexible sensors and printed electronics. This study employs Hartree Fock (HF) and Density Functional Theory (DFT) calculations to investigate the vibrational spectra of cellulose, identifying DFT: B3LYP/3–21 g** as the optimal model aligning with experimental spectra. Using this model, we examined the impact of functionalizing cellulose with various groups (OH, NH2, COOH, CH3, CHO, CN, SH) and graphene oxide (GO) on its electronic properties. The results indicate that cellulose functionalized with GO (Cellulose-GO) has the lowest bandgap energy (0.1687 eV), and improvements in reactivity, stability, and electronic properties were confirmed through Molecular Electrostatic Potential (MESP) and Total Dipole Moment (TDM) analyses. The spectrum of Density of States (DOS) for the cellulose functionalized with different groups shows several peaks, indicating various energy levels where electronic states are concentrated. The Projected Density of States (PDOS) analysis reveals how different functional groups affect the electronic structure of cellulose. Moreover, the (Cellulose-GO) composite was characterized using an Attenuated Total Reflection Fourier Transform Infrared (ATR-FTIR) spectrometer, revealing interaction through the OH group of CH2OH, as indicated by a new band at 1710 cm−1, consistent with theoretical predictions. Overall, this study demonstrates that functionalization with GO enhances cellulose’s responsiveness, degradation, and electrical properties, making it suitable for applications in flexible electronic devices and protective barriers against corrosion.

Synthesis, crystal structure, spectroscopic, electronic and vibrational properties of N′-[(E)-3-pyridinylmethylene]nicotinohydrazide trihydrate: Experimental and computational study

N′-[(E)-3-pyridinylmethylene]nicotinohydrazide trihydrate (C12H10N4O·3(H2O)) was synthesized and its structure was determined by single crystal X-ray diffraction method. X-ray analysis showed that the compound crystalized in the triclinic system P-1 with a = 7.1134 (3) Å, b = 10.0208 (4) Å, c = 10.3601 (4) Å, α = 96.386 (3)°, β = 96.995 (3)°, γ = 101.219 (4)°, V = 712.05 (5) Å3 and Z = 2 and exhibits that the title compound (I) consists of N′-[(E)-3-pyridinylmethylene]nicotinohydrazide (II) (C12H10N4O), and three water molecules of crystallization. The two water molecules are attached to the third water molecule through intermolecular two OH…O hydrogen bonds. At the same time, this water molecule is linked to the NH amide group of the hydrazone by an intermolecular NH…O hydrogen bond. Hirshfeld surface (HS) analyses were carried out are to visualise the intermolecular interactions in the crystals of Compound I. The geometric optimization of the titled compound has been carried out by different computational methods such as by Hatree Fock (HF) and Density Functional Theory (DFT) methods with the 6–311++G (d,p) basis set. The vibrational frequency, dipole moment (μ), polarizability (α), hyperpolarizability (β), and electronic properties including the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO–LUMO) of the compound have been calculated at the level of both theories. In the results of crystal analysis and geometry calculations of the compound I, it was observed that intermolecular hydrogen bonds, N2H2A…O3, O3H31…O2 and O3H32…O4, were formed. The energy band gap (Eg = ELUMO-EHOMO) values were also obtained by using ELUMO and EHOMO at the level of both theories. The value of equilibrium (ground state) dipole moment of the studied molecule was calculated to be 8.31 Debye in B3LYP and 7.55 Debye in HF. The calculated hyperpolarizability values at the B3LYP/6–311++G(d,p) of the compound are 2.53 × 10−30 esu and this value corresponds to 6.79 times the hyperpolarizability value of urea.

Pseudo-Spin Symmetry and the Hints for Unstable and Superheavy Nuclei

The pseudo-spin symmetry (PSS) provides an important angle to understand nuclear microscopic structure and the novel phenomena found in unstable nuclei. The relativistic Hartree–Fock (RHF) theory, that takes the important degrees of freedom associated with the π-meson and ρ-tensor (ρ-T) couplings into account, provides an appropriate description of the PSS restoration in realistic nuclei, particularly for the pseudo-spin (PS) doublets with high angular momenta (l˜). The investigations of the PSS within the RHF theory are recalled in this paper by focusing on the effects of the Fock terms. Aiming at common artificial shell closures appearing in previous relativistic mean-field calculations, the mechanism responsible for the PSS restoration of high-l˜ orbits is stressed, revealing the manifestation of nuclear in-medium effects on the PSS, and thus, providing qualitative guidance on modeling the in-medium balance between nuclear attractions and repulsions. Moreover, the essential role played by the ρ-T coupling, that contributes mainly via the Fock terms, is introduced as combined with the relations between the PSS and various nuclear phenomena, including the shell structure and the evolution, novel halo and bubble-like phenomena, and the superheavy magicity. As the consequences of the nuclear force in complicated nuclear many-body systems, the PSS itself and the mechanism therein can not only deepen our understanding of nuclear microscopic structure and relevant phenomena, but also provide special insight into the nature of the nuclear force, which can further enrich our knowledge of nuclear physics.

Spectroscopic, Hartree–Fock and DFT study of the molecular structure and electronic properties of functionalized chitosan and chitosan-graphene oxide for electronic applications

Chitosan is a natural biopolymer that is classified among the most important biodegradable polysaccharides widely used in different environmental and industrial applications, such as tissue engineering, biomedical devices, electronics and supercapacitors, water filtration, and food packaging. Theoretical infrared spectra of chitosan were computed using both Hartree–Fock (HF) and Density Functional Theory (DFT) methods, with different basis sets, including 3-21g, 6-31g, 6-311g, LANL2DZ, and LANL2MB, to identify the ideal basis set that is closest to the experimental results. DFT:B3LYP/3-21g** was the best model for chitosan and was used to investigate its functionalization with various functional groups such as (OH, NH2, COOH, CH3, CHO, CN, SH) and graphene oxide (GO). Molecular electrostatic potential, total dipole moment, and HOMO–LUMO band gap (∆E) calculations indicated that Chitosan-GO is the most reactive and stable structure, with a ∆E of 0.3023 eV. Consequently, Chitosan–GO composite was prepared and analyzed using ATR–FTIR spectroscopy. The spectra revealed a new band at 1620 cm−1, which was attributed to the COOH group of GO and was red-shifted owing to the hydrogen bonding between the GO and NH2 of chitosan, confirming the synthesis of Chitosan–GO composite. The significant improvement in the electronic properties of Chitosan-GO based on the obtained results promotes it to be used in electronic applications such as the development of electrodes for supercapacitors.

Quantum computing for electronic structure analysis: Ground state energy and molecular properties calculations

The computation of electronic structure properties at the quantum level is a crucial aspect of modern physics research. However, conventional methods can be computationally demanding for larger, more complex systems. To address this issue, we present a hybrid Classical-Quantum computational procedure that uses the Variational Quantum Eigensolver (VQE) algorithm. By mapping the quantum system to a set of qubits and utilising a quantum circuit to prepare the ground state wavefunction, our algorithm offers a streamlined process requiring fewer computational resources than classical methods. Our algorithm demonstrated similar accuracy in rigorous comparisons with conventional electronic structure methods, such as Density Functional Theory and Hartree–Fock Theory, on a range of molecules while utilising significantly fewer resources. These results indicate the potential of the algorithm to expedite the development of new materials and technologies. This work paves the way for overcoming the computational challenges of electronic structure calculations. It demonstrates the transformative impact of quantum computing on advancing our understanding of complex quantum systems.

STRUCTURE OF MOLTEN MX–NdX<sub>3</sub> (M – Na, K, Rb, Cs; X – F, Cl) SALTS: AN <i>ab initio</i> STUDY

The paper presents an ab initio study of neodymium containing clusters modeling the structure of corresponding molten salts. The relevance of such study is dictated by development of new methodologies and technologies for processing electronic and magnetic wastes, which are a valuable source of rare earth metals. In turn, quantum chemical calculations provide a powerful tool for investigation of structural features of model systems mimicking high temperature molten salts. In the present study, the simulations are performed within the Hartree–Fock and density functional theory approaches using the Firefly 8.20 software package. We propose a methodology for calculation of interaction energies in ternary systems including the neodymium complex, the outer-sphere cation shell, and the rest of the cluster. The interaction energies between the neodymium complex and other parts of a system are calculated. The dependence of interaction energies on the number of outer-sphere cations is investigated and the most stable “neodymium complex + outer-sphere shell” structures are determined. The calculated data are compared to direct spectroscopic investigations available in literature. The obtained interatomic Nd–X (X – F, Cl) distances coincide with experimentally deduced values. The computed Raman spectra for the 18MCl + M3NdCl6 (M – Na, K, Rb, Cs) model systems demonstrate a good agreement between calculated and experimentally observed positions of the most intense peak. Therefore, the chosen systems provide a reliable minimalistic model for quantum chemical investigations of molten salts structure.

On the localization regime of certain random operators within Hartree–Fock theory

Localization results for a class of random Schrödinger operators within the Hartree–Fock approximation are proved in two regimes: Large disorder and weak disorder/extreme energies. A large disorder threshold λHF analogous to the threshold λAnd obtained in Schenker [Lett. Math. Phys. 105(1), 1–9 (2015)] is provided. We also show certain stability results for this large disorder threshold by giving examples of distributions for which λHF converges to λAnd, or to a number arbitrarily close to it, as the interaction strength tends to zero.

Dark matter effects on the properties of neutron stars: Optical radii

We study the effects of dark matter on the properties of neutron stars by employing a DM-admixed model. The Brueckner–Hartree–Fock theory with realistic three-body forces and a generic bosonic self-interacting dark matter model describe the equations of state for nuclear matter and DM, respectively. We study the complete set of stable ‘dark’ neutron stars and in particular the observable radii of these objects. A rich variety of stellar configurations is found and discussed in detail.

Better performance of Hartree–Fock over DFT: a quantum mechanical investigation on pyridinium benzimidazolate types of zwitterions in the light of localization/delocalization issues

ContextWith the advent of fast computing facilities, combined with rapid emerges of many new and intricate quantum mechanical functionals, computations with pure Hartree–Fock (HF) theory are now-a-days regarded as trivial or obsolete, or even considered as not reliable by many researchers. Consequently, current trends in computational chemistry show extensive use of post-HF theories for smaller molecular systems and various DFT methods for organic and inorganic chemistry related problems (larger molecules/systems). In this contribution, I have tried to show that sometimes, HF might be more suitable over DFT methodologies in addressing structure–property correlations. Molecules studied here were previously synthesized by Boyd in 1966 and important experimental data were produced by Alcalde and co-workers in 1987. Comparison of computed and experimental results clearly shows that HF method was more effective in reproducing the experimental data compared to especially the DFT methodologies. Reliability of HF method was further assured from the very similar results shown by the CCSD, CASSCF, CISD and QCISD methods. Current study also indicates that the localization issue associated with HF proved to be advantageous over delocalization issue of DFT based methodologies, in correctly describing the structure–property correlation for zwitterion systems.MethodsAll computations were performed with Gaussian 09. A wide-range of quantum mechanical methodologies, HF, B3LYP, CAM-B3LYP, BMK, B3PW91, TPSSh, LC-ωPBE, M06-2X, M06-HF, ωB97xD, MP2, CASSCF, CCSD, QCISD, CISD and semi-empirical methods like, Huckel, CNDO, AM1, PM3MM and PM6, were used for investigations.Graphical abstract

Vibrational spectroscopic analysis of 2, 3:4,5-Bis-O-(1-methylethylidene)beta-D-fructopyranose Sulfamate(Topiramate) by density functional method

2,3:4,5-Bis-O-(1-methylethylidene)-beta-D- fructopyranose sulfamate otherwise called as Topiramate is a drug used for the treatment of alcohol dependence. Topiramate is a safe and consistently efficacious medication for treating alcohol dependence. The spectroscopic properties of Topiramate are investigated by Fourier Transform Infrared (FT-IR), Fourier Transform Raman (FT-Raman), Fourier Transform Nuclear magnetic Resonsnce(FT-NMR) andUltra Violet Visible (UV–visible) spectroscopic techniques. The FTIR, FT-Raman, FT-NMR and UV–visible spectra of Topiramate have been recorded and analyzed. Theoretical vibrational frequencies, geometric parameters, thermodynamic properties, Natural population analysis and Mulliken atomic charges of Topiramateare obtained by the Restricted Hartree–Fock (RHF) and density functional theory (DFT) using 6–31 + G(d,p) basis set. The calculated harmonic vibrational frequencies for Topiramate are compared with the experimental values of FTIR and FT-Raman spectra. The observed and the calculated frequencies are found to be in good agreement. Stability of the molecule arising from hyperconjugative interactions and charge delocalization has been analysed using natural bond orbital (NBO) analysis. The first-order hyperpolarizability (βtot) and other related properties such as dipole moment(µ), polarizability(αo)values of the investigated molecule are computed using HF and DFT/B3LYP with 6–31 + G(d,p) basis set. The calculated results also show that the Topiramate molecule may have microscopic nonlinear optical (NLO) behaviour.

Structural, Spectroscopic, Mechanical, and Nonlinear Optical Properties of 4-Dimethylaminopyridinium Picrate Single Crystal for Optoelectronic Applications

A novel organic nonlinear optical (NLO) material, 4-dimethylaminopyridinium picrate (4DMAPP) with molecular formula (C7H11N2)+.(C6H2N3O7)- has been synthesized. The single crystals have been grown from synthesized material by slow evaporation technique. The NLO behavior of the 4DMAPP has been investigated using the quantum chemical calculations with 6-311++G(d,p) basis set. The bond lengths, bond angles, and torsional angle of optimized structure of 4DMAPP are in good agreement with the X-ray diffraction experimental data. The global softness, electron affinity, global hardness, Ionization potential, electronegativity, global electrophilicity, and chemical potential have been estimated. The Meyer index is found to be 2.51 and the nature of the 4DMAPP NLO material is identified as soft. Thermodynamics and molecular parameters of 4DMAPP have been carried out with zero-point vibrational energy 186.191 and 171.908 kcal/mol using Hartree–Fock (HF) and density functional theory (DFT) methods, respectively. In optical absorption spectrum, the material 4DMAPP shows the lower cut off wavelength of 325 nm. The narrow energy gap between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) facilitates the intramolecular charge transfer (ICT) which makes the material to be NLO active.

The dilute interacting Bose gas: comparisons between Feynman diagrammatic expansion and the hierarchy equations for the imaginary time Green functions

We analyze the correspondence between two formalisms describing an interacting Bose gas, namely the standard Feynman diagrammatic expansion on the one hand, and the hierarchy equations for the imaginary-time Green functions on the other hand. We show that the Hartree–Fock approximation, as well as its first corrections at low density derived by Baym et al (2001 Eur. Phys. J. B 24 107–24), can be equivalently formulated in both formalisms. Within the hierarchy approach, the two-body correlations are expressed at lowest order in the interactions in terms of the full one-body Green function. This sheds light on the physical content of the corrections to the Hartree–Fock theory. Moreover, this representation of can be extended to higher orders, opening the way to systematic calculations of further corrections to the ideal critical temperature when the density increases.

Excited states in Hartree–Fock theory

Hartree Fock theory is extended to excited states of interacting N-particle Fermionic systems. In contrast to the orbital-by-orbital and state-by-state approach followed by previous attempts to such an extension, the present methodology provides, in principle, a systematic determination of all excited states in the Hartree Fock treatment of electronic many-particle states. The excited states are defined as the eigenstates of the Nth order density matrix for a Slater determinant of order KN that represents the ground state of a non-interacting collection of K replicas of an interacting N-particle system. The equations determining the KN orbitals entangled in the collection ground state increase linearly with K, while they give rise to CNKN=KNN excited states of all orders, 1 to N. The entire spectrum is populated as K→∞. The method goes beyond Koopman’s theorem allowing the incorporation into the ground state of the effects of particle excitations to states of higher energy.

Calculation of the ELF in the excited state with single-determinant methods.

Since its first definition, back in 1990, the electron localization function (ELF) has settled as one of the most commonly employed techniques to characterize the nature of the chemical bond in real space. Although most of the work using the ELF has focused on the study of ground-state chemical reactivity, a growing interest has blossomed to apply these techniques to the nearly unexplored realm of excited states and photochemistry. Since accurate excited electronic states usually require to account appropriately for electron correlation, the standard single-determinant ELF formulation cannot be blindly applied to them, and it is necessary to turn to correlated ELF descriptions based on the two-particle density matrix (2-PDM). The latter requires costly wavefunction approaches, unaffordable for most of the systems of current photochemical interest. Here, we compare the exact, 2-PDM-based ELF results with those of approximate 2-PDM reconstructions taken from reduced density matrix functional theory. Our approach is put to the test in a wide variety of representative scenarios, such as those provided by the lowest-lying excited electronic states of simple diatomic and polyatomic molecules. Altogether, our results suggest that even approximate 2-PDMs are able to accurately reproduce, on a general basis, the topological and statistical features of the ELF scalar field, paving the way toward the application of cost-effective methodologies, such as time-dependent-Hartree-Fock or time-dependent density functional theory, in the accurate description of the chemical bonding in excited states of photochemical relevance.

A multi-fragment real-time extension of projected density matrix embedding theory: Non-equilibrium electron dynamics in extended systems.

In this work, we derive a multi-fragment real-time extension of the projected density matrix embedding theory (pDMET) designed to treat non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static pDMET, the real time pDMET partitions the total system into many fragments; the coupling between each fragment and the rest of the system is treated through a compact representation of the environment in terms of a quantum bath. The real-time pDMET involves simultaneously propagating the wavefunctions for each separate fragment-bath embedding system along with an auxiliary mean-field wavefunction of the total system. The equations of motion are derived by (i) projecting the time-dependent Schrödinger equation in the fragment and bath space associated with each separate fragment and by (ii) enforcing the pDMET matching conditions between the global 1-particle reduced density matrix (1-RDM) obtained from the fragment calculations and the mean-field 1-RDM at all points in time. The accuracy of the method is benchmarked through comparisons to time-dependent density-matrix renormalization group and time-dependent Hartree-Fock (TDHF) theory; the methods were applied to a one- and two-dimensional single-impurity Anderson model and multi-impurity Anderson models with ordered and disordered distributions of the impurities. The results demonstrate a large improvement over TDHF and rapid convergence to the exact dynamics with an increase in fragment size. Our results demonstrate that the real-time pDMET is a promising and flexible method that balances accuracy and efficiency to simulate the non-equilibrium electron dynamics in heterogeneous systems of large size.

Hamiltonian sensitivity in calculating the electromagnetic moments and electroexcitation form factor for the sd nuclei using shell model with Skyrme–Hartree–Fock

In this work, the nuclear electromagnetic moments for the ground and low-lying excited states for sd shell nuclei have been calculated, resulting in a revised database with 56 magnetic dipole moments and 41 electric quadrupole moments. The shell model calculations are performed for each sd isotope chain, considering the sensitivity of changing the sd two-body effective interactions USDA, USDE, CWH and HBMUSD in the calculation of the one-body transition density matrix elements. The calculations incorporate the single-particle wave functions of the Skyrme interaction to generate a one-body potential in Hartree–Fock theory to calculate the single-particle matrix elements. For most sd shell nuclei, the experimental data are well reproduced, except for those spans near the island of inversion. In order to interpret the structure of low-lying excited states, the electric quadrupole and magnetic dipole transition form factors and the corresponding reduced transition probabilities in the sd shell nuclei have also been calculated, for which the experimental data are available. The present results demonstrate the nuclear electromagnetic moments’ sensitivity to many forms of the understanding of nucleon–nucleon interactions and provide a crucial baseline for future improvements in conceptual calculations.

Introducing the Random Phase Approximation Theory

Random Phase Approximation (RPA) is the theory most commonly used to describe the excitations of many-body systems. In this article, the secular equations of the theory are obtained by using three different approaches: the equation of motion method, the Green function perturbation theory and the time-dependent Hartree–Fock theory. Each approach emphasizes specific aspects of the theory overlooked by the other methods. Extensions of the RPA secular equations to treat the continuum part of the excitation spectrum and also the pairing between the particles composing the system are presented. Theoretical approaches which overcome the intrinsic approximations of RPA are outlined.

Synthesis, characterization, quantum chemical calculation, Hirshfeld surface analysis and antibacterial activity of a co-crystal of 4-Aminopyridine: p-Hydroxybenzoic acid with a water molecule

A novel co-crystal of 4-Aminopyridine with p-Hydroxybenzoic acid having a water molecule (4AP:PHBA·H2O) has been synthesized using solution technique. The three-dimensional structure of 4AP:PHBA·H2O has been confirmed by single-crystal X-ray diffraction (SCXRD) and the spectral characterization has been carried out using FT-IR, 1HNMR and 13CNMR spectroscopy. The structure analysis reveals that the O−H···N, N−H···O, O−H···O and C−H···π hydrogen bonds are mainly responsible for the stabilization of crystal packing. The strong O−H···N interactions play a vital role in the formation of the crystal structure of 4AP:PHBA·H2O. The quantum chemical calculations, HOMO – LUMO energy gap, Mulliken population analysis and molecular electrostatic potential map have been performed using Hartree Fock (HF) and density functional theory (DFT) methods with 6–311+G(d,p) basis set level. The non-covalent interactions present in the structure have been examined quantitatively using the Hirshfeld surface and fingerprint plot analysis. The water molecule connects the crystal structure by acting as a donor and acceptor. The contribution of C−H···π interactions is 35%, the maximum contribution, however, comes from H−H contacts (40%). The compound shows an encouraging antibacterial activity against the bacterial pathogens S. aureus, E. coli, P. aeruginosa, when compared with the standard antibiotic ciprofloxacin drug.

Gaussian basis functions for an orbital‐free‐related density functional theory of atoms

AbstractA representation of polymer self‐consistent field theory equivalent to quantum density functional theory is given in terms of non‐orthogonal basis sets. Molecular integrals and self‐consistent equations for spherically symmetric systems using Gaussian basis functions are given, and the binding energies and radial electron densities of neutral atoms hydrogen through krypton are calculated. An exact electron self‐interaction correction is adopted and the Pauli‐exclusion principle is enforced through ideas of polymer excluded‐volume. The atoms hydrogen through neon are examined without some approximations which permit cancellation of errors and spontaneous shell structure is observed. Correlations are neglected in the interest of simplicity and comparisons are made with Hartree–Fock theory. The implications of the Pauli‐exclusion potential and its approximate form are discussed, and the Pauli model is analyzed using scaling theory for the uniform electron density case where the correct form of the Thomas–Fermi quantum kinetic energy and the Dirac exchange correction are recovered.

Extreme ultraviolet spectral characteristic analysis of highly charged ions in laser-produced Cu plasmas

This paper reports the results of spectral measurements and a theoretical analysis of the temporal and spatial evolution of laser-produced Cu plasma in vacuum in the range of 8–14 nm. The time dependence of the extreme ultraviolet band spectrum at different positions near the target surface was obtained and found to be dominated by three broad-band features. The 3p and 3d excitations of Cu5+–Cu9+ ions were calculated using the Hartree–Fock theory with configuration interactions. The characteristics of the spectral line distribution for the 3p–nd and 3d–nf transition arrays were analyzed. Based on the steady-state collisional radiation model and the normalized Boltzmann distribution, the complex spectral structure in the band of 13–14 nm is accurately explained through consistency comparisons and benchmarking between the experimental and theoretical simulation spectra, demonstrating that the structure mainly stems from the overlapping contribution of the 3d–4f and 3p–3d transition arrays for the Cu5+–Cu9+ ions. These results may help in studying the radiation characteristics of isoelectronic series highly-charged ions involving the 3d excitation process.