Hartree Fork Research Articles

Calculate ground state energy of Hydro Helium Cation (2+) by Restricted Open shell Hartree Fork method

In this study, the focus is to calculate the ground state energy of the Hydro Helium Cation (2+) with the help of the Open Shell Restricted Hartree-Fock (ROHF) method. In this study, Python code was developed for the calculations and run on the high-performing computers. After calculation, we compare our result with previous work in which the ground state energy of the same molecule was calculated by using the same programming language but with different approximation method. There is some difference in value, and this is due to taking different trial wave functions, approximation of methods, limitations of programming techniques, and our computational knowledge.

Benchmark studies on the large errors of calculated binding energies in metallophilic interactions.

Aurophilicity is a d10-d10 closed-shell interaction, which is repulsively calculated by the Hartree-Fork (HF) method, whereas binding energies (Eb) are largely overestimated under the second-order Møller-Plesset (MP2) method, compared to the coupled cluster singles and doubles with perturbative triples [CCSD(T)] method. The unusual energy errors between different wave functional methods were also verified in other closed-shell metallophilic systems and even were taken as a label of metallophilic interaction. Here, we performed a benchmark study on a collection of structures with weak interactions, sp-sp bonds, sp-d bonds, and d-d bonds, to investigate the influence factor of the errors of HF and MP2 methods. It was found that the large energy errors of HF and MP2 methods were not specified for closed-shell interactions, and the errors could also be very large for many covalent bonds, which was strongly related to the azimuthal quantum number of interaction orbitals. Compared to the CCSD(T) method, the MP2 method weakens the s-s covalent interactions slightly, strengthens the p-p covalent interactions slightly, and overestimates the d-d covalent interactions largely (can be -170 kcal/mol for the Re-Requadruple bond). This benchmark study suggests that the special energy errors in metallophilicity may result from the participation of d orbitals. Benchmark studies on various density functional methods were also given for calculating binding energies of d-d bonds.

NLOphoric imidazole-fused fluorescent anthraquinone dyes.

The Z-scan and DFT techniques were explored to investigate the non-linear optical properties of anthraquinone fused imidazole-based D-π-A dyes. With the help of UV-visible spectral analysis, pH study, CV analysis, HOMO-LUMO interaction, MEP plots, and quinoidal character the influence of intramolecular charge transfer characteristics and H-bonding process on electronic and photophysical studies of anthraquinone derivatives were understood. The dyes 2-(4-(diethylamino)-2-hydroxyphenyl)-3H-anthra[1,2-d]imidazole-6,11-dione (AQ1) and 2-(2-hydroxynaphthalen-1-yl)-1H-anthra[1,2-d]imidazole-6,11-dione (AQ2) displayed a single emission with pronounced Stokes shift and thermal stability (upto 290°C). The dye AQ1 exhibited strong charge transfer character which is explained by the ICT process leading to high nonlinear susceptibility χ(3) in AQ1 3.43×10-13 e.s.u relative to the dye AQ2 which has only ESIPT core. But, the dye AQ2 6.27Jcm-2 showed better optical limiting value. The NLO properties of AQ1 and AQ2 were computed by DFT functionals based on Hartree Fork (HF) percentage exchange. The dye AQ1 exhibits noticeable NLO properties. The global hybrid functionals with HF composition beyond 50% (BHHLYP, M06-HF) and the long rang corrected functionals (CAM-B3LYP, ωB97, and ωB97X) demonstrated comparable NLO properties relative to B3LYP and PBE0. It was observed that the combined effect of ICT and the H-bonding cores enhance the NLO properties. The experimental findings (Z-scan) were successfully correlated with theoretical (DFT) results.

Z-scan and DFT approach for investigating the NLO properties of imidazole fused anthraquinone dyes

The NLO characteristics of anthraquinone imidazole-fused D-π-A dyes were investigated by Z-scan and density functional theory (DFT) methods. The electronic and photophysical studies i.e. the intramolecular charge transfer (ICT) characteristics were demonstrated by UV-visible analysis, cyclic voltammetry (CV) study, frontier molecular orbital (FMO), molecular electrostatic potential (MEP) and quinoidal character. Thermogravimetric analysis (TGA) of the dyes 2-(9-phenyl-9H-carbazol-3-yl)-3H-anthra[1,2-d]imidazole-6,11-dione (AQ CBZ) and 2-(4-(diphenylamino)phenyl)-3H-anthra[1,2-d]imidazole-6,11-dione (AQ TPA) revealed high thermal stability. The dye AQ TPA demonstrated strong ICT character with high nonlinear susceptibility χ(3) = 3.50×10−13 e.s.u. The dye AQ CBZ 4.40 J cm−2 showed better optical limiting data relative to AQ TPA. The NLO properties of AQ CBZ and AQ TPA were computed using different DFT functionals with varying Hartree Fork (HF) exchange. The dye AQ TPA revealed superior NLO properties in all the used functionals comparative to AQ CBZ. The long-range corrected (LC) functionals (CAM-B3LYP, ωB97 and ωB97X) exhibited almost equivalent NLO properties as proportional to global hybrid functionals (B3LYP, PBE0, BHHLYP and, M06-HF). The calculated NLO properties were correlated with the reference dye. The DFT findings were appropriately correlated with Z-scan results.

Ab Initio Computational Study of electronic structure of -O-C Bonding Formation on Chitosan Polymer-Part 1: Effects of NaOH

Carboxymethyl chitosan (CMC) is a biopolymer that has water-soluble properties, high viscosity, biocompatibility, biodegradable, and low toxicity. CMC can be made by direct alkylation using monocloroacetic acid to produce chitosan derivatives under certain reaction conditions with NaOH as a catalyst. This research aims to explain one the reaction mechanism of bonding formation of O-C and to compare with the effect of the presence of NaOH as a catalyst. The reaction mechanism of O-CMC formation studied by the computational method. Chitosan polymer is very complex, so the molecule model used for calculation is chitosan dimer segment. The stable molecular structure of chitosan dimer which is involved in the reaction mechanism was optimized using ab initio computational method based on Hartree Fork theory and 6-31G(d,p) basis set. Mechanism of O-CMC synthesis reaction was modeled into SN 2 reaction (bimolecular nucleophilic substitution) which results in PO-CMC-2. The study showed that the -O-C bonding formation by SN 2 model and NaOH as a catalyst was more preferred with an activation energy of 323,321 kJ⋅mol−1 than without NaOH as a catalyst with an activation energy of 533,22 kJ⋅mol−1. The mechanism of the synthesis reaction of O-CMC is an exothermic reaction and spontaneously.

NLO‐Phoric Emissive Quinoxaline Analog of Quinoline Yellow 54 and Z‐Scan Studies

AbstractQuinoxaline derivative QY 54 A, an analog of commercially available C.I. (Colour index) Disperse Yellow 54 (quinoline derivative) is synthesized and confirmed by 1H, 13C NMR, LC–MS, and CHN analysis. It is emissive (512 nm) with a quantum yield (ϕF) =0.34. The electrochemical properties of both the dyes were investigated using cyclic voltammetry (CV). The titled dyes are thermally stable (up to 350 °C). A comprehensive study of linear and nonlinear optical (NLO) properties of commercial dye (QY 54) and its analog (QY 54 A) are performed by Z‐scan and Density functional theory (DFT). The NLO (βo, γo) values obtained are compared with the NLO (βo, γo) values of urea. Ten different functionals are used to see the effect of %Hartree Fork (HF) exchange on computed NLO properties of both the dyes. The functional M06‐HF (100% HF) and ωB97 (0‐100% HF) perform better for evaluating NLO properties. The Z‐scan and DFT result reveal that QY 54 A and QY54 are excellent NLOphores. The stability and enhancement in NLO properties of QY 54 A are due to electrophilicity index (ω), the Intramolecular charge transfer (ICT) character is confirmed by HOMO‐LUMO study (2.19 eV), quinoid character (0.0230 A°) and molecular electrostatic potential (MEP) plots.

Quantum chemical approach for chemiluminescence characteristics of di-substituted luminol derivatives in polar solvents

The presence of electron donating substituents altered the electronic properties of the luminol and this phenomenon was evaluated in relation to the chemiluminescence potential of the studied disubstituted luminol derivatives using three different theoretical calculation methods: Restricted Hartree Fork (RHF), Density Functional Theory (DFT) with hybrid function of Becke three-parameters Lee, Yang and Parr (B3LYP), i.e. (DFT-B3LYP), and Møller-Plesset Perturbation Theory (MP2). Different behavior was observed for the studied molecular structures in different phases (gas, water, and dimethylformamide) to emphasize the influence of molecular environment on the chemiluminescence property, regardless of the theoretical methods employed. Time-dependent DFT with correction terms enabled accurate prediction of frontier orbital energies such that calculated energy gaps could reasonably correlate with the lowest excitation energies. Besides, the electron donating moiety induced better chemiluminescence property depending on the donating power, position as well as the number of such substituents. Dimethylamino-substituted luminol showed better quantum chemical parameters and spectra pattern to have much-enhanced chemiluminescence properties possibly. Specifically, its positional isomer named 6,8-bis(dimethylamino)-5-amino-2,3-dihydro-1,4-phthalazinedione showed a greater potential of being a better chemiluminescence reagent in various analytical assays.

Influence of donor and acceptor groups on the S-T energy gap for thermally activated delayed fluorescence emitters

ABSTRACTMolecules composed of different donors and acceptors are theoretically designed as potential thermally activated delayed fluorescence emitters, and their singlet–triplet (S-T) energy gap is studied using the optimal Hartree–Fork method. It is found that the S-T energy gap is in reverse proportional to the electron-donating ability. Stronger electron-donating ability of donors will induce smaller highest occupied molecular orbital–lowest unoccupied molecular orbital overlap and also a smaller S-T energy gap. Based on our calculation results, three molecules are proposed to have great potential to be used as thermally activated delayed fluorescence emitters in organic light-emitting diodes.

First-Principles Investigation on Triazine Based Thermally Activated Delayed Fluorescence Emitters

Three kinds of triazine based organic molecules designed for thermally activated delayed fluorescence (TADF) emitters are investigated by first-principles calculations. An optimal Hartree-Fork (HF) method is adopted for the calculation of energy gap between the first singlet state (S1) and the first triplet state (T1). The natural transition orbital, the electron-hole (e-h) distribution and the e-h overlap diagram indicate that the S1 states for the three systems include both charge-transfer and some localized excitation component. Further quantitative analysis of the excitation property is performed by introducing the index Δr and the integral of e-h overlap S. It is found that symmetric geometry is a necessary condition for TADF emitters, which can provide more delocalized transition orbitals and consequently a small S1-T1 energy gap. Artful inserting aromatic groups between donors and acceptors can significantly enhance the oscillator strength. Finally, the energy state structures calculated with the optimal HF method is presented, which can provide basis for the study of the dynamics of excited states.

Ground state properties and excitation properties of ZnSe under different external electric fields

The Hartree-Fork (HF) method with LANL2DZ basis set is used to investigate the equilibrium structures, atomic charge distributions, the highest occupied molecular orbital (HOMO) energy levels, the lowest unoccupied molecular orbital (LUMO) energy levels, energy gaps, dipole moments, harmonic frequencies and infrared intensities of ZnSe under different external electric fields ranging from -0.025 to 0.040 a.u. The excitation energies, transition wavelengths and oscillator strengths under the same external electric fields are calculated by the time-dependent-HF method. The results show that the bond length and electric dipole moment are proved to be first decreasing, and then increasing with the variation of the external field; the total energy is found to decrease linearly with the variation of external field; but the HOMO energy and energy gap are proved to increase with the variation of external field. The harmonic frequency and LUMO energy are found to first increase, and then decrease, but the infrared intensities are proved to first decrease, and then increase. The external electric field has significant effect on the excitation properties of ZnSe molecule. The excited energies from ground state to the first nine excited states are found to increase, and the transition wavelengths are decreasing with the variation of the external field. Meanwhile, the strongest excited state becomes very weak, and the weak excited state becomes strongest by the external field. The excitation properties of ZnSe material can be changed with external electric field.

Spectroscopic (FT-IR, FT-Raman, NMR and UV–Visible) and quantum chemical studies of molecular geometry, Frontier molecular orbital, NLO, NBO and thermodynamic properties of salicylic acid

The solid phase FT-IR and FT-Raman spectra of 2-hydroxybenzoic acid (salicylic acid) have been recorded in the region 4000–400 and 4000–100cm−1 respectively. The optimized molecular geometry and fundamental vibrational frequencies are interpreted with the aid of structure optimizations and normal coordinate force field calculations based on density functional theory (DFT) method and a comparative study between Hartree Fork (HF) method at 6-311++G(d,p) level basis set. The calculated harmonic vibrational frequencies are scaled and they are compared with experimentally obtained FT-IR and FT-Raman spectra. A detailed interpretation of the vibrational spectra of this compound has been made on the basis of the calculated potential energy distribution (PED). The time dependent DFT method is employed to predict its absorption energy and oscillator strength. The linear polarizability (α) and the first order hyper polarizability (β) values of the investigated molecule have been computed. The electronic properties, such as HOMO and LUMO energies, molecular electrostatic potential (MEP) are also performed. Stability of the molecule arising from hyper conjugative interaction, charge delocalization has been analyzed using natural bond orbital (NBO) analysis.

Studies of the molecular geometry, vibrational spectra, Frontier molecular orbital, nonlinear optical and thermodynamics properties of Aceclofenac by quantum chemical calculations

The solid phase FT-IR and FT-Raman spectra of 2-[2-[2-[(2,6-dichlorophenyl)amino]phenyl]acetyl] oxyacetic acid (Aceclofenac) have been recorded in the region 4000–400 and 4000–100cm−1 respectively. The optimized molecular geometry and fundamental vibrational frequencies are interpreted with the aid of structure optimizations and normal coordinate force field calculations based on density functional theory (DFT) method and a comparative study between Hartree Fork (HF) method 6-311++G(d,p) level basis set. The calculated harmonic vibrational frequencies were scaled and have been compared with experimental by obtained FT-IR and FT-Raman spectra. A detailed interpretation of the vibrational spectra of this compound has been made on the basis of the calculated potential energy distribution (PED). The time dependent DFT method employed to study its absorption energy and oscillator strength. The linear polarizability (α) and the first order hyper polarizability (β) values of the investigated molecule have been computed. The electronic properties, such as HOMO and LUMO energies, molecular electrostatic potential (MESP) were also performed. Stability of the molecule arising from hyper conjugative interaction, charge delocalization has been analyzed using natural bond orbital (NBO) analysis.

Terahertz spectroscopic investigations of caffeine and 3-acetylmorphine

Experimental and theoretical investigations of THz spectral features of caffeine and 3-acetylmorphine in the region of 0.2–2.6 THz have been presented. The refractive indices and absorption coefficients of the two drugs were obtained by a terahertz time-domain spectroscopy (THz-TDS) technique. The simulated absorption spectra using the density functional theory (DFT) and Hartree–Fork (HF) are in agreement with the experimental data. The observed spectral absorption features were assigned based on DFT and HF calculation.

Molecular Design of 1,2,4,5-Tetrazine-Based High-Energy Density Materials

The heats of formation (HOFs) for a series of 1,2,4,5-tetrazine derivatives were calculated by using density functional theory (DFT), Hartree Fork (HF), and Møller-Plesset (MP2) as well as semiempirical methods. The effects of different basis bets on HOFs were also considered. Our results show that the -CN or -N3 group plays a very important role in increasing the HOF values of the 1,2,4,5-tetrazine derivatives. An analysis of the bond dissociation energies for the weakest bonds indicates that substitutions of the -N3, -NH2, -CN, -OH, or -Cl group are favorable for enhancing the thermal stability of 1,2,4,5-tetrazine, but the -NHNH2, -NHNO2, -NO2, -NF2, or -COOH group produces opposite effects. The calculated detonation velocities and pressures indicate that the -NF2 or -NO2 group is very helpful for enhancing the detonation performance for the derivatives, but the case is quite the contrary for the -CN, -NH2, or -OH group. Considered the detonation performance and thermal stability, three derivatives may be regarded as potential candidates of high-energy density materials (HEDMs).

Investigation of the structures and electronic spectra of two coumarins with heterocyclic substituents through TD-DFT calculations

A theoretical study on various properties of the ground and first excited states of two 7-aminocoumarin dyes with heterocyclic substituents at the 3-position is presented. The ground-state and excited-state geometries were optimized at the Hartree–Fork and configuration interaction singles levels of theory, respectively. The geometric relaxation between the first excited state and the ground state was examined and explained in terms of the nodal patterns of the highest occupied and lowest unoccupied molecular orbitals. The most striking geometrical relaxation is the twisting motion between the parent coumarin and heterocyclic substituent at the 3-position. The absorption and emission wavelengths were calculated using the time-dependent density functional theory, and the solvent effect on geometries and spectra has been taken into account using the polarized continuum model. Our calculated results are in good agreement with the experimental measurements, and the influences of solvents and heterocyclic substituents on spectra are also discussed.

Geometric shielding corrections for calculation of electron scattering by CO 2, C 2H 2, CHCl 3, CH 2Cl 2, CH 3Cl, CHF 3, CH 2F 2 and CH 3F at 30–5000 eV

Taking into account the changes of the geometric shielding effect in a molecule as the incident electron energy varies, an empirical fraction, which depends on the energy of the incident electrons, the target's molecular dimension and the atomic and electronic numbers in the molecule, is presented. Using this empirical fraction, a new formulation of the additivity rule is proposed. Using the new additivity rule, the total cross sections of electron scattering by CO 2, C 2H 2, CHCl 3, CH 2Cl 2, CH 3Cl, CHF 3, CH 2F 2 and CH 3F are calculated at the Hartree–Fork level at 30–5000 eV. The quantitative total cross sections are compared with those obtained by experiments and other theories, and good agreement is obtained over a wide energy range, especially above 100 eV.

Isotopic shift in angle-resolved photoemission spectra of Bi2Sr2CaCu2O8 due to quadratic electron–phonon coupling

Abstract In connection with the experiment on oxygen isotope effect of Bi 2 Sr 2 CaCu 2 O 8 with the angle-resolved photoemission spectroscopy (ARPES), we theoretically study the isotope-induced band shift in ARPES by the Hartree–Fork and quantum Monte Carlo methods. We find that this band shift can be clarified based on a quadratically coupled electron–phonon ( e –ph) model. The large ratio of band shift versus phonon energy change is connected with the softening effect of phonon, and the positive–negative sign change is due to the momentum dependence of the e –ph coupling.

Density-functional theory and ab initio Hartree–Fork studies on the structural parameters and chemical activity of the free radicals generated by benzoquinone and hydroquinone

Density-functional theory (DFT) calculations were performed for calculation of the theoretical spectra and the chemical activities of free radicals generated by benzoquinone and hydroquinone as well as the transition states, and the calculated spectra were used for the assignment of the frequencies observed in the experimental IR spectra. The calculated geometrical parameters, the predicted IR spectra, and the chemical activities of free radicals and transition states were also compared with those of benzoquinone and hydroquinone. The reactive mechanisms of free radicals generated by benzoquinone and hydroquinone are also discussed using ab initio Hartree–Fork (HF) methods.

Synthesis reaction pathway of nitrogen-rich ionic compound N 7H 2+

The potential energy surface of nitrogen-rich ionic compound N 7H 2 + synthesized by N 5 + and cis-N 2H 2 was investigated. The structures involved in the PES of N 7H 2 + were optimized using Hartree–Fork, MP2, hybrid functional theory, and CASSCF methods. The barrier height of synthesis pathway was predicted to be 46.8 kcal/mol corrected by ZPVE at the B3LYP/6-311++G** level. Such high barrier makes the synthesis reaction challenging, but raising the hope to achieve it by suitable catalyst. Electron density and molecular shape analysis were calculated to test the synthesis pathway as well. The result will provide suggestions for experimental synthesis of N 7H 2 + as a high energy-density material.

An MP2 study of linear polarizabilities and second-order hyperpolarizabilities for centrosymmetric squaraines

The ground-state geometry, basis set, electron correlation, and frequency dependency of the longitudinal components of linear polarizabilities α zz and second hyperpolarizabilities γ zzzz of the centrosymmetric (2,4-diphenyl)squaraine and its derivatives have been studied using finite-field (FF) and time-dependent Hartree–Fork (TDHF) approaches, respectively. The substitution at the para and/or ortho positions at the phenyl rings is crucial to the magnitude and sign of γ zzzz , depending on the nature of the substituents. Going from powerful electron-withdrawing groups to powerful electron-donating groups at para positions, γ zzzz varies from positive to negative, while the ortho hydroxys at the phenyls enhance greatly the negative γ zzzz values. The computational methodology affects considerably the calculated γ zzzz values, especially for the squaraines with weak donors at both terminals.