Hartree-Fock Procedure Research Articles

Anomalous kinetics of the reaction between OH and HO2 on an accurate triplet state potential energy surface.

The reaction OH + HO2→ H2O + O2 is of great significance in interstellar media, the atmosphere, and combustion. In addition, it presents a prototypical reaction between two non-atom radical species. However, the temperature dependence of its rate coefficients has been debated for several decades. In this work, the rate coefficients are revisited by the quasi-classical trajectory (QCT) approach. To this end, a globally accurate full-dimensional potential energy surface of the ground triplet state for the title reaction is constructed using the permutation invariant polynomial-neural network (PIP-NN) method based on 108 000 points calculated at the level of CCSD(T)-F12a/AVTZ, in which particular attention is paid to the initial guess in the preceding Hartree-Fock procedure to obtain reliable ab initio energies. The QCT rate coefficients are compared to available experimental and theoretical results. It has been found that not only the trend, but also the magnitude, i.e. the large negative temperature dependence at low temperatures, and slightly positive temperature dependence at high temperatures, are consistent with some experiments.

Ab-initio and DFT methodologies for computing hyperpolarizabilities and susceptibilities of highly conjugated organic compounds for nonlinear optical applications

In this talk, after a short introduction on the methodologies used for computing dipole polarizability (α), second and third-order hyperpolarizability and susceptibility; the results of theoretical studies performed on density functional theory (DFT) and ab-initio quantum mechanical calculations of nonlinear optical (NLO) properties for a few selected organic compounds and polymers will be explained. The electric dipole moments (μ) and dispersion-free first hyperpolarizabilities (β) for a family of azo-azulenes and a styrylquinolinium dye have been determined by DFT at B3LYP level. To reveal the frequency-dependent NLO behavior, the dynamic α, second hyperpolarizabilities (γ), second (χ(2)) and third-order (χ(3)) susceptibilites have been evaluated using time-dependent HartreeFock (TDHF) procedure. To provide an insight into the third-order NLO phenomena of a series of pyrrolo-tetrathiafulvalene-based molecules and pushpull azobenzene polymers, two-photon absorption (TPA) characterizations have been also investigated by means of TDHF. All computed results of the examined compounds are compared with their previous experimental findings and the measured data for similar structures in the literature. The one-photon absorption (OPA) characterizations of the title molecules have been theoretically obtained by configuration interaction (CI) method. The highest occupied molecular orbitals (HOMO), the lowest unoccupied molecular orbitals (LUMO) and the HOMO–LUMO band gaps have been revealed by DFT at B3LYP level for azo-azulenes, styrylquinolinium dye, push–pull azobenzene polymers and by parametrization method 6 (PM6) for pyrrolo-tetrathiafulvalene-based molecules.

Second-order Nonlinearities of Anionic 3-dicyanomethylen-5,5-dimethyle-1-[2-(4-hydroxyphenyl)ethenyl)]-cyclohexene

Due to the connecting one π-conjugated group with the two backside donor and acceptor groups, anionic 3-dicyanomethylen-5,5-dimethyle-1-[2-(4-hydroxyphenyl)ethenyl)]-cyclohexene (1) might possess nonlinear optical (NLO) properties. To estimate the potential for second-order NLO behaviour; the electric dipole moments and dispersion-free dipole polarizabilities and first hyperpolarizabilities have been determined by density functional theory (DFT) at B3LYP/6-31++G(d, p) level. Quantum mechanical calculations using time-dependent Hartree-Fock (TDHF) procedure have been utilized to evaluate frequency-dependent second-order nonlinearities of 1. The one-photon absorption (OPA) characterization of 1 has been theoretically obtained by means of configuration interaction (CI) with 6-31G basis set. Our theoretical results on the maximum OPA wavelength, second-order susceptibilities and corresponding microscopic NLO responses are accorded with the previous experimental observations of the investigated compound. The highest occupied molecular orbitals, the lowest unoccupied molecular orbitals and the HOMO-LUMO band gaps for 1 have been also examined by DFT/B3LYP method.

A High-Precision Calculation of Bond Length and Spectroscopic Constants of Hg2 Based on the Coupled-Cluster Theory with Spin—Orbit Coupling**Supported by the Start-Up Funds of Xi'an Polytechnic University under Grant No BS1211, and the Scientific Research Program Funded by Shaanxi Provincial Education Department under Grant No 2013JK0679.

Based on the two-component relativistic effective core potential and matched basis sets cc-pwcvnz-pp (n=Q, 5), combining the completed basis-set extrapolation of electronic correlation energy and the fourth-order polynomial fitting technique, the bond length and spectroscopic constants of Hg2 are studied by the coupled cluster theory with spin—orbit coupling. Spin—orbit coupling is included in the post Hartree—Fock procedure, i.e., in the coupled-cluster iteration, to obtain more reliable theoretical results. The results show that our theoretical values agree with the experimental values very well and will be helpful to understand the spectral character of Hg2.

Magnetic properties of the quantum spin- $\frac{1}{2}$ XX diamond chain: the Jordan-Wigner approach

The Jordan-Wigner transformation is applied to study magnetic properties of the quantum spin- $\frac{1}{2}$ XX model on the diamond chain. Generally, the Hamiltonian of this quantum spin system can be represented in terms of spinless fermions in the presence of a gauge field and different gauge-invariant ways of assigning the spin-fermion transformation are considered. Additionally, we analyze general properties of a free-fermion chain, where all gauge terms are neglected and discuss their relevance for the quantum spin system. A consideration of interaction terms in the fermionic Hamiltonian rests upon the Hartree-Fock procedure after fixing the appropriate gauge. Finally, we discuss the magnetic properties of this quantum spin model at zero as well as non-zero temperatures and analyze the validity of the approximation used through a comparison with the results of the exact diagonalization method for finite (up to 36 spins) chains. Besides the m = 1/3 plateau the most prominent feature of the magnetization curve is a jump at intermediate field present for certain values of the frustrating vertical bond.

System of matrix-vector equations in the multiconfiguration Hartree-Fock method

A method for determining radial parts of one-electron functions entering the manyelectron basis is proposed within the multiconfiguration Hartree-Fock procedure. The solution of the Hartree-Fock equations is reduced to the solution of a system of matrix-vector equations. Rules of construction of these equations are formulated, and a stable numerical scheme of their solution is found.

Multiconfiguration Hartree-Fock method: Direct diagonalization for the construction of a multielectron basis

A method based on the direct diagonalization of basis states in the framework of the multiconfiguration Hartree-Fock procedure has been proposed for constructing the multielectron basis. With the use of the technique of ladder operators of the orbital angular momentum and spin, this method has been generalized to the case of arbitrary electron configurations. It has been shown that such an approach can be easily implemented on a computer and has low requirements for computational resources in the case of d and f-electrons. The calculations of the multielectron basis states have been exemplified for several electron configurations and various sets of quantum numbers.

First-principles cluster study of electronic structures, locations and hyperfine interactions of isolated atoms and ions in silicon

The electronic structures of the dilute transition metal (TM) impurities, V 2+ ,C r + ,M n 2+ ,a nd Mn 0 in silicon have been studied using the Hartree-Fock (HF) procedure combined with many-body perturbation theory (MBPT). The systems studied involved the TM impurities at the hexagonal interstitial (Hi), tetrahedral interstitial (Ti) and substitutional (S) locations. Investigations of the binding energy and local potential energy surface of the TM impurity-Si systems indicate that the TM impurities are binding at the Ti location. Hyperfine interaction constants (A) of the TM impurities at the Ti and S sites are presented and compared with available experimental results (Woodbury and Ludwig, J Phys Rev 117:102, 1960a, Phys Rev Lett 5:98, b) from Electron Paramagnetic Resonance (EPR) measurements.

Convergence difficulties in the hartree-fock procedure for the PPP model of alternant hydrocarbons

Calculations with the ppp model for alternant hydrocarbons of polyenic character, which exhibit the convergence difficulties in the usual Hartree-Fock iterative procedure are carried out. The standard process ends in oscillations of atomic charges when the geometry deviates enough from the prediction from a single Kekule structure. Deviations in geometry sufficient for non-convergence can be very small.

Investigation of the hyperfine properties of deoxy hemoglobin based on its electronic structure obtained by Hartree-Fock-Roothan procedure

The electronic structure of the heme unit of deoxyhemoglobin including the proximal imidazole has been studied using the first-principles Hartree-Fock procedure. Our results for the 57mFe isomer shift and asymmetry parameter are in very good agreement with the values obtained from Mossbauer spectroscopy measurements. The 57mFe nuclear quadrupole coupling constant is smaller than the experimental result and possible ways to improve the agreement in the future are discussed. Improved analysis of the Mossbauer data, removing some approximations made for deriving the magnetic hyperfine tensor for the 57mFe nucleus, is suggested to allow quantitative comparison with our results in the future.

Can STO basis sets do a good job in evaluating molecular electromagnetic properties? I. First hyperpolarizability of H2O, CH4, and NH3 according to the TDHF theory

The performance of STO basis sets for the ab initio estimation of the nonlinear electromagnetic response properties of molecules, in terms of a time-dependent Hartree–Fock procedure, is investigated. Applications to the case of the first dynamic hyperpolarizability of three simple polyatomics (H2O, CH4, NH3) adopting several extended basis sets are reported and discussed. Independent estimates for the observables investigated obtained by the same approach in terms of Gaussian basis sets are confronted with our findings in the search for recipes of possible utility.

Molecular electrostatic potential maps of the anti-cancer drugs daunomycin and adriamycin: an ab initio theoretical study

Molecular geometries of the anti-cancer drug molecules adriamycin and daunomycin were optimized using the restricted Hartree–Fock procedure and the 6-31G and 6-31G* basis sets. Molecular electrostatic potentials (MEP) were obtained on the van der Waals surfaces of the molecules using the MEP-derived CHelpG point charges. MEP minima and MEP surfaces corresponding to chosen MEP values were obtained using the continuous electron density distributions at the SCF level. Hydrogen bonding interactions involving the drug molecules, DNA and the surrounding environment suggested in experimental studies earlier are mostly supported by the present MEP values. However, this study also reveals additional useful information in the sense that the calculated MEP values near the different atoms vary over a wide range indicating that the hydrogen bond strengths involving them would also vary appreciably. Occurrence of a strong binding of a Na + ion to both O 4 and O 5 is indicated by the present MEP patterns. Further, the role of the binding of an oxygen atom that is present in adriamycin but not in daunomycin and is associated with a large negative MEP value with DNA appears to be very important due to which the former drug is more effective as an anti-cancer agent than the latter.

Theory of trapping of muon and muonium and associated hyperfine interactions in the organic ferromagnet p-NPNN (β-phase)

The ab initio unrestricted Hartree–Fock procedure has been applied to determine the trapping sites for the positive muon and muonium in β-phase ferromagnetic para-nitrophenyl nitronyl nitroxide and to calculate the associated electronic wave functions from which the corresponding contact and dipolar terms in the spin Hamiltonians have been obtained. For muonium, trapping sites were found near the oxygens of the two NO groups, resulting in a singlet electronic state for the overall molecular system, and also near the two oxygens of the NO 2 group, resulting in a triplet state for the overall system. For the muon a total of four trapping sites was found, corresponding to the oxygen and nitrogen atoms of the two NO groups. Using the easy axis along the b-axis of the orthorhombic sublattice, as found from muon spin rotation (μSR) measurements, and the calculated magnetic hyperfine interaction parameters, the observed 2.1 MHz zero-field μSR signal is assigned to the singlet state corresponding to muonium trapping near the oxygen of one of the NO groups. The large hyperfine constant of about 400 MHz inferred from longitudinal field repolarization measurements is assigned to a positive muon trapped near the nitrogen atom of one of the NO groups.

Analytic ab initio determination of the elastic modulus in stereoregular polymers: Analytical integral derivatives, long-range effects, implementation, and examples

An original scheme has been developed to compute, fully analytically, the Hartree–Fock Young modulus (second derivative of the Hartree–Fock energy with respect to the unit cell length) of stereoregular polymers. The evaluation of the elastic modulus is performed without the use of any intercell coordinate. The direct and efficient computation of the Young modulus requires the evaluation of the full Hessian (including cell and mixed components), and, subsequently, some specific integral derivatives and the use of a seven-step coupled-perturbed Hartree–Fock procedure. The long-range effects related to the Young modulus (and other second-order derivatives associated with vibrational frequencies) are evaluated by using a technique based on multiple Taylor expansions. The implementation of the integral derivatives in the McMurchie and Davidson framework is described in detail. Two examples show that the stability and accuracy of the technique proposed are excellent.

Theory of Nuclear Quadrupole Interactions of 14N, 17O, and 35Cl Nuclei in p-Cl-Ph-CH-N=TEMPO

The nuclear quadrupole coupling constants and asymmetry parameters have been studied for the 35Cl, 17O, and 14N nuclei in the molecular ferromagnet 4-(p-chlorobenzylideneamino)-TEMPO (2,2,6,6-tetramethyl- piperidin-1-yloxyl) using elctronic stuctures obtained by the Hartree-Fock procedure for the bare system and systems with trapped muon and muonium. Trends in the sizes of the coupling constants and asymmetry parameters for the various nuclei have been studied, and possible physical explanations have been proposed. For the systems with trapped muon or muonium, very substantial influences of the muon and muonium on the coupling constants and asymmetry parameters for the nuclei close to the trapping sites have been observed. The coupling constants and asymmetry parameters are found to be very different for the various nuclei, for the two cases where muon is trapped near chlorine and muonium near oxygen, indicating that, if experimental data were available to compare with theory, one could make conclusions about which of these two centers is responsible for the observed muon spin rotation frequency associated with the muon magnetic hyperfine interactions in these two trapped systems

Theory for relative strengths of trapping of He+ ions in solid, liquid and gaseous hydrogen

The study of trapping of He+ ion in solid hydrogen is important both as a problem in solid state physics and also as an applied physics problem in the field of muon catalyzed fusion (μCF). In μCF, He+ ion acts as a trap for μ−, interrupting the chain reaction aspect of the catalytic role of μ− in producing fusion of deuteron and triton and of triton and triton in solid hydrogen composed of 2H–3H and 3H–3H molecules, respectively. Using the Hartree–Fock procedure, combined with procedures for including many-body effects, as well as relaxation effects associated with the He+–H2 distances and the adjustment of the H–H separation, we have investigated the trapping of He+ in gaseous and solid state environments. For the former, the environment of He+ is simulated by a single hydrogen molecule and for the solid by clusters appropriately chosen to represent the hexagonal close-packed structure. Our results for the gaseous state indicate that the trapping is rather strong with a binding energy of 8.5 eV, with almost equal binding energy in the linear and triangular configurations with respect to the H–H direction. For the solid, both the likely sites for He+ trapping, namely the tetrahedral and octahedral interstitial sites, are also found to provide deep traps (8.6 eV) of almost equal strength, independent of the orientations of the neighboring molecules, showing that the trapping is not influenced by the orientational disorder in the surrounding hydrogen molecules. Further, the influence of next nearest neighbor hydrogen molecules is found to enhance the trapping energy for He+ substantially, by 0.6 eV, with the incorporation of the third nearest neighbors having a much smaller added effect, demonstrating the convergence of our results with respect to the size of the cluster chosen to simulate the solid. The substantial influence on the He+ trapping energy found for the neighbors beyond the nearest ones provides an explanation of the greater accumulation of helium in the solid state of hydrogen in μCF experiments as compared to the liquid. Suggestions are made regarding the possible reasons for the almost negligible accumulation of helium in the liquid state.

Theoretical investigation of muon and muonium trapping and hyperfine interactions in the chemical ferromagnet p-NPNN (β-phase)

The trapping sites for muon and muonium in β-phase ferromagnetic p-NPNN have been determined by the first-principles Unrestricted Hartree–Fock procedure. Four trapping sites are found for the muon near the two nitrogen and two oxygen atoms of the two NO groups. For the singlet state of trapped muonium, two trapping sites are found near the two oxygens of two NO groups and for the triplet state two trapping sites are found near the two oxygens of the NO2 group. The observed μSR signal at zero field with frequency 2.1 MHz is assigned to the singlet muonium sites near the two oxygens of the two NO groups and the high frequency signal ascribed to an isotropic hyperfine constant of 400 MHz is assigned to the two trapped muon sites near the two nitrogen atoms of the two NO groups.

Parity-violating effects in asymmetric chemical reactions: A theoretical study on the CHFClBr molecule

A coupled Hartree-Fock procedure has been employed to estimate the parity-violating energy contribution due to electroweak interaction in the vicinity of the transition point of a chemical reaction path starting from achiral reagents and producing the chiral CHFClBr molecule. The calculations demonstrate that (i) the S enantiomer is a reaction product more stable than its mirror image by approximately 1x10(-17) hartree; (ii) in the transition state of the reaction, the chiral activated complex evolving toward the S-CHFClBr species is more stable, by approximately 2.3x10(-17) hartree, than the enantiomeric activated complex that would yield the R-CHFClBr species. These results suggest that kinetic effects at work during chemical syntheses of chiral molecules might be more significant than the different thermodynamical stability of the two mirror-image reaction products in determining the final configuration and to explain homochirality.

Theoretical determination of parity-violating vibrational frequency differences between the enantiomers of the CHFClBr molecule

A coupled Hartree-Fock procedure has been employed to estimate the frequency shift in the infrared spectra of the S and R enantiomers of the CHFClBr molecule due to the parity-violating electroweak interaction. The calculations indicate that a resolving power $\ensuremath{\nu}/\ensuremath{\Delta}\ensuremath{\nu}\ensuremath{\approx}1\ifmmode\times\else\texttimes\fi{}{10}^{16},$ i.e., three orders of magnitude larger than that obtained in recent experiments, would be necessary to detect the parity-violating effects. The largest frequency shift was found for C-Cl stretching.

Growth morphology of zinc tris(thiourea) sulphate crystals

The growth morphology of crystals of zinc tris(thiourea) sulphate (ZTS) is investigated experimentally, and computed using the Hartman-Perdok approach. Attachment energies of the observed habit faces are calculated for determining their relative morphological importance. A computer code is developed for carrying out these calculations. A special procedure is adopted for computing the cohesive energy of a slice of the structure parallel to any rational crystallographic plane. For estimating the cohesive energies, formal charges on the experimentally determined atomic positions in the molecules of ZTS are calculated by ab initio molecular-orbital computations, with wave functions obtained by the Hartree-Fock procedure. Fairly good agreement with the observed crystal morphology is obtained for a model of growth mechanism in which ZTS is assumed to exist in solution sa szinc tris(thiourea) ions and sulphate ions.