Restricted Hartree-Fock Method Research Articles

Experimental and Theoretical Study of the Photophysics and Structures of Europium Cryptates Incorporating 3,3′‐Bi‐isoquinoline‐2,2′‐dioxide

A detailed photophysical study of [Eu within (biqO2.2.2)(CF3SO3)](CF3SO3)2. CH3CN.H2O (Eu within 1) and two other types of cryptates incorporating three 3,3'-biisoquinoline-2,2'-dioxide units has been performed. Structural crystallographic data of Eu within 1, electronic structure calculations and theoretical models were used to obtain the intramolecular energy transfer rates and the appropriate set of rate equations, which was solved numerically. Quantum yields and decay lifetimes were obtained from these results and compared to the experimental data. The role of the ligand-to-metal charge transfer (LMCT) states was ascertained. A theoretical ligand field and intensity analysis was carried out and the results agree very well with the emission spectra. The molecular structures of the lanthanide cryptates were successfully modelled by the YIII ion using the restricted Hartree-Fock (RHF) method, with the advantage of dealing with closed-shell systems. These molecular structures were used to explain the drastic differences in the photophysics of the three EuIII cryptates.

Auger-spectroscopic appearance of electron correlation at the Fermi surface of graphite

It is shown that, in Auger-electron spectra of three-dimensional semimetal graphite and two-dimensional graphite (a zero band-gap semiconductor), an energy gap should be observed between the thresholds (edges) of the forward and inverse processes (threshold gap). In the one-electron approximation, this gap is zero, since the threshold for the Auger spectrum of the forward process is the minimum hole energy in the valence band, while the threshold for the spectrum of the inverse process is the minimum energy of conduction electrons. Inclusion of the electron correlation at the Fermi surface within the quantum-chemical approximation of a single open electron shell for multiplet structures of the restricted Hartree-Fock method makes it possible to determine the threshold gap as 1.5 eV for a 48-atom cyclic model of three-dimensional graphite and as 2.0 eV for a 24-atom model of two-dimensional graphite. The threshold gap does not contain the Fermi energy, in contrast to the Auger spectrum thresholds, where \(\frac{1}{2}(4.0 eV - \varepsilon _F )\) for the forward Auger spectrum (holes) and \(\frac{1}{2}( - 1.1 eV + \varepsilon _F )\) for the inverse spectrum (conduction electrons), the sum of which gives this gap. The results of calculations for the forward Auger spectra of three-dimensional graphite (including the conclusion that electron correlation of holes in the top valence bands is weak in the Auger process) are shown to agree with the experimental data.

The importance of three-body terms in the fragment molecular orbital method.

A previously proposed two-body fragment molecular orbital method based on the restricted Hartree-Fock (RHF) method was extended to include explicit three-body terms. The accuracy of the method was tested on a set of representative molecules: (H(2)O)(n), n=16, 32, and 64, as well as alpha and beta n-mers of alanine, n=10, 20, and 40, using STO-3G, 3-21G, 6-31G, and 6-31++G(**) basis sets. Two- and three-body results are presented separately for assigning one and two molecules (or residues) per fragment. Total energies are found to differ from the regular RHF method by at most DeltaE(2/1)=0.06, DeltaE(2/2)=0.04, DeltaE(3/1)=0.02, and DeltaE(3/2)=0.003 (a.u.); rms energy gradients differ by at most DeltaG(2/1)=0.0015, DeltaG(2/2)=0.000 75, DeltaG(3/1)=0.000 20, and DeltaG(3/2)=0.000 10 (a.u./bohr), and rms dipole moments are reproduced with at most deltaD(2/1)=3.7, deltaD(2/2)=3.4, deltaD(3/1)=2.6, and deltaD(3/2)=3.1 (%) relative error, where the subscript notation n/m refers to the n-body method based on m molecules (residues) per fragment. A few of the largest three-body calculations were performed with a separated trimer approximation, which presumably somewhat lowered the accuracy of mostly dipole moments which are very sensitive to slight variations in the density distribution. The proposed method is capable of providing sufficient chemical accuracy while providing detailed information on many-body interactions.

Phase Transition and Energy Spectra of Some Ferroelectrics-Ferroelastics

We report the results of electronic structure calculations for several types of MoO4-clusters in the Gd2(MoO4)3 structure in ferroelectric and paraelectric phase by using cluster ab initio restricted Hartree Fock method. The results give a variational approximation to the ground state electron densities of these clusters within the framework of ab initio restricted Hartree Fock (RHF) MO LCAO method.

Phosphorus magnetic shielding tensors for transition-metal compounds containing phosphine, phosphido, and phosphinidene ligands: Insights from computational chemistry

The present study examines the quality of the restricted Hartree–Fock (RHF) ab initio, B3LYP hybrid density functional theory (DFT), and relativistic zeroth-order regular approximation (ZORA) DFT methods for the calculation of phosphorus chemical shift (CS) tensors in phosphine, phosphido, and phosphinidene transition-metal complexes. A detailed comparison of calculated and experimental 31P CS tensors allows us to identify the characteristic advantages of each computational method. The results from B3LYP and ZORA-DFT calculations indicate that a double-ζ quality basis set reproduces experimental values of the principal components of the 31P CS tensor in many of the phosphorus-containing transition-metal complexes investigated, whereas the RHF method requires a triple-ζ doubly polarized basis set, yet fails in the case of the terminal phosphido group. Inclusion of the spin-orbit relativistic correction with the ZORA-DFT formalism requires a triple-ζ quality basis set to reproduce the experimental data. We demonstrate the merit of modern computational methods for investigating theoretically the effect of geometric variations upon the phosphorus CS tensor by systematically altering the W—P bond length and the W-P-CMe bond angle in W(CO)5(PMe3). Additionally, a previously reported correlation, determined experimentally, relating the 31P CS tensor to the Fe-P-Fe bond angle in a series of iron phosphido-bridging compounds, has been reproduced with calculations using the model compound Fe2(CO)6(µ2-PPh2)(µ2-Cl). The results presented demonstrate the value of modern computational techniques for obtaining a greater understanding of the relationship between phosphorus chemical shifts and molecular structure.Key words: 31P chemical shift, phosphine, phosphido, phosphinidene, RHF, B3LYP, relativistic, ZORA-DFT.

A conformational analysis of histamine, and its protonated or deprotonated forms: an ab initio study

Histamine, a neurotransmitter contains an imidazole ring which may be protonated or deprotonated. The present study was dedicated to the two tautomeric and their protonated and deprotonated forms. Throughout the whole study, the side chain nitrogen was kept in its protonated form. Potential energy surface scanning and reaction path calculation between two optimized conformations were carried out using restricted Hartree-Fock method with 3-21G basis set (RHF/3-21G).

The Hartree–Fock Approximation Calculation of Electric Polarizability of Atoms with an Open Shell

Within the framework of the restricted Hartree–Fock method, equations of stationary “coupled” perturbation theory have been obtained for atomic-molecular systems with an open shell in orbital representation. Corrections to the Hartree–Fock orbitals are sought in the form of expansions in unperturbed orbitals which are assumed calculated in the LCAO approximation. The resulting inhomogeneous algebraic system for the expansion coefficients admits an exact solution. The static polarizability of atoms with an open shell from Li to Sc has been calculated with the use of an optimized basis set of Slater-type atomic orbitals.

Effects of Trifluoromethyl and Alkoxycarbonyl Groups on the Structure and Reactivity of Acrylates

Ab initio calculations with full geometry optimization have been performed for β-CF3-substituted cis- and trans-methyl crotonates, methyl-β,β-bis(trifluoromethyl) acrylate, and dimethylhexafluoroisopropylidene malonate using the restricted Hartree-Fock (RHF) method (6-31G* basis set). The effects of substituents at the multiple bond on the geometrical and electronic structure, dipole moments, polarizability and first molecular hyperpolarizability tensors, normal vibration frequencies, one-electron levels, electrostatic potentials, and local electron density at the C=C bond have been studied. Two substituents in the acrylic system prevent the conjugation of C=C and C=O bonds. The major effect on the structure and properties of the title compounds is produced by π-π interactions of the CF3 group with the multiple bond and by incoherent exchange interactions of substituents at the C=C bond.

Theoretical and experimental study of the structure and vibration spectra of 4,4′-carbonyl-di-morpholine

4,4′-Carbonyl-di-morpholine was synthesized and characterized by X-ray diffraction, the FTIR and NMR spectra. The extended MO calculations using density functional theory (DFT) and self-consistent field molecular orbital Hartree–Fock theory were carried out. The results of the calculations were compared with experimental data. The experimental and calculated results were supported each other. The performance of a hybrid B3LYP density functional was compared with the ab initio restricted Hartree–Fock method. With the basis sets of the 6-311G** quality, the DFT calculated bond lengths, dipole moments and harmonic vibrations were predicted in a very good agreement with available experimental data.

Cluster Ab Initio Calculations of the Shape of Local Potential Well and of Positions for Oxygen Atoms in PCN (C=Cd)

Potential relief and equilibrium positions for oxygen atoms in Cd--O--Nb, Cd--O--Cd and Nb--O--Nb chains are studied in Pb(Cd 1/3 Nb 2/3 )O 3 (PCN) and Ba(Cd 1/3 Nb 2/3 )O 3 (BCN). Total energy cluster calculations are performed using ab initio restricted Hartree-Fock method. The electron correlation contribution is calculated within Møller-Plesset method. It is revealed that in PCN the oxygen atoms in Cd--O--Cd and Cd--O--Nb chains move in multi-well potentials with four minima shifted transversely to fourfold [001] axis. Whereas the oxygen atom in Nb--O--Nb chain in PCN and all oxygen atoms in BCN move in single-well potentials.

Ab initio Study of the Geometrical and Electronic Structures of Sc(MDA)2 and Sc(MDA)3 Molecules

The geometrical parameters, force fields, and vibrational spectra of various geometrical configurations of Sc(MDA)2 and Sc(MDA)3 molecules were calculated using the restricted Hartree—Fock method taking into account electron correlation by second–order Moller–Plesset perturbation theory. The calculations were performed using effective pseudopotentials for describing atomic cores and valence double zeta basis sets supplemented by polarization functions. It was shown that the configurations of D 3 [Sc(MDA)3] and D 2h [Sc(MDA)2] symmetry correspond to the minimum on the potential energy surface of the ground electronic state. The configurations of D 3h symmetry for Sc(MDA)3 and D 2d for Sc(MDA)2 correspond to first–order saddle points. The ground electronic states of Sc(MDA)2 and Sc(MDA)3 molecules are the states of 2 A g and 1 A 1 symmetries, respectively. For both configurations (D 2h and D 2d of the Sc(MDA)2 molecule, the energies of vertical electron transitions were calculated using the CASSCF method. The formation of chemical bonding in the compounds considered was analyzed. It was shown that the Sc–O bond is predominantly ionic and the π conjugation is characteristic only of the oxygen–carbon skeleton of the chelate fragment. The results obtained are compared with literature experimental and theoretical data for related compounds.

Influence of Solvent Polarity and Hydrogen Bonding on the EPR Parameters of a Nitroxide Spin Label Studied by 9-GHz and 95-GHz EPR Spectroscopy and DFT Calculations

The isotropic and anisotropic hyperfine coupling constants and g-values of the nitroxide spin label (1-oxyl-2,2,5,5-tetramethylpyrroline-3-methyl)methanethiosulfonate (MTSSL) were determined from 9-GHz and 95-GHz electron paramagnetic resonance (EPR) measurements in various solvents with a large distribution in polarity and proticity. The parameters Aiso, giso, Azz, and gxx of MTSSL were found to be sensitive to changes in solvent properties, where A-values increased and g-values decreased due to increased solvent polarity or proticity. A linear correlation was found for the isotropic (giso, Aiso) and anisotropic (gxx, Azz) parameters, respectively. Furthermore, density functional theory (DFT) calculations of the same parameters were performed for a model spin label with the possibility to vary the dielectric constant (e) of the medium and the number of hydrogen bonds formed with the nitroxide oxygen. From a qualitative analysis of experimental and calculated results, it was possible to specify the causes of the parameter shifts in more detail. In the apolar region (e 25), the sensitivity to epsi, is small, and the shifts in Aiso and Azz are mainly determined by the proticity of the solvent. Methanol was found to form ~1 and water ~2 hydrogen bonds to the nitroxide on average. The DFT method determined the shifts in giso and gxx due to hydrogen bonding more accurately compared with the restricted open-shell Hartree-Fock method. The anisotropic spin label-solvent data can be used in the interpretation of rigid-limit data from spin-labeled proteins to gain further insight in local environmental properties.

Assignment of the Raman‐active modes of the antitumor agent azathioprine by normal‐mode calculations

AbstractAzathioprine is a slow‐release prodrug of 6‐mercaptopurine and an established clinical agent for the treatment of human leukemias and other immunologically mediated diseases. The Raman spectra (1600–600 cm−1) of solid and solution azathiopurine were recorded and are presented along with results from normal‐mode calculations. The band assignments were derived from semi‐empirical and ab initio molecular orbital calculations. The ab initio calculations were performed with the restricted Hartree–Fock method and the semi‐empirical methods utilized the AM1, PM3 and MNDO‐d methods. Copyright © 2001 John Wiley & Sons, Ltd.

Partially restricted Hartree-Fock method for singlet excited states

A version of the partially spin-restricted Hartree-Fock method is proposed to construct a reference Slater determinant in calculations of singlet excited states having the same symmetry as the ground one. On the one hand, this approach can be used for a rather simple, in comparison with the fully unrestricted determinant, construction of a pure spin state. On the other hand, it is suitable, in contrast to the Roothaan theory for open shells, for the development of the perturbation scheme for taking into account correlation effects in an excited state, which retains the calculation advantages of the Moller-Plesset perturbation theory with single annihilation for the ground state. The efficiency of the method is demonstrated by calculations of electronic excitation energies for BH and CH+ molecules.

The structure and spectra of 1-silylpropyne: scaled quantum-chemical force fields and vibrational effects

The geometric parameters and the force fields of two 1-silylpropyne conformers (eclipsed and staggered, both of C3v symmetry) were calculated by the restricted Hartree–Fock method and taking into account electron correlation in the approximation of Møller–Plesset second-order perturbation theory (6-311G∗∗ basis set). The total energies of the two conformers differ by less than 20calmol−1, which is evidence of virtually free internal rotation. The IR spectra of H3SiCCCH3 and D3SiCCCH3 were interpreted by scaling quantum-chemical force fields. The scale factors were found to be transferable in the series of Si and Sn acetylenides. The mean vibrational amplitudes and the harmonic corrections to internuclear distances were calculated taking into account nonlinear kinematic effects. Corrections for centrifugal distortions and anharmonic effects were calculated at the level of first-order perturbation theory. The introduction of these corrections into the experimental rij,a parameters allowed us to determine the parameters of the rh1 structure and estimate equilibrium internuclear distances.

Chemically accurate conformational energies for aziridine-2-carbonitrile

Extensive ab initio computations have been carried out to characterize the energy of trans-aziridine-2-carbonitrile relative to cis-aziridine-2-carbonitrile (also known as 2-cyanoaziridine). Correlation consistent basis sets of double-, triple-, quadruple-, and pentuple-ζ quality have been employed to approach the one-particle basis set limit for energies obtained with the restricted Hartree–Fock method and second-order Møller–Plesset perturbation theory. Contributions from higher-order excitations have been determined with the popular coupled-cluster technique which includes single and double excitations as well as a perturbative estimate of triple excitations [CCSD(T)] and with the Brueckner doubles method including a perturbative estimate of triple as well as quadruple excitations [BD(TQ)]. From a focal point analysis, the electronic energy separation is found to be 3.62 kJ mol−1, which is in excellent agreement with previous theoretical estimates, but is in disagreement with an experimentally estimated lower bound to the free energy difference of 11 kJ mol−1. The electronic energy of the transition structure connecting the two conformers was determined to be 77.15 kJ mol−1 higher than the cis-isomer.

A Hartree–Fock Calculation of the Geometry and Electronic Structure of an Al42Mn12Cluster

The equilibrium geometry and electronic structure of the main structural fragment of an Al0.86Mn0.14quasicrystal—the Mackay icosahedral cluster consisting of 54 atoms—are calculated by the restricted Hartree–Fock method. The charge transfer from manganese atoms to aluminum atoms is revealed. The energy diagrams of the contributions of the valence atomic orbitals to the molecular orbitals of the cluster are constructed.

X-OH 2 + (X = C, O) cations: Vibrational spectra, stability, and electron capture reactions

Calculations of the potential energy surfaces of X-OH 2 + cations (X = C, O) by the restricted and unrestricted Hartree-Fock methods (RHF, UHF) taking into account the correlation energy (MP-2) and by the CASSCF method are presented. All cations are found to be rather stable against X-O bond rupture and intermolecular rearrangement. The reaction of electron capture by these cations is studied.

AB initio Calculations of the structure and spectra of chromium, molybdenum, and tungsten tetrafluorides. nontetrahedral molecular structure of WF4

The properties of MF4 molecules (M = Cr, Mo, W) are investigated by the restricted Hartree-Fock method using Moller-Plesset second-order perturbation theory and by the second-order configuration interaction method using the multiconfigumtion wave function derived in a complete active space approximation, in wide bases complemented with polarization d and f functions. Relativistic effective potentials are used to describe the core electrons. For CrF4 and MoF4, the tetrahedral configuration of nuclei in the electronic state of3k2 symmetry is energetically most favorable. In the WF4 molecule, the least-energy structure is a D2hstructure in the singlet state 1A1. The D4h,(1 A1g) and Td ( 3A2) configurations in the WF4 molecule are higher on the energy scale than the ground state by 4 and 6305 cm’1 and are saddle points. For all of the analyzed configurations of MF4 molecules, the geometrical parameters, the vibrational spectra, and the energies of vertical electronic transitions are found. The chemical bonding is analyzed and a simple model is proposed to explain the variation of the relative energies of states in the series CrF4→MoF4→WF4.

A comparative ab initio and DFT study of neutral aniline oligomers

Comparative ab initio restricted Hartree–Fock (RHF) and density functional theory (DFT) calculations were performed to investigate the geometric and electronic structures of various neutral aniline oligomers. These oligomers were selected to model polyaniline (PANI) in different intrinsic oxidation states, with an aim to study the applicability and extendibility of the theoretical methods to conjugated polymers. In general, we found that DFT calculations produce results that are in good agreement with observations from x-ray diffraction, ultraviolet-visible absorption, ultraviolet photoelectron and x-ray photoelectron spectroscopy. The DFT method has reproduced well the ∼4.0 eV π–π* transition of leucoemeraldine base and the ∼2.0 eV Peierls gap transition of pernigraniline base. The valence band structure and the ∼1.2 eV energy separation of nitrogen core levels of emeraldine base are also correctly predicted. On the other hand, large discrepancies with experimental measurements are predicted by the RHF method. Single-point MP2 calculations show that the DFT-optimized structures are all at lower energy than the RHF-optimized ones.