Eine Berechnung der Feldgradienten am Ort der Fe- und Co-Kerne in Fe (C5H5)2 und [Co (C5H5)2]+

1963 ◽  
Vol 18 (10) ◽  
pp. 1074-1087
Author(s):  
Bernd Höfflinger ◽  
Jürgen Voitländer
Keyword(s):  
Zeta Function ◽  
Field Gradient ◽  
Metal Atom ◽  
Population Analysis ◽  
Basis Set ◽  
Overlap Integrals ◽  
Atomic Orbitals ◽  
Field Gradients ◽  
Approximation Formulas ◽  
Experimental Values

The second part of this series on the field gradient in Fe(C5H5)2 and [Co(C5H5)2] + attains an improved choice of the radial parts of the atomic orbitals (AO’s) according to population analysis. Thus new overlap integrals are found which favour the use of BALLHAUSEN and DAHL coefficients for the LCAO expansion of the molecular orbitals (MO’s) of the molecules cited above. All contributions to the field gradients at the sites of the metal atom nuclei can be written down formally using these coefficients and the AO basis set. One-center integrals lead back to the 〈r-3〉nl-values obtained in part I of this series. COULSON’S Molecular Zeta Function is used in order to compute the occuring two-center integrals. The results are confirmed by the application of approximation formulas, especially one which takes account of the symmetry of the field gradient operator. Without inclusion of STERNHEIMER corrections the theoretical field gradients thus obtained are 2.367 a. u. in [Co (C5H5) 2] + and 1.58 a. u. in Fe(C5H5)2 compared with experimental values of 2.11 and 1.25 a. u. respectively.

Molecular Structural and Vibrational Spectroscopic Assignments of n5-(4-Methoxyphenyl)-3-(1-methylindol-3-yl)-isoxazole using DFT Theory Calculations

2019 ◽  
Vol 4 (3) ◽  
pp. 147-151
Author(s):  
J. Jani Matilda ◽  
T.F. Abbs Fen Reji
Keyword(s):  
Molecular Orbital ◽  
Density Functional ◽  
Population Analysis ◽  
Nbo Analysis ◽  
Basis Set ◽  
Atomic Charges ◽  
Dft Methods ◽  
Mulliken Population ◽  
B3lyp Method ◽  
Experimental Values

In an effort to evaluate and design fast, accurate density functional theory (DFT) methods for 5-(4- methoxyphenyl)-3-(1-methylindol-3yl)isoxazole compound was done using Gaussion’ 09 program package using B3LYP method with the 6-31G basis set, which has been successfully applied in order to derive the optimized geometry, bonding features, harmonic vibrational wave numbers, NBO analysis and Mulliken population analysis on atomic charges in the ground state. Optimized geometries of the molecule have been described and collate with the experimental values. The experimental atomic charges demonstrates adequate concurrence with the theoretical prediction from DFT. The theoretical spectra values have been interpreted and compared with the FT-IR spectra. The calculated highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy gaps also confirm that charge transfer takes place within the molecule.

Measurement and Calculation of Electric Field Gradients in Hg-Mercaptides

1998 ◽  
Vol 53 (6-7) ◽  
pp. 404-410 ◽  
Author(s):  
Torsten Soldner ◽  
Wolfgang Tröger ◽  
Tilman Butz ◽  
Peter Blaha ◽  
Karlheinz Schwarz ◽  
...  
Keyword(s):  
Plane Wave ◽  
Electric Field ◽  
Basis Set ◽  
Full Potential ◽  
Hydrogen Atoms ◽  
Electric Field Gradients ◽  
Field Gradients ◽  
Unit Cells ◽  
Experimental Values ◽  
Linearized Augmented Plane Wave

Abstract Electric field gradients (EFG) at Hg were determined in mercury mercaptides Hg(S(CH2)i CH3)2 experimentally for i ∈ {0, 1, 2} using time differential perturbed angular correlation and theoreti-cally for i ∈ {0, 1} with the full potential linearized augmented plane wave code WIEN95. Due to the large unit cells and small hydrogen atoms not full convergence of the plane wave basis set could be reached. Nevertheless, the calculated EFGs agree with experimental values to better than 20%. Furthermore, isolated molecules for i ∈ {0, 1) were investigated theoretically, and strong differences to the values for the crystalline state, especially for the asymmetry parameters η, were found.

The Calculation of 14N Quadrupole Coupling Constants with Basis Sets of High Local Quality

1987 ◽  
Vol 42 (7) ◽  
pp. 753-760 ◽  
Author(s):  
Stefan Gerber ◽  
Hanspeter Huber
Keyword(s):  
Electric Field ◽  
Field Gradient ◽  
Coupling Constants ◽  
Basis Set ◽  
Basis Sets ◽  
Hartree Fock ◽  
Field Gradients ◽  
Empirical Correction ◽  
Quadrupole Coupling ◽  
Local Quality

An appropriate basis set to obtain electric field gradients close to the Hartree-Fock limit is evaluated for the nitrogen nucleus. An empirical correction for the error due to the neglect of electron correlation is given for sp-, sp2 - and sp3-hybrized nitrogen. The results are used to predict the full quadrupole coupling tensor for a few molecules. A breakdown of the electric field gradient into contributions from the single orbitals leads to a model for the field gradient due to the π-system and a partial rationalization of the part due to the σ-system. The results are discussed in relation to a Townes and Dailey analysis.

DFT Benchmark Study of the O--O Bond Dissociation Energy in Peroxides Validated with High-Level Ab-Initio Calculations

2019 ◽  
Author(s):  
Danilo Carmona ◽  
Pablo Jaque ◽  
Esteban Vöhringer-Martinez
Keyword(s):  
Reference Value ◽  
Basis Set ◽  
Basis Sets ◽  
Mean Deviation ◽  
Bond Dissociation ◽  
Dissociation Energies ◽  
The Mean ◽  
Experimental Values ◽  
High Level ◽  
Almost All

<div><div><div><p>Peroxides play a central role in many chemical and biological pro- cesses such as the Fenton reaction. The relevance of these compounds lies in the low stability of the O–O bond which upon dissociation results in radical species able to initiate various chemical or biological processes. In this work, a set of 64 DFT functional-basis set combinations has been validated in terms of their capability to describe bond dissociation energies (BDE) for the O–O bond in a database of 14 ROOH peroxides for which experimental values ofBDE are available. Moreover, the electronic contributions to the BDE were obtained for four of the peroxides and the anion H2O2− at the CBS limit at CCSD(T) level with Dunning’s basis sets up to triple–ζ quality provid- ing a reference value for the hydrogen peroxide anion as a model. Almost all the functionals considered here yielded mean absolute deviations around 5.0 kcal mol−1. The smallest values were observed for the ωB97 family and the Minnesota M11 functional with a marked basis set dependence. Despite the mean deviation, order relations among BDE experimental values of peroxides were also considered. The ωB97 family was able to reproduce the relations correctly whereas other functionals presented a marked dependence on the chemical nature of the R group. Interestingly, M11 functional did not show a very good agreement with the established order despite its good performance in the mean error. The obtained results support the use of similar validation strategies for proper prediction of BDE or other molecular properties by DF Tmethods in subsequent related studies.</p></div></div></div>

AlN Nanotubes: A DFT Study of Al-27 and N-14 Electric Field Gradient Tensors

2007 ◽  
Vol 62 (12) ◽  
pp. 711-715 ◽  
Author(s):  
Ahmad Seif ◽  
Mahmoud Mirzaei ◽  
Mehran Aghaie ◽  
Asadollah Boshra
Keyword(s):  
Electric Field ◽  
Electric Field Gradient ◽  
Field Gradient ◽  
Density Functional ◽  
Quadrupole Coupling Constant ◽  
Basis Set ◽  
Basis Sets ◽  
B3lyp Method ◽  
Package Program ◽  
Nqr Parameters

Density functional theory (DFT) calculations were performed to calculate the electric field gradient (EFG) tensors at the sites of aliminium (27Al) and nitrogen (14N) nuclei in an 1 nm of length (6,0) single-walled aliminium nitride nanotube (AlNNT) in three forms of the tubes, i. e. hydrogencapped, aliminium-terminated and nitrogen-terminated as representatives of zigzag AlNNTs. At first, each form was optimized at the level of the Becke3,Lee-Yang-Parr (B3LYP) method, 6-311G∗∗ basis set. After, the EFG tensors were calculated at the level of the B3LYP method, 6-311++G∗∗ and individual gauge for localized orbitals (IGLO-II and IGLO-III) types of basis sets in each of the three optimized forms and were converted to experimentally measurable nuclear quadrupole resonance (NQR) parameters, i. e. quadrupole coupling constant (qcc) and asymmetry parameter (ηQ). The evaluated NQR parameters revealed that the considered model of AlNNT can be divided into four equivalent layers with similar electrostatic properties.With the exception of Al-1, all of the three other Al layers have almost the same properties, however, N layers show significant differences in the magnitudes of the NQR parameters in the length of the nanotube. Furthermore, the evaluated NQR parameters of Al-1 in the Al-terminated form and N-1 in the N-terminated form revealed the different roles of Al (base agent) and of N (acid agent) in AlNNT. All the calculations were carried out using the GAUSSIAN 98 package program.

ON THE STUDY OF DIFFUSION USING SPIN ECHOES

1960 ◽  
Vol 38 (10) ◽  
pp. 1318-1327 ◽  
Author(s):  
B. Muller ◽  
M. Bloom
Keyword(s):  
Radio Frequency ◽  
Field Gradient ◽  
Spin Echo ◽  
Constant Field ◽  
Experimental Values ◽  
Spin Echoes

The decay of the primary spin echo due to diffusion is governed by the expression [Formula: see text]. This statement is independent of the angles through which the magnetization is rotated by the radio frequency (r-f.) pulses. For the usual range of experimental values, it is also independent of the intensity or homogeneity of the r-f. field, the duration of the r-f. pulse, and the magnitude of the constant field gradient.

scholarly journals Origin Invariant Full Optical Rotation Tensor in the Length Dipole Gauge without London Atomic Orbitals

2021 ◽  
Author(s):  
Marco Caricato
Keyword(s):  
Electron Correlation ◽  
Density Functional ◽  
Optical Rotation ◽  
Density Functional Method ◽  
Functional Method ◽  
Basis Set ◽  
Rotation Tensor ◽  
Atomic Orbitals ◽  
Complete Basis Set ◽  
Approximate Wave

<div> <div> <div> <p>We present an origin-invariant approach to compute the full optical rotation tensor (Buckingham/Dunn tensor) in the length dipole gauge without recourse to London atomic orbitals, called LG(OI). The LG(OI) approach is simpler and less computationally demanding than the more common LG-London and modified velocity gauge (MVG) approaches and it can be used with any approximate wave function or density functional method. We report an implementation at coupled cluster with single and double excitations level (CCSD), for which we present the first simulations of the origin-invariant Buckingham/Dunn tensor in the length gauge. With this method, we attempt to decouple the effects of electron correlation and basis set incompleteness on the choice of gauge for optical rotation calculations on simple test systems. The simulations show a smooth convergence of the LG(OI) and MVG results with the basis set size towards the complete basis set limit. However, these preliminary results indicate that CCSD may not be close to a complete description of the electron correlation effects on this property even for small molecules, and that basis set incompleteness may be a less important cause of discrepancy between choices of gauge than electron correlation incompleteness. </p> </div> </div> </div>

scholarly journals Quantum Calculations to Estimate the Heat of Hydrogenation Theoretically

2020 ◽  
Author(s):  
Ali Amir Khairbek
Keyword(s):  
Unsaturated Hydrocarbon ◽  
Experimental Results ◽  
Basis Set ◽  
Good Linear ◽  
Complete Basis ◽  
Complete Basis Set ◽  
Complete Basis Set Limit ◽  
The Mean ◽  
Experimental Values ◽  
Linear Correlations

Standard enthalpies of hydrogenation of 29 unsaturated hydrocarbon compounds were calculated in the gas phase by CCSD(T) theory with complete basis set cc-pVXZ, where X = DZ, TZ, as well as by complete basis set limit extrapolation. Geometries of reactants and products were optimized at the M06-2X/6-31g(d) level. This M06-2X geometries were used in the CCSD(T)/cc-pVXZ//M06-2X/6-31g(d) and cc-pV(DT)Z extrapolation calculations. (MAD) the mean absolute deviations of the enthalpies of hydrogenation between the calculated and experimental results that range from 8.8 to 3.4 kJ mol−1 based on the Comparison between the calculation at CCSD(T) and experimental results. The MAD value has improved and decreased to 1.5 kJ mol−1 after using complete basis set limit extrapolation. The deviations of the experimental values are located inside the “chemical accuracy” (±1 kcal mol−1 ≈ ±4.2 kJ mol−1) as some results showed. A very good linear correlations between experimental and calculated enthalpies of hydro-genation have been obtained at CCSD(T)/cc-pVTZ//M06-2X/6-31g(d) level and CCSD(T)/cc-pV(DT)Z extrapolation levels (SD =2.11 and 2.12 kJ mol−1, respectively).

From Atomic Orbitals to Molecular Orbitals and Chemical Bonds

2020 ◽  
pp. 150-187
Author(s):  
Jochen Autschbach
Keyword(s):  
Hydrogen Molecule ◽  
Atomic Orbital ◽  
Plane Waves ◽  
Basis Set ◽  
Orbital Method ◽  
Chemical Bonds ◽  
Atomic Orbitals ◽  
Hartree Fock ◽  
Generalized Matrix

It is shown how an aufbau principle for atoms arises from the Hartree-Fock (HF) treatment with increasing numbers of electrons. The Slater screening rules are introduced. The HF equations for general molecules are not separable in the spatial variables. This requires another approximation, such as the linear combination of atomic orbitals (LCAO) molecular orbital method. The orbitals of molecules are represented in a basis set of known functions, for example atomic orbital (AO)-like functions or plane waves. The HF equation then becomes a generalized matrix pseudo-eigenvalue problem. Solutions are obtained for the hydrogen molecule ion and H2 with a minimal AO basis. The Slater rule for 1s shells is rationalized via the optimal exponent in a minimal 1s basis. The nature of the chemical bond, and specifically the role of the kinetic energy in covalent bonding, are discussed in details with the example of the hydrogen molecule ion.

Small-angle scattering from collections of interacting hard ellipsoids of revolution studied by Monte Carlo simulations and other methods of statistical thermodynamics

1999 ◽  
Vol 32 (5) ◽  
pp. 917-923 ◽  
Author(s):  
Bo Sjöberg
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Small Angle ◽  
Chemical Potential ◽  
Compressibility Factor ◽  
Particle Method ◽  
Spherical Particles ◽  
Angle Scattering ◽  
Approximation Formulas ◽  
Experimental Values

Computer simulations using Monte Carlo methods are used to investigate the effects of interparticle correlations on small-angle X-ray and neutron scattering from moderate or highly concentrated systems of ellipsoids of revolution. Both oblate and prolate ellipsoids, of varying eccentricities and concentrations, are considered. The advantage with Monte Carlo simulation is that completely general models, both regarding particle shapes and interaction potentials, can be considered. Equations are also given that relate the nonideal part of the chemical potential, βμni, with the scattering at zero angle,I(0), and the compressibility factor,z. The quantity βμnican be obtained during the Monte Carlo simulations by using Widom's test-particle method. For spherical particles, the simulations are compared with approximation formulas based on the Percus–Yevick equation. A method is also suggested for the calculation of both βμniandzfrom experimental values ofI(0) recorded as a function of concentration.

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