The Dipole Polarizability of the Hydrogen Molecular Ion: A Variational Two-Center Calculation

1974 ◽  
Vol 52 (20) ◽  
pp. 3463-3467 ◽  
Author(s):  
R. P. McEachran ◽  
Sharon Smith ◽  
M. Cohen
Keyword(s):  
Electric Dipole ◽  
Hydrogen Molecule ◽  
Moment Function ◽  
Polarizability Tensor ◽  
Dipole Polarizability ◽  
Hydrogen Molecular Ion ◽  
Molecular Ion ◽  
First Order ◽  
Wide Range ◽  
Good Agreement

The electric dipole polarizability tensor of the hydrogen molecule-ion has been calculated variationally over a wide range of internuclear separations, using the accurate two center James (ref. 3) orbital as the unperturbed wavefunction. Our most accurate values, obtained with first order functions containing between three and five variational parameters, are in good agreement with some recent moment function values calculated by Bates (ref. 7).

Full Optical Rotation Tensor at CCSD Level in the Modified Velocity Gauge

2020 ◽  
Author(s):  
Kaihua Zhang ◽  
Ty Balduf ◽  
Marco Caricato
Keyword(s):  
Electric Dipole ◽  
Optical Rotation ◽  
Electric Quadrupole ◽  
Polarizability Tensor ◽  
Dipole Polarizability ◽  
Difficult Case ◽  
Computationally Efficient ◽  
Rotation Tensor ◽  
Approximate Methods ◽  
Velocity Gauge

<div> <div> <p> </p><div> <div> <div> <p>This work presents the first simulations of the full optical rotation (OR) tensor at coupled cluster with single and double excitations (CCSD) level in the modified velocity gauge (MVG) formalism. The CCSD-MVG OR tensor is origin independent, and each tensor element can in principle be related directly to experimental measurements on oriented systems. We compare the CCSD results with those from two density functionals, B3LYP and CAM-B3LYP, on a test set of 22 chiral molecules. The results show that the functionals consistently overestimate the CCSD results for the individual tensor components and for the trace (which is related to the isotropic OR), by 10-20% with CAM-B3LYP and 20-30% with B3LYP. The data show that the contribution of the electric dipole-magnetic dipole polarizability tensor to the OR tensor is on average twice as large as that of the electric dipole-electric quadrupole polarizability tensor. The difficult case of (1S,4S)-(–)-norbornenone also reveals that the evaluation of the former polarizability tensor is more sensitive than the latter. We attribute the better agreement of CAM-B3LYP with CCSD to the ability of this functional to better reproduce electron delocalization compared with B3LYP, consistently with previous reports on isotropic OR. The CCSD-MVG approach allows the computation of reference data of the full OR tensor, which may be used to test more computationally efficient approximate methods that can be employed to study realistic models of optically active materials. </p> </div> </div> </div> </div> </div>

scholarly journals Full Optical Rotation Tensor at CCSD Level in the Modified Velocity Gauge

2020 ◽  
Author(s):  
Kaihua Zhang ◽  
Ty Balduf ◽  
Marco Caricato
Keyword(s):  
Electric Dipole ◽  
Optical Rotation ◽  
Electric Quadrupole ◽  
Polarizability Tensor ◽  
Dipole Polarizability ◽  
Difficult Case ◽  
Computationally Efficient ◽  
Rotation Tensor ◽  
Approximate Methods ◽  
Velocity Gauge

<div> <div> <p> </p><div> <div> <div> <p>This work presents the first simulations of the full optical rotation (OR) tensor at coupled cluster with single and double excitations (CCSD) level in the modified velocity gauge (MVG) formalism. The CCSD-MVG OR tensor is origin independent, and each tensor element can in principle be related directly to experimental measurements on oriented systems. We compare the CCSD results with those from two density functionals, B3LYP and CAM-B3LYP, on a test set of 22 chiral molecules. The results show that the functionals consistently overestimate the CCSD results for the individual tensor components and for the trace (which is related to the isotropic OR), by 10-20% with CAM-B3LYP and 20-30% with B3LYP. The data show that the contribution of the electric dipole-magnetic dipole polarizability tensor to the OR tensor is on average twice as large as that of the electric dipole-electric quadrupole polarizability tensor. The difficult case of (1S,4S)-(–)-norbornenone also reveals that the evaluation of the former polarizability tensor is more sensitive than the latter. We attribute the better agreement of CAM-B3LYP with CCSD to the ability of this functional to better reproduce electron delocalization compared with B3LYP, consistently with previous reports on isotropic OR. The CCSD-MVG approach allows the computation of reference data of the full OR tensor, which may be used to test more computationally efficient approximate methods that can be employed to study realistic models of optically active materials. </p> </div> </div> </div> </div> </div>

scholarly journals The hyperfine structure of the hydrogen molecular ion

1960 ◽  
Vol 259 (1296) ◽  
pp. 100-109 ◽  
Keyword(s):  
Electron Spin ◽  
Ground State ◽  
Energy Levels ◽  
High Accuracy ◽  
Hydrogen Molecular Ion ◽  
Molecular Ion ◽  
First Order ◽  
Quantitative Results ◽  
Coupling Terms ◽  
Very High

A calculation is presented of the energy levels of the hydrogen molecular ion in the ground state for different orientations of the electron spin, taking into account the coupling of the electron spin to the nuclear spin and to the nuclear rotational angular momentum. The first-order coupling terms are evaluated to very high accuracy, and quantitative results are given for the level splitting for a number of rotational levels.

scholarly journals Kinetic regularities of alloying iron-carbon alloys with vanadium

2020 ◽  
Vol 329 ◽  
pp. 02036
Author(s):  
Alexander Klimov ◽  
Michael Zinigrad
Keyword(s):  
Volume Concentration ◽  
Calculated Data ◽  
Slag Viscosity ◽  
Electrochemical Studies ◽  
Process Rate ◽  
Diffusion Mode ◽  
First Order ◽  
Air Atmosphere ◽  
Wide Range ◽  
Good Agreement

The results of the vanadium reduction laboratory investigation are presented. Experiments were conducted with CaO-SiO2 -Al2 O3 -V2 O3 slags in a wide range of compositions in an air atmosphere. A saturated iron- carbon melt was used as a reducing agent. The reduction kinetics was studied by sampling. V2 O3 reduction from slags having a viscosity of more than 0.5 Pa⋅s and containing less than 7.5–8.0% V2 O3 proceeds in a diffusion mode. The reaction is of the first order in vanadium. The process rate is inversely proportional to the square root of slag viscosity. A good agreement between the obtained data and the results of electrochemical studies on the cathodic reduction of vanadium was found. One made possible to deduce the rate equation of vanadium reduction by an iron-carbon melt depending on the volume concentration, temperature and slag viscosity. The calculated data for different slags acceptably check with those found by experiment.

scholarly journals Dipole polarizability of the hydrogen molecular ion

1999 ◽  
Vol 60 (4) ◽  
pp. R2630-R2632 ◽  
Author(s):  
J. M. Taylor ◽  
A. Dalgarno ◽  
J. F. Babb
Keyword(s):  
Dipole Polarizability ◽  
Hydrogen Molecular Ion ◽  
Molecular Ion

Dipole polarizability of the hydrogen molecule: a single-center calculation

1970 ◽  
Vol 48 (17) ◽  
pp. 1991-1995 ◽  
Author(s):  
M. Cohen ◽  
B. W. Southern
Keyword(s):  
Perturbation Theory ◽  
Hydrogen Molecule ◽  
Polarizability Tensor ◽  
Dipole Polarizability ◽  
Single Center

The leading terms in a single-center expansion of the static dipole polarizability tensor of the hydrogen molecule has been calculated by means of perturbation theory.

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