scholarly journals Equations of Motion Theory for Electron Affinities

2005 ◽  
Vol 70 (5) ◽  
pp. 579-604 ◽  
Author(s):  
Jack Simons
Keyword(s):  
Total Energy ◽  
Equations Of Motion ◽  
Electronic Energy ◽  
Electron Affinities ◽  
Total Electronic Energy ◽  
Molecular Electron ◽  
Self Consistent Field ◽  
History Of ◽  
Moller Plesset ◽  
Extensive Quantity

The ab initio calculation of molecular electron affinities (EA) and ionization potentials (IP) is a difficult task because the energy of interest is a very small fraction of the total electronic energy of the parent species. For example, EAs typically lie in the 0.01-10 eV range, but the total electronic energy of even a small molecule, radical, or ion is usually several orders of magnitude larger. Moreover, the EA or IP is an intensive quantity but the total energy is an extensive quantity, so the difficulty in evaluating EAs and IPs to within a fixed specified (e.g., ±0.1 eV) accuracy becomes more and more difficult as the system's size and number of electrons grows. The situation becomes especially problematic when studying extended systems such as solids, polymers, or surfaces for which the EA or IP is an infinitesimal fraction of the total energy. EOM methods such as the author developed in the 1970s offer a route to calculating the intensive EAs and IPs directly as eigenvalues of a set of working equations. A history of the development of EOM theories as applied to EAs and IPs, their numerous practical implementations, and their relations to Greens function or propagator theories are given in this contribution. EOM methods based upon Møller-Plesset, multiconfiguration self-consistent field, and coupled-cluster reference wave functions are included in the discussion as is the application of EOM methods to metastable states of anions.

scholarly journals Solving the Non-Relativistic Electronic Schrödinger Equation with Manipulating the Coupling Strength Parameter over the Electron-Electron Coulomb Integrals

2019 ◽  
Author(s):  
Sandor Kristyan
Keyword(s):  
Coupling Strength ◽  
Correlation Effect ◽  
Electronic Energy ◽  
Basis Set ◽  
Strength Parameter ◽  
Repulsion Energy ◽  
Consistent Field ◽  
Self Consistent Field ◽  
Moller Plesset ◽  
Coulomb Integrals

The non-relativistic electronic Hamiltonian, H(a)= Hkin+Hne+aHee, extended with coupling strength parameter (a), allows to switch the electron-electron repulsion energy off and on. First, the easier a=0 case is solved and the solution of real (physical) a=1 case is generated thereafter from it to calculate the total electronic energy (Etotal electr,K) mainly for ground state (K=0). This strategy is worked out with utilizing generalized Moller-Plesset (MP), square of Hamiltonian (H2) and Configuration interactions (CI) devices. Applying standard eigensolver for Hamiltonian matrices (one or two times) buys off the needs of self-consistent field (SCF) convergence in this algorithm, along with providing the correction for basis set error and correlation effect. (SCF convergence is typically performed in the standard HF-SCF/basis/a=1 routine in today practice.)

scholarly journals Solving the Non-Relativistic Electronic Schrödinger Equation with Manipulating the Coupling Strength Parameter over the Electron-Electron Coulomb Integrals

2019 ◽  
Author(s):  
Sandor Kristyan
Keyword(s):  
Coupling Strength ◽  
Correlation Effect ◽  
Electronic Energy ◽  
Basis Set ◽  
Strength Parameter ◽  
Repulsion Energy ◽  
Consistent Field ◽  
Self Consistent Field ◽  
Moller Plesset ◽  
Coulomb Integrals

The non-relativistic electronic Hamiltonian, H(a)= Hkin+Hne+aHee, extended with coupling strength parameter (a), allows to switch the electron-electron repulsion energy off and on. First, the easier a=0 case is solved and the solution of real (physical) a=1 case is generated thereafter from it to calculate the total electronic energy (Etotal electr,K) mainly for ground state (K=0). This strategy is worked out with utilizing generalized Moller-Plesset (MP), square of Hamiltonian (H2) and Configuration interactions (CI) devices. Applying standard eigensolver for Hamiltonian matrices (one or two times) buys off the needs of self-consistent field (SCF) convergence in this algorithm, along with providing the correction for basis set error and correlation effect. (SCF convergence is typically performed in the standard HF-SCF/basis/a=1 routine in today practice.)

scholarly journals The formation of vortices from a surface of discontinuity

1931 ◽  
Vol 134 (823) ◽  
pp. 170-192 ◽  
Keyword(s):  
Steady State ◽  
Plane Surface ◽  
Equations Of Motion ◽  
Steady Motion ◽  
Small Oscillations ◽  
Approximate Form ◽  
History Of ◽  
State Increase ◽  
Liquid Surfaces

Helmholtz was the first to remark on the instability of those “liquid surfaces” which separate portions of fluid moving with different velocities, and Kelvin, in investigating the influence of wind on waves in water, supposed frictionless, has discussed the conditions under which a plane surface of water becomes unstable. Adopting Kelvin’s method, Rayleigh investigated the instability of a surface of discontinuity. A clear and easily accessible rendering of the discussion is given by Lamb. The above investigations are conducted upon the well-known principle of “small oscillations”—there is a basic steady motion, upon which is superposed a flow, the squares of whose components of velocity can be neglected. This method has the advantage of making the equations of motion linear. If by this method the flow is found to be stable, the equations of motion give the subsequent history of the system, for the small oscillations about the steady state always remain “small.” If, however, the method indicates that the system is unstable, that is, if the deviations from the steady state increase exponentially with the time, the assumption of small motions cannot, after an appropriate interval of time, be applied to the case under consideration, and the equations of motion, in their approximate form, no longer give a picture of the flow. For this reason, which is well known, the investigations of Rayleigh only prove the existence of instability during the initial stages of the motion. It is the object of this note to investigate the form assumed by the surface of discontinuity when the displacements and velocities are no longer small.

scholarly journals Thermodynamic investigation of promethazine, loratadine, cetirizine and buclizine as antihistamine drugs; monte carlo and semi-empirical studies

2020 ◽  
Vol 33 (01) ◽  
pp. 94-108
Author(s):  
Mina Zakeri ◽  
Majid Monajjemi ◽  
Ali Ebrahimi
Keyword(s):  
Total Energy ◽  
Frequency Analysis ◽  
Empirical Studies ◽  
Zero Point ◽  
Heat Of Formation ◽  
Electronic Energy ◽  
Basis Set ◽  
Amber Force Field ◽  
Environment Temperature ◽  
Semi Empirical

In this article, we discussed about four antihistamine drug called promethazine, loratadine, cetirizine and buclizine. Promethazine in this list is the only one in first generation antihistamine classification with CNS sedation effect and the other three belongs to second generation antihistamine group which are non-sedation and used to treat in many different anti-allergenic fields. In the following we optimized potential, kinetic and total energy of these molecules at body temperature (310 k˚) and environment temperature (298 k ˚) using Mont Carlo method in Amber force field in 500 ns. The quantum mechanics calculations and molecular structure of these molecules investigated using B3LYP level of theory with 6-31 G (d) as a basis set. Theoretical computations were performed to study thermodynamic parameters and frequency analysis. Electronic, thermal, zero point and gibs free energy and enthalpy were estimated in frequency analysis. Semi empirical computations were summarized to pm3 method and different energy parameters (total energy, Binding Energy, Isolated Atomic Energy, Electronic Energy, Core–Core Interaction and Heat of Formation.

Electronic Energy and Short-Range Order in Binary Alloys

1982 ◽  
Vol 19 ◽  
Author(s):  
Mark O. Robbins ◽  
L.M. Falicov
Keyword(s):  
Transition Metals ◽  
Total Energy ◽  
Ab Initio ◽  
Model Calculation ◽  
Entire Range ◽  
Short Range ◽  
Short Range Order ◽  
Binary Alloys ◽  
Electronic Energy ◽  
Range Order

ABSTRACTAn electronic theory for the total energy of binary alloys is presented. It treats the entire range of concentration and short-range order. The method in not ab initio, but requires only information about the pure elemental constituents of the alloy. Results for two very different metal series, monovalent metals and 4-d transition metals, are calculated and compared to experiment and other models. The model calculation allows us to examine the physical basis for experimental trends.

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