Quasi-Linear Buildup of Coulomb Integrals via the Coupling Strength Parameter in the Non-Relativistic Electronic Schrödinger Equation

The non-relativistic electronic Hamiltonian, Hkin+Hne+aHee, is linear in coupling strength parameter (a), but its eigenvalues (electronic energies) have only quasi-linear dependence on it. Detailed analysis is given on the participation of electron-electron repulsion energy (Vee) in total electronic energy (Etotal electr,k) in addition to the wellknown virial theorem and standard algorithm for vee(a=1)=Vee calculated during the standard- and post HF-SCF routines. Using a particular modification in the SCF part of the Gaussian package, we have analyzed the ground state solutions via the parameter “a”. Technically, with a single line in the SCF algorithm, operator was changed as 1/rij-> a/rij with input “a”. The most important findings are, 1, vee(a) is quasi-linear function of “a”, 2, the extension of 1st Hohenberg-Kohn theorem (PSI0(a=1) <=> Hne <=> Y0(a=0)) and its consequences in relation to “a”. The latter allows an algebraic transfer from the simpler solution of case a=0 (where the single Slater determinant Y0 is the accurate form) to the physical case a=1. Moreover, we have generalized the emblematic Hund’s rule, virial-, Hohenberg-Kohn- and Koopmans theorems in relation to the coupling strength parameter.

Quasi-Linear Buildup of Coulomb Integrals via the Coupling Strength Parameter in the Non-Relativistic Electronic Schrödinger Equation

The non-relativistic electronic Hamiltonian, Hkin+Hne+aHee, is linear in coupling strength parameter (a), but its eigenvalues (electronic energies) have only quasi-linear dependence on it. Detailed analysis is given on the participation of electron-electron repulsion energy (Vee) in total electronic energy (Etotal electr,k) in addition to the wellknown virial theorem and standard algorithm for vee(a=1)=Vee calculated during the standard- and post HF-SCF routines. Using a particular modification in the SCF part of the Gaussian package, we have analyzed the ground state solutions via the parameter “a”. Technically, with a single line in the SCF algorithm, operator was changed as 1/rij-> a/rij with input “a”. The most important findings are, 1, vee(a) is quasi-linear function of “a”, 2, the extension of 1st Hohenberg-Kohn theorem (PSI0(a=1) <=> Hne <=> Y0(a=0)) and its consequences in relation to “a”. The latter allows an algebraic transfer from the simpler solution of case a=0 (where the single Slater determinant Y0 is the accurate form) to the physical case a=1. Moreover, we have generalized the emblematic Hund’s rule, virial-, Hohenberg-Kohn- and Koopmans theorems in relation to the coupling strength parameter.

Quasi-linear dependence of Coulomb forces on coupling strength parameter in the non-relativistic electronic Schrödinger equation and its consequences in Hund’s rule, Mølle -Plesset perturbation- , virial - , Hohenberg-Kohn - and Koopmans theorem

<p> The extended non-relativistic electronic Hamiltonian, H_Ñ+ H_ne+ aH_ee, is linear in coupling strength parameter (a), but its eigenvalues (interpreted as electronic energies) have only quasi-linear dependence on “a”. No detailed analysis has yet been published on the ratio or participation of electron-electron repulsion energy (V_ee) in total electronic energy – apart from virial theorem and the highly detailed and well-known algorithm for V_ee, which is calculated during the standard HF-SCF and post-HF-SCF routines. Using a particular modification of the SCF part in the Gaussian package we have analyzed the ground state solutions via the parameter “a”. Technically, this modification was essentially a modification of a single line in an SCF algorithm, wherein the operator r_ij^-1 was overwritten as r_ij^-1 ® ar_ij^-1, and used “a” as input. The most important finding beside that the repulsion energy V_ee(a) is a quasi-linear function of “a”, is that the extended 1^st Hohenberg-Kohn theorem (Y₀(a=1) Û H_ne Û Y₀(a=0)) and its consequences in relation to “a”. The latter allows an algebraic transfer from the simpler solution of case a=0 (where the single Slater determinant is the accurate form) to the realistic wanted case a=1. Moreover, we have generalized the emblematic theorems in the title in relation to the coupling strength parameter. </p>

Quasi-linear dependence of Coulomb forces on coupling strength parameter in the non-relativistic electronic Schrödinger equation and its consequences in Hund’s rule, Mølle -Plesset perturbation- , virial - , Hohenberg-Kohn - and Koopmans theorem

<p> The extended non-relativistic electronic Hamiltonian, H_Ñ+ H_ne+ aH_ee, is linear in coupling strength parameter (a), but its eigenvalues (interpreted as electronic energies) have only quasi-linear dependence on “a”. No detailed analysis has yet been published on the ratio or participation of electron-electron repulsion energy (V_ee) in total electronic energy – apart from virial theorem and the highly detailed and well-known algorithm for V_ee, which is calculated during the standard HF-SCF and post-HF-SCF routines. Using a particular modification of the SCF part in the Gaussian package we have analyzed the ground state solutions via the parameter “a”. Technically, this modification was essentially a modification of a single line in an SCF algorithm, wherein the operator r_ij^-1 was overwritten as r_ij^-1 ® ar_ij^-1, and used “a” as input. The most important finding beside that the repulsion energy V_ee(a) is a quasi-linear function of “a”, is that the extended 1^st Hohenberg-Kohn theorem (Y₀(a=1) Û H_ne Û Y₀(a=0)) and its consequences in relation to “a”. The latter allows an algebraic transfer from the simpler solution of case a=0 (where the single Slater determinant is the accurate form) to the realistic wanted case a=1. Moreover, we have generalized the emblematic theorems in the title in relation to the coupling strength parameter. </p>

Progressively Doping Graphene with S i: from Graphene to Silicene, a Numerical Study

For three different sizes of graphene nanosheets, we computed the Density of states when these nanosheets are progressively doped with an increasing percentage of S i atoms. The pure graphene nanosheets are semi conducting or not depending on their size. The pure silicene nanosheets are conducting with a conduction due to π (pi) electrons. <br />The S i doped graphene nanosheets are also semi conducting or not depending on their size: for small sizes, there are semi conducting and they become conducting for larger sizes and larger percentages of S idoping. We computed also the total electronic energy which is linked to the mechanical stability of all our nanosheets. This mechanical stability decreases regularly as a function of the S i percentage of doping , but for the pure silicene nanosheets, the mechanical stability decreases more abruptly.

Equations of Motion Theory for Electron Affinities

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.

Radiation Induced Nucleation of Nanoparticles in Silica

In this paper, we present the results of our investigation of producing nanoclusters of gold in silica at fluences of two orders of magnitude less than what is traditionally used This is accomplished by implanting 2.0 MeV Au into silica followed by MeV bombardment by MeV Si ions. The size of the nanoclusters, ranging from one to 10 nanometers, is controlled by the implantation dose and by the total electronic energy deposited by each post bombarding ion in the implanted layer. By both indirect measurement methods, such as optical absorption spectrophotometry (non-destructive), and direct methods, such as transmission electron microscopy (destructive) we show how and at what concentrations gold nucleates to form nanoparticles by radiation-enhanced nucleation at a dose below that needed for spontaneous nanoparticle formation.

Mechanism for Breakage of Si-O Networks of SiO2 Films in HF Solutions

ABSTRACTAn extended Hiickel calculation was employed to calculate the total electronic energy and the electron density during the breakage of the Si-O networks of a (F3SiO)2FSiOSiF(OSiF3)2 cluster modelled on the a-cristobalite structure. The Si-O networks are opened by the attack of F- ions on the silicon atoms, and the reaction is exthothermic by 2.7 eV through the attack of H+ ions on the oxygen atoms. Although the hydrogen termination of the oxygen atoms is an early reaction, the fluorine termination of the silicon atoms is a late reaction. The atomic bond population on the Si-O bonds decreases to zero by opening the Si-O networks. We conclude that the a-cristobalite and a-quartz SiO2 are dissolved in HF solutions since the Si-O networks are easily opened by the attack of F- ions. Our conclusion indicates that both cosite and stishovite SiO2, which are not dissolved in the HF solutions, are composed of Si-O networks that can be hardly opened by the attack of F- ions. Moreover, we propose the continual breakage of Si-O networks without the desorption of H2O molecules as an etching mechanism of SiO2 films.