HARTREE–FOCK WAVE FUNCTIONS FOR EXCITED STATES: THE 2 1S STATE OF HELIUM

1965 ◽  
Vol 43 (10) ◽  
pp. 1867-1881 ◽  
Author(s):  
Maurice Cohen ◽  
Paul S. Kelly
Keyword(s):  
Excited State ◽  
Ground State ◽  
Wave Functions ◽  
State Function ◽  
Hartree Fock ◽  
Singlet States ◽  
Low Energies ◽  
Orthogonality Constraint ◽  
Satisfactory Approximation ◽  
Excited Singlet States

Hartree–Fock wave functions for the first-excited singlet states of several members of the helium isoelectronic sequence have been calculated. It is shown that unphysically low energies result if the excited-state function is not constrained to be orthogonal to the ground-state eigenfunction, and the excited-state orbitals are chosen orthogonal.If the excited-state orbitals are not chosen orthogonal, the effect of the overall constraint is small, raising the total energy very slightly; however, the effect of imposing both constraints simultaneously is appreciable. It is concluded that the most satisfactory approximation involves nonorthogonal excited-state orbitals, together with an overall orthogonality constraint towards the ground state.

The photochemistry of indenyl alcohols and esters: Substituent effects on the competition between ion- and radical-derived products

2003 ◽  
Vol 81 (10) ◽  
pp. 1083-1095 ◽  
Author(s):  
J A Pincock ◽  
I S Young
Keyword(s):  
Excited State ◽  
Ground State ◽  
Fluorescence Emission ◽  
Substituent Effects ◽  
Sharp Contrast ◽  
Carboxylate Anion ◽  
Excited Singlet ◽  
Heterolytic Cleavage ◽  
Singlet States ◽  
Excited Singlet States

The photochemistry of the indenyl acetates 1 and pivalates 2, substituted with X = H, 5-CH3O, and 6-CH3O, have been examined in both methanol and cyclohexane. The precursor alcohols 3 were also found to be photoreactive. Although only radical-derived products were obtained in cyclohexane, both ion- and radical-derived products were formed in methanol. The absence of significant fluorescence emission from any of the substrates 1, 2, and 3 indicates that the excited singlet states are highly reactive. A mechanism is proposed for the ion-derived products that proceeds through direct heterolytic cleavage to give an indenyl cation – carboxylate anion pair. The indenyl cations generated are anti-aromatic in the ground state and their efficient generation by this photochemical solvolysis is in sharp contrast to the very low reactivity of related ground-state substrates. For the pivalate esters 2, an excited-state migratory decarboxylation is proposed for the formation of tert-butyl derived products.Key words: ester photochemistry, indenyl cations, indenyl radicals.

scholarly journals Energy Calculation for Excited Lithium Atom in Position Space

2015 ◽  
Vol 12 (4) ◽  
pp. 808-813
Author(s):  
Baghdad Science Journal
Keyword(s):  
Excited State ◽  
Ground State ◽  
Lithium Atom ◽  
Wave Functions ◽  
Energy Calculation ◽  
Expectation Values ◽  
Position Space ◽  
Hartree Fock ◽  
Energy Expectation ◽  
Partitioning Technique

The energy expectation values for Li and Li-like ions ( , and ) have been calculated and examined within the ground state and the excited state in position space. The partitioning technique of Hartree-Fock (H-F) has been used for existing wave functions.

scholarly journals Studying the x- ray atomic Scattering form Factor and Nuclear Magnetic Shielding Constant for Be atom in its Excited state (1s2 2s 3s) and the Be - like ions

2015 ◽  
Vol 12 (1) ◽  
pp. 204-209
Author(s):  
Baghdad Science Journal
Keyword(s):  
Form Factor ◽  
Excited State ◽  
Computer Software ◽  
Wave Functions ◽  
Magnetic Shielding ◽  
Electron Systems ◽  
X Ray ◽  
Hartree Fock ◽  
Atomic Scattering ◽  
Nuclear Magnetic

The division partitioning technique has been used to analyze the four electron systems into six-pairs electronic wave functions for ( for the Beryllium atom in its excited state (1s2 2s 3s ) and like ions ( B+1 ,C+2 ) using Hartree-Fock wave functions . The aim of this work is to study atomic scattering form factor f(s) for and nuclear magnetic shielding constant. The results are obtained numerically by using the computer software (Mathcad).

scholarly journals Structures, dipole moments and excited state lifetime of isolated 4-cyanoindole in its ground and lowest electronically excited singlet states

2019 ◽  
Vol 21 (27) ◽  
pp. 14766-14774 ◽  
Author(s):  
Marie-Luise Hebestreit ◽  
Michael Schneider ◽  
Hilda Lartian ◽  
Vivienne Betz ◽  
Michael Heinrich ◽  
...  
Keyword(s):  
Excited State ◽  
Dipole Moments ◽  
Excited State Lifetime ◽  
Excited Singlet ◽  
Singlet States ◽  
Electronically Excited ◽  
Excited Singlet States

The rotationally resolved electronic Stark spectrum of 4-cyanoindole and some N-D and C-D deuterated isotopologues has been measured and analyzed.

Hartree–Fock calculation for the electronic structure of H+3 using numerically optimized orbitals

2001 ◽  
Vol 79 (2-3) ◽  
pp. 673-679
Author(s):  
J D Talman
Keyword(s):  
Electronic Structure ◽  
Ground State ◽  
Equilateral Triangle ◽  
Wave Functions ◽  
Equilibrium Geometry ◽  
Molecular Ion ◽  
Interatomic Spacing ◽  
Hartree Fock ◽  
Gaussian Orbitals

The Hartree–Fock wave functions for the ground state of the H2 molecule and the H+3 molecular ion are computed using radial orbitals that are numerically optimized. It is shown that these orbitals yield results comparable in accuracy to those obtained using much larger bases of Gaussian orbitals. As in previous calculations, the equilibrium geometry for H+3 is found to be that of an equilateral triangle, with an interatomic spacing of 1.64a0. PACS No.: 13.15+q

Inelastic Scattering of High Energy Electrons by Helium

1973 ◽  
Vol 51 (3) ◽  
pp. 311-315 ◽  
Author(s):  
S. P. Ojha ◽  
P. Tiwari ◽  
D. K. Rai
Keyword(s):  
Ground State ◽  
High Energy ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Final States ◽  
Interaction Type ◽  
Hartree Fock ◽  
High Energy Electrons ◽  
Approximate Wave ◽  
Accurate Wave

Generalized oscillator strengths and the cross section for excitation of helium by electron impact have been calculated in the Born approximation. Transitions from the ground state to the n1P (n = 2 and 3) states have been considered. Highly accurate wave functions of the Hartree–Fock and "configuration–interaction" type have been used to represent the ground state. Approximate wave functions due to Messmer have been employed for the final states. The results are compared with other calculations and with experiment.

Coherent X-ray Scattering Factors for Various Configurations of Lanthanides and Their Positive Ions

1975 ◽  
Vol 53 (1) ◽  
pp. 93-96 ◽  
Author(s):  
Robert Benesch ◽  
K. M. S. Saxena
Keyword(s):  
Ground State ◽  
Wave Functions ◽  
X Ray ◽  
Hartree Fock ◽  
Positive Ions ◽  
X Ray Scattering ◽  
Scattering Factor ◽  
Ray Scattering

Coherent X-ray scattering factors have been computed from numerical Hartree–Fock wave functions for the neutral lanthanides and for their single-, double-, and triple-positive ions having the most commonly occurring 6sm4fn ground state configurations. For small scattering angles, the scattering factors for the ions vary among the various configurations. At large scattering angles all configurations for a given ion yield similar values for the scattering factor.

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