Wave Functions of Excited States of Atoms and Simple Molecules in the Hartree–Fock Approximation

2021 ◽  
pp. 119-139
Author(s):  
Miron Ya. Amusia ◽  
Larissa V. Chernysheva
Keyword(s):  
Excited States ◽  
Wave Functions ◽  
Hartree Fock ◽  
Simple Molecules

HARTREE–FOCK WAVE FUNCTIONS FOR EXCITED STATES: II. SIMPLIFICATION OF THE ORBITAL EQUATIONS

1966 ◽  
Vol 44 (12) ◽  
pp. 3227-3240 ◽  
Author(s):  
Maurice Cohen ◽  
Paul S. Kelly
Keyword(s):  
Total Energy ◽  
Excited States ◽  
Wave Functions ◽  
Lower State ◽  
Hartree Fock ◽  
Orthogonality Constraint ◽  
State Functions

Hartree–Fock wave functions have been calculated for a number of excited states of the helium sequence, the wave functions being constrained to be orthogonal to all lower state functions. The effect of choosing the inner 1s orbital so that the orthogonality constraint is satisfied automatically has been examined, and it is shown that such a choice has a very small effect on the total energy. An extension to heavier systems is proposed.

HARTREE–FOCK WAVE FUNCTIONS FOR EXCITED STATES: III. DIPOLE TRANSITIONS IN THREE-ELECTRON SYSTEMS

1967 ◽  
Vol 45 (5) ◽  
pp. 1661-1673 ◽  
Author(s):  
Maurice Cohen ◽  
Paul S. Kelly
Keyword(s):  
Excited States ◽  
Wave Functions ◽  
Electron Systems ◽  
Matrix Elements ◽  
Isoelectronic Sequence ◽  
Hartree Fock ◽  
Transition Matrix Elements ◽  
Simplified Procedure ◽  
Good Agreement ◽  
Dipole Length

Hartree–Fock wave functions for a number of S, P, and D states of the lithium isoelectronic sequence have been calculated, using a simplified procedure described in an earlier paper. Transition matrix elements for all permitted dipole transitions between these states have been computed using both the dipole length and the dipole velocity formulations. The results are in good agreement with earlier calculations.

HARTREE–FOCK WAVE FUNCTIONS FOR EXCITED STATES: IV. OSCILLATOR STRENGTHS IN THE HELIUM ISOELECTRONIC SEQUENCE

1967 ◽  
Vol 45 (6) ◽  
pp. 2079-2090 ◽  
Author(s):  
Maurice Cohen ◽  
Paul S. Kelly
Keyword(s):  
Matrix Element ◽  
Excited States ◽  
Transition Matrix ◽  
Transition Matrix Element ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Isoelectronic Sequence ◽  
Hartree Fock ◽  
Good Agreement

Orbital wave functions for a number of singlet and triplet S, P, and D states of the helium sequence through C+4 have been calculated using an approximation described earlier. The wave functions have been employed to calculate the oscillator strengths for all allowed dipole transitions between these states, using both the length and velocity forms of the transition matrix element. Our results are in good agreement with the most accurate values available.

scholarly journals Valence: A Massively Parallel Implementation of the Variational Subspace Valence Bond Method

2018 ◽  
Author(s):  
Graham Fletcher ◽  
Colleen Bertoni ◽  
Murat Keçeli ◽  
Michael D'Mello
Keyword(s):  
Excited States ◽  
Software Package ◽  
Parallel Implementation ◽  
Valence Bond ◽  
Wave Functions ◽  
Massively Parallel ◽  
Hartree Fock ◽  
External Software ◽  
Single Configuration ◽  
Bond Method

This work describes the software package, Valence, for the calculation of molecular<br>energies using the variational subspace valence bond (VSVB) method. VSVB is a highly scalable ab initio electronic structure method based on non-orthogonal orbitals. Important features of practical value include: Valence bond wave functions of Hartree–Fock quality can be constructed with a single determinant; excited states can be modeled with a single configuration or determinant; wave functions can be constructed automatically by combining orbitals from previous calculations. The opensource software package includes tools to generate wave functions, a database of generic orbitals, example input files, and a library build intended for integration with other packages. We also describe the interface to an external software package, enabling the computation of optimized molecular geometries and vibrational frequencies.

scholarly journals Valence: A Massively Parallel Implementation of the Variational Subspace Valence Bond Method

2018 ◽  
Author(s):  
Graham Fletcher ◽  
Colleen Bertoni ◽  
Murat Keçeli ◽  
Michael D'Mello
Keyword(s):  
Excited States ◽  
Software Package ◽  
Parallel Implementation ◽  
Valence Bond ◽  
Wave Functions ◽  
Massively Parallel ◽  
Hartree Fock ◽  
External Software ◽  
Single Configuration ◽  
Bond Method

This work describes the software package, Valence, for the calculation of molecular<br>energies using the variational subspace valence bond (VSVB) method. VSVB is a highly scalable ab initio electronic structure method based on non-orthogonal orbitals. Important features of practical value include: Valence bond wave functions of Hartree–Fock quality can be constructed with a single determinant; excited states can be modeled with a single configuration or determinant; wave functions can be constructed automatically by combining orbitals from previous calculations. The opensource software package includes tools to generate wave functions, a database of generic orbitals, example input files, and a library build intended for integration with other packages. We also describe the interface to an external software package, enabling the computation of optimized molecular geometries and vibrational frequencies.

Theoretical calculations of transition probabilities for individual and multiplet lines between some excited levels of atomic potassium

2008 ◽  
Vol 86 (3) ◽  
pp. 487-494 ◽  
Author(s):  
Gültekin Çelik ◽  
Şule Ateş
Keyword(s):  
Excited States ◽  
Potential Model ◽  
Transition Probabilities ◽  
Theoretical Calculations ◽  
Wave Functions ◽  
Expectation Values ◽  
Data Bases ◽  
Hartree Fock ◽  
Coulomb Approximation ◽  
Bound Electron

The transition probabilities for individual and multiplet lines between some excited levels of atomic potassium are calculated using weakest bound electron potential model theory (WBEPMT). The numerical nonrelativistic Hartree–Fock wave functions for the expectation values of radii in all excited states, unlike the Numerical Coulomb Approximation method traditionally used for WBEPMT and experimental ionization energies, have been employed to determine the parameters. The results obtained during this work agree very well with the accepted values taken from National Institute Standards and Technology. Moreover, some transition probabilities not existing on the data bases for highly excited levels in atomic potassium have been obtained using this method. PACS No.: 32.70.Cs

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