Cluster expansion of the wavefunction. Symmetry‐adapted‐cluster expansion, its variational determination, and extension of open‐shell orbital theory

1978 ◽  
Vol 68 (5) ◽  
pp. 2053-2065 ◽  
Author(s):  
H. Nakatsuji ◽  
K. Hirao
Keyword(s):  
Cluster Expansion ◽  
Open Shell ◽  
Orbital Theory

scholarly journals LOCALLY PROJECTED MOLECULAR ORBITAL THEORY FOR MOLECULAR INTERACTION WITH A HIGH-SPIN OPEN-SHELL MOLECULE

2006 ◽  
Vol 05 (04) ◽  
pp. 819-833 ◽  
Author(s):  
SUEHIRO IWATA
Keyword(s):  
Molecular Orbital ◽  
High Spin ◽  
Closed Shell ◽  
Open Shell ◽  
Coefficient Matrix ◽  
Molecular Orbitals ◽  
Orbital Method ◽  
Stationary Condition ◽  
Orbital Theory ◽  
Stationary Conditions

Locally projected molecular orbital method for molecular interactions is extended to a cluster consisting of a high-spin open-shell molecule and many closed-shell molecules. While deriving the equations, the Hartee–Fock–Roothaan equation without the orthonormal condition is obtained. The stationary conditions for molecular orbitals are expressed in a form of a generalized Brillouin condition. To obtain the molecular orbital coefficient matrix, which satisfies the stationary condition, a single Fock operator form is presented. For the locally projected molecular orbitals for the open-shell cluster, the working matrix representaion is given.

A Cluster Expansion Formalism for Direct Calculation of Ionisation Potential and Excitation Energy of Many Electron Systems Using H-F Ground State as Vacuum

1978 ◽  
Vol 33 (12) ◽  
pp. 1549-1551
Author(s):  
D. Mukherjee ◽  
A. Mukhopadhyay ◽  
R. K. Moitra
Keyword(s):  
Excitation Energy ◽  
Cluster Expansion ◽  
Ground State ◽  
Shell Theory ◽  
State Energy ◽  
Direct Calculation ◽  
Electron System ◽  
Open Shell ◽  
Electron Systems ◽  
Ionisation Potential

Abstract In this note, the authors’ recently developed non-perturbative open-shell theory is adapted for direct calculation o f ionisation potential and excitation energy of m any-electron systems. The H -F ground state is used as the “vacuum ” or “ core” in order to achieve a transparent separation o f the ground state energy. An application to a simple 4 π-electron system is discussed as an illustration o f the workability of the theory.

Molecular orbital studies of carbyne reactions: addition and insertion reaction paths for the reaction

1985 ◽  
Vol 63 (7) ◽  
pp. 1689-1693 ◽  
Author(s):  
Ratnakar K. Gosavi ◽  
Imre Safarik ◽  
Otto P. Strausz
Keyword(s):  
Activation Energy ◽  
Potential Energy ◽  
Molecular Orbital ◽  
Geometry Optimization ◽  
Open Shell ◽  
Basis Set ◽  
Insertion Reaction ◽  
Orbital Theory ◽  
Asymmetric Reaction ◽  
Geometry Analysis

Potential energy hypersurfaces have been studied for the [Formula: see text] addition and insertion reactions by abinitio molecular orbital theory. 6-31G basis set was used for complete geometry optimization of CH, C2H4, the cyclopropyl and allyl radicals as well as the reaction intermediates involved, with the RHF open shell SCF method. CI calculations were then performed at the SCF level optimized geometry. Analysis of the potential energy hypersurfaces predicts, in agreement with reported experimental data, a zero activation energy for the addition reaction via a non least motion, asymmetric reaction path, while the insertion reaction features a computed activation energy of 15 kcal mol−1.

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