Valence universal exponential ansatz and the cluster structure of multireference configuration interaction wave function

1989 ◽  
Vol 90 (5) ◽  
pp. 2714-2731 ◽  
Author(s):  
Bogumil Jeziorski ◽  
Josef Paldus
Keyword(s):  
Wave Function ◽  
Configuration Interaction ◽  
Cluster Structure

On the basis of orbital theories

1955 ◽  
Vol 232 (1188) ◽  
pp. 114-135 ◽  
Keyword(s):  
Wave Function ◽  
Configuration Interaction ◽  
Singlet Ground State ◽  
New Techniques ◽  
Hartree Fock ◽  
Basic Set ◽  
Spin Eigenfunctions ◽  
Spin Degeneracy ◽  
One And Many ◽  
Reduced Density

In molecular theory the wave function is usually constructed from antisymmetrized products, or ‘Slater determinants’, of one-electron ‘orbitals’. A single determinant of suitably chosen, doubly occupied orbitals is often a fair approximation to a singlet ground state; but when more general products are admitted, as in ‘configuration interaction’ calculations, it is first necessary to resolve a high ‘spin degeneracy’ by constructing spin eigenfunctions (SE’s). In §1, the fundamental basis of recent methods (McWeeny 1954 b ) is clarified by a group theoretical approach. Next, in §2, the energy expression, using as wave function an arbitrary mixture of similar SE’s, is written very simply in terms of the reduced density matrices for one and two particles, and formulae for the calculation of these matrices are given. The remaining problem is to get a ‘best’ wave function, usually with limited configuration interaction, by (i) variation of SE coefficients and (ii) variation of the orbitals appearing in the SE’s; this problem is formally solved in §3. (i) is the usual configuration interaction process; but (ii) is new and leads, when the orbitals are expressed in terms of a standard basic set (e.g. of atomic orbitals), to a complete generalization of the Roothaan 1951) equations. These (matrix) equations are simple in appearance, but their numerical solution calls for new techniques; and it is possible that the Roothaan (i.e. Hartree–Fock) approach, followed by configuration interaction, provides about the best working compromise between (i) and (ii). In §4, some points of contact between one- and many-configuration theories are noted. In particular, certain density matrix elements provide appropriate generalizations of the ‘charges’ and ‘bond orders’ of Coulson and Longuet-Higgins and continue to describe the response of a system to changes in its ‘Coulomb’ and ‘resonance’ integrals.

DESCRIPTION OF 8Be AS DEFORMED GAS-LIKE TWO-ALPHA-PARTICLE STATES

2003 ◽  
Vol 18 (02n06) ◽  
pp. 170-173
Author(s):  
Y. FUNAKI ◽  
H. HORIUCHI ◽  
A. TOHSAKI ◽  
P. SCHUCK ◽  
G. RÖPKE
Keyword(s):  
Wave Function ◽  
Excited States ◽  
Ground State ◽  
Cluster Structure ◽  
Test Case ◽  
Weakly Bound ◽  
Generator Coordinate Method ◽  
Spatial Deformation ◽  
Generator Coordinate ◽  
Spin Excitations

In order to study non-zero spin excitations of the recently proposed α-cluster condensation in the self-conjugate 4n nuclei, spatial deformation is introduced into the model wave function of the α-cluster condensate. The rotational band states of 8 Be are investigated as a first step of a test case for the study of the deformation of the α-cluster condensate. Calculations reproduce well the binding energy of the 0+ ground state and also the excitation energy of the 2+ state. Our 0+ wave function is found to be exactly equal to the 0+ wave function obtained by the generator coordinate method using Brink's 2α wave function. The study shows that both the 0+ ground and 2+ excited states can be considered as having a gas-like (i.e. weakly bound) 2α-cluster structure.

Transition probability approach for direct calculation of coefficients of Configuration Interaction wave function

2017 ◽  
Author(s):  
Arijit Bag
Keyword(s):  
Wave Function ◽  
Configuration Interaction ◽  
Correlation Energy ◽  
Transition Probability ◽  
Direct Calculation ◽  
Energy Curve ◽  
Equilibrium Bond Length ◽  
Hydrogen Water ◽  
Hartree Fock ◽  
A New Technique

To reduce the computation cost of Configuration Interaction (CI) method, a new technique is used to calculate the coefficients of doubly excited determinants directly from orbital energies, orbital overlap matrix and electron population obtained from Hartree Fock level run. This approach to approximate the coefficients of CI wave function is termed as <b>transition probability approximated CI (TPA-CI).</b> In principle, calculated dynamical electron correlation energy of TPA-CI and Full CI (FCI) are equivalent. It is observed that computed TPA-CI correlation energies of hydrogen, water, ammonia and ozone are very close to FCI values, within 5% error. The potential energy curve of the hydrogen molecule is also studied and it is found that the energy is minimum at its equilibrium bond length.<br><br>

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