Configuration interaction calculations

In a standard Hartree-Fock self-consistent-field (HF-SCF) calculation the ground state wavefunction is approximated by a product of one-electron wavefunctions. As a result, electron-electron correlation is neglected (mean-field approximation). The configuration interaction (CI) approach accounts for electron-electron correlation effects by considering the mixing of different electron configurations. It is an example of a post-Hartree-Fock method.

Background: A CI calculation begins by performing a HF-SCF calculation for the system’s ground state, yielding a set of occupied and unoccupied (virtual) molecular orbitals. Then, a new set of electronic configurations is generated by promoting electrons from the occupied molecular orbitals to the virtual orbitals. The overall wavefunction (𝜓) is expressed as a linear combination of ground state and symmetry-adapted Slater determinants,

where the coefficients expand the overall wavefunction in a basis of symmetry-adapted Slater determinants . These symmetry-adapted Slater determinants are referred to as configuration state functions (CSFs), and each CSF has a corresponding electronic configuration. Each CI state is a linear combination of CSFs.

Electron configurations corresponding to the four lowest energy singly excited CSFs of an arbitrary system with five molecular orbitals.  The active space is restricted to single-electron promotions from the highest occupied molecular orbital.

Practical Considerations: Because the number of possible configurations can be large even for "small" systems, CI calculations are computationally expensive. Possible strategies include, reducing the size of the structural model (fewer electrons), and limiting the active space of the calculation. The second strategy involves considering excitations from only a select few orbitals while the electrons in the remaning orbitals make up a frozen core.

CI Calculations with GAMESS: Below is a partial input file for carrying out a CI singles calculation with GAMESS.

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$CONTRL SCFTYP=RHF CITYP=CIS EXETYP=RUN RUNTYP=ENERGY MAXIT=200 COORD=UNIQUE NPRINT=9 $END   
$SCF NCONV=6 $END                     
$CIS NACORE=383 NSTATE=9 IROOT=0 CISPRP=.T. HAMTYP=SAPS MULT=1 NDAVIT=500 DAVCVG=1.0E-05 PRTTOL=0.0 $END                       
$BASIS GBASIS=N31 NGAUSS=6 NDFUNC=1 $END  
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CITYP=CIS specifies single excitations, NACORE sets the number of orbitals that make up the frozen core, NSTATE is the number of CI states that will be calculated, and PRTTOL sets the tolerance to print out CI state coefficients (by default only coefficients larger than 0.05 are printed). For futher information, the reader should consult the GAMESS documentation.