Re: Regarding Dynamic and nondynamic correlation index

dummy@example.com (sobereva) — Sat, 23 May 2020 16:33:05 +0000

Usually, the two indices should be calculated using multi-configurational methods, as illustrated in Section 4.A.6 of Multiwfn manual, since non-integer natural orbital occupations can be obtained in this case.

In my opinion, if you use UKS to calculate open-shell singlet system such as biradical via symmetry-broken formalism, and then obtain the so-called UNO (unrestricted natural orbital, which is generated by diagonalizing total density matrix of UKS wavefunction), the occupation numbers may also be used in nondynamic correlation index to judge nondynamic correlation, but I didn't have a try. More specifically, after loading an .fch/fchk file containing UKS wavefunction, you should input commands like follows

...ignored
 14 Adaptive natural density partitioning (AdNDP) analysis
 15 Fuzzy atomic space analysis
 16 Charge decomposition analysis (CDA) and plot orbital interaction diagram
 17 Basin analysis                    18 Electron excitation analysis
 19 Orbital localization analysis     20 Visual study of weak interaction
 21 Energy decomposition analysis
 100 Other functions (Part 1)         200 Other functions (Part 2)
 300 Other functions (Part 3)
200

               ============ Other functions (Part 2) ============
 0 Return
 1 Calculate core-valence bifurcation (CVB) index and related quantities
 2 Calculate atomic and bond dipole moments in Hilbert space
 3 Generate cube file for multiple orbital wavefunctions
 4 Generate iso-chemical shielding surfaces (ICSS) and related quantities
 5 Plot radial distribution function for a real space function
 6 Analyze correspondence between orbitals in two wavefunctions
 7 Parse output of (hyper)polarizability task of Gaussian
 8 Study (hyper)polarizability by sum-over-states (SOS) method
 9 Calculate average bond length and average coordinate number
 10 Output various kinds of integral between orbitals
 11 Calculate center, the first and second moments of a real space function
 12 Calculate energy index (EI) or bond polarity index (BPI)
 13 Evaluate orbital contributions to density difference or other grid data
 14 Domain analysis (Obtaining properties within isosurfaces of a function)
 15 Calculate electron correlation index (PCCP, 18, 24015)
 16 Generate natural orbitals based on the density matrix in .fch/.fchk file
 17 Calculate Coulomb and exchange integrals between two orbitals
 18 Calculate bond length/order alternation (BLA/BOA)
 20 Bond order density (BOD) and natural adaptive orbital (NAdO) analyses
16
 Input type of density, e.g. SCF, MP2, CI, CC, MP4...
 e.g. If the .fch was produced under MP2, you may input "SCF" or "MP2"
SCF
 Select natural orbitals you want to obtain
 1 Spatial natural orbitals (diagonalization of total density matrix)
 2 Alpha and beta natural orbitals (diagonalization of respective DM)
 3 Spin natural orbitals (diagonalization of spin density matrix)
1
 Loading density matrix...
 Density matrix was loaded from .fch/.fchk file

 Generating NOs, please wait...
 Occupation numbers:
    2.000000    2.000000    1.999999    1.999999    1.999977    1.999974
    1.999965    1.999963    1.999845    1.999798    1.999779    1.999773
    1.999188    1.999005    1.998891    1.309524    0.690476    0.001109
    0.000995    0.000812    0.000227    0.000221    0.000202    0.000155
    0.000037    0.000035    0.000026    0.000023    0.000001    0.000001
    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000
    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000
    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000
    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000
    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000
    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000
    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000
    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000
    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000
    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000
    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000
    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000
    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000
   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000
   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000
   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000
   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000
   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000
   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000
   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000
   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000
   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000
   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000
   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000
   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000
   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000   -0.000000
   -0.000000   -0.000000
 Done! Basis function information now correspond to natural orbitals

 If next you intend to analyze real space functions based on the NOs, you should
 export new.molden in current folder and then reload it, so that GTF information
 will also correspond to NOs
 Would you like to do this immediately? (y/n)

After exporting and load the new.molden containing UNO orbitals, you can perform dynamic/non-dynamic correlation index calculation as exemplified in Section 4.A.6 of Multiwfn manual.

Regarding Dynamic and nondynamic correlation index

dummy@example.com (anupthms000) — Sat, 23 May 2020 13:56:47 +0000

Can we get the nondynamic and dynamic correlation index from Unrestricted DFT studies using multiwfn.

Look forward to hear from you.

Regards
Anup