Output Guide¶

edf writes all output to stdout. A typical run produces five sections:

Header and input echo
Wavefunction summary
EDF probability tables
Populations and delocalization indices
Timer

1. Header and input echo¶

The output begins with an ASCII banner, then echoes the input file verbatim between # The Input file is and # End of the Input file markers. Verify this against your input to catch silent truncation or encoding issues.

2. Wavefunction summary¶

# AOM file                          = h6.aom
# Wave Function file                = h6.wfn
# Input number of Primitives        48 reduced to       48
# Description of the Primitive Basis Set
# Total number of Primitive Gaussians:     48
# CENTER   1
# S Shell (Z=0.33865E+02) :    1
...

This section lists: - The AOM and WFN filenames. - The basis set (number of Gaussian primitives per shell per center). - For CASSCF: the number of determinants, core/active/virtual orbital counts, and the CI coefficients.

If the primitive count after reduced to differs from Input number, some primitives were eliminated by the wavefunction reader — check TOLAOM if the AOM normalization is suspect.

3. EDF probability tables¶

Spin-split (full) EDF¶

# Spin-Splitted probabilities
# M-BASINS ELECTRON NUMBER PROBABILITY DISTRIBUTION INCLUDING SPIN
# NUMBER OF GROUPS               =                  6
# TOTAL NUMBER OF PROBABILITIES  =               3136
# Gi(a) Gi(b) ARE THE NUMBER OF ALPHA AND BETA ELECTRONS IN GROUP i
# -------------------------------------------------------------------------------------
#     Probability           G1(a) G1(b) G2(a) G2(b) ...
#     0.0000000075662346      3     3     0     0     0     0     0     0     0     0     0     0
#     0.0000001158377170      3     2     0     1     0     0     0     0     0     0     0     0

Each row: probability followed by the alpha (Gi(a)) and beta (Gi(b)) electron counts for each group. The total number of rows is (Nα+1)^G × (Nβ+1)^G before truncation by PROBCUT.

The section ends with:

#     0.9994921681758134  <- SUM (     3136 PROBS with P_{a} & P_{b} >  0.0E+00)
#     0.9994921681758134  <- TOTAL SUM

The sum should be close to 1.0; the deviation reflects the probability carried by configurations below the PROBCUT threshold.

Alpha spinless EDF¶

# M-BASINS ELECTRON NUMBER PROBABILITY DISTRIBUTION FOR ALPHA ELECTRONS
# FOR EACH VALUE, A SUM OVER ALL BETA  RESONANT STRUCTURES HAS BEEN DONE
# NUMBER OF GROUPS                                  =        6
# TOTAL NUMBER OF PROBABILITIES FOR ALPHA ELECTRONS =       56
#     Probability            n1    n2    n3 ...
#     0.0000869620157188      3     0     0     0     0     0
...
#     0.9994921681758127  <-- SUM,      56 PROBABILITIES >  0.000000000E+00

The alpha EDF is obtained by summing the spin-split EDF over all beta configurations for each alpha configuration. Similarly, the beta EDF (printed next) sums over alpha configurations.

Spinless (total) EDF¶

After the alpha and beta tables, a total-electron spinless EDF sums both spins:

#     Probability            n1    n2    n3 ...
#     0.0002607553   1  1  1  1  1  1    <- dominant: 1 electron per H
#     0.0001234281   2  1  1  1  1  0

For a closed-shell molecule with equal alpha and beta, the spinless EDF is the convolution of alpha and beta EDFs.

4. Populations and delocalization indices¶

Average populations¶

<n(  1)_alpha>                  =      0.499746084
<n(  1)_beta>                   =      0.499746084
<n(  2)_alpha>                  =      0.499760074
...

\(\langle n_i \rangle_\alpha\) is the average number of alpha electrons in fragment \(i\), and similarly for beta. For a closed-shell molecule these are equal. The total population is \(\langle n_i \rangle = \langle n_i \rangle_\alpha + \langle n_i \rangle_\beta\).

Two-body expectations¶

<n(  2)_alpha n(  1)_alpha>     =      0.139042602
<n(  2)_alpha n(  1)_beta>      =      0.249880037

Mixed two-body populations \(\langle n_i n_j \rangle\) enter the delocalization index:

\[\delta(i,j) = 2\left[\langle n_i n_j \rangle - \langle n_i \rangle \langle n_j \rangle\right]\]

Delocalization indices¶

 Delocalization indices, Eq. (28) J. Chem. Phys.  126, 094102 (2007)
 # delta_(  2  1)         =      0.443349226
 # delta_(  3  1)         =      0.060120455
 # delta_(  3  2)         =      0.443399770

Two-center DIs measure electron sharing: \(\delta(i,j) \approx 1\) for a covalent bond, \(\delta(i,j) \ll 1\) for non-bonded pairs. Three-center DIs \(\delta(i,j,k)\) quantify three-center bonding.

The localization index for fragment \(i\) is:

# delta_(  1  1)         =      0.439111188  % Localization =  43.9334

\(\delta(i,i) = 2 \left[\langle n_i^2 \rangle - \langle n_i \rangle^2\right]\) measures how "localized" the electrons of fragment \(i\) are; the percentage is \(\delta(i,i)/\langle n_i \rangle \times 100\).

Covariance matrix¶

# Covariance Matrix
      0.56038098     -0.22167461 ...
# Covariance Eigenvalues
      0.00050886      0.42511057 ...
# Covariance Eigenvectors
      0.40824829      0.40827125 ...

The covariance matrix \(\sigma_{ij} = \langle n_i n_j \rangle - \langle n_i \rangle \langle n_j \rangle\) (diagonal entries are variances). Its eigenvalues and eigenvectors encode the collective electron fluctuation modes across fragments.

5. Timer¶

#    timer:
#    -pid----name--------------cumtime-------pcalls--popen-
#     1     _edf               0.017662          1     T
#     4     _binedf            0.014454          1     F
#     6     _linearsys         0.000534          1     F
#     7     _splitedf          0.000009          1     F

Field	Meaning
`cumtime`	Cumulative wall time in seconds
`pcalls`	Number of times this timer was entered
`popen`	Whether this timer is still open at exit

_linearsys and _splitedf are the parallelized regions in binedf.f. Compare their wall times between 1-thread and N-thread runs to measure parallel speedup. See Performance.