N,N-Dimethylformamide: An interesting case

Here's N,N-Dimethylformamide in the gas phase compared to several ab initio computations using the structure found by Kimball.exe with standard parameters:
 
Dimethylformamide - Energies
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                              Kimball     Gamess/6-31g      same,opt   G94W/6-31g,opt
Nucleus-Nucleus      Vnn   :  180.23058    180.23066       180.08970       180.08979
Electron-Electron    Vee   :  256.72510    264.77374       264.76824       264.76824
Nucleus-Electron     Vne   : -929.98466   -938.69044      -938.70460      -938.70460
Electronic energy    Eel   : -426.74952                                   -426.92614

potential energy     V     : -493.02898   -493.68604       -493.84666     -493.84667
kinetic   energy     T     :  246.51004    246.87115        247.01022      247.01022

total     energy     Etot  : -246.51894   -246.81489       -246.83644     -246.83644

Virial ratio        -V/T   :    2.000036     1.99977          1.99930        1.9993
Coordinates:

NC(CH3)                   Å:          1.4743             ¦             1.4612 (avg.)
NC(CHO)                    :          1.4743             ¦             1.4137
CO                         :          1.2102             ¦             1.2054
CH(CH3)                    :          1.1003             ¦             1.0843 (avg.)
CH(CHO)                    :          1.1003             ¦             1.0900
OCN                  deg   :        125.73               ¦           124.30
HCH(CH3)                   :        112.39               ¦           108.85
OCH(CHO)                   :        111.91               ¦           119.60
CNC(CH3,CH3)               :        106.36 (C's have     ¦           115.61
C(CH3)NC(CHO)              :        106.36  equal param.)¦           114.60

Dimethylformamide - Energies (Hartree)       
-------------------------------------------------  
One electron energy               :  -684.81120    
Two electron energy               :   257.85617    
Nuclear repulsion Energy          :   180.41847    
                                    -----------    
Total Energy                 Etot :  -246.53656    
                                                   
Nucleus-Electron  pot.Energy Vne  :  -931.33467    
Electron-Electron pot.Energy Vee  :   257.85617    
Nucleus-Nucleus   pot.Energy Vnn  :   180.41847    
                                    -----------    
Total potential energy       V    :  -493.06003    
Total kinetic   energy       T    :   246.52348     
Virial ratio                -V/T  :     2.00005    
                                                   
Electronic energy            Eel  :  -426.95503    
Electron potential           Vel  :  -673.47850    
                                                    
DMA2 - Interatomic Distances and Angles            
                                                   
NC(CH3)              :     1.4716526 Å             
NC(CHO)              :     1.4699199 Å             
CH(CH3)              :     1.0987654 Å             
CH(CHO)              :     1.0727132 Å             
CO                   :     1.2184562 Å             
OCN                  :   122.57056 deg             
CNC(CH3)             :   106.71502 deg             
C(CHO)NC(CH3)        :   106.71502 deg             
OCH                  :   113.50472 deg             
NCH(CH3)             :   106.70849 deg             
HCH                  :   112.08696 deg 
            
DMA2 - Cartesian Coordinates                       
12                                                    
N   0.             0.           0.                 
C   0.42326436    -1.409471     0.                 
C  -1.4716526      0.           0.                 
H   1.5220297     -1.4093458    0.                 
H   1.0165492E-2  -1.8633589   -0.91138382         
H   1.0165492E-2  -1.8633589    0.91138382         
H  -1.7875504      1.0523754    0.
H  -1.7875504     -0.52618769   0.91138382
H  -1.7875504     -0.52618769  -0.91138382
C   0.42276603     0.56837388  -1.2879769
O   1.1483951      1.543931    -1.3678916
H   0.12947952     0.17406669  -2.2415064
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This Trace file from Kimball.exe comes from a second run of DMA which created the figure at the top. The numbers are slightly different from the comparison table above. In this run C4's distance from N1 has been variied independently from the N1C2 distance. Furthermore the p-clouds were allowed to move along the CO-bond. This created 22 variables for the optimization and a slightly more stable result. Several distances and angles have changed a bit. However the N1C4 bond has not moved near the much lower value of the ab initio optimized structures. The reason is, that Kimball presently cannot model well the partial NC4 double bond character of the NC=O moiety. It gives, however, correctly the planar arrangement of NCHO. The figure at bottom contains the numbered classes, referred to, and shows a better view on the NCHO region. The p-bond has moved nearer the C4 core and not, as perhaps expected, towards the more electronegative O core. It appears that the nearby N-atom and repulsion by the two compact oxygen lone pairs make up for this result. At the next step an sp2 N-Atom with two pz electrons would share in a three-center 4-electron p-bond system with C and O. This would generate a planar(C2)NCO moiety as obtained with most ab initio calculations, see the discussion on p. 105/106 in "Exploring Chemistry with Electronic Structure Methods", 2nd ed., J.B. Foresman & Ae. Frisch, Gaussian Inc. Pittsburgh, 1996.- Only the most exact model chemistries with RHF-SCF give non planar geometry, as known to be true from experiment. Interestingly Sto-3G monitors a transition state for the planar arrangement. Kimball is, of course, too much nonplanar as expected from a pyramidal N-node with the lone pair at one corner, see figure below.

and here is a Kimball model of DMA from Mathematica-9 notebook: The five "heavy" atoms are all in a plane