problems with $fermi /negative HOMO-LUMO gap

[Andi K]

Hello All,

I've encountered some problems with the use of $fermi in TURBOMOLE V6.0

I want to optimize the structure of some hydrocarbons with DFT (using the pbe functional for instance). For this purpose I use the jobex script with relax or statpt.
Seemingly during the optimization everything works quite alright. When I check the occupation with eiger after the run has finished, I see a negative HOMO-LUMO gap. To cope with this problem I tried to use $fermi with the following parameters

Code: [Select]

$fermi tmstrt= 25.00 tmend= 25.00 tmfac=1.000 hlcrt=1.0E+00 stop=1.0E-09.

However, as the result of an ridft run I still don't get a positive HOMO-LUMO gap, even though the occupation is calculated with $fermi until the energy converges. The problem seems to be that after convergence an additional energy calculation step takes place, where $fermi for unknown reasons does not apply any more. Here are the details of the last few steps of my ridft output file:

ITERATION  ENERGY          1e-ENERGY        2e-ENERGY     NORM[dD(SAO)]  TOL
  62  -1179.8455826780    -6122.2798253     2670.1641575    0.523D-04 0.225D-12
                            Exc = -161.191934466     Coul =  2831.35609200   
                              N = 181.99989069   
                            current damping = 1.050
 
          Norm of current diis error: 0.39805E-04
          max. resid. norm for Fia-block=  3.340D-06 for orbital     91a         
          max. resid. fock norm         =  3.475D-06 for orbital     91a         
          irrep a   : virtual orbitals shifted by    0.10846
         -------------------- FON Calculation ---------------------
                                 Fermi level F =        -0.12539
                   Total number of electrons N =       182.00000
           Occupation numbers calculated for T =        25.00000
                         Current HOMO-LUMO gap =     0.48780E-01
         ----------------------------------------------------------

 ITERATION  ENERGY          1e-ENERGY        2e-ENERGY     NORM[dD(SAO)]  TOL
  63  -1179.8455826783    -6122.2798664     2670.1641986    0.326D-04 0.225D-12
                            Exc = -161.191933054     Coul =  2831.35613170   
                              N = 181.99989069   
                            current damping = 1.100
 
          Norm of current diis error: 0.34798E-04
          max. resid. norm for Fia-block=  3.484D-06 for orbital     91a         
          max. resid. fock norm         =  6.557D-06 for orbital    366a         
          irrep a   : virtual orbitals shifted by    0.06828
         -------------------- FON Calculation ---------------------
                                 Fermi level F =        -0.12539
                   Total number of electrons N =       182.00000
           Occupation numbers calculated for T =        25.00000
                         Current HOMO-LUMO gap =     0.15104E-01
         ----------------------------------------------------------

 ENERGY CONVERGED !

          Overall gridpoints after grid construction =        665045

 ITERATION  ENERGY          1e-ENERGY        2e-ENERGY     NORM[dD(SAO)]  TOL
  64  -1179.8455516457    -6122.2798324     2670.1641956    0.326D-04 0.790D-12
                            Exc = -161.191902780     Coul =  2831.35609842   
                              N = 182.00000695   
                            current damping = 1.150
 
          Norm of current diis error: 0.25621E-04
          max. resid. norm for Fia-block=  2.367D-06 for orbital     91a         
          max. resid. fock norm         =  2.453D-06 for orbital     91a         

 End of SCF iterations

   convergence criteria satisfied after   64 iterations

Using the eiger script I get the following occupation:

Total energy =  -1179.8455516460 H =    -32105.2492441 eV

 HOMO-LUMO Separation
   HOMO:    92.    91 a     -0.12635850 H =     -3.43839 eV
   LUMO:    91.    92 a     -0.14829956 H =     -4.03544 eV
   Gap :                    -0.02194106 H =     -0.59705 eV
        !! WARNING: HOMO-LUMO Gap is negativ !!

Number of MOs=    396, Electrons=    182.00, Symmetry: c1

   Nr.   Orbital    Occupation       Energy
  108.   108 a                     +0.085909 H =        +2.338 eV
  107.   107 a                     +0.084492 H =        +2.299 eV
  106.   106 a                     +0.074339 H =        +2.023 eV
  105.   105 a                     +0.072635 H =        +1.976 eV
  104.   104 a                     +0.065869 H =        +1.792 eV
  103.   103 a                     +0.063547 H =        +1.729 eV
  102.   102 a                     +0.055610 H =        +1.513 eV
  101.   101 a                     +0.053687 H =        +1.461 eV
  100.   100 a                     +0.039238 H =        +1.068 eV
   99.    99 a                     +0.037697 H =        +1.026 eV
   98.    98 a                     +0.001710 H =        +0.047 eV
   97.    97 a                     -0.029023 H =        -0.790 eV
   96.    96 a                     -0.050084 H =        -1.363 eV
   95.    95 a                     -0.057593 H =        -1.567 eV
   94.    94 a                     -0.069351 H =        -1.887 eV
   93.    93 a                     -0.103417 H =        -2.814 eV
   92.    91 a        2.000        -0.126358 H =        -3.438 eV
   91.    92 a                     -0.148300 H =        -4.035 eV
   90.    90 a        2.000        -0.216450 H =        -5.890 eV
   89.    89 a        2.000        -0.221611 H =        -6.030 eV
   88.    88 a        2.000        -0.223412 H =        -6.079 eV
   87.    87 a        2.000        -0.241772 H =        -6.579 eV
   86.    86 a        2.000        -0.245310 H =        -6.675 eV
   85.    85 a        2.000        -0.253361 H =        -6.894 eV
   84.    84 a        2.000        -0.268394 H =        -7.303 eV
   83.    83 a        2.000        -0.293210 H =        -7.979 eV
   82.    82 a        2.000        -0.298763 H =        -8.130 eV
   81.    81 a        2.000        -0.303391 H =        -8.256 eV
   80.    80 a        2.000        -0.310105 H =        -8.438 eV
   79.    79 a        2.000        -0.332052 H =        -9.036 eV
   78.    78 a        2.000        -0.334060 H =        -9.090 eV
   77.    77 a        2.000        -0.334539 H =        -9.103 eV
   76.    76 a        2.000        -0.349200 H =        -9.502 eV

What exactly is happening here? And as a general question: Why is this last energy step calculated, after the energy is converged?

Thanks very much for your help,
Andi

[uwe]

Hi,

your start and end temperatures are identical (although quite low), the annealing factor is 1.0, and your HOMO-LUMO gap is very small. It also seems that you have switched off the automatic stop of Fermi during the SCF iterations by setting the criterias (hlcrt and stop) to numbers that will never be reached.

The last iteration is done after convergence and it is due to the gridsize settings in $dft - most likely you have been using the default 'm3' which uses the larger grid only after convergence. That should not be the reason for the wrong occupation, but perhaps setting it to 3 or 4 instead of m3 can help if you have small gaps.

Some comments:

• $fermi in geometry optimizations can be dangerous, because it does not keep the multiplicity fixed (which can result in switching the potential energy surface during optimization) - however, you have a closed shell case, so it could be acceptable in this case.
• the $fermi option was thought as a black-box method to find the lowest spin state. If you know that you have a singlet, $fermi will most likely not help a lot.
• the homo-lumo (hlcrit) and the stop criteria are reasonable because if Fermi found a state with integer occupation, you will most likely want keep it

Some ideas on how to solve your problem:

• set the gridsize in $dft to 4
• remove $fermi
• add $denconv 1d-7 to the control file for a more tight density convergence
  
• use Turbomole 6.1 instead of 6.0 and add the new keyword $lastdiag - it might give more accurate orbital energies in cases the HOMO-LUMO gap is very small

Hope it helps,

Uwe