Optimization Convergence Issue

Optimization Convergence Issue

smpat 17 Jul 2013 18:38

I've been running the optimization process outlined in "General Lattice Optimization" (alternating between c/a and volume) for over a week (as I haven't been able to use this feature on the university HPC, it's running extraordinarily slowly on a MacBook Air). I've performed about seven alternating optimization runs for my specific structure, with no sign of convergence in sight.

My primary concern is that on every c/a run, the c parameter is increased and the a parameter is decreased, to the point where I'm about to have an entirely new structure. I'm using GGA (PBE '96), and accordingly started with parameters similar to those found in literature from other LAPW researches on the same structure with the same functional.

Does this sound familiar to anyone, or is this suggestive of an obvious operator error that I'm missing?

Re: Optimization Convergence Issue

PasqualePavone 18 Jul 2013 08:49

Dear smpat,

in order to analyze the results you have got, we would need more information. Could you post your initial input file and, if possible, the files n-VOL.xml and n-COA.xml that you get as a result of each optimization step?

yours sincerely,

Pasquale Pavone
(exciting team)

Re: Optimization Convergence Issue

smpat 18 Jul 2013 11:33

Dear Pasquale,

Here is my initial input file:

<input>

<title>TiO2: Lattice optimization</title>

<structure speciespath="/Applications/exciting/species">

<crystal scale="1.0">
<basevect> 7.15131000 0.00000000 0.00000000 </basevect>
<basevect> 0.00000000 7.15131000 0.00000000 </basevect>
<basevect> 0.00000000 0.00000000 18.2359000 </basevect>
</crystal>

<species speciesfile="Ti.xml" rmt="1.92">
<atom coord="0.00000000 0.25000000 0.37500000"/>
<atom coord="0.50000000 -0.25000000 -0.12500000"/>
<atom coord="0.00000000 -0.25000000 -0.37500000"/>
<atom coord="0.50000000 0.25000000 0.12500000"/>
</species>

<species speciesfile="O.xml" rmt="1.60">
<atom coord="0.00000000 0.25000000 -0.41934884"/>
<atom coord="0.50000000 -0.25000000 0.08065116"/>
<atom coord="0.00000000 -0.25000000 -0.16934884"/>
<atom coord="0.50000000 0.25000000 0.33065116"/>
<atom coord="-0.00000000 -0.25000000 0.41934884"/>
<atom coord="0.50000000 0.25000000 -0.08065116"/>
<atom coord="-0.00000000 0.25000000 0.16934884"/>
<atom coord="0.50000000 -0.25000000 -0.33065116"/>
</species>

</structure>

<groundstate ngridk="2 2 2"
swidth="0.01"
rgkmax="7.0"
xctype="GGAPerdew-Burke-Ernzerhof"
nempty="40">
</groundstate>

<structureoptimization/>

</input>

Here are my n-VOL.xml and n-COA.xml files, to n=7:

1-VOL.xml:

<?xml version='1.0' encoding='UTF-8'?>
<input>

<title>TiO2: Lattice optimization</title>

<structure speciespath="/Applications/exciting/species">

<crystal scale="0.9957734193">
<basevect> 7.15131000 0.00000000 0.00000000 </basevect>
<basevect> 0.00000000 7.15131000 0.00000000 </basevect>
<basevect> 0.00000000 0.00000000 18.2359000 </basevect>
</crystal>

<species speciesfile="Ti.xml" rmt="1.92">
<atom coord="0.00000000 0.25000000 0.37500000"/>
<atom coord="0.50000000 -0.25000000 -0.12500000"/>
<atom coord="0.00000000 -0.25000000 -0.37500000"/>
<atom coord="0.50000000 0.25000000 0.12500000"/>
</species>

<species speciesfile="O.xml" rmt="1.60">
<atom coord="0.00000000 0.25000000 -0.41934884"/>
<atom coord="0.50000000 -0.25000000 0.08065116"/>
<atom coord="0.00000000 -0.25000000 -0.16934884"/>
<atom coord="0.50000000 0.25000000 0.33065116"/>
<atom coord="-0.00000000 -0.25000000 0.41934884"/>
<atom coord="0.50000000 0.25000000 -0.08065116"/>
<atom coord="-0.00000000 0.25000000 0.16934884"/>
<atom coord="0.50000000 -0.25000000 -0.33065116"/>
</species>

</structure>

<groundstate ngridk="2 2 2" swidth="0.01" rgkmax="7.0" xctype="GGAPerdew-Burke-Ernzerhof" nempty="40">
</groundstate>

<structureoptimization/>

</input>

2-COA.xml:

<?xml version='1.0' encoding='UTF-8'?>
<input>

<title>TiO2: Lattice optimization</title>

<structure speciespath="/Applications/exciting/species">

<crystal scale="0.9957734193">
<basevect> 7.1087844891473733 0.0000000000000000 0.0000000000000000 </basevect>
<basevect> 0.0000000000000000 7.1087844891473733 0.0000000000000000 </basevect>
<basevect> 0.0000000000000000 0.0000000000000000 18.4547308000000001 </basevect>
</crystal>

<species speciesfile="Ti.xml" rmt="1.92">
<atom coord="0.00000000 0.25000000 0.37500000"/>
<atom coord="0.50000000 -0.25000000 -0.12500000"/>
<atom coord="0.00000000 -0.25000000 -0.37500000"/>
<atom coord="0.50000000 0.25000000 0.12500000"/>
</species>

<species speciesfile="O.xml" rmt="1.60">
<atom coord="0.00000000 0.25000000 -0.41934884"/>
<atom coord="0.50000000 -0.25000000 0.08065116"/>
<atom coord="0.00000000 -0.25000000 -0.16934884"/>
<atom coord="0.50000000 0.25000000 0.33065116"/>
<atom coord="-0.00000000 -0.25000000 0.41934884"/>
<atom coord="0.50000000 0.25000000 -0.08065116"/>
<atom coord="-0.00000000 0.25000000 0.16934884"/>
<atom coord="0.50000000 -0.25000000 -0.33065116"/>
</species>

</structure>

<groundstate ngridk="2 2 2" swidth="0.01" rgkmax="7.0" xctype="GGAPerdew-Burke-Ernzerhof" nempty="40">
</groundstate>

<structureoptimization/>

</input>

3-VOL.xml:

<?xml version='1.0' encoding='UTF-8'?>
<input>

<title>TiO2: Lattice optimization</title>

<structure speciespath="/Applications/exciting/species">

<crystal scale="0.9965720514">
<basevect> 7.1087844891473733 0.0000000000000000 0.0000000000000000 </basevect>
<basevect> 0.0000000000000000 7.1087844891473733 0.0000000000000000 </basevect>
<basevect> 0.0000000000000000 0.0000000000000000 18.4547308000000001 </basevect>
</crystal>

<species speciesfile="Ti.xml" rmt="1.92">
<atom coord="0.00000000 0.25000000 0.37500000"/>
<atom coord="0.50000000 -0.25000000 -0.12500000"/>
<atom coord="0.00000000 -0.25000000 -0.37500000"/>
<atom coord="0.50000000 0.25000000 0.12500000"/>
</species>

<species speciesfile="O.xml" rmt="1.60">
<atom coord="0.00000000 0.25000000 -0.41934884"/>
<atom coord="0.50000000 -0.25000000 0.08065116"/>
<atom coord="0.00000000 -0.25000000 -0.16934884"/>
<atom coord="0.50000000 0.25000000 0.33065116"/>
<atom coord="-0.00000000 -0.25000000 0.41934884"/>
<atom coord="0.50000000 0.25000000 -0.08065116"/>
<atom coord="-0.00000000 0.25000000 0.16934884"/>
<atom coord="0.50000000 -0.25000000 -0.33065116"/>
</species>

</structure>

<groundstate ngridk="2 2 2" swidth="0.01" rgkmax="7.0" xctype="GGAPerdew-Burke-Ernzerhof" nempty="40">
</groundstate>

<structureoptimization/>

</input>

4-COA.xml:

<?xml version='1.0' encoding='UTF-8'?>
<input>

<title>TiO2: Lattice optimization</title>

<structure speciespath="/Applications/exciting/species">

<crystal scale="0.9965720514">
<basevect> 7.0875536269332278 0.0000000000000000 0.0000000000000000 </basevect>
<basevect> 0.0000000000000000 7.0875536269332278 0.0000000000000000 </basevect>
<basevect> 0.0000000000000000 0.0000000000000000 18.5654591848000017 </basevect>
</crystal>

<species speciesfile="Ti.xml" rmt="1.92">
<atom coord="0.00000000 0.25000000 0.37500000"/>
<atom coord="0.50000000 -0.25000000 -0.12500000"/>
<atom coord="0.00000000 -0.25000000 -0.37500000"/>
<atom coord="0.50000000 0.25000000 0.12500000"/>
</species>

<species speciesfile="O.xml" rmt="1.60">
<atom coord="0.00000000 0.25000000 -0.41934884"/>
<atom coord="0.50000000 -0.25000000 0.08065116"/>
<atom coord="0.00000000 -0.25000000 -0.16934884"/>
<atom coord="0.50000000 0.25000000 0.33065116"/>
<atom coord="-0.00000000 -0.25000000 0.41934884"/>
<atom coord="0.50000000 0.25000000 -0.08065116"/>
<atom coord="-0.00000000 0.25000000 0.16934884"/>
<atom coord="0.50000000 -0.25000000 -0.33065116"/>
</species>

</structure>

<groundstate ngridk="2 2 2" swidth="0.01" rgkmax="7.0" xctype="GGAPerdew-Burke-Ernzerhof" nempty="40">
</groundstate>

<structureoptimization/>

</input>

5-VOL.xml:

<?xml version='1.0' encoding='UTF-8'?>
<input>

<title>TiO2: Lattice optimization</title>

<structure speciespath="/Applications/exciting/species">

<crystal scale="0.9967899902">
<basevect> 7.0875536269332278 0.0000000000000000 0.0000000000000000 </basevect>
<basevect> 0.0000000000000000 7.0875536269332278 0.0000000000000000 </basevect>
<basevect> 0.0000000000000000 0.0000000000000000 18.5654591848000017 </basevect>
</crystal>

<species speciesfile="Ti.xml" rmt="1.92">
<atom coord="0.00000000 0.25000000 0.37500000"/>
<atom coord="0.50000000 -0.25000000 -0.12500000"/>
<atom coord="0.00000000 -0.25000000 -0.37500000"/>
<atom coord="0.50000000 0.25000000 0.12500000"/>
</species>

<species speciesfile="O.xml" rmt="1.60">
<atom coord="0.00000000 0.25000000 -0.41934884"/>
<atom coord="0.50000000 -0.25000000 0.08065116"/>
<atom coord="0.00000000 -0.25000000 -0.16934884"/>
<atom coord="0.50000000 0.25000000 0.33065116"/>
<atom coord="-0.00000000 -0.25000000 0.41934884"/>
<atom coord="0.50000000 0.25000000 -0.08065116"/>
<atom coord="-0.00000000 0.25000000 0.16934884"/>
<atom coord="0.50000000 -0.25000000 -0.33065116"/>
</species>

</structure>

<groundstate ngridk="2 2 2" swidth="0.01" rgkmax="7.0" xctype="GGAPerdew-Burke-Ernzerhof" nempty="40">
</groundstate>

<structureoptimization/>

</input>

6-COA.xml:

<?xml version='1.0' encoding='UTF-8'?>
<input>

<title>TiO2: Lattice optimization</title>

<structure speciespath="/Applications/exciting/species">

<crystal scale="0.9967899902">
<basevect> 7.0678209884894878 0.0000000000000000 0.0000000000000000 </basevect>
<basevect> 0.0000000000000000 7.0678209884894878 0.0000000000000000 </basevect>
<basevect> 0.0000000000000000 0.0000000000000000 18.6692696502717652 </basevect>
</crystal>

<species speciesfile="Ti.xml" rmt="1.92">
<atom coord="0.00000000 0.25000000 0.37500000"/>
<atom coord="0.50000000 -0.25000000 -0.12500000"/>
<atom coord="0.00000000 -0.25000000 -0.37500000"/>
<atom coord="0.50000000 0.25000000 0.12500000"/>
</species>

<species speciesfile="O.xml" rmt="1.60">
<atom coord="0.00000000 0.25000000 -0.41934884"/>
<atom coord="0.50000000 -0.25000000 0.08065116"/>
<atom coord="0.00000000 -0.25000000 -0.16934884"/>
<atom coord="0.50000000 0.25000000 0.33065116"/>
<atom coord="-0.00000000 -0.25000000 0.41934884"/>
<atom coord="0.50000000 0.25000000 -0.08065116"/>
<atom coord="-0.00000000 0.25000000 0.16934884"/>
<atom coord="0.50000000 -0.25000000 -0.33065116"/>
</species>

</structure>

<groundstate ngridk="2 2 2" swidth="0.01" rgkmax="7.0" xctype="GGAPerdew-Burke-Ernzerhof" nempty="40">
</groundstate>

<structureoptimization/>

</input>

7-VOL.xml:

<?xml version='1.0' encoding='UTF-8'?>
<input>

<title>TiO2: Lattice optimization</title>

<structure speciespath="/Applications/exciting/species">

<crystal scale="0.9954111749">
<basevect> 7.0678209884894878 0.0000000000000000 0.0000000000000000 </basevect>
<basevect> 0.0000000000000000 7.0678209884894878 0.0000000000000000 </basevect>
<basevect> 0.0000000000000000 0.0000000000000000 18.6692696502717652 </basevect>
</crystal>

<species speciesfile="Ti.xml" rmt="1.92">
<atom coord="0.00000000 0.25000000 0.37500000"/>
<atom coord="0.50000000 -0.25000000 -0.12500000"/>
<atom coord="0.00000000 -0.25000000 -0.37500000"/>
<atom coord="0.50000000 0.25000000 0.12500000"/>
</species>

<species speciesfile="O.xml" rmt="1.60">
<atom coord="0.00000000 0.25000000 -0.41934884"/>
<atom coord="0.50000000 -0.25000000 0.08065116"/>
<atom coord="0.00000000 -0.25000000 -0.16934884"/>
<atom coord="0.50000000 0.25000000 0.33065116"/>
<atom coord="-0.00000000 -0.25000000 0.41934884"/>
<atom coord="0.50000000 0.25000000 -0.08065116"/>
<atom coord="-0.00000000 0.25000000 0.16934884"/>
<atom coord="0.50000000 -0.25000000 -0.33065116"/>
</species>

</structure>

<groundstate ngridk="2 2 2" swidth="0.01" rgkmax="7.0" xctype="GGAPerdew-Burke-Ernzerhof" nempty="40">
</groundstate>

<structureoptimization/>

</input>

Thank you!

Best,

Sean

Re: Optimization Convergence Issue

PasqualePavone 22 Jul 2013 07:53

Dear Sean,

I repeated part of your calculation on a serial machine and the running times I checked are compatible with the ones you have. The most expensive part of the calculations is the optimization of the internal degree of freedom for each set of cell parameters. (By the way, a new (faster) algorithm for the optimization of internal coordinates will be available in the next exciting release, planned in few monthes). What seems strange to me is the non converging behaviour of the c/a ratio after the last COA iteration. You should have in your directories png files showing graphically the behaviour of the energy vs. the lattice parameters. Could you post (or sending to me at pavone (at) physik.hu-berlin.de) these files (vol.png and cao.png) indicating the corresponding optimization step?
Could you also post a summary table of your results, similar to the one you can find at the end of General lattice optimization?

Best,

Pasquale Pavone
(exciting team)

Re: Optimization Convergence Issue

smpat 22 Jul 2013 14:27

Dear Pasquale,

Here are the results for each step:

-	V	Emin	c/a
1-VOL	925.6294	-4018.12676844	2.55001
2-COA	''	-4018.13074682	2.59605
3-VOL	920.8588	-4018.13140664	''
4-COA	''	-4018.13299174	2.61945
5-VOL	926.5143	-4018.13323839	''
6-COA	''	-4018.13485476	2.64145
7-VOL	916.7441	-4018.13505699	''

I have just emailed the .png documents to you. Please let me know if you have not received them.

Thanks,

Sean

Last edited on 22 Jul 2013 14:41 by smpat Show more

Re: Optimization Convergence Issue

smpat 31 Jul 2013 14:51

Any thoughts, Pasquale?

Re: Optimization Convergence Issue

PasqualePavone 15 Aug 2013 14:22

Dear Sean,

sorry for the late answer.

I analyzed your plots and I noticed the following:

• Plot 1-vol.png: The behaviour is ok, however, one can see that the difference between the fit and the calculated points is of the order of 0.5 mHa. This is usually quite large, a possible reason could be the too coarse k-point grid used in the calculation. You could also increse the accuracy of the calculated total energy by reducing of one or two order of magnitude the value of the attribute epsengy of the groundstate element (this will obviously increase the computational effort…, try first by only increasing the size of the k-point grid).
• Plot 2-coa.png: Here is a crucial point, as you can see in the plot, the minimum value of the c/a ratio lies outside the range reported in the plot: The initial value for the c/a ratio seems not to be chosen properly. As a consequence of this fact, the further calculations are no longer reasonable. By the way the minimum of the energy vs. volume (or vs. the c/a ratio) curves can also depend strongly on the parameter used in the calculation (k-point grid, etc.).

In summary, I would repeat the calculation with a larger k-point grid (e.g., (4,4,4)). After each (volume or c/a ratio) optimization run, please check the plots, in case repeat the step with more appropriate initial values. Finally, the range of variation should not be smaller than 1% for the first 2-3 runs.

I hope this will be useful for you.

Yours sincerely
Pasquale Pavone
(exciting team)