The energy/force/stress with symmetry on is large with compared with symmetry off

[pxlxingliang]

Describe the bug

I performed calculations on a series of structures with symmetry on and off, and found that the deviations in energy/force/stress are quite large. This difference also seems to be larger than the deviations in VASP.

ABACUS:
The maximum deviations of energy is about 3 meV/atom
The maximum deviations of force is about 0.88 eV/A
The maximum deviations of stress is about 84 kbar.

Example	NormalEnd	KPoints	IBZK	PointGroup	PointGroupInSpaceGroup	DeltaEnergy(meV)	DeltaEnergy/atom(meV)	MaxDeltaF(eV/A)	MaxDeltaStress(kbar)
+	TRUE	125	16	C_3v	C_4v	1.58	0.4	0.38	16.94
C_1+	TRUE	64	18	C_1	C_1h	13.46	3.36	0.02	11.8
C_2v+	TRUE	64	12	C_2v	C_3h	2.07	0.35	0.11	1.34
C_3+C_3v	TRUE	196	55	C_3	C_3v	-5.8	-2.9	0.05	84.29
C_3+D_3h	TRUE	196	24	C_3	D_3h	-0.04	-0.02	0.47	0.01
C_3h+	TRUE	64	12	C_3h	C_3h	5.55	0.93	0.23	1.53
C_3v+	TRUE	125	20	C_3v	C_3v	8.06	2.01	0.88	33.27
C_6+C_6	TRUE	64	20	C_6	C_6	5.07	0.85	0.1	12.58
D_2h+D_2h	TRUE	98	32	D_2h	D_2h	6.51	1.3	0.01	2.09
D_3h+T_d	TRUE	125	10	D_3h	T_d	-0.05	-0.02	0.33	0.01
T_d+O	TRUE	125	10	T_d	T_d	-0.1	-0.02	0.14	2.89

VASP:

Example	NormalEnd	KPoints	IBZK	PointGroup	PointGroupInSpaceGroup	DeltaEnergy(eV)	DeltaEnergy/atom(eV)	MaxDeltaF(eV/A)	MaxDeltaStress(kbar)
+	FALSE	---	---	D_3h	D_3h	---	---	---	---
C_1+	FALSE	---	---	C_1	C_1	---	---	---	---
C_2v+	FALSE	---	---	C_2v	C_2v	---	---	---	---
C_3+C_3v	TRUE	196	24	C_3v	D_3h	-1.25E-05	-6.24E-06	1.60E-05	0.01
C_3+D_3h	FALSE	---	---	C_2v	D_2h	---	---	---	---
C_3h+	FALSE	---	---	C_3h	C_3h	---	---	---	---
C_3v+	FALSE	---	---	D_3h	D_3h	---	---	---	---
C_6+C_6	FALSE	---	---	C_6	---	---	---	---	---
D_2h+D_2h	TRUE	98	32	D_2h	---	-1.65E-05	-3.29E-06	0.01	1.08
D_3h+T_d	TRUE	125	10	T_d	---	-1.33E-05	-4.45E-06	6.30E-05	0.01
T_d+O	TRUE	125	10	T_d	O_h	4.60E-07	1.15E-07	1.60E-05	0.04

sym.zip

Expected behavior

The deviation of energy/force/stress is smaller than results of VASP.

To Reproduce

No response

Environment

No response

Additional Context

No response

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[pxlxingliang]

I have chosen more systems (around 100) and tested different symmetry_prec, and compare the results to the results with symmetry closed. (https://labs.dp.tech/projects/abacustest/?request=GET%3A%2Fapplications%2Fabacustest%2Fjobs%2Fjob-abacustest-v0.3.53-d70a17)

symmetry_prec=1e-6

symmetry_prec=5e-6

symmetry_prec=1e-5

symmetry_prec=5e-5

symmetry_prec=1e-4

Different symmetry_prec will induce different symmetric operations, but when setting 1e-6 and 1e-4, the points with significant deviation in the results are the least.

[pxlxingliang]

I conducted another test using more configurations. And also compared the results of symmetry turned on with symmetry turned off.

We can find that the results of structure with C_2 point group has a large deviation in force, especially for the cases with point_group_in_space_group is D_2.

Example	KPoints	IBZK	PointGroup	PointGroupInSpaceGroup	DeltaEnergy/atom(meV)	MaxDeltaF(eV/A)	MaxDeltaStress(kbar)
C_2+D_2_1	486	100	C_2	D_2	9.64E-04	1.32	0.71
C_2+D_2_3	486	100	C_2	D_2	-7.32E-04	1.28	1.56
C_2+D_2_4	486	100	C_2	D_2	1.24E-03	1.36	0.28
C_2+D_2_7	486	100	C_2	D_2	2.57E-03	1.26	0.78
C_2+D_2_9	486	100	C_2	D_2	9.64E-04	1.32	0.71
C_2+D_3_4	320	93	C_2	C_2	1.44	0.77	8.1
C_2+D_3_5	486	142	C_2	C_2	4.13	0.37	11.67
C_3v+C_3v_6	507	56	C_3v	C_3v	4.28E-04	0.4	7.03E-04

Jobs with symmetry = 0: https://labs.dp.tech/projects/abacustest/?request=GET%3A%2Fapplications%2Fabacustest%2Fjobs%2Fjob-abacustest-v0.3.53-99e2b8
Jobs with symmetry = 1: https://labs.dp.tech/projects/abacustest/?request=GET%3A%2Fapplications%2Fabacustest%2Fjobs%2Fjob-abacustest-v0.3.53-a7c8cb

[QuantumMisaka]

Is there any explanation for the physical property difference for symmetry on/off ? Is just modify the default symmetry_prec a best way to improve it ?

[maki49]

Is there any explanation for the physical property difference for symmetry on/off ? Is just modify the default symmetry_prec a best way to improve it ?

The difference comes from the symmetrization according to different space group (analyzed with different symmetry_prec) that directly change the value of charge density, force and stress.
You can regard using a smaller symmetry_prec as a compromize between symmetry on and off.

[pxlxingliang]

Hi @maki49, although we can reduce the symmetric operations by reducing symmetry_prec, and thus reduce the occurrence of large result deviations, we cannot ignore the fact that in some cases, there may be significant deviations in the results of opening symmetry calculations.

And need your help to find the reason for the large deviation of those special cases. Or we need to find out under what conditions there will be a significant deviation in the results.

Otherwise, for users, turning on symmetric computation is a very dangerous thing, because they cannot confirm whether the calculation result is available or not. In actual calculations, it is impossible for users to perform another calculation that turns off symmetry to verify the correctness of the calculation result of opening symmetry.

[pxlxingliang]

Hi @maki49 , I try to use spglib to search the symmetric operations for C_3+C_3v, but there has only unit operation when I set the symmetry prec to 1e-5/1e-4/1e-3/1e-2. Why ABAUCS/VASP can find other special operations?

https://dptechnology.feishu.cn/docx/TGzYdX3kAo8NMHxyF3gcjbWInpb

[maki49]

Hi @maki49 , I try to use spglib to search the symmetric operations for C_3+C_3v, but there has only unit operation when I set the symmetry prec to 1e-5/1e-4/1e-3/1e-2. Why ABAUCS/VASP can find other special operations?

It seems that spglib has a bug on searching symmetry operations for Hexagonal lattices.
The following code gives C2h point group, but the right answer should be D_6h:

double lattice[3][3] = { {2.0, 0,0},{-1.0,std::sqrt(3), 0}, {0,0,2} };
double symprec = 1e-5;
char symbol[7];
int types[1] = { 1};
int nat = 1;
double position[1][3] = { {0.0, 0.0, 0.0} };
spg_get_schoenflies(symbol, lattice, position, types, nat, symprec);

[pxlxingliang]

As PR #3175 modify the default of symmetry_prec to 1e-6, it will increase the frequency of below error:

Optimized lattice type of reciprocal lattice cannot match the optimized real lattice. 
It is often because the inaccuracy of lattice parameters in STRU.
 
 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
                         NOTICE                           
 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
 Possible solutions: 
 1. Refine the lattice parameters in STRU;
 2. Use a different`symmetry_prec`.  
 3. Close symemtry: set `symmetry` to 0 in INPUT. 
 4. Set `symmetry_autoclose` to 1 in INPUT to automatically close symmetry when this error occurs.
 CHECK IN FILE : OUT.ABACUS/warning.log
 
 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
                         NOTICE                           
 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

I have done a test, the ratio to suffer this error is increased to about 40%, and this may cause a poor user experience.

symmetry_prec	Symemtry_prec error number (total example number is 200)	Error ratio
1e-4	13	6.5%
1e-5	17	8.5%
1e-6	79	39.5%

https://dptechnology.feishu.cn/docx/V3cldgMkAoVobvxBvWsc2bhRnXb

I think we should set the symmetry_autoclose to True to run continue with closed symmetry when suffer this error.

[maki49]

I think we should set the symmetry_autoclose to True to run continue with closed symmetry when suffer this error.

You can set symmetry_autoclose to True in your special test cases. Usually a structure with enough precision will not meet this problem.