Spin-polarization

This guide aims to give a general overview of spin-polarized (sp)GFNn-xTB calculations within the xtb program package.

Note

This feature is available in xtb in version 6.6.1 and upward via the tblite.

General description

GFN1-xTB and GFN2-xTB both treat open-shell systems in an restricted open-shell fashion since their energy expressions are spin-independent. Therefore, higher electron spin multiplicities will always be higher in energy than the low-spin multiplicities. However, the methods are occupation dependent and the geometries of high-spin states can still be optimized.

spGFNn-xTB

To remedy this issue the spin-polarized GFN1 and GFN2-xTB methods (spGFNn-xTB) have been developed and are available in xtb via the tblite library with the call:

> xtb <geometry_file> --spinpol --tblite

Note

The spin polarization will only affect the energies of open-shell configurations and not of singlets

Example

As example we will calculate the spin splittings of a mixed-valence FeCo complex with spGFN2-xTB to find the electronic ground state:

_images/spgfn.png
96

Co   4.2981   7.8875  -2.4539
Fe   4.2936   7.6860  -0.2490
N    4.3177   8.2394  -4.7611
N    2.5367   8.7591  -2.6654
N    2.3093   8.5146  -0.4585
C    2.8977   8.4151  -5.0518
H    2.4313   7.4287  -5.0575
H    2.7341   8.8807  -6.0379
C    2.1870   9.2538  -3.9732
H    2.4985  10.3023  -4.0724
H    1.1027   9.2137  -4.1534
C    1.8587   9.0585  -1.5831
C    0.5926   9.8363  -1.6028
C   -0.5637   9.2492  -1.0959
H   -0.5146   8.2451  -0.7007
C   -1.7596   9.9421  -1.0971
H   -2.6509   9.4763  -0.7029
C   -1.8155  11.2325  -1.5975
H   -2.7493  11.7751  -1.5960
C   -0.6674  11.8282  -2.0926
H   -0.7045  12.8389  -2.4730
C    0.5294  11.1352  -2.0985
H    1.4270  11.6140  -2.4622
C    1.9785   8.9213   0.8129
C    1.6789  10.2428   1.1731
H    1.6533  11.0098   0.4144
C    1.4548  10.5742   2.4929
H    1.2329  11.6001   2.7502
C    1.5192   9.6137   3.4891
H    1.3431   9.8845   4.5191
C    1.8213   8.3036   3.1506
H    1.8771   7.5470   3.9204
C    2.0494   7.9614   1.8355
H    2.2654   6.9364   1.5551
C    5.3288   9.1918   1.9786
H    5.5540   8.1404   1.7923
H    5.1441   8.9630   4.0893
N    5.5471   9.4758  -2.5880
N    5.4239   9.4980  -0.3630
C    5.1066   9.4430  -4.9974
H    4.4198  10.2884  -5.0609
H    5.6486   9.3764  -5.9534
C    6.1233   9.7533  -3.8739
H    7.0099   9.1183  -4.0024
H    6.4521  10.7963  -3.9819
C    5.8484  10.0894  -1.4741
C    6.6871  11.3166  -1.4253
C    6.2995  12.4761  -2.0920
H    5.3646  12.4913  -2.6351
C    7.0867  13.6116  -2.0320
H    6.7762  14.5093  -2.5474
C    8.2677  13.6012  -1.3084
H    8.8808  14.4891  -1.2624
C    8.6554  12.4529  -0.6380
H    9.5718  12.4449  -0.0664
C    7.8701  11.3159  -0.6942
H    8.1642  10.4190  -0.1694
C    5.2950  10.0694   0.8789
C    5.0337  11.4236   1.1229
H    4.9714  12.1140   0.2955
C    4.8255  11.8729   2.4115
H    4.6221  12.9211   2.5798
C    4.8647  10.9989   3.4848
H    4.6959  11.3605   4.4876
C    5.1147  9.6533    3.2589
N    5.5409  5.9316   -0.8551
C    6.9688  4.5777   -2.3437
N    5.5363  6.4511   -3.0183
H    6.1674  5.3706   -4.7257
H    6.9044  6.9670   -4.5066
C    4.8934  7.0165   -5.3047
C    5.9719  6.3998   -4.3893
C    6.0308  5.6968   -2.0668
H    4.0923  6.2814   -5.4031
H    5.3284  7.1836   -6.3039
C    6.0102  5.4138    0.3274
C    7.6940  4.5970    1.8539
C    5.0873  5.3600    1.3878
C    5.4599  4.9302    2.6424
C    6.7691  4.5391    2.8839
C    7.3321  5.0289    0.5932
H    8.0785  5.0923   -0.1832
H    8.7188  4.3056    2.0376
H    4.7300  4.8956    3.4388
H    7.0654  4.1993    3.8647
H    4.0598  5.6485    1.1710
C    6.5768  3.2760   -2.0424
C    8.6681  2.4371   -2.8654
C    8.2226  4.7949   -2.9076
H    7.1084  1.2072   -2.0670
H    5.6060  3.1067   -1.6000
C    9.0673  3.7296   -3.1624
C    7.4214  2.2136   -2.3040
H    8.5451  5.8037   -3.1213
H   10.0420  3.9086   -3.5932
H    9.3287  1.6068   -3.0670
> xtb mol.xyz --spinpol --tblite --uhf <UHF>

with <UHF> being the number of unparied electrons 0, 2, 4, 6, and 8 (with the correspond multiplicities 1, 3, 5, 7, and 9). The ground state is experimentally known to be a septet. The total energies in Hartree are shown below:

Multiplicity

E(GFN2-xTB)

E(spGFN2-xTB)

1

-145.1025

-145.1025

3

-145.0996

-145.1185

5

-145.0870

-145.1712

7

-145.0574

-145.1904

9

-144.9653

-145.1209

and the spin-splittings with respect to the septet ground-state in kcal/mol are:

Multiplicity

ΔE(GFN2-xTB)

ΔE(spGFN2-xTB)

1

-28.3

55.2

3

-26.4

45.2

5

-18.5

12.1

7

0.0

0.0

9

57.8

43.6

The correct gound state can be found with spGFN2-xTB but not with GFN2-xTB.

Please find more information on spGFNn-xTB methods in our publication:

H. Neugebauer, B. Bädorf, S. Ehlert, A. Hansen, S. Grimme, J. Comput. Chem., 2023, 44(27), 2120. DOI: 10.1002/jcc.27185