Inorganic Materials Modelling
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In this example, we will optimize the geometry of strontium borate hydride Sr5(BO3)3H using PBE0 hybrid density functional method. This example demonstrates the use of a basis set including effective core potential (ECP).

Sr5(BO3)3H has been published in Borate Hydrides as a New Material Class: Structure, Computational Studies, and Spectroscopic Investigations on Sr5(BO3)3H and Sr5(11BO3)3D, T. Wylezich, R. Valois, M. Suta, A. Mutschke, P. Walke, C. Ritter, A. Meijerink, A. J. Karttunen, N. Kunkel, Chem. Eur. J. 2020, 26, 11742–11750, https://doi.org/10.1002/chem.202002273.

Table of contents

Crystal structure of Sr5(BO3)3H

Sr5(BO3)3H crystallizes in the orthorhombic crystal system, space group Pnma (no. 62). Here is the crystal structure optimized at the DFT-PBE0/TZVP level of theory, as found in the supporting information of the paper: Sr5_BO3_3H_DFT-PBE0.cif. As the point of this tutorial is to discuss basis sets and effective core potentials, we will start from an already optimized structure.

Let's convert the CIF to CRYSTAL input format with cif2cry:

cif2cry Sr5_BO3_3H_DFT-PBE0.cif > Sr5_BO3_3H_PBE0_TZVP_opt.d12

The file names are Sr5_BO3_3H instead of Sr5(BO3)3H because I generally recommend to avoid parentheses in file names.

The resulting file Sr5_BO3_3H_PBE0_TZVP_opt.d12 looks like this:

Sr5_BO3_3H_PBE0_TZVP_opt.d12
Converted by cif2cry from Sr5_BO3_3H.cif
CRYSTAL
1 0 0
P 21/n 21/m 21/a
7.2013607500 14.1085813100 9.8041155600
12
238    0.02887    0.11255    0.25356
8      0.09710    0.59102    0.15210
5      0.20101    0.53879    0.06109
238    0.25406    0.62039    0.37444
8      0.27778    0.06849    0.42767
8      0.28041    0.04495    0.10319
8      0.11557    0.25000    0.04406
1      0.12436    0.25000    0.73570
8      0.28425    0.25000    0.25172
5      0.28279    0.25000    0.11069
238    0.28893    0.25000    0.52137
8      0.44483    0.25000    0.03810
ENDGEOM

Space group notation

As the original CIF had been created by FINDSYM, the space group name is given in the long notation P 21/n 21/m 21/a. However, CRYSTAL does not understand the long notation, and we need to change this to P n m a.

Note that it is much better to use the space group name instead of the space group number for orthorhombic and monoclinic crystal systems. There are so many different settings for each space group that using the name is the only way to be sure that CRYSTAL interprets the structure correctly (for more information, see the list of alternative settings for orthorhombic space groups). Space group no. 62 has six different settings listed:  P n m a, P n a m, P m c n, P c m n, P b n m, and P m n b. If your CIF would be given in non-standard setting P b n m, but you would give the space group as a number in the input (62), CRYSTAL would interpret it incorrectly.

Lattice parameters

Note how in an orthorhombic crystal structure, we must give lattice parameters a, b, and c. The angles between the lattice vectors are 90 degrees and must not be given (only minimal set of lattice parameters is given to CRYSTAL).

Effective core potential

As you can notice, cif2cry used atomic number 238 for Sr (Z = 38). In CRYSTAL, the atomic number given in the input is actually called the conventional atomic number. If the atomic number is increased by 200, it means that the atom will be associated with a basis set that contains an effective core potential (ECP). Typically, it is a good idea to apply scalar-relativistic effective core potentials for Z > 37. This has two benefits: (1) core electrons are replaced by an ECP, reducing the number of electrons and making the calculation faster, and (2) scalar relativistic effects are accounted for. The latter point becomes increasingly important for heaver elements and is absolutely crucial for elements starting from Cs.

Conventional atomic number

The conventional atomic number can also be used to assign different basis sets for atoms of same type. For example, if you would like to assign different basis sets for two oxygen atoms (Z = 8), you could denote them as 8 and 308 in the coordinate input and in the basis set input you would give different basis sets for conventional atomic numbers 8 and 308. The "additive number" 200 is reserved for ECPs, other numbers can be used for assigning different basis sets to different atoms (1, 3, 4, ...).

Complete input file

For the calculation, we will be using TZVP level basis sets for elements other than Sr and SVP level basis set (with ECP) for Sr. In Sr5(BO3)3H, the electropositive Sr atoms can be in practice described as Sr2+ cations, and a smaller SVP-level basis set is enough to describe them properly. Generally, for group 1 and group 2 elements, SVP-level basis sets are normally enough to describe them as cations. Larger TZVP basis sets would be necessary only in intermetallics or other materials where the group 1 or group 2 elements behave like metals. 

Here is the complete input file (with a new title and space group name shortened):

Sr5_BO3_3H_PBE0_TZVP_opt.d12
Sr5(BO3)3H. Chem. Eur. J. 2020, 26, 11742-11750.
CRYSTAL
1 0 0
P n m a
7.2013607500 14.1085813100 9.8041155600
12
238    0.02887    0.11255    0.25356
8      0.09710    0.59102    0.15210
5      0.20101    0.53879    0.06109
238    0.25406    0.62039    0.37444
8      0.27778    0.06849    0.42767
8      0.28041    0.04495    0.10319
8      0.11557    0.25000    0.04406
1      0.12436    0.25000    0.73570
8      0.28425    0.25000    0.25172
5      0.28279    0.25000    0.11069
238    0.28893    0.25000    0.52137
8      0.44483    0.25000    0.03810
OPTGEOM
ENDOPT
ENDGEOM
1 4
0 0 3 1.0 1.0
  45.351741106      0.60251978000E-02
  6.8233001522      0.45021094000E-01
  1.5944879907      0.20189726000
0 0 1 0.0 1.0
 0.44546978735      1.00000000000
0 0 1 0.0 1.0
 0.13000000000      1.00000000000
0 2 1 0.0 1.0
 0.80               1.00000000000
5 7
0 0 6 2.0 1.0
  8564.8660687      0.22837198155E-03
  1284.1516263      0.17682576447E-02
  292.27871604      0.91407080516E-02
  82.775469176      0.36342638989E-01
  27.017939269      0.11063458441
  9.8149619660      0.23367344321
0 0 2 2.0 1.0
  3.9295537119      0.41818777978
  1.6980409139      0.22325473798
0 0 1 0.0 1.0
 0.57483069645      1.0000000000
0 1 1 0.0 1.0
 0.17000000000      1.0 1.0
0 2 3 1.0 1.0
  28.577505088      0.50265575179E-02
  6.7104492541      0.32801738965E-01
  2.0721954358      0.13151230768
0 2 1 0.0 1.0
 0.64922416350      1.0000000000
0 3 1 0.0 1.0
 0.50000000000      1.0000000000
8 7
0 0 6 2.0 1.0
  27032.382631      0.21726302465E-03
  4052.3871392      0.16838662199E-02
  922.32722710      0.87395616265E-02
  261.24070989      0.35239968808E-01
  85.354641351      0.11153519115
  31.035035245      0.25588953961
0 0 2 2.0 1.0
  12.271113873      0.39768730901
  4.9159842006      0.24627849430
0 0 1 0.0 1.0
 0.90086482370      1.0000000000
0 1 1 0.0 1.0
 0.25000000000      1.0 1.0
0 2 4 4.0 1.0
  75.300554155      0.60685103418E-02
  17.743733858      0.41912575824E-01
  5.5355828651      0.16153841088
  2.0685535103      0.35706951311
0 2 1 0.0 1.0
 0.78238772422      1.0000000000
0 3 1 0.0 1.0
 1.2000000000       1.0000000000
238 6
INPUT
10. 0 2 2 2 1 0
7.400074 135.479430 0
3.606379 17.534463 0
6.484868 88.359709 0
3.288053 15.394372 0
4.622841 29.888987 0
2.246904 6.659414 0
4.633975 -15.805992 0
0 0 3 2.0 1.0
  5.9276428767      0.19698765364
  3.0691274814     -0.64852205985
  0.70675488028     0.62064729022
0 0 1 2.0 1.0
 0.33824024280      1.0000000000
0 1 1 0.0 1.0
 0.13              1.0 1.0
0 2 4 6.0 1.0
  2.4324720000     -0.37145059848
  1.6642340000      0.37856824234
  0.59455471858     0.59874487803
  0.26152621998     0.35314019512
0 3 2 0.0 1.0
  3.6180810000     -0.75010000000E-02
  0.99665600000     0.10809800000
0 3 1 0.0 1.0
  0.22              1.0
99 0
END
DFT
PBE0
END
SHRINK
0 4
4 2 3
TOLINTEG
8 8 8 8 16
MAXCYCLE
100
FMIXING
80
EXCHSIZE
30000000
BIPOSIZE
30000000
END

The Sr basis set definition, including a Stuttgart/Cologne ECP, starts on line 80. The ECP describes 28 core electrons (1s22s22p63s23p63d10), leaving 10 electrons in the valence space (4s24p65s2).

Submitting the job

Prerequisites for submitting the job to queue:

  1. You need to have a terminal connection to the server.
  2. You need to be in the same directory as the input file.

Submit the job using 8 CPUs:

jsub -np 8 crystal Sr5_BO3_3H_PBE0_TZVP_opt.d12

Short review of the results

The complete output file is available as Sr5_BO3_3H_PBE0_TZVP_opt.o. Because we started from an already optimized geometry, the job finishes immediately after the first step:

Sr5_BO3_3H_PBE0_TZVP_opt.o
 MAX GRADIENT      0.000163  THRESHOLD              0.000450 CONVERGED YES
 RMS GRADIENT      0.000067  THRESHOLD              0.000300 CONVERGED YES

 WARNINGWARNINGWARNINGWARNINGWARNINGWARNINGWARNINGWARNINGWARNINGWARNINGWARNING

 CONVERGENCE ON GRADIENTS SATISFIED AFTER THE FIRST OPTIMIZATION CYCLE
 GEOMETRY OPTIMIZATION STOPPED

 WARNINGWARNINGWARNINGWARNINGWARNINGWARNINGWARNINGWARNINGWARNINGWARNINGWARNING

 ******************************************************************
 * OPT END - CONVERGED * E(AU):  -3.626237512979E+03  POINTS    1 *
 ******************************************************************

   BAND GAP:                      7.0759  eV

CRYSTAL always prints out a warning when the optimization converges immediately. From the MAX GRADIENT and RMS GRADIENT values we can see that we indeed appear to be in a stationary point. The nature of the stationary point can be confirmed with a harmonic frequency calculation. Spoiler alert! In this case, the optimization ended in a true local minimum.

The predicted band gap of this insulating material is relatively large (7 eV). 

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