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9.5 Application of Pressure

9.5.4 Gaussians On Surface Tesserae Simulate HYdrostatic Pressure (GOSTSHYP)

(April 13, 2024)

The Gaussians On Surface Tesserae Simulate HYdrostatic Pressure (GOSTSHYP) method, which was introduced by Scheurer and co-workers, 1087 Scheurer M. et al.
J. Chem. Theory Comput.
(2021), 17, pp. 583.
overcomes the problems associated with the mechanochemical models of pressure, i.e. HCFF and X-HCFF. GOSTSHYP uses a uniform field of Gaussian potentials that is placed on the tessellated molecular surface and that compresses the electron density. Each Gaussian potential Gj has the form

Gj=pjexp(-wj(𝐫-𝐫0)2) (9.43)

During the GOSTSHYP routine, the parameters of the Gaussian potentials, pj and wj, are adjusted such that a user-defined pressure is applied. Atoms and molecules can be treated, and the pressure-induced increase in the electronic energy is physically sound. During the SCF, the energy expression takes the form

EGOSTSHYP =jEj=jGj(𝐫)ρ(𝐫)𝑑𝐫
=jμ,νaχμ|Gj|χνcμa*cνa (9.44)

Due to the availability of nuclear gradients, geometry optimizations under pressure using the GOSTSHYP model are possible. At present, GOSTSHYP is implemented at the SCF level, allowing calculations with Hartree-Fock and Density Functional Theory (DFT).

For good performance GOSTSHYP needs relatively large amounts of available RAM. If not enough available RAM is detected, GOSTSHYP will switch to a memory efficient algorithm at the cost of performance, a warning containing the needed amount of RAM for better performance will be printed in the output.

We found, that at the edges between the tessellation spheres of two atoms "negative amplitudes" pj may appear. Since those would lead to nonphysical attractive pressure potentials they are generally blacklisted in GOSTSHYP calculations. This however leads to instabilities within SCF calculations. We found that negative amplitudes appear very rarely for VDW-scaling factors larger than 1.5 but become more likely to appear for smaller scaling factors. Thus we recommend to use a scaling factor of at least 1.5 in GOSTSHYP calculations.

Example 9.17  Geometry optimization of cyclopentadiene and ethylene under a pressure of 40 GPa using the GOSTSHYP model

   0 1
   C    1.1148422354   -0.6418674001    0.7279292386
   C    1.1148422354   -0.6418674001   -0.7279292386
   C    0.5936432126    0.5363396649    1.1772168767
   C   -2.0464511598   -0.6129291257    0.6711240568
   C   -2.0464511598   -0.6129291257   -0.6711240568
   C    0.5936432126    0.5363396649   -1.1772168767
   C    0.2915208637    1.4128825196    0.0000000000
   H    0.9756522868    2.2894492537    0.0000000000
   H   -0.7374232239    1.8214336422    0.0000000000
   H    1.4681344173   -1.4690333337   -1.3527755131
   H    1.4681344173   -1.4690333337    1.3527755131
   H   -2.3879086093    0.2541525765    1.2531118994
   H   -1.7231567891   -1.4887031107    1.2461940178
   H   -1.7231567891   -1.4887031107   -1.2461940178
   H   -2.3879086093    0.2541525765   -1.2531118994
   H    0.4773764265    0.8454441265    2.2200767812
   H    0.4773764265    0.8454441265   -2.2200767812

   JOBTYPE               opt
   METHOD                pbe
   BASIS                 cc-pvdz
   SCF_ALGORITHM         diis_gdm
   MAX_SCF_CYCLES        150
   USE_LIBQINTS          1
   GEN_SCFMAN            1
   DISTORT               1

   model                 gostshyp
   pressure              40000
   npoints_heavy         302
   npoints_hydrogen      302
   scaling               1.8