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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 G${}_{j}$ has the form

 $G_{j}=p_{j}\cdot\exp\left(-w_{j}(\textbf{r}-\textbf{r}_{0})^{2}\right)$ (9.43)

During the GOSTSHYP routine, the parameters of the Gaussian potentials, $p_{j}$ and $w_{j}$, 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

 $\displaystyle E_{\text{GOSTSHYP}}$ $\displaystyle=\sum_{j}E_{j}=\sum_{j}\int G_{j}(\textbf{r})\rho(\textbf{r})d% \textbf{r}$ $\displaystyle=\sum_{j}\sum_{\mu,\nu}\sum_{a}\left<\chi_{\mu}|G_{j}|\chi_{\nu}% \right>c_{\mu a}^{*}c_{\nu a}$ (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" $p_{j}$ 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

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

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

$distort model gostshyp pressure 40000 npoints_heavy 302 npoints_hydrogen 302 scaling 1.8$end