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# 9.5.4 Gaussians On Surface Tesserae Simulate HYdrostatic Pressure (GOSTSHYP)

(July 14, 2022)

The Gaussians On Surface Tesserae Simulate HYdrostatic Pressure (GOSTSHYP) method, which was introduced by Scheurer and co-workers, 1058 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).

Example 9.15  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