9.5 Application of Pressure and Forces 9.5.1 Application of External Forces 9.6 Potential Energy Scans

9.5.2 Application of Pressure

(May 7, 2024)

Q-Chem features a number of methods to apply pressure to a chemical system during a geometry optimization or an AIMD simulation. ¹²¹¹ Stauch T.
Int. J. Quantum Chem.
(2021), 121, pp. e26208. Link The following methods are implemented:

Hydrostatic Compression Force Field (HCFF) ¹²⁰⁸ Stauch T., Chakraborty R., Head-Gordon M. ChemPhysChem (2019), 20, pp. 2742. Link	Section 9.5.2.1
eXtended Hydrostatic Compression Force Field (X-HCFF) ¹²¹⁰ Stauch T. J. Chem. Phys. (2020), 153, pp. 134503. Link	Section 9.5.2.2
Gaussians On Surface Tesserae Simulate HYdrostatic Pressure (GOSTSHYP) ¹¹²⁶ Scheurer M. et al. J. Chem. Theory Comput. (2021), 17, pp. 583. Link	Section 9.5.2.3

To invoke one of these methods, set DISTORT = TRUE in the $rem section. By setting the $rem variable scf_final_print = 1, the energy contribution due to pressure is printed in the output.

DISTORT

DISTORT
       Specifies whether to apply pressure or external force to a chemical system
TYPE:
       LOGICAL
DEFAULT:
       False
OPTIONS:
       False Do not use pressure or force True Use pressure or force
RECOMMENDATION:
       Set to true to apply pressure or force.

The parameters of the jobs are set via options specified in the $distort input section. The format of the $distort section is analogous to the $rem section:

$distort
  <Keyword>  <parameter/option>
$end

Note: The following job control variables belong only in the $distort section. Do not place them in the $rem section.

Model
       Specifies which model is used to distort the molecule.
INPUT SECTION: $distort
TYPE:
       STRING
DEFAULT:
       None
OPTIONS:
       HCFF Hydrostatic Compression Force Field ¹²⁰⁸ Stauch T., Chakraborty R., Head-Gordon M.
ChemPhysChem
(2019), 20, pp. 2742. Link XHCFF eXtended Hydrostatic Compression Force Field ¹²¹⁰ Stauch T.
J. Chem. Phys.
(2020), 153, pp. 134503. Link GOSTSHYP Gaussians On Surface Tesserae Simulate HYdrostatic Pressure ¹¹²⁶ Scheurer M. et al.
J. Chem. Theory Comput.
(2021), 17, pp. 583. Link EFEI External Force is Explicitly Included (Section 9.5.1)
RECOMMENDATION:
       Please refer to the following subsections for recommendations on which model to use.

Pressure
       Specifies the pressure (in MPa) used to compress the molecule.
INPUT SECTION: $distort
TYPE:
       DOUBLE
DEFAULT:
       None
OPTIONS:
       User defined
RECOMMENDATION:
       None

NPoints_Heavy
       Specifies the number of tessellation points per non-hydrogen atom.
INPUT SECTION: $distort
TYPE:
       INTEGER
DEFAULT:
       110
OPTIONS:
       User defined
RECOMMENDATION:
       Use the default.

NPoints_Hydrogen
       Specifies the number of tessellation points per hydrogen atom.
INPUT SECTION: $distort
TYPE:
       INTEGER
DEFAULT:
       110
OPTIONS:
       User defined
RECOMMENDATION:
       Use the default.

Scaling
       Specifies the scaling factor of the atomic van der Waals radii used in the tessellation of the molecular surface, which is used in the pressure models.
INPUT SECTION: $distort
TYPE:
       DOUBLE
DEFAULT:
       1.2
OPTIONS:
       User defined
RECOMMENDATION:
       Increase when modeling a chemical complex to make sure that the complex is placed inside a single cavity. ¹¹²⁶ Scheurer M. et al.
J. Chem. Theory Comput.
(2021), 17, pp. 583. Link A value of 1.0 was suggested to be used in the X-HCFF model. ¹²¹⁰ Stauch T.
J. Chem. Phys.
(2020), 153, pp. 134503. Link

Screener
       Enables/disables Integral screening for gostshyp calculations.
INPUT SECTION: $distort
TYPE:
       BOOL
DEFAULT:
       True
OPTIONS:
       True Enable integral screening for gostshyp False Disable integral screening for gostshyp
RECOMMENDATION:
       Use default. Disabling integral screening will lead to much higher memory usage and severe performance drops.

9.5.2.1 Hydrostatic Compression Force Field (HCFF)

The Hydrostatic Compression Force Field (HCFF) model was introduced by Stauch, Chakraborty and Head-Gordon. ¹²⁰⁸ Stauch T., Chakraborty R., Head-Gordon M.
ChemPhysChem
(2019), 20, pp. 2742. Link In HCFF, mechanical forces that point towards the non-mass-weighted molecular centroid are used to compress a molecule. Care must be exercised when modeling extended molecules due to the tendency of HCFF to generate spherical geometries under very high pressure. ¹²¹¹ Stauch T.
Int. J. Quantum Chem.
(2021), 121, pp. e26208. Link Also, the pressure input by the user is only a guess for the pressure that is applied to the molecule. The latter is calculated a posteriori based on the generated geometry and the molecular surface and is output as HCFF Macroscopic Pressure. Typically, the applied pressure is lower than the input pressure. It should be noted that the dependence on the nuclear gradient precludes the application of pressure to single atoms in HCFF. Moreover, the increase in electronic energy when compressing a molecule is typically underestimated by HCFF, since the pressure acts only on the nuclei, whereas the compression of electron density is not modeled directly. HCFF works with any electronic structure method for which a nuclear gradient is available.

Example 9.15 Geometry optimization of diborane under pressure using the HCFF model with an input pressure of 3808 MPa

$molecule
   0 1
   B     0.0000000000    0.0000000000    0.8917854534
   B     0.0000000000    0.0000000000   -0.8917854534
   H    -0.5244343500    0.9105724300    1.4720415209
   H     0.5244343500   -0.9105724300    1.4720415209
   H    -0.5244343500    0.9105724300   -1.4720415209
   H     0.5244343500   -0.9105724300   -1.4720415209
   H     0.8561835151    0.4929549655    0.0000000000
   H    -0.8561835151   -0.4929549655    0.0000000000
$end

$rem
   JOBTYPE            opt
   METHOD             m06-2x
   BASIS              6-311++G(d,p)
   DISTORT            true
$end

$distort
   model              hcff
   pressure           3808
   scaling            1.0
   npoints_heavy      590
   npoints_hydrogen   590
$end

9.5.2.2 eXtended Hydrostatic Compression Force Field (X-HCFF)

The eXtended Hydrostatic Compression Force Field (X-HCFF) approach was introduced by Stauch to solve the problems associated with HCFF. ¹²¹⁰ Stauch T.
J. Chem. Phys.
(2020), 153, pp. 134503. Link In X-HCFF, mechanical forces are used to compress the molecule as well, but, in contrast to HCFF, these forces are strictly perpendicular to the tessellated molecular surface, thus simulating truly hydrostatic conditions. As a result, chemically feasible geometries are retained even at high pressures. In addition, the user is able to input the precise pressure that is applied to the molecule during the simulation. It was suggested to use the unscaled atomic van der Waals radii in the tessellation routine. ¹²¹⁰ Stauch T.
J. Chem. Phys.
(2020), 153, pp. 134503. Link X-HCFF works with any electronic structure method for which a nuclear gradient is available. It is also possible to perform an analytic Hessian calculation with X-HCFF using JOBTYPE = FREQ, to obtain related structural properties such as IR and Raman frequencies.

As in HCFF, the application of pressure to atoms cannot be modeled realistically with X-HCFF, and the observed pressure-induced increase in electronic energy is typically too low.

Example 9.16 Geometry optimization of the CO ${}_{2}$ dimer under a pressure of 100 GPa using the X-HCFF model

$molecule
   0 1
   O    2.6192991230   -0.0571311942    0.0000000000
   C    1.6782610262    0.6502025480    0.0000000000
   O    0.7413912820    1.3674070371    0.0000000000
   C   -1.6782610262   -0.6502025480    0.0000000000
   O   -2.6192991230    0.0571311942    0.0000000000
   O   -0.7413912820   -1.3674070371    0.0000000000
$end

$rem
   JOBTYPE            opt
   METHOD             pbe
   BASIS              cc-pvdz
   DISTORT            true
$end

$distort
   model              xhcff
   pressure           100000
   scaling            1.0
   npoints_heavy      302
   npoints_hydrogen   302
$end

9.5.2.3 Gaussians On Surface Tesserae Simulate HYdrostatic Pressure (GOSTSHYP)

The Gaussians On Surface Tesserae Simulate HYdrostatic Pressure (GOSTSHYP) method, which was introduced by Scheurer and co-workers, ¹¹²⁶ Scheurer M. et al.
J. Chem. Theory Comput.
(2021), 17, pp. 583. Link 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.

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 required amount of memory 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

Search Results

9.5.2 Application of Pressure

9.5.2.1 Hydrostatic Compression Force Field (HCFF)

9.5.2.2 eXtended Hydrostatic Compression Force Field (X-HCFF)

9.5.2.3 Gaussians On Surface Tesserae Simulate HYdrostatic Pressure (GOSTSHYP)