periodic
in the $embed section: periodic 3
means
a bulk three-dimensional system, periodic 2
denotes a
two-dimensional surface with an aperiodic z direction.
cell
and content
of the
$embed section.
charges
, or a charge value for each
point charge, using the subsection ch_list
. Note that only one of the
subsections can be defined.
cluster
of the $embed section.
Example 1. Ca4F19 cluster embedded in bulk CaF2
In this example a QM cluster with the composition Ca4F19, surrounded by 212 ECPs and 370 explicit point charges, representing Ca2+ cations and F- anions is embedded in a periodic field of point charges (+2 for Ca and -1 for F) corresponding to the CaF2 fluorite lattice.
First, the program has to know that this is a three-dimensional
periodic system. This is specified by the keyword periodic 3
,
meaning periodicity in three dimensions. The dimensions of the unit
cell for bulk CaF2 are given in the subsection cell
of the
$embed keyword. By default, the unit cell dimensions are
specified in atomic units and can be changed to Å using cell ang
.
The positions of the point charges in the unit cell are
specified in the subsection content
. In this example positions
are given in fractional crystal coordinates (content frac
). You
can change this by specifying content
for Cartesian coordinates
in atomic units or content ang
for Cartesian coordinates in
Å. The values of point charges for Ca and F are given in the
subsection charges
.
$embed periodic 3 cell 10.47977 10.47977 10.47977 90.0 90.0 90.0 content frac F 0.00 0.00 0.00 Ca -0.25 -0.75 -0.75 F 0.50 -0.50 0.00 F 0.50 0.00 -0.50 F 0.00 -0.50 -0.50 F 0.50 -0.50 -0.50 F 0.00 0.00 -0.50 F 0.50 0.00 0.00 F 0.00 -0.50 0.00 Ca -0.25 -0.25 -0.25 Ca 0.25 -0.75 -0.25 Ca 0.25 -0.25 -0.75 end ... charges F -1.0 Ca 2.0 end
The above input defines a periodic, perfect, and infinite
three-dimensional lattice of point charges corresponding to the bulk
CaF2 structure. In order to use this lattice for PEECM calculation
we have to make ``space'' for our QM cluster and the isolating
shell. This is done by specifying the part of the lattice that is
virtually removed from the perfect periodic array of point charges
to make space for the cluster. The positions of the removed point
charges are specified in the subsection cluster
of the
$embed keyword. Note, that the position of the QM cluster
and the isolating shell must exactly
correspond to the removed part of the crystal, otherwise positions of
the cluster atoms would overlap with positions of point charges in the
periodic lattice, resulting in a ``nuclear fusion''.
cluster F 0.00000000000000 0.00000000000000 0.00000000000000 Ca -2.61994465796043 -2.61994465796043 -2.61994465796043 Ca 2.61994465796043 -2.61994465796043 2.61994465796043 Ca 2.61994465796043 2.61994465796043 -2.61994465796043 Ca -2.61994465796043 2.61994465796043 2.61994465796043 F -5.23988931592086 0.00000000000000 0.00000000000000 F 0.00000000000000 0.00000000000000 -5.23988931592086 F 5.23988931592086 0.00000000000000 0.00000000000000 F 0.00000000000000 -5.23988931592086 0.00000000000000 F 0.00000000000000 0.00000000000000 5.23988931592086 F 0.00000000000000 5.23988931592086 0.00000000000000 F -5.23988931592086 -5.23988931592086 0.00000000000000 F -5.23988931592086 0.00000000000000 -5.23988931592086 F -5.23988931592086 0.00000000000000 5.23988931592086 F -5.23988931592086 5.23988931592086 0.00000000000000 F 5.23988931592086 -5.23988931592086 0.00000000000000 ...repeated for Ca216F389
end
By default, the positions of point charges are specified in atomic
units as Cartesian coordinates. You can change this by specifying
cluster frac
for fractional crystal coordinates or
cluster ang
for Cartesian coordinates in Å.
Finally, you have to specify the coordinates of the QM cluster along with the surrounding ECPs representing cationic sites and explicit point charges representing anions. This is done in the usual way using the $coord keyword.
$coord 0.00000000000000 0.00000000000000 0.00000000000000 f -2.86167504097169 -2.86167504097169 -2.86167504097169 ca 2.86167504097169 2.86167504097169 -2.86167504097169 ca -2.86167504097169 2.86167504097169 2.86167504097169 ca 2.86167504097169 -2.86167504097169 2.86167504097169 ca 0.00000000000000 -5.24009410923923 0.00000000000000 f -5.24009410923923 0.00000000000000 0.00000000000000 f 0.00000000000000 5.24009410923923 0.00000000000000 f 0.00000000000000 0.00000000000000 -5.24009410923923 f 5.24009410923923 0.00000000000000 0.00000000000000 f 0.00000000000000 0.00000000000000 5.24009410923923 f 0.00000000000000 -5.24009410923923 -5.24009410923923 f -5.24009410923923 -5.24009410923923 0.00000000000000 f 5.24009410923923 -5.24009410923923 0.00000000000000 f 0.00000000000000 -5.24009410923923 5.24009410923923 f 0.00000000000000 5.24009410923923 -5.24009410923923 f ...repeated for Ca216F389
$end
This is the standard TURBOMOLE syntax for atomic coordinates. The actual distinction between QM cluster, ECP shell, and explicit point charges is made in the $atoms section.
$atoms f 1,6-23 \ basis =f def-TZVP ca 2-5 \ basis =ca def-TZVP ca 24-235 \ basis =none \ ecp =ca ecp-18 hay & wadt f 236-605 \ basis =none \ charge= -1.00000000In the example above the F atoms 1 and 6-23 as well Ca atoms 2-5 are defined as QM atoms with def-TZVP basis sets. The Ca atoms 24-235 are pure ECPs and have no basis functions (
basis =none
) and F atoms
236-605 are explicit point charges with charge -1, with no basis functions
and no ECP.
This step ends the input definition for the PEECM calculation.
Example 2. Al8O12 cluster embedded in α-Al2O3 (0001) surface
In this example a QM cluster with the composition Al8O12, surrounded by 9 ECPs representing Al3+ cations is embedded in a two-dimensional periodic field of point charges (+3 for Al and -2 for O) corresponding to the (0001) surface of α-Al2O3.
As in the first example, the program has to know that this is a
two-dimensional periodic system and this is specified by the keyword
periodic 2
. The dimensions of the unit cell for the (0001)
α-Al2O3 surface are given in the subsection cell
of the $embed keyword. The aperiodic direction is always the
z direction, but you have to specify the unit cell as if it was a 3D
periodic system. This means that the third dimension of the unit cell
must be large enough to enclose the entire surface in this
direction. The unit cell dimensions are specified in Å using
cell ang
. The positions of the point charges in the unit cell
are specified as Cartesian coordinates in Å (content ang
).
The values of point charges for Al and O are given in the
subsection charges
.
$embed periodic 2 cell angs 4.8043 4.8043 24.0000 90.0000 90.0000 120.0000 content ang Al 2.402142286 1.386878848 5.918076515 Al -0.000013520 -0.000003382 7.611351967 Al -0.000008912 2.773757219 8.064809799 Al 2.402041674 1.386946321 0.061230399 Al -0.000005568 -0.000003223 10.247499466 Al 2.402137518 1.386872172 9.977437973 Al 0.000000070 2.773757935 5.390023232 Al 0.000006283 -0.000005607 3.696748018 Al 2.402151346 1.386879444 3.243290186 Al 0.000100868 2.773690462 11.246870041 Al -0.000001982 -0.000005796 1.060600400 Al 0.000004853 2.773764610 1.330662251 O -0.731205344 1.496630311 6.749288559 O 0.743527174 1.296469569 8.957922935 O 1.588027477 0.104536049 11.127140045 O 1.471626759 2.779079437 6.749288559 O 3.309734344 -0.004341011 8.957920074 O 3.919768333 1.323050499 11.127141953 O -0.740424335 4.045563698 6.749289513 O -1.651123047 2.868478537 8.957910538 O 1.698525310 2.733071804 11.127161026 O 3.133347750 2.664006472 4.558811665 O 1.658615232 2.864167213 2.350177050 O 0.814115047 4.056100845 0.180959582 O 0.930515707 1.381557465 4.558811188 O 1.494558096 0.004332162 2.350180149 O -1.517625928 2.837586403 0.180958077 O 3.142566681 0.115072958 4.558810234 O -0.751034439 1.292158127 2.350189686 O 0.703617156 1.427564979 0.180938885 end ... charges O -2.0 Al 3.0 end
The above input defines a periodic, perfect, and infinite
two-dimensional lattice of point charges corresponding to the (0001)
α-Al2O3 surface. In order to use the lattice for PEECM
calculation we have to make ``space'' for our QM cluster and the
surrounding ECP shell. This is done by specifying the part of the
lattice that is virtually removed from the perfect periodic array of
point charges to make space for the cluster. The positions of the
removed point charges are specified in the subsection cluster
of the
$embed keyword. Note, that the position of the QM cluster must exactly
correspond to the removed part of the crystal, otherwise positions of
the cluster atoms would overlap with positions of point charges in the
periodic lattice, resulting in a ``nuclear fusion''.
cluster ang Al -0.000012482 5.547518253 9.977437973 Al 2.402141094 6.934402943 8.064809799 Al 2.402144432 4.160642624 10.247499466 Al 4.804287434 5.547518253 9.977437973 Al 2.402250767 6.934336185 11.246870041 Al -0.000005568 8.321288109 10.247499466 Al 2.402137518 9.708164215 9.977437973 Al 4.804294586 8.321288109 10.247499466 O 0.907584429 4.156304836 8.957920074 O 1.517618299 5.483696461 11.127141953 O -0.703624666 6.893717766 11.127161026 O 3.145677090 5.457115650 8.957922935 O 3.990177393 4.265182018 11.127140045 O 0.751026928 7.029124260 8.957910538 O 4.100675106 6.893717766 11.127161026 O 0.743527174 9.617761612 8.957922935 O 1.588027477 8.425827980 11.127140045 O 3.309734344 8.316950798 8.957920074 O 3.919768333 9.644342422 11.127141953 O 5.555326939 7.029124260 8.957910538 Al 4.804400921 11.094982147 11.246870041 Al -0.000008912 2.773757219 8.064809799 Al -2.402049065 6.934336185 11.246870041 Al 4.804400921 2.773690462 11.246870041 Al 2.402136564 4.160642624 7.611351967 Al -0.000013520 8.321288109 7.611351967 Al -0.000008912 11.095048904 8.064809799 Al 7.206440926 6.934402943 8.064809799 Al 4.804286480 8.321288109 7.611351967 end
The positions of point charges are specified in Å as Cartesian coordinates.
Finally, you have to specify the coordinates of the QM cluster along with the surrounding ECPs. This is done in the usual way using the $coord keyword.
$coord -0.00002358760000 10.48329315900000 18.85463057110000 al 4.53939007480000 13.10412613690000 15.24028611330000 al 4.53939638280000 7.86247730390000 19.36497297520000 al 9.07879006320000 10.48329315900000 18.85463057110000 al 4.53959732680000 13.10399998250000 21.25351019750000 al -0.00001052200000 15.72496001430000 19.36497297520000 al 4.53938331720000 18.34577677080000 18.85463057110000 al 9.07880357850000 15.72496001430000 19.36497297520000 al 1.71508649490000 7.85428007030000 16.92802041340000 o 2.86788376470000 10.36268741690000 21.02725683720000 o -1.32965829240000 13.02724227310000 21.02729288000000 o 5.94446987180000 10.31245694970000 16.92802581990000 o 7.54034461170000 8.06002818410000 21.02725323160000 o 1.41923561090000 13.28312353520000 16.92800239300000 o 7.74915508620000 13.02724227310000 21.02729288000000 o 1.40506312580000 18.17494056150000 16.92802581990000 o 3.00093786570000 15.92251179600000 21.02725323160000 o 6.25449323900000 15.71676368210000 16.92802041340000 o 7.40729073370000 18.22517102690000 21.02725683720000 o 10.49804944110000 13.28312353520000 16.92800239300000 o 9.07900452260000 20.96648359440000 21.25351019750000 al -0.00001684120000 5.24164297480000 15.24028611330000 al -4.53921616520000 13.10399998250000 21.25351019750000 al 9.07900452260000 5.24151682240000 21.25351019750000 al 4.53938151440000 7.86247730390000 14.38337475740000 al -0.00002554910000 15.72496001430000 14.38337475740000 al -0.00001684120000 20.96660974680000 15.24028611330000 al 13.61820356690000 13.10412613690000 15.24028611330000 al 9.07878826040000 15.72496001430000 14.38337475740000 al $end
This is the standard TURBOMOLE syntax for atomic coordinates. The actual distinction between QM cluster and ECP shell is made in the $atoms section.
$atoms al 1-8 \ basis =al def-SV(P) o 9-20 \ basis =o def-SV(P) al 21-29 \ basis =none \ ecp =al ecp-10 hay & wadtIn the example above the Al atoms 1-8 and O atoms 9-20 are defined as QM atoms with def-SV(P) basis sets. The Al atoms 21-29 are pure ECPs and have no basis functions (
basis =none
).
This step ends the input definition for the PEECM calculation.