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## Computational details: SCF calculations

To carry out a PE-SCF calculation with the DSCF or RIDFT module, you have to specify the following in the control file:

$point_charges pe [options] <length unit> <no. MM sites> <order k> <order pol> <length exclude list> <list of MM sites: exclude list, xyz coords, multipole mom., pol. tensor>  length unit specifies the unit for the MM site coordinates (use AA or AU) no. MM sites the amount of MM sites (length of the list) order k the order of multipoles used (0: point charges, 1: dipole moments, 2: quadrupole moments, 3: octupole moments) order pol the treatment of polarizabilities (0: none, 1: isotropic, 2: anisotropic) length exclude list number of elements in the exclude list list of MM sites each MM sites is described on one line, entries separated by blanks; first entry is the exclude list of with as much elements as defined in the head line (If the first element in the exclusion list of one site occurs in the exclude list of another site, they do not contribute to each others polarization); next follows the MM site coordinates in (x,y,z positions), the point charge, the dipole moment (for k≥1 , x,y,z component), the quadrupole moment (for k≥2 , xx, xy, xz, yy, yz, zz component), the octupole moment (for k = 3 , xxx, xxy, xxz, xyy, xyz, xzz, yyy, yyz, yzz, zzz component), the polarizability ( one component for pol-order 1, xx, xy, xz, yy, yz, zz component for pol-order 2) An example for a polarizable embedding with coordinates given in Å, point charges and isotropic polarizabilities: $point_charges pe
AA
6 0  1  1
39   -0.2765102481    2.5745845304    3.5776314866    0.038060  15.217717
39    1.3215071687    2.3519378014    2.8130403183   -0.009525  14.094642
39   -0.5595582934    1.2645007691    4.7571719292   -0.009509  14.096775
39   -1.5471918244    2.5316479230    2.3240961995   -0.009519  14.096312
39   -0.3207417883    4.1501938400    4.4162313889   -0.009507  14.096476
41   -1.1080691595    4.9228723099   -1.6753825535    0.038060  15.217717
41   -0.9775910525    6.5274614891   -2.4474576239   -0.009525  14.094642
41   -2.5360480539    4.8923046027   -0.6040781123   -0.009509  14.096775
41    0.3630448878    4.6028736791   -0.7155647205   -0.009519  14.096312
41   -1.2817317422    3.6689143712   -2.9344225518   -0.009507  14.096476


All values are given in atomic units (except coordinates if stated otherwise). These data are mandatory. In addition, you can specify further options on the same line as the $point_charges flag. These are: • rmin=<float>: minimum distance between an active MM site and any QM center (in a.u.), treatment is handle by option iskip, (DEFAULT: 0.00 a.u.) • iskip=(1,2) : treatment of too close MM sites • (1) zeroing all contributions • (2) distribute values to nearest non-skipped MM site (DEFAULT) • rmax=<float>: maximum distance between an active MM site and QM center of coordinates (in a.u.), sites too far away are skipped (zeroed) (DEFAULT: 1000.00 a.u.) • nomb: no treatment of many body effects between induced dipoles (all interaction tensors on the off-diagonal of the response matrix are set to Zero); works best with isotropic polarizabilities, speeds up calculations (especially for large response matrices), has reduced accuracy, not well tested so far • longprint=(1,2,3): sets a flag for additional output • (1) print all MM site input information • (2) additionally: print all induced dipoles due to nulcei/multipole/electron electric filed • (3) additionally: print response matrix • file=<input file>: specifies a file from which the data group$point_charges is read. Note that all options which are following on the line the control file are then ignored because reading continues in the input file (But here, further options can be specified after the $point_charges flag). The file has to start with$point_charges as top line and should be finished with \$end

Limitations with respect to standard SCF computations:

• In PE-SCF computations, symmetry cannot be exploited.
• PE-SCF computations do not work in parallel (MPI parallelization).

The energy of a PE-SCF calculation printed in the output contains the following terms:

 EPE-SCF = EQM + EQM/MM, es + Epol (9.29)

Here, EQM is the energy of the quantum mechanical method of your choice, EQM/MM, es the electrostatic interaction energy between the QM and the MM region, and Epol the energy gain due to the total of induced dipole moments. If necessary, missing terms can be computed without knowledge of the electron distribution.

At the moment, TURBOMOLE does not offer the possibility to generate the necessary potentials or to create a potential file from a set of coordinates. Embedding potentials can be obtained from literature or generated by approaches like the LoProp method.[122] Atom centered polarizabilities are also available from other methods or from experiment. Finally, there are some polarizable force fields which, in principle, can be used for the PE method (for example, the AMOEBA force field).

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