3.16 Embedding in external fields

If the order of the multipole is greater than zero (presently, only monopoles or dipoles are supported), a dipole moment must be specified in addition to the data provided with the multipole tag itself. To that end, a line must immediately follow the original multipole line, adhering to the following format:
data m_x m_y m_z
Here, m_x, m_y, m_z are the $x$, $y$, and $z$ components of the dipole moment, in $e\cdot$Å.

Warning: Note that monopoles amount to Coulomb singularities. When inside the basis function radius of any atom, such monopoles should be covered with an integration grid in geometry.in, as explained in the beginning of this section.

For most purposes, embedding into an external potential will involve a change to the electronic structure of the structure which is embedded. However, in some instances one may wish to embed a given charge density non-selfconsistently, i.e., by calculating the electron density without an external field and then computing the energy of that unperturbed electron density in the external field.

This feature is useful if multipoles are located too close to the quantum-mechanical region of the calculation. These act as Coulomb-like potentials, just like any other potential in the systems. If there are basis functions that cover the location of that potential, some electronic charge may artificially become trapped there, creating a bad approximation to the core / valence electrons of an atom with a nucleus of charge charge. In most cases, this is clearly undesirable behaviour, and apart from that will create unwanted numerical noise since the electronic structure near the Coulomb-like singularity of the multipole will be represented solely by basis functions that are inadequate for this purpose in the first place.

For quantum-mechanics / molecular-mechanics (QM/MM) “hybrid” molecular dynamics simulations, one must evolve both the quantum and classical subsystems with time. In that case, it is necessary to know the derivatives of the quantum-mechanical total energy with respect to the positions of the classical multipoles (see keyword multipole), i.e., the forces on the multipoles that originate from the quantum-mechanical region.

The computation of these forces is switched on by adding the qmmm keyword to control.in. The actual QM/MM simulation must still be performed using an outside framework, for example ChemShell [278] that uses the energies and forces provided by FHI-aims as a “plugin”.

FHI-aims can also perform embedding into numerically tabulated external potentials stored in Gaussian Cube files. The practical context for this functionality would typically be the simulation of tip-enhanced Raman spectroscopy (TERS) for surface systems and the embedding potential would represent the near field induced by the laser-irradiated STM tip following the methodology described in Refs [200, 44]. Hence, the embedding potential is expected to assume the following form

where $E_z$ represents the $z$-oriented homogeneous_field (far-field) embedding. Both terms can be input through Gaussian Cube files and positioned arbitrarily with respect to the molecular geometry (as documented below). Note that either of the two terms can be used (or both at the same time) according to the tailored goals and needs of the user. For $z$-oriented slabs, periodic boundary conditions are allowed.