Hey there N. Shukla! When it comes to incorporating charges into atoms within a periodic boundary conditions (PBC) structure during a Density Functional Theory (DFT) investigation, it's crucial to follow a systematic approach.

In DFT, the charged state of an atom is often represented by adjusting the total number of electrons in the system. For example, if you're investigating a Na+ ion in a TiO2 structure, you'd need to consider the removal of one electron from the system to represent the positive charge on the sodium ion.

Here's a general guide:

1. **Modify the Input Structure:**

- Start with your initial structure, which likely contains a neutral Na atom.

- Adjust the input file or script to reflect the removal of an electron from the Na atom.

2. **Update the Electronic Structure Calculation:**

- Run your DFT calculations with the modified input.

- Ensure that the computational parameters are suitable for accurately describing charged species.

3. **Analyze Results:**

- Examine the electronic structure results, such as the charge density and Mulliken charges, to confirm the presence of the desired charge on the Na+ ion.

4. **Consideration of Periodic Effects:**

- In PBC, be attentive to the interactions between neighboring unit cells. These interactions can affect the charge distribution, especially in the vicinity of the charged ion.

5. **Verification and Validation:**

- Validate your results by comparing them with experimental data if available or with results from other reliable theoretical methods.

Remember, the key is to maintain consistency with physical principles while adapting your calculations to represent the charged species accurately.

Now, go out there and unravel the mysteries of charged ions in PBC structures! If you N. Shukla have more questions or need further clarification, feel free to ask.

Kaushik Shandilya Thank you for such an elaborative description. Now I have two confusions:

1. "Adjust the input file or script to reflect the removal of an electron from the Na atom." when you say this, we have two options in the script: tot_charge and starting_charge(i). So, in the case mentioned shall I be just scripting starting charge for Na atom keeping total charge unmentioned or should both these parameters need to be defined in the input file?

2. "Ensure that the computational parameters are suitable for accurately describing charged species." What exactly do you mean by this?

In general, it is impossible to describe a continuous charge distribution with a finite set of point charges, so there is no “correct” set of “atomic charges” in a molecular or materials system. (This fact is frequently underappreciated.) Nevertheless, approximate atomic charges are a useful qualitative tool and several schemes for determining them are in use. The most common is population analysis. If the code that you are using uses an atom-centered basis, the contribution from a given atom is determined from the occupancy vector and the expansion coefficients that correspond to functions centered on the atom in question. (Section 3.4.7 of the book, “Modern Quantum Chemistry” by Szabo and Ostlund describes the procedure in full mathematical detail.) Alternatively, if the code that you are using employs a plane-wave basis, the wavefunction is first projected onto an atom-centered basis and then the contributions from each atom are determined as above. (CASTEP uses this latter approach. The relevant references are given below. Other codes include a similar option, or a 3rd party add-on code to do so may be available.) Both approaches have shortcomings: In the former case, the contribution from each atom will be highly basis-set dependent. It is possible, for example, to obtain an accurate electronic structure for the H2O molecule using a set of basis functions that are all centered on the O atom, as long as the basis is sufficiently complete. In this case, only the O atom will appear to have any contribution to the wavefunction and carry a charge of -2, which is clearly unreasonable. The basis therefore needs to be distributed across all atoms in the system in a "balanced" way, although there is no universal definition of "balanced". In the case of a plane-wave basis, typically some of the wavefunction will be lost during the projection because no finite basis is complete. In this case, the sum of all projected contributions will not recover the full wavefunction. Moreover, upon projection the problem of using a balanced AO basis remains.

Segall, M. D.; Pickard, C. J.; Shah, R.; Payne, M. C. "Population analysis in plane wave electronic structure calculations", Mol. Phys., 89, 571-577 (1996).

Segall, M. D.; Shah, R.; Pickard, C. J.; Payne, M. C. "Population analysis of plane-wave electronic structure calculations of bulk materials", Phys. Rev. B, 54, 16317-16320 (1996).