Hi! Could you give me a tip about how to represent molecules in the minimal basis? I want to learn a manner to do that in computational basis for any type of molecules.

My goal is learn how to simulate molecules using VQE but firstly I want to learn how to do it by hand (without libraries) in order to understand the process.

Thank you!

Hi @Anton_Simen and welcome to the forum!

To simulate a molecule with VQE, we first need to perform Hartree-Fock calculations which provide us with parameters that are needed to build the qubit Hamiltonian of a molecule. In the Hartree-Fock method, the many-body wave function of a molecule is approximated by a Slater determinant. The components of this determinant are molecular spin-orbitals where each spatial molecular orbital is represented as a linear combination of atomic orbitals. A basis set represents a set of functions that are used to construct the atomic orbitals. For example, we can use Slater functions or Gaussian functions to define our basis set. In a minimal basis set, only one basis function is used for each atomic orbital. We can go beyond the minimal basis by adding extra functions to our basis set.

However, please note that Hartree-Fock calculations are not straightforward and are typically done by using quantum chemistry packages such as PySCF or Psi4 which have built-in basis sets. PennyLane uses these programs to perform Hartree-Fock calculations and the user only needs to specify the name of the basis set which, for example, can be sto-3g.

If you are interested to construct your basis set manually, I recommend reading Reference #2 given in this tutorial first. I also recommend reading the manuals of PySCF or Psi4 programs and maybe doing some basic calculations with them to get a better understanding of the Hartree-Fock calculations. This website also provides a wide range of basis sets for the periodic table elements.

Please let us know if you need any help or if you have any further questions.

Thank you very much for your answer! I will follow all these tips and after a while I will come back here to discuss what has evolved. I’m sure it’s will be help me a lot.

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That is great @Anton_Simen! We will be happy to help.