# Continuously-varying Hartree-Fock transition matrix?

Suppose we have a parametrized molecular Hamiltonian $$H(R)$$, where $$R$$ are the nuclear coordinates. If we let $$B(R)$$ be some chosen atomic basis set (like STO-3G) centred at $$R$$, then using $$B(R)$$, we let $$C(R)$$ denote the transition matrix from atomic to molecular orbitals at $$R$$.

In general, there are many different choices for $$C(R)$$ at a given $$R$$, as HF can converge to different unique solutions. However, I want $$C(R)$$ to vary continuously over some range of $$R$$. In general, is it possible to enforce this condition when performing Hartree-Fock? If so, how?

I tried starting at a set of parameters $$R_0$$, computed $$C(R_0)$$, and then computed $$C(R_0 + \Delta)$$, $$C(R_0 + 2\Delta), ...$$ iteratively by using the density matrix yielded by the previous Hartree-Fock step, but this didn't seem to work: I'm still getting some large jump discontinuities in $$C(R)$$ at certain values of $$R$$.

• Are the molecular orbitals canonical orbitals, or are they allowed to become non-canonical? Jul 26, 2022 at 15:54

First, notes on terminology: $${\bf C}$$ are molecular orbital coefficients, not transition matrices. In general one has many nuclei so you have a set of nuclear coordinates $$\{{\bf R}_A\}$$ instead of a single vector $${\bf R}$$; atomic basis sets are typically (but not always!) centered on the individual atoms $${\bf R}_A$$.