Analytical GIAO and hybrid-basis integral derivatives: application to geometry optimization of molecules in strong magnetic fields

Abstract

Analytical integral evaluation is a central task of modern quantum chemistry. Here we present a general method for evaluating differentiated integrals over standard Gaussian and mixed Gaussian/plane-wave hybrid orbitals. The main idea is to have a representation of basis sets that is flexible enough to enable differentiated integrals to be reinterpreted as standard integrals over modified basis functions. As an illustration of the method, we report a very simple implementation of Hartree-Fock level geometrical derivatives in finite magnetic fields for gauge-origin independent atomic orbitals, within the London program. As a quantum-chemical application, we optimize the structure of helium clusters and some well-known covalently bound molecules (water, ammonia and benzene) subject to strong magnetic fields.

Coupled-cluster theory for atoms and molecules in strong magnetic fields

“…For lithium (see Figure 5), the 2 S state is paramagnetically stabilized by the spin-Zeeman term only, see also Ref. 38. It first goes down in energy but starts to behave diamagnetically at around 0.3 B 0 .…”

“…The picture looks different when turning to He 3 (see Figure 21), which shows strong paramagnetic bonding in the magnetic field. While the system is unbound at the HF level until 1.0 B 0 (note that it becomes bound earlier when geometries are optimized at the HF rather than CCSD(T) level 38 ), calculations at the CCSD(T) level predict a weak van-der-Waals bonding already in the field-free case.…”

Perspective: Coupled cluster theory for atoms and molecules in strong magnetic fields

“…The same mechanism is also encountered in other systems: As mentioned earlier, geometry optimizations for helium clusters were carried out at the HF level of theory in Ref. , revealing planar structures for fields perpendicular to the molecular plane that are stabilized via paramagnetic bonding and that point to the existence of hexagonal 2D lattices in strong magnetic fields. To investigate the effect of electron correlation, building on this work, the binding energy of equilateral He 3 as a function of the magnetic field was investigated at the CCSD(T) level of theory.…”

“…First, the perpendicular paramagnetic bonding mechanism was discovered on the basis of finite‐field HF and FCI calculations for the lowest and the He states which both become bound in a sufficiently strong field perpendicular to the molecular axis . Second, a HF gradient code was implemented making it possible to explore changes in geometry as a function of the magnetic field. In that work, helium clusters were also found to be stabilized by perpendicular paramagnetic bonding and to exhibit planar structures which may well exist on white dwarfs.…”

Three-electron atoms and ions in a magnetic field

“…The effect of magnetic field on the energy levels of molecules has also been extensively studied [50][51][52][53][54][55][56][57][58][59]. High magnetic fields drastically change the binding energies, bond lengths [59], and can lead to new bonding mechanisms [53].…”