Abstract: Quantum nuclear effects such as tunneling, delocalization and zero-point energy are relevant in simulations of the phases of ice and the local structure of water and are involved in the recently observed sieving of hydrogen and deuterium by graphene [1]. Nonadiabatic corrections to the Born-Oppenheimer approximation are essential to several physical and chemical processes, e.g., the sticking of atoms on metal surfaces. All of the above effects are not present in standard density functional theory (DFT), although they can be included in DFT-based approaches after quite involved calculations of adiabatic potential energy surfaces and nonadiabatic couplings.

As DFT is a widely-used electronic structure method, it is interesting to ask whether it is possible, starting from the full Schrödinger equation for electrons and nuclei and without making the Born-Oppenheimer approximation, to derive Kohn-Sham-like equations that produce the exact nonadiabatic electronic density directly, i.e. without the need to calculate the coupling between several adiabatic potential energy surfaces. This is indeed possible if one assumes the exchange-correlation energy is a functional of a quantity called the quantum geometric tensor in addition to the density [2]. Making the energy stationary with respect to variations of the quantum geometric tensor leads to a set of Euler-Lagrange equations. These equations also determine the exact, as opposed to adiabatic, Berry curvature and hence all geometric phase effects in the nuclear Schrödinger equation, including nonadiabatic corrections to the Longuet-Higgins molecular geometric phase near conical intersections [3].

After introducing nonadiabatic DFT, I will present applications to a model pseudorotating molecule and dynamical Jahn-Teller system.

References:

[1] M. Lozada-Hidalgo, et al., Science 351, 68-70 (2016).

[2] R. Requist and E. K. U. Gross, Phys. Rev. Lett. in press.

[3] R. Requist, F. Tandetzky and E. K. U. Gross, Phys. Rev. A 93, 042108 (2016).