Molecular Hamiltonian | EPFL Graph Search

In atomic, molecular, and optical physics and quantum chemistry, the molecular Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule. This operator and the associated Schrödinger equation play a central role in computational chemistry and physics for computing properties of molecules and aggregates of molecules, such as thermal conductivity, specific heat, electrical conductivity, optical, and magnetic properties, and reactivity. The elementary parts of a molecule are the nuclei, characterized by their atomic numbers, Z, and the electrons, which have negative elementary charge, −e. Their interaction gives a nuclear charge of Z + q, where q = −eN, with N equal to the number of electrons. Electrons and nuclei are, to a very good approximation, point charges and point masses. The molecular Hamiltonian is a sum of several terms: its major terms are the kinetic energies of the electrons and the Coulomb (electrostatic) intera

High-order geometric integrators for nonadiabatic molecular quantum dynamics and their applications to explore conical intersections

Seonghoon Choi

Accurate simulations of molecular quantum dynamics are crucial for understanding numerous natural processes and experimental results. Yet, such high-accuracy simulations are challenging even for relatively simple systems where the Born-Oppenheimer approximation is valid. Worse still, due to the ubiquity of conical intersections in molecules, it is often necessary to go beyond this celebrated approximation and employ even more sophisticated methods that can describe nonadiabatic processes involving multiple coupled electronic states.Geometric integrators provide a way to simulate nonadiabatic quantum dynamics with high accuracy while exactly conserving geometric properties, such as norm, energy, symplecticity, and time reversibility. However, the exact conservation of these properties typically leads to a higher computational cost when compared with non-geometric integrators of the same order of accuracy. We remedy this lack of efficiency by employing various composition methods to obtain high-order geometric integrators, competitive in efficiency even with some non-geometric integrators.To overcome the limited applicability of the popular split-operator algorithms, we present geometric integrators that can solve the time-dependent Schroedinger equation efficiently regardless of the form of the Hamiltonian. Employing these integrators, we systematically compare the different representations of the molecular Hamiltonian for their suitability for simulating nonadiabatic dynamics at a conical intersection and find that the rarely used exact quasidiabatic Hamiltonian, which includes the often-neglected residual nonadiabatic couplings, yields the most accurate results. Accordingly, we present a method for quantifying the validity of ignoring these residual couplings and show that depending on the system, initial state, and employed quasidiabatization scheme, neglecting the residual couplings can indeed result in inaccurate dynamics.The computational cost of exact quantum simulations quickly becomes prohibitively high as the system size increases. For high-dimensional simulations, one can either optimize the available basis set, e.g., by employing adaptive phase space grids or, alternatively, employ a more approximate approach, such as mixed quantum-classical Ehrenfest dynamics, that provides a useful qualitative picture. Although Ehrenfest dynamics and exact quantum dynamics simulated on an adaptive grid may appear unrelated, we show that, surprisingly, the high-order geometric integrators for these two problems can, in fact, be obtained by using the same splitting and composition methods.

EPFL2022

Nitranilic acid hexahydrate, a novel benchmark system of the Zundel cation in an intrinsically asymmetric environment: spectroscopic features and hydrogen bond dynamics characterised by experimental and theoretical methods

Nitranilic acid (2,5-dihydroxy-3,6-dinitro-2,5-cyclohexadiene-1,4-dione) as a strong dibasic acid in acidic aqueous media creates the Zundel cation, H5O2+. The structural unit in a crystal comprises (H5O2)(2)(+)(2,5-dihydroxy-3,6-dinitro-1,4-benzoquinonate)(2-) dihydrate where the Zundel cation reveals no symmetry, being an ideal case for studying proton dynamics and its stability. The Zundel cation and proton transfer dynamics are studied by variable-temperature X-ray diffraction, IR and solid-state NMR spectroscopy, and various quantum chemical methods, including periodic DFT calculations, ab initio molecular dynamics simulation, and quantization of nuclear motion along three fully coupled internal coordinates. The Zundel cation features a short H-bond with the O center dot center dot center dot O distance of 2.433(2) angstrom with an asymmetric placement of hydrogen. The proton potential is of a single well type and, due to the non-symmetric surroundings, of asymmetric shape. The formation of the Zundel cation is facilitated by the electronegative NO2 groups. The employed spectroscopic techniques supported by calculations confirm the presence of a short H-bond with a complex proton dynamics.

Royal Soc Chemistry2014

Which form of the molecular Hamiltonian is the most suitable for simulating the nonadiabatic quantum dynamics at a conical intersection?

Seonghoon Choi, Jiri Vanicek

Choosing an appropriate representation of the molecular Hamiltonian is one of the challenges faced by simulations of the nonadiabatic quantum dynamics around a conical intersection. The adiabatic, exact quasidiabatic, and strictly diabatic representations are exact and unitary transforms of each other, whereas the approximate quasidiabatic Hamiltonian ignores the residual nonadiabatic couplings in the exact quasidiabatic Hamiltonian. A rigorous numerical comparison of the four different representations is difficult because of the exceptional nature of systems where the four representations can be defined exactly and the necessity of an exceedingly accurate numerical algorithm that avoids mixing numerical errors with errors due to the different forms of the Hamiltonian. Using the quadratic Jahn-Teller model and high-order geometric integrators, we are able to perform this comparison and find that only the rarely employed exact quasidiabatic Hamiltonian yields nearly identical results to the benchmark results of the strictly diabatic Hamiltonian, which is not available in general. In this Jahn-Teller model and with the same Fourier grid, the commonly employed approximate quasidiabatic Hamiltonian led to inaccurate wavepacket dynamics, while the Hamiltonian in the adiabatic basis was the least accurate, due to the singular nonadiabatic couplings at the conical intersection.

2020

High-order geometric integrators for nonadiabatic molecular quantum dynamics and their applications to explore conical intersections

Seonghoon Choi

EPFL2022