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Register a new userAb-Initio Molecular Dynamics with Screened Lorentz Forces. Part II. Efficient Propagators and Rovibrational Spectra in Strong Magnetic Fields
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Strong magnetic fields have a large impact on the dynamics of molecules. In addition to the changes of the electronic structure, the nuclei are exposed to the Lorentz force with the magnetic field being screened by the electrons. In this work, we explore these effects using ab-initio molecular dynamics simulations based on an effective Hamiltonian calculated at the Hartree-Fock level of theory. To correctly include these non-conservative forces in the dynamics, we have designed a series of novel propagators that show both good efficiency and stability in test cases. As a first application, we analyze simulations of He and H$_2$ at two field strengths characteristic of magnetic white dwarfs (0.1 $B_0 = 2.35 times 10^4$ T and $B_0 = 2.35 times 10^5$ T). While the He simulations clearly demonstrate the importance of electron screening of the Lorentz force in the dynamics, the extracted rovibrational spectra of H$_2$ reveal a number of fascinating features not observed in the field-free case: couplings of rotations/vibrations with the cyclotron rotation, overtones with unusual selection rules, and hindered rotations that transmute into librations with increasing field strength. We conclude that our presented framework is a powerful tool to investigate molecules in these extreme environments.
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The dynamics of a molecule in a magnetic field is significantly different form its zero-field counterpart. One important difference in the presence of a field is the Lorentz force acting on the nuclei, which can be decomposed as the sum of the bare nuclear Lorentz force and a screening force due to the electrons. This screening force is calculated from the Berry curvature and can change the dynamics qualitatively. It is therefore important to include the contributions from the Berry curvature in molecular dynamics simulations in a magnetic field. In this work, we present a scheme for calculating the Berry curvature numerically, by a finite-difference technique, addressing challenges related to the arbitrary global phase of the wave function. The Berry curvature is calculated as a function of bond distance for H$_2$ at the restricted and unrestricted Hartree--Fock levels of theory and for CH$^{+}$ as a function of the magnetic field strength at the restricted Hartree--Fock level of theory. The calculations are carried out using basis sets of contracted Gaussian functions equipped with London phase factors (London orbitals) to ensure gauge-origin invariance. In the paper, we also interpret the Berry curvature in terms of atomic charges and discuss its convergence in basis sets with and without London phase factors. Calculation of the Berry curvature allows for its inclusion in textit{ab initio} molecular dynamics simulations in a magnetic field.
We describe a simplified approach to simulating Raman spectra using ab initio molecular dynamics (AIMD) calculations. Our protocol relies on on-the-fly calculations of approximate molecular polarizabilities using a sum over orbitals (as opposed to states) method.
Ab initio molecular dynamics (AIMD) is a valuable technique for studying molecules and materials at finite temperatures where the nuclei evolve on potential energy surfaces obtained from accurate electronic structure calculations. In this work, a quantum computer-based AIMD method is presented. The electronic energies are calculated on a quantum computer using the variational quantum eigensolver (VQE) method. We compute the energy gradients numerically using the Hellmann-Feynman theorem, finite differences, and a correlated sampling technique. Our method only requires additional classical calculations of electron integrals for each degree of freedom, without any additional computations on a quantum computer beyond the initial VQE run. To achieve comparable accuracy, our gradient calculation method requires three to five orders of magnitude fewer measurements than other brute force methods without correlated sampling. As a proof of concept, AIMD dynamics simulations are demonstrated for the H2 molecule on IBM quantum devices. To the best of our knowledge, it is the first successful attempt to run AIMD on quantum devices for a chemical system. In addition, we demonstrate the validity of the method for larger molecules using full configuration interaction (FCI) wave functions. As quantum hardware and noise mitigation techniques continue to improve, the method can be utilized for studying larger molecular and material systems.
We develop a Python-based open-source package to analyze the results stemming from ab initio molecular-dynamics simulations of fluids. The package is best suited for applications on natural systems, like silicate and oxide melts, water-based fluids, various supercritical fluids. The package is a collection of Python scripts that include two major libraries dealing with file formats and with crystallography. All the scripts are run at the command line. We propose a simplified format to store the atomic trajectories and relevant thermodynamic information of the simulations, which is saved in UMD files, standing for Universal Molecular Dynamics. The UMD package allows the computation of a series of structural, transport and thermodynamic properties. Starting with the pair-distribution function it defines bond lengths, builds an interatomic connectivity matrix, and eventually determines the chemical speciation. Determining the lifetime of the chemical species allows running a full statistical analysis. Then dedicated scripts compute the mean-square displacements for the atoms as well as for the chemical species. The implemented self-correlation analysis of the atomic velocities yields the diffusion coefficients and the vibrational spectrum. The same analysis applied on the stresses yields the viscosity. The package is available via the GitHub website and via its own dedicated page of the ERC IMPACT project as open-access package.
This paper reports an implementation of Hartree-Fock linear response with complex orbitals for computing electronic spectra of molecules in a strong external magnetic fields. The implementation is completely general, allowing for spin-restricted, spin-unrestricted, and general two-component reference states. The method is applied to small molecules placed in strong uniform and non-uniform magnetic fields of astrochemical importance at the Random Phase Approximation level of theory. For uniform fields, where comparison is possible, the spectra are found to be qualitatively similar to those recently obtained with equation of motion coupled cluster theory. We also study the behaviour of spin-forbidden excitations with progressive loss of spin symmetry induced by non-uniform magnetic fields. Finally, the equivalence of length and velocity gauges for oscillator strengths when using complex orbitals is investigated and found to hold numerically.
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