Related papers: Neural Wave Functions for High-Pressure Atomic Hyd…
The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the…
The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical…
We developed a deep generative model-based variational free energy approach to the equations of state of dense hydrogen. We employ a normalizing flow network to model the proton Boltzmann distribution and a fermionic neural network to model…
We derive the wave function for N-dimensional hydrogen atom in the momentum representation with the phase factor using the generating function method and Hankel's integral.
The hydrogen phase diagram has a number of unusual features which are generally well reproduced by density functional calculations. Unfortunately, these calculations fail to provide good physical insights into why those features occur. In…
We consider general theoretical models of water and in particular the nature of the motions of the hydrogen nuclei. If the motion of hydrogen nuclei is classical, then the thermodynamic pressure equation of state for heavy water wherein the…
Strongly interacting quantum systems described by non-stoquastic Hamiltonians exhibit rich low-temperature physics. Yet, their study poses a formidable challenge, even for state-of-the-art numerical techniques. Here, we investigate…
The states of hydrogen atom with principal quantum number $n\le3$ and zero magnetic quantum number in constant homogeneous magnetic field ${\cal H}$ are considered. The coefficients of energy eigenvalues expansion up to 75th order in powers…
Quantum mechanics is considered to arise from an underlying classical structure (``hidden variable theory'', ``sub-quantum mechanics''), where quantum fluctuations follow from a physical noise mechanism. The stability of the hydrogen ground…
In this note, variational Monte Carlo method based on neural quantum states for spin systems is reviewed. Using a neural network as the wave function allows for a more generalized expression of various types of interactions, including…
A basis set of generalized nonspherical Gaussian functions (GGTOs) is presented and discussed. As a first example we report on Born-Oppenheimer energies of the hydrogen molecule. Although accurate results have been obtained, we conclude…
It is shown that all of the basic properties of the hydrogen atom can be consistently described in terms of classical electrodynamics instead of taking the electron to be a particle; we consider an electrically charged classical wave field,…
Hydrogen has been the subject of intense research following the discovery of high-temperature superconductivity in hydrides, and as a result of continuous efforts to produce solid hydrogen. The Born-Oppenheimer approximation is the central…
We report on highly accurate calculations of Born-Oppenheimer potentials for excited $n\,\Sigma^{+}$ states of the hydrogen molecule for all possible combinations of singlet/triplet and gerade/ungerade symmetries up to $n=7$. A relative…
The ground-state properties of spin polarized hydrogen H$\downarrow$ are obtained by means of diffusion Monte Carlo calculations. Using the most accurate to date ab initio H$\downarrow$-H$\downarrow$ interatomic potential we have studied…
We consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schr\"odinger perturbation theory, using the Sturmian…
We present an accurate theoretical determination of rovibrational energy levels of the hydrogen molecule and its isotopologues in its electronic ground state. We consider all significant corrections to the Born-Oppenheimer approximation,…
We present an efficient quantum algorithm for beyond-Born-Oppenheimer molecular energy computations. Our approach combines the quantum full configuration interaction method with the nuclear orbital plus molecular orbital (NOMO) method. We…
An interatomic potential for high-pressure high-temperature (HPHT) crystalline and liquid phases of sodium is created using a neural-network (NN) representation of the ab initio potential energy surface. It is demonstrated that the NN…
We construct a system of coherent states for the hydrogen atom that is expressed in terms of elementary functions. Unlike to the previous attempts in this direction, this system possesses the properties equivalent to the most of those for…